KOBE ECONOMIC &BUSINESS RESEARCH SERIES
No.16, 2003

!

Copyright
2003 by Research Institutefor Economics & Business Administration
Kobe University
Kobe, JapanAll right reserved. No part of this bookmay be reproduced in any means without
permission in writing from the publisher.

ISSN 1348-5040
Printed in Japan
by Kishimoto Printing

New Developments inInternational Trade:
Theoretical and EmpiricalInvestigations

New Developments inInternational Trade:
Theoretical and EmpiricalInvestigations

Edited by

Seiichi Katayama andKaz Miyagiwa

The Research Institute for Economics and Business Administration
Kobe University

Contents

Preface
Contributing Authorsix

Introduction
Seiichi Katayama and Kaz Miyagiwa

1

Ⅰ. The Various Trade Models
1. Fragmentation in Simple Trade Models
Alan Deardorff

9

2. Trade, Technology, and Income Distribution
Ronald Jones27

3. Trade and Personal Distribution of Wealth andIncome: Beyond the Stolper-Samuelson Theorem 39
Satya Das
4. Unilateralism in a Multilateral World
Wilfred Ethier65

5. Trade, Income Transfers, Developing Countries,
and the Core
99
Carsten Kowalczyk and Tomas Sjöström

Ⅱ. Policy Towards International Trade
6. Endogenous Corrections of Economic Policies
under Majority Voting
Wolfgang Mayer111

7. Lobbying for Tariff Protection and Allocation of
Entrepreneurial Resources
129
Arye Hillman, Ngo Van Long,
and Antoine Soubeyranvii

Contents

8. Merger Policies and Trade Liberalisation
Henrik Horn and James Levinsohn
9. Why not Set Tariffs Uniformly Rather than
Optimally
Tatsuo Hatta

147

187

10. Local Content Requirements and International
Market Share Rivalry
207
M. Özgür Kayalica and Sajal Lahiri
11. Balance of Payment Adjustment
under Capital Mobility
Michihiro Ohyama

225

Ⅲ. Empirical Studies on Trade
12. Technology, Geography, and Trade
Jonathan Eaton and Samuel Kortum
13. Bilateral Trade Patterns and Welfare:
An Egypt-EU Preferential Trade Agreement
Denise Konan and Keith Maskus
14. Is Free Trade Good for the Environment?
Werner Antweiler, Brian R. Copeland,and M. Scott Taylor
Acknowledgements to the Publishers
The Conference Program

viii

247

293

307

355
357

Preface

This volume contains the papers presented at the RIEB (The ResearchInstitute for Economics and Business Administration) International Conference held at Kobe University, on March 22-24, 1998. The papers were invited for presentation at the conference under the heading of international
trade theory and empirical research. All the papers have been revised since
the conference, and many of them have been published in a variety ofjournals. This book includes all the published papers as well as previously
unpublished contributions.
Although it has been nearly five years since the conference, these papers
offer insights that are still of considerable interest to researchers in economics, especially to those who study international trade. The editors believe that this volume brings together important contributions to economics
at the dawn of the new millennium.
We are grateful to all the authors and the conference participants, especially those who cheerfully served as discussants and chairpersons. Our
thanks also go to colleagues at the Research Institute for their encouragement, and especially to the Directors, Professors Ken-ichi Ishigaki andShoji Nishijima, for their support of the project. In the editorial process wewere fortunate to have an excellent and able team of Shoko Iwaki,
Manami Sumino, Minako Okuno, Junko Doi, Masakazu Fukuzumi, Junpei
Tanaka, Atsushi Miyake and Tetsuya Saitoh. We are also grateful to Professor Stephen J. Davies at the RIEB who kindly read parts of the manuscript and supplied useful comments and suggestions.
Finally, we wish to thank the Japanese Ministry of Education, the Kanematsu Foundation, the 90th Anniversary Enterprise Fund of Kobe University, and RIEB for the grants that made this research work possible.

Seiichi Katayama, Kobe University
Kaz Miyagiwa, Emory Universityix

Contributing Authors

Werner Antweiler
Brian R. Copeland
Satya Das
Alan Deardorff
Jonathan Eaton
Wilfred Ethier
Tatsuo Hatta
Arye Hillman
Henrik Horn
M. Özgür Kayalica
Denise Konan
Samuel Kortum
Carsten Kowalczyk
Ronald Jones
Sajal Lahiri
James Levinsohn
Ngo Van Long
Keith Maskus
Wolfgang Mayer
Michihiro Ohyama
Tomas Sjöström
Antoine Soubeyran
M. Scott TaylorxUniversity of British Columbia
University of British Columbia
Indian Statistical Institute
University of Michigan
New York University
University of Pennsylvania
University of Tokyo
Bar Ilan University
Stockholm University
Istanbul Technical University
University of Hawaii
University of Minnesota
Tufts University
University of Rochester
Southern Illinois University
University of Michigan
McGill University
University of Colorado
University of Cincinnati
Keio University
Pennsylvania State University
Université d’Aix-Marseille
University of Wisconsin

Introduction
Seiichi Katayama and Kaz Miyagiwa

The last few decades have been a remarkable period for international
trade economists. During that time world trade has expanded at a spectacular pace. Traditional tariffs and quotas have virtually disappeared in industrial nations under GATT-WTO initiatives, and developing countries hitherto averse to free trade have come to embrace it as a way to prosperity.
Improved communications around the world have also contributed to the
expansion in trade and facilitated international capital mobility.
Freer and expanding world trade however has given rise to a host of
new challenges confronting many governments today. Disappearing tradebarriers have induced relocation of production from high-cost to low-cost
countries. Changing production and trade patterns have raised income distributional concerns. What is more, to cope with the adverse impacts oftrade liberalization, many governments have instituted new protectionist
measures such as antidumping levies and safeguards. At the same time
trading blocs have been formed or expanded, challenging the multilateralapproach to free trade.
This volume collects 14 articles that address important issues concerningor arising from trade liberalization. The articles are divided into threegroups. Section I gathers articles that examine various consequences offreer trade. The articles in Section II investigate trade policy and trade policy formation from national and international perspectives. Section III contains three empirical examinations of the consequences of international
trade.
I. Freer Trade and Its Consequences
As we noted above, falling trade barriers have allowed firms to split a
production process into two or more stages and deploy them in different
12

Seiichi Katayama and Kaz Miyagiwa

countries of the world. This phenomenon, which has come to be known as
fragmentation, is the subject of the first two chapters. Deardorff (chapter
1) applies simple trade models of small open economies and of a twocountry world to examine the effect of fragmentation on trade patterns,
welfare and income distribution. His elegant analysis indicates that fragmentation benefits the country where it occurs if it induces no pricechange, but can hurt a country if it worsens the terms of trade. Even if
there is a favorable terms of trade effect, some factors can still be hurt byfragmentation. If there is no factor price equalization in absence of fragmentation, however, fragmentation can contribute to factor price equalization.
While Deardorff works with the standard Ricardian and the HeckscherOhlin model, Jones (chapter 2) chooses a multi-sector Heckscher-Ohlinmodel. His analysis yields some surprising results not predicted by the 2×2
version. For example, a country losing out in a labor-intensive stage of
production to foreign competition may nonetheless experience increases inreal wages. Motivated by the recent debates in the U.S. about the effects ofinternational trade on the skilled-unskilled wage gap, Jones also examines
income-distributional implications of price changes and technical progress.
Again, the model yields results unexpected in the standard model. For example, a change in a commodity price can produce diametrically oppositechanges in factor incomes in two countries without factor intensity reversals.
The concern over income distributions is further explored in chapter 3.
Whereas conventional research has focused on factor incomes, Das investigates the effect of trade on personal income and wealth distribution. His
dynamic model of North-South trade preserves the two-sector HeckscherOhlin feature on the production side but departs on the demand side in that
consumers derive utility from both consumption and bequest of land to thenext generation. Thus, land plays a dual role as a commodity and as an asset. Diverse preferences over land lead to the endogenous formation of
three classes of households: lower (landless workers), middle (workers
with land) and upper class (landlords). Das shows that moving from autarky to free trade leads to more wealth and income inequality in the Northand less in the South.
The multilateral approach to free trade under GATT-WTO initiatives has
been based on the principle of reciprocity and nondiscrimination. However,member nations are also allowed to impose temporary protective measures
such as voluntary export restraints and antidumping and countervailing tariffs, which are by nature unilateral and discriminatory. What role these
unilateral policies play within the multilateral framework has attracted attention from researchers. Ethier (chapter 4) addresses this issue by presenting a multi-country multi-period model of the world economy. Letting thegovernments negotiate tariff reductions multilaterally, starting from high3

Introduction

initial tariffs, he finds that the rate of multinational tariff reduction is limited to the lowest reduction any country would prefer but that the rate canbe accelerated by the introduction of unilateral protectionism, which mitigates the losses nations will suffer should they happen to be technologicallaggards in an uncertain world. Thus Ethier concludes that contemporary
unilateralism is necessary for the sustenance and success of multilateralism.
In Ethier’s model unilateral protection serves as insurance in the presence of uncertainty to facilitate multilateralism [Bagwell and Staiger (1990,
1998) examine similar issues in different contexts]. Direct compensationfrom winners to losers from tariff changes will also induce governments toparticipate more readily in free trade agreements. This insight leads Kowalczk and Sjostrom (chapter 5) to consider the role of the direct income
transfers in a multi-country model. In this chapter, the authors extend theirearlier work (Kowalczk and Sjöström 1994), focusing on a particular income transfer scheme proposed by Grinols (1981), which in turn generalizes the Kemp-Wan (1976) theorem on formation of customs unions. The
main results of the chapter are that the Grinols’ transfers can be expressed
as side payments from nations who lose little to those who lose much andthat such transfers support the grand coalition or global free trade as a core
allocation.
II. Policy Towards International Trade
Traditional trade theory ascribed protectionist policies to rational welfare-maximizing governments manipulating the terms of trade or administeringcorrective measures in the presence of domestic distortions. In contrast, recent research has emphasized the role of voters, pressure groups and lobbyists in influencing policy outcomes; see, for example, Mayer (1984),
Young and Magee (1986), Grossman and Helpman (1994). The first two
chapters of this section contribute to this strand of research.
Mayer (chapter 6) presents a dynamic two-sector model with heterogeneous agents to study the policy response when policy choices are determined by majority voting and are adjusted periodically by referendum. If
labor allocation is costly and time-consuming, a one-time shock leads to a
gradual adjustment of resources, which in turn affects the preferences ofindividuals with respect to the adoption of economic policies. Focusing on
production subsidies, Mayer shows that individuals in the subsidized industry initially gain but that these gains are gradually eroded as resources
move from the losing to the winning industry. The politically chosen subsidy rate may rise or fall to slow down the erosion but national income
falls as the reallocation of resources deepens the distortion introduced by
the initial subsidy.
The pressure group theory of policy formation [for example, see Olson(1965)] implies that smaller groups are more successful in obtaining favor-

4

Seiichi Katayama and Kaz Miyagiwa

able policies. However, empirical support for this presumption has been
mixed. To account for lukewarm empirical support Hillman (1991) has
presented a model in which competitive firms allocate resources between
lobbying and cost-reducing activities. Hillman, Long and Soubeyran (2001)
have extended this model to the case of an oligopolistic industry protectedby import quotas. Hillman, Long and Soubeyran (chapter 7) further extend
the model to tariff protection under oligopoly. The analysis with tariff protection reinforces the conclusion that the presumption holds only in limited
cases, depending on various measures of comparative advantage in lobbying and on the industry demand curve.
The present WTO system allows the use of trade policy only in very
limited cases. At present, however, no comparable international agreement
exists that aims to align competition policies among individual countries.
Since competition policies are nationally chosen, there is the concern thatthe restriction of trade policy induces individual countries to use competition policies to promote national interests at the expenses of others. Levinsohn (chapter 8) investigates this issue in a Counrnot oligopoly model withmultiple home and foreign firms. He allows the governments to choose themerger policy nationally with or without GATT restrictions on the use ofexport subsidies, and finds no theoretical support for the presumption thatthe restriction on use of trade policy induces individual countries to pursue
slack merger policies as a form of a beggar-thy-neighbor policy.
Chapter 9 takes a look at the World Bank, where there have been ongoing debates over the appropriate tariff structure to raise given revenue indeveloping countries. Economists at the Bank’s operation divisions recommend uniform tariff rates because they fear divergent tariff rates cause
price distortions, while those in its research divisions advocate non-uniform
tariff rates from the efficiency point of view. Hatta reconciles these twoviews within the framework of optimum tax theory and shows that the uniform tariff structure is a good approximation of the revenue-constrained
optimum tariff structure as long as substitutability among commodities isdominant.
The next two chapters examine issues concerning increases in international investments. Host country governments often grant foreign investors
tax holidays and other investment inducements [see, for example, Miyagiwa and Ohno (2002)], while at the same time trying to regulate themwith various performance requirements such as local content requirements
for exports. The previous literature on performance requirements [e.g.,
Davidson et al. (1985), Lahiri and Ono (1991)] has assumed that there is
only one foreign firm and/or one host country, neglecting the strategic aspects of performance requirements among multiple host governments. To
study such strategic interactions Kayalica and Lahiri (chapter 10) present amodel with two host countries with many foreign firms. There are two versions; in one the number of foreign firms is given and in the other there is5

Introduction

free entry and exit. In either case, the non-cooperative levels of local contents are higher than the cooperative levels for both host countries. Comparing the optimal levels of content requirements across countries and between the two cases, the authors show that allowing for free entry in one
host country reduces the levels in both countries.
Increased capital mobility also raises the macroeconomic concern about
the long-run adjustment of current account imbalances under flexible exchange rates. Assuming perfect international capital mobility and unequal
time preferences across two nations, Ohyama (chapter 11) considers two
adjustment mechanisms: interest rates and money supply (or exchange
rates). The adjustment process by interest rates is stable but leaves thecountry having a greater time preference in persistent and impoverishingindebtedness. In contrast, adjustment by money supply to peg interest rates
is potentially unstable but may succeed in dissolving international indebtedness under certain conditions.
III. Empirical Studies on International Trade
Although theoretical models help us understand the basic structure of
economic environments that interest us, often everything hangs on empirical results. This section collects three articles that go towards settling important theoretical issues using up-to-date data and estimation techniques.
Today there exists a large literature testing trade theories, especially the
Heckscher-Ohlin model [see reviews by Deardorff (1984) and Leamer andLevinsohn (1995)]. However, empirical support for the theory has been
mixed at best. Deardorff (1984, p. 512), for example, observes that “[thefactor proportions model] does reasonably well at explaining the commodity composition of trade, but beyond that it is fairly helpless.” Eaton andKortum (chapter 12) argue that the factor proportions theories have notcome to grips with these basic facts: (1) trade diminishes with distance, (2)prices vary across locations (3) factor prices are not equal (4) countries’
relative productivities vary across industries. To incorporate these facts Eaton and Kortum focus on a Ricardian model, which yields two key structural equations for bilateral trade with parameters relating to absolute andcomparative advantages and to geographical barriers. The authors estimate
these parameters using manufacturing data from 19 OECD countries andsolve for the world equilibrium. They then quantify the gains from trade,the effect of technology and geography on patterns of specialization, therole of trade in spreading the benefits of new technology, and the consequences of tariff reductions. In particular, it is found that a unilateral removal of U.S. tariffs makes every other country better off except Americans. The fact that the total benefits exceed the American loss indicates theimportance of pursuing freer trade multilaterally.
Trade theory indicates that the net benefit of preferential trade agree-

6

Seiichi Katayama and Kaz Miyagiwa

ments (PTAs) depends on the relative strength of trade creation and diversion effects, which in turn are functions of the pre-liberalization volumesof trade with the partner. Whether the net benefit is positive is however an
empirical matter. Konan and Maskus (chapter 13) apply a computational
general equilibrium model to estimate the potential gain for Egypt from its
preferential trade agreement with the EU. The simulation results indicatethat aggregate welfare gains increase with the initial partner trade share,
implying that the greater the initial trade share with Europe the more
Egypt gains from a PTA. However, the simulation also shows that its potential gains are modest.
The last chapter deals with one of the most contentious trade issues today: the link between free trade and environmental damage. At the core ofrecent debates lies the pollution haven hypothesis, which suggests that low-income developing countries will be polluted by openness to trade. Previous empirical studies however have failed to discover a convincing link
between trade and pollution due to the lack of firm theoretical underpinnings. To correct this shortcoming Antweiler, Copeland and Taylor (chapter 14) first present a theoretical model based on the Heckscher-Ohlin
framework to divide trade’s impact on pollution into scale, technique, andcomposition effects. They then use data on sulfur dioxide concentration toestimate these effects. Their results show that international trade creates
relatively small changes in sulfur dioxide concentrations by altering thecomposition of national output. Combining this result with estimates ofscale and technique effects yields a surprising result: if trade liberalization
raises GDP per person by 1 percent, pollution concentrations fall by about
1 percent. Free trade is good for the environment.

References
Bagwell, K. and R. W. Staiger. 1990. A Theory of Managed Trade. American Economic Review 80: 779-995.
–––– . 1999. An Economic Theory of GATT. American Economic Review 89: 215248.
Davidson, C., S. J. Matusz, and M. E. Kreinin. 1985. Analysis of PerformanceStandards for Direct Foreign Investment. Canadian Journal of Economics 101:
876-890.
Deardorff, A. V. 1984. Testing Trade Theories and Predicting Trade Flows, chapter
10. In Handbook of International Economics, vol. 1, eds. R. W. Jones and P. B.
Kenen. Amsterdam: Elsevier Science Publishers: 467-517.
Grinols, E. L. 1981. An Extension of the Kemp-Wan Theorem on the Formation ofCustoms Union. Journal of International Economics 11: 259-266.
Grossman, G. and E. Helpman. 1994. Protection for Sale. American Economic Review 84: 833-850.
Hillman, A. 1989. The Political Economy of Protection. Cambridge: Harwood Academic Publishers.

7

Introduction–––– . 1991. Protections, Politics and Market Structure. In International Trade andTrade Policy, eds. Helpman E. and Razin A. Cambridge, Mass: MIT Press: 118140.
Hillman A., N. V. Long and A. Soubeyran. 2001. Protection, Lobbying, and Market Structure. Journal of International Economics, vol. 54(2): 383-409.
Kemp, M. C. and H. Y. Wan. 1976. An Elementary Proposition Concerning theFormation of Customs Unions. Journal of International Economics 6: 95-97.
Kowalczyk, C. and T. Sjöström. 1994. Bringing GATT into the Core. Economica
61: 301-367.
Lahiri, S. and Y. Ono. 1999. Export-Oriented Foreign Direct Investment and Local
Content Requirement. Pacific Economic Review 8: 1-14.
Leamer, E. E. and J. Levinsohn. 1995. International Trade Theory: The Evidence,
chapter 26. In Handbook of International Economics, vol. 3. eds. G. M. Grossman and K. Rogoff. Amsterdam: Elsevier Science Publishers: 1339-1394.
Miyagiwa, K. and Y. Ohno. 2002. Top Dogs, Puppy Dogs and Tax Holidays.
Working Paper.
Mayer, W. 1984. Endogenous Tariff Formation. American Economic Review 74:
970-985.
Olson, M. 1965. The Logic of Collective Action: Public Goods and the Theory ofGroups. Cambridge, Mass: Harvard University Press.
Young, L. and S. Magee. 1986. Endogenous Protection, Factor Returns and Resource Allocation. Review of Economic Studies 53: 407-419.

1

Fragmentation in Simple Trade Models
Alan Deardorff

1. Introduction
The subject is fragmentation: the splitting of a production process into
two or more steps that can be undertaken in different locations but thatlead to the same final product. Also called “intra-product specialization” byArndt (1996) and by the more loaded term “outsourcing” in some economic literature as well as in the popular press, fragmentation occurs bothwithin countries and across countries.1 Within countries, if domestic factor
markets are well integrated and markets are competitive, then fragmentation would be expected to occur only if the combined resources used by
the fragmented steps were less than those used by the original process, inwhich case fragmentation would also represent a technological improvement. In this paper I will assume instead that fragmentation does not
economize on resources, and therefore I will focus on fragmentation that
occurs across countries.2
Internationally, fragmentation has become increasingly common in recent years as barriers to international trade and investment have fallen and
1. The term “fragmentation” comes from Jones and Kierzkowski (2001). Several
other terms for this phenomenon were also suggested at the NAEFA session, none
seeming to generate a consensus.
2. Even without any saving in resources, fragmentation could occur within acountry for a variety of reasons. Perhaps the most obvious is if labor markets are
not competitive, so that wages are bid up in some sectors by the bargaining powerof unions. Fragmentation in order to divert some parts of a production process outside the purview of the union then makes obvious economic sense. Even with perfect competition, if a country is “lumpy”––that is, if different equilibrium wages
are paid in different regions within the country as in Courant and Deardorff (1992)––then fragmentation may occur across regions for much the same reasons as theinternational fragmentation I will examine here.
910

Alan Deardorff

as an increasingly competitive world environment has forced producers tolook outside their own borders for ways to reduce costs. In the debate overthe causes of increased wage inequality in the United States in the 1980s
and 90s, “globalization” and technology have both been suggested as important causes of the increased wage differential paid to skilled labor,
globalization being represented variously by international trade, foreign direct investment, factor mobility, and outsourcing.3 In fact, fragmentation
may be thought of as a manifestation of globalization and technology combined, since in many industries it is only advances in technology that havemade the splitting of production processes and the coordination of the resulting parts possible.
In any case, with the exception of Arndt (1997) and Jones and Kierzkowski (2001), the economic effects of fragmentation do not seem tohave been given the theoretical treatment they deserve, and in this paper I
will attempt to correct that.4 Using several familiar and simple models ofinternational trade, I will examine the implications of fragmentation on
trade, patterns of specialization, and factor markets, looking especially at
its effects on factor prices and on the overall welfare of the countries involved.
I will examine the effects of fragmentation first in a Ricardian model insection 2, then in a Heckscher-Ohlin model in section 3. Section 4 concludes.
2. Fragmentation in Ricardo
I will look first at the effects of fragmentation on a small open economy,
then at a large country in a two-country world.
2.1. A Small Open Ricardian Economy
Consider first the textbook case of only two goods. The country is endowed with a fixed amount of labor, L, and it can use this labor to produce either of two (final) goods, X and Y . The unit labor requirements ofeach are fixed at aX and aY respectively. As a small open economy, thecountry faces fixed prices of the two goods on a world market, pX and pY,
at which it can buy or sell unlimited quantities. As usual, if the wage in
3. There have been many surveys of this voluminous “trade and wages” literature, most recently by Johnson and Stafford (1997). One pair of papers that has focused attention on outsourcing is Feenstra and Hanson (1996, 1999).
4. The literature now also includes two of the other papers prepared for the
NAEFA session for which this was written. Not coincidentally, they are by thesame authors: Arndt (1998) and another paper by Jones and Kierzkowski for which
I do not have the exact citation. The empirical literature on fragmentation has also
been expanded with a new paper by Slaughter that I also don t have.

11

Fragmentation in Simple Trade Models

the country were w, then the supply prices of the two goods would be waX
and waY respectively, and profits would be made if either of these were below the corresponding world price. Therefore the market equilibrium wage
is instead⎛p p ⎞
w0 = max ⎜ X , Y ⎟ .
⎝ a X aY ⎠(1)

The country specializes in whichever good yields this highest wage, exporting X if pX/aX > pY/aY and vice versa. Equivalently, if
aX
p
< X ,
aY
pY

(2)

then the country has a comparative advantage in X and will export it. I
will assume this to be the case.
Now suppose that fragmentation becomes possible in the X industry. In
general, this means that the process for producing one unit of good X canbe split into multiple parts, i=1,...,nX, each requiring an amount of labor aXi,
and since I do not want to conflate fragmentation with technological pronX
gress, I assume thati =1 a Xi ≥ a X . Coordination of these fragmented parts
might in general require oversight by a single entity such as a multinational enterprise (whose function could itself be represented by one of theparts), but to consider explicitly how the parts are organized would takeme too far afield.5 Instead I will define each part as producing one unit of
an intermediate good, ZXi, that is also an intermediate input to the next partthat produces one unit of ZXi+1, the final step producing a unit of good X
itself: ZXn X X Thus production of a unit of each intermediate input except the first requires, in addition to the labor aXi, one unit of the preceding
intermediate good, ZXi−1.
In general not all of these intermediate goods need be regarded as tradable; their tradability indicates whether two adjacent parts of the fragmented production process can take place in different countries. However,if they are not tradable, then their separate identities will play no role inthe model here with an integrated competitive domestic labor market, andthey could be combined into one. Therefore, I will assume that all of these!

! !

5. The analysis here is general enough, both in this section and the next, to include the sorts of disembodied contributions to a firm’s operations that Helpman(1984) took to be the hallmark of a multinational corporation. Although I will define each fragmented part of the production process as producing an intermediate
input that is then used in the next stage of production, this intermediate input canbe a fiction, at least until one attempts to apply this approach to the data.

12

Alan Deardorffintermediate goods are internationally tradable.
What I have described is a fairly general formulation of fragmentation,
but in the spirit of my initial 2-good model, let me start with the simple
case of nX=2. That is, let production of X be fragmented into just two parts,
requiring amounts of labor aX1 and aX2, the first of which produces an intermediate good Z , that is required one-for-one with production of good X
in the second part. The result is simply a 3-good Ricardian model, where
the three goods are X , Y , and Z , and where the demand for Z is the quantity of X that is produced using the fragmented technology. Since Z is
tradable, introduction of fragmentation also requires that the world market
provide an additional price for it, pZ. The question is, what does all of this
do to the small open economy facing this and the other prices?

Figure 1

The answer depends in part on whether those other prices––pX and pY––
also change as a consequence of fragmentation. This is an issue that will
come up more clearly in the 2-country model below, so for now I simply
assume that they do not. This will in fact be the case if the large rest-ofworld with which our small country trades is itself a fully integrated economy. In that case, there is a single wage of labor prevailing throughout therest-of-world, and fragmentation that does not lower total labor requirements cannot lower the price of X . Its price cannot rise, either, since theoriginal unfragmented technology is still available.
What matters for the small country, then, is the price of Z , which will
depend on the parameters of the fragmented technology in the rest-ofworld. Since this is a Ricardian model, these are not necessarily the sameas in the small country, and I will therefore just examine how behavior in
the small country depends on pZ.
The answer is simple. Labor now has two additional options for employment, in addition to producing X from scratch and producing Y . It can
produce Z , earning a wage pZ/aX1, or it can produce X from Z , earning a

13

Fragmentation in Simple Trade Models

wage (pX − pZ)/aX2. Labor will therefore engage in whichever of the four
activities earns it the most, and it will do more than one thing only if two
or more of the activities yield the same wage. Thus the equilibrium wage
in the fragmented small open economy, wF, is(3)⎛ p p p ( p X − pZ ) ⎞.
wF = max ⎜ X , Y , Z ,a X 2 ⎟⎠
⎝ a X aY a X 1

The country will engage in whichever activity or activities yields thismaximum wage.
The country’s production and trade are summarized in Figure 1. By assumption (2) that it has a comparative advantage in good X , it will neverproduce good Y . Whether and how it produces good X , however, depends
on the price of the intermediate input. Taking good X as numeraire, comparison of the arguments in (3) shows that if pZ is sufficiently low––below(aX − aX2)/aX––then the country will employ only the second fragmented
part of the new technology for producing X , importing all it needs of good
Z from the rest-of-world. For a somewhat higher price of the intermediate
input, however––above (aX − aX2)/aX but below aX1/aX––it will continue to
produce X from scratch with the old technology. Finally, if the price of theintermediate is high enough––above aX1/aX––then it will produce only Z .
In the latter case, since it does not produce X and therefore does not needZ , it exports all of its output of Z . The figure shows these responses of
output to price as the heavy solid line for X and the heavy dashed line for
Z . In addition, it shows net trade in Z (exports if positive, imports if negative) as the heavy dotted line.6
For some prices, then, Figure 1 shows the fragmented technology not
being used at all. This occurs only if aX1/aX is in fact greater than aX−aX2/aX,
which it may not be. This requires that(4)

aX1 + aX2 > aX,

6. Trade in X and Y are not shown, since they depend on preferences and income. Good Y , which is not produced, must be imported for all pZ, although thequantity imported will be somewhat larger when the fragmented technology is being used, due to the country’s higher income, and it will fall with pZ for low pZ andrise with pZ for high pZ due to changes in the terms of trade in Z . When only good
X is produced, then part of it must be exported in exchange for Y , while it must be
imported when it is not produced. Again, the quantities kept or imported depend onreal income, which is larger when the fragmented technology is being employed
and depends then on the pZ.

14Alan Deardorff

or in other words that the fragmented technology use more resources thanthe original, or that fragmentation is, in this sense, “costly.” I will take thisto be the normal case in this section, although the justification for doing so
most easily relies on transportation costs, which I am assuming away inthe rest of the model.
In any case, the model says that if fragmentation is costly, then for someparameters and prices it will not be used, but for other parameters it will.
Also, if fragmentation is not costly, then the middle range of behavior in
Figure 1 collapses to a single price, and fragmentation is used at all prices
but one, aX1/aX, where all are indifferent between producing Z , producing
X from scratch, and producing X from Z .
It might seem in the case of costly fragmentation that welfare might fall,since the country is using part of what seems to be an inefficient technology. In fact, however, we see immediately from (3) that welfare cannot fallwith the introduction of fragmentation in this Ricardian Model. The entire
population is labor, and everyone earns a common wage that is at least as
great as it was before, in real terms since prices of consumer goods are
fixed. The reason, of course, is that while using both parts of the fragmented technology would indeed be inefficient, the country does not dothat. On the contrary, it uses only one part of it, and the other part is not
used anywhere. It is the latter part that is really inefficient at prevailing
prices.
So far I have assumed that fragmentation occurs only in the export industry. That, of course, need not be the case. If fragmentation were to become possible in producing good Y instead, then the above analysis would
be modified but only slightly. Parameters aY1 and aY2 would replace their X
counterparts, and Y would replace X in the third and fourth arguments of(3). The result is again a range of prices of the intermediate good Z forwhich fragmentation is not observed, although in this case it will continue
to be good X , not the potentially fragmented good Y , that is produced in
the mid-range.7 If the price of the intermediate is outside this range, however, good X , will not be produced at all, and the country will either produce and export the intermediate or produce and export Y . Thus fragmentation may give a country a comparative advantage in a good where it had
no comparative advantage before.
This is about all that the simple Ricardian model of a small economy
can tell us, but the results are pretty clearly robust to expansion of themodel to include, say, more goods or more degrees of fragmentation. With
both of these arbitrarily large, the wage is set as

7. This mid-range will exist even if fragmentation in the import-competing goodis costless, since fragmented production must now overcome the comparative disadvantage in (2).

15

(5)

Fragmentation in Simple Trade Models

(

)

⎛
⎞
p j p ji j − p ji j −1⎟,
wF = max ⎜ ,j =1,..., n ⎜ aa ji j⎟ji j =1,...n j ⎝⎠where the technology for producing each of n goods j is potentially fragmented into nj parts, the last of which produces the final good itself. pj, aj
are the prices and unit labor requirements for producing the jth good,
j=1,...,n, using the original Ricardian technology. pji j aji j are the prices
and unit labor requirements for the ij th intermediate input to goodj, ij =1,...,nj, with pj0 = 0 and pjn j = pj.
From this, it follows that the country will tend to specialize in using
only one fragment of one technology, unless parameters and prices coincidentally align so that more than one process yields the same wage. Comparative advantage now refers most appropriately to processes, not goods,
although we may identify them with the intermediate goods that they produce. As in the 2-good model, as long as prices of final goods in the restof-world are given and unchanged by the introduction of fragmentation,
the small country cannot lose from it. Patterns of production and trade will
not be determined quite as simply as in the 2-good model, but one of thepatterns suggested in Figure 1 will continue to hold: given the prices of allother goods and fragments, a particular fragment will be employed and its
intermediate product exported if its price is high enough. A low price, on
the other hand, will not necessarily assure that it will be imported, sincethat also requires a high price in the next stage of production.

!

2.2. A Two Country Ricardian World
A small country in the Ricardian model, then, cannot lose from fragmentation so long as prices of final goods remain fixed. And fixity ofprices has a certain plausibility if the rest-of-world is integrated, as noted
above. However a large country can surely not take prices as given, andthe problems that arise for a large country are also those that arise for a
non-integrated rest-of-world. We therefore need to look at a two-country
world in order to explore these problems. In that context, I will focus only
on one issue: whether a country can lose from fragmentation. Along theway we will incidentally see a bit more about how fragmentation affects
specialization and trade.
For a country to lose from fragmentation, prices must turn against it,
and this requires that it be trading initially so that there is scope for its
terms of trade to worsen. I will consider, therefore, a country that specializes initially in good X , and try to see whether fragmentation can lower
the relative price of good X sufficiently for it to lose. I will consider thesame simple form of fragmentation that I looked at before, splitting pro-

16

Alan Deardorff

duction of good X into two parts. For simplicity and to avoid the costs offragmentation itself being the source of any loss, I will now assume thatfragmentation is costless. Analogous other cases should not be hard to find.
Figure 2 tells us most of what we need to know, although some explanation is required. In the upper left corner is drawn the production possibility frontier (PPF) for the country of interest, Country A, which is assumed again to have a comparative advantage in good X . Its customary
Ricardian transformation curve is TATA′in the X-Y plane, showing the
maximum amounts of goods X and Y that it can produce without fragmentation. Fragmentation expands its production possibilities into a third dimension, with the Z axis measuring its net output of intermediate good Z ,positive if it produces it, negative if it is a net user of Z in production of X.
Point ZA shows the maximum amount that can be produced if all labor isdevoted to production of good Z . Production possibilities include the trian. It is also possible to be a net user of Z
gular plane through ZA, TA, and TA′
in producing X , and the maximum amount of X that can be produced thatway is graphed together with the equal negative input of Z at point ZA′(which is on the dotted 45°line in the horizontal (X ,−Z ) plane). Again,
linear technologies also permit production anywhere on the triangular planethrough ZA′, TA, and TA′If fragmentation were costly, the surface combining
these two triangles would be kinked along TATA′(i.e., the straight line connecting ZA and ZA′would pass to the left of TA′). But with costless fragmentation as I assume here, the two triangles are part of the same plane, andthe full PPF of country A with fragmentation consists of the larger triangle
TAZAZA′. To assure that Country A will have a comparative advantage in X
both with and without fragmentation, I have drawn these production possibilities as skewed in the X direction.
The top right portion of Figure 2 shows the PPF for Country B, with its
greatest productivity being in the directions of final good Y and intermediate good Z . Otherwise the graph for Country B has exactly the same interpretation as for Country A.

17

Fragmentation in Simple Trade Models

Figure 2

Now combine these two PPFs, to get the PPF of the world in the bottom
part of the figure. The construction is a little messy but actually not all thatdifficult if you draw it carefully. As is familiar in the 2-good Ricardianmodel, one simply places the origin for one PPF on the surface of theother, then slides it around in all possible ways to generate the largest outputs possible. In two dimensions only, this process of adding together
TATA′and TBTB′would yield the world frontier TWTW′
TW′′that appears in the
X-Y plane in the bottom graph. It is linear with just one kink (at TW′), andthe two linear segments are exact replicas of the transformation curves of
the two individual countries.
To construct the PPF in three dimensions, I place the origin of Country
A’s PPF on the surface of Country B’s PPF, TBZBZB′. As a result of the
shapes to the two PPFs, point ZA′of A’s PPF traces out a duplicate of B’s
PPF: the triangle ZW′
′
ZW′
′
′
ZW′
′
′
′
. The bottom edge of A’s PPF, ZAZA′traces out
the parallelogram ZWZW′
ZW′
′
ZW′
′
′
′as its origin traverses TBZB. And A’s PPF
itself becomes the topmost facet of the world PPF, the triangle TWZW′
ZW′′.
Note that the parameters underlying these figures are such that only threepatterns of specialization are possible: County B produces only good Y(the top triangle); Country A produces only good X using the fragmented

18

Alan Deardorff

technology and imported inputs of good Z (the lower triangle); and Country B produces a mix of Y and Z while Country A produces only X , mixing the original and the fragmented technology (the parallelogram).
However, the world cannot be in equilibrium just anywhere on the threedimensional surface. By assumption, good Z has no use except in producing X , so the world’s net output of Z must be zero. Therefore the only
relevant part of the world PPF is the solid heavy kinked line,
TWTW′
TW′
′
′
TW′
′
′
′
. Just where on this curve the equilibrium will be found depends on preferences of consumers in both countries for consuming goods
X and Y .
The potential gains for the world from fragmentation are now evident.
Without fragmentation, the world was confined to the output combinations
on TWTW′TW′′, and if preferences put the equilibrium on the steeper segment,
TW′
TW′
′
, then fragmentation permits an increase in the world consumption ofboth goods. These gains should not be surprising: they are simply the result of comparative advantage being followed within the fragmented technology for producing good X .
What are prices in the world equilibrium? They are given by the slopesof a plane tangent to the world PPF wherever the equilibrium is located.
As usual in a Ricardian model, these may be determined mostly by preferences if the equilibrium is at one of the kinks, TW′or TW′′′, or they may be
determined entirely by parameters of production if the equilibrium is in
one of the straight segments. Note that if demand for X is sufficiently highso that the equilibrium is in the steeper of these segments, TW′
′
′
TW′
′
′
′
, thenprices are those of Country B in autarky and do not change with fragmentation. That is the situation addressed in our analysis of the small country
above, thus indicating that the assumptions made there were appropriate.
Of course in this case, represented for example at point I in Figure 2,
Country A does not lose from fragmentation, as already noted.
The possibility of loss arises in the other segment, TW′
TW′
′
′
′
, at points likethe one marked II . Here the relative price of good X falls as a result offragmentation, and since Country A initially exported X , this constitutes afall in its terms of trade. This is not enough to show that it loses, however,since it would have gained a positive amount from the fragmentation itself
had prices not fallen. It turns out, though, that Country A must lose fromfragmentation in this case. Segment TW′
TW′′′′is part of the parallelogram
traced out by the lower edge of Country A’s PPF as its origin traverses theupper left edge of B’s PPF. Therefore the price plane tangent to the world
PPF in this segment includes the entire bottom edge of A’s PPF. This isenough to assure that there are no gains to it from shifting resources toward fragmented production, and the reduced terms of trade therefore
causes an unambiguous loss.
Both results are illustrated in Figure 3. In the left panel, prices remain
fixed with fragmentation and country A gains unambiguously. Initially19

Fragmentation in Simple Trade Models

trading only X and Y , it consumed at point C along the two-dimensional
price line given it by Country B. With fragmentation prices do not change,
but Country A shifts all of its labor to producing good X with inputs of Z
and the fragmented technology. Production moves to point ZA′and it tradesfrom there to point C ′along the price plane, also given it by Country B.
The nature of the trade, incidentally, is that it imports both Y and Z , since
it produces neither.
The other case is shown in the right-hand part of the figure. Here again
Country A starts at point C , but now with fragmentation it trades along a
price plane that is both flatter (lower pX/pY) and rotated clockwise fromabove (lower pX/pZ), as shown. The loss in welfare is unambiguous. Production, incidentally, is somewhere on the bottom edge between points TA′
and ZA′, and the country imports Y and Z . The main difference between
this and the case on the left is that the country also produces some of good
X from scratch, and indeed it is this that requires prices that make the twoprocesses for producing X equivalent and prevents any gain to Country A
from using the fragmented technology. Country B, of course, now doesgain.

3-1: Equilibrium at I in Figure 2

3-2: Equilibrium at II in Figure 2
Figure 3

3. Fragmentation in Heckscher-Ohlin
The simplicity of the Ricardian model is valuable for the insights that it
can yield into the behavior of more complicated models. For example, a
Heckscher-Ohlin (H-O) model can approximate arbitrarily closely to the
Ricardian model of Section 2, and therefore we can conclude immediatelythat a large country can lose from fragmentation, even in a H-O world.
However, there are other details that are assumed away in a Ricardianmodel that it therefore cannot address. The most obvious and important is20

Alan Deardorff

the existence of separate factors of production and the possibility that somefactors may gain while others may lose from a change such as fragmentation. I will explore that possibility here.
The first thing to note about a H-O model, however, is that fragmentation as defined here will not occur in the kinds of equilibria most often
considered in the H-O literature. That is, if prior to fragmentation there isfactor price equalization (FPE), and if fragmentation is costly, then there
will be no incentive to fragment production. Therefore, in order for the issue of fragmentation to be interesting, we must start with a world economy
in which factor prices are different. That is, I will assume that factor endowments differ sufficiently across countries that they are unable, in free
trade, to produce enough goods in common to cause FPE. I will also assume, for simplicity, that fragmentation is costless, although one could easily think of there existing an infinitesimal fragmentation cost, ε , that is too
small to show up in the diagrams. Again, I will start with a small country
and then move to a 2-country model.
3.1. A Small Open H-O Economy
Figure 4 shows what can happen in a 2-good model. The solid lines
show the initial situation before fragmentation. It is a familiar Lerner diagram with good X chosen as numeraire so that the unit value isoquant for
X is also its unit isoquant.
A small country trades with a large rest-of-world in which prices of thetwo goods, X and Y , are given and imply the unit value isoquants shown.
The diversification cone is given by the rays kX and kY, with corresponding
factor prices w̃ and r̃ . The small country, however, is not inside the cone.
Its endowment point is E , and it therefore specializes in good X with factor prices w0 and r0.

Figure 4

21

Fragmentation in Simple Trade Models

Now fragmentation becomes possible everywhere. The technology for
producing good X now includes the possibility of producing an intermediate input, Z , one unit of which requires the factors shown by the new isoquant labeled Z =1.8 A unit of good Z can be used together with additional
inputs of capital and labor to produce a unit of X . Since I am now assuming that fragmentation is costless, the isoquant for producing a unit of X
from Z is simply the factors that are left over out of the original X =1 isoquant. That is, the isoquant for producing X from Z can be drawn upside
down relative to, say, point OXZ as an origin, and it will then be just tangent to the Z =1 isoquant.9
Note that I have drawn the technology for producing Z as more capitalintensive than for producing X . With that assumption, the activities available to the world now include one whose factor requirements (at the restof-world’s factor prices) are given by the ray kZ. The diversification coneis therefore enlarged by fragmentation. In the case shown, the small country is now inside it, and it will therefore now be able to fully employ its
factors at the world’s factor prices. This is now a 3-good, 2-factor H-O
model, so exact outputs and the pattern of trade are indeterminate à la
Melvin (1968). But we can be sure in this case that the small country willproduce some of intermediate good Z together with some of either X
and/or Y .
More important here, however, is what happens to factor prices. Evidently from the figure, the wage has fallen from w0 to w̃ , while the rental
on capital has risen from r0 to r̃ . Since prices are fixed, these changes arereal as well as nominal.
Thus we have a case here where a country gains from fragmentation,10
but not all factor owners within that country share in the gain. On the contrary, workers here are made worse off as the production process for theirproduct fragments into a capital-intensive and a labor-intensive part, only
the former of which necessarily remains viable within their country.
8. Again, this intermediate input need not be a physical entity, and therefore
could represent, say, the “headquarter services” that Helpman (1984) and others
have used to model multinational corporations. For my purposes, it is immaterial(literally) whether the different fragments of production are performed within a single firm or between firms. This generality is desirable, of course, but it also meansthat none of the results of this section are really new. They are merely extensionsof what was shown by Helpman (1984) and Helpman and Krugman (1985). I am
grateful to Steve Matusz for pointing this out.
9. If these were drawn correctly, then the X =1 isoquant could be traced out by
the origin for the XZ =1 isoquant as it slides around the Z =1 isoquant. The construction is much the same as we used to use to construct Scitovsky indifference
curves. Remember them?
10. I have not shown that gain, but I hope it is clear. Fragmentation has expanded the small country’s production possibilities, and at fixed prices this canonly help.

22

Alan Deardorff

Figure 5

3.2. A Two-Country H-O World

What happened in Figure 4 did not really require that the country inquestion be small. To see this, consider a two-country world of the same
sort. Figure 5 shows the Travis-Dixit-Norman11 integrated world economy(IWE) diagram that Helpman and Krugman (1985) exploited so successfully for a variety of purposes. Without fragmentation, the FPE region is
the parallelogram OAFOBF ′. Fragmentation, which makes it possible to duplicate the X output of factor vector OAF with the two fragmented vectors
F′. Thus, for some
OAG and GF , expands the FPE region to OAGFOBG ′allocations of the world’s factors for which FPE would not have been possible, fragmentation leads to FPE.
For example, if the allocation were at point E , then there could not havebeen FPE without fragmentation. What exactly would have happened instead we don’t know, since prices would not have been those prevailing in
the IWE, but it seems plausible that Country A would have produced only

11. Years ago, I incorrectly attributed this diagram to Helpman and Krugman in
the presence of both Elhanan Helpman and Avinash Dixit and had my attention
gently directed toward Dixit and Norman (1980). More recently, Bob Baldwin has
sent me further back, to Travis (1964). While Travis did not speak by that name ofan “integrated world economy,” he certainly used the concept and drew the diagram (on p. 16) for exactly the purpose of identifying a factor price equalization
region. Travis in turn called it an Edgeworth box, although I am not aware (never
having read Edgeworth) that Edgeworth ever used his boxes quite this way, withfactor endowments measured from the corners. All of this is surely known to scholars, but the rest of us have to pick it up wherever we can.

23

Fragmentation in Simple Trade Models

good X and Country B would have produced a mix of X and Y .12 Fragmentation again permits Country A to shift resources into the most capitalintensive fragment of producing Z , and again it is likely to raise the returnto capital and lower the wage. There may also be small effects on factor
prices in Country B, as market clearing prices of X and Y change, butthese are difficult to determine.
This result illustrates the more general phenomenon that fragmentation
enhances the possibility of factor price equalization. With arbitrary numbers of goods, factors, and countries, I showed in Deardorff (1994) thatFPE requires that factor endowments be more similar than factor intensities
in a certain well-defined sense: the set of vectors that can be constructedfrom parts (or all) of the factor endowment vectors––called the “factor endowment lens”––must lie inside the analogous set of vectors defined by
the factors used in the IWE––the “factor use lens.” Costless fragmentation
unambiguously enlarges the factor use lens and thus makes FPE possible
for factor allocations for which it was not possible before.
To see this, note that a factor use lens is defined as(6){

L(v ) = x ∈ R f x = bv for some g - vector}b ∈I g ,where there are f factors and g goods, I g is a set of g-vectors whose elements are in the unit interval, [0,1], and v is a g × f matrix of factor-use
row vectors. Then let v 0 be the matrix of factor uses without fragmentation,
vj0 , j=1,...,g, and let v 1 be the matrix of factor uses in which some or all
goods have been fragmented into 2 or more parts. Numbering the rows ofvji1 , i=1,...,nj, the cost of fragmentation will be zero if vj0 =! v . It is
nj
i =1

1
ji

then easily shown that13,14(7)

L (v 1 )!L (v )!
0This tells us that the possibility of FPE is increased by fragmentation.
That is, there may be allocations of the word’s factor endowments forwhich FPE is not possible without fragmentation and for which FPE becomes possible with fragmentation. It also says that if FPE is possible
12. If we assume fixed-coefficient technologies, then this is necessarily the case,since good and factor prices will leave the factor use vectors unchanged. Of coursein that case, part of the capital in Country A of Figure 5 would be unemployed andthe rental on capital would be zero. However the changes in factor prices identified
in Figure 4 would still occur, in amplified form.
10
1
0
13. Suppose x ∈ L(v ). Then from (6) ∃b ∋ x = bv = bΣvi which implies x ∈ L(v ).
14. See Debaere and Demiroglu (1997), who note the same thing in a different
context. Their result is that the measured factor use lens will lie within the true one
if measured industries are aggregated.

24

Alan Deardorff

without fragmentation, then it must remain possible if fragmentation is introduced. If one were comfortable thinking of the world’s allocations offactors as being somehow randomly determined given its total endowments
and the parameters of technology and tastes, then it would say that thelikelihood of FPE either rises or stays the same with fragmentation; it cannot fall.
Thus fragmentation may well cause factor prices to become equalized
across countries. The analysis here does not say, however, that, failing that,factor prices will be drawn closer together by fragmentation. Figure 4 certainly suggests that result in a special case. There, if the endowment point
were above the kZ ray rather than below it as drawn, then indeed factor
prices in the country would remain different from those in the world afterfragmentation but would be drawn closer to them.15 As far as I know,
however, that is not a general result. In fact, we are surprisingly ignorant(or at least I am) of how the higher-dimensional H-O model behaves outside of the FPE region, or when the lens condition of Deardorff (1994) is
not satisfied.
4. Conclusion
The underlying question addressed in this paper is, “Does fragmentation
matter?” Or, since this is a theoretical piece, not empirical, “Can it matter?” The answer seems to be a relatively strong “Yes.”
Of course, fragmentation will not matter if factor prices are equal everywhere, for then the fragmented technologies will at best duplicate what
was done without them and there will be no reason to use them. But iffactor prices are not equal across countries, either because technologies differ as in the Ricardian model or because factor endowments are less similar than factor intensities in the H-O model, then fragmentation can certainly make a difference. The main effects of fragmentation, at least as I
have been able to identify them from these simple models, are as follows(all assuming that fragmented technologies are used at all):
1. If fragmentation does not change the prices of goods, then it must increase the value of output of any country where it occurs and that of theworld.
2. If fragmentation does change prices, then fragmentation can lower thewelfare of a country by turning its terms of trade against it.
3. Even in a country that gains from fragmentation, it is possible (but notnecessary) that some factor owners within that country will lose.
15. Such a result may exist, but I am pessimistic. After wasting several years
trying to show that free trade must draw factor prices closer together, only to findthe counter-example presented in Deardorff (1986), I will not be surprised if fragmentation admits of equally poorly behaved possibilities in a general model.

25

Fragmentation in Simple Trade Models

4. To the extent that factor prices are not equalized internationally without
fragmentation, fragmentation may be a force toward factor price equalization.

References
Arndt, S. W. 1997. Globalization and the Open Economy. North American Journalof Economics and Finance 8(1): 71-79.
--------- . 1998. Super-Specialization and the Gains from Trade. Contemporary Economic Policy 16: 480-485.
Courant, P. N. and A. V. Deardorff. 1992. International Trade with Lumpy Countries. Journal of Political Economy 100: 198-210.
Deardorff, A. V. 1986. FIRless FIRwoes: How Preferences Can Interfere with the
Theorems of International Trade. Journal of International Economics 20: 131142.
--------- . 1994. The Possibility of Factor Price Equalization, Revisited. Journal of International Economics 36: 167-175.
Debaere, P. and U. Demiroglu. 1997. On the Similarity of Country Endowments
and Factor Price Equalization among Developed Countries. In process, November 1.
Dixit, A. K. and V. Norman. 1980. Theory of International Trade. London: Cambridge University Press.
Feenstra, R. C. and G. H. Hanson. 1996. Globalization, Outsourcing, and Wage Inequality. American Economic Review 86: 240-245.
--------- . 1999. Productivity Measurement, Outsourcing, and Its Impact on Wages:
Estimates for the U.S., 1972-1990. Quarterly Journal of Economics 114: 907940.
Helpman, E. 1984. A Simple Theory of International Trade with Multinational Corporations. Journal of Political Economy 92: 451-471.
Helpman, E. and P. R. Krugman. 1985. Market Structure and Foreign Trade: Increasing Returns, Imperfect Competition, and the International Economy. Cambridge, MA: MIT Press.
Johnson, G. E. and F. Stafford. 1997. The Labor Market Implications of International Trade. In Handbook of Labor Economics, vols. 3 and 4, eds. O. Ashenfelter and D. Card. North-Holland: 2215-2288.
Jones, R. W. and H. Kierzkowski. 2001. Globalization and the Consequences of International Fragmentation. In Money, Factor Mobility and Trade, eds. R. Dornbusch, G. Calvo and M. Obstfeld. Cambridge, MA: MIT Press: 365-383.
Melvin, J. R. 1968. Production and Trade with Two Factors and Three Goods.
American Economic Review 58: 1248-1268.
Travis, W. P. 1964. The Theory of Trade and Protection. Cambridge, MA: Harvard
University Press.

2

Trade, Technology, and Income
Distribution
Ronald Jones

1. Introduction
Recent debates, primarily in the United States, about the effects of international trade on unskilled wage rates, have involved trade economists andlabor economists in empirical and theoretical investigations as to the reasons why and how inequalities in the distribution of income have beenbrought about.1 American experience does not support the view that unskilled labor must continuously lose to skilled labor in a wage comparison,since in the postwar period up to the 1970’s, unskilled labor’s relative
wage was rising. My purpose here is not to examine the causes of changes
in income distribution in any one country or any particular time period. Instead, I wish to appraise several simple strands of reasoning in the international trade literature which serve to link income distribution to changes inrelative prices of internationally traded products, to changes in technology
which may be biased by sector or by factor-saving, and by recent tendencies to split vertically integrated production processes into separate components which may be produced in different regions of the world. I shall argue that excessive reliance on the standard two-commodity, two-factor
Heckscher-Ohlin model yields predictions about income distribution which
are significantly at odds with theoretical frameworks that allow a richer
and wider variety of commodities to be produced and traded, or permit
some factors to be limited in their mobility from sector to sector.

1. See the contributions in S. Collins (1997), as well as R. Freeman (1995), J. D.
Richardson (1995), A. Wood (1995), and R. Jones and S. Engerman (1996).
27

28

Ronald Jones

2. A Price Change in the World Market
Probably the easiest place to start is with the Stolper-Samuelson theorem,
since this seems to provide most of the rationale behind popular and media
coverage in the United States. This theorem, more than 50 years old in theprofessional literature (1941), is referred to by name in the Economist andother current sources.2 It states that if a country produces a pair of commodities with two factors, say unskilled labor and capital (a composite ofphysical and human capital), and if the import-competing product is intensive in its use of unskilled labor, a fall in the world price of such a commodity would (unless protective measures are taken) eventuate in a decline
in the real return to unskilled labor. That is the bottom line； no caveats are
made about technological parity between this country and the rest of theworld. This theorem, seemingly so applicable to describing the fate of unskilled workers in the United States or (in terms of high unemployment
rather than decreased wages) in Western Europe, is often confused with the
Factor-Price Equalization Theorem, which points to the effect of free tradein equalizing wage rates among trading regions. Thus opponents of the
NAFTA accord in North America, or to its extension to Chile and othercountries of the Western Hemisphere, point to the drastic consequences for
American wages should freer trade result in binging wage levels down to
the levels in their partner areas. Most international trade economists would
hesitate to suggest that this latter proposition is relevant to today’s tradingworld, since unlike the Stolper-Samuelson theorem the Factor-PriceEqualization dictum presumes that countries not only share the same technology (including the requirement of comparable labor skills) but that theircapital/labor endowment proportions are sufficiently close together that thecountries will produce the same pair of commodities.
One of the fundamental results in international trade theory is that countries which are linked together by trade rid themselves of the necessity to
produce as many commodities as their populace demands. Specialization in
production can be severe, and it takes a model with many commodities effectively to underscore the consequences for income distribution of thepossibilities of widespread concentration of productive activity with trade.
Consider, therefore, a country facing an initial set of world prices for commodities 1-5. Suppose, furthermore, that this country’s factors are not well
suited to producing commodity 5, either because technology is inferior tothat found elsewhere, or the skills of its labor and capital are deficient, butthat there are techniques available for producing the other four commodities which would allow this country to compete effectively with the rest of
the world at prevailing prices in a competitive setting. Stated more for2. For an appraisal of this theorem after 50 years, see A. Deardorff and R. Stern(1994).

29

Trage, Technology, and Income Distribution

mally, the home country’s technology and the given set of world prices determine a set of unit value isoquants for these commodities, and the convex hull of these isoquants is illustrated by the heavy curve in Figure 1.
This is made up of curved sections, along which only a single commodity
is produced with trade, and of linear segments along which two commodities are produced； for points along any such segment the standard 2 × 2 results of Heckscher-Ohlin theory are relevant for small changes. Suppose
the world price of commodity 2 is reduced, say as a consequence of increased world market participation by countries whose output is primarily
in industry 2’s sector. This has the effect of shifting the unit value isoquantfor commodity 2 radially away from the origin, since now a greater input
bundle must be employed to produce enough of commodity 2 to earn $1
on world markets. The new Hicksian composite unit value isoquant is illustrated by curve 2′
in Figure 2.

Figure 1. Composite Unit Value Isoquant

The same set of information is illustrated in Figure 3. The lightly
sketched upward sloping curves reveal the home country’s technologicallink between the factor price ratio, w/r, and the capital/labor ratios thatwould be adopted. Prevailing world prices determine which techniques
could be used. As Figures 1 or 2 reveal, at very low relative wage rates,
only commodity 1 is produced. At a slightly higher relative wage it becomes possible to produce commodity 2 as well as 1, and such a factor
price ratio is consistent with many combinations of outputs of these two
commodities. For higher wage/rental ratios the composition of productionchanges yet again alternating between patterns of complete and incomplete
specialization. The dashed lines in Figure 3 correspond to the situation illustrated in Figure 2, in which commodity 2’s world price has fallen. Thus
there is now a more narrow range in which commodity 2 would be produced.

30

Ronald Jones

Figure 2. A Fall in 2’s Price

Figure 3. Factor Prices and Endowments

Figure 3 is useful in illustrating how such a fall in commodity 2’s pricewould affect real and relative wage rates for unskilled labor. This effectclearly depends upon the pattern of production in the home country, which
in turn is based upon its endowment proportions. Consider, first, the position of a very labor-abundant country producing only the first commodity.
Its relative wage rate is unaffected, and the real wage for unskilled workers would rise since the price of one of the consumption goods has fallenwith no change in the nominal wage. A similar promising result holds forunskilled labor in very capital abundant countries producing no commodity
2. The fate of countries producing commodity 2 is different. A welfare loss
is shared by both types of income recipients if the country’s endowment
proportions have it producing only commodity 2 before and after the pricerise. But if another commodity is produced as well, the effect of the pricechange on unskilled labor is even more damaging for relatively capitalabundant countries producing commodities 2 and 3 (such as a country with

31

Trage, Technology, and Income Distribution

endowment proportions shown by point A), since commodity 2 is relatively labor-intensive. This is the magnification effect familiar in 2 × 2
models. For a more labor abundant country (such as shown by point B’s
endowment ratio) the price drop serves unambiguously to raise the real
wage of unskilled labor, since commodity 2 is the more capital-intensive
commodity produced there. These results on the change in the real wage
are summarized in Figure 4.

Figure 4. Changes in Real Wage as P2 Falls

The fact that the same world price change can be unambiguously favorable to unskilled workers in some countries but damaging to the same kindof workers in another, even if it is assumed they have access to the same
technology, is a property of simple trade models exhibiting factor-intensity
reversals. In the literature stimulated by the Leontief Paradox in the
1950’s and 1960’s such a phenomenon could reflect a comparison of technologies of producing the same pair of commodities in two countries,
wherein the commodity using capital-intensive techniques in one country
uses labor-intensive techniques in another, so that a price change for that
commodity results in factor prices moving in opposite directions in the twocountries. Here something different is at work––there are not assumed to
be any intensity reversals of this kind. Instead, it must be the case that for
two countries having sufficiently close endowment proportions (and sharing the same technology) such that they produce some commodity in common but are each incompletely specialized to a different other commodity,a price change for the commonly-produced commodity will cause real
wages of unskilled workers to rise in one country and fall in another. Thus
compare the situation of countries with endowment proportions shown by
A and B in Figures 3 and 4. Note that it is the unskilled workers in the
more capital-abundant country which are the losers. (Nonetheless, for such
workers in even more capital-abundant countries no longer producing commodity 2, its price fall in world markets serves to raise real wages.)32

Ronald Jones

3. Technical Progress
Many economists point to the nature of technical progress as a better explanation of why in some countries the wage rate of unskilled workers has
fallen, especially relative to the return on human capital. If technical progress, e.g. developments in computer software, is biased in saving on theuse of unskilled labor, what does standard 2 × 2 international trade theory
tell us about the effect on the distribution of income? Nothing. We need toknow more––in particular, in which sector has technical progress takenplace? (And we assume here commodity prices remain unchanged). If, say,Hicksian labor-saving technical progress takes place only in the laborintensive sector, real wages will unambiguously rise, whereas if such progress, with whatever factor bias one assumes, takes place in the other sector, the real wage rate will fall. This is standard fare in this kind of trademodel if the degree of technical progress is very small. In such a case, thesector in which technical progress takes place causes the distribution of income to change precisely as would a (small) price rise––the StolperSamuelson result once again. But with finite changes in a world in which
many commodities can be produced, technical progress may have the effect of shifting the pattern of production and thus resulting in a different
response of wage rates and returns to human or physical capital. And, if
the change is finite, the factor bias of technical progress may influence theproduction pattern.
This issue is illustrated in Figure 5 for the two-commodity case. Commodity 2 is capital-intensive, and in the initial equilibrium it uses technique A along its unit-value isoquant, while labor-intensive commodity 1
adopts technique B. The initial wage/rental ratio is shown by the slope ofthe line tangent at A and B. Factor endowment proportions are shown by
ray 0R. Now suppose technical progress takes place only in capital-

Figure 5. Technical Progress in Capital-Intensive Sector (2)33Trage, Technology, and Income Distribution

intensive sector 2. Two possibilities are shown, with different factor biases： 2′
and 2″, either of which would lead to the same new lower wage/
rental ratio shown by the slope of DEC if both goods should be produced
after the technical change. But this is a big “if”, one not satisfied for thiseconomy with indicated endowment ray OR if technical progress leads tothe new isoquant 2″instead of 2′. Such an economy would drop its production of commodity 1 and produce only the second commodity with awage/rental ratio shown by the slope at F. That is, if the bias in technicalprogress leads this country to shift its production pattern (to specialize inthe capital-intensive product), a rise in the real wage could result fromtechnical progress in the capital-intensive sector.
There is no doubt that the frequent reliance trade theorists place on the
2 × 2 Heckscher-Ohlin model to trace out the effects of price changes ortechnical progress on income distribution leads to results at odds with theintuition which many labor economists place on partial equilibrium techniques. The specific-factors model helps to bridge the gap. It is a legitimate form of production structure for use in general equilibrium analysis,
but leads to more common sense results for some questions. For example,
in the 2 × 2 setting with given commodity prices, a nation would respondto an influx of immigration of unskilled labor by altering the production
mix without any change in factor prices. By contrast, suppose in each of
two sectors a type of capital (human and physical) is used that is specificto that sector and not used in the other. As well, suppose each sector dips
into a common pool of unskilled labor. Increased supplies of such labor
would unambiguously lead to wage declines. As for technical progress, inthe specific-factors model the factor bias does matter, along with the rate
at which each individual sector is affected. (See Jones, 1996 for details). If
technical progress were Hicksian neutral (so that at an unchanged factorprice ratio the same capital/labor proportions would be utilized as in theinitial state), the wages of unskilled labor would rise regardless of the sectoral distribution of technical progress. If progress were biased in the labor-saving direction, which most commentators fear has been the case for recent advances in technology, downward pressure on wages would indeed
exist, much as in the case of increases in labor supply. However, a mobile
factor such as labor would tend to gain from the existence of technicalprogress, as would all income earners in the neutral case. What can be saidof the balance in these opposing forces? As proved in Jones (1996), evenin the case of pure Hicksian labor-saving progress at the same rate in eachsector, labor’s real wage will rise if technology is sufficiently “flexible”.
By this is meant if the elasticity of substitution between labor and capitalin the two sectors is high enough. A value of unity is more than sufficient.
(On average a value exceeding the ratio of capital to labor shares will beenough).

34

Ronald Jones

4. Fragmentation and Loss of a Labor-Intensive Activity
Developed countries in the United States and Western Europe are fearfulthat technological advances in service sectors such as telecommunications
and transportation will encourage previously vertically-connected production processes to fragment, with more labor-intensive segments losing out
to foreign competition. Need this be a concern? Figure 6 helps to clarify
the issue.

Figure 6. Fragmentation in Sector 2

For convenience, it is assumed in Figure 6 that each productive activity
displays absolutely rigid technology in the sense that no substitution possibilities between labor and capital are available. Thus originally suppose thehome country’s Hicksian unit-value isoquant is made up of corner points
for producing activities 1 through 4, and the linear segments connecting
these points. This state of affairs is disturbed by developments in service
activities (not shown) which allow vertically-integrated activity 2 to be
fragmented into two fixed-coefficient activities, one more capital-intensive
than the other. In particular, suppose that this finer division of productive
activities allows world gains in productivity in that a more intensive application of the Ricardian doctrine of comparative advantage tends to result ina lower world price for the aggregate of the two components of commodity 2 than previously. This is revealed in Figure 6 by the two fragments 2Aand 2B, and the fact that the convex combination of these two points lies
above the corner of previously integrated activity 2. (Details of this fragmentation procedure are found in Jones and Kierzkowski 2001). Arbitrarily
shown in Figure 6 is the dominance of capital-intensive activity 2A overthe labor-intensive component 2B, ensuring that with fragmentation the lat-

35

Trage, Technology, and Income Distribution

ter activity lies strictly within the convex hull denoted by the dashed lines.
What are the consequences for factor prices and employment in thehome country in this new, more fragmented world? This depends on the
country’s factor-endowment proportions. For example, if the capital/laborendowment ray is shown by 0R2, the wage/rental ratio falls. Indeed, the replacement of activity 2 by the fragment 2A in the country’s portfolio of
production (it also produces commodity l) is akin, in its affect on factor
prices, to a labor-saving technical progress in the country’s capitalintensive activity. Thus the real wage unambiguously is driven down. Figure 7 explicitly reveals this loss in the real wage. (For a capital/labor endowment ratio between rays 02A and 02, the drop in the real wage is especially severe since wages were originally higher when the country originally produces commodities 2 and 3). By contrast, the situation at home if
it originally had the higher capital/labor endowment proportions shown by
ray 0R1 is different. In this case the country is originally producing commodities 2 and 3, so that the replacement of integrated activity 2 by themore capital-intensive segment, 2A, has its analogy in a technical progressin producing the labor-intensive commodity. This results in standard 2 × 2
fashion in an increase in the wage/rental ratio and, as Figure 7 illustrates,
an increase in the real wage as well. For countries so capital abundant that
commodity 2 is not initially produced, there results the standard improvement in the real wage as a consequence of the lowering of commodity 2’s
price to consumers.
Although this model is not designed to address the issue of aggregate
employment (indeed it assumes factor prices represent market-clearing
wages and returns to human and physical capital), it can show what happens to employment in sector 2, in which this country is shown to lose thelabor-intensive fragment, 2B, to world competition. The answer to thisquestion depends on whether the country is relatively capital abundant,such as shown by ray 0R1, or labor-abundant, as shown by ray 0R2. In thelatter case not only do wages fall, but sectoral employment shifts awayfrom commodity 2 to more labor-intensive commodity 1. Consider the fateof a more capital-abundant country, the very type of country which is apt
to be worried about the effect of losses of labor-abundant fragments on
wage rates in a more competitive and fragmented world market. Its real
wage rises, as previously noted, and employment of labor in the capitalintensive segment 2A actually exceeds previous employment levels in the
fully integrated activity 2. The reason： Point P in Figure 6 is a weighted
average of points 3 and 2A, with a greater weight given to 2A than is given
to 2 in point Q’s weighted average of points 3 and 2. Finally, compare theshapes of the loci in Figures 4 and 7. If greater international competition
forces down the price of commodity 2, it is the real wage in more capitalabundant countries (producing 2) that is lowered. By contrast, increased
fragmentation which causes a country to lose the labor-intensive fragment,

36

Ronald Jones

2A, results in a lowered real wage not for more capital abundant producing
countries, but for those which are more labor-abundant.

Figure 7. Fragmentation and Changes in Real Wage

5. Concluding Remarks
The analysis of the effects of changing terms of trade or a change intechnology or the degree of fragmentation in world markets on a country’s
distribution of income stressed in these remarks is based on a multicommodity trading world. Abandoning the standard assumptions of 2 × 2
international trade theory leads to a wider variety of results without any
substantial increase in the difficulty of analysis. To be sure, a drop in theworld price of a commodity produced in a country by labor-intensive techniques still spells difficulty for the return to unskilled labor. But even thisconclusion needs to be qualified. For suppose that the price drop is itself
the consequence not of new supplies of the commodity as new developing
countries enter the world market, but rather of technological progress
which is shared by the country in question. In such a case the price drop is
accompanied by an increase in the real wage. Indeed, this was the analogy
pointed out in the preceding section, in which reductions in costs of fragmentation caused a country to lose the labor-intensive segment of a previously vertically integrated activity, an activity which utilized laborintensive techniques relative to another actively produced commodity.
A Heckscher-Ohlin world in which factors are mobile between sectors is
one in which production is concentrated to a few commodities if trade allows consumption to be obtained from abroad. This implies that as prices
fall for some traded commodities, many countries may experience a rise inreal incomes for all factors because none of that commodity is produced.
This was the source of gain in real wages at very low and very high capital/labor endowment ratios in Figures 4 and 7. Suppose instead there aremany specific factors, indeed an (n + 1) × n version of the model in some37

Trage, Technology, and Income Distribution

country. Then all commodities are produced. However, the lower the pricefor any commodity, the less labor will be devoted to its production, so thatonce again the gains to workers as consumers will eventually exceed any
losses in real wages as the price to local producers falls.
The specific-factors model is both simple and useful if a distinction isdesired between human capital and physical capital as well as unskilled labor. For example, suppose for the American case that import-competing
goods are produced with unskilled labor and physical capital whereas in
the export sector the specific factor is skilled labor (human capital) andphysical capital is mobile between sectors. If a fall in the price of imports
is the primary shock coming from world markets, such a scenario suggests
a rise in real wages for skilled workers, a fall in real wages for the unskilled, and not much real change in the return to physical capital. Not a
bad fit for the American scene.
There is no doubt that changing conditions of international trade canhave important repercussions on the distribution of income in all trading
nations. And so can changes in other conditions, such as technical progressor advances in services which allow an international dispersal of previously vertically integrated components. These changes are more sensibly
analyzed in models with many commodities. The competitive forces oftrade can then encourage greater degrees of concentration so that evencountries with similar technologies and factor skills but somewhat different
endowment proportions can produce a different range of commodities. The
effects of any world shocks on real wages and returns to human and physical capital may then be different from one country to another.

References
Collins, S. 1997. Imports, Exports and the American Worker. Washington, D.C.:
Brookings Institution.
Deardorff, A. and R. Stern. 1994. The Stolper-Samuelson Theorem: A Golden Jubilee. Ann Arbor: University of Michigan Press.
Freeman, R. 1995. Are Your Wages Set in Beijing? Journal of Economic Perspectives 9(3): 15-32.
Jones, R. 1996. International Trade, Real Wages, and Technical Progress: The
Specific-Factors Model. International Review of Economics and Finance 5(2):113-124.
Jones, R. and S. Engerman. 1996. Trade, Technology, and Wages: A Tale of Two
Countries. American Economic Review 86(2): 35-40.
Jones, R. and H. Kierzkowski. 2001. Globalization and the Consequences of International Fragmentation. In Money, Capital Mobility, and Trade: Essays in Honor
of Robert A. Mundell. eds. G. Calvo, R. Dornbusch and M. Obstfeld. Cambridge,

38

Ronald Jones

MA: MIT Press: 365-383.
Richardson, J. D. 1995. Income Inequality and Trade: How to Think, What to Conclude. Journal of Economic Perspectives 9(3): 33-56.
Wood, A. 1995. How Trade Hurt Unskilled Workers. Journal of Economic Perspectives 9(3): 57-80.

3Trade and Personal Distribution of
Wealth and Income: Beyond the
Stolper-Samuelson Theorem
Satya Das*

1. Introduction
It is well-known that major trade policy changes have serious distributional implications. This is why such changes are often controversial. The
justly famous Stolper-Samuelson theorem, henceforth “The Theorem”, isthe theoretical center-piece, around which the effect of trade on distribution
is understood and discussed. Published over sixty years ago (Stolper andSamuelson (1941)), it still enjoys a central status in trade theory. Perhaps
for the first time, the supremacy of The Theorem is being questioned now
amidst recent controversy on the trade-relative-wage nexus (Leamer(1996)). At the same time however, there is no serious alternative being
proposed or developed (Burtless (1995)). Some continue to believe that
The Theorem is an ‘eternal truth’––something which must hold ‘in thelong run’. Within a broader factor endowment framework with more than
two goods, Jones (1997) analyzes a wide variety of predictions other than
The Theorem. At the worst, The Theorem is still the eye of the storm andhence enjoys its status in a different way.
The objective of this paper is not to challenge The Theorem but to‘stand on its shoulder’ so-to-speak and attempt to explore the more complex territory of personal distribution of income and wealth. Specifically, it
examines how international trade, based on difference in factor endowments, may affect personal distribution of wealth and income within acountry, given its implication for functional distribution according to The
Theorem. The modern market economy is quite different from the landlord* This paper has benefitted from a referee’s comment and seminar presentation
at Chinese University of Hong Kong, I.S.I. − Delhi Centre, Jawaharlal Nehru University and participants in an International Economics conference at Kobe University, especially Shumpei Takemori. Remaining errors are mine.
39

40

Satya Das

/capitalist-or-labor class economy in the immediate post-IndustrialRevolution period. The transaction costs of participation in asset markets
are quite small and many households provide labor services as well as own
land/capital. Casual observations tell us that the proportion of households
owning and trading in land/capital and common stocks (which provides
ownership of land/capital indirectly) is increasing over time, and, it is a
global phenomenon. Thus, in order to judge equity implications of policychanges, personal distribution seems more relevant as an object of study
than functional distribution––with which trade theory has been preoccupied
for a long time.
It is only very recently that the issue of trade policy and personal distribution of income has been taken up in the literature, e.g. Fischer and Serra(1996). It develops a Lucas-type endogenous growth model with humancapital. Different households have different initial endowments of humancapital which is partly consumed and partly passed on to the posterity.
Freer international trade between countries have short term, but no longterm, effects on wealth and income distribution. The emphasis is on income convergence across countries.
In contrast, this paper is entirely focused on the effect of trade on distribution (a) in the long run and (b) without any consideration of growth––
exogenous or endogenous. In the process, our analysis also develops in a
precise way (at least theoretically) the common notions of lower class,
middle class and the upper class, whose sizes change responding to policy
variations.
The basic scenario to be explored is the following. There are two countries, North and South, which possess the standard Heckscher-Ohlin characteristics. The North and South are respectively the relatively more land(or equivalently nonreproducible capital) and labor abundant countries. In
each country land is tradable.1 There are two goods differing in factor intensities, both factors are mobile between the two sectors, instantaneous
utility function is the same across the two countries and satisfies homotheticity, and so on.
This scenario is exactly the same as in Mayer (1984) except that there isa market for land (and there are no political economy aspects). It is alsosimilar to Eaton (1988) in that land is tradable; it is less general than Eaton’s as reproducible capital is not considered but more general in that
there are heterogeneous households or dynasties. Reproducible capital isignored in order to focus entirely on the distributional aspects of an economy.
We interpret households as dynasties (we will see why). The number ofdynasties and the total endowment of land are given. In particular, the dy1. Empirical evidence indicating that land is a significant component of wealth isprovided by Goldsmith (1985) which is reproduced in Eaton (1988).

41

Trade and Personal Distribution of Wealth and Income

nasties differ in their propensity to accumulate land.2 This is the source ofheterogeneity and inequity in wealth and income. It is similar to Stiglitz(1969) and models of heterogeneous rate of time preference such as Uzawa(1968), Epstein and Hynes (1983), Lucas and Stokey (1984) and Das(1993). Those with greater propensity to accumulate hold more land in thesteady state.3
We consider two types of model economies within the broad features
just described. In one, our basic model, each dynasty is endowed with one
unit of labor and thus there is only rental income inequality. In the other,labor supply is variable. Through wealth effect and because of varying
propensity to accumulate, wage incomes (‘earnings’) are unequal. Thismodel gives rise to the notion of lower, middle and upper classes. Those in
the higher end of the propensity to accumulate hold so much of wealth(land) that, by the wealth effect, they decide not to work. They are purelandlords or capitalists and constitute the upper class. Intertemporal preferences are specified such that land holding is not ‘necessary’. Thus in thelower end of the propensity to accumulate, there are dynasties which do
not possess land at all. These are landless workers and define the lower
class. Those in the middle hold land as well as work and constitute themiddle class. They can be called ‘working landlords’ or ‘working capitalists’. An important feature of this classification is that the size of eachclass is endogenous since labor-leisure choice and whether to hold zero or
positive amount of land depend on the wage-rental ratio and return to capital. This is similar to the (five-) class structure developed by Roemer(1982). However, his classification is based on exogenously specified distribution of wealth endowments and hence on exogenous class sizes.4 In
summary, in contrast to a ‘standard’ static model, in our analysis both
wealth distribution and class sizes are endogenous.
In this scenario, our analysis offers the following results.
(1) Free trade in commodities, compared to autarky, entails more wealthand income inequality in the North and less in the South.
(2) The above result holds in the basic model of rental income inequality.
The extended three-class model predicts that free trade in goods leads
to a middle class squeeze in the North and a middle class expansion in
the South.
(3) Lastly, assuming a Benthamite utilitarian social welfare index, the resultant change in distribution due to free trade is a source of welfare
loss for the North and welfare gain for the South.
2. There is of course no aggregate accumulation. Individuals however attempt toaccumulate or decumulate.
3. The difference, which is not essential for our purpose, is that these works assumed reproducible capital. But their distributive implication is exactly the same ashere with land or nonreproducible capital.
4. Eswaran and Kotwal (1989) apply Roemer’s concepts to the credit market anddevelop an agrarian class structure.

42

Satya Das

We find result (2) particularly interesting. There is mounting empiricalevidence that over the last two/three decades wealth and income inequalities have risen in many developed countries (e.g. Das (1993)). There isconstantly a talk of middle class shrinkage. On the other hand, one also
reads about middle-class boom in many developing countries following
economic liberalization. Our analysis suggests that these phenomena ispartly attributed to freer trade between developed and developing countries.
Section 2 develops our basic model and examines the effect of free tradeon wealth and income inequality in the presence of rental income inequality only. The three-class model is developed in Section 3. Equity as well
as aggregate welfare implications of free trade are examined. Section 4
concludes the paper.
2. The Basic ModelAn economy is endowed with a given number of households (equal to
H ) and a given amount of land (equal to K ). To begin with, consider aclosed economy. The production side is of the standard HO (HeckscherOhlin) type. Let the two goods be denoted by x and y, respectively laborand land intensive.
On the household side there are dynasties indexed by h. Following
Aghion and Bolton (1997) and Piketty (1997), everyone lives for one period. As soon as a person dies, a replica is born. Each individual derives
utility from his/her own consumption and bequests he/she leaves. The
overlapping generations setup is assumed away so as to separate inequity
across households/dynasties from inequity in terms of age.5 There is riskaversion in terms of consumption (i.e. diminishing marginal utility fromconsumption) and in terms of overall utility from consumption and bequests. The latter is not essential; it will be used only in assessing aggregate welfare effects later in section 3.
At time t, a dynasty h’s preferences are specified by the utility function⎧γ 1nxht + (1 − γ )1ny ht + s1n( Kht +1 + h − a )
(1) ⎨
⎩−∞

when Kht +1 ≥ a − hotherwise.

where 0 < γ < 1, s > 0 and
(R1)

a

! b.

5. The source of heterogeneity in our analysis is however different from thatanalyzed by the above mentioned authors as well as Banerjee and Newman (1991)––namely, risky returns on investment and lack of perfect insurance markets.

43

Trade and Personal Distribution of Wealth and Income

The parameter b will be introduced later. xht and yht are the respective consumption and Kht+1 is the amount of land bequeathed to the next generation.
The first two terms represent felicity; γ is therefore the share of good x in
the total expenditure:

(2)

xht =

γE ht
;
p xt

yht = (1 − γ ) E ht ,where pxt is the relative price of good x in terms of good y, the numeraire
good, and, Eht is the dynasty’s total expenditure. The indirect static utility
function is: ∆ − γ ln(pxt) + ln(Eht), where ∆ ≡ γ ln γ + (1−γ ) ln(1−γ ). Theintertemporal utility function is accordingly stated as(3)∆ −γ ln(pxt) + ln(Eht) + sln(Kht+1+h−a).

A dynasty’s savings are in the form of bequests.
That the quantity of exactly what is being bequeathed affects utility represents “joy of giving” or “warm-glow” preferences over bequests (see Andreoni (1989) also, along with Fischer and Serra (1996), Aghion and Bolton (1997) and Piketty (1997)).6
The warm-glow bequest approach implies that land has an asset value aswell as a direct commodity value. Therefore, the ‘yield’ on land (therental) is not the only determinant of the asset price (price of land). Later
this will imply that factor price equalization across countries would not imply asset price equalization.
The parameter s is just a coefficient, which we set to one henceforth.
The dynasty type is indicated by h. Let its support be (0, b), b > 0, andthe density function be f (h). There is no restriction imposed on this function, except that it is continuous. A higher value of h implies a lower marginal utility schedule of bequest, implying that, along the steady state, adynasty with a higher h holds less land. Define mean h ash≡b

∫ hf (h)dh.
0

The restriction a > b implies that the marginal utility of bequest satisfies
Inada condition for all h. Hence in equilibrium all dynasties will hold positive amount of land (to be relaxed in the three-class model). Borrowing is
6. This is in contrast to the Ricardian specification as in Barro (1974) where aparent’s utility is, in part, a function of the child’s utility, which is equivalent to to
an infinite-horizon chain. See Aghion and Bolton for a discussion on why, in modelling bequests, the warm-glow approach may be preferred to the Ricardian approach.

44

Satya Das

prohibited.7 Further, it will be assumed that
K > H (a−h).

(R2)This states that the total endowment of land is not too small. The significance of this will be seen later.
Finally, that the value of h is the same over generations of any given
dynasty captures the notion of dynasty itself in that a tradition or a practiceis being passed on from one generation to the next.
In this section we assume that each dynasty possesses a unit of labor endowment which is offered to the labor market. Hence the total labor endowment is the number of dynasties, H . The total income of a dynasty
equals Ih = wt + rtKht, where wt and rt are the respective factor rewards (interms of good y). The price of land denoted by pkt, the intertemporalbudget constraint reads as(4)Eht + pktKht+1! w + (r + p ) K .
t

t

kt

ht

A dynasty maximizes (3) subject to (4). The first-order condition is" !a #p !

Eht
Kht "1 h(5)kt

Transitional Dynamics
Since there is no aggregate accumulation, in the aggregate an economy is
the same as the standard, static HO economy; Qxt, Qyt, wt, rt and pxt are all
constant over time and henceforth will be indicated without the time subscript. These are determined by the two zero profit conditions, the two full
employment conditions and one product market clearing condition. Next,
we aggregate (4) and (5), eliminate Et and obtain wH +rK =pkt(K +Hh−Ha),
which implies that pkt is constant over time also. Finally, we go back to (4)and (5), elimiate Eht and express distributional dynamics as(6)

Kht +1 =a − h + ωρ + ( ρ + 1) Kht,
2

7. This can be relaxed by specifying the utility from bequest as ln(Kht+1−Dht+1/(rt+1 −pkt+1)+h−a), where Dht+1 is the debt passed on to the posterity, rt is the yield(rental) on land at t and pkt is the price of land at t. Thus Kht+1−Dht+1/(rt+1+pkt+1) is
the net wealth bequeathed. The results of this paper remain unchanged as long as
there is borrowing and lending inside a country but not across countries and there
is a cap on debt such that negative bequests cannot be passed on.

45

Trade and Personal Distribution of Wealth and Income

! "

!"
"
" !

w r , and ρ r pk is the rate of return on capital. Given (R1),
where ωi.e., a b , it follows that a h for any h. This implies that Kht #1 as afunction of Kht has a positive intercept. Later it will be established that
ρ < 1. Thus 0 dKht #1 dKht 1 . Hence for any h, there exists a uniquesteady state level of land holding and the adjustment process towards it ismonotonic. From now on––in this economy as well as the model economies to be considered––we will confine ourselves to steady state only.

"!

Steady State
Equating Kh+1 = Kht = Kh in (6),

(7)

Kh =

ωρ + a − h
,
1− ρ

(8)

⇒ Ih =r (ω + a − h),1− ρRestriction (R1) implies that the numerators of these expressions are positive. As we shall see, (R2) would imply that, in equilibrium, 0 < ρ < 1.
Thus positive solutions of Kh and Ih are assured. These are decreasing in
h.8
Eq. (7) is also the demand function for land. The following properties ofthis demand function would be important in understanding the model’s
prediction on wealth and income inequality.
1. The demand for land is an increasing function of ω by the ‘income effect’.
2. The rate of return on land also has a positive ‘price effect’ on demand
for land, which is decomposed into an income effect (represented by ρas the coefficient of ω in the numerator of Kh) and a substitution effect(through ρ in the denominator).
3. The income effect of an increase in ρ equals ω /(1−ρ ) and is the samefor all dynasties. The substitution effect, equal to ( ωρ + a−h)/(1-ρ )2, isless for higher h or poorer dynasties.
Given these properties, consider the difference in land holding by any
two dynasties. Suppose h1 < h2 so that K1 > K2. Then

8. As observed by the referee, substituting these into the utility function, it iseasy to see that utility is also decreasing in h. This can be interpreted as sayingthat the rich (poor) choose to remain rich (poor). One can also say that the rich(poor) remain rich (poor) because of their behavioral difference.

46

Satya Dash2 − h1,1− ρK1 − K2 =(9)which is an increasing function in ρ . All else remaining the same, an increase in ρ motivates both rich and poor to demand more land. Income effect is the same but the substitution effect is greater for the richer dynasties.
Thus the difference between land holdings widens due to the substitution
effect. This indicates that the variance of Kh increases with ρ .
bb

The total demand for land equals∫ K f (h)dh. Thus ∫ K f (h)dh = K
0

h

0

h

spells the land market clearing condition. In the light of (7),ωρ + a − h K
=
,
1− ρ
H

(10)

which essentially determines the price of land or equivalently ρ given w
and r. Note that the left-hand-side is the mean demand for land. At ρ = 0,
it equals a−h and as ρ → 1, it approaches ∞. Hence there exists a uniquesolution of ρ (0 1), if K > H (a−h). The last inequality is the same as
our restriction (R2). Thus (R2) ensures that 0 < ρ < 1.
Observe that the price of land is not a function of factor prices alone. In
particular, it is not equal to the discounted value of the stream of yields (r).
It is because land, in the form of bequest, provides utility directly––notjust indirectly through the intertemporal budget constraint by being asource of rental income. Put differently, land has a direct commodity valuealso, implying that, in equilibrium, the price of land is affected by factor
endowments.
Finally, how are wealth and income inequalities measured? We shall use
the coefficient of variation. For a random variable z, the coefficient ofvariation is given by, σ z/ z, the ratio of standard deviation to the mean. For
this section, the results hold if we use Gini coefficient as well (see Appendix, Part 1). The model to be developed in the next section is more complicated however and tracking the Gini coefficient becomes a very difficult
task.

!!

2.1. Free Trade
All the relations described thus far hold for both North and South. Between them, KN/HN > KS/HS, so the land-abundant North has comparativeadvantage in the land intensive good, good y, and the labor-abundantSouth in good x. To fix ideas, suppose that in the free trade equilibrium
both countries incompletely specialize and factor price equalization (FPE)47

Trade and Personal Distribution of Wealth and Income

holds. The Theorem then captures the effect of trade on functional distribution: ω decreases in the North and increases in the South. Turn now to theland market clearing condition (10). The aggregate demand for land being
an increasing function of both ω and ρ , the variation in ω implies that ρ
increases in the North and decreases in the South. Intuitively, in the Northfor example, a decrease in ω lowers the aggregate demand curve for landby the income effect and tends to push pk down. In equilibrium, ρ increases; thus dρ /dpx < 0.
Once the effect on ρ is determined, the implications of trade for wealthand income inequality are immediate. The mean land holding is given by
assumption. Hence the change in wealth inequality is entirely dictated by
the change in its standard deviation. From (7), σ K = σ h/(1−ρ ), which is anincreasing function of ρ . Since ρ rises (falls) in the North (South), it follows that wealth inequality increases (decreases) in the North (South).
The intuitive explanation is the following. Free trade leads to an increase(decrease) in the land rent in the North (South). This tends to push ρhigher (lower) in the North (South). As shown earlier (see (9)), an increasein ρ increases the dispersion of land holding. The average land holding remaining unchanged, the coefficient of variation increases (decreases) in the
North (South).
Now, from (8),

σ1
σh
=
.
I
ω +a−hThis is a decreasing function of ω . We already know that ω falls (rises)in the North (South). Thus income inequality moves the same way as does
wealth inequality. In summary,
Proposition 1. Free Trade in goods between North and South leads tomore wealth and income inequality in the North and less in the South.
Notice that a model of exogenous distribution of land would predict, on
the basis of The Theorem, that, if, for example, ω decreases and r increases, there would be more income inequality. Thus, in some sense, The
Theorem ‘anticipates’ more inequality in the North and less in the South.
Our basic model of endogenous distribution reinforces this. However, amodel of exogenous distribution of land is incapable, by definition, of predicting changes in wealth distribution––which our model does. Also, ouranalysis provides a definite mechanism through which both income andwealth distributions change. Furthermore, as we move on to the 3-classmodel in Section 3, it would be apparent that a model of exogenous distri-

48

Satya Das

bution of land would have been unable to endogeneize class sizes.9
3. A Three-Class Model
Our basic model is extended now to incorporate labor income inequality
as well as three classes of dynasties: workers, working landlords and landlords. This is done by allowing (a) variable labor supply decision and (b)by not allowing bequest to be ‘essential’ for all dynasties. As a result of(a) and (b), some dynasties obtain labor income only (the workers), someonly rental income (landlords) and some both (working landlords). They
are respectively the so-called lower class, upper class and the middle classrespectively. As mentioned in the Introduction, this is related to Roemer’s(1982) class structure. The fundamental difference however is that the basis of heterogeneity in Roemer’s lies in heterogeneous wealth endowmentsthat are given so that the class sizes are fixed also, whereas here preference heterogeneity is the primitive, and wealth holding and class sizes areendogenous.
Let a dynasty’s intertemporal utility be dependent upon current expenditure, bequest, and, in addition, leisure:(11)

Uh = ∆−γ ln(pxt) + ln(Eht) + sln(Kht+1 + h−a) + ln(T −Lht),!

!

where Tthe total time available per period and L
the labor time supplied. The index h varies from 0 to b with the same density function. Ourparametric restrictions are however partly different:
K

(R2)
(R3)

" H (a−h),0 < a < b,

(R4)

T

!〜T .

The first one is (R2), same as in the basic model, which ensures the existence of equilibrium in the land market. (R3) contrasts (R1) and means that
the Inada condition is not satisfied for all h. The implication is that bequest is not necessary for some high-h dynasties. These dynasties holdzero land in equilibrium. (Negative land holding or borrowing is not per〜
mitted.) The parameter T will be defined later.
A dynasty maximizes (11) subject to the intertemporal budget constraint
Eht pkt Kht #1 wt Lht (rt pkt )Kht , and the nonnegativity constraints

#

"

# #

9. Finally, note that Proposition 1 is a long term prediction regarding the effectof trade on distribution, in comparison to a similar short term prediction obtained
by Fischer and Serra (1996).

49

Trade and Personal Distribution of Wealth and Income##

Kht 0 and Lht 0. Assuming (for now) that nonnegativity constraints do
not bind, the first-order conditions, along the steady state, are:

T !L
E
p
$h !a %p ; K $h !a % w !
Together with I %wL $rK , these equations solve K , L and I :
h

h

h

k

k

Kh

h

h

h

h

h

h

T ωρ + 2(a − h)
,
2−ρ

(12)

Kh =

(13)

Lh =

T (1 − ρ )ω + h − a,(2 − ρ )ω

(14)

Ih =

r
( T ω + a − h) .
2−ρGiven our restrictions, it will be shown that ρ < 1. Thus, Kh and Ih arenegatively related to h as in our basic model. The new feature here is thelabor supply. Higher h implies less wealth, and, via wealth effect on leisure, more labor supply.
From (12) and (13), we derive the critical dynasties for whom the landholding or the labor supply is zero. Setting Lh = 0 and Kh = 0 in the respective expression, we have
h1 = a − T (1 − ρ )ω ,(15)

h2 = a +

(16)

T ρω
.
2

Given 0 < ρ < 1, h2 > h1. Let T be not so large, such that h1 > 0 and h2 < bin the relevant range of comparison between autarky and free trade. This is
our restriction (R4). The necessary condition for h2 < b is that a < b,which is our restriction (R3). We then have 0 < h1 < a < h2 < b. (R3) and(R4), together with ρ < 1, imply the existence of all three classes of dynasties.
Note that the solutions for Kh, Lh and Ih stated above are valid for the
middle class (h 1 h h2 ). For the upper and lower classes, we solve therespective constrained optimization problem. The solutions are summarizedin Table 1. Note that the upper class does not work and has rental income

" "

50

Satya Das

only, whereas the lower class does not possess land and has labor income
only. The middle class possesses both.

Table 1. Solutions for Various Classes

! !

! !

! !

0 h h1upper classh1 h h2
middle classh2 h blower class

Kh

a−h
1− ρ

Tωρ + 2(a − h)
2−ρ

0

Lh

0

T (1 − ρ )ω + h − a(2 − ρ )ω

T2Ihr ( a − h)1− ρr (Tω + a − h)
2−ρ

rT ω
2

It is interesting in passing that this 3-class classification results from the
distribution of a single parameter, not from any joint distribution of parameters.
The ‘demand functions’ for land (bequest) have reasonable properties. It
increases with ρ and there is a positive income effect when there is labor
income. Moreover, it decreases with h. The supply function of labor does
not have all the desirable properties one may wish it to have: with respect
to the wage rate, it is increasing for low values of h(h < a), decreasing for
medium-range values of h(a < h < h2) and inelastic for higher values of h.
These are results of income and substitution effects vis-a-vis consumption
and demand for land. However, labor income increases with w, a desirable
property, and, decreases or remains the same with respect to h. For the
lower class, there is no intertemporal decision; hence labor supply is thesame for all dynasties. Wealth (Kh) and income (Ih) as functions of h are
exhibited in Figure 1.
Given different levels of land holding, the land market clearing condition is:(17)
D( ρ , ω ) =

h2
1 h1
1
K
(a − h) f (h)dh +T ρω + 2(a − h) f (h)dh = .
0
h
H
1− ρ
2−ρ 1

∫

∫ [

]

We have (i) D (0, ω ) = a−h, (ii) D (ρ , ω ) increasing in ρ in (0, 1) and(iii) approaching ∞ as ρ → 1.

51

Trade and Personal Distribution of Wealth and Income

Figure 1. Autarky Equilibria: Endogenous Capital Stock

Hence a unique solution of ρ exists between (0, 1) as long as K /H > a−h,which is our restriction (R2).
It is easy to verify that ∂D / ∂ω > 0.
Thus dρ /dω < 0 as in the basicmodel. We can also express D( ρ , ω ) = D( ρ , ωρ ) with ∂ D / ∂ρ > 0 and∂ D / ∂ (ωρ ) > 0. Hence, totally differentiating the land market clearing condition, d (ωρ )/dρ < 0 and therefore d (ωρ )/dω > 0; these comparative static
properties will be used later.
The aggregate labor supply is variable in the economy. In view of Table
1, it equals(18) L =a + T ρω / 2
1
TT (1 − ρ )ω + h − a f (h)dh +(2 − ρ )ω a − T (1− ρ )ω
2

∫

[

]

∫

b

a + T ωρ / 2

f (h)dh.

The elements of the model are all laid out. We now characterize autarky
and free trade equilibria and compare.
3.1. Autarky and Free Trade
Unlike in the basic model, the aggregate behavior of an economy is not
the standard HO Type, because of variable labor supply. The effect of a
product price change on sectoral outputs has two components: (a) a movement along the PPF (production possibility frontier) and (b) a shift of the
PPF. Effect (b) is akin to the Rybczinski effect and has two ‘sub-effects’.
A change in px affects ω via The Theorem which then affects the aggregate labor supply L; this is a ‘direct effect’. Secondly, a change in ω affects ρ , which also has an impact on L; this is an indirect effect. From(18), we have52

Satya Das

(19) dL =dω(2 − ρ )ω 2

h2

dρ

h2

∫ (h − a) f (h)dh − (2 − ρ ) ω ∫ (T ω + h − a) f (h)dh.
h1

2

h1

The coefficient of dω , the direct effect, is ambiguous, while, in view ofthe expressions of Lh in Table 1, the coefficient of dρ , the indirect effect,
is negative. The net effect of a change in ω ––and hence a change in px––
on L turns out ambiguous.
Now consider the effect of an increase in px on the output ratio, Qx/Qy.
Given L, the ratio increases for standard reasons. By The Theorem, ω increases since sector x is labor intensive. From the land market clearing, we
already have dρ /dω < 0. Thus d ρ < 0, which tends to increase L. By the
Rybczinski effect, Qx/Qy increases. This reinforces the standard effect. The
effect through the direct impact of ω on L is ambiguous. Hence it islikely that the overall effect of px on Qx/Qy is positive. We assume so––which amounts saying that the own price-output response is positive.
In the demand side, homotheticity implies, as usual, that the ratio ofconsumption of good x to good y is negatively related to px. Thus autarky
equilibrium is unique.
For the HO theorem of trade pattern to hold, it is now sufficient that, at
any given px, Qx/Qy decreases as K /H increases. This indeed holds. Givenpx, ω is given. From the land market clearing condition, an increase in K /H
increases ρ, which, in turn, decreases L. We have K /L = (K /H )・(H /L).
Hence an increase in K /H coupled with a decrease in L implies an increase in K /L. By the Rybczinski effect, Qx/Qy decreases.
We assume once again that, although KN/HN > KS/HS, the difference is
not large enough and FPE holds. The effect of free trade on functional distribution is then captured entirely by The Theorem: ω decreases in the
North and increases in the South.
We first determine the impact on class sizes, in the light of (15), (16) as
well as the signs of dρ /dω and d (ωρ )/dω , which are already discussed.
Differentiating we have

(20)

dh1
dh2 T d ( ρω )
dρ ⎞
⎛
= ⋅
> 0.
= −T ⎜1 − ρ − ω⎟ < 0;
⎝
2 dω
dω
dω ⎠
dω

In the North for example, ω decreases; hence h1 increases and h2 decreases, implying respectively that upper class and lower class sizes increase. Thus the middle class shrinks! The opposite happens in the South.
Proposition 2. Free international trade between North and South leads toan increase (a decrease) in the sizes of upper and lower classes and a53

Trade and Personal Distribution of Wealth and Income

shrinkage (an expansion) of the middle class in the North (South).
The intuition behind the last proposition is as follows. In the North forexample, as ω decreases, the lowermost upper class dynasties decide notto work because of the substitution effect in the labor-leisure decision. This
expands the upper class. By the income effect on demand for bequest(land), the lowermost middle class dynasties cannot afford to hold land.
Hence they ‘move’ to the lower class and lower class expands also. As aresult, the number of dynasties in the middle class falls. Our analysis indicates that the much talked about middle class squeeze in the North may bepartly due to freer trade among North and South countries.
The implication for overall inequality is that it increases in the Northand decreases in the South. The proof of it, somewhat complicated in thismore general model, is relegated to Appendix, Part 2. We have
Proposition 3. Proposition 1 continues to hold in the three-class model.
3.2. Welfare
Suppose that initially the two economies are along their respective steadystate in autarky, and there is a policy change in both countries to free trade.
How are individual welfare levels and aggregate welfare affected? Whether
it is individual or aggregate welfare, as long as there is some transitional
dynamics, welfare losses or gains occur during the transition period and at
the steady state. However, it is generally difficult to characterize the former since the speed of adjustment and its change to the regime change
have to be accounted for. Furthermore, because the agents in the economy
have finite lives, there is no natural discount factor to choose. Therefore,
we shy away from analyzing welfare changes outside the steady state andlimit ourselves to comparing long-run welfare levels: one steady state (autarky) vis-a-vis another (free-trade).
Individual WelfareLand holding by the upper class, equal to (a−h)/(1−ρ ), is an increasing
function of ρ , which increases in the North and falls in the South. Thus,
land held by an upper class dynasty increases (decreases) in the North(South). The land rent also moves in the same way. Hence the income of
the upper class, consisting of rental income only, moves in unison also.
From the utility function, it is clear that the upper class benefits (loses)in the North (South). By similar logic, the lower class loses (benefits) in
the South (North). Note that because of the magnification effect, changes
in commodity prices are dominated by factor price changes.
Labor supply and land holding are both continuous in h, and this conti-

54

Satya Das

nuity implies the following proposition:
Proposition 4. There exists critical dynasties in the North and South (sayhN and hS respectively) belonging to the middle class (at the autarky equilibrium) such that dynasties lower (higher) than hN benefit (lose) as the
economies move from autarky to free trade, and those lower (higher) thanhS lose (gain).
Aggregate Welfare
In the presence of heterogenous preferences, the problems of interpersonal comparison of utility naturally arise. But they are no more severe
than when preferences are the same, endowments are different and there is
risk-aversion: at the margin the utility value of one dollar for one person
may differ from that for another. The usual practice, in the presence of risk
-aversion, is to use a Benthamite utilitarian index––the sum of utilities(which is as good as any other indicator).10 We assume the same here; heterogeneous preferences, in principle, do not exacerbate the problem of interpersonal utility comparison. On the other hand, in the presence of inequality, the utilitarian index captures something which may be considered‘desirable’, by putting higher weight on welfare as we go down from richto the poor (the marginal weights being proportional to the risk-premia).
This implies that, ceteris paribus, more inequality means less welfare. In
other words, inequality is viewed not only through its possible impact on
efficiency (although in the model economy at hand there is none) but also
as a separate entity which adversely affects aggregate welfare.
Obviously then, the effect of free trade on aggregate welfare is governedby aggregate changes as well as by redistribution. In the present context
there are two aggregate effects: the standard (production and consumption)
gains from trade by both countries as well as the change in the total labor
supply which is endogenous. The latter arises since only steady states orlong-run effects are taken into consideration. This effect is however ambiguous because of the ambiguous effect of a change in ω on L as discussed earlier. The redistribution effect of trade on welfare follows readily
from Proposition 3:
Proposition 5. Given that social welfare function is utilitarian, the redistribution effect of trade on welfare is negative for the North and positive
for the South.

10. See for example Atkinson and Stiglitz (1980, ch. 13) and Strawczynski(1998)).

55

Trade and Personal Distribution of Wealth and Income

Put differently, redistributive effects of trade are a source of welfare loss
(gain) for the North (South). In spirit, this goes against the popular belief
in some ‘Southern’ countries that free trade with the North may not be‘profitable’ proposition for them. Our model, on the other hand, argues
that free trade moves the distribution in the ‘right’ way in the South. It isin the North where it moves the ‘wrong way’ and free trade may not be
welfare improving because of it. A related implication is that to ensure a
positive gain from trade for the North, free trade may have to be coupledwith redistributive policies.
To save space however, the formal welfare analysis is relegated to Appendix, Part 3.
4. Concluding Remarks
This paper has examined the effect of international trade on distributionof wealth and income in an Heckscher-Ohlin world economy. The muchcelebrated Stolper-Samuelson Theorem is taken as the base upon whichmodels of wealth and income distribution are constructed. In terms ofmodelling, we have walked on a thin line balancing between the richnessof the 2 × 2 × 2 trade model and general complexities in allowing for acontinuous distribution of wealth and income on one hand and tractabilityon the other. Preference heterogeneity in a dynastic setting forms the basisof difference in wealth and income. In the process, we also develop a precise definition of the so-called lower class, middle class and upper classwhich invariably features in a discussion on wealth and income distribution.
By ‘the effect of international trade’, it is meant, as usual, a movementfrom autarky to free trade. Our central result is that free trade in goods between North and South increases inequity in the North and decreases thatin the South. More specifically, the middle class shrinks and the other twoclasses expand in the North, and, the opposite holds in the South. Moreover, the redistribution effect of free trade on aggregate welfare is negative
for the North and positive for the South.
There are some obvious routes that related future research can take. One
is the allowance of reproducible capital and eventually endogenous growth.
There are closed economy models of addressing the former issue (such as
Aghion and Bolton (1977) and Piketty (1997)) and the latter (such as Alesina and Rodrik (1994), which assumes exogenous distribution, and Galor
and Zeira (1993)). As mentioned earlier, an open economy model withland and reproducible capital (but with no endogenous growth or acrossthe-household distributional aspects) has been developed by Eaton (1988).
As mentioned before, Fischer and Serra (1996) have developed an endogenous growth model with human capital, trade and inequality; but forces
implying positive inequality in the long run are not considered.
Another obvious line of investigation should be to examine various

56

Satya Das

political-economy aspects of trade and trade related policies when wealthand income distributions are endogenous. Mayer’s (1984) analysis will be
the natural point of reference.
There are two standard paradigms of trade: trade among dissimilar countries, such as the North-South trade examined in this paper, and trade
among similar countries (the so-called North-North trade). That latter has
been analyzed in a companion paper (Das (2000)), which incorporates
capital accumulation (but not endogenous growth). The main finding thereis that the degree of relative risk-aversion is a critical parameter that determines whether or not North-North trade implies more wealth and income
inequality among Northern countries.
Our analysis abstracts from the implications of international borrowing
and lending. It will be of interest to contrast the effects of free international movement of assets with those of free trade in goods.
Other sources of inequity than preference heterogeneity (e.g. idiosyncratic shocks to individual productivities or risky returns to land) should
also be explored in the context of international trade.
It is hoped that future research will be directed toward some of these issues raised.
Appendix
Part 1
It is shown here that in our basic model the effect of trade on wealthand income inequality, summarized in Proposition 1, continues to hold if
inequality is measured by the Gini coefficient.
In this model the Gini coefficients with respect to land holding and income are given by
gK = 1 −b⎡ b Kz⎤b⎡ b Iz0h⎤∫ ⎢⎣∫ K f ( z)dz⎥⎦ f (h)dh; g = 1 − ∫ ⎢⎣∫ I f ( z)dz⎥⎦ f (h)dh .
0hINote that the inner integral runs from h to b rather than vice versa because
wealth is less with higher h. We haveKz ωρ + a − z=;
K(1 − ρ )KIz
ω +a−z.
=I
H (ω + a − h )

Thus
⎡
1
d (ωρ )dρ ⎤⎛K ⎞+ (ω + a − z ) ⎥.
d⎜ z ⎟ =(1 − ρ )⎢2⎝ K ⎠ (1 − ρ ) K ⎣
dp x
dz ⎦

57

Trade and Personal Distribution of Wealth and Income

From (10) it follows that(1−ρ )d(ωρ ) = −(ωρ + a−h)dρ .

(A1)
Substituting thisdρ / dp x⎛K ⎞d⎜ z ⎟ = −(z − h ) .
⎝K ⎠(1 − ρ ) 2 K

Define F (h) ≡b(h∫ f ( z)dz (the cumulative density function) and0)

φ (h) ≡ ∫ z − h f ( z)dz. Thenhdg Kdρ / dp x=
dp x (1 − ρ ) 2 K

=

b

⎡ b

dρ / dp x⎤b∫ ⎢⎣∫ ( z − h ) f ( z)dz⎥⎦ f (h)dh = (1 − ρ) K ∫ φ (h) f (h)dh
0

2

h

0

b
dρ / dp x ⎡φ(h) F (h)|b0 + (h − h ) f (h) F (h)dh⎤, integrating by parts.
20⎦⎥(1 − ρ ) K ⎣⎢∫The first term in the square bracket is zero as φ (b) = F (0) = 0. The second term is simply Cov[h, F (h)], which is positive since F ′(h) = f (h) > 0.
Together with dρ /dpx < 0 (proved in the text), it follows that dgK/dpx < 0.
In the South, px increases and thus gK falls. Opposite holds for the North.
Turning to income inequality, we haved ( I z / I ) dω / dp x
z−h ,
=
H
dp x

(

)

which has the same sign as of d (Kz/K )/dpx for any z, since dω /dpx > 0. It
follows that dgI/dpx < 0 also. So, income inequality moves the same way
as does wealth inequality.

Part 2The effects of trade on wealth and income inequality in the 3-class model
are proved here. In general, let z(h, θ ) be random, where h is a random

58

Satya Dasvariable with density f (h) and support (b1, b2), and θ is a parameter. The
coefficient of variation is given by⎛ b2 ⎡ z(h,θ ) ⎤ 2⎞
vz = ⎜ ⎢− 1⎥ f (h)dh⎟⎦⎝ b1 ⎣ z (θ )
⎠

1/2

∫

,

Thus
b2 ⎡ z(⋅)⎡ d [ z(⋅) / z (⋅)] z(⋅) ⎤dvz2⎤ d [ z(⋅) / z (⋅)]
=2 ⎢f (h)dh = 2Cov ⎢
,
− 1⎥
⎥.
b1
dθ
z
d
θ
dθ
z (⋅) ⎦
(
)
⋅
⎣
⎦
⎣

∫

In our context, the change in wealth inequality due to a change in px isthen given by[]⎡ d Kh / K K ⎤dv K2, h ⎥.
= 2Cov ⎢dp x
K ⎥⎢⎣ dp x⎦But Kh is a decreasing function in h. Thus the covariance and hence
dv K <d 2 ( Kh / K ) <0
as0.
dp x >
dp x dh >This is equivalent to
dv K <
d 2 Kh <0
as0.
dp x >
dp x dh >Similarly for income inequality,
dv I <d 2 (Ih / I ) <0
as0.
dp x >
dp x dh >We next derive the signs of these cross partials.
Wealth Inequality
From Table 1, in the range 0!h !h !
1

59

Trade and Personal Distribution of Wealth and Income

d 2 KhdKh
a − h dρ
dρ
1
=
⇒
=−
> 0.
2
2
dp x dhdp x (1 − ρ ) dp x
(1 − ρ ) dp x
In the range h1"h "h "
2[]

dKh T (2 − ρ )d (ωρ ) / dp x + ωρT + 2(a − h)dρ / dp x
d 2 Kh
dρ
2
=
⇒
=−
> 0.
2
dp x
dp x dh(2 − ρ )(2 − ρ ) 2 dp x

Thus, in the range in which there is positive holding of land, the cross partial is positive. Therefore, dvK/dpx < 0. With px rising in the South, wealthinequality falls and opposite holds for the North.
Income Inequality
Turning to income inequality, the critical expression is the cross partial:
d 2 ( I h / I ) d 2 (ih / i )=,dp x dhdp x dhwhere ih!I #r and i #I #r !We haved (ih / i )dp xhd (ih / i ) 1 ⎛ d 2 ih
i dih / dp x − ih di / dp x
di di ⎞⇒
= 2 ⎜i− h⎟.
2
dp x dhii ⎝ dp x dh dh dp x ⎠2=

We have⎧− 1 −1 ρ < 0 for 0 ≤ h ≤ h1
dih ⎪⎪ 1= ⎨−< 0 for h1 ≤ h ≤ h2 ;dh ⎪ 2 − ρfor h2 ≤ h ≤ b.
⎩0⎧− (1 −1ρ )⎪d ih⎪= ⎨− (2 −1ρ )dpx dh ⎪
⎪⎩0
2

2

2

dρ
dpx

> 0 for 0 ≤ h ≤ h1dρdpx

> 0 for h1 ≤ h ≤ h2
for h2 ≤ h ≤ b.

Thus
d 2ih
≥ 0.
dpx dh# $0"or d !I #r "#dp $0"which

It is sufficient to show that di dp x
would implyx60

Satya Dasd 2 (ih / i )> 0.
dpx dhBy definition, I = wL + rK ⇒ I /r = ω L + K . Hence, d (I /r)/dpx =Ldω /dpx + ω dL/dpx. Using the expression for dL from section 3,
h2
d ( I / r) ⎡1T=⎢
(1 − ρ )T ω + h − a f (h)dh +
h1
dp x
(
2
−
ρ
)
ω
2
⎣

∫ {

−

dρ / dp x(2 − ρ ) 2dρ / dp x(2 − ρ ) 2dω / dp x⎤ dωb∫ f (h)dh⎥⎦ dph2x∫ {ωT + h − a} f (h)dh − (2 − ρ )ω ∫ (h − a) f (h)dhh2

h1⎡ (1 − ρ )T
=⎢
⎣ 2−ρ
−

}

h2

h1

T

h2

⎤ dω

b

∫ f (h)dh + 2 ∫ f (h)dh⎥⎦ dp
h1

h2

x

∫ (ωT + h − a ) f (h)dh > 0.
h2

h1Part 3It deals with the aggregate welfare effects of trade in the 3-class model.
Given (11), the utilitarian social welfare index is given by(A2) U = H [ ∆ − γ 1n( p x )] +∫ [1n( I ) + 1n( K + h − a) + 1n(T − L )] f (h)dh.
b

0

h

h

h

For notational simplicity and without loss of generality, let H be normalized to one from now on. Technically, a change in the aggregate welfare
due to international trade is a comparative statics of U with respect to px(keeping in mind that px decreases for the North and increases for theSouth). We have(A3)b ⎡ dI / dp
d ( Kh + h − a ) / dp x d (T − Lh ) / dp x ⎤
dU
γ
x
=−
+ ⎢ h
+
+
⎥ f (h)dh.
0
dp x
px
I
Kh + h − a
T − Lhh⎣⎦∫We re-express the individual terms and come up with a convenient expression of dU /dpx, which we can economically interpret. Consider first61

Trade and Personal Distribution of Wealth and Income∫ [(dI / dp ) / I ] f (h)dh. It can be restated asbthe term

h

0

x

h

b⎛ 1
dI h / dp x
1 b dI h
1 ⎞ dIf (h)dh =f (h)dh + ⎜ − ⎟ h f (h)dh
0
0 ⎝ I
Ih
I 0 dp x
I ⎠ dp x
h

∫

b

∫

(A4)

∫

=

⎛ 1 dI h ⎞1 dI h 1 b−
Ih − I ⎜⎟ f (h)dh0
I dp x I⎝ I h dp x ⎠=⎛dL ⎞ 1
1 dI h ⎞1⎛⎜ Qx + w⎟ − Cov⎜ I h ,⎟,I⎝
dp x ⎠ I
I h dp x ⎠
⎝

∫(

)

where, recall that I and I are respectively the total and mean income. The
term dI /dpx has the envelop term Qx and the effect of px on the aggregate
labor supply. In the similar manner, one obtains

∫

b

0

(A5)

d ( Kh + h − a ) / dp x
f (h)dh =Kh + h − a−d (T − Lh ) / dp x
f (h)dh =0
T − Lh∫(A6)⎛d ( Kh + h − a ) ⎞1
1Cov⎜ K + h − a ,
⎟,
+
−
K
h
a
dp x
K +h −a
⎝
⎠

b

−

⎛
1 dL
1
1 d (T − Lh ) ⎞Cov⎜ T − Lh ,−⎟,T − L dp x T − L
T − Lhdp x⎝⎠

where the bar on the top indicates the respective mean. In particular, in deb

riving (A5), we have used the fact that

∫ K f (h)dh = K , a constant. Sub0hstituting (A4)-(A6) into (A3) and noting that Cx = γ I /Px, we havedU ⎛ Qx − Cx ⎞ ⎛ w
1 ⎞ dL=⎜⎟⎟ +⎜ −⎠ ⎝ I T − L ⎠ dp x
dp x ⎝
I⎛ 1 dI h ⎞⎛d ( Kh + h − a ) ⎞1
1⎪⎧ 1
Cov⎜ Kh + h − a ,(A7) + ⎨− Cov⎜ I h ,⎟−⎟I dp x ⎠ K + h − a
Kh + h − a
dp x
⎝
⎝
⎠
⎪⎩ I
⎛
1
1 d (T − Lh ) ⎞ ⎫⎪−Cov⎜ T − Lh ,
⎟ ⎬.
T −L
T − Lh
dp x
⎠ ⎪⎭
⎝

62

Satya Das

The term inside the first pair of brackets is the standard efficiency effectof terms of trade change due to international trade: it is positive for the
North and negative for the South. Since px decreases (increases) from theperspective of North (South), both countries benefit.
The term inside the second pair of brackets is the aggregate labor supply effect on welfare. This is ambiguous in sign. Using the expressions for
Ih and Lh from Table 1 and aggregating, it is found that the coefficient of
dL/dpx is negative. However, as discussed earlier, dL/dpx itself is ambiguous in sign.
Finally, the terms inside the last pair of curly brackets constitute the redistribution effect on welfare.11 The signs of all covariance terms are negative and it is indeed possible to check this for all three classes. From Table
1 observe that Ih, Kh + h−a and T −Lh are nonincreasing in h. Hence it remains to show that the terms (1/Ih)(dIh/dpx), [1/(Kh+h−a)][d (Kh+h−a/dpx)]
and [1/T −Lh][d (T −Lh)/dpx] are nondecreasing in h.
Turning to Table 1, in the range 0 h h1

# # "

A≡

∂A
1 dI h 1 − ρ d [r / (1 − ρ )]
=
⋅
⇒
= 0.
I h dp xr
dp x∂hAlso, Kh + h−a = (a−h)ρ /(1−ρ ). HenceB≡d ( Kh + h − a ) 1 − ρ d [ ρ / (1 − ρ )]
∂B
1
=
⋅
⇒
= 0.
ρ
∂h
Kh + h − a
dp x
dp x

As Lh = 0 in this range of h, T −Lh = T , invariant with respect to h; hence∂C / ∂h = 0, where

!! "
!
C "
T!
In the range h #h #h "
1

1

A=

d T Lh
dp x
Lh

2

∂A
T
dω
T
dω
2 − ρ [r / ( 2 − ρ ) ]
⋅
+
⇒
=
⋅
> 0.
∂h (T ω + a − h) 2 dp xr
dp x
T ω + a − h dp2

11. In the representative agent framework, all these terms are zero.

63

Trade and Personal Distribution of Wealth and Income

In this range,
Kh + h − a =ρ( T ω + a − h) ,2−ρT − Lh =Thus
B=Tω + a − h.
(2 − ρ )ω

2 − ρ d [ ρ / (2 − ρ )]
T
dω
⋅
+
,
ρ
dp x
T ω + a − h dp xC=−d [(2 − ρ )ω ]
1
T
dω
⋅
+
⋅
.
(2 − ρ )ω
dp x
T ω + a − h dp x

∂B / ∂h and ∂C / ∂h are equal to ∂A / ∂hIt follows immediately that bothand hence positive.
Finally, in the range h2 h b these partials are zero. This completes
the proof that all covariance terms in (A7) are negative, implying that thewhole expression inside the pair of curly brackets is positive. This meansthat for the North and South respectively, it is a negative and a positive redistributive effect of free trade.

! !!

References
Aghion, P. and P. Bolton. 1997. A Theory of Trickle-Down Growth and Development. Review of Economic Studies 64: 151-172.
Alesina, A. and D. Rodrik. 1994. Distributive Politics and Economic Growth.
Quarterly Journal of Economics 109: 465-490.
Andreoni, J. 1989. Giving with Impure Altruism: Applications to Charity and Ricardian Equivalence. Journal of Political Economy 97: 1447-1458.
Atkinson, A. B. and J. E. Stiglitz. 1980. Lecture Notes on Public Economics. New
York: McGraw-Hill.
Banerjee, A. and A. Newman. 1991. Risk-Bearing and the Theory of Income Distribution. Review of Economic Studies 58: 211-255.
Burtless, G. 1995. International Trade and the Rise in Earnings Inequality. Journalof Economic Literature 33: 800-816.
Das, S. P. 1993. New Perspectives on Business Cycles: An Analysis of Inequality
and Heterogeneity. Aldershot: Edward Elgar.
--------- . 2000. Trade Among Similar Countries and Personal Distribution of Income

64Satya Dasand Wealth. Economica 67: 265-281.
Davis, S. 1992. Cross-Country Patterns of Change in Relative Wages. NBER Macroeconomics Manual 7: 239-292.
Eaton, J. 1988. Foreign Owned Land. American Economic Review 78: 76-88.
Eswaran, M. and A. Kotwal. 1989. Credit and Agrarian Class Structure. In The
Economic Theory of Agrarian Institutions, ed. P. Bardhan. Oxford: Oxford University Press: 166-184.
Epstein, L. G. and J. A. Hynes. 1983. The Rate of Time Preference and Dynamic
Economic Analysis. Journal of Political Economy 91: 611-635.
Fischer, R. D. and P. J. Serra 1996. Income Convergence with and between Countries. International Economic Review 37: 531-551.
Galor, O. and J. Zeira. 1993. Income Distribution and Macroeconomics. Review of
Economic Studies 60: 35-52.
Goldsmith, R. W. 1985. Comparative National Balance Sheets. Chicago: University of Chicago Press.
Jones, R. W. 1997. Trade, Technology, and Income Distribution. mimeo, University of Rochester.
Leamer, E. 1996. In Search of Stolper-Samuelson Effects on U.S. Wages. NBER
Working Paper no. 5427.
Lucas, R. E. and N. Stokey. 1984. Optimal Growth with Many Consumers. Journalof Economic Theory 32: 139-171.
Mayer, W. 1984. Endogenous Tariff Formation. American Economic Review 74:
970-985.
Piketty, T. 1997. The Dynamics of the Wealth Distribution and the Interest Ratewith Credit Rationing. Review of Economic Studies: 173-189.
Roemer, J. 1982. A General Theory of Exploitation and Class. Cambridge, Massachusetts: Harvard University Press.
Stiglitz, J. E. 1969. Distribution of Income and Wealth Among Individuals. Econometrica 37: 382-397.
Stolper, W. and P. A. Samuelson. 1941. Protection and Real Wages. Review of
Economic Studies 9: 58-73.
Strawczynski, M. 1998. Social Insurance and the Optimum Piecewise Linear Tax.
Journal of Public Economics 69: 371-388.
Uzawa, H. 1968. Time Preference, the Consumption Function, and Optimum Asset
Holdings. In Value, Capital and Growth: Papers in Honor of Sir John Hicks, ed.
J. N. Wolfe. Chicago: Aldine: 485-504.

4

Unilateralism
in a Multilateral World*
Wilfred EthierInternational trade policy has a split personality. As the nations of theworld have gradually and collectively adopted historically low levels ofprotection for more than half a century, they have gradually and individually initiated protectionist actions at an increasing pace. What’s going on
here?
1. Introduction
Contemporary international trade policy is built upon two pillars: multilateralism (the rounds of multilateral trade negotiations sponsored by theGeneral Agreement on Tariffs and Trade (GATT) and the multilateralWorld Trade Organization (WTO)); unilateralism (rules––explicit and implicit––for national governments to respond to political pressures for protection).1 This paper concerns the relationship between these two components and the nature of the system they jointly determine. I shall argue that* I gratefully acknowledge useful comments from Arye Hillman, Henrik Horn,and Rodney Ludema, and from helpful discussions during presentations of this research at EPRU in Copenhagen, the Institute of World Economics in Kiel, the
ISER at Osaka University; the RIEB at Kobe University; Doshisha, Keio, Konstanz,Southern Methodist, Texas A&M, Tohoku, and Tokyo Universities; the Universities
of Helsinki, Maryland, New Orleans, Paris I, Texas, and Wisconsin; the 1999
North American Summer Meetings of the Econometric Society.
1. A third pillar––regionalism––has been resurrected during the past decade, but
I shall ignore this below because I have discussed it at length elsewhere (Ethier,
1998a, b). See Ethier (2004) for a discussion of why multilateralism is what it is,
Ethier (2001) for an overview of multilateralism and unilateralism, and Ethier(1998c) for an overview of the relation between unilateralism, multilateralism, andregionalism.
65

66

Wilfred Ethierneither can be properly understood in isolation, and that familiar tools of
trade policy appear in a dramatically different light when the two aretreated together.
My analysis will be positive, but conclusions will have normative applications. In particular, I shall address the following basic questions: How do
the two components, and their interactions, determine the pace of trade liberalization? Why does unilateralism take the very special form that it does?
In what follows, I first describe the stylized facts of multilateralism andunilateralism. I next present a multi-country model with high initial tariffbarriers. These initial barriers would not have been chosen by the policy
makers in the model subsequently presented. Rather, the barriers are assumed to be a legacy of an earlier, different, regime (just as, in the decades since World War II, the world has had to deal with the protection resulting from the radically different inter-war years), but the existence of
these barriers produces special interests that resist their removal. Governments negotiate successive tariff reductions in a sequence of periods––acaricature of the GATT negotiating rounds of the last 5-6 decades.
My model is very special but not arbitrary: I attempt to find the simplest
structure consistent with the two concerns that have dominated tariff negotiations for centuries:
Dealing with special interests that desire protection
Negotiators’ concerns that the ex post environment may turn out significantly different from what they expected when they made the agreements.
This is achieved by the assumed sequence of moves within each period.
First, forward-looking labor allocates itself between the export andimport-competing sectors, remaining for the rest of the period specific tothe sector it has chosen. Next, governments negotiate tariff reductions. After this, a technology shock occurs. Then trade takes place, with the newtechnology and constrained by the negotiated tariffs. Because negotiations
occur when labor is sector specific, there are special interests; because thenegotiations occur before the technology draw, the governments do notthen know to what environment the results of those negotiations will apply.
I describe a process of multilateral negotiation resulting in steady liberalization at a moderate rate. I next investigate the possible role of a systemof rules allowing countries, whose import-competing sectors face competition from exports from countries with a favorable technology draw, to impose temporary protection. If such protection also benefits those countries
whose exporters must compete with the countries with a favorable technology draw, while being acceptable to the latter (the ‘insurance triangle’), it
can accelerate the rate of liberalization and increase the allocation of resources to comparative-advantage sectors. But a time-consistency problem
compounded by an externality ensures that negotiators would never themselves adopt such rules for their respective countries: The ‘split personal-

!
"

67

Unilateralism in a Multilateral Worldity’ of trade policy is essential. In short, features remarkably similar tocontemporary unilateralism turn out to be crucial, with subtle and essential
relationships to multilateralism, that cannot be understood in a two-country
context.
2. The Background
This section briefly describes the essential features of multilateralism
and of unilateralism motivating the subsequent model.
2.1. The Stylized Facts of Multilateralism
I mean the entire GATT-WTO structure, but shall distill it into six stylized facts.
1 Tariffs are the instruments of protection.
2 The countries of the world multilaterally negotiate tariff reductions.
3 The negotiated liberalization is gradual.
4 Negotiated agreements feature reciprocity: the mutual exchange of concessions.
5 Nondiscrimination characterizes trading relations: each country is a mostfavored nation (MFN) of every other country.2
6 Punishments for alleged violations of past agreements have consistently
been commensurate with the violation, that is, tit-for-tat.
Reducing multilateralism to these stylized facts is deficient in one way.
Multilateral liberalization has increasingly shifted from the further reduction of already reduced tariffs to broadening liberalization into additional
areas, notably agriculture, services, and intellectual property. Attention has
necessarily shifted to government policies other than tariffs. Considerationof these would not alter the following argument, so I abstract from themand pretend that continued multilateral liberalization is only the continued
reduction of tariffs.
In an earlier paper (Ethier 2004), I used a model like that which follows
to show how, with initial high protection consisting only of tariffs, most of
the other stylised facts––multilateral negotiations, gradual liberalization,
reciprocity, and MFN––will develop endogenously, if government behavior
is dictated by a political support function consistent with how governments
claim to behave, and if reasonable substitutes for each country’s exports
are produced elsewhere. Therefore, in this paper, I shall simply take thestylised facts of multilateralism as given. Other authors have also discussed
why multilateralism has the properties it has; see Staiger (1995) for a dis2. One country extends MFN status to another if the former agrees that goods
from the latter will never face a duty higher than the duty applied to similar goods
from any other country. In practice, this raises the issue of defining ‘similar goods’,
but I shall abstract from such problems.

68

Wilfred Ethiercussion of earlier contributions. The recent papers that come closest to addressing these same properties are Bagwell and Staiger (1999a, b).
2.2. The Stylized Facts of Unilateralism
Unilateralism consists of rules for intervention rather than tariff rates,and both the nature of the rules and the way they are used have beenchanging over time. The more important rules, and the changing use, aredescribed in Appendix 1. Here I identify five stylised facts that characterize––more or less––a common denominator for the rules of unilateralism.3
2.2.1. Exporters are Compensated, at Least in Part
Rents generated by voluntary export restraints (VERs) accrue to the exporters, who administer the quotas. Usually, the exporting firms themselves
capture the rents. Safeguards explicitly require that exporters be compensated, but the compensation is to the exporting country rather than the exporting firms.
Antidumping and countervailing duties are ostensibly tariffs, but a closer
look at how these instruments are actually used reveals that they also confer significant compensation.
Roughly one third of US antidumping petitions result in duties, about
one third are rejected, and the others are withdrawn. Of these, many arewithdrawn after a settlement between domestic and foreign firms. Typically, the foreign firms collectively undertake to raise prices or restrict exports. Prusa (1992) reports that withdrawn petitions restrict trade almost as
much, on average, as petitions resulting in duties, implying that negotiatedsettlements are, on average, more restrictive than antidumping duties.
If, instead, a petition does produce an antidumping duty, the result is
usually higher export prices, not tariff revenue. Tariffs collected are often
rebated when authorities determine, ex post, that the goods were not, infact, dumped.4 The exporter, realising that the price in the importing country is going to rise by the dumping margin no matter what he or she does,
raises the export price by that amount. The purpose of an antidumping law
is not to impose temporarily a conventional tariff; it is to force exporters
to raise prices. Just as with VERs, the exporters usually get the rents.5
I do not claim that unilateralism benefits foreign firms, or that it leaves
3. See also Hillman (1982, 1990).
4. But, in the USA at least, the importer will incur additional liability if it is determined that the goods were, in fact, dumped by more than the duty. This implies
that it is riskier to buy goods from a country against which there is an outstanding
dumping determination than from some other source at the same price.
5. Usually, but not always. Sometimes the duty is large enough to reduce imports drastically, or to eliminate them altogether, so that the higher price is little
consolation to exporters. Sometimes, (particularly in Europe) administration hinders
the ability of the exporter to capture the price rise. And countries not in the WTO
may apply the label ‘antidumping law’ to any sort of protectionist measure.

69

Unilateralism in a Multilateral World

them more or less indifferent. This is possible. But the first stylised fact of
unilateralism is just that countries denied market access receive significant––if only partial ––compensation.
It is curious that governments should want, in effect, to hand over tariff
revenue to foreigners. But this is exactly what they do, routinely, in the
conduct of unilateralism. Why? I shall argue that unilateralism is what it isbecause of successful multilateralism.
2.2.2. The Instruments Provide Temporary (at least in original intent) Protection
Temporary measures are not necessarily short-lived: they can be renewed.
Renewals allow for adjustments and so add flexibility (relative to measuresthat require congressional action and/or multilateral negotiation).
2.2.3. The Restrictions are Discriminatory
Some industries have displayed a comprehensive web of voluntary export
restraints (e.g. textiles and apparel), but individual VERs are bilateral andthus inherently discriminatory.
Antidumping and countervailing duty laws are WTO-consistent, but discriminatory, since they apply to the products of specific countries. Safeguards alone are nondiscriminatory. So it is significant that their use has
greatly declined relative to that of the other three instruments and that, inthe future, it will sometimes be permissible to employ them in a discriminatory manner.
2.2.4. Tariff -Quota Equivalence is HighThe proposition of tariff-quota equivalence asserts that any equilibriumthat can be supported by a tariff policy can also be supported by an appropriate quota policy, and vice versa. However, tariffs and quotas are seldom
equivalent in fact. If an equilibrium is disturbed, the response depends onwhether a tariff or a quota is in place, so if a policy must be implemented
before all circumstances are known, it matters what tool is used. Unilateralism is one theater where tariff-quota equivalence is really relevant: each
instrument seeks to attain a particular outcome with a restriction that canbe readjusted frequently. So it matters little whether the restriction is quantitative.

5. Usually, but not always. Sometimes the duty is large enough to reduce imports drastically, or to eliminate them altogether, so that the higher price is little
consolation to exporters. Sometimes, (particularly in Europe) administration hinders
the ability of the exporter to capture the price rise. And countries not in the WTO
may apply the label ‘antidumping law’ to any sort of protectionist measure.

70

Wilfred Ethier

2.2.5. The Restrictions are Designed by Officials Distinct from Those who
Negotiate International Trade Agreements
This applies to some degree to most industrial countries, but most dramatically to the USA. For over 60 years, the Congress has repeatedly
ceded to the executive considerable authority to set actual tariff levels via
reciprocal trade negotiations and, throughout this period, the executive has
consistently been less protectionist than Congress. Yet, at the same time,
Congress has repeatedly revised the laws governing administered protection to limit executive discretion and to make protection a more likely response to petitions for relief.

3. The ModelI now describe a simple formal model of successive multilateralism. I
will then inquire into the possibility of a role for unilateralism. I construct
the model to reflect those features of the world that, in fact, have been of
the most concern to policy makers. Since this is necessarily subjective to atleast some degree, I shall, from time to time, pause to defend a modelingchoice.
3.1. The ConstituentsAssume two goods, A and B , one factor of production, labor (L), and2N identical (almost) countries. Normalize L = 1 for each country. Everyone spends equally on the two goods. N countries have a comparative advantage in A and the other N in B . Labour productivity is a in thecomparative-advantage good and a in the other good, with > 1. I will
examine symmetric equilibria in which each country makes the same allocation, , to the comparative advantage sector.
Assume a succession of periods. Labor is mobile between sectors acrossperiods, but immobile within each period. Initially, each country starts witha common, historically given, tariff t on all imports and an initial state, a,of technology. The state of the world each period is indicated by (t, a),since t and a will remain common to all countries across the symmetricequilibria I consider. At the start of each period, countries differ from eachother only in regard to which sector possesses a comparative advantage.
Technology is improving across periods. Since my topic is trade policy
rather than growth, I am content to assume that this occurs at an exogenously determined rate, that is, ∆ a / a = −1 > 0. Technical progress, regardless of where it originates, spills over––subject to a qualification introduced below––to all countries: It constitutes an international externality.

!

!

"

!

71

Unilateralism in a Multilateral World

3.2. Negotiators’ Objectives
Governments may negotiate tariff reductions. I want an objective function accurately reflecting how government negotiators behave; I build on
Corden’s (1997, pp.74-76) description of a conservative social welfare
function: governments avoid policies that would seriously harm any interest group. In particular, I assume that, in each period, each government’s
negotiators want to maximizeφ (τ ) = ∆rx (τ ) − [ − ∆rm (τ )]

1+γ

(1)

,

where τ denotes the rate of tariff reduction.

⎛ −t ⎞⎜⎟,⎝ 1+ t ⎠∆rx the negotiators’ perception of the increase in the real reward of the factor specific to exports, and ∆rm the negotiators’ perception of the increasein the real reward of the factor specific to imports.6
Appendix 2 shows that liberalization will cause ∆rx > 0 and ∆rm < 0,with a positive gain overall. So, liberalization will be desirable if either γ
or the degree of liberalization is modest enough. The parameter γ measures the negotiators’ averseness to allowing anyone to suffer a large loss:
the Corden sensitivity.
3.3. Sequence of Moves within Each Period
At the start of each period, the common tariff and technology, (t, a), is
inherited from the close of the previous period. The following sequencethen takes place.
• First, L allocates itself among A and B . The allocations become specificfor the rest of the period, so each worker decides which sector to enter
based on his/her rational forecast of the real rewards that will be offeredin the respective sectors during the current period.
• Second, the governments negotiate tariff reductions. These negotiations
will be multilateral and feature nondiscrimination. I assume that eachgovernment, like the owners of L, does not look beyond the current period, but is forward-looking within that period.
• Third, some countries succeed in anticipating the technological improvement that will be generally realized at the end of the period: n < N of
the exporters of one of the goods will now have the large technology
gain, ∆a/a = −1, for their exportables. The identities of the good andof the specific exporters of that good that will succeed in anticipating
the technological improvement is determined by a random draw (so, if!

6. The results that follow would not be qualitatively affected if the objectivefunction were over real incomes instead of over real rewards.

72

Wilfred Ethierπ ≡n/N , then π /2 = the probability of early technical progress for eachcountry). NB: The identity of the gainers (both which good and whichcountries) is determined after the negotiations.
• Fourth, tariff reductions are implemented and trade is realized. The latter
will be described subsequently. In each country, tariff revenue is distributed to the populace in lump-sum fashion.
• Finally, the period ends, ∆a is realized by all countries and both sectors
for the next period, and the negotiated t becomes the initial t for the
next period, when new governments will again determine policy.
I intend a period to correspond, in some rough fashion, to the time between the start of one GATT round and the start of the next. I have tried
to build the simplest model I can that captures the two features that havealways been paramount to those undertaking trade negotiations:
The existence of divergent special interests.
Concern that any agreement might have unforeseen and unfavorable future consequences.
This is achieved by my description of within-period timing, which will be
crucial to what follows. The assumption that factors are specific when negotiations take place produces the divergent interests.
The assumption that negotiations are conducted before the economic environment to which their results will apply is fully known serves to introduce the second paramount feature.7 This point has, in fact, always been(since long before the GATT) of acute concern to policy makers. Tradeagreements routinely included safeguards (then known as escape clauses)
enabling participants to readjust their concessions should events not turnout as they had hoped. When the USA first established safeguards as amatter of law, material injury had to be due to increased imports and thelatter had to be due to a prior trade concession. The GATT itself provided,in Article XXVIII, opportunities for the modification or withdrawal of concessions.
Introducing additional instruments could neutralize both features. Lumpsum transfers would deal with the first, and the ability to implement fullystate-contingent trade agreements would do it for the latter. The absence ofboth instruments from my model does no violence to its realism.

!
"

4. Multilateralism
Labor allocates itself across sectors on the basis of a rational forecast of
the rate of liberalization that governments will subsequently negotiate, and7. For example, participants in prior GATT rounds had not known that Japanese
automobile firms would become the most efficient producers in the late 1970s.

73

Unilateralism in a Multilateral World

when those negotiations take place the allocation of labor is given. I firstinvestigate what rate of liberalization will be negotiated for a given allocation , and then go backwards to investigate what labor, armed with anunderstanding of this relation between and liberalization, will actually do.

!

!

4.1. Multilateral Negotiations
What rate of tariff reduction will be negotiated? At the negotiations,
governments know the allocation of resources, but they do not know whichcountries will be the leaders, the followers (whose exporters compete withthe leaders), and the laggards (who import from the leaders) when the tariff reductions are implemented. I assume no external commitment mechanism: A government will actually implement the reduction it has agreed toonly if, ex post, that government believes its interests will be served bydoing so, taking into account credible threats of retaliation.
I assume the retaliation is tit-for-tat. That is, if Country 1 lowers its tariff 5% less than promised, its trading partners follow suit. Why tit-for-tat?
The sixth stylised fact of multilateralism (punishments for alleged violations of past agreements have consistently been commensurate with theviolation, that is, tit-for-tat) gives me little choice. When countries retaliate or threaten to retaliate against some alleged transgression by a trading
partner, they consistently emphasize that the threatened retaliation is commensurate with the transgression (i.e., tit-for-tat). The WTO and the GATT
before it have consistently operated on the premise that punishment shouldmatch violation. Countries have often squabbled over which tit matches
what tat, or whether there was a tat in the first place, but as far as I know
no country has ever challenged the principle. Given my goal of modellingcountries as they actually behave, this makes the tit-for-tat assumptioncompelling.8
Note also that tit-for-tat punishment fits neatly into the present model.
With the symmetric equilibria that I consider, such a threat will be welldefined.
Furthermore, the use of tit-for-tat in my model implies government behavior very much in the spirit of the Corden political support function I
use. To see this, note that such a threat can support any negotiated tariff
reduction which, ex post, every country wants to have generally adopted.
However, it can support no reduction in excess of what any country regards, ex post, as optimal. Thus the outcome of the multilateral negotiation
will be: the smallest of the various tariff reductions which, if generally
adopted, would maximize ex post the objective functions of the respective
8. Adding a lag between deviation and retaliation would complicate the following algebra without affecting the essentials of the argument.

74

Wilfred Ethier

negotiating governments. That is, no government negotiator will be taking
the risk that its import competing sector might have to take a bigger hit
than that negotiator would have been willing to allow.
4.2. Negotiated Multilateral Liberalization
Let Pi and Qi respectively denote international and domestic relative
prices of B in terms of A, when the technical advance occurs first in goodi, i = A, B . An asterisk distinguishes the country with a comparative advantage in B . Then, with t common to all countries,
Qi#P (1 "t )" Q1!#1 P"t !
i

i

i

!

We have, recalling that
denotes the labor allocated to the comparativeadvantage sector, (see Appendix 2 for details),
PA ( , t ) = π ( β − 1)α+ 1,
α + (1 + t )(1 − )if A is the leader, and Pi = PB = 1/PA if B is the leader. Then PA > 1 > PB.
The hypothesised spending pattern is consistent with the following indirect utility function:v = Q −1/2 I,(2)where I denotes income in terms of good A. Factors are paid the values of
their marginal products, so that their real rewards, using the utility function(2), are as follows, for a country with a comparative advantage in A:

βαa,
Q1A/ 2

(3)

rxL =

(4)

rmL = aQ1A/ 2 ,

Let

rxF =

αa
,
Q1A/ 2rmF = aQ1A/ 2 ,

rxG =

αa
QB1/ 2 ,rmG = aQB1/ 2 ,.
⎛ −t ⎞
τi = ⎜ i ⎟⎝ 1+ t ⎠denote the rate of tariff reduction optimal ex post for a country that ends
up in state i = L (leader), F (follower), or G (laggard). For simplicity, I
consider a continuous-time approximation to the negotiated rate of tariff

75

Unilateralism in a Multilateral World

reduction. Then, the ex post value of each country’s objective function reduces to1+γ⎡ dr i⎤dr i
φ (τ ) = − x (τ ) − ⎢ m (τ ) ⎥ ,
dt
⎣ dt
⎦
where i denotes the state the country finds itself in ex post. If γ = 0, φ
can be made arbitrarily large by making τ arbitrarily large: The government will want free trade at once. I will accordingly refer to the Corden
sensitivity γ, which reflects the government’s reluctance to let any sector
experience a large hit, as the willingness to protect. Now
drxL
βαa
rL
= − 1/ 2 (1 + t ) −3/2 = − x
,
dt
2 PA
2(1 + t )

and

drmL
a
rL
= − (1 + t ) −1/ 2 PA1/ 2 = − m ,dt
22(1 + t )etc. The first-order condition that τ maximize the objective function, given
the value of Pi, reduces to(τ i ) γ =⎛ dr i ⎞−⎜ x ⎟⎝ dt ⎠⎛ dr i ⎞(1 + γ )⎜ m ⎟⎝ dt ⎠,

1+γ(1 + t )γ

where i = L, F, or G. Substituting yields

L γ(τ ) =

−1−

βα
⎛ a⎞
⎜ ⎟
⎝ 2⎠

γ

γ

QA 2
,
1+ γ

α

−1−

γ

QA 2
(τ ) =,γ⎛ a ⎞ 1+ γ
⎜ ⎟
⎝ 2⎠
F γ

α

−1−

γ

QB 2
(τ ) =.
γ⎛ a ⎞ 1+ γ
⎜ ⎟
⎝ 2⎠
G γ

Since β > 1, τ L > τ F, and QA > QB implies that τ G > τ F. Intuitively, leaders prefer a relatively liberal regime because of their technological advantage. Laggards take a hit in their import-competing sector, but this is ameliorated by a more favorable terms of trade. Followers, competing with theadvantaged leaders in export markets, take the hit in their export sectors,
with no terms of trade improvement.
Proposition 1. The multilaterally negotiated rate of tariff reduction, τ M,
equals the rate most preferred, ex post, by those countries that turn out tobe the followers:

76

Wilfred Ethier
1

⎡
⎤γ
1 1
+
⎢
⎥
γ 2
⎡
⎤
1
1
α
M
⎥
.
τ =⎢
⎢ ⎛ a ⎞ γ 1 + γ ⎥ ⎢⎣ PA (1 + t ) ⎥⎦
⎢⎜ ⎟
⎥
⎣⎝ 2⎠
⎦

(5)

"

"!

"

Proposition 1 in turn implies ∂τ M ∂ γ < 0, ∂ τ M ∂ > 0, and ∂ τ M ∂ τ < 0.
Thus,
Proposition 2. A greater willingness to protect implies a smaller rate oftariff reduction, and the rate of tariff reduction accelerates over successive
rounds.
4.3. The Allocation of Resources
Consider next where labour, understanding the above negotiating process,will have chosen to locate. Let ri, i = x, m, denote the expected quasi-rentof labour specific to sector i, where x refers to the sector in which a country has a comparative advantage. Then
ri =

(6)

π L 1− π F 1 Gri +ri + ri ,222!

where riL riF and riG respectively denote the rent when the country is atechnological leader, has a comparative advantage in the leading good but
is not itself a leader (i.e. is a follower), and has a comparative advantage
in the laggard good.9
The ex post real quasi-rents (3) and (4) imply the expected returns to thequasi-specific factors, net of tariff revenue:rx ( PA , t ) =⎡ π ( β − 1) + 1⎤
αa+ PA1/ 2 ⎥,1/ 2 ⎢
1/ 2
2(1 + t ) ⎣
PA
⎦

!"

rm (PA t )a(12!t ) "
1 2

!1

"!

1 2

PA

"

" .

1 2
PA

Here t has the value that labour expects to pertain after the subsequent negotiations: t = t1 −τ M(1 + t1), where t1 denotes the tariff inherited from theprevious period. Assume that labor allocates itself between sectors accord9. For example, in the early 1980s, the Japanese automobile firms, having developed ‘lean’ production methods, were the leaders, the high-cost European andfledgling Korean firms the followers, and the import-competing US firms the laggards.

77

Unilateralism in a Multilateral Worlding to the relative expected quasi-rents. Note that rx(PA,0) > rm(PA, 0): If
free trade were expected ex ante, no labor would allocate itself to the import competing sector. If in fact rm = rx,(7)απ ( β − 1) + PA ( , t ) + 1= 1 + t.
PA ( , t ) + 1!

Let t o solve this equation for = 1. Then, when the forecast value of t falls
at least to t o，labour will allocate itself fully to the comparative advantage
sector. I assume that, at this point, ∆rm receives zero weight in the government’s objective function: Multilateral negotiations will deliver free trade.
Next, consider the responsiveness of the quasi-rents to the allocation oflabor:∂rx 1 PA − 1 − π ( β − 1) ⎛
dPA ⎞
=
⎜
⎟,
rx ∂
2 PA + 1 + π ( β − 1) ⎝ PA d ⎠dPA ⎞∂rm 1 PA − 1 ⎛
=
⎜
⎟,
rm ∂
2 PA + 1 ⎝ PA d ⎠Now,
dPA ∂PA ⎛ ∂PA ⎞ ⎛ ∂t ⎞ ∂PA ⎛ ∂PA ⎞ ⎛ ∂τ M ⎞
=
+⎜
+⎜
.
⎟⎜ ⎟ =⎟t −⎝ ∂t ⎠ ⎝ ∂ ⎠ ∂⎝ ∂t ⎠ 1 ⎜⎝ ∂ ⎟⎠
d
∂

!

!

This expression is positive, by the definition of PA( , t) and by Proposition
2. Thus rm and rx will be positively related to and rx will increase proportionally less in response to a rise in than will rm, so, in a neighborhoodof rm = rx,!

∂rx ∂rm<.
∂∂
This ensures stability of the process whereby labor allocates itself between
sectors, in response to the rational forecast of t, to equilibrate the quasirents (see Figure 1).

Figure 1

78

Wilfred Ethier

Proposition 3. Suppose that t, the common tariff expected to prevail after
this period’s negotiations are complete, is greater than t o．Then the equilibrium allocation of labour is determined by (7).
Next, I investigate the implications for resource allocation of a common
rate of tariff reduction. Implicit differentiation of (7) yieldsd=dt[ PA ( , t ) + 1]2 − ∂PAαπ ( β − 1)
∂PA
∂t

∂t

< 0,

!

by definition of PA ( , t).
Geometrically, the expectation of liberalization in the negotiations tocome shifts the ex ante rm schedule down and the ex ante rx schedule up,
implying that the equilibrium rises. When the expected tariff falls as low
as t o，it instantaneously falls to zero. All labor allocates itself to the comparative advantage sector.
The theory of gradual multilateral liberalization developed in this section
can be interpreted as based on time inconsistency. Labour allocates itself tothe comparative-disadvantage sector because it knows that, once it is allocated there, the government will not negotiate protection away. Could thegovernment credibly commit to free trade, no labor would enter thecomparative-disadvantage sector. Thus there would exist no interest opposed to free trade. Staiger and Tabellini (1987) provide a related analysis.

!

5. Unilateralism
The rate of multilateral tariff reduction is limited to the lowest reduction
any country would prefer ex post. Perhaps, as Bagwell and Staiger (1990)
argued in another context, a system of unilateralism can improve on this.
Would such a system be developed and used? What would it look like?
The following subsection argues intuitively what properties such a systemshould have to produce affirmative answers, and this is followed by a formal analysis.
5.1. The Potential for Unilateralism
Suppose countries establish, before some negotiating round, a rule stipulating circumstances under which, after the completion of negotiations andafter the revelation of which goods and countries are the technologicalleaders, protection might be granted to beleaguered import-competing interests. Since the purpose is to preserve, at least partly, an outcome for spe-

79

Unilateralism in a Multilateral Worldcial interests in the face of unanticipated developments, they should beeither quantitative or sufficiently nimble in execution that it does not matter whether they are quantitative (i.e., tariff-quota equivalence).
The countries that turn out to be laggards could ex post apply such arule. Would they wish to do so? Clearly they would not if they were confident that this would prompt retaliation: This would be a roll-back of thenegotiated tariff reductions which are already less than what the laggards
want ex post. So, would the leaders retaliate? Such a roll-back would
move the common tariff reduction even further from what the leaders
would want. Still, if the laggards unilaterally increase protection, the leaders are likely to retaliate. Unilateral protection would be concession reneging: Since the leaders do not receive all the market access they had bargained for, they will not want to grant all the access they have promised.
If everyone realises the leaders will retaliate, such a rule would be of novalue. It would be neither instituted nor used, unless the rule eliminates the
motive to retaliate.
To make concession reneging acceptable, the rule could compensate theleaders. They need not be fully compensated, just enough so that they do
not forsake the compensation by retaliating instead. Allowing them thetrade rents generated by the unilateral measures would contribute to this.
There may be a second source of compensation as well: a greater common
tariff reduction, if unilateralism allows that to be negotiated.
To see when that might happen, consider the followers. They end up
competing, at a disadvantage, with the leaders in the import markets of thelaggards. The rents associated with unilateral protection would be worthmuch less to the followers, with no cost reductions, than to the leaders.
Also, they would not gain from any increase in tariff reduction. So, prospects are dim that these countries would be compensated enough to forestall retaliation. More important, since the followers’ preferences determine
the rate of common tariff reduction, no increase would in fact take place;indeed, that rate may well decrease. Thus the whole case for unilateralism
will unravel unless the interests of the followers are addressed. For thisreason, the unilateral measures should be discriminatory. If they apply tothe leaders but not to the followers, the latter would have nothing to retaliate against. The unilateral measures would, instead, enhance the ability of
the followers to compete in the markets of the laggards. Consequently,
they would now prefer a greater common rate of tariff reduction: the negotiated tariff reduction should increase.
The above argument assigns leaders, followers, and laggards distinct
roles in the exercise of unilateralism, but the identification of these countries is fixed only for the current period. Thus the unilateral measures
should be temporary––for the rest of the current period only.

80

Wilfred Ethier

Hypothesis. Multilateralism may induce the introduction of tools of temporary unilateral protection that are quantitative, discriminatory, and givecompensation to restrained exporters. Such an introduction might accelerate the rate of multilateral tariff reduction.
Note that four of the five stylised facts of unilateralism have been utilised.
I now turn to a formal analysis.

5.2. A Model of Unilateralism
I now model unilateralism as a rule allowing laggard countries, after therealisation of the technology draw, to apply temporary (i.e., for the rest of
the current period only) quantitative restraints on imports from the leaders,allowing the latter the resulting trade rents. Let ρ denote the (randomly selected) fraction of the leaders whose imports will be restrained by all laggards. I treat ρ as exogenous and use it to index the breadth of unilateralism. Restrained leaders can export only XRL = δ XF + (1 − δ )XUL, where XF
denotes the volume exported by followers and XUL that exported by unrestrained leaders. The parameter δ (0 δ 1), also exogenous, will index
the intensity of unilateralism. This model reflects the properties both argued for in the previous subsection and described in Section 2.
Suppose the leaders have a comparative advantage in A. Then, with theassumed tastes, followers will be in equilibrium when

" "

!

(8)

QA B

"
#PX $A !X !
FFAEquilibrium for the unrestrained leaders requires

!

(9)

"
$A !X "
Q B#
A

XUL
PA

L

UL

where XUL denotes exports of the unrestrained leaders and AL production
by the leaders of good A. For the restrained leaders

!

(10)

QARL B"#XP $A !X ,
RL

L

RL

A

where QARL denotes the relative domestic price of imports for the restrained
leaders. From (9) and (10), XUL > XRL, which implies that QARL > QA. X denotes the average level of A exports
X = (1−π ) XF+ρπ XRL+ (1−ρ ) π XUL = [1 − π (1−ρδ )] XF+π (1− ρδ ) XUL.

81

Unilateralism in a Multilateral World

Finally, for the laggards,!

"!PX $A "#X .

QA" B "A

Now, (8) and (9) imply⎛
X⎞ ~QA ⎜ B + ⎟ = A − X ,
PA ⎠
⎝
where

! = [1 − π (1 −ρδ )]A + π (1 −ρδ )A . From this and the above,
L

PA ( , t ; ρ , δ ) =""~A + (1 + t ) A*,
B * + (1 + t ) B""

so that ∂PA ∂ ρ, ∂ QA ∂ ρ, ∂ PA ∂ δ, ∂ QA ∂ δ < 0 .
Also,~
AB * + (1 + t ) 2 A* B
X=.
(2 + t ) B * + (1 + t ) B[

Furthermore, (8) and (9) imply
XUL]!X $A2 #!tA !
L

F

while (8) and (10) give
QARL = QA(11)
where Â ＝ δ A

AL − X RL,
Aˆ − X RL#(1 !δ ) A .
L

5.3. The Followers
Suppose that the breadth ρ of unilateralism is raised above zero, with δ
fixed at some positive level. I now investigate whether, as expected, thiswill improve the fate of the countries that turn out to be followers by reducing competition in their export markets from the leaders. For a given
common tariff t and rate of tariff reduction τ , the value of the objectivefunction of each follower government will beφ (τ ) =αa −1/ 2 ⎛ a 1/ 2 ⎞QA τ − ⎜ QA τ ⎟
⎝2
⎠
2

1+γ

.

82

Wilfred Ethier

Each government, realizing its country is small, takes PA as independent of
its own actions, but this common value will be affected by the increase inρ . Consider the marginal effect on the φ of each follower government of
increasing ρ after τ has been implemented.

(12)

ρ ∂QA
1+γ
∂φ F
QA ∂ρ ⎡ αa 1
⎛ a 1/ 2 ⎞ 1 ⎤=−+ (1 + γ )⎜ QA ⎟
⎥.
⎢
⎠ τ⎥
⎝2
2 ρ ⎢⎣ 2 Q1A/ 2
∂ρ τ
⎦

"

Then, since ∂ QA ∂ρ < 0, an increase in ρ will always raise the φ of eachfollower government, at any τ . So these governments would welcome theexercise of unilateralism, and they would prefer its breadth to be comprehensive (ρ = 1) and its intensity complete (δ = 1). Furthermore, it follows
from (5) that ∂ τ M ∂ ρ > 0, ∂ t M ∂ δ > 0, implying that a system of unilateralism will cause the negotiated liberalisation rate to increase and that theincrease will be greater the greater the breadth and intensity of unilateralism.

""

Proposition 4. If unilateralism without retaliation is introduced, the negotiated rate of liberalisation will increase, the governments of the countries
that turn out to be followers will be better off, and these governments
would wish unilateralism to be comprehensive and complete (which would
also maximize the rate of liberalisation).
5.4. The Unrestrained Leaders
I next investigate whether, as expected, the increase in ρ would benefit
unrestrained leaders. Again, there are no surprises. For a given common t
and rate of tariff reduction τ , the value of the objective function of eachunrestrained leader government will be

φ UL =

βαa −1/ 2 ⎛ a 1/ 2 ⎞QA τ − ⎜ QA τ ⎟
⎝2
⎠
2

1+γ

.

So,

ρ ∂QA
1+γ
dφ UL
1 ⎤ ∂φ UL ∂τ M
QA ∂ρ ⎡ βαa 1⎛ a 1/ 2 M ⎞
=−
+
(
+
γ
)
τ
.
1
Q
(13)
⎢
⎥+
⎟
⎜
⎝2 A
⎠ τ M ⎥ ∂τ ∂ρdρ
2 ρ ⎢⎣ 2 Q1A/ 2⎦
The first term on the right-hand side of (13), which I call the protective effect, measures the gain to each unrestrained leader from decreased competition in export markets; this is similar to the right-hand side of (12) but
larger, since > 1. The second term, the liberalising effect, measures theeffect on unrestrained leaders of the change in the negotiated tariff reduc-!

83

Unilateralism in a Multilateral Worldtion implied by the increase in ρ . Since the negotiated rate of tariff reduction is always less than what the unrestrained leaders wish ex post，∂ φ UL ∂ τ > 0, and the previous subsection showed that ∂ τ M ∂ ρ > 0.
Thus an increase in ρ will raise the φ of each unrestrained leader government via both effects. It would welcome unilateralism, and also prefers tobe the only unrestrained leader (that is, that ρ = (n − 1) n), and to havethe intensity of unilateralism complete.

!

!

!

Proposition 5. If unilateralism without retaliation is introduced, the governments of the unrestrained leaders will be better off, and these governments will wish complete intensity and as few other unrestrained leaders
as possible.

5.5. The Restrained Leaders
The national income of restrained leaders, at domestic prices, equals⎛⎛ Q RL − QA⎞X ⎞QARL ⎜ B + F ⎟ + AL − X F = ( AL + QARL B) + (tX F ) + ⎜ A
X F⎟.
PA ⎠
PA
⎝
⎝
⎠
The first term on the right is the value of production, paid to the workers
as wages. The second term equals total tariff revenue, distributed in lumpsum fashion. The third term, which I denote below by R RL, is the rent generated by the restraints, and I assume that this accrues to the export sector.
Then the ex-post reward of labor employed in the export sector of the restrained leaders is

(14)

( )

rxRL = QARL

−1/ 2

⎛ AL R RL ⎞
+
⎜
⎟,
⎝
⎠

and labour in the import-competing sector will earn
(15)

rmRL= a(QARL)1/2.

After some manipulation, (14) and (15) yield
R RL ⎛ 1 + t dR RL ⎞1 + t drxRL
1 ⎛ 1 + t dQARL ⎞= − ⎜ RL⎜
⎟ < 0,⎟+
RLrx
dt
2 ⎝ QA dt ⎠ AL + R RL ⎝ R RL dt ⎠and1 + t drmRL
1 ⎛ 1 + t dQARL ⎞=−⎟ > 0.
⎜
rmRL dt
2 ⎝ QARL dt ⎠84

Wilfred EthierSuppose that initially δ = 0, with ρ set at some arbitrary positive value:
unilateralism has no intensity. So the objective function of restrained leaders initially equals that of unrestrained leaders: φ RL= φ UL. Then consider
the effect of d δ > 0 on the restrained leaders; denote this increment, in theabsence of retaliation, by ∂ φ RL ∂δ . I assume that, should these (now effectively) restrained leaders retaliate, the laggards convert their unilateralmeasures into conventional (nondiscriminatory) tariffs, allowing themselvesto appropriate R RL, that is, unilateralism plus retaliation is equivalent10 to a
reduction in the rate of liberalisation τ . The incremental effect is accordingly

!

−

∂φ RL
∂φ UL
=−
.
∂τ δ =0,τ =τ M
∂τ τ =τ M

Thus the restrained leaders will find retaliation tempting only if

(16)

∂φ RL
∂φ UL
<−
.
∂δ δ =0∂τ τ =τ M

Now
γ

RL
∂φ RL
dr RL
∂φ RL ∂τ⎛a⎞ drm
= x + (1 + γ )⎜ Q1A/ 2τ M ⎟
+
.
⎝2
⎠ dδ
∂δ δ |=0dδ∂τ ∂δThe effect of a marginal restraint on the return to labor in the export sector
isdrxRL
1 r RL ∂QARL
1 ∂R RL=− x+ QA−1/ 2.
dδ δ = 0
2 QA ∂δ δ = 0∂δ δ =0
The first term on the right is the direct effect of the export restriction andthe second term is the compensating emergence of trade rent. From (11),

∂QARL
A −A
∂Q
= QA L+ A,∂δ δ =0
AL − X UL ∂δ
10. Alternatively, the laggards might convert their unilateral measures into conventional tariffs that apply only to the products of the restrained leaders, i.e., that
discriminate. But I will not consider this possibility as it would presumably makeretaliation even more likely.

85

Unilateralism in a Multilateral Worldand from the definition of R RL,⎛ ∂Q RL∂R ARL∂Q ⎞ XA −A=⎜ A− A ⎟ UL = (1 + t ) X UL L
> 0.
∂δ δ =0 ⎝ ∂δ δ =0 ∂δ ⎠ P
AL − X ULThen the net effect on the real reward of labor in the export sector reduces
to

∂rxRL
AL − A QA−1/ 2 ⎡1 ⎤=⎢⎣(1 + t ) X UL − 2 AL ⎥⎦.
∂δ δ =0 AL − X ULThis will be positive if the term in brackets is positive: a large enough initial export position will generate enough rent to compensate fully for the
restrictions. Next, the effect on labor in the import-competing sector reduces to∂rmRL
1
A − A ⎡ (1 − π ) A + π (1 − ρ ) AL + (1 + t ) A* + πρX UL ⎤= rmRL L⎢⎥.
∂δ δ =0 2
AL − X UL ⎣(1 − π ) A + πAL + (1 + t ) A*⎦
So, labour in the import-competing sector benefits from unilateralism at a
sufficiently small intensity. The overall effect on the objective function of
the negotiators of restrained leaders is thenAL − X UL ∂φ RL
AL − A ∂δ= QA−1/ 2 (1 + t )δ =0

X UL ∂φ UL+ρ∂ττ =τ M⎛ AL − X UL ∂τ ⎞⎞⎛a
+ 1⎟ + (2 + γ )⎜ Q1A/ 2τ M ⎟⎜⎠⎝2⎝ AL − A ∂δ ⎠1+γ

1 (1 − π ) A + π (1 − ρ ) AL + (1 + t ) A* + πρX UL
× M> 0.
(1 − π ) A + πAL + (1 + t ) A*τ

Each of the three terms on the right is positive. Thus, as long as δ is sufficiently small, leaders will not only not be tempted to retaliate, they will
also perceive the exercise of unilateralism as beneficial, according to thegovernment negotiators’ objective function.
Proposition 6. Unilateralism, at any breadth, will necessarily be perceived
as beneficial by the governments of restrained leaders, if the intensity issmall enough.
5.6. The Laggards
The value of the laggards’ negotiators’ objective function is
1⎛1⎞
φ = rxGτ M − ⎜ rmGτ M ⎟
⎝2
⎠
2
G

1+γ

.

86

Wilfred EthierBut, since the laggards would potentially implement unilateralism, I now
need to specify the objective function of the bureaucrats who would administer it. The fifth stylised fact of unilateralism (The restrictions are designed by officials distinct from those who negotiate international trade
agreements) now becomes relevant. I accordingly allow administrators an
objective function that, although of the same form as the negotiators’ (1),
has its own willingness to protect, . Thus the value of the laggards’ administrators’ objective function is now!

φ GA =

1 G M ⎛ 1 G M⎞
rx τ − ⎜ rm τ ⎟
⎝2
⎠
2

1+ µ

.

Perhaps the easiest way to assess the importance of allowing administrators
a distinct objective function of their own is to suppose initially that they
do not have one and deduce the implications. So I initially suppose that= γ and, therefore, φ AG = φ G.
The total marginal effect on φ G of raising ρ above zero, assuming no
retaliation, is!

dφ G ∂φ G ∂φ G dτ M
=
+
,
dρ
∂ρ
∂τ dρ
where the first term on the right indicates the direct protective effect andthe second the indirect liberalizing effect. Now,µ(17)

⎡ ∂r G⎤ ∂rmG∂φ G ∂rxG=+ (1 + µ ) ⎢ m τ M (1 + t ) ⎥
∂ρ
∂ρ
⎣ ∂t
⎦ ∂ρ
µ
⎫⎪ 1 ∂Q⎧⎪ ∂r G⎡ ∂r G⎤ ∂rmG∂φ G 1 ∂Q A
A=
= ⎨ x (1 + t ) + (1 + µ ) ⎢ m τ M (1 + t ) ⎥(1 + t ) ⎬.
∂τ Q A ∂ρ
⎣ ∂t
⎦ ∂t
⎪⎩ ∂t
⎪⎭ Q A ∂ρ

The negotiated liberalization rate τ M is less than what the laggards’ negotiators most prefer ex post, if =γ . Thus ∂φ G ∂ τ > 0, which implies that∂ φ G ∂ ρ > 0. Since a higher rate of liberalisation is perceived as beneficial, a change in the welfare of exporters must, on the margin, dominate
the accompanying change in the welfare of import-competitors.
But the indirect liberalising effect will be beneficial, again with =γ .
Thus unilateralism will, on balance, benefit the governments of laggards
when the latter effect dominates, which will be so when

"

!

"

!

G
dφ G ⎛ ∂τ M
1 ∂QA ⎞ ∂φ=⎜+⎟dρ ⎝ ∂ρ QA ∂ρ ⎠ ∂τ > 0,

87

Unilateralism in a Multilateral World

which, in turn, will hold if and only if

τM >

1
.
1/µ + 1/ 2!
!

The right-hand side is strictly increasing in and τ M and decreases in γ ,ranging from infinity to zero. Thus, with constrained equal to γ , there。
exists a unique γ with the property that unilateralism confers a net benefit。
on the laggards if and only if γ < γ ．
。
But this is not all. Suppose that γ < γ and that governments commit
themselves to practice unilateralism should they become laggards. Whenever a country is a laggard, it then shoots itself in the foot, but this benefits all non-laggard countries, raising the rate of liberalisation. If γ is suffi。
ciently close to γ ，the loss when a laggard will be dominated by the gain
when not a laggard, so that, ex ante, every country is better off.

!

。

Proposition 7. If= γ is not sufficiently greater than γ ，all countries
can benefit ex ante, according to the objective function (1) , if each country adopts unilateralism at some intensity. This will raise the rate of liberalisation.
6. Implications of Unilateralism
The section examines the consequences for the international economy ofa system of unilateralism.
6.1. The Effect of Unilateralism on Resource Allocation!

The previous section examined the effect of unilateralism for a given
pattern of resource allocation ．However, if unilateralism exists, forward-looking labor will take that into account when deciding where to locate.
With a system of unilateralism in place, the real ex-post quasi-rents become as follows, for a country with a comparative advantage in A:

βαa,
Q1A/ 2(18)

rxURL =

(19)

rmURL = aQ1A/ 2 ,rxRL =βαa,(QARL ) 1/ 2

rxF =

( ) ,

rmF = aQ1A/ 2 ,rmRL = a QARL

1/ 2

αa
,
QA1/ 2rxG =αa,QB1/ 2rmG = aQB1/ 2 ,and the expected returns accordingly become(20)ri ( ; t , ρ , δ ) =(1 − ρ )π URL ρπ RL 1 − π F 1 G
ri
+
ri +
ri + ri ,
2
2
2
2

88

Wilfred Ethier!

"for i = x, m. Here t denotes the common tariff rate expected (correctly) toprevail after the current round of negotiations––that is, t = t1 τ M (1 t1 ),where t1 denotes the tariff inherited from the previous period––and ρ andδ denote the parameters of the system of unilateralism that is in place or
expected (correctly) to be put in place. Given the values of these policy
variables, the allocation of resources is determined byrx ( ; t , ρ , δ ) = rm ( ; t , ρ , δ ).
Differentiate this expression implicitly to determine the effect of an increase in the intensity of unilateralism on the ex-ante allocation of resources.
⎛ ∂rx ∂rm ⎞ ⎛ ∂rx ∂rm ⎞
−
−
⎜
⎟ ⎜
⎟
⎝ ∂δ ∂δ ⎠ ⎝ ∂td∂t ⎠ ∂τ=+t.
∂rm ∂rx∂rm ∂rx 1 ∂δ
dδ
−
−
∂
∂
∂
∂
The first term on the right is the direct effect of unilateralism on resource
allocation, and the second term is the indirect effect due to the fact that theexistence of unilateralism will alter the liberalisation expected (correctly) tobe negotiated. Consider a differential increase of δ above zero, i.e. the introduction of unilateralism at an arbitrarily low intensity. Then, the discussion in Section 4 establishes that the denominators and the first bracketed
term in the numerator of the second term on the right are each positive,
and Proposition 7 establishes that ∂τ ∂ δ > 0. Thus the indirect effect ispositive. So, consider the numerator of the first term on the right, the direct effect.

!

∂rx ∂rm ρπ ⎛ ∂rxRL ∂rmRL ⎞ ⎛ ∂QA ⎞ a −1/ 2
−
=
−
⎟ QA
⎟ + ⎜−⎜
2 ⎝ ∂δ∂δ ∂δ∂δ ⎠ ⎝ ∂δ ⎠ 4⎧
1+ t ⎫
α× ⎨α [( β − 1)π (1 − ρ ) + (1 − ρπ )]QA −+ (1 − ρ ) −
⎬.
1+ t
QA ⎭
⎩

!

Since QA > 1 and ∂ QA ∂ δ < 0, a sufficiently small value of ρ will guarantee that this term is positive: the direct effect of unilateralism, as well as
the indirect effect, will be to reallocate resources toward the comparativeadvantage sector.
Proposition 8. The introduction of unilateralism at a sufficiently small intensity and breadth will induce an increased allocation of labour to thecomparative advantage sectors.

89

Unilateralism in a Multilateral World

6.2. The Insurance Triangle
Note two curious features of how unilateralism functions. First, unilateralism is appealing to governments if their willingness to protect (γ ) is low,
not high. This is because a lower willingness to protect produces a greater
beneficial liberalising effect.
Second, unilateralism functions as a form of insurance. Unlike the literature on tariffs-as-insurance (Eaton and Grossman, 1985; Dixit 1987; 1989)
though, the role for insurance is itself a product of a positive willingness toprotect, and its value is not that a laggard government itself have something to fall back on (ex post such a government would prefer not to implement it––see below) but rather that its effect on others allows all to negotiate a greater rate of liberalisation.11 Countries know that, should theyturn out to be followers (the most reluctant liberalisers), their interests will
be safeguarded by the efforts of the laggards to protect their own importcompeting interests, and that these efforts will be acceptable to the leaders.12 This cannot be appreciated in a two-country model. The insurancefunctions through a subtle interplay between all three groups: the insurance
triangle.
If this is how unilateralism works, could it not take the form of export
subsidies by followers, either instead of or along with, import protection
by laggards? An answer will emerge below.
6.3. The Split Personality
The analysis thus far in this section, culminating in Propositions 7 and 8,
has focused on the possibility that multilateralism might imply a role forunilateralism: causation has been from the former to the latter. But unilateralism, to be effective, also requires a multilateral component. This is because Proposition 7, by itself, does not get us far enough. The reason, inpart, is time consistency.
Unilateralism will be effective only if countries choose to implement it
when they become laggards. They benefit only when the beneficial indirect
liberalising effect dominates the harmful protective effect. However, theformer will be past history when the laggards decide whether to implement
unilateralism. Thus the laggard governments, according to the negotiators’
objective function, will decline to implement unilateralism ex post.
This time-consistency problem is compounded––and this is absolutely
11. There is a (very rough) analogy here with the role for trade adjustment assistance advanced by Fung and Staiger (1996).
12. Thus, in the early 1980s, the US automobile industry (laggards) acquired
protection acceptable to the Japanese industry (leaders) and beneficial to the Europeans and Koreans (followers).

90

Wilfred Ethieressential––by an externality. Governments with the objective function (1)。
would like, if γ < γ ，to convince each other that they will practice unilateralism when they turn out to be laggards, because this would produce ahigher rate of tariff reduction, to the ex ante benefit of all. However, allknow that, ex post, the government of a laggard with the objective function (1) would not implement unilateralism. What if governments can precommit to implement unilateralism should they become laggards? Because
the time consistency problem is compounded by an externality, no government would undertake such a pre-commitment unilaterally: The beneficial
liberalising effect depends on a general adoption of unilateralism.
Proposition 9. The introduction of unilateralism (raising ρ above zero)
will have no effect, if implemented by authorities who have discretion andwho set = γ , because they will always decline ex post to implement it.
Furthermore, no government negotiator with = γ would be willing unilaterally to delegate authority to implement unilateralism ex post to someother agent.

!

!

Potentially, there are two ways around this problem, and both require a
multilateral component to unilateralism. The first is simply to internalise
the externality by having the countries jointly adopt binding unilateralism.
That is, the latter could itself be the product of multilateral negotiation. (Orthey might jointly bind themselves to subsidise exports whenever they turnout to be followers).
This does not correspond to reality, though: The fifth stylised fact of
unilateralism (The restrictions are designed by officials distinct from those
who negotiate international trade agreements) is at variance with this possibility. So consider instead the consequences of countries individuallyadopting unilateralism systems with ≠ γ . Let τ AG(µ ) denote the rate ofliberalisation that is optimal, ex post, for administrators with a willingness
to protect of , in a country that turns out to be a laggard.
Define (γ ) to be the solution to

!

!

!

τ GA [ µ (γ )] = τ M (γ ).

!

Propositions 1 and 2 imply that (γ ) > γ . Further, Proposition 2 implies
that, if(γ ), the negotiated rate of liberalisation will be no less thanwhat the laggard administrators most prefer ex post. Thus, from (17)∂ φ AG ∂τ < 0, whence ∂ φ AG ∂ρ < 0. Therefore, the administrators will indeed implement unilateralism when their countries turn out to be laggards:
The time consistency problem disappears.

"

!! !

"

!! !

Proposition 10. If( γ ) > γ , laggards will implement unilateralism
and, at some intensity, this will benefit all other countries; if
is suffi-!

91

Unilateralism in a Multilateral World

ciently small, this will also benefit the laggards, according to the objectivefunction (1) .
Four comments are in order.
• For unilateralism to work, the willingness to protect of the administrators
must not merely marginally exceed that of the negotiators, it must significantly exceed the latter.
• This is not an example of individual countries strengthening the bargaining positions of their negotiators by pre-committing to ex post action.
The benefit of unilateralism to an individual country comes from the assurance that all other countries will practice it when they are laggards.
Regardless of how forward-looking they may be, the negotiators of nocountry will wish their own country to adopt such a system of unilateralism. The fifth stylised fact of unilateralism (The restrictions are designed by officials distinct from those who negotiate international trade
agreements) is absolutely critical here.
• The higher rate of liberalisation will be perceived as undesirable by theadministrators, and, if
is significantly great, this undesirable indirect
effect from introducing a small ρ will necessarily overwhelm the direct
protective effect: Unilateralism will be on the whole undesirable fromthe administrators’ point of view. However, this has no effect on feasibility, because the liberalising effect will be past history when the administrators are called on to act. That is, such unilateralism will be time
consistent.
• With unilateralism in place, there is no longer a possibility of subsidising
the exports of followers, since any such subsidies would be neutralisedby the laggards.13!

6.4. The Compatibility Problem
If the restrictions must be designed by officials distinct from those who
negotiate international trade agreements, can we be assured that the systems of unilateralism they adopt will possess the desired properties (i.e. theother stylised facts)? Since these officials would prefer unilateralism without complete retaliation rather than with it, and since Propositions 4, 5 and
6 continue to apply, the logic of this section, offering an explanation for
those stylised facts, also continues to apply: the desired properties shouldbe there. However, there is no reason to think that either the breadth, ρ , or
the intensity, δ , of the unilateralism the officials provide will be desirablefrom the negotiators’ point of view.
This is the compatibility problem: if unilateralism is not a deliberate
multilateral creation (and, in fact, it is not) then it can be useful to the ne13. Countervailing duties, of course, do just that.

92

Wilfred Ethier

gotiators only if imposed by officials whose objectives are significantly atodds with those of the negotiators.
Once systems become common, they could be perceived as of potential
benefit by government negotiators meeting together, even though no negotiator would have been willing to adopt such a system individually. An immediate implication of the compatibility problem (also in accord with actual experience) is that these negotiators have an incentive to expand multilateral negotiations to address the conduct of unilateralism.
Proposition 11. Government negotiators will, together, have an incentive
to accept unilateralism but also to include codes of conduct for it in theirmultilateral negotiations.
7. Concluding Remarks
I have argued that unilateralism and multilateralism comprise a coherent
international commercial system.
I have reduced each of these to a few basic principles, and discussed
how they relate to each other. The essential argument follows.
• Multilaterally negotiated tariff reduction is limited by the smallest reduction any country will want ex post: that most advantageous to thosecountries who compete with the exports of the technological leaders.
• This pace can be accelerated, and the allocation of resources to the comparative advantage sectors can be increased, if those countries that import the exports of the technological leaders make universal use of temporary, quantitative, discriminatory protection compensating restricted
exporters.
• Such unilateralism works by conferring a form of social insurance resulting from a subtle interplay between three distinct sets of countries: theinsurance triangle.
• The use of such a system is constrained by a time––consistency problem
compounded by an externality.
• With unilateralism adopted by countries individually rather than collectively, to be useful, it must be designed by officials significantly more
willing to protect than are the negotiators themselves, who would be unwilling to delegate such authority: trade policy needs its ‘split personality’.
• This compatibility problem implies an incentive to address the conduct of
unilateralism multilaterally.
This theory of unilateralism depends critically on the existence of a multilateral world. The key concepts––the insurance triangle, time-consistencycompounded by an externality, the necessity of a split personality, thecompatibility problem––cannot be understood at all in a two-country environment.

93

Unilateralism in a Multilateral World

The process of multilateral trade liberalisation generates a potential motive for protectionist policy tools with exactly those properties that I haveargued do in fact constitute contemporary unilateralism. This in turn requires––again in accord with actual experience––a multilateral component.
It all fits together.
Appendix 1: Instruments of Unilateralism
Unilateralism consists of rules, or instruments, that may be explicit or
implicit. This appendix describes several of the most important instruments,
and then describes how their nature and their application has been changing over time.
The Instruments
I describe four prominent instruments.
1 Voluntary export restraints (VERs)14 fall outside both national laws andinternational agreements. The Uruguay Round made them more extralegal than ever. The following instruments, ‘administered protection’, areprovided for in many national laws and sanctioned by the WTO.
2 Antidumping duties Dumping15 is pricing for export below either thecost of production or the price for comparable domestic sales. Antidumping laws provide a two-pronged investigation: determination of the
dumping margin, if any; determination of material injury to domestic
import-competing firms. If both determinations are positive, a temporary
duty equal to the dumping margin is imposed on the good from thecountry whose firms have dumped. The national interest plays no role,and (in the USA) the President cannot decline to impose the duty. Theselaws define certain behaviour as objectionable and force importprices up when it occurs. Whether the behaviour should be objectionable is beside the point: arbitrary circumstances determine which importcompeting interests may obtain temporary protection.
3 Countervailing duties apply to imports subsidised for export. Administration is similar to that of antidumping laws.
4 Safeguards provide16 temporary protection for domestic industries
harmed by increased imports. Again, a material injury test is applied.
But, in the USA, the President may decline to impose a duty. More generally, duties imposed should be nondiscriminatory and should not increase protection overall: duties should be reduced (in a nondiscriminatory way) on goods that are important exports of the exporting countries
14. See Harris (1985), Kostecki (1987), Krishna (1989), and Ethier (1991a, b).
15. See Ethier (1991b, 1993, 1994), Prusa (1992), Baldwin and Steagall (1994),
and Tharakan and Waelbroeck(1994).
16. See Ethier (1994).

94

Wilfred Ethiermost affected by the safeguard measures.
This list of four instruments excludes other tools, notably those for aggressive export expansion (e.g. Super 301 in the USA). These are morecharacteristic of the USA than of other countries. Also, I have analysedthese before (Ethier and Horn, 1996), and this paper concerns unilateralism
as protection.
Changing Instrument Use
Use of these instruments has changed dramatically. First, usage has
greatly increased since the 1960s. With the freedom to conduct traditionaltariff policy progressively constrained by multilateral agreements, protectionist pressures have increasingly found outlets in the new protectionism.
Second, multilateral negotiation is broadening to encompass unilateral
actions. The Tokyo Round established voluntary codes for the conduct ofadministered protection, and these were made mandatory for WTO members by the Uruguay Round. Curiously, though, the code for safeguards
has been loosened. Countries are now allowed, sometimes, to use themmuch as VERs have been used. The final outcome is far from clear.
Third, individual countries have continually changed their laws. Thesechanges have generally reduced administrative discretion and made protection more likely.
Fourth, the mix among the instruments has changed dramatically, with
the number of safeguard cases declining absolutely as well as relatively
and the number of countervailing-duty and (especially) antidumping cases
exploding.

Appendix 2: Prices
Relative Commodity Prices
Recall that everyone spends half of his/her income on each good. Then,if A, B, A ! and B ! denote national production levels and M each nation’s
trade in B ,Qi (B +M )=A – Pi M

Q!
i ( B !– M )= A !+ Pi M .

andThese expressions can be rewritten as
Pi (1
Thus

#t #1)M $A !P (1 #t )B
i

and

#
#

Pi (1 t )M
(1 t )"i$B1 #Pt !A ".

(1 #t )B
(1 #t )AB
# ! 2 #t $M $2 #t !(2 #t )P .

A
Pi (2 t )

"

"

i

95

Unilateralism in a Multilateral World

These, in turn, imply:
Pi
and$AB "##(1(1##t t)A)B ,
"

!! #
M $
# # # "AB " (1 t ) A "B.
(2 t ) A (1 t )A "
2

!!

!

Pi will assume one of two alternative values, depending on which good is
the technological leader. Since A = [πβ + (1 − π )] a , B = (1− ) a,
A != (1− ) a, and B != a ,!

!!

Pi = PA ( , t ) = π ( β − 1)α+ 1,
α + (1 + t )(1 − )if A is the leader, and Pi = PB = 1/PA if B is the leader. Then PA > 1 > PB.
Real Rewards
The responsiveness of rents to the common tariff vector t is⎡⎤
( PA − 1) π ( β − 1) − ( PA − 1) ⎥1 + t ∂rx
1⎢
1
= − ⎢1 −⎥ < 0,
α
rx ∂t
2⎢
PA
PA + 1 + π ( β − 1) ⎥1+⎢⎣⎥⎦
1+ t 1−⎤⎡( PA − 1) 2 ⎥1
1 + t ∂rm1⎢
= − ⎢1 −⎥ > 0.
αrm ∂t2⎢
PA ( PA − 1) ⎥1+⎥⎦⎢⎣
1+ t 1−""

These imply, when rm = rx, ∂ rx ∂ t+∂ rm ∂ t< 0.

References
Bagwell, K. and R. W. Staiger 1990. A Theory of Managed Trade. American Economic Review 80: 779-795.
--------- . 1999a. An Economic Theory of GATT. American Economic Review 89(1):215-248.
--------- . 1999b. Multilateral Trade Negotiations, Bilateral Opportunism and theRules of GATT. Working Paper. Department of Economics, University of Wisconsin.

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Wilfred Ethier

Baldwin, R. E. and J. W. Steagall. 1994. An Analysis of US International Trade
Commission Decisions in Antidumping, Countervailing Duty and Safeguard
Cases. CEPR Discussion Paper no. 990.
Corden, W. M. 1997. Trade Policy and Economic Welfare, 2nd ed. Oxford: Oxford
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Dixit, A. 1987. Trade and Insurance with Moral Hazard. Journal of International
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--------- . 1989. Trade and Insurance with Adverse Selection. Review of Economic
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Eaton, J. and G. M. Grossman. 1985. Tariffs as Insurance: Optimal Commercial
Policy When Domestic Markets Are Incomplete. Canadian Journal of Economics 18(2): 258-272.
Ethier, W. J. 1991a. The Economics and Political Economy of Managed Trade. In
Markets and Politicians, ed. A. L. Hillman. Boston: Kluwer Academic Publishers: 283-306.
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--------- . 1993. An Antidumping Law with a Distorted Home Market. chapter 17. In
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--------- . 1998b. Regionalism in a Multilateral World. Journal of Political Economy
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--------- . 2004. Political Externalities, Nondiscrimination, and a Multilateral World.
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Harris, R. 1985. Why Voluntary Export Restraints are ‘Voluntary’. Canadian Journal of Economics 18: 799-809.
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Kostecki, M. 1987. Export Restraint Arrangements and Trade Liberalization. The
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Krishna, K. 1989. Trade Restrictions as Facilitating Practices. Journal of International Economics 26: 251-270.
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5

Trade, Income Transfers,
Developing Countries, and the Core
Carsten Kowalczyk and Tomas Sjöström*

1. Introduction
Individual nations or groups of them may find that protection is preferable to free trade and will hence strive to prevent the implementation of aliberal trading order. We have argued in Kowalczyk and Sjöström (1994)
that a natural solution concept for the problem of implementing a worldwide trade agreement is the core which is defined as the collection of situations no nation or coalition of nations, whether actual or potential, could
or would block, i.e., prevent from being implemented. We showed further,in that paper, for a many-country model of international trade in monopoly
goods, that implementing a core allocation may require that nations transfer income to each other. We derived an explicit formula for income transfers (sidepayments) between nations which together with the formation of
the grand coalition (“free trade”) would support a Pareto optimal trading
situation, in particular the Shapley value. Since the Shapley value constitutes a core allocation in that model, our transfer mechanism supports anallocation in the core.1* We thank the organizers of the Kobe Conference for the opportunity to present
this work, and Noritsugu Nakanishi and conference participants for helpful comments. We have benefited also from comments at the Berlin EEA Meetings. This
paper provides an extended presentation of the results in Kowalczyk and Sjostrom(2000).
1. Raymond Riezman (1985) considers the core in a three-country exchange
model where a single nation or a customs union can block global free trade. Inés
Macho-Stadler, David Pérez-Castrillo, and Clara Ponsati (1998) discuss the core ina three-country model under varying assumptions regarding the weighting of nations’ sources of income. Both papers rule out sidepayments between nations.
99

100

Carsten Kowalczyk and Tomas Sjostrom

Another transfer scheme has been discussed in the international trade literature. Thus Earl Grinols (1981), in further development of work on compensation by Jean Grandmont and Daniel McFadden (1972), and on customs unions by Michihiro Ohyama (1972) and Murray Kemp and Henry
Wan (1976), showed that assigning to each country its pre-change trade
vector ensures that no nation loses by integrating into a customs union
which sets its compensating common tariff , i.e., the tariff that leaves tradewith non-member nations and hence their welfare unaffected.2 None ofthese papers considered the core.
This paper analyzes the properties of the Grinols transfer mechanism in
our model of monopoly trade. We show that Grinols transfers go fromcountries with small profit losses from integration to those with large profit
losses， Grinols transfers, when combined with the global trading arrangement, constitute a core allocation， Grinols and Shapley value transfers are identical except that Shapley transfers adjust for differences in reduced deadweight losses, and Grinols transfers constitute minimal compensation necessary to reach the core. The Shapley value has the desirable
properties that it is a central point in the core, and that it shares the gains
from cooperation equally, and thus can be obtained as the solution to a
non-cooperative bargaining game. Yet, we propose that Grinols transfers
may be preferable to our Shapley transfer mechanism since Grinols transfers are easier to calculate and hence implement, and since Grinols transfers may, in some circumstances, be kinder to developing countries asthese countries tend to experience large gains in deadweight losses fromliberalization and hence with Grinols transfers would receive larger or pay
smaller net transfers than with the Shapley transfer scheme.3

!

"

#

$

2. The Model
We consider the world of monopoly trade introduced in our previous paper. Thus assume a world of n countries indexed by i. The representative
consumer in country i has, and strives to maximize, the following quasilinear preferences where coi is consumption of a non-taxed numeraire good,cji is consumption of good j, and ji is a taste parameter:!

2. Jaroslav Vanek (1965) introduced this concept.
3. In the present model of monopoly trade, a country loses monopoly profits inforeign markets from joining those nations in trade agreements. In a more generalenvironment where, in addition, the imports of some goods are taxed, a country’s
national income could also be changing from trade liberalization, whether comprehensive as in a multilateral agreement or preferential as in a customs union, via
changed terms of trade or changes in trade flows. Sidepayments could then beneeded to compensate for the net loss in national income from the combined effectfrom these changes.

101

(1)

Trade, Income Transfers, Developing Countries, and the Core( )u i c i = c0i +

i
i θj
j

(c ) , 0 < θ < 1,

n

∑ θ
j =1

i
j

i
j

i, j = 1,..., n.

Each consumer i is endowed with loi units of good zero which can be consumed, sold to the single domestic firm as an input, or given away as income transfers. If I i denotes consumer i’s full income (which equals loi if idoes not receive any transfers of income), and pji is the domestic price ofgood j in country i, consumer i’s budget constraint becomes
(2)

c0i +

n

∑p c =I ,
i i
j j

i

i = 1,..., n.

j =1

The solution to the consumer’s problem implies that country i demand for
non-numeraire good j is

(3)

( )(

c ij = p ij),

1/ θ ij −1

i, j = 1,..., n.

Substitution of these demands into (2) for all goods j then yields demand
for good 0 as the residual.
Country i has only one firm. It produces x i units of good i, and faces
given technology as expressed by the constant input-output coefficient β i.
Its labor demand is therefore
(4)

loi

!!x "
i

i

i = 1,..., n,which also defines its total costs since, in equilibrium, the wage rate must
equal the unit price of the numeraire good.
We assume that markets are segmented, and that firm i can sell xji units
jof good i to foreign country j at unit price (p e )i . Firm i profits are thengiven by
n

(5)

( )

j
π i = ∑ ⎡ p e − β i ⎤ x ij ,
⎢
i
⎣
⎦⎥
j =1

i = 1,..., n.

[ (

)]

Since the price elasticity of demand implied by (3) is −1 / θ ij − 1 , themark-up price charged by firm i in market j is(6)i( p ) = θβ ,
e

j

i

i
j

i, j = 1,..., n.

102

Carsten Kowalczyk and Tomas Sjostrom

In an equilibrium in which governments do not intervene, firms will
charge everywhere the prices given by this rule. In the remainder of thepaper we analyze the scope for policy intervention and coordination inwhich nations agree to price at cost and use Grinols income transfers.
3. Trade Agreements and the Policy GameWe assume that the policy instrument at hand is a government-enforced
price ceiling and we define a trade agreement between two countries i andj as an agreement to apply such ceilings at marginal cost on the exports toeach other’s markets.4 Country i gains consumer surplus equal to δ ji as
j(p e )i is reduced from the monopoly mark-up price in (6) to cost β j , and it
loses profits π ji on its exports to market j. Country j experiences an analogous welfare calculus from integration with country i. Since an agreement
eliminates the deadweight loss from monopoly pricing, the increase in consumer surplus in j must exceed i’s profit loss, that is, ( δ ij π ji ) is positiveby the deadweight loss triangle, as is illustrated in Figure 1. The collective
gains to the two countries from a trade agreement, ( δ ji π ij ) + ( δ ij π ji ),are thus positive. However, a country may find its gains in consumer surplus to fall short of the lost profits abroad from the agreement and would
thus not enter into it unless it were compensated through a sidepayment. A
final property of our model is that the grand coalition, i.e., the world-wide
trade agreement, is Pareto optimal since it equates price with marginal costfor every good in every country. We assume that the purpose of GATT/WTO is to aid countries in establishing the grand coalition of world-wide
marginal cost pricing.
We view the world economy as a transferable utility game where the setof players is the collection of nations N = {1, ..., n}, and a coalition K isa (preferential) trade agreement in the sense discussed above with |K |members, where K N . Coalition K can guarantee itself a payoff given by
the characteristic function v(K ) which is a mapping from all subsets of N
into a real number. A vector of payoffs y is said to be blocked by coaliiv (K ) The core is the set of payoff vectors that istion K if
i #K yblocked by no coalition. It is important for the application of the character-

!

!

!

"

!

"

!

4. With the assumed constant elasticity import demand, an ad valorem importtariff leaves price constant but reduces import volume while a specific import tariff
reduces the firm’s perceived elasticity and thus worsens the importer’s terms oftrade. Thus governments would not want to use import taxes. A specific importsubsidy would raise both the importer’s welfare and the exporting firm’s profits, as
discussed in Kowalczyk and Skeath (1994). An import price ceiling would also be
used unilaterally by any government, and it would, therefore, lead to a noncooperative Pareto optimal equilibrium. Since the focus of our analysis is the useof sidepayments (income transfers) as an instrument in supporting cooperation, we
will here, as we did in our earlier paper, rule both of these policies out.

103

Trade, Income Transfers, Developing Countries, and the Core

istic function approach that a coalition not affect the payoffs of other nations. This requirement is satisfied in our model since the preferential trade
agreements we consider do not cause price changes on trade with nonmembers due to the assumptions of separable demand, zero income effects,
and constant costs for non-numeraire goods.
4. Grinols Transfers and the Core
Grinols (1981, p.262) proposes a transfer scheme where “[T]he compensation to each country is given by its pre-union trade vector.” He stresses(p.260) that it has the property that “[Using] world prices for evaluationeach and every country breaks even under the proposed scheme, receiving a transfer which has zero value. [...] Using post-union internal prices
for valuation, member nations may have to pay or receive a net transfer.”
Lemma. In a model of international trade of monopoly goods, Grinols
transfers TGi are
TGi =

(7)

∑ (π − π ),
i
j

j
i

i = 1 ,..., n.

j ≠i

Proof
Consider an initial situation where country i is a member of no trade
agreement. Since country j charges the mark-up price implied by equation(6), it follows from (3) that i’s demand for and hence imports of good j is⎛βj⎞c =⎜ i ⎟⎝θ j ⎠
i
j

(8)

(

)

1/ θ ij −1,

i, j = 1 ,..., n.

Switching i and j in the above equation determines country j’s imports
from i and hence i’s exports. Finally, country i may also be trading goodzero in the initial equilibrium in order to settle its trade balance. Evaluatedat the prices of the initial equilibrium the corresponding trade in good zero,
moi !equals(9)⎛ βi ⎞m =pi ⎜ j ⎟
⎝θi ⎠
j ≠i
i
0

∑

j

(

1/ θ ij −1)⎛βj⎞− p⎜ i ⎟⎝θ j ⎠
j ≠i

∑

i
j

(

1/ θ ij −1),

i, j = 1,..., n.

104

Carsten Kowalczyk and Tomas Sjostrom

Denote the transfers recommended by Grinols by TGi . When evaluated at“post-union domestic prices,” which for our problem equal marginal cost,
Grinols transfers become
TGi =

(10)

∑β c − ∑β c +m ,
j i
j

j ≠i

i

i

j

j ≠i

i
0

i, j = 1,..., n.

Substituting into this from equations (8) and (9) finally yields, after somemanipulations which are summarized in the Appendix, expression (7).
Q.E.D.
Thus Grinols transfers imply that country i receives compensation forthe profits it loses from the grand coalition forming while country i pays
compensation to its trading partners for their profit losses in i’s market.
We define Sji to be consumer surplus from good j in country i whencountry j charges only marginal cost on its sales to i. If the grand coalition
forms without sidepayments country i’s payoff is_n

Φ i ( N , v ) = l0i + ∑ S ij ,(11)

i = 1 ,..., n.

j =1Hence, the grand coalition with Grinols sidepayments implies that country
i’s payoff is
_

n

n

j =1

j =1

[(

)]

Φ i ( N , v ) = l0i + ∑ S ij + ∑ π ij − π ij ,(12)

i = 1,..., n.

The main result of the paper can now be shown:!

Proposition. Forming the grand coalition, and implementing the vector ofinternational side-payments TG (N v ) which assigns to country i the net
transfer
(7)

TGi =

∑ (π − π ),
i
j

j ≠i

j
i

i = 1, ..., n,will bring GATT/WTO into the core.
Proof
See Appendix.
We discussed in our earlier paper under which conditions sidepayments
are needed to implement the grand coalition, and we showed, in particular,that the grand coalition could form without the use of sidepayments if
countries are similar. We showed also that the transfer scheme which gives
to country i the net transfer

105

Trade, Income Transfers, Developing Countries, and the Core

Ti =

(13)

∑ [(

)]

1
π ij − δ ij − π ij − δ ij ,2 j ≠i) (

i = 1, ..., n,

supports the Shapley value, another core allocation of this world economy,
with payoff to country i given by
n

_

(14)

Φ i ( N , v ) = l0i + ∑ sij +
j =1

1 n
π ij − δ ij − π ij − δ ij , i = 1,..., n.
2 j =1

∑ [(

) (

)]

At first glance, the main difference between Shapley and Grinols transfers
appears to be that the latter ignores any effects on consumer surplus. However, consider again Figure 1. When integrating, country j loses profits π ij
equal to area I while country i gains consumer surplus δ ji equal to areas I
and II．Let ε ji be the deadweight loss given by area II，and henceδ ji π ij +ε ji. Substituting this into (14), and similarly for profits earned in jand the corresponding consumer surplus in j, (14) can be rewritten as

!

Ti =

(15)

1

∑ (π − π ) + 2 ∑ (ε − ε ),
i
j

j
i

j
i

i
j

i = 1,..., n.

i≠ j

j ≠i

Figure 1
pij(pe)ij
Ⅰ
β

j

Ⅱ

cij

Thus our earlier Shapley transfers are equivalent to Grinols’ scheme except
for a term comparing reductions in deadweight losses between nations. The
two transfer schemes imply, therefore, different distributions of the aggregate global gains from the grand coalition forming relative to an initialsituation of no trading clubs. From the earlier definition of Sji as the consumer surplus in i on good j when j is priced at cost, and δ ji as the gain in

106

Carsten Kowalczyk and Tomas Sjostrom!

consumer surplus in i when good j’s price is reduced from mark-up to cost,(Sji δ ji )is consumer surplus in i when good j is priced at mark-up. Thus
country i’s payoff in the initial situation of no trade agreements equals
_

(16)

n

[(

)

]

Φ i ( N , v ) = l0i + ∑ S ij − δ ij + π ij ,j =1

i = 1,..., n.

Denote the gains to country i from moving from this situation to the grandcoalition with Shapley payoffs by gSi , and let gGi be the gains from movingfrom no trading clubs to the grand coalition with payoffs implied by Grinols transfers. Subtracting (16) from (14) to obtain the former, and (16)from (12) to obtain the latter, and substituting for δ ji = π ij + ε ji, for all iand j, yields(17)

g Si =

1 n i
ε j + ε ij ,2 j =1∑()

i = 1,..., n,

and

(18)

gGi =

n

∑ε ,
i
j

i = 1,..., n.

j =1

Thus the Shapley value implies that country i gains half of each of its
trading partners’ consumption gains in return for keeping only half of its
own consumption gains while the Grinols scheme implies that country i retains its own consumption gains but does not obtain a share in the trading
partners’ gains.5 The magnitude of ε ji is in part determined by the curvature of the demand curve for good j, and in part by the cost of producing
good j. Given our choice of policy instrument, the curvature of country i’s
demand curve for good j is not affected directly by country i policy, and itis therefore through firm j’s pricing decision that income is forgone in thatmarket in the initial equilibrium. It is an interesting feature of the Grinols
mechanism that firm j, and thus country j, do not share in the gains from
5. The finding that country i’s payoff increases by its own consumption gains is
consistent with that of Grinols (1981) for a country joining a customs union of thetype discussed by Kemp and Wan (op. cit.), and Ohyama (op. cit.) in an ArrowDebreu-McKenzie world economy. If the world economy, rather than being an endowment economy (as in Grinols’ example) or one of constant costs (as in ourmodel), exhibits variable cost then the change in country i’s payoff should be augmented with country i’s production gains, which is the non-negative change invalue of production as firms adjust output; see Grinols (1987).

107

Trade, Income Transfers, Developing Countries, and the Core

reduced deadweight loss created by the reduction of the price of good j.
The Shapley transfers, on the other hand, do share these gains, although at
the price that country j’s own gains must be shared with others in return.
5. Discussion and Conclusion
We discussed in our earlier work how the Shapley value has the properties of being a central point in the core and of sharing equally the gains
from cooperation and thus having a non-cooperative foundation. Grinols
transfers do not share, in general, these properties-----indeed, we are notaware of a non-cooperative approach that would yield the payoffs impliedby the grand coalition with Grinols transfers. It could therefore be viewed
as surprising that Grinols transfers succeed in supporting a core allocationeven though they ignore deadweight losses. And indeed, Grinols transfers
barely make it, as they constitute, in general, the minimum transfers required to implement a core allocation: When integrating, a country loses
the profits earned in foreign markets, it gains consumer surplus on imports.
Its profit losses are its only losses. For every profit loss there is a corresponding gain in foreign consumer surplus. Those gaining can and will bewilling to pay to compensate for the lost profits. Smaller compensation
might not suffice to induce undistorted trade; larger compensation taxes
consumer gains more. Thus Grinols transfers favor consumers over firms
relative to Shapley transfers. If mark-ups are higher in developing than indeveloped countries then developing countries stand to gain relatively morein consumer surplus from the grand coalition forming than do developed
countries.6 But then Grinols transfers would be preferred to Shapley transfers by those who wish to favor developing countries since Grinols transfers do not tax these regained deadweight losses while Shapley transfers
do.7 Add to this that Grinols transfers are informationally efficient relative
to Shapley transfers since the former do not require estimates of deadweight losses or demand curves (calculations which could be both difficultand contentious in an international bargaining situation), and Grinols trans-

6. While we do not analyze tariffs or quotas, developing countries do tend to be
more protective than are developed countries, and they should therefore experiencelarger price changes and hence consumption gains (and production gains) fromtrade liberalization than developed countries.
7. However, and as was the case in our analysis of Shapley transfers, even with
Grinols transfers it is possible that payments go from low to high income countries
if the former gain and the latter lose from the grand coalition forming. We recognize that many readers might find this feature unappealing. However, in our work,
sidepayments play the sole purpose of inducing nations to cooperate, and the payments will never exceed the gains from cooperation. In other words, a country----whether poor or not-----will only be willing to be a net contributor to the financial
mechanism if it is better off at the grand coalition with transfers than at the statusquo or at any other attainable situation.

108

Carsten Kowalczyk and Tomas Sjostromfers appear preferable to our original transfer scheme, derived from theShapley value, at least by those who wish to favor developing nations.
We recognize that our approach of viewing the problem as one of cooperative game theory has many limitations including that we ignore strategic
considerations. This is unrealistic to the extent trade flows are choice variables. Nevertheless, we view the main result of this paper-----that there exists a transfer mechanism, Grinols transfers, which has attractive properties
compared to those we derived from the Shapley value-----as bringing ourinvestigation of international sidepayments as a means to helping establish
a liberal trading order a small step closer to implementation.
Appendix
Derivation of Equation (7)Substituting (6) into (3) gives initial demand for non-numeraire good j.
Substituting the resulting demands into equations (8) and (9) which, in turn,are substituted into (10) then yields

(

∑

)

1/ θ ij −1⎛βj⎞(A1) T = β ⎜ i ⎟⎝θ j ⎠j ≠i
i
Gj⎛ βi ⎞− β ⎜ j⎟
⎝θi ⎠
j ≠i

∑

(

)

1/ θ ij −1iθ ij / (θ ij −1) ⎤⎡ i θ ij / (θ ij −1)
⎛βj⎞
⎛β ⎞
⎢
⎥,
−⎜ i ⎟+ ⎢⎜ j ⎟⎥θj⎠⎝j ≠i ⎝ θ i ⎠
⎢⎣
⎥⎦

∑

i, j = 1,..., n,or) ⎡⎢ 1 1/ (θ −1) − 1 θ / (θ −1) ⎤⎥ −(ij

θ ij / θ ij −1(A2) TGi = ∑ (β j )

i
j

i

θ ij

⎢⎣ θ j

j ≠i

i
j

(
∑ (β )⎥⎦) ⎡⎢ 1 1/ (θ −1) − 1 θ / (θ −1) ⎤⎥,ji

jji θ i / θ i −1

j ≠i

j
i

j

j
i

θ ij

⎢θ i
⎣

⎥
⎦

i, j = 1,..., n.
But⎡ 1 1/ (θ ij −1) 1 θ ij / (θ ij −1) ⎤ 1 θ ij / (θ ij −1) ⎡ 1 (1−θ ij ) / (θ ij −1) ⎤ 1 θ ij / (θ ij −1)
⎢ i
⎥= i
⎢ i
− 1⎥ = i− i
θ ij − 1 ,θj⎥⎦ θ j⎢⎣ θ j⎥⎦ θ j⎢⎣ θ j[]i, j = 1,..., n.
Hence (A2) can be written as(A3)

TGi = −( ) 1−θ + β θ ( ) 1−θ ,( ) ∑( )( )∑ (β θ )
j

j ≠i

i
i θj
j

θ ij −1

i
j

i

j
j θi
i

θ ij −1jij ≠i

i, j = 1,..., n.

109

Trade, Income Transfers, Developing Countries, and the Core

But using equation (A8) in our earlier paper this can be rewritten as
TGi = −

(A4)

∑ π + ∑ π = ∑ (π − π ),
i
j

i
j

j
i

j
i

i, j = 1,..., n,

j ≠i

i≠ j

j ≠i

which is equation (7) of the text.
Proof of Proposition
Define Sji to be consumer surplus from good j in country i when country j charges only marginal cost on its sales to i. From the earlier definition of δ ji as the gains in consumer i surplus from country j reducing its
price on i to marginal cost, it follows that (Sji δ ji ) is consumer i surplus
on good j when j charges its mark-up price in country i. Coalition K is
(weakly) better off with the grand coalition and Grinols transfer than at anarbitrary alternative situation if

!

∑

(A5)

i ∈K

_

l0i +

n

∑ ∑ S + ∑ T ≥ v( K ), ∀K , K ⊆ N .
i ∈K j =1

i
j

i
G

i ∈K

Substituting
_
i
0

n

∑ T =∑ ∑ (π − π ) and v( K ) = ∑ l +∑ ∑ S − ∑ ∑ δ + ∑ ∑ π ,
i
G

i ∈K

i
j

j
i

i ∈K j ∉K

i ∈K

i
j

i ∈K j =1i
ji ∈K j ∉Ki
ji ∈K j ∉K∀K , K ⊆ N ,into this yields
_

n

(

)

_

n

i
i
i
i
j
i
i
i
(A6) ∑ l0 + ∑ ∑ S j + ∑ ∑ π j − π i ≥ ∑ l0 + ∑ ∑ S j − ∑ ∑ δ j + ∑ ∑ π j ,i ∈Ki ∈K j =1

i ∈K j ∉Ki ∈Ki ∈K j =1

i ∈K j ∉K

i ∈K j ∉K∀K , K ⊆ N ,or(A7)∑ ∑ (π − π ) ≥ ∑ ∑ (π − δ ), ∀K , K ⊆ N ,
i
j

j
i

i ∈K j ∉K

i
j

i
j

i ∈K j ∉K

or

(A8)

∑ ∑ δ ≥∑ ∑ π , ∀K , K ⊆ N ,i
ji ∈K j ∉K

ji

i ∈K j ∉K

110

Carsten Kowalczyk and Tomas Sjostrom!

which holds in this model since δ ji π ij for all i, j. It follows that coalition
K will not block the proposal to implement the grand coalition with Grinols transfers.
The Grinols transfer scheme will be said to be feasible if
0 i.e., if governments collect at least what they pay out. But
TGi
B# !"# ! !
! ! (π − π ) = 0 since ! ! π = ! ! π are both equal to total
B #
"#
"#
"#
j i

i

i j i

j

j

i

i

i j i

j

j

i j i

i

profits earned in foreign markets by all the world’s firms.
Q.E.D.

References
Grandmont, J. M. and D. McFadden. 1972. A Technical Note on Classical Gainsfrom Trade. Journal of International Economics 2: 109-125.
Grinols, E. L. 1981. An Extension of the Kemp-Wan Theorem on the Formation ofCustoms Unions. Journal of International Economics 11: 259-266.
--------- . 1987. Transfers and the Generalized Theory of Distortions and Welfare.
Economica 54: 477-491.
Kemp, M. C. and H. Y. Wan. 1976. An Elementary Proposition Concerning theFormation of Customs Unions. Journal of International Economics 6: 95-97.
Kowalczyk, C. and T. Sjöström. 1994. Bringing GATT into the Core. Economica
61: 301-367.
---------- . 2000. Trade as Transfers, GATT and the Core. Economics Letters 66: 163169.
Kowalczyk, C. and S. Skeath. 1994. Pareto Ranking Optimal Tariffs under Foreign
Monopoly. Economics Letters 45: 355-359.
Macho-Stadler, I., D. Pérez-Castrillo and C. Ponsati. 1998. Stable Multilateral
Agreements. Economica 65: 161-177.
Ohyama, M. 1972. Trade and Welfare in General Equilibrium. Keio Economic
Studies 9: 37-73.
Riezman, R. 1985. Customs Unions and the Core. Journal of International Economics 19: 355-365.
Shapley, L. S. 1971. Cores of Convex Games. International Journal of Game Theory 1: 11-26.
Vanek, J. 1965. General Equilibrium of International Discrimination. Cambridge:
Harvard University Press.

6

Endogenous Corrections of Economic
Policies under Majority Voting
Wolfgang Mayer*

1. Introduction
The economic policies of democratically governed countries reflect theconflicting economic interests of heterogeneous populations. Political pressures to adjust policies arise when at least some individuals experiencechanges in their economic interests. The most direct cause of economic interest changes are exogenous events, such as increased competitiveness offoreign economies, oil price shocks, natural catastrophes, or consumer tastechanges. Indeed, most major economic policy changes can be seen as immediate and direct responses to such exogenous events.
In addition to these major, immediate policy responses, one observes minor, but quite frequently occurring corrections of existing economic policies. The origin of existing policies can be traced back to an exogenous
event that occurred some time in the past. The need to correct policies
might arise much later and quite frequently, with no new exogenous development occurring. Although each policy correction tends to be small, thetotal impact of many corrections over a longer time period is often quite
sizable.
The specific purpose of this paper is to shed light on the time path of
economic policy adjustments when policy changes are frequent, small, andcorrective in nature rather than one-time, large, and immediate responses toexogenous events. At a more general level, the paper emphasizes the im* An earlier version of this paper circulated under the title “Endogenous Limitsof Politically Motivated Distortions”. Comments by Costas Syroupoulos, Neil
Vousden, Nancy Chau, and an anonymous referee, as well as by audiences at theWestem Economics Meetings, the Midwest International Economics Meetings,
Florida International University, and Southern Illinois University at Carbondale motivated me to completely rework the earlier paper.
111

112

Wolfgang Mayer

portance of time in the political choice of economic policies. The standard
political economy approach is essentially timeless. Given the diverse characteristics of individuals, such as factor ownership, preferences, and age,and the economy-describing parameters, such as overall factor endowments,
production technologies, world prices, and prevailing economic policies,
these individuals’ economic interests in policies are determined independent of the specific time at which they participate in the political process.
This paper, in contrast, demonstrates how peoples’ economic interests adjust over time, even though their individual characteristics and the economy’s parameters remain constant. At a given time, a person’s economic
interests in policies are closely tied to current and expected prices in factor
as well as commodity markets which, in turn, are linked to the economywide allocation of factors of production. The standard political economy
approach assumes timeless relationships between these prices, the allocation of factors, and the economy’s parameters. This paper, on the other
hand, focuses on the need for time in reallocating factors and on the resulting time-dependence of individual economic interests, as well as actual
collective policy choices. The short-run economic policy responses to exogenous changes, therefore, must be distinguished from the long-run responses, and account must be taken of frequent corrective policy adjustments in between.
The story of the policy adjustment process is a story of how losers ofpast economic policy actions might react to cut their losses. Given an
economy’s allocation of factors, an initial political choice of economic
policies reflects the relative strengths of individuals and groups whose economic interests are diverse. Over time, all participants in the political process experience changes in their economic interests because some losers ofpast policy actions shift their economic resources and political weight tothe winning side, thereby upsetting the prevailing political balance. In general, losers of political actions have some ability to react to newly adopted
policies, even though these reactions might be delayed. Provided some
adaptive reactions on the part of losers are possible, the initial winners will
be hurt. Frequent, small policy corrections by the policy-controlling winners can be seen as attempts at retaining as much as possible of graduallyeroding gains.
A large segment of the political economy literature ties the self-interestsof individuals permanently to the performance of the industry which employs their factor of production1. Factors are treated as industry specific,
and economic policies that favor a certain industry simultaneously favor its
specific factor owners. Those who gain from a policy retain these gains as
1. See, for example, the classic model of Findlay and Wellisz (1982), in which
landowners, whose resource is specific to food, and capital owners, whose resourceis specific to manufactures, lobby for protectionist trade policies.

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Endogenous Corrections of Economic Policies under Majority Voting

long as the policy remains in effect. The policy, in turn, remains in effectas long as no new exogenous event disturbs the prevailing political equilibrium.
A smaller segment of the literature adopts models in which factors are
perfectly mobile among industries2. An individual factor owner’s interests
are no longer tied to the industry which employs the factor. Instead, a factor owner’s economic interests are tied to the fate of all other individuals
who own the same factor, independent of where and how it is employed.
Economic interests of individuals and policy choices of society, however,are still permanent reactions to exogenous events.
Neither the assumption of perfect industry specificity nor the assumptionof perfect mobility between industries reflects reality well. In most realworld situations, the interests of factor owners are partially and temporarily
tied to the interests of the industries which employ them. Typically, individuals find the reallocation of factors to be costly and time consuming.
Furthermore, one observes that the cost of reallocating a given factor is not
the same for all people. Factor owners are heterogeneous and their opportunity costs of switching employment among sectors might vary greatly.
This paper introduces partial mobility of factors, which enables some, but
not all, people to escape the fate of being employed by a losing industry.
A political economy model of corrective policy adjustments requires thatfactors of production are both heterogeneous and partially mobile. Heterogeneity of factor owners generates the conflicting interests which guide theactions of players in the political game. Partial factor mobility generates
the need for frequent policy corrections. The political economy literature
has explicitly modeled factor heterogeneity, but not partial factor mobility.
The international trade literature has explicitly modeled partial factor mobility, but not heterogeneity of factor owners3. This paper develops a newmodel of partial factor mobility in which heterogeneous factor owners
make rational choices as to whether and when they will move their factor
to another sector. We employ a simple, two-sector, small, open economy
framework. Each industry employs workers as the only providers of productive factors. Different from the standard Ricardian model, however, labor is not homogeneous. One industry is assumed to require low-skill , repetitive, assembly-line work, while the other one is assumed to require
high-skill , adaptable, problem-solving work. Workers can offer these services to either industry, but their capacity to do so varies among them. They
are born with different innate abilities. Some individuals are relatively better suited for low-skill work, while others are relatively better suited for
2. This is the case in Heckscher-Ohlin type models in which workers and capitalowners compete for policies independent of the industries that employ them. For a
direct democracy model with perfectly mobile factors, see Mayer (1984).
3. Neary (1982), Mussa (1978, 1982), and Grossman (1983) have developed different approaches to deal with the issue of imperfect and partial factor mobility.

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Wolfgang Mayer

high-skill work. Given a person’s abilities, he or she will consider the two
industries’ wages and seek employment in that industry which promises
the highest present value of income.
When current and expected industry wages change, incentives arise forat least some workers to switch to the other industry. Job switching is feasible but neither costless nor instantaneous. Although a person has the ability to work in the other industry, this ability must first be converted into
marketable labor services before employment can start. The conversion ofability into marketable labor services requires learning of tasks to be performed at the new job. Learning is costly because it is time consuming.
While a person is learning a new task, he or she cannot be working at thesame time. Accordingly, job switching entails a learning period during
which income from the presently held job is diminished4. The learning period’s duration is not exogenously given, but can be chosen by potential
job switchers. In our model, people with different innate abilities vary withrespect to the optimal duration of learning periods. Consequently, a onetime disturbance results in a gradual rather than instantaneous reallocationof labor that eventually leads to a new long-run equilibrium.
This paper employs a direct democracy political process in which policy
choices are made through majority voting, and there is only one issue tobe decided on. The single issue under consideration is a production tax imposed on or subsidy paid to the firms of one of the industries. Under theusually made assumption of individuals’ single-peaked policy preferences,the median voter dictates the outcome. The median voter-determined policy
choice is made through a referendum and remains in force for one period.
At the beginning of the next period a new referendum is conducted. It provides an opportunity to either confirm or correct the previously chosen policy.
The paper sheds light on the adjustment paths of three variables: thevalue of the politically chosen production tax or subsidy, the incomes ofindividual workers in the winning industry, and the value of national income as a whole. Concerning the choice of production tax or subsidy, themedian voter will always opt for subsidization of his or her industry, butpreferences for the degree of subsidization are shown to change over time.
The ultimate long-term policy will be different from the immediate shortterm policy that had been adopted as a first response to an exogenous disturbance. The direction of the policy revision, however, crucially depends
on the ability of individuals to switch their labor service to the subsidized,
expanding industry. We explicitly assume that every person has the sameability to provide low-skill labor services, but that the ability to provide
high-skill labor services is quite unevenly distributed. If the subsidized in4. Each job switcher will be learning new tasks and performing the old job at thesame time. But different job switchers do this in different proportions.

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Endogenous Corrections of Economic Policies under Majority Voting

dustry employs low-skill, assembly-line labor services, then the politicallychosen production subsidy will decline over time. If the expanding industry employs high-skill, problem-solving labor services, then the politicallychosen production subsidy will rise over time.
The initial industry affiliation of the median voter determines which industry becomes the winning industry. Workers in the winning industry
greatly gain in the short run when a production subsidy is adopted throughthe first referendum. Over time, as the number of workers in the winningindustry rises and in the losing industry declines, the negative-sum natureof the political game inevitably lowers these initial gains of the medianvoter5. The policy corrections of future referenda cannot reverse this decline in gains; they can only ameliorate them.
Any non-zero production subsidy distorts this small, open economy andreduces its national income at world prices. The initial distortion deepens
and the loss in national income worsens over time, as more resources
move into the subsidized sector. If the initial production subsidy rate overshoots the long-run target, later policy corrections moderate that loss in income which would have come about at a constant subsidy policy. The opposite will hold when the initial production subsidy rate undershoots thelong-run target.
2. A Two-Sector Economy with Heterogeneous LaborThis section constructs a simple general equilibrium production model inwhich a one-time disturbance leads to a gradual reallocation of resources.
There is heterogeneity of resource ownership and the optimal timing forreallocating an individual’s resource is not the same for all people.
The economy under consideration is small and open, and its two competitive industries have production functions:(1)

X (t ) = L X (t ) a X , Y (t ) = LY (t ) aY .

The variable j(t) denotes output of good j = X, Y in time period t, Lj(t) indicates the number of labor efficiency units employed by industry j, and aj
is a technology parameter that expresses the amount of labor required to5. The political process of economic policy formation is a negative-sum gamefor two reasons. First, the politically decisive individual or group maximizes its
own rather than society’s welfare. The adopted policy introduces a distortion that
reduces the nation’s consumption possibilities. Second, the political process itself isresource consuming, as Tullock (1967), Bhagwati (1982), and others have emphasized; the political actions of individuals and groups use up resources but add nothing to the economy’s value of output. This paper focuses on the distortion component of the negative-sum game by pointing out that damage from the distorting policy grows over time.

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Wolfgang Mayer

produce one unit of good j. Production technologies remain constant for alltime periods under consideration.
Both industries are perfectly competitive. The corresponding zero profit
condition is:(2)

a j w j (t ) = p j (t ),where wj(t) is the wage rate paid per labor efficiency unit in industry j andpj(t) is the domestic price of good j during period t. Good Y is chosen as
the numeraire and an ad valorem production subsidy (tax), paid to (collected from) firms in industry X during period t, is denoted by s(t) > 0(< 0). In period t, the domestic price of good X in terms of good Y isstated as:
(3)

[

]

p(t ) = π 1 + s(t ) ,where π is the world price of good X . The world price is given and remains constant for the small country under consideration. The production
tax or subsidy, on the other hand, is determined through the domestic political process and might vary over time.
Labor is supplied by the country’s N people whose lifetimes are assumed to be infinite. All people have the same time preference, the common discount factor being 0 < δ < 1; and all people have perfect foresightconcerning the rational choice of future production taxes and subsidies as
determined through the political process. The latter assumption implies thatpeople, when acting as workers and voters, make their current employment
and voting decisions in correct anticipation of future economic policy
adoptions, as well as of future employment choices.
People are heterogeneous. They vary with respect to their innate abilities
to provide labor services to the two industries. Specifically, person i has
abilities:(4)[LX(i), LY(i)],where Lj(i) expresses the number of labor efficiency units individual i iscapable of supplying to industry j, provided the requisite training has been
completed. We assume that one industry employs assembly-line, low-skilllabor while the other industry employs problem-solving, high-skill labor.
The distinguishing feature of low-skill labor is that every person is equallycapable of providing it. Should industry X be the low-skill labor industry,then LX(i) is the same for all i. Conveniently, we set LX(i) = 1 in this case.
High-skill labor, on the other hand, cannot be provided equally well by all
individuals. Some people are far more talented in performing problemsolving work than others. We explicitly assume that abilities for117

Endogenous Corrections of Economic Policies under Majority Voting

work in the high-skill industry are uniformly distributed, on the interval(0, 1). Should industry Y be the high-skill labor industry, then LY is uniformly distributed with density 1 for 0 < LY < 1 and 0 elsewhere.
At the time of the disturbance each person is employed in one of thetwo industries and nobody can benefit from switching employment. Disturbance of this long-run equilibrium creates incentives for, at least, some individuals to move to the other industry. Switching employment, however,is not costless. It requires time-consuming training to fully develop a person’s innate ability for work in the new industry. A person, currently employed in industry Y and intent on switching to industry X , must sacrifice
one hour of work in industry Y for each hour of training for industry X . A
fixed number of tasks has to be learned, but the total time required to learn
these tasks is not constant; it critically depends on the number of time periods over which the learning process is stretched. Following Alchian(1959)6, we assume that total training cost is larger the fewer the numberof time periods within which all training is to be completed7. Training costis measured in terms of income lost when work in industry Y is reduced.
More precisely, we define 0c(τ )1 as the fraction of a time period
which a person must spend on training in each period when the entire
training lasts for τ periods. If training is to be completed in period τ ,worker i sacrifices

!

(5)

!

c(τ )wY (t ) LY (i )of income in period 0 < t < τ , and the present value of total training cost
becomes:

(6)

τ
⎤
⎡
γ (τ ) LY (i ) = ⎢c(τ )∑ δ t wY (t )⎥ LY (i ).
0⎦⎣

The assumption that total training cost decreases the longer the timespan for training completion implies that γ (τ ) > γ (τ + 1).
The assumption that total training cost decreases with time is quite realistic for shorter time spans, but unrealistic for very long time horizons. Accordingly, we add the restriction that lengthening the time horizon for
training lowers total training cost up to period T only. For simplicity’ssake, total training cost is assumed to become zero when training is ex6. Alchian (1959) appears to have been first in explicitly introducing time as avariable in describing the relationship between cost and output. Alchian postulates
that total cost rises at an increasing rate with the speed at which output is produced.
In our model, output is measured in terms of completed training schedules.
7. Total training time is the number of periods over which training takes place
times the amount of time spent on training during each of these periods.

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Wolfgang Mayer

tended to the full T periods; that is

γ (T ) = 0.

(7)

The implication of the above-made set of assumptions is that many individuals might make the decision to switch industry employment exactly at
the same time but that they will begin work in the new industry at very
different times. Some complete their training quicker and switch earlier
than others, resulting in a gradual rather than instantaneous reallocation of
resources after an exogenous shock. How a person chooses the time ofswitching is examined next.
2.1. The Employment Decision
The economy’s long-run equilibrium is disturbed at the beginning oftime period 0. The disturbance might, for example, be the result of a
newly legislated production subsidy paid to firms in industry X . The workers of industry X receive a higher wage and industry Y workers assess
their incentives to switch industry employment. The latter consider current
wages, as well as wages anticipated in future periods, whereby their foresight is assumed to be perfect. Based on equations (2) and (3), period t
wage rates paid by the respective industries are:[]w X (t ) = π 1 + s(t ) a X and wY (t ) = 1 aY .

(8)

Person i, currently employed in industry Y and providing LY(i) labor efficiency units, will receive a present value income of∞[ L (i ) a ]∑ δ ,

(9)

Y

Y

t

0

if he or she remained in industry Y . Alternatively, if the individual
switched to industry X , with work starting at the beginning of period τ ,the person first would train for τ periods and remain partly employed byindustry Y before performing full-time work in industry X from period τ
on. Accounting for training cost during the first τ periods, as expressed byequation (6), the present value income of individual i, when switchingfrom industry Y to X at time τ , is:

(l0)

⎡ τ

⎧∞

⎤

⎫

[ L (i ) a ]⎢∑ δ − a γ (τ )⎥ + [πL (i ) a ]⎨∑ [1 + s(t )]δ ⎬,
Y

Y

⎣ 0

t

Y

⎦

X

X

⎩τ

t

⎭

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Endogenous Corrections of Economic Policies under Majority Voting

where the first term measures income from old, part-time work in industry
Y up to period τ and the second term indicates income from the new, industry X job for all subsequent periods. Worker i has an incentive toswitch employment in period τ if two conditions are satisfied. First, thevalue of the expression in equation (10) must exceed that of the expressionin equation (9) for at least some τ < T ; that is, there must be a time whenswitching is better than not switching. Second, the difference between
these two expressions, which states the net benefit from switching, must be
at least as high for period τ as for any other time period; that is, period τ
must be the optimal switching period.
The net benefit from switching in period τ , denoted as B (i, τ ) and obtained by subtracting equation (9) from (10), can be stated as:

(11)

∞
∞
⎧⎪
⎡
⎤ ⎫⎪
B(i , τ ) = L X (i ) aY ⎨ Aπ
1 + s(t ) δ t − e(i )⎢aY γ (τ ) + δ t ⎥ ⎬,
⎪⎩
τ
τ
⎣
⎦ ⎪⎭

{

}

∑[

]

∑

where A = aY/aX, and e(i) = LY(i)/LX(i) indicates the ability bias of person
i for work in industry Y . The higher the value of e(i), the better suited aperson is for work in industry Y . If, for example, industry Y were the high-skill industry, then a high value of e(i) would mean that person i is relatively capable of performing high-skill tasks. Equation (11) reveals that,ceteris paribus, a person’s net benefit from leaving industry Y and switching to X is less the greater his ability bias for work in industry Y .
The net benefit function B (i, τ ) is assumed to be strictly concave withrespect to switching periods for all τ < T ; that is,∆B(i , τ ) − ∆B(i , τ − 1) < 0,

(12)

(13)

∆B(i , τ ) = B(i , τ + 1) − B(i , τ )

{

} {

[

]

where

[

]}

= L X (i ) aY δ τ − Aπ 1 + s(τ ) + e(i ) 1 − δ −τ aY ∆γ (τ ) ,measures the change in net benefit as switching is postponed by one period.
In interpreting equation (13), it should be noted that the present value of
total training cost declines up to period T , making ∆γ (τ ) = [γ (τ + 1) −γ (τ )] < 0 for any time before T . Person i, born with ability bias e(i),finds it optimal to switch industry employment in period τ if
(14)

∆B(i , τ − 1) > 0 and ∆B(i , τ ) < 0,that is, if the benefit from switching cannot be increased by entering industry X either earlier or later than period τ . All individuals whose ability
bias value satisfies equation (14) will definitely switch in period τ . In ad-

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Wolfgang Mayer

dition to those definite switchers, there are marginal switchers in period τ ,whose ability bias is denoted by e(τ ). The marginal switcher is indifferent
between switching in periods τ and (τ + l), as ∆B (τ , τ ) = 0. Using equation (13), the identity of the marginal switcher in period τ is determined
by:
(15)

{ [

]} [1 − δ a ∆γ (τ )].

e(τ ) = Aπ 1 + s(τ )−τY

The Appendix shows that strict concavity of B (i, τ ) implies that themarginal switcher’s ability bias is lower in period τ than period τ + 1, forall relevant switching periods. Accordingly, the initial exogenous disturbance to the economy results in a gradual reallocation of labor that follows
a well-defined pattern of sequential job switching. The time period inwhich individuals switch jobs to industry X is inversely related to theirability bias for work in industry Y ; the less a person’s relative ability forwork in industry Y , the faster he or she will switch employment to industry X . Accordingly, the order of marginal switchers, from the period of the
disturbance in the very short run until the adjustment is completed in thelong run, can be described by:(16)e(0) < e(1) < e(2) <.... < e(T ).

The identity of a given period’s marginal switcher, and therefore the period level of industry X employment and production, can be affected
through a change in that period’s production subsidy, s(τ ). As one can see
from equation (15), an increase in the value of the subsidy rate, s(τ ),raises the value of e(τ ) and thereby expands the number of people who will join industry X in period τ .
2.2. Employment, Industry Output, and National Income
The economy is populated by N people. It was shown above that thecritical variable for determining the allocation of workers between industries at a given time is the marginal job switcher’s ability bias for that period, measured by e(τ ). In order to determine total industry production, we
furthermore must specify whether a given industry employs high-skill or
low-skill labor. In the low-skill industry, the identity of individual employees is irrelevant, as all people are able to provide exactly one unit of efficiency labor. In the high-skill industry, on the other hand, the identity of
individual employees is of great importance for determining output; themost capable people are hired first and industry expansion is possible only
by adding less productive workers.
Here we are going to explicitly develop the case in which industry X
employs low-skill labor. Hence, LX(i) = l, while LY(i) is uniformly distrib-

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Endogenous Corrections of Economic Policies under Majority Voting

uted on the interval (0, 1). In time period τ , all people with ability biase(i) = LY(i)e(τ ) work in industry Y ; the remaining population is employed in industry X . Denoting the number of people employed in industry
j = X, Y by Nj, their respective period τ employment levels are:

"

(17)

N X (τ ) = e(τ ) N[]

N Y (τ ) = 1 − e(τ ) N ,andwhere 0 < e(τ ) < 1.
To determine industry output, we make use of the production functionsof equation (1). Since each employee of the low-skill industry X provides
exactly one efficiency unit of labor, such that LX = NX, period τ output ofindustry X is:
X (τ ) = e(τ ) N a X .

(18)

!

!

In industry Y , each individual with ability bias equal to or greater thane(τ ) provides e(τ )e(i)1 units of efficiency labor. Since LY is uniformly distributed, and LY(i) = e(i), industry Y produces:

(19)

[

]

Y (τ ) = 1 − e(τ ) N [2aY ].
2

The industry output equations of (18) and (19) must be amended whengood X is produced by a high-skill and good Y by a low-skill work force.
In this case, ownership of labor efficiency units for work in industry X,
LX(i), is uniformly distributed on the interval (0, 1), and LY(i) = 1 for each
person. Noting that e(i) = 1/LX(i) in this case, the two industries’ output
equations become:
(18’)
(19’)

[

]

X (τ ) = 1 − 1 e(τ ) N [2a X ]
2

[

and

]

Y (τ ) = N aY e(τ ) .

No matter which industry employs high-skill labor, the marginal
switcher’s ability bias, e(τ ), rises over time as more workers move into industry X . During this adjustment process, the amount of good Y (τ ) thatmust be sacrificed to gain an extra unit of X (τ ) is e(τ )/A since:(20)[e(τ ) A][dX (τ ) de(τ )] + [dY (τ ) de(τ )] = 0.

Clearly, the rate at which good Y is sacrificed for good X rises over time
as people with relatively high skills for work in industry Y make the employment switch later than people with relatively low skills.

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Wolfgang Mayer

3. The Political Choice of Production Taxes and Subsidies
For this small, open economy, the world price of good X, π, is given
and beyond control of the political process. The country’s people, however,are able to vote on a production subsidy for period t, s(t) > 0, or tax, s(t)< 0, which affects the domestic price faced by firms, p(t). Political choices
are made through majority voting, and all individuals are assumed to participate in the voting. The initial vote takes place at the beginning of period zero. For convenience sake, it is assumed that, prior to this initial vote,economic policies were chosen through autocratic methods by a benevolent
dictator; the resulting social welfare-maximizing policy, therefore, wass = 0. It follows from equation (15), interpreted for a long-run equilibrium
in which ∆γ (.) = 0, that the pre-voting marginal worker’s ability bias wasgiven by e = A π. Whatever the initial referendum’s outcome, the newly
established democratic process permits follow-up referenda at the beginning of each subsequent period. Each time, voters can either confirm or
correct their earlier made choice of a production policy for industry X .
At each referendum, person i knows which production policy is most
preferred by him or her. The person would impose this policy on the restof the economy if politically empowered to do so. This most preferred production policy maximizes the present value of person i’s spendable income.
Spendable income is gross wage income adjusted for redistributed tax
revenues in the case of production taxes and income taxes collected for thefinancing of subsidy payments. Worker i, employed in industry j, receives
gross wage income Lj(i)wj(t) during period t, where wj(t) was defined inequation (8).
If the government pays out production subsidies, it finances themthrough a factor income tax that is assumed to be unbiased. The tax is unbiased in the sense that it does not affect any person’s income share; each
person’s net factor income share, evaluated after collecting income taxes tofinance the subsidy, is the same as his or her gross factor income share,calculated on the basis of factor income before the collection of income
taxes8. This unbiasedness feature of the income tax is assumed to be constitutionally guaranteed; and it is not subject to voting in each of the referenda. In case the government imposes production taxes, the redistributionof the collected tax revenues is also unbiased.
At the initial vote, it is industry X which is assumed to employ more
8. This assumption, frequently made about trade taxes in the political economy
of international trade literature, serves the purpose of separating the political choiceof a production tax or subsidy from the choice of an income transfer or tax system.
For an application in the context of trade taxes, see Mayer (1984). Note that in ourmodel of temporarily part-time working job-switchers, the base for collecting income tax is income a person is capable of,rather than actually, producing. Correspondingly, the variables X , Y and I express potential rather than actual values

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Endogenous Corrections of Economic Policies under Majority Voting

than half of the labor force. The initial referendum’s median voter, therefore, comes from industry X . Person i, of industry X , receives spendable
income:}{ [{] [ p(t ) X (t ) + Y (t )]},I (i , t ) = φ X (i , t ) I (t ) = L X (i )π a X 1 + s(t )Y (t )

(21)

!

during period t, where X(i, t) = [LX(i)wX(t)]/[p(t)X (t) + Y (t)]} measures
the ith person’s gross factor income share and I (t) = [π X (t) + Y (t)]} expresses potential national income at world prices. Note that, in deriving
equation (2l), we made use of equation (3).
The initial vote is taken at the beginning of period zero. The ith voter’s
most preferred production subsidy, denoted by s *i(0), is that value of s(0)which maximizes his (her) present value of net income9.
∞∑ I (i , t )δ .

(22)

t

0

Accounting for equation (2l), the optimization problem can be reduced to:∞∑ δ [s(t )Y (t )] [ p(t ) X (t ) + Y (t )].
( )

max
i

(23)

s 0

t

0

It is immediately clear from equation (23) that the ith voter’s optimal
choice of s(0) is the same for all workers who are already employed in industry X . Importantly, the policy choice is independent of the innate abilities of the industry X worker in general and the politically decisive medianworker in particular. The median voter’s optimal policy choice, madethrough a referendum at the beginning of period 0, is indicated by s *(0).
The first-order conditions of the above-stated optimization problem imply that:{ []} {[πe(0)][e(0) X (0) A + Y (0)][dX (0) de(0)]} ,(24)s (0 ) = Y (0 ) πX (0 ) + Y (0 )*where we substituted equation (20), as well as de(0)/ds(0)=e(0)/[1+s(0)], derived from equation (15), and where all variables on the right-hand side
9. In doing so, the political choices of future production policies are correctly
anticipated.

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Wolfgang Mayer

are evaluated at s *(0). Depending on the type of skills employed by industry X , we furthermore have:(25)⎧⎪ X (0) e(0) when industry X is low − skill ⎫⎪dX (0) de(0) = ⎨⎬.
2⎪⎩ AY (0) e(0) when industry X is high − skill.⎪⎭

The most obvious conclusion to be drawn from equation (24) is that all
workers of industry X , including the median voter, choose a production
subsidy, s * > 0, rather than a tax, as their most preferred policy; all termson the right-hand side of equation (24) must be positive.
The median voter’s choice of a production subsidy, s *(0) > 0, creates a
distortion, evidenced by a decline in national income at world prices, I (t).
To show this decline, we first recall that, prior to the initial vote, the marginal job switcher’s ability bias was e. Enticed by the production subsidy,
the least-efficient workers of industry Y immediately engage in extensive
training and switch to industry X in period 0 already. As a result, the marginal switcher’s ability bias rises to e(0) > e. This short-term effect of thesubsidy lowers national income at world prices right away; but the reallocation of labor continues over time, further raising the ability bias of themarginal job switcher and further lowering national income.
The relationship between national income at world prices and the marginal switcher’s ability bias can be seen by differentiating I (t) = [π X (t)+ Y (t)] with respect to e(t) and solving for{ []}{dX (t ) de(t )} < 0 for all e(t ) > e = πA.

(26) dI (t ) de(t ) = π − e(t ) A

The referendum choice of a production subsidy at the beginning of period 0 unleashes adjustments that are felt long after period 0. If the
adopted production subsidy s *(0) were to remain constant for all future periods, more workers, with increasingly higher ability bias for work in industry Y , would move from Y to X . The adjustment process is completed
in period T , when all workers who have any kind of incentive to switch
have completed their training10. During this adjustment process, both thenation as a whole and the winners in the first referendum, the politicalcontrol-exerting industry X workers, become worse off. The gradual decline in the entire nation’s well-being follows from equation (26) since e(t)rises over time. The decline in spendable income of industry X workers,!

10. Nobody has an incentive to stretch out training beyond period T since∆ γ (t) = 0 for t
T . It follows from equation (15) that in long-run equilibrium
the ability bias of the marginal switcher is e(T ) = A π [l + s(T )].

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Endogenous Corrections of Economic Policies under Majority Voting

on the other hand, can be seen from evaluating I (i, t) in equation (22).
With e(t) rising over time, Y (t) must decline, while national income at domestic prices, [p(t)X (t) + Y (t)], must rise. The latter follows from

[

[

]

][

]

d p(t ) X (t ) + Y (t ) de(t ) = δ − t aY ∆γ (t ) dY (t ) de(t ) > 0,(27)

where we made use of equations (20) and (15) and we recall that∆γ (t) < 0. Hence, the advantage for industry X workers of exerting political control diminishes over time.
This gradual decline in period income for the politically influential median voter, evaluated at a constant subsidy rate, raises the question ofwhether the median voter will try to revise the subsidy rate at the next referendum, at the beginning of period 1. In answering this question, we firstnote that the median voter of the follow-up referendum remains a worker
who was already employed by industry X before the first referendum.
" t Hisobjective is to choose that value of s(1) which maximizes 1 δ I (i t ),again correctly anticipating future optimal subsidy rate choices of s *(2),s *(3), etc. Analogous to equation (24), the first-order conditions imply that:

!

{ [

!

]} {[πe(1)][e(1) X (1) A + Y (1)][dX (1) de(1)]} ,(24’) s (1) = Y (1) πX (1) + Y (1)*where all variables on the right-hand side are evaluated at s *(1).
In order to see if and how the median voter adjusts his or her production
subsidy choice, we examine whether the right-hand side expression ofequation (24’), evaluated at s *(0) (rather than s *(1)), is larger, the same as,or smaller than the right-hand side expression of equation (24), also evaluated at s *(0). If the former exceeds the latter, then s *(1) > s *(0); if the former falls short ofthe latter, then s *(1) < s *(0). Going beyond the first two
periods, we make this comparison for all periods 0
t < T in order to establish whether subsidy rates rise or decline over time until the adjustment
process is completed at time T . With this mind, we examine how

!

(28)

{Y (t )[πX (t ) + Y (t )]} {[πe(t )][e(t ) X (t ) A + Y (t )][dX (t ) de(t )]},

evaluated at s *(t), changes over time as e(t) rises.
The time path of production subsidies, chosen by the median voter, iscrucially dependent on the skill-type of workers in the policy-controllingindustry X . It will be shown next that it makes a great deal of difference

126

Wolfgang Mayer

whether industry X is a low-skill or high-skill industry. If it is a low-skill
industry, every new worker who leaves industry Y provides exactly thesame additional labor input to industry X . If it is a high-skill industry,
early job switchers add more labor efficiency units to industry X than late
job switchers and expansion of industry X over time attracts workers withincreasingly lower productivity.
When industry X is low skill, equation (28) reduces to:(28’){Y (t )[πX (t ) + Y (t )]} {[πX (t )][e(t ) X (t ) A + Y (t )]} ,after substituting dX (t)/de(t) = X (t)/e(t) from equation (18). Over time, as
e(t) rises, both terms in the numerator decline, while both terms in the denominator rise. Accordingly, the politically chosen production subsidy
must decline over time when workers gradually move from the high- to thelow-skill industry. The initially chosen production subsidy overshoots theultimate long-run choice, and the distortion becomes less than it would be
at a constant subsidy rate.
When industry X is high skill, equation (28) reduces to:(28”){e(t ) [πA]}[πX (t ) + Y (t )] [e(t ) X (t ) A + Y (t )] ,where we substituted dX (t)/de(t) = AY (t)/e(t)2 from equation (18). Again
it is the case that the value of the denominator rises and the second braced
term of the numerator declines as e(t) increases. These downward pulling
forces, however, are more than offset by an increase in the term e(t)/A, as
shown in the Appendix. Accordingly, the politically chosen production
subsidy for a high-skill industry increases over time when more workers
move from the declining low-skill to the expanding high-skill industry.
The initially chosen production subsidy undershoots the ultimate, long-run
production subsidy and the distortion becomes more severe than it would
have been at a constant subsidy rate.
4. Concluding Remarks
This paper formulated a simple, general equilibrium production modelwith partial factor mobility in which factor-owning voters decide on a production tax or subsidy through majority voting. The median voter’s policy
choice changes over time in response to labor becoming increasingly mobile. In the short run, when little labor reallocation is feasible, the winnersof the political game can grab huge benefits by imposing a distorting sub-

127

Endogenous Corrections of Economic Policies under Majority Voting

sidy. As some labor slowly moves to the winning sector, the impact of the
distortion deepens and both national income and well-being of the winners
decline. The winners again and again correct past policies to retain asmuch as possible of their gains. When the winning industry is made up ofpeople whose skills are easily acquired, the winners must cut back on thesubsidy over time. When the winning industry is made up of people whoseskills are increasingly difficult to find, the response is to raise the subsidy11.
This model formulates a very specific type of resource reallocation,
namely retraining of existing resources. Alternative models also can bringout the feature that factor owners react to current policies and thereby set
the stage for the choice of different future policies. An alternative model
might emphasize that resources have a finite lifetime and that, over time,
old workers and old capital are replaced by new workers and new capital.
New generations of factors are fully mobile when making employment decisions, whereas old generations of factors have become sector specific. In
such a political economy model, the median voter of different referenda
comes from different generations. The basic issue to be resolved throughthe political process, namely how policies are corrected over time as resource use adapts to prevailing policies, remains the same, however.
A third type of model might consider resource reallocation not justwithin a country but also between countries. The losers of a political policy choice might leave the country and thereby limit the gains to the winners even more. This is most likely when resources are owned in the formof pure human capital. Again, such emigration tends to be gradual and thewinners must react to it by adjusting their policies.

Appendix A. The Marginal Switcher’s Ability Bias Over TimeThe marginal switcher of period τ , identified as i = τ , is indifferent between switching in period τ + 1 and τ , such that ∆B (τ , τ ) = 0. Combined with the strict concavity property of the net benefit function, as
stated in equation (12), this implies that:

{

[

]}

τ −1
− τ +1(Al) ∆B(τ ,τ − 1) = [ LX (i ) aY ]δ − Aπ [1 + s(τ − 1)] + e(τ ) 1 − δ aγ ∆γ (τ − 1) > 0.

Use of equation (15) for e(τ −1) and substitution of e(τ −1) in (A1) implies that e(τ ) > e(τ −1).
11. In neither case can the correction of the subsidy reverse the decline of thewinners’ income over time, as can be seen from differentiating equation 2l with respect to e(t), after substitution of the optimal subsidy rate.

128

Wolfgang Mayer

B. Adjustment of the Expression in Equation (28”) Over Time
Differentiating equation (28”) with respect to e(t) yields:

[

]

⎫⎪
s(t ) ⎧⎪ Y (t ) 1 − πA e(t )e(t ) X (t )
−
⎨1 −
⎬,
e(t ) ⎪
+
+
π
X
t
Y
t
e
t
X
t
AY
t
(
)
(
)
(
)
(
)
(
)
⎪⎭
⎩

(A2)

[

] [

]

where we made use of equations (18’), (19’), (20), and (26) and we notethat the value of the expression in equation (28”) equals s(t). The sign of(A2) is the same as the sign of the terms inside the brace which, in turn,has the sign of(A3)[πX (t ) + Y (t )] − [e(t ) X (t ) A + Y (t )] + [πA e(t )][e(t ) X (t ) A + Y (t )] =[πA e(t )][e(t ) X (t ) A + Y (t )][s(t ) − e(t ) (πA) + 1].

Substituting for e(t)/(π A) from equation (15) and noting that ∆γ (t) < 0,
one can seethat the sign of (A3) is always positive. Hence, the expressionof (28”) rises over time.

References
Alchian, A. A. 1959. Costs and Outputs. In The Allocation of Economic Resources,
eds. M. Abramovitz et. al. Stanford: Stanford University Press: 23-40.
Bhagwati, J. N. 1982. Directly Unproductive, Profit-Seeking (DUP) Activities.
Journal of Political Economy 90: 263-290.
Findlay, R. and S. Wellisz. 1982. Endogenous Tariffs, the Political Economy ofTrade Restrictions, and Welfare. In Import Competition and Response, ed. J. N.
Bhagwati. Chicago: University of Chicago Press: 223-234.
Grossman, G. M. 1983. Partially Mobile Capital: A General Approach to TwoSector Trade Theory. Journal of International Economics 15: 1-17.
Mayer, W. 1984. Endogenous Tariff Formation. American Economic Review 74:
970-985.
Mussa, M. 1978. Dynamic Adjustment in the Heckscher-Ohlin-Samuelson Model.
Journal of Political Economy 86: 775-791.
--------- . 1982. Government Policy and the Adjustment Process. In Import Competition and Response, ed. J. N. Bhagwati. Chicago: University of Chicago Press:
73-120.
Neary, J. P. 1982. Intersectoral Capital Mobility, Wage Stickiness, and the Case for
Adjustment Assistance. In Import Competition and Response, ed. J. N. Bhagwati.
Chicago: University of Chicago Press: 39-69.
Tullock, G. 1967. The Welfare Cost of Tariffs, Monopolies and Theft. Western
Economic Journal 5: 224-232.

7

Lobbying for Tariff Protection and
Allocation of Entrepreneurial
Resources
Arye Hillman, Ngo Van Long, and Antoine Soubeyran*

1. Introduction
According to the conventional analysis (see, for example, Todd Sandler,
1992) of the roles of pressure groups in policy formulation, one can expect
that, under representative democracy, “the small exploits the large”. This isbecause under institutions of representative democracy, government officials and political parties have needs that can be better satisfied by cohesive coalitions, because, compared with “diffuse” coalitions, these are lessprone to defection and free-riding. Olson (1965) argued that small groupsize is advantageous in influencing policies. An implication of this is thatthe degree of concentration of an industry should be positively correlatedwith the extent of trade protection it receives. Empirical studies have however failed to give conclusive support for this hypothesis1. (See the surveys
by Baldwin (1984), Hillman (1989, chapter 11), and Potters and Sloof(1996)).
Recently, Hillman et al. (2001) considered the theoretical foundations
for the source of the above-mentioned empirical ambiguities. They reviewed the literature and developed a model of lobbying in which entre* We would like to thank Professor Sajal Lahiri for many helpful comments andsuggestions.
1. Potters and Sloof (1996, pp.417-418) summarize the diversity of the extensive
empirical evidence as follows: “Most scholars indeed find an increased scope forpolitical influence with higher degrees of concentration, but there are many thatfind no effect or even a negative effect. Equally ambiguous are the results of theuse of numbers for the free rider effect. A large number of participants to collective action is usually hypothesized to increase the free riding problem. Sometimes
indeed a negative effect of numbers on influence is reported. More often, however,a positive effect is found. Hence there appears to be relatively little direct empiricalsupport for the Olson (1965) influential theoretical study on collective action.”
129

130

Arye Hillman, Ngo Van Long, and Antoine Soubeyranpreneurs must allocate their limited resources (such as time) between political activities and internal control activities. In their model, domestic oligopolists supply their output for the domestic market, and lobby for quota
protection against imports. They assumed that the quota is binding, andtherefore in their model it is irrelevant whether foreign firms are oligopolists or perfectly competitive. The purpose of the present paper is to extend
their model to the case where lobbying results in tariff protection rather
than import quota. It is a well-known result that there is a fundamental non-equivalence between tariff and quota protections when domestic firms areoligopolists (see Vousden (1990)). Furthermore, when foreign firms arealso oligopolists, then it would seem that, unlike the quota case, the ratioof domestic firms to foreign firms becomes a key parameter that influences
the equilibrium amounts of lobbying.
Lobbying by individual firms for tariff protection is an instance of private contribution to a public good. If the contributions by firms are purely
monetary, then the cost of contributions is only an income loss, and insuch a situation, there seems to exist a parallel between a model of lobbying by firms and the familiar model where consumers voluntarily contribute for the provision of a public good (see Cornes and Sandler (1996)).
Given that the public good is a normal good, when any given consumer increases his or her Nash contribution, the substitution and income effects on
the contribution decisions of other consumers are in opposite directions.
Therefore a larger contribution by one consumer needs not decrease thecontribution of other consumers. An increase in group size (by adding newprospective contributors to the public good) therefore may result in an increase or decrease in total contribution. Furthermore, the total contribution
by all individuals to provision of a public good is independent of the distribution of income among those consumers who are not at a corner solution (Warr (1983), Kemp (1984), Bergstrom, Bloom and Varian (1986)).
Hillman (1991), and Hillman et al. (2001), model lobbying by owners offirms who allocate time between the privately beneficial activity of monitoring internal production activities, and lobbying that yields the publicgood benefit of increased protection for the entire industry. Firm owners
have different comparative advantages in these activities. In Hillman(1991), the domestic industry consists of price-taking firms in a competitive world market. The world price of import-competing output is exogenously given, and the domestic price is determined by the given world
price plus the tariff level obtained as a consequence of lobbying efforts.
The strategic interdependence among firms is thus only with respect tocontributions to influence policy, and not with respect to rivalry in the
product market. This permits the industry seeking protection to be placed
within the broader context of a competitive small-country model of international trade.
In Hillman et al. (2001), domestic firms are oligopolists. They are heterogeneous in terms of costs and lobbying ability (see also Long andSoubeyran (1996)). The instrument of protection is an import quota that is

131

Lobbying for Tariff Protection

endogenously responsive to the total amount of resources contributed bydomestic firms to influencing policy. The amount of resources that an oligopolist devotes to lobbying influences the cost structure of the oligopoly.
In their model, it is assumed that either each firm faces a resource constraint, or each firm faces an increasing schedule of cost of funds that are
to be allocated between political activities and internal cost-reducing activities. Because of these factors, as well as the oligopolistic market structure
and the endogeneous determination of domestic price, contributions byfirms to lobbying no longer have the characteristics of contributions to a“pure” public good. The industry equilibrium is therefore dependent on thecharacteristics of the lobbying technology and the domestic demand function. Hillman et al. (2001) asked the following questions i What are theproperties of the equilibrium allocations of resources between privately
profitable monitoring and collectively beneficial lobbying activities? Can
the ranking of firms’ profitability be reversed by the introduction of lobbying possibilities? And most basically
Does the model lend support tothe conventional wisdom that one should expect a positive correlation between the degree of concentration of an industry and its ability obtain protection?
In the present model of lobbying for tariff (rather than quota) protection,
we ask the same questions. The results turn out to be very similar, though
not identical to those obtained by Hillman et al. (2001). For the case of cooperative lobbying, we in fact obtain stronger results than the corresponding ones in Hillman et al. (2001).
Section 2 presents the model. We consider the outcomes when lobbying
by firms is non-cooperative and cooperative in Sections 3 and 4 respectively. The final section offers some concluding remarks.
Before proceeding with the model, it is important to note that ourendogenous-policy specification, which is in the same vein as Hillman et al.
(2001), is quite general: it does not presuppose any one particular mechanism which translates lobbying inputs into endogenous policy outcomes. It
is assumed that an increase in the resources available to the industry to influence policy enhances the lobbying effectiveness. The model is thus consistent with (a) an underlying political-support function of an incumbent
government (for example Hillman (1982)) or (b) influence over candidates’
trade policy platforms in the context of political competition (Hillman and
Ursprung (1988), Mayer (1998)). With the notable exception of Hillman etal. (2001), in neither type of specification in the literature do we find an
investigation of the collective-action incentives associated with industry
concentration with which we are concerned2. As remarked by Hillman et al.
(2001),“in the micro-foundations for political support proposed by Grossman
and Helpman (1994), either an industry has been successful in perfectly in-

!

#

"

2. The issue is also not addressed in the surveys by Magee (1984) and Rodrik(1995).

132

Arye Hillman, Ngo Van Long, and Antoine Soubeyran

ternalizing collective action problems to permit collectively optimal political behavior, or otherwise the industry is not at all politically active. Hence,in Grossman-Helpman, the issue of the market structure of the industry,
and the consequences for collective action in responding to the policy
maker’s readiness to “sell protection”, do not at all arise. In models wheretrade policy is endogenously determined as the equilibrium outcome of political competition (as in Hillman-Ursprung (1988)), market structure implicitly affects the competing candidates’ policy platforms, but in a rather
simple way because of the homogeneity of firms; the political competition
models can in principle address the issue of the relation between concentration and effectiveness of policy influence, but only in the sense of measurement of industry concentration in terms of the number of identical firms
composing the industry.”
2. The Model
We consider a “home-market model” with n oligopolistic firms producing a homogenous good. The first k firms are domestic firms and the remaining n − k = k ! firms are foreign firms. Let K and K ! be the index
sets of domestic and foreign firms respectively: K = {1, 2, ..., k} andK ! = {k+1, ..., k+k !}. We denote their outputs by qi, i
K , and qf !,!
f K . We define aggregate output of the domestic firms, and that of theforeign firms, byQ=
qi , Q * =
qf .

"

"

∑
i ∈K

∑

f ∈K *

Both Q and Q ! are sold in a single market: that of the home country. The
inverse demand function is P = P (Z ), where Z = Q + Q !, with P ′< 0.
The marginal cost of firm i is ci. We assume that ci is independent of qi,
but is dependent on mi, the amount of resources spent on internal costreducing activities (such as monitoring or R&D). We assume thatci(0) = c > 0 and ci′(mi) < 0. Domestic firm i has a fixed amount hi of resources, of which mi is used in cost-reducing activities and ai = hi − mi isused for lobbying. (Alternatively, one could consider the case where theamount hi can be chosen, but the firm must incur a cost Ω(hi)0 to obtain hi, and Ω′, the marginal cost of obtaining hi, is an increasing functionof hi; the results of this paper apply to this case, with only minor modifica-!

3. Note that if the resources are funds rather than entrepreneurial time, then the
fixity of hi or the increasingness of Ω(hi) imply that there is some sort of capital
market imperfection in the background. It is well known that capital markets may
be ridden by moral hazard and adverse selection problems. In the finance literature,
many authors have suggested that credit rationing is a response to asymmetric information, and rising marginal cost of loans is a reflection of firm-specific risks,
which make the market consider the I.O.U. s issued by the firm as a special asset
without perfect substitutes.(See Milne 1975, Hellwig 1989, and Bester and Hellwig
1987.)

133

Lobbying for Tariff Protection

tions3.)
The time allocation formulation does reflect an important feature of realworld lobbying. As Hillman et al. argued,“While a great deal of lobbying activities are undertaken by hired professional lobbyists, the importance of entrepreneurial time in lobbying andin public relation activities is also well recognized in the business world.
The frequent public appearances of well-known individuals such as Lee
Ioccoca and Bill Gates are not without opportunity costs in terms of internal controls. In Canada, when chief executive officers are chosen, an important criterion is their connection with Ottawa.”
Unlike Hillman et al., in the present model, we assume that firms lobby
in order to convince the government to impose a tariff rate t on the imported of good. We postulate that t is an increasing function of aggregate
lobbying effort, Ai #K ai and that there is diminishing returns to lobbying:$!

t′(A) > 0, t′
′
(A)

! 0.

We envisage a two-stage game. In Stage 1, the ai’s are chosen, either
cooperatively or non-cooperatively, and this determines both the tariff ratet, and the amount mi = hi − ai
0 which is spent on internal costreducing activities. In Stage 2, given t, domestic firms choose noncooperatively their output levels, and so do foreign firms. (This is in sharp
contrast with Hillman et al. (2001), where the behavior of the foreign firms
is not modelled.) As usual, we use the backward solution method, andsolve the game in Stage 2 first. It is a simple Cournot game, with heterogenous firms.
Firm i’s unit cost is ci(mi) = ci(hi − ai)≡ i(ai) which we denote by i forshort. Since ci′< 0, i′(ai) > 0. This indicates that if the firm allocates moreresources to lobbying activities, then less cost reduction will be achieved.
Firm i K takes as given the tariff rate t and the total output of all otherfirms which we denote by Z -i. It chooses qi to maximize profit

"

#

!

!

!

!

π i = P (Z -i + qi)qi − iqi.

(1)
The first order condition is(2)!

(Z -i + qi) + P (Z -i + qi) = i.
qiP ′The second order condition is
(3)

!

qiP ′
′
+ 2P ′ 0.

Similarly, for foreign firm f ∈ K *, we have

!

qfP ′
(Z -f + qf) + P (Z-f + qf) = cf + t(A)≡ f (A).

134

Arye Hillman, Ngo Van Long, and Antoine Soubeyran

Summing the first order conditions for all firms yields(4)

ZP ′( Z ) + nP( Z ) = C ≡ k *t ( A) +∑ θ ( a ) + ∑ c ≡ C.
ii

ff ∈K *i ∈K

It follows from equation (4) that industry output Z is a function of thesum of unit costs, C , which depends on the whole vector a = (a1, ..., ak)
and on A, which is the sum of the elements of vector a. Let us denote theleft-hand side of (4) is assumed to be decreasing in Z . This condition may
be expressed as(5)

E < n + 1.

where E is the elasticity of the slope of the demand curve. Condition (5) is
one of the usual stability conditions of a Cournot equilibrium, see Dixit(1986). From equation (4) we obtain the equilibrium output Z as a function of the ai(6)

k *t ′( A) + θ i′
∂Z
=
< 0.
∂ai [ − P ′] [ E − n − 1]

As indicated by equation (6), lobbying by firm i has two effects on
equilibrium industry output. An increase in ai will increase the tariff rate t,thus reducing the outputs of foreign oligopolists. In addition, an increase inai means that, for a given hi, less resources will be available for costreducing activities in firm i, hence its production cost will rise, reducing
its equilibrium output. Note that while t depends only on the sum of theai’s, the variable C depends on the whole vector a = (a1, ..., ak) and notjust on the sum of the ai’s. It follows that the model of Bergstrom, Blumeand Varian (1986), which postulates that for each agent i, only ai and thesum of the contributions of other agents matter, does not apply to ourmore complex model.
The equilibrium output of firm i ∈ K is

(7)

qi =

P[ Z (a )] − θ i (ai )[ − P ′],and its equilibrium profit is(8)

π i = { P − θ i } qi = [ − P ′] qi2 =2
1
P −θi .
[ − P ′]

[

]

135

Lobbying for Tariff Protection

Similarly, for the foreign firms f ∈ K !,

(9)

qf =

P[ Z (a )] − c f − t ( A)

[ − P ′]≡P[ Z (a )] − θ f,[ − P ′]

and

(10)

{

π f = P −θ f

} q = [− P ′] q = [−1P ′] [ P − θ ] .
2

2
f

f

f

These expressions will be useful in the analysis that follows.
3. Non-Cooperative Lobbying
Domestic firms may behave non-cooperatively or cooperatively in allocating resources to lobbying activities. In this section we consider the former case, leaving the latter case to Section 4. The non-cooperative lobbying case is an instance of a class of problems known as “the private provision of a public good.” A special case of this class of problems has been
considered by Bergstrom, Blume, and Varian (1986), who base their analysis on the assumptions that i in the production of the public good, only
the sum of the contributions, A
ai, matters, and that the payoff toeach player depends only on this sum, A, and on his own contribution, independently of how much each of the other players contributes. Because of
their restrictive assumptions, their model cannot be applied to our problem,
where each firm i’s payoff depends not only on A but also on C, and thelatter is a function of the vector a = (a1, ..., ak), not just of the sum A.
To proceed further, we follow Hillman et al. (2001), and focus on three
types of functional relationship between ci and mi. Let us write

!

!!

"

ci(mi) = c − ri(mi),where ri(mi) may be Interpreted as the reduction in unit cost due to monitoring.
Specification 1. Increasing returns to monitoring.
ri(mi) = δ imai ,α > 1,

δ i > 0,0"m "h.
i

i

Specification 2. Decreasing returns to monitoring.
ri(mi) = δ imai ,0 < α > 1,

δ i > 0,0"m "h.
ii

136

Arye Hillman, Ngo Van Long, and Antoine Soubeyran

Specification 3. Constant returns to monitoring.
ri(mi) = δ imi,δ i > 0,0

#m #h.
i

i

Recall that mi = hi − ai. Then!(a ) &c !r (h !a ),

(11)

i

i

i

i

i

and θ i′(ai) measures the marginal opportunity cost of lobbying, because anincrease in ai raises production cost, as entrepreneurial resources are diverted away from monitoring. From (8), firm i’s profit in stage 2 is2(12)

⎡ P[ Z (a )] − θ i (ai ) ⎤π i = [ − P ′]q = [ − P ′] ⎢⎥ .
[ − P ′]
⎢⎣
⎥⎦
2
i

%&
$

$

Given the aj’s (ji), firm i chooses ai to maximize (12) subject to theconstraints hi − ai0 and ai
0. From the Lagrangian function
L = πi +! [h − a ] + "a ,
i

i

i

i

i

we obtain the first order condition∂L ∂π i=
− λ i + µ i = 0.
∂ai ∂ai
At an interior maximum, we have(13)

θ i′ (ai ) =[θ ′ + k t ′](s E − 2) ,i*i

2( E − n − 1)

where si is firm i’s market share:
si

"qZ ．
i

Equation (13) is intuitive appealing: at an interior maximum, an increase in
the amount of resources devoted to lobbying will increase production costby θ i′, and this must be equated to the marginal gain from lobbying (theright-hand side of (13)), which reflects the increase in price (modified forfactors such as market share, and the effect of a price rise on revenue)
brought about by a tariff increase. (In general, the maximum may occur at(0) exceeds the marginal gain;a corner: zero contribution to lobbying, if θ i′or maximum contribution, ai = hi, if θ i′(hi) is smaller than the marginal

137

Lobbying for Tariff Protection

gain. In what follows, we restrict attention to interior maxima.)
It is useful to re-write first order condition (13) as
siE = 2 − 2 γ i [n + 1 − E ] ,(14)with γ i being defined by

γi ≡

(15)

θ i′ (aˆi ),ˆθ i′ (ai ) + k *t ′( Aˆ)

where all the derivatives are evaluated at the Nash equilibrium, and the hatover a variable indicates its equilibrium value. Equation (14) establishes a
relationship between firm i’s equilibrium market share si to γ i, which is ameasure of its comparative advantage in monitoring.
One of our aims is to find out how the heterogeneity among firms withrespect to lobbying skills affect their relative contributions and their profits.
Following Hillman et al. (2001), we make use of several measures of comparative and absolute advantage.
A measure of absolute advantage in monitoring: If δ i > δ j then wesay firm i has absolute advantage in monitoring over firm j.
A measure of comparative advantage in monitoring: Firm i is said tohave comparative advantage in monitoring over firm j if and only if
γ i > γ i , where γ i is defined by (15). This definition is motivated by theidea that a firm that has comparative advantage in monitoring would
have a high i′, i.e., a high marginal cost of undertaking lobbying activities.
Several remarks are in order. Firstly, an equivalent ranking can be obtained by the following definition

!
"

!

βi =

(16)

1
− 1.
γi

If β j > β i then firm j is said to have comparative advantage in lobbying.
Note that β j > β i if and only if γ i < γ i. Secondly, it should be noted that
(17)

[

]

[

]

sgn γ i − γ j = sgn θ i′ (aˆi ) − θ ′j (aˆ j ) ,where sgn means ‘the sign of’. Thirdly, under Specification 3 (constant returns to monitoring), γ i > γ i if and only if δ i > δ j. Thus, under constantreturns to monitoring, comparative advantage amounts to the same thing as
absolute advantage.

138

Arye Hillman, Ngo Van Long, and Antoine Soubeyran

The Case of Linear Demand
We now present some results for the case of linear demand, P = P 0−bZ,
where P 0 > 0, and b > 0.
Proposition 3.1. Assume linear demand and “increasing returns” in monitoring (i.e., specification 1). Thena at an interior Nash equilibrium of the lobbying game for “tariff” protection, firms that are less efficient in monitoring in absolute terms(low δ j) will devote more entrepreneurial resources to monitoring,
and achieve lower cost and greater profit than other firms. Thus, theavailability of lobbying opportunities reverses the ranking of firms’
profitability if the Nash equilibrium is interior.
b there may exist a corner solution which also has the property of profitability ranking reversal.

!
!

Proof
(a) From (13), at an interior equilibrium (with E = 0)"#(â ) $!δ m !! $"#(â ) "B ,
i

1

i

i

i

j

i

where B is the common value at equilibrium, for all domestic firms. It follows that if δ i > δ j > 0, then,
⎡δ ⎤
=⎢ i⎥
mi ⎢⎣ δ j ⎥⎦mj!

1/ ( α −1)> 1,since > 1.
Thereforecj(mj) = c − Bmj < ci(mi).
Thus, for any pair of firms (i, j) withr δ i > δ j > 0 and hi = hj, in the absence of lobbying opportunities, firm i has lower cost and thus higher
profit than firm j, but, when lobbying opportunities become available, at
an interior Nash equilibrium, firm i will have higher cost and thus lower
profit than firm j.
(b) To prove part (b), it suffices to provide a numerical example. Suchan example can be constructed, see Hillman et al. (2001). □Proposition 3.1 is similar to its counterpart in the quota case analysed in
Hillman et al. (2001). We may explain Proposition 3.1 as follows. If there
are no lobbying opportunities then, other things being equal, firms with ahigher δ will have lower costs and therefore higher outputs and profits.

139

Lobbying for Tariff Protection

When lobbying opportunities become available, these large firms will tend
to divert a lot of entrepreneurial resources to lobbying activities, because
they expect a large gain from the rise in price that accompanies a higher
tariff. Consider two domestic firms, 1 and 2, where firm 1 is more efficientin monitoring (δ 1 > δ 2). Then firm 1’s marginal-cost-of-lobbying schedule,′
1(a1) is everywhere above that of firm 2 if h1 is equal to or is not too different from h2. These schedules are downward-sloping because α > 1.
Firm 1, anticipating that the equilibrium â2 is small (the hat denotes theequilibrium value), perceives correctly that its marginal-benefit-of-lobbying
schedule is quite high. Therefore it chooses a high â1. Firm 2, knowingthat â1 is high, perceives its marginal-benefit-of-lobbying schedule to bequite low, so its low â2 is justified. The outcome is almost a free-ride forfirm 2.
For the case of decreasing returns in monitoring, then it can be shownthat profitability ranking is not reversed when lobbying opportunities fortariff protection are available. (The same result was obtained by Hillman etal. in the quota case.)!

Proposition 3.2. Assume linear demand and decreasing returns in monitoring (i.e., specification 2). Then, at an interior Nash equilibrium, firmsthat are less efficient in monitoring in absolute terms (low δ j) will devote
less entrepreneurial time to monitoring, and achieve higher cost and lower
profit than other firms.
We now turn to the question of whether an increase in the number offirms will reduce the aggregate lobbying effort for tariff protection. The
answer is given by Proposition 3.3, which is somewhat different from thequota case.
Proposition 3.3. Assume that the demand function is linear, P= a−bZ, andthat all domestic firms are identical. Then an increase in the number offirms, without changing the endowment hi of each firm, will reduce aggregate lobbying effort for tariff protection if and only if a θ ′′(a)/ θ ′(a) < k/k *(i.e., iff the elasticity of θ ′is less than the ratio of domestic firms to foreign firms 4) .
Proof
The first order condition (13) may be re-written as⎡ E (2 − si ) − 2n ⎤ θ i′ (ai ).
t ′( A) = ⎢⎥*Esi − 2⎣⎦ k
4. In the quota case, the condition is the elasticity of θ ′is less than unity.

140

Arye Hillman, Ngo Van Long, and Antoine Soubeyran

With linear demand and identical firms, at a symmetric equilibrium thiscondition becomes
⎛ A⎞
⎛ k⎞
⎜ 1− ⎟ t ′( A) = θ ′⎜ ⎟ .
⎝ n⎠
⎝ n⎠
This equation yields
dA 1 ⎡ A
1 ⎤θ ′′ − t ′ ⎥,=dk D ⎢⎣ m2
n ⎦
where
D=

1
⎛ k⎞
θ ′′ − ⎜ 1 − ⎟ t ′′ > 0,
⎝ n⎠mbecause, in the linear demand case, the second order condition obtained
from (13) implies −D < 0.
It follows thatk ⎤⎛ dA ⎞⎡
sgn⎜ ⎟ = sgn ⎢ε − * ⎥,⎝ dk ⎠k ⎦⎣whereε ≡a θ ′′(a)/ θ ′(a)is the elasticity of θ ′. □We now turn to the non-linear demand case.

The Case of Non-Linear Demand
When the demand function is linear, it is convenient to make use of
condition (14).
The following proposition relates the comparative advantage in monitoring with equilibrium market shares and profits.
Proposition 3.4. Assume non-linear demand. Then at an interior Nashequilibrium,a If the demand curve is locally concave (E < 0), then firms that havegreater “comparative advantage” in monitoring will have greater
market shares and greater profits.

!

141

Lobbying for Tariff Protection!b If the demand curve is locally convex (E > 0), then firms that havegreater “comparative advantage” in monitoring will have smallermarket shares and smaller profits. (In other words, the availability oflobbying opportunities “reverses” the profit ranking.)

Proof
From (14)(18)

si − s j =2(γ j − γ i )[ k + 1 − sE ]
E

.

Thus
(19)

sgn[si − sj] = sgn[− E ] sgn[γ i − γ j] ,that is, si − sj has the same sign as that of γ i − γ j if E < 0, and has opposite sign as that of γ i − γ j if E > 0. Finally, from!

π i[ P "]qi2(8)#[!P "]Z s . □2 2iRemarkIn order to understand the intuition behind Proposition 3.4, we must explicate the role of E . The following lemma, reported in Collie (1993) andLong and Soubeyran (1997), is useful for that purpose.
Lemma 3.1. If E < 0 [respectively, E > 0] so that the demand curve isconcave [respectively, convex], then an exogenous increase in tariff will
expand the equilibrium output of lower cost domestic firms by more [respectively, by less] than that of higher cost domestic firms.
Proof
Assume without loss of generality that firm i has lower cost than firmj(cj − ci > 0). From (7) and (6),qi

!q #[!1P "] (c !c ),jji

and hence1d⎡ ∂Z ⎤
qi − q j =(c j − ci ) P ′′ ⎢ ⎥,2dt
⎣ ∂t ⎦[ − P ′][]

which is positive if E < 0. □

142Arye Hillman, Ngo Van Long, and Antoine Soubeyran

It follows from Lemma 3.1 that if E < 0 then lower cost firms have astronger incentive to contribute to lobbying. They devote more resources tolobbying, while still maintaining lower production costs. When firm 1 has
a comparative advantage in monitoring, its marginal cost of lobbying, θ 1′
is higher. If it expects a2 to be small in equilibrium, then its marginal
benefit curve (as a function of a1) is also high (recall that E is negative)
and in equilibrium, its contribution to lobbying could be slightly more thanthat of firm 2, without harming its cost ranking. In the opposite case whereE > 0, all domestic firms still gain from lobbying, but the higher costfirms expand more relative to the lower cost firms.
4. The Cooperative CaseLet us turn to the case where firms coordinate their lobbying activities
in the first stage, even though they are Cournot rivals in the product market in the second stage. This specification is in the spirit of the theory ofsemi-collusion (as exemplified by the works of Friedman and Thisse(1993), Fershtman and Gandal (1994), Nalebuff and Brandenburger (1996),
among others), which is based on the observation that firms often cooperate in some spheres (such as R&D) while compete in other spheres.
Analysis of cooperative case can be complicated because in the firststage of the game there are incentives for firms to change the cost structure
within the industry so as to reduce rivalry in the second stage. In otherwords, allocation of lobbying efforts now serves two distinct purposes: ito increase tariff protection against foreign imports, and to alter thecomposition or degree of concentration of the domestic industry. Because
of ，coordination of lobbying is a surrogate for cooperation in the second
stage (which is often prohibited by anti-trust laws). Thus it is possible thateven if firms are ex-ante identical in all respects, their optimal coordinationof lobbying effort may call for asymmetric contributions. Non-symmetricoutcomes in a more general framework for cooperative oligopolistic games
have been treated by Long and Soubeyran (1999, 2000). Hillman et al.
(2001) provides a specific illustration.
In what follows, we consider only the case where the optimum is symmetric. The domestic firms agree on coordinating their ai to maximize theirjoint profit

"

"

Π=

∑π .
i

i ∈K

Then

∂π j
∂Π
=∑
.
∂ai j ∈K ∂ai

!

143

Lobbying for Tariff Protection

It can be shown that∂π j

⎡ Es j − 2 ⎤*=⎢⎥ θ ′j + k t ′ q j > 0.
∂ai ⎣ E − n − 1 ⎦[]It follows that the first order condition for joint maximization is

(20)

∂Π ⎡
EH K − 2 sK⎤= (θ i′ + k *t ′)− 2 siθ i′ ⎥ Z = 0,∂ai ⎢⎣
E − n −1
⎦

where
HK =

∑s ,
2
j

j ∈K

is the Herfindahl index of concentration of the domestic firms, andsK≡Q /Z the market share of the domestic firms.
It is interesting to ask the following question: does more heterogeneity
among domestic firms lead to a higher tariff rate? The answer turns out todepend on the curvature of the demand curve. Recall that Lemma 3.1 saysthat if the demand curve is convex (E > 0), then a given reduction in import quota tends to have an equalizing effect on firms’s sizes (i.e., the big
firms will expand by less than the smaller firms.) Therefore the marginal
gain in domestic industry’s profit, caused by an increase in A, is relatively
low. This means that the industry will not spend much on lobbying. Thiseffect will be mitigated, however, if firms are ex-ante sufficiently different.
Thus we would expect that if E is positive, then A will be greater, thegreater is the heterogeneity among firms. Now the Herfindahl index HK isa measure of heterogeneity: given the number of firms, this index is smallest when firms are identical. Our reasoning suggests that, if E is positive,
one should expect a positive correlation between HK and the size of the domestic industry’s market share.
We now can state the following proposition:
Proposition 4.1. If E > 0, then aggregate lobbying effort A will tend to be
inversely related to the degree of domestic concentration, as measured by
the Herfindahl index of concentration of domestic firms. If E < 0, then aggregate lobbying effort A will tend to be positively correlated to the degreeof domestic concentration.
Proof
From (20) and the definition of β i, we get
(21)

βi =

2 si ( E − n − 1).
EH K − 2 sK

144

Arye Hillman, Ngo Van Long, and Antoine Soubeyran

Summing (21) over all i ∈ K , we obtaint "(A )!
"
#G1 2sEH(E !!n2s!1) !1 ,
i

K

K

where
G≡k

1

∑θ′.
i ∈K

i

This concludes the proof. □Proposition 4.1 is stronger than its counterpart in Hillman et al. (2001),
where nothing definite could be said for the case E < 0.

5. Concluding Remarks
This paper deals with a model of an asymmetric oligopoly where domestic firms allocate entrepreneurial time between lobbying for tariff protection and internal control (monitoring). Our results reinforce the conclusions of the paper by Hillman et al. (2001) which dealt with the case oflobbying for quota protection. It was shown in both models that the availability of lobbying opportunities may have differential effects on the profitof heterogenous domestic firms. In particular, under non-cooperative lobbying, the ranking of profits may well be reversed when lobbying becomes
possible. This profitability reversal result may be attributed to free riding
in a non-cooperative equilibrium. In the cooperative lobbying case, bydefinition there is no free riding, and the optimal allocation of lobbying effort reflects both the desire for a higher tariff and the motive of altering
the cost structure of the domestic industry. Both models lend only limited
support to the conventional wisdom that industries with greater concentration tend to enjoy more protection.
In this paper, it was taken as exogenous whether firms cooperate or not.
It would seem desirable to develop a theory of endogenous coalition formation in the lobbying game. Such a theory would have a flavor similar tothat of the theory of endogenous vertical integration5.

5. See Gaudet and Long (1996) for a model of endogenous vertical integration.

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Lobbying for Tariff Protection

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8

Merger Policies and Trade
Liberalisation
Henrik Horn and James Levinsohn*This paper is about interactions between trade policy and a narrow but
important aspect of competition policy, namely merger policy. The notionthat trade policy and competition policy might be inter-related is not new.
From a purely intuitive viewpoint, it is natural to suspect that the two
types of policies might interact. After all, the large literature on trade policy in imperfectly competitive markets relies on the same sorts of market
structures that have led industrial organisation economists to consider possible roles for competition policy. The market imperfections that give rise
to pure profits motivate the potentially welfare-enhancing role for government intervention in both the domestic (competition policy) and international (trade policy) contexts.
Recent developments in the policy arena have elevated concern about
possible links between trade and competition policy. In particular, as international economic integration has progressed, policy makers have started toponder the possible conflicts arising from nationally pursued competition
policies in more unified goods markets. An idea that is underlying much ofthis discussion is the notion that international trade liberalisation, by limiting countries’ abilities to promote their self-interest with beggar-thyneighbour trade policies, will induce countries to use competition policies
instead to pursue the same goals (with similar beggar-thy-neighbour consequences.)* This paper was partly written while Horn worked at the World Trade Organization. The views expressed in this paper are not intended to reflect those of theWorld Trade Organization. Horn thanks Jan Wallander and Tom Hedelius Research
Foundations and Levinsohn thanks the Ford Foundation and Jan Wallander Research Foundation for research support. We are also grateful for helpful commentsfrom participants in a seminar at Erasmus University.
147

148

Henrik Horn and James Levinsohn

International organisations traditionally concerned with trade policies
have also turned their attention to competition policies. For example, themembers of the World Trade Organisation (WTO) noted the importance ofgiving more attention to competition policies in their first ministerial-levelmeeting in December 1996. Also, for more than a decade, the OECD has
focused attention on the interaction between trade and competition policies.
The European Union has gone even further, suggesting an international
agreement in competition policies. The EU has also in practice sought tosolve the problem of often conflicting competition policies in the context
of a unified European market through supra-national competition policies.
A recent example of the alleged interplay between national competition
policies and multilateral trade liberalisation is the Kodak-Fuji dispute concerning Japanese imports of consumer photographic film and paper. The
United States accused Japan of (among other things) nullifying or impairing benefits accruing to the United States from the GATT by pursuingslack competition policies (widely interpreted.) However, a Panel Report
adopted by the WTO Dispute Settlement Body rejected the United States
claims on the grounds that they were not substantiated.
The appropriate design of competition policies has been discussed in a
voluminous literature that almost exclusively disregards open-economy aspects of the issues. The role of any one of these policies, though, maychange when one analyses an open, as opposed to closed, economy. In thispaper, we choose to focus on links between merger policies and trade liberalisation. We put special emphasis on the role that international agreements such as the GATT play when merger policies are nationally chosen.
As noted above, of particular concern is the possibility that liberalisation ofinternational trade will induce countries to use competition policies increasingly to promote national interests at the expense of others. We examine the incentives for a welfare maximising government to make such a
substitution. Interpreting merger policy as a choice of degree of industrial
concentration, we investigate how the merger policy that is optimal fromthe point of view of an individual country is affected by restrictions on theuse of tariffs and export subsidies.
We show that the intuition with which many informed economists approach the links between trade and merger policy may be misleading. Thisintuition is the following: trade liberalisation increases competition in thedomestic market so liberalisation acts as a substitute for a stricter competition policy. Hence, as trade is liberalised, there is less of a need for competition policy, and rationally acting countries will therefore pursue slacker
policies than before liberalisation. The main message of this paper is thatwhile the first part of this logic––the pro-competitive effect of liberalisation––often would be correct, this reasoning does not provide the basis fordetermining whether trade liberalisation will lead to a more lax competition policy.

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Merger Policies and Trade Liberalisation

The paper focuses on structural aspects of merger (and industrial) policies, rather than on details of specific merger cases. Thus, it can perhaps
be viewed as being concerned with the formulation of the framework inwhich the day-to-day decisions are made; that is, the writing of the Merger
Guidelines, rather than the implementation of them.
Two general points emerge from our analysis. First, merger policies areindeed associated with international externalities in open economies. Thissuggests that there are potential gains from international policy coordination, even though the magnitude of these gains in practice is unclear. The
second point is perhaps more surprising. We argue that one should not expect to find any particular relationship between trade policy and merger
policy. We do indeed an unambiguous relationship in all the parametricmodels we analyse––a relationship which runs in the opposite direction towhat is commonly suggested. However, considering this relationship in aslightly more general framework strongly suggests that it could be of any
nature. Thus, we find no theoretical presumption that international tradeliberalisation induces countries to pursue merger policies that have more ofa beggar-thy-neighbour flavour. In our view, the burden of proof falls
rather heavily on those who argue that trade liberalisation necessitates aninternational agreement on competition policy.
The remainder of the paper is organised as follows. In Section 1, wevery briefly review the literature on trade and competition policy. Section
2 then presents our general framework. In Section 3, we ask how the presence of international trade impacts on a country’s incentives to concentrate
production. In this Section and those that follow, we begin our analysis using a more general representation of demand, which frequently enables us
to decompose the influences that policy makers face. We are seldom able
to derive specific results, however, since too much simply depends on the
shape of demand functions. We therefore turn to an even more specificframework––with linear demand––and analyse the issue at hand in thisspecial but familiar context.
In Section 4, we introduce trade policy in the form of export subsidies.
We first analyse the home country’s optimal merger policy when the homecountry imposes an export subsidy. We next examine the issue when it is
the foreign country that imposes the export subsidy. Section 5 introduces aforeign country that also pursues a merger policy, and analyses how tradeliberalisation impacts on the equilibrium degree of industry concentration.
This is done in the context of four different model specifications. Section 6
returns to the question of whether trade liberalisation increases the desirability of supranational merger policies. Section 7 concludes. Finally, theanalytics of the linear model are gathered in the Appendix.

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Henrik Horn and James Levinsohn

1. The Literature
Links between trade and competition policy were analysed by Acquierand Caves (1979) who examined tradeoffs between domestic consumer
welfare and monopoly profits from abroad. One of the first reviews of thestrategic trade policy literature, Dixit (1984), investigates how domestic
welfare, in an oligopolistic model of international trade, depends on thenumber of home firms, the number of foreign firms, and export subsidies.
Dixit raises ‘the commonly expressed view that the existence of foreigncompetition makes domestic anti-trust policy unnecessary, and may evenmake it desirable to encourage mergers of domestic firms, or prevention ofexcessive entry, so as to keep the home industry strong enough to withstand the competition’, although he does not explicitly analyse how optimal trade and merger policies interact.1 At about the same time, industrialorganisation economists, who traditionally thought about mergers in astrictly domestic context, gave consideration to the role of international
markets in analysing mergers. (See, for example, Ordover and Willig(1986).) From the outset of the literature on trade and imperfect competition, there has been a realisation that trade and merger policy may interact.
The literatures on strategic trade policy and domestic merger policy seemto have then treated each other like relatives that, once introduced, werebest ignored. Very few, if any, of the strategic trade policy papers that followed gave much consideration to the existence of domestic competition
policy, and similarly most of the developments in the merger policy literature ignored the role of international competition or trade policy.
In the last few years, attention has again focussed on links between tradeand competition policy. This rapidly expanding literature typically focuses
on merger policy in the presence of international competition. These papers,
which might be thought of as ‘open-economy industrial organisation’, typically analyse how implications of domestic merger policy change when thedomestic country trades with other countries. In these papers, while tradematters, trade policy is usually either very much in the background or simply absent. A much smaller set of papers explicitly considers the impact oftrade policy.
Examples of economics-oriented papers analysing merger policy in thepresence of international trade (but not trade policy) are Barros and Cabral(1994), Head and Ries (1997), and Levinsohn (1996), while more laworiented papers appear in Hawk (1994), and in the proceedings from the
ABA’s Antitrust Law Journal’s symposium on The Role of Foreign Competition in the U.S. Merger Enforcement’ (1996). These papers recognise
1. Another early example is Brander and Spencer (1984) who consider an oligopoly model in which the importing country sets a tariff and the exporting country responds by setting the number of firms in the exporting industry.

151

Merger Policies and Trade Liberalisationthat the optimal design of merger policy may change drastically as one
moves to an open-economy context. Another economics-oriented paper is
Bliss (1996), in which the author argues generally against international harmonisation of competition policies and analyses the possible role of competition policies to promote exports in a Krugman cross-hauling model.
There is also a related literature in international regulation which investigates the issue of the delegation of regulatory powers from national
authorities to an international body. This question has been addressed by
Bhagwati (1991) in connection with the broadening of the international
policy agenda as well as by Gatsios and Seabright (1990) and Neven(1992), in relation to regulatory reforms in the European Community.
These authors have attempted to identify the policies which should be subject to international negotiations or assigned to higher levels of government.
Policy spillovers are identified as the key issue in this discussion because
they are at the source of prisoners’ dilemma outcomes.
Another branch of the literature consists of papers which more explicitly
examine links between trade policy and competition policy. Indeed, titles
such as ‘Competition and Trade Policy: Identifying the Issues After the
Uruguay Round’, (Lloyd and Sampson (1995)) ‘Competition Policy andTrade Policy: Mediating the Interface’, (Trebilcock (1996)) Competition,‘Competition Policy and the GATT’ (Hoekman and Mavriodis (1994)) and‘Trade Policy and Competition Policy’ (Motta and Onida (1997)) suggestthat we are not the first to think about these links. Here, papers are aptly
divided into more applied policy papers and more analytically formal papers. The papers listed immediately above fall into the former category.
We now discuss in more detail examples of the latter which are mostclosely related to this paper.
Neven and Seabright (1997) formally show that trade liberalisation andcompetition policy might be substitutes in terms of their effects. For instance, in one of the several models in their paper, they show how liberalising trade might increase competition in the home market and hencemight perform the same task as competition policy, with the latter interpreted as promoting competition.2 Their focus is not on optimal policy responses by the government, but rather on the changes in firms’ incentives
to engage in anti-competitive practices. They write that ‘static models ...
confirm the widely held presumption that trade liberalisation has procompetitive effects’. Neven and Seabright are careful, though, to point out
that in more complicated, often repeated game frameworks, the insightsfrom the static framework may not be robust. They conclude that ‘Overall,
our analysis suggests that unalloyed confidence that trade liberalisation will
2. With ‘competition policy’ we refer in this paper to the usage of anti-trust instruments, rather than policies that promote competition as such. Hence, the lastqualification in the statement in the text.

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Henrik Horn and James Levinsohn

address problems of uncompetitive market structure ... would be inappropriate. Nevertheless, it supports the general presumption that trade and domestic competition policies are substitutes, albeit imperfect ones.’ (Ouritalics.)
Bond (1997) develops a political economy model of merger policy inwhich the government maximises a social welfare function to decide
whether or not to allow various mergers. Bond argues that the sorts ofmergers that would be allowed when competing states make the decisiondiffer from those that would be allowed when a federal government makes
the decision. The model is then used to analyse how merger policy differed in the era during which United States’ states set competition policy
and more recently when the federal government set the policy. Bond draws
analogies between setting policy at the federal level and setting competition policy in the context of a customs union.
Rysman (2000) is more closely related to ours. Rysman uses a linear
Cournot model in which a country first selects the number of firms in theindustry, then sets the optimal trade policy, and firms then compete in a
Nash fashion. Rysman’s model only considers a scenario in which firms
from the home and foreign countries compete in a third market. Rysman
finds that the strategic benefits from choosing a large number of firms dueto the commitment this confers are negated by the foreign subsidy in thesecond period. Since, by assumption, there is no consumer surplus to consider, Rysman finds that countries choose a monopoly and subsidise thatmonopoly. When subsidies are restricted, such as under the GATT, countries move toward greater competition.
Francois and Horn (2000) examine the setting of national competition
policy in a two-country setting, emphasising the relationship of trade patterns to the goals of competition policy. They study in particular the relationship of national competition policies to terms-of-trade gains and losses,
and the general equilibrium distributional effects of competition policy.
However, in contrast to the present analysis, they do not focus on the roleof trade liberalisation.
Our paper is most closely related to work done concurrently and independently by Richardson (1999). The approaches and issues addressed arequite similar. Like us, Richardson works with a model in which countries
strategically set both merger policy and trade policy. We differ by placing
the issues in a more general context, addressing the role of a broader rangeof trade policies (i.e. subsidies as well as tariffs), and considering merger
technologies that give rise to both fixed cost savings and lower marginal
costs. Richardson, though, examines issues relating to customs unions
which we ignore.

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Merger Policies and Trade Liberalisation

2. The Model
The model is a two country partial equilibrium set-up. Merger policy
takes the particular form of choosing the optimal level of industry concentration.3 The number of identical firms in the home (foreign) country isgiven by m(n). We assume that markets are segmented and that firms produce with constant marginal costs c and fixed costs f . In a later formulation, we will allow the constant marginal cost to depend on the degree ofconcentration, in order to capture the notion of ‘marginal cost synergies’.
Firms compete in Cournot fashion. The markets are thus strategically separated in the sense that firms’ decisions concerning one market do not affecttheir incentives in the other market. On the demand side of the model, we
consider the homogeneous products case. Introducing the next-simplest
case of symmetrically differentiated products as in the CES utility representation significantly complicates the welfare analysis, both since entry
will introduce variety effects, and since firms first order conditions becomemuch more involved.4
As noted above, the intention is to focus on structural aspects of merger
policy. The paper will not explicitly take into consideration firms’ incentives to merge. To do this would require a theory of endogenous merger
formation, something that would substantially complicate the analysis.5
One cannot generally assume that the government can achieve any level ofconcentration it desires simply by deciding on an upper degree of concentration, since firms may not want to merge to this extent. Nevertheless, we
assume that our governments, in the long run, can set the desired degree ofindustrial concentration, and our merger policy hence also borrows featuresof industrial policy.6 In our defence, note that our disregard of the shortrun merger incentives has a direct counterpart in much of the industrial organisation and strategic trade policy literature: if firms do not have incentives to merge in these models (whatever the appropriate theory of merger
formation is), they are likely to want to divest. However, for unexplained
reasons this is typically not permitted in these models.
3. In our use of the term domestic industry concentration’ below, we refer to thenumber of domestic firms in the domestic market.
4. As noted below, much of the analysis requires second-order, or mixed, derivatives of a social welfare function. We investigated differentiated products in both
the Cournot and Bertrand case. In each, we were unable to make much headway
due to the complexity of the higher order derivatives.
5. Note that the traditional criterion for merger incentives––that the merging
group’s profit after merger is larger than in the initial situation––in itself does notprovide a theory of merger formation, since it is constrained to a comparison of
two out of many possible configurations of merging firms. (See Horn and Persson(2001)).
6. As long as profits are positive, as they are in our parametric models below,
the government can also influence entry.

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Henrik Horn and James Levinsohn

Trade policy for the home (foreign) country is represented by the choiceof a variable r(s). We initially concentrate on the case of export subsidies(or export taxes if negative), but we will later consider specific tariffs. Let
Пh(m, n, s) be the variable profits per firm in the home market, and let
Пf(m, n, r) be the corresponding profits in the foreign markets net of thesubsidy. The reduced form welfare level for the home country is given by
V (m, n, r, s), and consists of consumer surplus, CS (m, n, s); industry
variable profits from sales to the home market, H (m, n, s) mПh(m, n, s);industry variable profits from export sales to the other country net the export subsidy, E (m, n, r)mПf(m, n, r); and industry fixed costs, mf . In
general, then,!

!

V (m, n, r, s) = CS (m, n, s) + H (m, n, s) + E (m, n, r) − mf .
The model above is very, very simple. Somewhat surprisingly, even thismodel typically yields ambiguous answers to key questions. We believethis, in and of itself, is actually informative in that it warns us not to expect any simple relationships between trade and competition policies.
Nonetheless, in an effort to derive more definitive results, we will sometimes impose more structure on the model. In these instances, we will assume that there is a linear industry demand, p = a − bQ , in each national
market.
Before employing this model in any detail, it is useful to re-state why
we are doing the analysis in the first place. As noted in the introduction,
the policy concern that motivates this analysis is that as trade policy is liberalised, governments will have an increased incentive to act in a beggarthy-neighbour fashion in setting their competition policy. If this is true, therole of internationally coordinated competition policy may be enhanced.
The implicit assumption in this argument is that governments are acting rationally in their own (as opposed to global) self-interest and they do so before, as well as after, any trade liberalisation. For example, in our equilibrium framework, governments have an incentive to engage in trade policy.
The same market structures that underlie this incentive also provide an incentive for the government to engage in competition policy. At the heart of
the analysis is the interaction of these two sets of incentives. The question
then becomes one of how this rational behaviour is impacted by trade liberalisation. Formally, this involves analysing how first-order conditions
with respect to merger policy are affected by the trade policy regime. Notethat this approach differs fundamentally from that of asking how the ‘need’
to pursue vigorous competition policies is affected by trade liberalisation.
Our approach is, in this respect, the same as that of Richardson (1999),
Bond (1997), and Rysman (2000).
We will consider cases where the trade policy is discretionarily determined by each country, and where it is constrained by an international

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Merger Policies and Trade Liberalisation

trade agreement (the ‘GATT’). Similarly, we will consider cases where
merger policies are set at a national as well as at an international level. To
understand this interaction between policies and between countries better, it
is useful initially to highlight the channels through which trade by itself affects an individual country’s incentives with regard to merger policy(which is modeled here as the country’s optimal degree of concentration.)
This is only an intermediate step, since the full analysis will have to take
into consideration the interplay between the setting of trade and merger
policies in the two economies.

3. Trade and the Incentives to Concentrate Production
In this Section, we use the framework developed above to begin to investigate links between international trade and a country’s optimal degreeof concentration while assuming there is no trade policy intervention.
When there is no international trade, the utility of the home country isdetermined by the number of domestic firms m and is given by CS(m, 0,・)
+ H (m, 0, ・) − mf . Hence, with consumer surplus increasing in the number of firms (Cm > 0) and industry variable profits declining in the numberof firms (Hm < 0), the optimal industrial concentration is in standard fashion such that the gain in consumer surplus from one more firm equals thesum of the resulting loss in industry profits and the additional fixed cost.
Let m a be the optimal degree of concentration in autarky.
There are two basic reasons why the optimal degree of concentration
may differ in closed and open economies––trade enables home country
firms to sell in foreign markets and it enables foreign firms to sell in thehome country market. The home country’s optimal degree of concentration
is affected by trade through both these channels. Each is discussed in turn.
3.1. Foreign Consumers
Consider first how the presence of foreign consumers affects the optimal
degree of concentration, assuming that there are no foreign firms, and thatthe home country does not use its trade policy. Home country welfare is
now given by:
V (m, 0, 0,・) = CS (m, 0, 0,・) + H (m, 0, 0,・) + E (m, 0, 0,・) − mf .
Differentiating this expression w.r.t. m, and evaluating Vm at the autarky
optimal level of industrial concentration yields:
Vm(m a, 0, 0,・) = Em(m a, 0, 0,・).

!

Since E (m, 0, 0)mПf (m, 0, 0), and industry profits typically decreasein the number of firms, Em(m, 0, 0) is in general negative. This is because

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Henrik Horn and James Levinsohn

there are no foreign firms and hence no foreign profits to shift. Domestic
profits from the foreign market, then, are going to be maximised with collusion as any competition in the foreign market is destructive. With
Vm(m a, 0, 0, ・) < 0, adding a firm, relative to the autarky number of firms,
reduces welfare, hence the optimal number of firms in the exporting free
trade equilibrium will be smaller than the optimal number of firms in theautarkic equilibrium. Thus, the presence of foreign consumers yields an incentive for the domestic country to increase the degree of concentration.
3.2. Foreign Producers
International trade also implies competition from foreign firms, and thedegree of this competition is influenced by the degree of foreign concentration. We begin by examining how foreign concentration affects the optimal degree of concentration among home firms, i.e., whether the two policies are strategic substitutes or complements. For the sake of clarity, we
continue to assume that neither country uses trade policies. The impact on
the home country’s incentives is now captured by the relevant mixed derivativeVmn(m, n, 0) = CSmn(m, n, 0) + Hmn(m, n, 0) + Emn(m, n, 0).
Given our assumption of a symmetric demand structure, the lack of tradebarriers means that we can write welfare as
V (m, n, 0, 0) = CS ( N ) + m ∏( N ) − mf ,where N = m + n, and П(N ) is total variable profits per firm resulting
from home and foreign markets. The mixed derivative can hence be expressed as
Vmn = CS NN + ∏ N + m ∏ NN .

(1)This expression shows how the incentives for domestic concentration
change with the introduction of another foreign firm.
To interpret (1), note that since output is homogeneous, we can rewrite theconsumer surplus as~
CS (m, n, s) ≡ CS Q≡!

Q

∫ P(ξ )dξ − P(Q)Q,0where Q
Q (m, n, s) is the total output volume sold in the home country market, and P (Q ) is the inverse demand function. We then have

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Merger Policies and Trade Liberalisation~
CSQQ Q = − P'− QP".
~
Hence, a sufficient condition for CS to be convex in total output is thatP’’ 0.
Now return to (1). The first term shows how the benefit to consumers ofanother domestic firm changes with the introduction of another foreign~
firm. Expressing the consumer surplus as CS[Q( N )], we have:!

~~
CS NN = CSQQ QN2 + CSQ QNN .
With general demands, the term QNN will depend on the third order derivatives of demand, and will thus be ambiguously signed. But, with linear demands, CSNN is unambiguously negative: consumer surplus is convex in to~tal output (CSQQ > 0), but the latter is concave in the number of firms(QNN < 0), and the latter effect dominates the former.
The second term in (1) represents the fall in profit per domestic firmwith the introduction of another foreign firm to the market, and hence isnegative. This effect tends to make foreign and domestic concentration
strategic substitutes.
To interpret the third term in (1), think of mПN as the industry-levelprofit destruction effect of entry of another domestic firm. The third termthen gives how this industry profit destruction changes when a foreign firm
enters. Without more structure, this term is also ambiguously signed. Thisis even true in the linear model. With industry demand given by
p = a − bQ and marginal costs given by c,2(a − c) (2m − n − 1)2

Hmn = Emn =b(m + n + 1)

4,

(still assuming the export subsidies are nil). This term can take on either
sign, and will tend to be negative the lower is the degree of foreign concentration.7
The sign of Vmn is important in that it yields information about the strategic relationship between merger policies in the two countries, similar to
the issue of whether outputs or prices of competing firms are strategic substitutes or complements. If Vmn < 0 (> 0), the optimal response on part of
the home country to increased foreign concentration, is less (more) concen7. Details of the linear model are gathered in the Appendix.

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Henrik Horn and James Levinsohn

tration. We cannot sign this derivative in general. However, it is note worthy that it is not sign-able even in the linear case:3(a − c) (2m − 2n − 1)
2

Vmn =

b(m + n + 1)

4.

We conclude that the fundamental issue of whether more foreign competition yields incentives for more or less domestic competition cannot be determined unambiguously, and that restricting the analysis to the linear
model does not change this ambiguity. This may appear somewhat surprising, considering the intuitively appealing notion that increased international
competition should lessen the need for domestic competition, and thus fora restrictive merger policy. It is indeed correct in that international competition is a substitute for domestic competition, in the sense that it can perform the same role of disciplining firms serving the domestic market.
However, the impact of international competition on incentives with regard
to merger policy are determined by how increased foreign competition affects the marginal benefits and costs of domestic concentration. Whether
foreign and domestic competition are strategic substitutes or complements
is a much more subtle issue. From an analytic point of view, this is a simple point. But it is a crucial point if one is to understand why our results
differ from those of the earlier literature, and it has not been appreciated in
the policy discussion.
4. Export Subsidies and the Incentives to Concentrate Production
The previous Section looked at how international trade affects competition policy incentives assuming free trade. The main goal of this paper,
though, is to consider the impact of trade liberalisation on the equilibrium
degree of concentration. In this Section, we take a step towards that goalby introducing export subsidies. We first investigate how a country’s
merger policy interacts with its choice of export subsidy. We then investigate how the home country’s merger policy interacts with the export subsidy of its trading partner.
4.1. Domestic Export Subsidies
Because of the strategic separability between the two markets, the optimal export subsidy depends only on conditions in the foreign market. The
optimal subsidy is implied by the first order condition:
Vr (m, n, r , s) = 0 = m ∏ rf (m, n, r ),

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Merger Policies and Trade Liberalisation

hence its sign depends on whether home profits in the foreign market increase or decrease with the subsidy. In the special case where there are no
foreign firms, the optimal subsidy would be negative. In this case, thenegative subsidy (tax) works to deter destructive competition. More generally, the optimal subsidy would be positive with foreign firms in the foreign market in the Cournot case, as shown by Brander and Spencer (1985)
and negative in the Bertrand case, as demonstrated by Eaton and Grossman(1986).
The direct impact of an exogenous change in the domestic export subsidy on the incentives with regard to the domestic degree of concentration,is given by∂2m ∏ f (m, n, r , s)∂m∂rf
= ∏ rf (m, n, r ) + m ∏ mr
(m, n, r ),

Vmr =

[

]

since a change in the subsidy has no impact on domestic consumer surplus
or profits from the domestic market. In order to disentangle the various
forces determining the sign of this expression, we will first assume the absence of foreign competition in the export market, so that the role of theexport subsidy is to facilitate the extraction of foreign consumer surplus.
We will then consider the case when it is used as a ‘strategic trade policy’
instrument, i.e., to shift foreign producer surplus.
When there is no foreign competition, there are two basic forces at workin determining the sign of Vmr. To see this, let X (m, r) be the industry output sold in the foreign market: X (m, r)mx(m, r) where x(m, r) is the
reduced form output per firm in the foreign market. Due to the linear cost
structure, variable profits in the foreign market can then be written as:

!

[

]

m ∏ f (m, 0, r ) = P X (m, r ) X (m, r ) − cX (m, r )[]≡ ∏ M X (m, r ) .
Note that ПM(X ) is simply the profit function that a monopolist would
face if selling in the foreign market at constant marginal cost c. We assume that this profit is concave in the output volume. Also, let r !(m) be
the optimal trade policy, given some arbitrary degree of domestic concentration m:
Vr(m, 0, r !(m), ・)Hence,! 0.

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Henrik Horn and James Levinsohn

( (

))

∏ MX X m, r * (m) = 0.
When there is no foreign competition, the optimal export subsidy induces the firms in the industry to jointly act as a monopolist in the foreign
market. Since the oligopoly is over-producing compared to the optimal behaviour of the monopolist, the optimal trade policy is to tax the foreign
sales of the oligopolists. This is welfare maximising since subsidy revenue
is a pure transfer and any competition in the foreign market would just destroy profits.
Now return to the mixed derivative linking trade and merger policy inthe case of no foreign firms:
M
Vmr = ∏ XX
X m X r + ∏ mX X rm .

At the optimal trade policy, r *, this derivative is given by:()

M
Vmr m, 0, r * (m) = ∏ XX
Xm Xr ,

since ∏ mX = 0. The first element of the product on the right-hand side isnegative by the concavity of the profit function. The second element, Xm,
gives the effect on industry output of the entry of an additional firm, andthis will be positive. (Were this not the case, consumers would lose fromthe entry of an additional firm.) The third element, which equals mxr, isagain positive and gives the impact on industry output of an increase in thesubsidy. Hence, Vmr < 0.
It is reasonable to think of trade liberalisation as r moving toward zero.
The above finding then implies that in the absence of foreign competition,
the optimal degree of domestic concentration increases with a small movetoward home country trade liberalisation. Intuitively, the negative mixed
derivative Vmr directly reflects on the link between a country’s optimal
merger policy and its trade policy. Starting at the optimal export tax, asmall reduction in this tax (an increase in r) will induce the home country
to reduce the number of firms. This is simply a reflection of the fact noted
above: When there are no export subsidies and there is no foreign competition, it is optimal for the domestic economy to be a monopolist in the foreign market. Adding domestic consumers into the picture introduces a
trade-off and calls for a larger number of firms. The domestic export subsidy tends to ease this conflict between what is the optimal degree of concentration in the domestic and in the foreign markets. In fact, with twomarkets, the two policy tools m and r allow the home country to reach afirst best with regard to capturing surplus in the foreign market.

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Merger Policies and Trade Liberalisation

Finally, in the case of the linear Cournot model we can also show that
Vmr(m, 0, r) < 0 even if the export subsidy is not optimally set, as long asrr *(m) (recall that r *(m) < 0 in this case). This can be seen from thefact that for n = 0,!

Vmr = −(a − c)(3m − 1) + mr .
3b(m + 1)Since this expression is negative at r = r !(m), it must be so a fortiori forlarger values of r.
Next, we add foreign producers back into the calculations. Export subsidies (or taxes) play a role in addition to just restricting destructive competition in the foreign market. Now, export subsidies may serve to shift profits from the foreign to the domestic firms, as demonstrated by Brander andSpencer (1985). These subsidies, though, may also interact with the optimal degree of concentration––this is indeed the expressed fear behindsome of the calls for international agreements on competition policies. It isdifficult in general to draw any affirmative conclusions regarding the link
between the two types of policies. Formally, the question boils down towhether Vmr is positive or negative for n > 0. The reasoning in the previous subsection is not directly applicable, since it relied on the absence of
foreign firms. However, in the linear model, we have that Vmr < 0 also inthe presence of foreign firms, as long as the export subsidy is at the optimal level
r* = −(a − c)(m − n − 1) ,2m(n + 1)

since in this caseVmr = −(a − c)(n + 1) < 0.
2b(m + n + 1)

But, when r is not optimal, the presence of foreign firms makes the sign ofthe mixed derivative unclear. For instance, at r = 0,
Vmr = −(a − c)(n + 1)(3m − n − 1) .
3b(m + n + 1)

This expression is positive for n > 3m−1. In such a case the introduction

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Henrik Horn and James Levinsohn

of a small positive export subsidy, which in itself would increase welfare
since
Vr = −(a − c)m(m − n − 1) > 02b(m + n + 1)

at r = 0, would give an incentive to the home country to reduce the degreeof domestic concentration.
In sum, there is no unambiguous relationship between the level of thedomestic export subsidy and the optimal degree of concentration––not evenin the linear case.
4.2. Foreign Export Subsidies
We next consider export subsidies levied by the foreign government.
The direct impact of the foreign subsidy on domestic welfare is
Vs = CSs(m, n, s) + Hs(m, n, s).
In a standard model, the first term is positive, reflecting the gain to consumers from increased total supply to the market, and the second term isnegative, since the subsidy yields a smaller market share for the domestic
producers. The balance of these terms cannot be determined a priori: thenegative profit shifting effect may outweigh the gain to consumers. This istrue even in the linear model.8
Now turn to the implication of the foreign subsidy for the incentives
with regard to the optimal degree of concentration:
Vms = CSms(m, n, s) + Hms(m, n, s).
Not surprisingly, this is also of ambiguous sign. The basic impact of theforeign subsidy is to increase the output of foreign firms, to reduce that ofdomestic firms, while in the aggregate yielding an output expansion. The
term CSms measures the change in the sensitivity of consumer surplus to
the number of domestic firms. With homogeneous outputs, it can be rewritten as
8. For instance, in the linear model Vs = {n/[b(m + n + 1)2]}[(a − c)(n − m) +ns(2m + 1)], a foreign export subsidy definitely benefits the domestic economy
if n m, while it will be detrimental if n < [(a − c) m]/(a − c + 2sm + s). Theseequations are very similar to those derived in Dixit (1984). The key difference between Dixit’s work and ours is that Dixit was concerned with the first derivatives(i.e. Vs) whereas we focus on the second mixed derivatives. Dixit’s work, then, isan essential building block to ours.

!

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Merger Policies and Trade Liberalisation~~
CSms = CSQQ Qs Qm + CSQ Qsm .
~Again, both CSQQ and Qsm are of ambiguous sign, with the latter involving
third-order derivatives of the demand function. A similar ambiguity applies
to the sign of Hms. This basic lack of a clear impact of s on the incentives
w.r.t. m is also evidenced by the fact that in the linear Cournot model,
sgn[Vms] = sgn[(a − c)(m − 3n −1) − 2ns (m − n)],which clearly can take on either sign. We conclude that the impact of theforeign export subsidy on the optimal degree of domestic concentration
simply depends on the details of the situation even in the linear case.
5. Multilateral Trade Liberalisation and the Equilibrium Degree ofConcentration
Thus far we have examined the incentives the home country faces without considering the fact that the foreign country may also be strategicallysetting trade and merger policy. In order to consider the impact of multilateral trade liberalisation, however, one must take into consideration the factthat the foreign country will also change its policies in response to thetrade liberalisation. To fix ideas, suppose one wishes to analyse the impactof the GATT, and that this is modelled as a move toward freer trade byboth countries. In terms of the model, this amounts to reductions in both rand s, both of which will affect the home country’s optimal degree of concentration. But this liberalisation will also affect the foreign country’s chosen degree of concentration, and this will in turn affect the home country’s
decision problem with regard to the degree of concentration. Thus, severalof the affects we considered one-by-one in the previous sections will now
jointly impact the outcome.
We begin in Section 5.1 with export subsidies in the more general case.
Here, we outline the forces that come into play and we provide a generalmodelling strategy. In order to obtain more determinate results, we thenturn to variants of the linear demand model. Using the linear model wefirst examine, in Section 5.1.1, the case in which fixed costs give rise to
economies of scale, but there are no marginal cost synergies. Since our focus is on the equilibrium degrees of concentration that result from tradeliberalisation, we need to characterise the degree of concentration somehow.
We do so in two ways––by counting the number of firms and in terms of
the resulting Lerner index. We then investigate in Section 5.1.2 the case inwhich merger policy is more long run than trade policy. In Section 5.1.3,
we consider the (still linear) case in which mergers convey marginal costsynergies, and we again compare the resulting equilibrium degrees of concentration. We conclude this Section by changing our focus from export

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Henrik Horn and James Levinsohn

subsidies to import tariffs (Section 5.2). We again characterise the resulting
equilibrium degrees of concentration in terms of both the number of firms
and in terms of Lerner indices.
5.1. Export Subsidies
We begin by assuming that countries simultaneously determine the degree of concentration and their export subsidies (if these are permitted by
the trade regime).
In order to facilitate the analysis, we concentrate throughout on cases
where the countries are identical, so as to allow symmetric equilibria withr = s and m = n. There are four types of equilibria (in addition to autarky)that are of interest. In the ‘discretionary’ equilibrium, given by the pair(m d, r d), each country discretionarily chooses both its trade policy and thedegree of concentration among domestic firms. This equilibrium is givenby:Vm (m, m, r, r) = 0,
Vr (m, m, r, r) = 0.
In the ‘GATT’ equilibrium (m g, 0), countries continue to choose concentration discretionarily, but have agreed not to utilise export subsidies:
Vm (m, m, 0, 0) = 0.
There are two cases where the degree of concentration is set by a supranational agency that maximises world welfare. A first case, which is obviously of less practical relevance (but is still of interest in that it yields information about the externalities involved in the merger policies) is where
the countries retain the possibility to choose their export subsidies in a discretionary manner. The resulting degree of concentration and export subsidies are denoted (m k, r k), and are given by
Vm (m, m, r, r) + Vn (m, m, r, r) = 0,
Vr (m, m, r, r) = 0.
The other, and practically perhaps more interesting, case is where the‘GATT’ is augmented by a supranational merger policy. We denote the resulting concentration level as m S. Because of the assumed symmetry between the markets, it is given by:
Vm (m, m, 0, 0) + Vn (m, m, 0, 0) = 0.

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Merger Policies and Trade Liberalisation

Our interest is in comparing the degrees of concentration in the different
policy regimes. An indication of the relative magnitude of m d and m g
could be obtained by considering a marginal reduction in the subsidy fromthe discretionary level, assuming national merger policies:
V + Vmsdm= − mr.
dr
Vmm + Vmn
However, note that the mixed derivatives that appear in the above equation
are exactly the same as those we have already investigated, with the exception of Vmn, which has implicitly been assumed to be negative to ensurethat one of the second-order conditions for the government’s optimisation
problem is fulfilled. As was seen above, most of these derivatives are ofambiguous sign. While in principle it is possible that the assumed symmetry between the countries might have helped to determine the direction inwhich concentration moves, we found that even in the symmetric case one
should not expect international trade liberalisation to have any particulareffect on the equilibrium degree of concentration. Instead, in order to getclear-cut results we turn now to models with linear demands to investigate
these issues.
5.1.1. Fixed Cost Savings
In this subsection and those that follow, we work with a linear demandmodel. Before going further, we quickly review notation. As before, m denotes the number of home firms and n the number of foreign firms. Inverse demand is given by p = a − bQ . Fixed costs are denoted f and marginal costs are denoted c.
We begin by comparing the equilibria for the four cases considered
above when fixed costs give rise to economies of scale, but where there
are no marginal cost synergies. In the benchmark case of autarky, the equilibrium (and optimal) degree of concentration m a is given by9(m + 1)3 = h,(2)where h! (a − c) /(bf ).
2

10Secondly, the ‘pre-GATT’ equilibrium degree of concentration, m d, ischaracterised by the equation(3)

2(m + 1)(2m + 1) = h.

9. The derivations for the parametric models in the paper are done with the aideof the computer programs Derive-XM Ver. 3.0, and Scientific workplace 2.5. Further details about the calculations are provided in the Appendix.
10. Please see Section A.l.l in the Appendix for derivations of (2) to (6).

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Henrik Horn and James Levinsohn

Thirdly, in the ‘GATT’ equilibrium, the degree of concentration, m g is
given by(4)

(2m + 1)3 = h.
2(m + 1)

The fourth case is where there is a supra-national merger policy thatmaximises world welfare, but where trade policies are decided upon unilaterally. The resulting degree of concentration, m k, is characterised by(5)4m(m + 1)2 = h.

Finally, the equilibrium degree of concentration, m s, pertaining to thecase where the present GATT is extended to include a supra-national
merger policy that maximises world welfare, is given by(6)

1(2m + 1)3 = h.
2

As can be seen, in all five cases the equilibrium degree of concentration
is determined by the parameter h. Note also that in all cases under consideration, firms make non-negative profits.
There are at least two ways of characterising merger policy in the different equilibria––by a measure of concentration and by a measure of monopoly power such as a Lerner index. Because of the symmetry, a Herfindahl
concentration ratio simply corresponds to the number of firms. We canthen characterise the degree of concentration in the different equilibria as
follows:
Proposition 1. For values of h such that the equilibrium number of firms
in allcases exceeds 1, m k < m s < min(m a, m d) < max(m a, m d) < m g.
Several points are noteworthy. First, while m a < m d for low values of h,and conversely for h sufficiently large, it is always the case that m g > m a.
Hence, the equilibrium degree of concentration is unambiguously lower
with free trade than in autarky. That is, there are more firms in each economy with free trade than in autarky.
This result contrasts to those usually found in models where the numberof firms is determined through zero-profit (‘free entry and exit’) restrictions. In the latter models, trade typically implies a ‘rationalisation’ in thatit reduces the number of firms in each economy, even though the combined number is larger than in either economy in autarky. The same effectcaptured in these models––the lowered profitability because of the intensi-

167

Merger Policies and Trade Liberalisation

fied competition––is also present here. Here, however, firms do not makezero profit in autarky, since the government restricts socially inefficient entry in order to exploit economies of scale. Hence, the intensified competition need not lead to a reduction in the number of firms.
Secondly, assuming countries pursue national merger policies, trade liberalisation reduces the optimal degree of concentration compared to thesituation where the countries discretionarily determine trade policies:m g > m d. The ‘GATT’ is thus in this sense pro-competitive. Note, however,that the difference m g − m d is never larger than 1/2. Thus, if the integer
constraint is taken seriously, the difference between the two concentrationlevels could not be more than one firm. In the context of the model, the
GATT has insignificant consequences for the optimal degree of concentration. We are undecided about exactly how to interpret this fact, but at thevery least, the model does not suggest a strong impact of international
trade liberalisation on nationally pursued merger policies.
Thirdly, the two equilibria involving a supranational merger policy feature significantly more concentration than the other equilibria. That is, thebasic distortion caused by nationally pursued merger policies is insufficient exploitation of economies of scale. With nationally pursued merger
policies, both countries strive to increase their market share by increasing
the number of firms. The reason why a larger number of firms tends to increase the market share is exactly the same as the reason why the oligopoly as a whole produces more the larger the number of firms––it yields a
commitment.
Our second measure of the restrictiveness of the merger policy is the
Lerner index. Denoting this index by L, L = (p − c)/p, the value of the index is in the linear model in autarky
La =

a−c
.
a + ma c

In the case of trade it is generally given by
L(m, r ) =a − c − mr,
a + m(2c − r )so that() a + 2am− c+ 1 c .
()

L md, r d =Hence,d168

Henrik Horn and James Levinsohn

Proposition 2. L d < L g < L s.
Note, first, that for any particular m, L(m, r d) < L(m, 0), providing atendency for GATT to be anti-competitive. But on the other hand, both indices are decreasing in the number of firms. Hence, to the extent that there
are more firms with than without the GATT, it has a tendency to be procompetitive. The latter of these two forces dominates the former when
2m d + 1 > 2m g. This will indeed be the case since, as was noted above,m g − m d < 1/2. Hence, it follows that on balance trade liberalisation is anti-competitive, in the sense of being associated with a higher mark-up overtrue marginal costs: L(m g, 0) > L(m d, r d).
The intuition behind this result is simple. The export subsidies tend toincrease production where, due to imperfect competition, there was too little production. When countries are then constrained not to use subsidies,
they find it optimal to enforce a market structure with more firms, and thispartially, but not fully, off-sets the negative impact of the trade liberalisation.
Secondly, we have seen that m s < m g. Hence, since the Lerner index
falls in the number of firms in the absence of subsidies, we have thatL(m s, 0) > L(m g, 0). That is, absent export subsidies, with an supranational
merger policy, the mark-ups are higher than with national policies. Again,
the problem with nationally pursued competition policies is not that they
are too lax, but rather that they are too restrictive.
Finally, observe that L s < L a if and only if 2 m s > m a. This indeed holds,
since

(

)

2ms − ma = 3 h 3 2 − 1 > 0.
Hence, as expected, the autarky equilibrium features higher mark-ups than
the free trade equilibrium with supranational merger policies, hence reflecting the size differences between the two economies. It can also be seenthat the mark-ups are higher in the autarky than in the discretionary equilibrium: L a > L d if and only if m a < 2m d + 1. It can be shown that
2md − ma = −1 / 2 + 1 / 2 (1 + 4h) − 3 h .

!

This is positive for h > 2 + 5. Hence, in the range of h considered here,
the discretionary equilibrium implies lower mark-ups than in autarky.
5.1.2. When Merger Policy is More Long-Run than Trade Policy
In the previous Section, trade and merger policy were set simultaneously.
However, one might view merger policy to be of a more long-run nature

169

Merger Policies and Trade Liberalisation(and hence changed less frequently) than the trade policy. In this subsection, we will briefly consider a variant of the model which seeks to capture
this intuition.
Let the technology and demand be as in the previous section. However,assume now that in situations where countries unilaterally decide on export
subsidies, this is done simultaneously in the two countries, but after they
have simultaneously determined their respective degrees of industrial concentration.11 The new element that appears now is that when determining
their merger policies, countries have to take into account how the consequent decisions on subsidies will be affected. In the general case, this has
the consequence of introducing derivatives of demand of an even higher
order than above, and would clearly add to the ambiguity of the outcomesin the general case. However, with the linear parameterisation we can stillsolve for the various equilibria.
It is straightforward to show that when countries set both the export subsidies and the merger policies discretionarily, the equilibrium degree ofconcentration m d is characterised by the expression.
4(m + 1)
m+2

3

= h.

In this case, the optimal concentration for one country is independent ofthat of the other country. Of course, both the ‘GATT’ equilibrium (withsubsidies constrained to be zero, but with discretionary setting of merger
policies) as well as the equilibrium with supranational merger policies (andno export subsidies), m s, are the same as in the previous model.
We can then establish the following result:12!

Proposition 3. For values of h such that the number of firms is at least
one in each equilibrium, it holds that m s < m d m g.
In other words, the basic finding in the previous subsection––that, relative to the discretionary equilibrium, the degree of concentration would fall(or at least not increase) with the agreement on the GATT, and would increase with a supranational merger policy––is at least robust to one particular specification of the sequence of decisions.
5.1.3. Marginal Cost Synergies
The model above highlighted one aspect of strategic merger policies––

11. This timing is similar to that in Rysman (2000).
12. Strictly speaking, m d < m g when treating m as a continuous variable. However, we conjecture that the difference between the two values never exceeds one.

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Henrik Horn and James Levinsohn

the incentive for individual governments to capture foreign firms’ market
shares by promoting domestic entry. In that model, entry also benefited individual governments by increasing consumer welfare, but was restrictedby its associated cost of less exploitation of economies of scale. However,mergers did not affect the competitive position of individual firms. That is,
firms were no more efficient after merging. However, much of common
thinking about mergers is that they do exactly this––indeed, this belief iswhat seems to motivate the promotion of ‘national champions’. We will
therefore in this subsection briefly consider a case where mergers lower
marginal costs of the participating firms; that is, where mergers give rise tovariable cost ‘synergies’, but where there are no fixed cost savings frommergers. Governments will again face a trade-off with regard to the merger
policy, but the incentive to hold back entry will now stem from the cost an
unconcentrated market structure has in terms of unexploited synergies.
The model is identical to the one in the previous subsection except for
two differences. First, as mentioned above, there are no fixed costs: f = 0.
More importantly, in order to capture the marginal cost synergies, we will
use a simple formulation that is similar to the one employed by Perry andPorter (1985). To this end, let the marginal cost in a firm i be k/ki2 , where
k is a constant and ki is the amount of capital employed in this firm. Let
the total fixed amount of capital be K = 1. Since all domestic firms are
symmetric, ki = K /m, so that the marginal cost in each domestic firm is
km 2. Intuitively, the government will have incentives to pursue a lax
merger policy in order to achieve low marginal costs for domestic firms,
partly for the sake of consumers (even though from their point of view thecost in terms of increased monopolisation matters) and partly in order toenhance the competitive position of domestic firms vis-a-vis their foreigncounterparts.
How does the introduction of marginal cost synergies affect countries’
incentives? We will consider three of the equilibria with trade again. First,
in the case where both subsidies and and the degree of concentration arechosen unilaterally by each country, the equilibrium degree of concentration m d is given by) ak .

(

m 12m2 + 13m + 2 =In the ‘GAIT’ equilibrium, with nationally determined industrial concentration, but with export subsidies set to zero, the corresponding value m gsolvesm2
a12m2 + 15m + 5 = .
m+1
k

(

)

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Merger Policies and Trade Liberalisation

Finally, in the absence of export subsidies, but with supranationally set
industrial concentration, the equilibrium degree of concentration m s isgiven by) ak .

(

m2 8m2 + 12m + 5 =A comparison of these three equations yields the following result:13"

Proposition 4. For values of a/k such that the number of firms in eachequilibrium is at least one, m s < m d m g.
Hence, the ranking of m s, m d, and m g is exactly the same as in the two
previous cases.
5.2. Tariffs
It might be argued that the consistency of the results above is due to thefact that in all cases, the trade policy was an export subsidy. We therefore
now turn to investigating the interaction between tariffs and merger policies, first briefly applying a more general approach, and then turning to alinear Cournot model. We assume throughout this section that tariffs are
the only trade policy at the disposal of the home and foreign countries.
In the presence of tariffs, the welfare function has to be modified to take
into account the allocational effect of tariffs and the tariff revenue. With
tariffs, welfare is now given by:! CS(m, n, t ) + H(m, n, t ) + E(m, n, t ) − mf + t ny (m, n, t ),where H (m, n, t ) ! mП (m, n, t ), E (m, n, t ) ! mП (m, n, t ), andV(m, n, th, tf)

h

h

h

h

f

h

h

h

f

h

f

y(m, n, th) is the sales of the representative foreign firm in the domestic
market.
Consider the welfare maximising degree of concentration in the domestic economy for given concentration in the other country and for given tariffs. It is obtained by equating

(

)

(

)

Vm = CSm + ∏ h + ∏ f − f + m ∏ hm + ∏ mf + tnym ,with zero. The direct impact of trade liberalisation (interpreted as a restriction on the use of tariffs) on merger policy incentives, is given by themixed derivative Vmth :13. As above, m d < m g when treating m as a continuous variable.

172

Henrik Horn and James Levinsohn

Vmt h = CSmt + ∏ ht + m ∏ hmt + n( ym + tymt ).
As was the case when we investigated the implications of an export subsidy for the optimal degree of concentration (Vms), the sign of Vmt is ambiguous. A restriction on the use of tariffs might provide an incentive forgovernments to either relax or restrict industry concentration.
With a linear demand, and equal marginal costs c and fixed costs f ,

( )

[

]

sgn Vmth = − sgn (a − c)(m − n) + t h n(2m + 1) .
This expression can clearly take on either sign. But, in the symmetric case,a reduction in a country’s tariff level provides an incentive for the country
to reduce domestic concentration.
Characterising merger policy by the degree of concentration: The autarky equilibrium number of firms m a is, of course, the same as in the previous section, and is given by (2). Likewise, the equilibrium industrial concentration ‘with GATT’, i.e., with tariffs constrained to zero, and with national control of merger policies, is the solution m g as given by (4), andthe supranational competition authority would still choose m s, as given by(6).
The difference between the case of tariffs and subsidies arises in the discretionary case. The equilibrium degree of industrial concentration with thand tf unilaterally decided by the countries, is given by(m + 2)2 (2m + 1)3 = h.
8m2 + 12m + 5

We can then show the following:
Proposition 5. m s < m d < m a < m g.
Note that the ranking of industrial concentration in this case of tariffs is
identical to the ranking in the case of export subsidies!
Characterising merger policy by Lerner indices: The Lerner index withGATT (i.e., th = tf = 0), is the same as in the case of export subsidies in
Section 5.1. The Lerner index without GATT is now
L(m, t h ) =a − c + th m.
a + m(2c + t h )173Merger Policies and Trade Liberalisation

It can be shown, that for any particular value of m, the Lerner index ishigher without GATT than with GATT. This only says that prices arehigher with the tariffs. However, the number of firms will not be the samein the two equilibria. We have already seen that m g > m d. Therefore, sinceboth the Lerner indices fall in the number of firms, we have the following:
Proposition 6. L g < L d < L s.
To summarise, the general conclusions concerning the impact of international trade liberalisation on industrial concentration are almost the same inthe case of tariffs as they are in the case of export subsidies. In particular,
the removal of tariffs will induce countries to reduce industrial concentration, while from a global point of view it would be preferable that countries did just the opposite. The main difference between the tariffs and subsidies is that when tariffs are removed, the degree of monopoly power, as
measured by a Lerner index, decreases whereas it increases in the case ofexport subsidies. The concern that GATT might induce countries to pursue
less vigorous merger policies hence finds even less support in the case oftariffs than with export subsidies.
6. Trade Liberalisation and the Desirability of Supra-National Merger
Policies
As noted at the beginning of the paper, some observers have suggested
that trade liberalisation increases the desirability of, or need for, supranational merger policies. The implicit assumption is presumably that there
are also gains to be had from supranational merger policies prior to tradeliberalisation, but that these gains have increased as a result of the tradeliberalisation. We will in this subsection briefly take a look at whether
such a claim is warranted within the confines of the above model.
6.1. What Constitutes a ‘Beggar-Thy-Neighbour’ Merger Policy?
A basic conceptual problem with the above-mentioned claim is the lackof a precise meaning of the terms ‘desirability’ or ‘need’. Implicit in thestatement seems to be the presumption that trade liberalisation induces acountry to change its merger policies in a direction that is detrimental toother countries. This raises the basic question of what direction this would
take. What constitutes a beggar-thy-neighbour merger policy? Concentration among foreign firms will be detrimental to the domestic economy if:
Vn = CSn + Hn + En > 0,
while it would be beneficial in the opposite case. The entry of a foreign

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Henrik Horn and James Levinsohn

firm will increase the total output, and will thus bring gains to consumers,
but will bring losses for producers. The balance of these two effects is ambiguous, and will partly hinge on the relative importance of consumer andproducer surplus. For instance, if profits are small initially, the positive effect of entry on consumer surplus may dominate. In this case, increased
concentration abroad would amount to more of a beggar-thy-neighbour
policy. On the other hand, if the domestic market is small relative to theforeign market, the opposite may prevail. We are thus led to the unsatisfactory conclusion that we cannot determine a priori whether concentrationin one country is good or bad for other countries. Nor are we able to do soin the linear fixed cost model, even absent active trade policies. For instance, in the latter case
Vn =

h2

(m + n + 1)3(n − 3m),the sign of which is ambiguous in general.
6.2. The Claim in Four Different Versions
One possible interpretation of the above argument would then be to lookat the situation from the point of view of an individual country, say thehome country. Trade liberalisation could then be said to lead to more of a
beggar-thy-neighbour merger policy if it induces the foreign country tochange its merger policy in a direction that is unfavourable to the homecountry, given that the home country does not change any of its policies.
Interpreting the liberalisation as a marginal reduction in the foreign trade
policy instrument s, this situation would prevail if simultaneously
Vnh < 0 and Vnsf < 0, or Vnh > 0 and Vnsf > 0, for s > 0,
where superscripts h and f denote home and foreign welfare, respectively.
A second interpretation would be that trade liberalisation undertaken byboth countries changed the foreign country’s incentives with regard tomerger policy in an unfavorable direction for the home country, for agiven home country merger policy. Considering a symmetric situation withan equivalent small reduction in both r and s, this would correspond to thecase where either
Vnh < 0 and Vnsf + Vnrf < 0, or Vnh > 0 and Vnsf + Vnrf > 0, for r , s > 0.
A third possible interpretation is that trade liberalisation fosters a beggar-thy-neighbour merger policy in the foreign country if the combined effect175

Merger Policies and Trade Liberalisationof the reductions in export subsidies and the induced change in the merger
policies of the two countries result in a foreign degree of concentration
which is less preferable than the pre-liberalisation concentration. Thus,
comparing for instance the discretionary equilibrium and the ‘GATT’ equilibrium, trade liberalisation would be said to induce more of a beggar-thyneighbour merger policy in the foreign country if
V h(m g, m g, 0, 0) < V h(m g, m d, 0, 0).
There are also other possible interpretations, but no single interpretation
has a claim to general superiority. Instead, what constitutes the best measure depends on exactly what is being asked. However, if one wants to argue that the gains from supranational merger policies are larger after liberalization than before, then a more suitable approach would be to comparechanges in welfare levels from supranational merger policies with andwithout trade (before and after) trade liberalisation. If
V (m s, m s, 0, 0) − V (m g, m g, 0, 0) > V (m c, m c, r c, r c) − V (m d, m d, r d, r d),then the welfare gain from a supra-national merger policy is larger withthan without trade liberalisation. Of course, this would be equivalent to establishing the claim that the gains from trade liberalisation are larger withsupranational merger policies than with nationally pursued policies:
V (m s, m s, 0, 0) − V (m c, m c, r c, r c) > V (m g, m g, 0, 0) − V (m d, m d, r d, r d).
It is simply not obvious under what intuitively interpretable conditions theabove inequalities might hold, and this is true for the linear model as wellas the more general model. Hence, in even the linear model, the notionthat the gains from supranational merger policies are larger after trade liberalization than before is not verifiable or refutable unless one resorts tonumerical examples.
7. Concluding Discussion
At the outset of this paper, we noted that the intuition with which many
informed economists approach the links between trade and merger policy
is often not correct. While it is true that trade liberalisation is typically pro-competitive, this does not provide the basis for determining whether tradeliberalisation will lead to a more lax competition policy. Instead, what is atstake are the consequences of trade liberalisation for the marginal incentives facing merger policy.
We have investigated the related notion that international trade liberalisation has the undesirable consequence of inducing countries to adjust their

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Henrik Horn and James Levinsohn

merger policies in a beggar-thy-neighbour direction. The analysis above,
simple as it is, points to some potentially serious weaknesses in this argument. First, it is not clear whether a beggar-thy-neighbour policy involves
more or less concentration among domestic firms, and this is true even in
the linear case. More generally, the very notion of a beggar-thy-neighbour
competition policy is somewhat amorphous. We suggest several plausible
interpretations and their implications vary depending on what definition isadopted.
As we examined the impact of trade liberalisation on the equilibrium industry structure (i. e. competition policy) in a fairly general framework, wewere not able to draw many unambiguous conclusions. Yet when we thenmoved to several specifications of the linear model, for example with andwithout synergies, and simultaneous and sequential setting of merger andtrade policies, the results are remarkably similar across all the specifications. In particular, in all the parametric cases examined above, trade liberalisation results, in equilibrium, in a stricter standard for competition policy. Thus, even in very simple models, replacing intuition with a more
analytic approach matters.
When we considered supra-national merger policy, we found that the
problem is not that there are too few firms with mark-ups that are too high,but rather the contrary: countries foster too little concentration, and they doso in order to increase the market share in export markets. This proves
costly since it implies an under-exploitation of economies of scale.
Nonetheless, the paper finds little support for the idea that, because of astrong trade policy-merger policy linkage, merger policies should be internationally regulated. Of course, a lack of a clear link between trade andmerger policies does not preclude the possibility that there are substantial
gains to be had from international agreements on merger policies. Indeed,this paper has shown how nationally pursued merger policies may be associated with externalities between countries.14 The rationale for such an
agreement would not stem from the inter-linkage between trade policy andmerger policy, but rather from the fact that there are negative international
externalities from nationally pursued merger policies, just like in the case
14. For example, note (for what it is worth) that in the symmetric linear Cournot
model, the quantitative impact of a supranational merger policy seems to dependvery little on whether trade is or is not liberalised. Note also that it has a muchlarger impact than trade liberalisation. These observations are at least consistent
with the view that a supranational merger policy could be defended in its own right,
regardless of whether or not there is an international trade agreement even though
they certainly do not constitute a formal justification.
15. However, as argued by Bacchetta et al . (1998), such a theoretical argument
is only a necessary, but not sufficient, reason for implementing such policies. It
must also be shown that the externalities involved are empirically large enough tojustify intervention and that there are no better legal alternatives than an international agreement.

177

Merger Policies and Trade Liberalisationof trade policies.15
Finally, the list of restrictive assumptions underlying the models is painfully long. Some are special in the sense of relying on specific functional
forms and symmetry. But these are pretty obvious. Let us instead point tofive more general weaknesses that need to be modified in subsequent work.
First, the notion of capturing merger policy by the choice of the degreeof concentration seems to be a natural starting point, but not more thanthat. Instead, one needs to take into consideration firms’ incentives tomerge, and the impact of the merger policy on mergers. This requires atheory of endogenous merger determination.
Secondly, much of the policy debate has focused on the possibility thatgovernments might treat firms differently depending on their nationality,
whereas the analysis here has concerned the more general policy of choosing an industrial structure. It is not clear to us whether this focus in the debate reflects commentators’ beliefs that the discriminatory aspects are empirically more important than the general aspects, or if it stems from thefact that discrimination violates much of the spirit of the GATT. In any
event, it is clear that we need to study the incentives of governments toemploy merger and competition policies in a discriminatory fashion.
Thirdly, the assumption that governments maximise social welfare ismuch neater than reality. A first problem is the fact that many governments seem to have other objectives. Here, one could easily modify theobjective by weighting the components in the welfare function differently
as done by, for example, Richardson (1999). A more serious problem,
which this paper shares with most other papers in economics, is the assumption concerning the information at the disposal of the government. In
actuality, it is very hard to evaluate welfare consequences of most mergers
with any degree of precision. This lack of information makes the conductof competition policy much more of a ‘trial-and-error’ process than is usually acknowledged. As a consequence, there are gains to be had from aworld perspective of not harmonising competition laws, in order to learn
the most efficient form of legislation.
Fourthly, in the tradition of the two sets of theories on which the paperbuilds, those of industrial organisation and strategic trade policy, the analysis has been done in partial equilibrium. However, an international agreement on merger policy, and more generally competition policy, will most
likely not be sector specific, but apply to the whole tradeables sector.
There are therefore reasons to believe that a general equilibrium approach
might be more suitable.
Lastly, this paper does not consider the possibility of multinational firms
as only purely domestic mergers are analysed. Relaxing this restriction
would complicate the analysis, but would be an important advance sinceinternational mergers are an increasingly important policy concern.

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Henrik Horn and James Levinsohn

Appendix
The following expressions pertain to the models in Subsections 5.1.1–
5.1.3. Let the output of a Home country firm in its home market be x, leta foreign firm’s sales be y, and let ch(cf) be the home (foreign) country
firm’s marginal cost.
As in the text, we maintain the following assumptions. Markets are segmented, countries are identical, firms compete in a Cournot fashion, andfirms face a linear industry demand curve given by p = a − bQ .
In equilibrium:(a − (n + 1)ch − n c f − sx=b(m + n + 1)(),

a − mch − (m + 1) c f − sy=b(m + n + 1)).

Taking account of the symmetry between markets, the total profits of ahome country firm, including subsidies, equal[a − (n + 1)c − n(c − s)] + [a − nc − (n + 1)(c − r )] − f .
2

2

h

f

f

h

b(m + n + 1)

2

b(m + n + 1)

2

Consumer surplus (CS ) is[(m + n)a − mc − n(c − s)] ,2h2b(m + n + 1)

f2

and the government outlays on export subsidies are[a + nc − (n + 1)(c − r )] r.
−m
2

f

h

b(m + n + 1)

Home country welfare (V ( ) in the text) is then the sum of these expressions.
A.1. The Model in Subsection 5.1.1
In the model in subsection 5.1.1, ch = cf

! c.

179

Merger Policies and Trade Liberalisation

A.1.1. Equilibria in the Different Policy Regimes
Note that by Proposition 1 (which is established below), m k is the lowest
among equilibrium concentrations under consideration. In order to ensurethat ink m k 1, we restrict attention to cases where h 16
hmin. Withch = cf c, the equilibria are the following.
(i) The equilibrium degree of concentration in autarky is

!

"

" !

f a(m)! (m + 1) = h.
3

It is clear that there is a unique solution to this equation for any h.
(ii) With discretionary setting of both trade and merger policies, the subsidies are given by

(A1)

rj =

(a − c)()

2bm j m j + 1; j = d , k.

The equilibrium degree of concentration is given byf d(m)! 2(m + 1)(2m + 1) = h.

f d(1) < hmin, f d is continuous and monotonically increasing in m, andgoes to infinity as m goes to infinity. Hence, a unique solution exists
for any h.
(iii) With r = s = 0, and discretionary determination of merger policies:
32m + 1)(f (m) ≡= h.
2(m + 1)g

f g(1) < hmin, f g(m) increases monotonically in m
d g
1
2 4m + 5
f (m) = (2m + 1)
> 0,
dm
2
(m + 1)2
andlim f g (m) = ∞.

m→∞

Hence, there exists a unique solution for any h.
(iv) With a supra-national merger policy, and discretionarily determinedtrade policies, the subsidies are again given by the expression above,and the equilibrium degree of concentration is given by:

180

Henrik Horn and James Levinsohn

f k(m)! 4m(m + 1) = h.
2

f k(1) < hmin, f k is monotonic in m, and approaches infinity as m becomes very large. Hence, there is a unique solution for any h.
(v) Finally, with a supra-national merger policy and r = s = 0:1(2m + 1)3 = h,2f s (m) ≡which also has a uniques solution for any h.
A.1.2. Non-Negativity Constraints
Consider first the constraint ensuring positive outputs: a−c>max(ns,mr).
By the symmetry of the equilibrium, and using the expression for the optimal r above, this corresponds to the requirement thata−c>(a − c) ; j = d , k ,()

2b m j + 1

or m j > 1/2b−1; this condition is definitely fulfilled for b > 1/4.
Now turn to profits. There are three types of situations. First, profits are
non-negative in autarky iff

α a(m)! (m + 1) "h.
2

Secondly, with discretionary determination of export subsidies (includes
the equilibria m d and m k) profits are non-negative iff

α d (m) ≡4m2 (m + 1)
≤ h.
2 m2 + 2 m + 1
2

Thirdly, with merger policy set discretionarily, and with r = s = 0, profits
are non-negative iff

α g (m) ≡1(2m + 1)2 ≤ h.
2

Clearly, since m g > m s, this also ensures that profits are positive in thecase with supranational merger policies and the GATT.
Note that

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Merger Policies and Trade Liberalisation

1
< 0,
2
1 6m2 + 6m + 1
α d (m) − α g (m) = −< 0.
2 2 m2 + 2 m + 1

α a (m) − α g (m) = − m2 +"Hence, if the constraint α g(m)h is fulfilled for all m, then the otherconstraints are also fulfilled. This is indeed the case, since32m + 1)(
1
2
f (m) − a (m) =− (2m + 1)
2(m + 1) 2
g

g

=

m
1
> 0.
(2m + 1)2m+1
2

Hence, profits are positive in all equilibria.
A.1.3. Proof of Proposition 1
In order to establish Proposition 1, we make pairwise comparisons of theequilibrium expressions:1
4m + 3> 0,(2m + 1)2m+1
f a (m) − f d (m) = (m + 1) m2 − 2m − 1 >< 0,
f d (m) − f g (m) =()

f k (m) − f a (m) = (3m − 1)(m + 1) > 0,2

f k (m) − f s (m) = 2m2 + m −

1
> 0.
2

It follows from the facts that: (i) f d(m) − f g(m) > 0; (ii) both functions aremonotonically increasing in m; and (iii) there is a unique solution for any
h, that for any h, m d < m g. The other claims in the Proposition follow
analogously.
A.2. The Model in Subsection 5.1.2!

We continue to have ch = cf
c. The expressions for equilibrium quantities and the welfare function are thus the same as for the model in Subsection 5.1.1, and the equilibrium values m g and m s are also the same as inthat model. The only new case to consider is the discretionary equilibrium.
The optimal subsidies are still given by (Al). But, when optimising overthe number of firms, the countries take into consideration the fact that the182

Henrik Horn and James Levinsohn

subsidies are determined as in (Al). As it turns out, the optimal number ofhome country firms m d is independent of the number of foreign firms, andis given byf d (m) ≡ 4(m + 1)3 = h.
m+2This expression has a unique solution for any h, since f d(1) < hmin, f d is
dcontinuous and monotonic in m, and limm→∞ f (m) = ∞. It is also straightforward to show that the second order condition for the optimisation w.r.t.
m is always fulfilled.
A.2.1. Proof of Proposition 3
The Proposition follows from the above, and from the facts thatf d (m) − f g (m) =1 4m3 + 18m2 + 19m + 6> 0,(m + 2)(m + 1)
2

f s (m) − f d (m) =1 8m4 + 20m3 + 6m2 − 11m − 6> 0 for m > 1.
m+2
2

A.3. The Model in Subsection 5.1.3
We now assume that ch = mk 2 and that cf = nk 2, and furthermore thatf = 0. We are only concerned with situations where a/k
25, in order form 1 in all three equilibria. The expressions for equilibrium quantities andthe welfare function, are the same as for the model in Subsection 5.1, withch = mk 2 and cf = nk 2.
(i) With discretionary determination of both trade and merger policies:!

!

) ak ,(f d (m) ≡ m 12m2 + 13m + 2 =which clearly has a unique solution for any h. It can also be shownthat the second order conditions are fulfilled locally in this equilibrium.
(ii) In the ‘GATT’ equilibrium:f g (m) ≡m2
a
12m2 + 15m + 5 = .
m+1
k

(

)

This has a unique solution for any a/k, since f g (1) < 25,183

Merger Policies and Trade Liberalisationd g
18m3 + 39m2 + 25m + 5
f (m) = 2m
> 0,dm
(m + 1)2
andlim f g (m) = ∞.

m→∞

Again, the second order conditions can be shown to be fulfilled locallyin this equilibrium.
(iii) With supranational merger policy and no export subsidies:) ak ,(f s (m) ≡ m2 8m2 + 12m + 5 =which clearly has a uniques solution for any a/k. Again, the second order conditions are fulfilled locally in this equilibrium.
A.3.1. Proof of Proposition 4
The ranking of the merger policies follows from the fact that
5m2 + 5m + 1> 0,
m+1
4 m2 + 4 m + 1
f s (m) − f g (m) = 2m3> 0.
m+1
f d (m) − f g (m) = 2m

A.4. The Model in Subsection 5.2
We now turn to the case of specific tariffs th and tf, and with identicalmarginal and fixed costs. In equilibrium home market quantities, consumer
surplus, total profits of a home country firm, and government revenue,
are:16x=y=a − c + nt h,
m+ n +1

a − c − (m + 1)t h,
m+ n +1

16. The parameter b is unity in this subsection.

184

Henrik Horn and James Levinsohn[(m + n)(a − c) − nt ] ,CS (m, n, t ) =2

h2(m + n + 1)

h

2

[

(a − c + nth ) + a − c − (n + 1)t f~
Π m, n, t h , t f =(m + n + 1)2(m + n + 1)2

(

2

)

] − f,
2

and
G(m, n, r ) = n

a − c − (m + 1)t h
th .
m+ n +1

The only equilibria here that differ from the corresponding ones in thecase of export subsidies are those with discretionary setting of trade policies, and among those, we only consider that with both merger and trade
policy discretionarily set:2
3
m + 2) (2m + 1)(
f (m) ≡= h.
2d8m + 12m + 5

The second order conditions supporting this equilibrium can be shown tobe fulfilled. This equilibrium condition has a unique solution for any h,since f d(1) < hmin,
24m2 + 40m + 23
d d
2
> 0,
f (m) = 2(2m + 1) (m + 2)(m + 1)2
dm
8m2 + 12m + 5

(

)

and
lim f d (m) = ∞.

m→∞

A.4.1. Proof of Proposition 5
The Proposition follows from the findings above, combined with thefacts thatf d (m) − f a (m) =8m4 + 21m3 + 14m2 + m − 1> 0,
8m2 + 12m + 5

185

Merger Policies and Trade Liberalisationandf s (m) − f d (m) =1
6m2 + 4m − 3> 0.
(2m + 1)3 2
2
8m + 12m + 5

References
American Bar Association. 1996. Symposium: The Role of Foreign Competition in
the U.S. Merger Enforcement. Antitrust Law Journal 65(1): 223-276.
Auquier, A. and R. Caves. 1979. Monopolistic Export Industries, Trade Taxes, andOptimal Competition Policy. Economic Journal 89: 559-581.
Bacchetta, M., H. Horn, and P. Mavroidis. 1998. Do Negative Spillovers from Nationally Pursued Competition Policies Provide a Case for Multilateral Competition Rules? In European Competition Law Annual 1997: Objectives of Competition Policy, eds. C-D. Ellermann and L. L. Laudati. Oxford: Hart Publishing:271-309.
Barros, P. and L. Cabral. 1994. Merger Policy in Open Economies. European Economic Review 38: 1041-1055.
Bhagwati, J. 1991. Fair Trade, Reciprocity and Harmonization: The Novel Challenge to the Theory and Policy of Free Trade. Paper Presented to the Conference
on Analytical and Negotiating Issues in the Global Trading System, Universityof Michigan, Ann Arbor.
Bliss, C. 1996. Trade and Competition Control. In Fair Trade and Harmonization,
eds. J. Bhagwati and R. Hudec. Cambridge MA: MIT Press: 313-328.
Bond, E. 1997. Competition Policy in Customs Unions: A “Natural Experiment”
Using State Level Antitrust Enforcement. Penn State University, Department of
Economics, mimeo.
Brander, J. and B. Spencer. 1984. Trade Warfare: Tariffs and Cartels. Journal ofInternational Economics 16: 227-242.
–––– . 1985. Export Subsidies and International Market Share and Rivalry. Journalof International Economics 18(1-2): 83-100.
Dixit, A. 1984. International Trade Policy for Oligopolistic Industries. Economic
Journal 94 Supplemental Issue: 1-16.
Eaton, J. and G. Grossman. 1986. Optimal Trade and Industrial Policy under Oligopoly. Quarterly Journal of Economics 101(2): 383-406.
Francois, J. and H. Horn. 2000. Competition Policy in an Open Economy. Tinbergen Institute Discussion Paper no. TI98 092/2.
Gatsios, K. and P. Seabright. 1990. Regulation in the European Community. Oxford Review of Economic Policy 5(2): 37-60.
Hawk, B. ed. 1994. Antitrust in a Global Economy. Proceedings of the Fordham
Corporate Law Institute. Dordrecht: Kluwer.
Head, K. and J. Ries. 1997. International Mergers and Welfare under Decentralized
Competition Policy. Canadian Journal of Economics 30(4): 1104-1123.
Hoekman, B. and P. Mavroidis. 1994. Competition, Competition Policy and the
GATT. CEPR Working Paper no. 876.
Horn, H. and L. Persson. 2001. Endogenous Mergers in Concentrated Markets. International Journal of Industrial Organization 19(8): 1213-1244.
Levinsohn, J. 1996. Competition Policy and International Trade Policy. In Fair

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Trade and Harmonization, eds. J. Bhagwati and R. Hudec. Cambridge MA: MIT
Press: 329-356.
Lloyd, P. and G. Sampson. 1995. Competition and Trade Policy: Identifying the Issues after the Uruguay Round. World Economy 18: 681-705.
Motta, M. and F. Onida. 1997. Trade Policy and Competition Policy. Giornale degli Economisti e Annali di Economia 56(1-2): 67-97.
Neven, D. 1992. Regulatory Reform in the European Community. American Economic Review 82(2): 98-103.
Neven, D. and P. Seabright. 1997. Trade Liberalization and the Coordination ofCompetition Policy. In Competition Policy in the Global Economy, Modalities
for Cooperation, eds. L. Waverman, W. Comanor and A. Goto. London: Routledge: 381-406.
Ordover, J. and R. Willig. 1986. Perspectives on Mergers and World Competition.
In Antitrust and Regulation, ed. R. E. Grieson. Lexington, Mass. and Toronto:
Heath, Lexington Books: 201-218.
Perry, M. and R. Porter. 1985. Oligopoly and the Incentive for Horizontal Merger.
American Economic Review 75(1): 219-227.
Richardson, M. 1999. Trade and Competition Policies: Concordia Discors? Oxford
Economic Papers 51(4): 649-664.
Rysman, M. 2000. Competition Policy in Strategic Trade. Industry Studies Program Working Paper no. 100. Boston University.
Trebilcock, M. 1996. Competition Policy and Trade Policy––Mediating the Interface. Journal of World Trade 30(4): 71-105.

9

Why not Set Tariffs Uniformly
Rather than Optimally
Tatsuo Hatta*

1. Introduction
The World Bank economists in the operation divisions have been recommending the adoption of a uniform tariff to the developing countries, while
economists in the research divisions have been emphasizing that therevenue-constrained optimum tariff structure is non-uniform.1
This dichotomy of thought between practitioners and researchers as tothe desirability of uniform tariff rates is similar to the dichotomy that exists between practitioners and researchers in tax policy regarding uniform
commodity tax rates. Although the optimum tax rules have been the focusof research in public economics during the last quarter of century, the policy makers of the recent Japanese and U.S. tax reforms have taken for
granted the desirability of uniform commodity tax rates for the efficiency
purpose. Indeed, the Japanese reform substituted a uniform value added tax
system for a highly divergent excise tax system, and the main slogan of
the 1986 U.S. reform was “leveling the playing field.”
The arguments of tax policy practitioners for a uniform commodity tax
are well known: If different tax rates were imposed on a pair of substitutes,
a consumer would be able to reduce the amount of tax payment by substituting the commodity with the lower tax rate for the commodity with the* I would like to thank Arvind Panagariya and Shanta Devarajan, who introduced me into the topic of the revenue-constrained optimum tariff. Their insightfulcomments and encouragements are also greatly appreciated. An earlier version of
the paper was presented at a workshop of the World Bank. I would like to thank its
participants for their useful comments.
1. See Rajaram (1994) for a review of the World Bank’s tariff recommendations.
See Dahl, Devarajan, and van Wijnbergen (1994) and Mitra (1994) for researchers’
view.
187

188

Tatsuo Hatta

higher. These tax avoidance activities will cause distortions. Thus, a uniform commodity tax is most efficient. Musgrave’s classic work (1959) is
well known for taking this position.
Optimum tax theorists agree that the optimum commodity tax rates
would be uniform if leisure were taxed at the same rate. They argue, however, that since leisure is untaxable in the real economy, a uniform commodity tax will inevitably distort the choice between leisure and commodities. In their view, therefore, commodity tax rates have to be adjusted so as
to offset the leisure-commodity distortion as much as possible.
The revenue-constrained optimum commodity tax structure is clearly
non-uniform. But there is also some truth in practitioners’ hunch that divergences among commodity tax rates cause their own distortions. Thus,
there must be a trade-off in making tax rates divergent. To make this trade-off explicit, Hatta (1986) and Hatta and Haltiwanger (1986) formalizedpractitioners’ hunch within the framework of optimum tax theory. Using
this formulation, they observed that the uniform commodity tax structure is
likely to be a good approximation of the optimum structure in an economy
where substitution among commodities is dominant. This observation integrates practitioners’ intuition for uniform taxes into the framework of optimum tax theory. Since this observation gives a new justification for theuniform tax, it may be called the neo-Musgravian perspective. Empiricalevidence by Fukushima and Hatta (1989) and Fukushima (1989) further
support this perspective. It justifies the fact that most tax policy practitioners use uniform commodity taxation as their policy guideline.
The purpose of the present paper is to apply this observation to therevenue-constrained optimum tariff structure.
Unlike the optimum tax, however, the revenue-constrained optimum tariff is discussed in the models of fixed labor supply, where nonobservability of leisure consumption is not an issue. Nevertheless, optimum
tax theory is directly relevant to the revenue-constrained optimum tariffstructure. Just as commodity taxes discourage the consumption of commodities (which is “imported” from the market) and encourage that of leisure (which is “exported” to the market as labor), import tariff is discourage the consumption of imported goods and encourage that of exported
goods. Thus any import tariffs create distortions in the choice between the
consumption of imported and exported goods. When import tariffs alone
have to raise a given revenue, therefore, the optimum import tariff structure has to be non-uniform. In the simplest setting, the model of revenueconstrained optimum tariff rates under fixed labor supply becomes identical with that of optimum tax rates under flexible labor supply.
In view of the neo-Musgravian perspective regarding optimum commodity taxation, therefore, there is a possibility that a uniform tariff structure
can be regarded as a good approximation to the optimum structure. We
will examine the similarities and the differences between the optimum tax

189

Why not Set Tariffs Uniformly Rather than Optimallysituation and the revenue-constrained optimum tariff situation.
Section 2 defines the issue of revenue-constrained optimum tariffs, while
section 3 does the same for optimum taxation for a two good economy. In
section 4, we derive a revenue-constrained optimum tariff formula for athree-good economy. In section 5, we first discuss the implications of thisformula in the optimum tax context, and then apply them to the revenueconstrained tariff situation. Section 6 discusses the efficiency effects of tax
and tariff reforms for the economy with four or more goods. In particular,
we formally interpret the tax policy practitioners’ hunch for recommending
tax reforms toward uniformity. This interpretation is applied to the optimum tariff situation. A few concluding remarks are given in the final section.
2. Revenue-Constrained Optimum Tariff Rules: The Issue
Consider a small open economy where a fixed commodity bundle issupplied. In this economy, uniform excise taxes can attain the first best solution under the constraint of raising a given revenue. No combination oftariffs, however, can attain this first best solution. Revenue-constrained optimum tariff is thus become a non-trivial issue. In this section, we will illustrate this by a two-good model.
A. Optimality of Uniform Excise Taxes
Figure 1 depicts a small open economy which produces two goods, X
and Y . Point Q is the production bundle. The slope of the bold line represents the relative prices of the two goods. Thus the bold line in this figureis the budget line that the consumers of this economy face in the absenceof taxes. The indifference curves in the diagram represent the representative consumer’s preferences. Consumption takes place at point F , which is
the tax-free consumption bundle.
Let us now suppose that the government has to raise a revenue equal to
the length AC measured in the Y unit. Suppose first that a lump-sum tax islevied to raise this revenue. Then his budget line will be the line CD ,which starts at C and is parallel to the bold line. The consumption bundle
will then move to point L.
Suppose that the government imposes an excise tax on commodity Y .
The line BH in Figure 2 will then represent the consumer’s budget line. It
starts at point B , but cuts the vertical axis below A. Utility is then maximized at point E , and the government revenue equals the length of the line
segment AC . In this diagram, therefore, the tax rate on commodity Y is sochosen that the resulting government revenue is exactly equal to the revenue raised by the lump sum tax in Figure 1.

190

Tatsuo Hatta

Figure 1

If excise taxes can be imposed both on commodities X and Y , the consumer’s budget line will pass through a point to the left of B . By equating
the tax rates on both commodities, the budget line can be made identical to
the line segment CD in Figure 1. This combination of excise taxes
amounts to a lump-sum tax. After all, a tax payer cannot reduce theamount of his tax obligation by changing the consumption mix. Thus, uniform excise tax rates on both commodities attain the optimum under theconstraint of raising a given government revenue.

Figure 2

B. Suboptimality of Tariff Equilibrium
Let us now suppose that import tariffs rather than excise taxes are imposed on commodity Y as the only source of government revenue. The

191

Why not Set Tariffs Uniformly Rather than Optimallyline QK in Figure 3 represents the budget line under an import tariff. The
vertical distance between this line and the bold line measures the tariff
revenue of the government at each point of the budget line. The tariff rate
on Y corresponding to the budget line QK is so chosen that the government revenue under the optimized consumption bundle M is equal to AC .
If X is a normal good, point M in Figure 3 is the only point on the line
CD that is attainable by an import tariff.2 Therefore, an import tariff equilibrium can not attain the first best.
Can a combination of import and export tariffs attain the first best? Just
as an import tariff, an export tariff reduces the size of trade, increasing thedomestic relative price of the imported commodity. Indeed, the line QK
can also represent the consumer’s budget line under an export tariff on X .
By changing the tariff rates on exports and imports, the consumer’s budget
line pivots around the point Q . Thus no combination of tariffs, including
the one that equalizes tariff rates on import and export goods, can makethe budget line parallel to the bold line. In other words, no combination ofimport and export tariffs can attain the first best in the model of Figure 3.

Figure 3

C. Revenue-Constrained Optimal Tariff Structure
The above discussion shows that if X is a normal good, point M in Figure 3 is the only point on the line CD that is attainable by a combinationof tariff rates.3 In the two commodity setting, therefore, there is no room
2. Note that point M corresponds to infinitely many combinations of import andexport tariffs. In the following, therefore, we will normalize the tariff rates by assuming that one of the export tariff rates is always zero.
3. If X is an inferior good, a point other than M may be attainable on the line
CD by a combination of tariff rates. See Hatta (1977a).

192

Tatsuo Hatta

for choosing the equilibrium by adjusting tariff, and the concept of an optimal structure of tariff rates is meaningless.
The concept of an optimum tariff makes sense, however, in an economy
with more than two commodities. To see this, generalize the economy described above to a three commodity economy where two commodities areimported and one commodity is exported. Then the equal revenue line CD
of Figure 3 is generalized to an equal revenue plane. Again no combination of tariffs can attain the first best on this plane. This time, however,many different points on this plane are attainable by different combinationsof tariff rates on the two imports, and choice of the optimal import tariff
rates under a constrained revenue becomes a meaningful issue.4
3. Optimum Tax Rules: The Issue
The revenue-constrained tariff rules outlined above have a similar theoretical structure to the “optimal tax rules” studied in public economics. In
the following, we will present those findings of this literature that are relevant to the “revenue-constrained tariff rules.”We have so far implicitly assumed that labor supply, and hence leisuredemand, is fixed. In such an economy, imposing an equal ad valorem excise tax rate on all commodities would amount to a lump-sum tax. (Hereand in the following, a good is called a commodity if it is not a leisure.
Thus the phrase “all commodities” will not include leisure, while “allgoods” consists of leisure and all commodities.)
In the optimal taxation literature, however, a critical role is played by
the assumption that leisure consumption is endogenously determined. Of
course, even under this assumption, an efficient resource allocation would
be attained for the given revenue if an equal ad valorem excise tax rate
could be imposed on all goods including leisure.
The problem is that leisure is untaxable in reality. A tax payer has astrong incentive to under-state his leisure consumption; by doing so hecould reduce his claimed tax base for the leisure tax. Thus the tax officecannot gather precise information on the leisure consumption of each tax
4. Note that this topic of “revenue-constrained optimum tariff rule” is entirely
different from the traditional topic of “optimum tariffs”. The latter examines thesituation where the country concerned is large, facing an upward-sloping supply
curve of its imports. This literature usually assumes that the entire tariff revenue isreturned to the consumers through a lump-sum tax. This means that any change intariffs is accompanied by a revenue-offsetting change in a lump-sum tax. If thecountry were small, therefore, the optimum tariff rates in this situation would be
zero. Non-zero rates become optimal only because the country considered in the
traditional optimum tariff theory is large.
On the other hand, “the revenue-constrained optimum tariff rates” of a small
country are non-zero because no lump-sum taxes are available by assumption.

193

Why not Set Tariffs Uniformly Rather than Optimally

payer, and hence cannot levy tax on leisure.
The tax office, however, can easily obtain data on the wage income of atax payer from his employer. In the real economy, therefore, tax is imposed on wage income, rather than on leisure consumption. An importantdifference between the two taxes is that a tax on wage income encourages
leisure consumption, while a tax on leisure consumption discourages it.
Thus a tax on wage income could not neutralize the effect of a commodity
tax upon leisure consumption. Optimality cannot be generally attained,
therefore, by a simultaneous imposition of taxes on all commodities andwage at the same rate cannot generally attain the optimality.
To use the terminology of international trade, wage tax is imposed on
the export of leisure, rather than on its consumption. This creates a similar
situation as in Figure 3, where no combination of import and export tariffs
can attain the efficient consumption bundle L. Figure 4 depicts this situation. The horizontal axis now represents the leisure consumption of thiseconomy, while the vertical axis represents the consumption of the commodity. The initial endowment of leisure is OQ and that of the commodity
is zero. Thus the point Q represents the consumers’ initial endowment
bundle. The wage rate in terms of units of the commodity is represented
by the slope of the bold line.

K
O

Figure 4

Suppose that the government has to raise a revenue equal to AC . The
first best consumption bundle would then be L. But it is not possible to attain L by adjusting the commodity tax rate or the wage tax rate. Such an
adjustment would pivot the consumer budget line around Q . In the figure,the given government revenue is attained by the budget line QK at the distorted consumption bundle M . In the model of Figure 4, therefore, the degree of freedom of feasible tax rates is again limited as in the model of
Figure 3, and hence the issue of optimal tax rules does not arise.

194

Tatsuo Hatta

If we consider an economy where two or more commodities are consumed along with leisure, a degree of freedom is added, and different combinations of commodity tax rates become compatible with a given revenue.
Yet, the distortions that encourage over-consumption of leisure are inevitable under any combination of taxes on wage and commodities. (In particular, a simultaneous imposition of taxes on all commodities and wage at thesame rate cannot generally attain the optimality.) It therefore becomes necessary to design the least cost combination of distortionary commodity
taxes and the wage tax that raises a given revenue. Optimal tax theory
characterizes the structure of such taxes.
The formal structure of the revenue-constrained optimum tariff rules is
identical with that of optimum tax rules in a simple setting. In the following, we will first present an explicit solution of revenue-constrained optimum tariffs in a three commodity model. We will next give interpretations
to this solution in terms of optimum tax rules. We will then examine theimplications of these interpretations to the revenue-constrained optimum
tariff rules.
4. A Revenue-Constrained Optimal Tariff RuleIn this section we will construct a simple three-commodity model oftrade, and present an explicit solution of revenue-constrained optimum tariffs in that model.
A. The Model
Assume that a small open economy exports good 0, and imports goods 1
and 2. Denote the economy’s output vector by y’ = (y 0, y 1, y 2), and its private consumption vector by x’ = (x 0, x 1, x 2). Define this economy’s excess
demand vector z’ = (z 0, z 1, z 2) byz = x − y.
Note that z 0 is the excess demand for the export good, and hence it is
the negative of the exported amount. Denote the vector of international
prices of the three goods by p’ = (1, p 1, p 2). Then z, r, and p must satisfy(1)p’z + r = 0,

where r is the value of the public good.
Ad valorem export tariff t 0 and import tariffs t 1 and t 2 are imposed sothat the domestic price vector q’ = (q 0, q 1, q 2) is given by(2)

q i = (t i + 1) p i, i = 0, 1, 2.

195

Why not Set Tariffs Uniformly Rather than Optimally

The aggregate consumer faces the budget equation(3)

q’z = 0.

! t p z "r must2

(Since tariff revenues must finance the public good,

i

i i

0

hold. This equation, however, is implied by (1), (2), and (3). So we will
not explicitly consider this equation below.)
Without loss of generality we will assume5
t 0 = 0.

(4)

Assume that the aggregate consumer maximizes the value of his utility
function u = U (x) under the budget equation (3). We denote his compensated demand function for leisure and commodities by x = x(q, u). Then
we have(5)z = z(q, u),

wherez(q, u)! x(q, u) − y.

By assumption we have(6)

z 0(q, u) < 0, z 1(q, u) > 0, and z 2(q, u) > 0.

Equations (1), (3), and (5) can be combined into the following equations:(7)

q’z(q, u) = 0,(8)

p’z(q, u) + r = 0.

When r and p are given, q can be chosen to maximize u in the system ofthese two equations, which contains variables q and u. In view of (2) and(4), the solution for q will yield the optimal tariff vector.6
B. The Rule
It is well known that in the three-good model of (2), (7), and (8), the
5. See Hatta (1993, p. 130).
6. We can also assume that y is not fixed. In that case, we have to redefine thefunction z as (17) below.

196

Tatsuo Hatta

optimal t 1 and t 2 satisfy the following:(9)t 1 η 20 + η 12 + η 12=,
t 2 η 10 + η 12 + η 12

where

η ij ≡∂ i qj∂q j iThis formula is due to Harberger (1958). Diamond and Mirrlees (1971,
p. 263) and Auerbach (1985, p. 92) give its simple proofs. In the next section, we will give a detailed interpretation of this formula.
5. Implications of Optimal Tax Rules
The model of equations (7) and (8) is formally identical with the modelof optimal taxation, and the optimal solution (9) can be interpreted inmany different ways in the context of optimal taxation. Here we will givesome of those interpretations that are most relevant to the revenueconstrained optimum tariff.
A. Optimal Tax Rules
A combination of wage and commodity taxes encourages leisure consumption and discourages commodity consumption, distorting the leisurecommodity consumption choice. A non-uniform commodity tax structure
can mitigate this distortion ultimately created by the non-availability of leisure tax. Imposing a high tax rate on complements of leisure (e.g., yachts
and concerts) and subsidizing substitutes for leisure (e.g., dish washers andmicrowave ovens) would reduce leisure consumption,7 serving to counteract this distortion.
This type of non-uniformity among the commodity tax rates will reducethe distortion in the leisure-commodity consumption choice. But it will create new distortions in the choice among commodities. In making commodity tax rates non-uniform, therefore, a policy maker faces a trade off between distortion in the leisure-commodity consumption choice and distortions among commodities. The optimal tax structure is the one that strikes
the balance in this trade off. Formula (9) can be interpreted as formally expressing this perspective.

7. Note that the word “leisure” here is used in the sense of non-working hours.

197

Why not Set Tariffs Uniformly Rather than Optimally

1. The Corlett and Hague RuleFirst, this formula proves that optimum taxation requires that the higher
tax rate be imposed on the commodity with the higher wage elasticity ofcompensated demand. In particular, the formula implies that a higher tax
rate should be imposed on complements of leisure than on substitutes forleisure. We may call this implication the Corlett and Hague Optimum Tax
Rule, after its founders Corlett and Hague (1953). This ranking of tax rates
counteracts the distortions created by the non-availability of the leisure tax.
In the extreme case where cross elasticities among commodities, i.e., η 21
and η 12, are zero, equation (9) boils down tot 1 1 / η 10=⋅
t 2 1 / η 20

(10)

Thus the tax rate of a commodity is inversely proportional to the wage
elasticity of demand for that commodity.
2. Substitutability Rule
Second, equation (9) implies that given the values of η 01 and η 02, themore strongly substitutable the two commodities are, the closer the optimalcommodity tax structure is to uniformity. As we remarked earlier, the nonuniformity of the commodity tax rates may reduce the distortion in theleisure-consumption choice, but will create new distortions in the choiceamong the commodities. In particular, when cross elasticities among commodities are high, a non-uniform commodity tax structure creates strong
distortionary effects in the choice among the commodities. The optimum
tax structure then tends to be close to uniform. In other words, high crosselasticities among commodities create a strong power that pulls the optimalcommodity tax rates toward uniformity.
3. The Inverse Elasticity Rule
When cross elasticities among commodities are zero,! #!!"
i
0

(11)

i
i

holds.8 Thus equation (l0) may be rewritten as
t 1 1 / η 11=⋅
t 2 1 / η 22

(12)

8. This follows directly from! "! "! #0 and ! #! #0.
i
0

i
1

i
2

1
2

2
1

198

Tatsuo Hatta

In words, the commodity tax rate is inversely proportional to the own demand elasticity of that commodity. This is called the Inverse Elasticity
Rule and is attributed to Ramsey (1927).9 This Rule implies that a low tax
rate should be imposed on a commodity with a high demand elasticity.
Equation (12) is well known, and is often cited as evidence for a widely
divergent optimal commodity tax structure. But that is misleading. In thereal economy, substitutability among commodities dominates, which pulls
the optimal commodity tax rates toward uniformity. The Inverse Elasticity
Rule is valid only when this pulling power is non-existent.
4. Wage Elasticity vs Own Elasticity
It is often believed that the Inverse Elasticity Rule holds because taxing
the commodity with a high own demand elasticity is distortionary, regardless of its cross substitutability with the other commodity.
This reasoning, however, is not correct. In fact, the commodity with thehigher own demand elasticity can have the higher optimum tax rate. To
see this, note that when 21 and 12 are not zero, (9) can be rewritten as

!

(13)

!

t 1 − (η 11 + η 22 ) − η 10=.
t 2 − (η 11 + η 22 ) − η 20

This expresses the tax ratio solely in terms of the own elasticities andwage elasticities of the two commodities, revealing that the wage elasticity,and not the own elasticity, of each commodity plays a decisive role in the
ranking of the two tax rates. In particular, this equation shows that thecommodity with the higher own demand elasticity must have the higher
optimum tax rate, if the wage elasticity of this commodity is the higher of
the two. This is in contrast to the qualitative implication of the Inverse
Elasticity Rule regarding the ranking of the two tax rates.
Indeed, the Inverse Elasticity Rule holds because its assumption of zerocross elasticities among commodities implicitly ranks the wage elasticitiesof the two commodities in accordance with their own elasticities. Under
this assumption, equation (11) implies that the commodity with the higher
demand elasticity is necessarily the stronger substitute for leisure from (11).
From (13), therefore, this commodity must have the lower optimum tax
rate, which yields the Inverse Elasticity Rule.
Both the Inverse Elasticity Rule and (10) are obtained under the assumption of zero cross substitutability among commodities. Even when this assumption is dropped, however, the qualitative implication of (10) is robust;
the ranking of the wage elasticities alone determines the ranking of the op-

9. Ramsey himself, however, derived this formula for uncompensated elasticities.

199

Why not Set Tariffs Uniformly Rather than Optimallytimal tax rates whether or not commodities are substitutable. On the contrary, once this assumption is dropped, the qualitative implication of the
Inverse Elasticity Rule breaks down.
In the real world, moreover, a commodity with a high demand elasticity
is usually a strong substitute for another commodity. But the Inverse Elasticity Rule only considers the situation where a highly demand elastic commodity has no substitutes among commodities. It is not easy to come up
with an example of such a commodity. The Inverse Elasticity Rule, therefore, is not as practical as it first looks.
B. Revenue-Constrained Optimum Tariff Rules
Let us now apply the optimal tax rules to the three-commodity open
economy model of Section 4. Formula (9) has three implications:First, the higher tariff rate should be imposed on the good that is more
substitutable for leisure than the other. Second, the more substitutable thetwo imports are, the better the uniform tariff structure approximates the optimal tax rate structure.
Third, the own elasticities of demand are not as important as generally
believed in ranking tariff rates. The crucial parameters in determining the
ranking of tax rates are the wage elasticities of demand for the commodities.

6. Implications of Tax Reform Rules
A. Revenue-Constrained Tax Reform Rules
Let us consider the optimum tax rules for the case where there are threeor more commodities.10 In this case, a simple, explicit expression of optimal tax rates no longer exists, unlike (11) in the model of two commodities and leisure. Optimal tax rules then are obtained from the optimality
conditions that implicitly contain tax rates as variables. Many of them giveinsightful characterizations of optimal tax rates,11 but do not give guidance
as to in which direction the tax structure should be reformed, unless weknow the exact point estimates of demand elasticities of all goods.
Theory of revenue-constrained tax reform, on the other hand, gives explicit criteria that tells whether or not a particular tax reform improves efficiency without requiring exact point estimates of demand elasticities of all
goods. They require only the signs and the relative magnitudes of demand
elasticities of a selected number of goods.

10. Then the number of goods, which include leisure, is four or more.
11. Sandmo (1976) and Hatta (1993), for example.

200

Tatsuo Hatta

1. Grouping of Commodities
A new element that appears in the case of three or more commodities isthe different degrees of substitutability among different commodity pairs. If
different tax rates are imposed on a pair of strong substitutes, such as
chicken and fish, a consumer will be able to avoid a substantial amount oftax payment by substituting the commodity with the lower rate for theother, regardless of the tax rates of the commodities outside of this pair.
An economist’s intuition would tell that a revenue-neutral reduction of the
tax rate differential of this pair leaving all other tax rates intact would improve efficiency. This argument is the usual justification for broad-basedtaxes.
Indeed, Hatta and Haltiwanger (1986) established an empirically testable
criteria of strong substitutability of a commodity pair under which squeezing their tax rates improves efficiency, when all other tax rates are kept
constant.
2. The Corlett and Hague Term and the Practitioner’s Hunch Term
Revenue-neutral commodity tax reform rules can be derived for a commodity pair that may not be strongly substitutable. For that purpose, wefirst analyze a formula that shows whether or nor a particular revenueneutral tax reform improves efficiency.
Throughout the rest of this section we assume that:the tax rates of goods 1 and n are both revenue-increasing.
This means that raising the tax rate of commodity 1 (commodity n) keeping all other tax rates constant increases the revenue.
Hatta (1986) showed that under this assumption, efficiency is improvedby an increase in t 1 accompanied by a revenue-neutralizing decrease in t n
if and only if N 1n is positive, wheren⎤⎡ n n i i n(t i − t 1 ) p i i1 ⎥
⎢ (t − t ) p i
−
(
τ
η
τ
η
)
⎥,
+⎢ 1 n n+ 1 1 1
N 1n ≡⎢
t +1(t + 1)(t + 1) ⎥
⎥
⎢
⎦
⎣
i
i
0
i
j
i
r ≡ (t − t ) / (t + 1), and i = ∂ j / ∂q .
n

(14)

n
0
0

1

1
0

∑

∑

The first term of the RHS of equation (14) may be called the Corlett
and Hague term. Corlett and Hague (1953) considered the situation where
the initial commodity tax rates are equal. Then the second term in (14)vanishes, and the first term alone dictates the direction of the welfare effect. Besides, τ l = τ n holds in this situation, and hence the sign of the first201

Why not Set Tariffs Uniformly Rather than Optimallyterm is solely dependent upon the sign of η 0n − η 01. Thus the aforementioned result by Corlett and Hague follows from the sign of this term. Thisjustifies the naming of the term.
On the other hand, the second term in (14) is positive if the following
conditions are satisfied:12(a) The 1st commodity is imposed the lowest tax rate among all commodities, and is substitutable for all other commodities.
(b) The n-th commodity is imposed the highest tax rate, and is substitutable for all other commodities.
In other words, the second term in (14) is made positive by increasing
the lowest commodity tax rate and reducing the highest commodity tax
rate so as to keep the revenue constant, when the commodities with the extreme tax rates are substitutable for all other commodities. Equation (14)makes it clear, therefore, that the second term pulls the extreme commodity tax rates toward uniformity when commodities are substitutable. We
will call this term the practitioners’ hunch term, since practitioners of tax
policy usually recommend equalization of tax rates so as to reduce distortions among commodities, without paying much attention to wage elasticities.
3. The Integrated Effect of a Tax Reform 13
It is readily seen that the Corlett and Hague term is non-negative if andonly if14(15)!!

τ nη 0n − τ 1η 01 0

The discussion above makes it clear that if (15) holds in addition to (a)and (b) above, then efficiency is improved by an increase in t 1 accompanied by a simultaneous reduction in t n so as to maintain the initial revenue
level.
Since τ n > τ 1 under (a) and (b), inequality (15) is automatically satisfied if the n-th good is more or equally substitutable for leisure than thefirst good is, i.e.,
(16)

η 0n

!η .
1
0

Thus the revenue-constrained squeezing of extreme commodity tax rates
improves efficiency when (a), (b), and (16) are satisfied. This may be
12. Condition (a) implies that t 1 < t i and xi1 > 0 for i = 2,..., n, while condition(b) implies that t i < t n and xin > 0 for i = 1,..., n − 1.
13. The discussion here follows Hatta (1986).
14. Under a wage taxation, t 0 < 0 (See Hatta (1993, p. 127)). t 0 + 1 must be
positive since the wage tax rate would be 100% or more, otherwise.

202

Tatsuo Hatta

viewed as a generalization of the Corlett and Hague result to the situation
where the initial commodity tax structure is not uniform.
Upon scrutiny, however, the relative magnitude of the wage elasticities
of substitution between the first and the n-th good does not play a criticalrole as a condition for welfare improving tax reform. To begin with, inequality (15) is satisfied even if (16) is violated, especially if t n is muchgreater than t 1. In any case, whether or not the economy satisfies (15) canbe verified empirically. Besides, (15) is only a part of a set of sufficientconditions for efficiency improvement, and hence, even if it is violated, thesqueezing of the tax rates can improve efficiency under conditions (a) and(b). These observations imply that unless commodity 1 is strongly complementary with leisure or commodity n is strongly substitutable for leisure,the sign of the practitioner’s hunch term can easily dominate the sign of
the Corlett and Hague term.
As the extreme tax rates are squeezed, either the highest tax rate will become equal to the second highest or the lowest will become equal to thesecond lowest, sooner or later. Suppose that the former takes place first.
Then a joint reduction of the two highest tax rates will improve efficiency
if the commodities with these rates are substitutable for all other commodities, and if a condition similar to (15) is not flagrantly violated. Tax reform
can proceed in this manner and more and more commodities will shareeach of the extreme tax rates. As the reform progresses, the wage elasticityof the group of the commodities that share the highest tax rate will become
similar to the wage elasticity of the group of the commodities that sharethe lowest tax rate, and a generalized version of condition (15) becomes
unlikely to be violated. Thus we can expect that in an economy where substitutability dominates, tax reforms toward uniformity are likely to improve
efficiency monotonically, unless tax rates are already close to uniform.
Fukushima and Hatta (1989) discusses various modifications to the tax
reform schemes toward uniformity when some of the efficiency improvement conditions are violated.
4. Strategy of Tax Reform
The discussion above suggests a three-step implementation of optimal
tax rules to an arbitrarily divergent initial tax system.
First, bundle together closely substitutable commodities, and make thetax rates within each bundle uniform, while leaving the tax rates acrossdifferent bundles different. Each bundle may be called a composite commodity.
Second, equate the tax rates across composite commodities, thus making
commodity tax rates uniform. Here we apply the extreme tax rate squeezing rule, treating each composite commodity as if it were a commodity.
Since composite commodities are likely to be substitutable for each other,
the sufficient conditions for efficiency improvement are likely to be satis-

203

Why not Set Tariffs Uniformly Rather than Optimallyfied at each successive squeezing of the extreme tax rates.
Third, fine tune the tax rates of composite commodities by applying theCorlett and Hague rule to commodity pairs that flagrantly violates (15).
A large efficiency gain will be obtained by the second step, if a uniform
tax is a good approximation of the optimal tax. This prognosis, however, isin direct conflict with the celebrated empirical estimation by Atkinson andStiglitz (1972), which showed rather divergent optimal tax rates.
It turns out, however, that their estimate of the divergent optimal tax
rates is due to their assumption of extremely high elasticity of labor supply.
If the elasticity of labor supply were high, wage elasticities of commodities
can be widely divergent, and the Corlett and Hague term can be negative
at some stage in the second step of the reform above. Under such an assumption, therefore, Atkinson and Stiglitz’s result of divergent optimal tax
rates is consistent with our theoretical analysis.
Fukushima and Hatta (1989) have established, however, that when thiselasticity is changed to realistic values in the Atkinson-Stiglitz model, theoptimal tax rates become much closer to uniformity. It shows that if thecompensated wage elasticity of labor supply is 0.5 or less, the efficiency
cost of adopting a uniform tax structure rather than the optimal one is lessthan 5% of the government revenue in all three regions considered by Atkinson and Stiglitz.15 Thus large efficiency gains will be obtained by the
first and the second steps of our tax reform strategy, and the gains obtained from the last stage will be relatively small.
B. Revenue-Constrained Tariff Reform
The tax reform rules discussed above can also be directly applied to therevenue-constrained tariff reform situation.
First, bundle together closely substitutable importables, and make thetariff rates within each bundle uniform, while leaving the tariff rates acrossdifferent bundles different. Second, equate the tariff rates across the bundles, thus making all the tariff rates uniform. Third, fine-tune the tariff rateof each commodity by applying the Corlett and Hague rule to the commodity pairs that flagrantly violates (15). Again we can expect that a close
approximation of the optimal tariff structure is at the end of the second
step if imports are substitutable among themselves.
Some modifications are needed, however, in applying the optimal tax
rules and reform rules to the tariff situation.
First, assuming that there is only one export good is obviously unrealistic. The export in the model of Section 4 should be interpreted as a compound of export goods.
15. In contrast, this efficiency cost would be 36.52% in Sweden if its wage elasticity were 2.03 as implicitly assumed by Atkinson and Stiglitz.

204

Tatsuo Hatta

Second, substitutable rather than fixed supply of outputs is essential in
the trade model. This can be brought into the analysis by redefining thefunction z as
(17)z(q, u)" x(q, u) − y(q),where y(q) is the supply function of the producers. In this interpretation,
substitution terms in tariff rules discussed above should be interpreted aszji"x !y !
ijijwhere the subscript shows the variable with which the given function isdifferentiated.
Third, under the presence of production subsidies and consumption taxes,
the prices that the producers face become different from those that the consumers face. Then modifications are needed in the formal analysis itself.
Fourth, the existence of non-traded goods brings in a new element. But
extension of the existing theory to this case does not seem particularly difficult. The revenue-constrained tax reform formula given in (14) was obtained in Hatta (1986) as a straightforward modification of the revenueunconstrained version of the tax reform formula of Hatta (1977a). On theother hand, revenue-unconstrained versions of the tariff reform formulae
for the economy with non-traded goods are already derived in Hatta(1977b) and Fukushima (1979). Thus a revenue-constrained tariff reform
formulae for an economy with non-traded goods should be similarly obtained by a straightforward modification of the revenue-unconstrained versions.
Fifth, determining the tariff rates on the imported intermediate inputs isan entirely new element in the problem of revenue-constrained optimum
tariff.16
7. Concluding Remarks
The reason why the optimum tax theory and the revenue-constrained tariff theory have similar formal structures is that both models have untaxable
goods. Consumption of leisure is untaxable in the taxation model, while
the consumption of the exportable commodity is untaxable in the tariffmodel.
Note, however, that if consumption taxes can be levied on the exportables along with import tariffs, the first best can be attained by equating
tariff rates and consumption tax rates. To see this, consider again the econ-

16. See Panagariya (1994), Chambers (1994), and Mitra (1994).

205

Why not Set Tariffs Uniformly Rather than Optimallyomy depicted in Figure 2. Suppose that an import tariff on commodity Y
is combined with a consumption tax on commodity X with an equal rate.
Then the consumers’ budget line will coincide with the line CD , making
this combination equivalent to a lump sum tax. Point L will be the resulting consumption bundle.
The non-availability of the leisure taxation in the taxation model is anatural assumption; it is based on the intrinsic nature of leisure. On theother hand, the reason for the non-availability of consumption taxes on exportables is ad hoc, reflecting a particular political situation or development stage of an economy. In many situations, consumption taxes are feasible as policy instruments. Then the policy should aim at uniform rates oftariffs and consumption taxes on commodities other than imported commodities.
What we showed in this paper is that, even during a period when suchconsumption taxes are not available, a uniform tariff structure can be agood approximation of the optimum when importables are substitutes
among themselves.
In the present paper, we note the formal similarity between the revenueconstrained optimum tariff and the optimum commodity tax structures.
This enabled us to exploit the neo-Musgravian perspective for taxes incharacterizing the revenue-constrained optimum tariffs. More theoreticaland empirical research are needed in order to clarify how closely the uniform tariff approximates the revenue-constrained optimum tariff structure.
The neo-Musgravian perspective sheds light on the directions of this research.

References
Atkinson, A. B. and J. E. Stiglitz. 1972. The Structure of Indirect Taxation andEconomic Efficiency. Journal of Public Economics 1: 97-119.
Auerbach, A. J. 1985. The Theory of Excess Burden and Optimal Taxation. In
Handbook of Public Economics, eds. A. J. Auerbach and M. Feldstein. Amsterdam: North-Holland: 61-127.
Chambers, G. R. 1994. Tariff Reform and the Uniform Tariff. Economic Studies
Quarterly 45(3): 246-264.
Corlett, W. C. and D. C. Hague. 1953. Complementarity and the Excess Burden of
Taxation. Review of Economic Studies 21: 21-30.
Dahl, H., S. Devarajan and S. van Wijnbergen. 1994. Revenue-Neutral Tariff Reform: Theory and an Application to Cameroon. Economic Studies Quarterly 45(3): 213-226.
Dalton, T. R. and F. Sadka. 1979. A Many-Good Corlett-Hague Tax Rule. Economics Letters 3: 169-172.
Diamond, P. A. and J. A. Mirrlees. 197la. Optimal Taxation and Public Production
I. American Economic Review 61: 8-27.

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Tatsuo Hatta--------- . 197lb. Optimal Taxation and Public Production II: Tax Rules. American
Economic Review 61: 261-278.
Diamond, P. A. and D. L. McFadden. 1974. Some Uses of the Expenditure Function in Public Finance. Journal of Public Economics 3: 3-22.
Fukushima, T. 1979. Tariff Structure, Nontraded Goods and Theory of Piecemeal
Policy Recommendations. International Economic Review 20: 427-435.
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Economic Studies Quarterly 40: 349-354.
Fukushima, T. and T. Hatta. 1989. Why not Tax Uniformly Rather than Optimally?
Economic Studies Quarterly 40: 220-238.
Harberger, A. C. 1964. Taxation, Resource Allocation and Welfare. In The Role of
Direct and Indirect Taxes in the Federal Reserve System. Princeton University
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Hatta, T. 1977a. A Theory of Piecemeal Policy Recommendations. Review of Economic Studies 44: 1-21.
--------- . 1977b. A Recommendation for a Better Tariff Structure. Econometrica 45:
1859-1870.
--------- . 1986. Welfare Effect of Changing Commodity Tax Rates toward Uniformity. Journal of Public Economics 29: 99-112.
--------- . 1993. Four Basic Rules of Optimal Commodity Taxation. In Public and International Economics, ed. A. M. E1-Agraaed. St. Martins Press: 125-147.
Hatta, T. and J. Haltiwanger. 1986. Tax Reform and Strong Substitutes. International Economic Review 27: 303-315.
Mirrlees, J. A. 1987. The Theory of Optimal Taxation. In Handbook of Mathematical Economics, vol. 3. Amsterdam: North-Holland: 1197-1249.
Mitra P. K. 1994. Protective and Revenue Raising Trade Taxes: Theory and an Application to India. Economic Studies Quarterly 45(3): 265-287.
Musgrave, R. A. 1959. The Theory of Public Finance. New York: McGraw-Hill
Book Company, Inc.
Panagariya, A. 1994. Why and Why-not of Uniform Tariffs. Economic Studies
Quarterly 45(3): 227-245.
Pechman. A. J. 1990. The Future of the Income Tax. American Economic Review
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Rajaram. A. 1994. Tariff and Tax Reforms––Do World Bank Recommendations Integrate Revenue and Protection Objectives? Economic Studies Quarterly 45(4):321-338.
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Sadka, E. 1977. A Theorem on Uniform Taxation. Journal of Public Economics 7:
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Sandmo, A. 1976. Optimal Taxation––An Introduction to the Literature. Journal of
Public Economics 6: 37-54.

10

Local Content Requirements andInternational Market Share Rivalry
M. Özgür Kayalica and Sajal Lahiri

1. Introduction
Foreign firms locate themselves in a host country for a number of reasons. It could be for lower labour costs in the host country. For example,
many Japanese firms make foreign direct investments (henceforth to be referred to as FDI) in many Asian countries as labour costs there are a fraction of that in Japan. Typically, in such cases the commodities produced in
the host country are exported in their entirety to a third country (called theconsuming country). FDI also takes place in order to have access to a market which is otherwise not penetrable. The host country does not lose out
if there are no domestic firms there, and in fact it encourages FDI in orderto reduce the level of unemployment. However, foreign firms often import
inputs from their home countries and therefore the host country does notbenefit fully from having the foreign firms. In order to reap the full benefitof having FDI, host countries tend to impose local content requirements on
foreign firms.1 However, if there are more than one host countries whocompete in the oligopolistic market in a third country, the host countries
1. Local content regulations, which require that a foreign firm uses a certain
minimum amount of domestically produced inputs in producing its final output, arecommonplace internationally and have been increasing in popularity in developed
and developing countries alike (see UNIDO, 1986). The automobile industries, forexample, in many countries are subject to these regulations (see Herander and Thomas (1986)). There are numerous other examples of these regulations in other industries, the oil refining industry in the United States of America being one ofthem (see Krugman and Obstfeld (1994, pp.212-4)). The WTO is very much cognisant of the fact that local content requirement is used pervasively to restrict the international mobility of capital and has incorporated in the WTO Treaty the elimination of it as its long term objective.
207

208

M. Özgür Kayalica and Sajal Lahiri

may want to use local content requirements strategically in order for theforeign firms located on their soil to gain a higher share of the market andthus create more employment. This is particularly so when the host countries do not have effective access to instruments such as export subsidies toraise their market share, as they often fall foul of WTO regulations.
Given the prevalence of local content agreements, it is surprising thatthe existing literature has ignored this as a possible instrument for the hostcountry. Since the work of Grossman (1981), a small theoretical literature
on content protection has developed (see Davidson et al., 1985; Krishna
and Itoh, 1988; Richardson, 1991, 1993; Lopez-de-Silanes et al., 1996; Lahiri and Ono, 1998a).2 However, in none of these papers, with the exception of Lahiri and Ono (1998a, 2003), local content is considered as a policy instrument. Moreover, final goods are taken to be competitive in
Grossman (1981), Krishna and Itoh (1988) and Richardson (1991, 1993),
and in the case where the final goods are imperfectly competitive (Davidson et al., 1985; Lopez-de-Silanes et al., 1996), only one foreign firm isconsidered. In Lahiri and Ono (1998a), the final goods are produced underimperfect competition, and the number of foreign firms is endogenous.
However, the good there is non-tradeable. Lahiri and Ono (2003) consider
export oriented FDI and local content requirements, but foreign firms arelocated only in one country. Therefore, they do not consider the strategic
use of local content requirement as an instrument to gain market share.
The theoretical literature on foreign direct investment is very large (see,for example, Brander and Spencer, 1987; Dixit, 1984; Ethier, 1986; Helpman, 1984; Hillman and Ursprung, 1993; Hortsman and Markusen, 1992;
Katrak, 1977; Lahiri and Ono, 1998a, 1998b, & 2003; Motta, 1992; Ono,
1990; Smith, 1987).3 However, most of the literature analyse the problem
from the viewpoint of foreign firms.
In this paper we consider a model in which foreign firms locate themselves in two host countries and export their produce in their entirety to athird country, the consuming country. These firms compete in the consuming country in an oligopolistic market there.4 We assume the existence of

2. There is also a related literature on rules of origin. See, for example, Krishna
and Krueger (1995) and Falvey and Reed (1998).
3. Foreign investment is, broadly speaking, of two types: (i) FDI where a firm
locates its plant in a foreign country along with necessary managerial resources,and (ii) portfolio investment where a firm simply owns a part of the capital stockof a foreign firm. In the latter type, which is prevalent in the literature of tax competition, foreign investment is equivalent to international mobility of the factor of
production capital (see Ruffin (1984) for a survey of the theoretical literature on international factor movements).
4. It may be helpful to think of the two host countries as China and Malaysia,
the third country as the USA, and the oligopolistic good to be VCR or digital camera.

209

Local Content Requirements and International Market Share Rivalry

unemployment in both host countries. The two host country governmentschoose local content requirements to maximise welfare. We consider twocases. In the first case, there is one foreign firm in each host country. In
this case, a local content restriction would not affect the number of firms,
but it would influence the output decisions of the firms. In the second case,the number of foreign firms in one of the countries is endogenous. In bothcases we try to characterise both cooperative and non-cooperative levels of
optimal local content requirements in the two host countries. We also examine if the two countries can benefit from a coordinated policy reform.
The basic economic model for the case of fixed number of foreign firms
is spelt out in details in the following section. Section 3 then carries out aformal analysis for the basic model. The case of free entry and exit of foreign firms is analysed in section 4. Finally, some concluding remarks are
made in section 5.
2. The Benchmark ModelIn our model there are two exporting (host) countries (labelled as country 1 and country 2) and one consuming (importing) country. There are
two foreign firms (one located in each exporting country) competing forthe oligopolistic market of a homogeneous good in the consuming country.5 The two foreign firms can originate from two different countries orfrom one country. In section 3 we should consider the case of free entry
and exit of foreign firms in one of the two exporting countries. We assume
the existence of unemployment in the two exporting countries. The inverse
demand function for oligopolistic good is given by(1)

p = α − βD ,where p is price and D is the total demand for the good, which is equal to
the sum of output produced by the two firms, i.e.
(2)

D = x1 + x2,

where xi (i = 1, 2) is the output of a foreign firm in country i. The profits
of a foreign firm located in country i, π i, (i = 1, 2), is given by

5. This benchmark model is an extension of the international market share rivalry model of Brander and Spencer (1985). There are three main differences between the present model and that of Brander and Spencer (1985). First, the firms
are foreign owned in our model whereas they are domestic in their model. Second,
we consider the existence of unemployment, the Brander-Spencer model is a full
employment one. Finally, the policy instruments considered are different: they use
export subsidies and we consider local content requirement.

210

M. Özgür Kayalica and Sajal Lahiri

π i = (p − ci) xi, i = 1, 2,(3)

where the marginal costs of the foreign firms located in country 1 and 2,
denoted respectively by c1 and c2, are taken to be constants, and therefore
they are also the average variable costs. As an extreme assumption, we
take that each foreign firm would prefer to use inputs from its home country as it is cheaper to do so, but it faces a stipulation that at least a δ i,(i = 1, 2), proportion of total inputs has to be bought in the host country inwhich the foreign firm is located. Let bi (bˆi ) be the unit input cost in country i if all the inputs are bought in the host (home) economy. With theaforesaid stipulation on local contents, the marginal costs for the foreign
firms in country 1 and 2 are given byci = bˆi (1 − δ i ) + δ i bi ,(4)

i = 1, 2,

where bi > bˆi , (i = 1, 2).
The firms are assumed to behave in a Cournot-Nash fashion. Hence,
profit maximisation yields

β xi = p − ci, i = 1, 2.

(5)Given the policy decisions of the governments, the equilibrium output of
a foreign firm can be found from (5) as
xi =

(6)

α − 2ci + c j
3β,i , j = 1, 2

i ≠ j.

As stated before, we assume that there is unemployment in countries 1
and 2. Following Brander and Spencer (1987), factor input costs are taken
to be the income of the factors which would remain unemployed in the absence of the production of the oligopolistic good. With this and assumingthat the entire profits of the foreign firms are repatriated, the welfare levelin country i, (i = 1, 2), denoted by Wi is given by
W i = xi bi δ i ,(7)

i = 1, 2.

This completes the description of the model structure, and we now turnto analysis.
Substituting (4) in (6), and totally differentiating the result we obtain(8)dxi = −(b j − bˆ j )2(bi − bˆi )dδ i +dδ j
3β
3β

i , j = 1, 2

i ≠ j.

211

Local Content Requirements and International Market Share Rivalry

The intuition is straightforward. Each foreign firm will decrease (increase)its production if it faces a higher (lower) local content requirement or if
the local content required from the rival firm is reduced (raised). This isbecause a more severe local content restriction for a firm gives its rival acompetitive advantage.
Totally differentiating the welfare functions we get(9)3β dW 1 = A1dδ 1 + A2 dδ 2 ,(10)

3β dW 2 = A3dδ 1 + A4 dδ 2 ,

where

[

]

A1 = 3βx1b1 − 2b1δ 1 (b1 − bˆ1 ) ,A2 = b1δ 1 (b2 − bˆ2 ),A = b δ (b − bˆ ),
3

[

2

2

1

1

]

A4 = 3βx2 b2 − 2b2δ 2 (b2 − bˆ2 ) .
A more severe local content on a firm has two opposing effects on its
host’s welfare, and one positive effect on the other country. First, for agiven level of output, it raises employment and this is good for the host.
Second, it gives the firm in the other country a competitive advantage raising employment in the other country and lowering that at home. This is
why A1 and A4 are ambiguous, and A2 and A3 are unambiguously positive.
3. The Determination of Local Content Restriction
In this section, we first consider the case where the governments behave
in a non-cooperative fashion. We find the non-cooperative Nash levels of
local content restrictions, δ 1N and δ 2N , by setting A1 and A4 equal to zero,6(11)

δ 1N =

(12)

N
2

3βx1
> 0,
2(b − bˆ )
1

δ

1

3βx2
=
> 0.
2(b − bˆ )2

2

6. Both welfare functions are concave in the local content parameters as
3βWδ11δ 1 = −4b1 (b1 − bˆ1 ) < 0 and 3βWδ22δ 2 = −4b2 (b2 − bˆ2 ) < 0.

212

M. Özgür Kayalica and Sajal Lahiri

We now turn to comparing the levels of restrictions in the two countries
under a number of scenarios. First of all, it can be verified that when b1=b2
and bˆ1 = bˆ2 , the non-cooperative optimal levels of the local content requirements would be the same in the two countries. Next, we assume that thetwo foreign firms face the same unit input costs at home, (i.e., bˆ1 = bˆ2 = bˆ(say)). By using the explicit solutions of (11) and (12) we obtain(δ − δ )N
1N2bˆ1 = bˆ2 = bˆ=−1 (α − bˆ )(b1 − b2 ).
3 (b1 − bˆ )(b2 − bˆ )It follows from the above that when bˆ1 = bˆ2 ,(δ − δ )N
1N2bˆ1 = bˆ2

>0 ⇔ b >b .
2 < 1<That is, when the unit input costs in the home countries are identical, therelative magnitude of non-cooperative optimal levels of local content restrictions in the two host (exporting) countries depends on the relative sizeof the input costs in the host countries. In particular, country 1 applies ahigher (lower) local content requirement if the unit input cost in that country is lower (higher) than that in country 2. This result can be explained
intuitively as follows. Suppose that the local content restriction level incountry 2 is the same as the optimal level in country 1 and b1 > b2. Clearly,
country 2 has a higher market share, and therefore a higher output base toraise employment by raising the restriction level. This is why the optimal
local content restriction is higher in country 2. This result is formallystated as
Proposition 1. When the unit input costs in the home countries of the two
firms are identical, a host country, in a Nash equilibrium, applies a higher(lower) local content requirement if the unit input cost in that country is
lower (higher) than that in the other host country.
Finally, suppose that the unit input costs in the two host countries are
identical (b1 = b2) whereas (bˆ1 ≠ bˆ2 ). From the explicit solutions we get
5α − 9b + 2(bˆ + bˆ )][(bˆ − bˆ ).
=(δ − δ )
N
1

1

N
2

b1 = b2 = b

215(b − bˆ1 )(b − bˆ2 )

1

2

213

Local Content Requirements and International Market Share Rivalry

In this case, no clear cut result emerges. However, if the size of the demand for the oligopolistic good is sufficiently large, i.e. if α >> 0 andb1 = b2, we findN
δ 1N ><δ2

ˆ⇔ bˆ1 >
< b2 .

The result is different from the previous case because an increase in δ 1 , atthe margin, increases marginal cost in country 1 by more than that incountry 2 when b1 > b2 and bˆ1 = bˆ2 , but increases marginal cost in country
1 by less than that in country 2 when bˆ1 > bˆ2 and b1 = b2.
Proposition 2. When the unit input costs in the two host countries are
identical and α >> 0, a foreign firm, in a Nash equilibrium, is subjected
to a higher (lower) local content requirement if the unit input cost in its
home country is higher (lower) than that in the other home country.
Having compared the two Nash values of the local content parameters,
we now examine the cooperative equilibrium. In order to find the cooperative equilibrium, we define total welfare by adding (9) and (10);3β dW = ( A1 + A3 )dδ 1 + ( A2 + A4 )dδ 2 .

(13)

For total welfare to be concave in δ 1 and δ 2 , we must have
3βWδ 1δ 1 = −4b1 (b1 − bˆ1 ) < 0,3βWδ 2δ 2 = −4b2 (b2 − bˆ2 ) < 0,[]

9 β 2 Wδ 1δ 1 Wδ 2δ 2 − Wδ21δ 2 = 16b1b2 (b1 − bˆ1 )(b2 − bˆ2 )

[

]

2

− b1 (b2 − bˆ2 ) + b2 (b1 − bˆ1 ) > 0.

Setting the coefficients of dδ 1 and dδ 2 equal to zero, and solving simultaneously for δ 1 and δ 2 , we find the cooperative solutions as(14)

2b x (b − bˆ ) + b x (b − bˆ )]
[
> 0,
δ =β
C
1

1 1

2

2

2 2

1

b1 (b2 − bˆ2 )(b1 − bˆ1 )

1

214

M. Özgür Kayalica and Sajal Lahiri

δ C2 = β(15)[b x (b − bˆ ) + 2b x (b − bˆ )] > 0.
1 1

2

2

2 2

1

1

b2 (b2 − bˆ2 )(b1 − bˆ1 )As before we compare the levels of restrictions in the two countries.
When the input costs bought in the two home countries are identical, (i.e.,bˆ1 = bˆ2 = bˆ ), by using the explicit solutions for (14) and (15) we obtain(δ − δ )C
1

C2bˆ1 = bˆ2 = bˆ=−[] (b − b ),(α − bˆ ) 6b1b2 − bˆ (b1 + b2 )

1

θ1

[

]

2

2

where θ 1 = 16b1b2 (b1 − bˆ )(b2 − bˆ ) − b1 (b2 − bˆ ) + b2 (b1 − bˆ ) > 0 from the concavity condition, and the numerator of the first term on the right hand sideof the above equation is positive since bi > b̂ , i = 1, 2. Therefore, whenbˆ1 = bˆ2 ,(δ − δ )C
1

C2bˆ1 = bˆ2

>0 ⇔ b >b .
2 < 1<That is, with bˆ1 = bˆ2 and the the governments cooperate, a country applies
a higher (lower) local content requirement if the unit input cost in thatcountry is lower (higher) than that in the other country, a similar result tothe non-cooperative case. Formally,
Proposition 3. When the unit input costs in the home countries of the two
firms are identical, a host country, in a cooperative equilibrium, applies ahigher (lower) local content requirement if the unit input cost in that country is lower (higher) than that in the other host country.
When the unit input costs in the two host countries are identical(b1 = b2 = b), from the explicit solutions we get(δ − δ )C1C
2

2(2α − 3b) + (bˆ + bˆ )][(bˆ − bˆ ),=1

b1 = b2 = b

2

1

θ1

[ [

where θ 1 = 16b 2 (b − bˆ1 )(b − bˆ2 ) − b 2 (b − bˆ1 ) + (b − bˆ2 )2]] > 0 from the con2

215

Local Content Requirements and International Market Share Rivalry

cavity condition. As in the non-cooperative case, for significantly large α
and b1 = b2,
Cˆ >ˆ
δ 1C >< δ 2 ⇔ b1 < b2 .

Once again, the qualitative result here is exactly the same as in the corresponding case in the non-cooperative equilibrium.
Proposition 4. When the unit input costs in the two host countries are
identical and α >> 0, a foreign firm, in a cooperative equilibrium, is subjected to a higher (lower) local content requirement if the unit input costin its home country is higher (lower) than that in the other home country.
3.1. Reform from a Non-Cooperative Equilibrium
In this subsection we examine the effects on welfare in both countries ofa small increase in the local content requirements when the initial levels
are set at the non-cooperative level. This can be seen as a multilateral effort to coordinate local content restriction policies. Substituting (11) in (9),and (12) in (10), we obtain

(16)

(17)

dW 1 δ =δ N =b1 x1 (b2 − bˆ2 )dδ 2 > 0,2(b − bˆ )dW 2 δ =δ N =b2 x2 (b1 − bˆ1 )dδ 1 > 0.
2(b − bˆ )

1

2

1

2

1

2

1

2

Equations (16) and (17) suggest that starting from the non-cooperativeequilibrium, a multilateral increase in the levels of local content requirements is strictly Pareto-improving.7 The intuition is straightforward. As wehave noted before, the international externalities associated with a stricter
local content restriction are positive. Since we start from the noncooperative equilibrium, due to envelope property, the own effects of thereform are absent and it is only the positive externalities that determine theoutcome.
Proposition 5. Starting from the non-cooperative equilibrium, when thenumber of foreign firms is exogenous, a multilateral increase in the levels
7. By strict Pareto improvement, we mean that the welfare levels in the two hostcountries are higher: we do not take into account the consuming country’s welfare.

216

M. Özgür Kayalica and Sajal Lahiri

of local content requirements is strictly Pareto-improving.
By using the above results, one can also compare the relative magnitudes of optimal local content requirements for the two countries under thecooperative and non-cooperative equilibria. From (10) and (13), we find3β

∂W
= A2 > 0,∂δ 1 δ 1 =δ 1N

3β∂W= A3 > 0.
∂δ 2 δ 2 =δ 2N

From the concavity of the global welfare it then follows that δ iC > δ iN ,i = 1, 2. It is the competition for FDI which keeps the non-cooperative
levels of the local content restrictions at a level that is lower than the cooperative levels. Formally,
Proposition 6. When the number of foreign firms is exogenous, all hostgovernments apply a more severe local content restrictions under a cooperative solution than under a non-cooperative solution.
4. Free Entry and Exit of Foreign Firms
In the preceding section we assumed that the number of foreign firms in
the two host countries are exogenously given. In this section, we relax thisassumption and assume that there are now n identical foreign firms fromthe rest of the world operate in country 1.8 It is assumed that country 1 issmall in the market for FDI. Hence, the foreign firms will move into (outof) country 1 if the profits they make in country 1 are larger (smaller) than
the reservation profit, π , that they can make in the rest of the world.
Therefore, in the FDI equilibrium we must have(18)

π 1 = π.

The total demand for the good is now given by(19)

D = nx1 + x2.

8. Unfortunately, it is not possible to endogenise the numbers of firms in bothcountries as then one group of firms––the ones with higher marginal costs––will beforced out of the market. One way out could be to relax the assumption that the
goods produced by the two groups of firms are homogeneous as was done in Lahiri
and Ono (1998b).

217

Local Content Requirements and International Market Share Rivalry

The closed form solutions to many of the key variables in the model canbe solved sequentially as:

(20)

n=

(21)

x1 =

(22)

x2 =

α − 2c1 + c2
π β

− 2,

α − 2c1 + c2
π=,
β (2 + n )β
π β + c1 − c2.
βSubstituting (4) into (20) to (22) and totally differentiating the results weobtain(23)dn = −π βdδ 1 +(b2 − bˆ2 )π βdδ 2 ,

dx1 = 0,

(24)

(25)

2(b1 − bˆ1 )dx2 =(b1 − bˆ1 )(b − bˆ )dδ 1 − 2 2 dδ 2 .
ββEquation (23) states that since there is free entry and exit of FDI in country 1, an increase in the level of local contents in country 2, or a decreasein the level of local contents in country 1, will encourage more foreign
firms to enter country 1. The foreign firm in country 2 will increase (decrease) production if it is allowed to use less (more) local contents or if thelevel of local contents for the firms in country 1 is raised (reduced) (equation (25)). This is because an increase in δ 1(δ 2) gives the firm in country 2
a competitive advantage (disadvantage) over the firm in country 1. Becauseof free entry and exit and the linearity of demand, the output of a foreign
firm in country 1 does not change with the policy instruments.
Adjusting the welfare equation (7) for country 1 (by multiplying it by n)and then totally differentiating W 1 and W 2, we get(26)

β dW 1 = A5dδ 1 + A6 dδ 2 ,(27)

β dW 2 = A7 dδ 1 + A8 dδ 2 ,218

M. Özgür Kayalica and Sajal Lahiri

where

[

) ]

(

A5 = b1 βx1n − 2 b1 − bˆ1 δ 1 ,( )A = b (b − bˆ )δ ,A = b [βx − (b − bˆ )δ ].
A6 = b1 b2 − bˆ2 δ 1 ,
7

2

8

2

1

1

2

2

2

2

2

Setting A5 and A8 equal to zero, we obtain the non-cooperative optimallevels of the two policy instruments as9(28)

δˆ 1N =

βnx1
> 0,2(b − bˆ )1(29)

δˆ 2N =1

βx2

2(b2 − bˆ2 )> 0.

Having found the non-cooperative levels for the free entry case, we now
compare the levels of local content restrictions by substituting the explicit
solutions of the variables in the expression and considering special cases.
It is to be recalled in the last section, i.e. when there is only one firm ineach country and b1 = b2 and bˆ1 = bˆ2 , the optimal non-cooperative level ofthe local content requirements were the same in the two countries. In thepresent case however that is not true. From (28) and (29), we find thatwhen b1 = b2 and bˆ1 = bˆ2 ,ˆNδˆ 1N >
<δ2

⇔

x2
< 1.
D δ 1 =δ 2 = 0 > 3

That is, country 2 imposes higher (lower) local content restrictions if themarket share of the foreign firm located in that country is more (less) than
one-third. An increase in the local content restriction in country 2 lower its
market share and increases the profitability of the firms in country 1, leading to an inflow of new firms in country 1. This lowers the market share
9. Both welfare functions are concave in the local content parameters as
βWδ11δ 1 = −4b1 (b1 − bˆ1 ) < 0 and βWδ22δ 2 = −2b2 (b2 − bˆ2 ) < 0.

219

Local Content Requirements and International Market Share Rivalryof country 2 even more. This second round effect via changes in the number of firms was absent before, and this explains why the result is qualitatively different in the presence of free entry and exit than under fixed
number of firms.
When bˆ1 = bˆ2 = bˆ , we obtain(30)(δˆ 1N − δˆ 2N ) bˆ = bˆ = bˆ = (b2 − b1 )(α − bˆ − 2 π β )12+ (b2 − bˆ )(α − bˆ − π β ) − 4(b1 − bˆ ) π β

where (α − bˆ − 2 π β ) = βx1n δ 1 =δ 2 = 0 > 0.
It follows from (30) that δˆ 1N > δˆ 2N if b2 > b1 and π

0, and that δˆ 1N < δˆ 2N

if b2 < b1 and π >> 0. Therefore in contrast to the no entry case, the relative size of local content requirements in the free entry case not only depends on the size of relative unit input costs in the two countries but also
on the number of foreign firms entering country 1. The above results are
summarised formally in the following proposition.
Proposition 7. When there is free entry and exit of foreign firms in country 1 and just one foreign firm in country 2, the following are true:(i)ˆNwhen b1 = b2 and bˆ1 = bˆ2 , δˆ 1N >
<δ2

(ii)

δˆ 1N > δˆ 2N if b2 > b1 and π(iii)δˆ 1N > δˆ 2N if b2 < b1 and π >> 0.

⇔

x2
< 1,
D δ 1 =δ 2 = 0 > 3

0, andBefore proceeding to the case where the governments cooperate, we
compare the non-cooperative restriction levels in the no entry case withthat in the free entry and exit case. Subtracting (28) from (11), and (29)from (12), and using the explicit solutions we find the following

220

M. Özgür Kayalica and Sajal Lahiri

5α + 45 π β − 4bˆ1 − bˆ2δ 1N − δˆ 1N => 0,
105 b1 − bˆ1()

10α − 15 π β − 8bˆ1 − 2bˆ2
δ 2N − δˆ 2N => 0,
105 b1 − bˆ1()

since the denominators are positive and it can easily be shown, by using
α − 2bˆ + bˆ − 2 π β = βx n
> 0, that the numerators are also posi121

δ 1 =δ 2 = 0

tive. This result shows that when there is free entry and exit in one of thecountries, both countries impose less severe restrictions than in the casewhere the number of firms are exogenous in both countries. This can be
explained intuitively as follows. Country 1 has to be more cautious about
raising the local content restriction in the presence of free entry and exit
because a higher restriction would lead to the exit of some of the firms(which is not possible in the absence of free entry and exit), reducing employment. If country 2 increases the restriction, as mentioned above, it
lowers the market share of the firm in country 1 and increases the profitability of the firms in country 1, leading to an inflow of more firms into
the market in the presence of free entry and exit. This lowers the market
share of the firm in country 2 even more. Therefore, the levels of optimal
local content restrictions are lower in both countries when there is free entry and exit in country 1 than when the number of firms in country 1 is
fixed.
Proposition 8. In a non-cooperative equilibrium, the host governments apply less severe local content restrictions when there is free entry and exitof foreign firms in one of the countries than in the case where the numberof firms are exogenous in both countries.
We now turn to the cooperative equilibrium. Total welfare is given byadding (26) and (27)(31)

β dW = ( A5 + A7 )dδ 1 + ( A6 + A8 )dδ 2

Setting the coefficients of dδ 1 and dδ 2 equal to zero, and solving simultaneously for δ 1 and δ 2, we find the optimal cooperative local content re-221

Local Content Requirements and International Market Share Rivalry

striction levels as10(32)

δˆ 1C = β(33)

δˆ C2 = β[b x n(b − bˆ ) + b x (b − bˆ )] > 0,
1 1

2

2

2 2

1

1

b1 (b2 − bˆ2 )(b1 − bˆ1 )[b x n(b − bˆ ) + 2b x (b − bˆ )] > 0.
1 1

2

2

2 2

1

1

b2 (b2 − bˆ2 )(b1 − bˆ1 )When bˆ1 = bˆ2 , subtracting (33) from (32), we obtainb1 x1n(b2 − bˆ )(b2 − b1 ) + b2 x2 (b1 − bˆ )(b2 − 2b1 )(δˆ 1C − δˆ 2C ) bˆ = bˆ = bˆ = β.
1 2
b1b2 (b1 − bˆ1 )(b2 − bˆ2 )It follows from the above equation that δˆ 1C > δˆ 2C if b2 > 2b1 , and δˆ 1C < δˆ C2 if
b2 ≤ b1 .
Proposition 9. When there is free entry and exit of foreign firms in country 1 and just one foreign firm in country 2 and bˆ1 = bˆ2 , the following are
true:
(i)

δˆ 1C > δˆ C2 if b2 ≥ 2b1 , and(ii)δˆ 1C > δˆ C2 if b2 ≤ b1 .

10. For the total welfare function to be concave in the policy parameters weneed
βWδ11δ 1 = −4b1 (b1 − bˆ1 ) < 0,βWδ22δ 2 = −2b2 (b2 − bˆ2 ) < 0,[]β 2 Wδ 1δ 1 Wδ 2δ 2 − Wδ21δ 2 = 6b1b2 (b1 − bˆ1 )(b2 − bˆ2 )[]− b12 (b2 − bˆ2 ) 2 + b22 (b1 − bˆ1 ) 2 > 0.

The condition is satisfied if 6b1b2 (b1 − bˆ1 )(b2 − bˆ2 ) > b12 (b2 − bˆ2 ) 2 + b22 (b1 − bˆ1 ) 2 .

222

M. Özgür Kayalica and Sajal Lahiri

On the other hand, when b1 = b2, we obtain(δˆ − δˆ )
C
1

C
2

b1 = b2 = b

=−

βx2

(b − bˆ2 )< 0.

When the unit input costs in the two home countries are the same, in thepresence of free entry and exit in country 1, country 2 applies more severe
local content restrictions than country 1.
Proposition 10. When there is free entry and exit of foreign firms in country 1 and just one foreign firm in country 2 and b1 = b2, country 2 applies
more severe local content restrictions than country 1.
Finally, since A6 and A7 are both positive (see (26) and (27)), as in theprevious section, the following two propositions can be proved easily
Proposition 11. Starting from the non-cooperative equilibrium, when there
is free entry of FDI in one of the host countries, a multilateral increase in
the levels of local content requirements is strictly Pareto-improving.
Proposition 12. When there is free entry of FDI in one of the host countries, the host governments apply more severe local content restrictions under the cooperative solution than that under the non-cooperative solution.
5. Conclusion
Foreign direct investment (FDI) has been an important tool in the integration of the world economy. There has been a phenomenal increase in
the level of FDI over the last two decades. The countries which have succeeded in achieving high growth rates of national income, tend to be thecountries which have been able to attract a large amount of FDI.
Because of international agreements, there are now limited number of
instruments that a host country government can employ, to encourage or
discourage foreign firms, and to make the best use of them. One such instrument is to specify that at least a certain fraction of inputs should bebought in the local market. This restriction on the input use is called the
local content requirement. This instrument is now widely used, and in thispaper we examine how this instrument can be used strategically by countries.
We develop a model of FDI in which foreign firms locate themselves in
two host countries and export their entire produce to another country,
called the consuming country. The commodity is produced under an oligopolistic condition. We assume the existence of unemployment in both

223

Local Content Requirements and International Market Share Rivalry

host countries. We consider two cases depending on whether or not there
is free entry and exit of foreign firms in one of the host countries. We findthat the non-cooperative levels of local contents are higher than the cooperative ones for both countries whether or not there is free entry and exitof foreign firms. The optimal levels of local content requirements are also
compared across countries and between the cases of no entry and free entry of foreign firms. It is shown that the relative unit cost structure plays
an important role in determining the relative level of local content requirements. Free entry and exit of foreign firms in one of the countries reduce
the levels of local content restrictions in both countries.

References
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11Balance of Payment Adjustment
under Capital Mobility
Michihiro Ohyama*

1. Introduction
The size of international capital and exchange transactions have increased enormously in recent years as a result of financial deregulation andrapid progress in information and communication technologies. Apparently,
the world has entered the era of perfect capital mobility and flexible exchange rates first envisaged by financial theorists such as Mundell (1960)
and Fleming (1959) a long time ago. With the globalization of financialtransactions the national rates of interest have tended to converge or atleast to co-move in the same directions and exchange rates have fluctuatedwildly in the short run and considerably even in the medium or long runs.
The purpose of this paper is to reconsider the roles which interest rates andexchange rates (or money supplies) play in the long-run adjustment of international imbalances under perfect capital mobility.1
There are already a bulky literature on the determinants of exchange
rates under international capital mobility. Since exchange rates are relative
prices of different currencies, the theory of exchange rates can be estab* I am indebted to Professors Kotaro Suzumura, Jota Ishikawa and Yoshiyasu
Ono for helpful comments on an earlier draft of this paper. Financial support fromthe Research and Education fund at the Department of Economics of Keio University is gratefully acknowledged.
1. In 70s exchange rates seemed to be affected by the behavior of accumulated
current account imbalances between countries. Their relationships have become lessevident in 80s but revived dramatically in 90s as exemplified by recent currency
crises in Latin America and Asia. In 70s there were apparently no definite correlation between exchange rates and international interest rate difierentials but 80s and
90s have witnessed their close co-movements. It is not completely clear, however,what roles their movements play in the world of globalized financial markets.
225

226

Michihiro Ohyama

lished only if the concept of money is clearly stipulated. The popular asset
market approach to exchange rate determination is based on the Keynsian
view of money as a store of value. It is powerful in explaining short-run
exchange rate fluctuations due to speculative bubbles, but appears to beless relevant to the long run trend of exchange rates. In this paper, we
adopt the orthodox view of money as an indispensable means of payment.
This view, coupled with the hypotheses of purchasing power parity and interest rate parity, seems to provide a useful explanation of the long-run behaviors of exchange rates and interest rates. This line of studies may be
traced back to the partial equilibrium analysis of exchange rates by Robinson (1959) and Metzler (1961), later extended and elaborated by Tsiang(1959) and Sohmen (1961) to cover forward exchange contracts. More recently, the general equilibrium models in this spirit are also developed by
Lucas (1982), Helpman and Razin (1982) and Svensson (1985).2
The plan of the paper is as follows. In Section 2, we explain the basic
structure of the model. In Section 3, we describe the equilibrium conditions of the model. There are potentially a number of interpretations of thegeneral equilibrium under capital mobility, but we consider two representative cases. The first interpretation regards the rate of interest as a major
factor of adjustment in the international capital and exchange market. Section 4 is devoted to the analysis of this version. In this case, the current
account imbalances are automatically adjusted through time, but the country with the higher rate of time preference tends to accumulate external
debt indefinitely until it starves under the pressure of interest payment. The
exchange rate plays no role staying stationary throughout the process ofadjustment. The second interpretation assigns a crucial role of international
adjustment to the exchange rate, or to the money supply of the keycurrency country. Section 5 is allotted for the discussion of this case. Here,foreign exchange market becomes potentially unstable in the short run andthe adjustment of international imbalances may not be achieved in the absence of correct monetary policy or appropriate interest rate target.
2. Production and Consumption
We consider a monetary model of two countries, home and foreign.
There is only one homogeneous good produced in fixed quantity in eachcountry. Each country has its own currency. It is indispensable as a meansof payment for purchasing the good produced in that country. There arebonds designated in the home and foreign currencies serving as a store ofvalue. The bonds and currencies are traded in perfectly competitive inter2. See Obstfeld and Rogoff (1996) for a brief survey of the more recent literature based on this view of money formalized as the cash-in-advance models ofmoney demand.

227

Balance of Payment Adjustment under Capital Mobility

national markets under the regime of flexible exchange rates. In this section, we describe the structure of the model and subjective equilibrium of
its agents.
Let us begin by explaining the home country’s structure. We assume theexistence of discrete time periods (t = 1, 2, ...). At the beginning of eachperiod, the representative consumer is assumed to receive payment in homemoney, Mt, (wages, dividends and monetary transfer from the government)
and engage in financial transactions. All markets open and operate simultaneously for bonds and foreign exchanges. The consumer’s consumption inperiod t, Ct, is constrained by(1)*
ptCt = Mt − (1 + it−1)BHt−1 − (1 + it−1
)etBFt−1 + BHt + etBFt,

where pt denotes the home country’s price of the good in period t, BHs and
BFs its external debts in period s in the form of bonds denominated in thehome and foreign currencies, is and i *s the home and foreign nominal interest rates in period s(s = t − 1, t) and et the exchange rate, or the price ofthe foreign currency in terms of the home currency. We adopt here andhenceforth the convention that the subscript (s = t, t − 1, t + 1) to a variable signifies the period it belongs to. Equation (1) means that the homecountry’s consumption and repayment of external debts made in periodt − 1 are financed by the representative consumer’s money income (wages,
dividends and government transfer) and new borrowings made in period t.
For simplicity, the home and foreign representative consumers are assumed to form the same static expectations with regard to exogenous variables in all future periods. To be precise, they expect that the home country’s price and real income levels in period t + 1, p t + 1 and M t + 1/p t + 1,
will repeat themselves in all future periods. Similarly, the exchange rate is
expected to be e t +1 and the home and foreign interest rates are expected tobe i t +1 and it*+1 in period t + 1 and thereafter indefinitely.3 To ease ouranalysis and exposition, they are further assumed to keep their consumption and external assets at the same levels in all future periods.4 Under thisassumption, the home consumer’s repayment of the debt made in period t
must be equal to its repayment of debt in made in period t + 1, i.e.,(2)(1+it)BHt + (1+it*)et +1BFt = (1+it +1)BHt +1 + (1+it*+1)et +1BFt +1.

3. This assumption may be arbitrary but does not necessarily imply that consumers are totally irrational. Even if they attempt to behave rationally, their rationality
is necessarily bounded when they lack information about the structure of economy
to predict future course of events rationally.
4. This assumption means that consumers do not difierentiate consumptions in
all future peiords.

228

Michihiro Ohyama

This ensures that the real values of planned consumption and external assets are kept at constant levels in period t + 1 and afterwards.
We also assume that the uncovered interest parity condition is satisfied
in the competitive international capital markets. Under the present assumption of static expectations, it may be expressed as5(3)(1+it)et = (1+it*)et +1,(4)

it +1 = it*+1.

~
Let us denote by Ct +1 the home country’s planned consumption in periodt + 1 and distinguish it from its actual consumption, Ct +1, in period t + 1.
In view of (2)-(4), it is constrained by(1 + it )it +1~( BHt + et BFt ).
pt +1Ct +1 = M t +1 −1 + it +1(5)

From (1), (3) and (5), we get the integrated budget constraint

(6)

Ct +

M
M
B
eB
1 ~
Ct +1 = t + t +1 − (1 + it −1 ) Ht −1 − (1 + it*−1 ) t Ft −1 ,rt
pt rt pt +1
pt
pt

where rt is the real effective rate of interest defined by6

(7)

rt =

pt (1 + it )it +1.
pt +1 (1 + it +1 )Equation (6) shows that the home country’s present value of planned consumption is equal to the present value of its outputs and external assets.
The home country’s consumer is assumed to maximize a utility functionof the Cobb-Douglas form:(8)~u = Ctρ Ct1+−1ρ ,*5. Formally, (4) is to be written (1 + it+1)et+1 = (1+it+1)et+2 just as (3), but it is simplified here by the assumption that et+1 = et+2.
6. Note that the real efiective rate of interest, rt, may difier from the nominal rateof interest, it, on account of expected changes not only in the price level but also
in the nominal rate of interest in the future. In the special case where pt = pt+1, rt
becomes the weighted average of it and it+1.

229

Balance of Payment Adjustment under Capital Mobility

subject to the constraint (7). Thus we may write the home country’s consumption function in period t as

(9)

⎡M
M
B
eB ⎤
Ct = ρ ⎢ t + t +1 − (1 + it −1 ) Ht −1 − (1 + it*−1 ) t Ft −1 ⎥.
pt
pt ⎦⎣ pt rt pt +1

Note that it is proportional to the present value of the home country’s
wealth by a constant factor ρ .
In a similar fashion, we obtain the foreign country’s consumption function in period t. It may be written

(10)

⎡ M*
M*
B*
B* ⎤
Ct* = ρ * ⎢ *t + * t *+1 − (1 + it −1 ) Ht −*1 − (1 + it*−1 ) Ft*−1 ⎥,rt pt +1
et pt
pt ⎦
⎣ pt

where we indicate foreign variables by asterisks. The foreign real effective
interest rate, rt*, is defined by
(11)

rt* =

pt* (1 + it* )it*+1.
pt*+1 (1 + it*+1 )In light of (3), (4), (7), and (8), the home and foreign real effective interest
rates are related to each other, i.e.,rt* = λ t rt ,

(12)
where
(13)

λt =

pt +1 pt* et,
pt pt*+1 et +1

on the assumption that the home and foreign consumers have the same expectations with regard to the exchange rate. We may rewrite (10) as

(14)

⎡ M*
M*
B
B ⎤
Ct* = ρ * ⎢ *t + * t *+1 + (1 + it −1 ) Ht −*1 + (1 + it*−1 ) Ft*−1 ⎥,rt pt +1
et pt
pt ⎦
⎣ pt

*
*
since BHt−1 + BHt−1= 0 and BFt−1 + BFt−1= 0 as a result of international capital transactions in period t − 1.
The home and foreign countries are assumed to produce one and thesame good. The familiar purchasing power parity condition

230

Michihiro Ohyama

ps

(15)

"e p ! (s = t, t + 1),
s sstates that the home and foreign price levels are equalized via the exchange rate in each period as a result of international price arbitrage. In
what follows, we shall confine ourselves to the case where this condition issatisfied.7 Thus we have rt = rt* in view of (12) and (13). In words, thehome and foreign real effective interest rates are equalized under the purchasing power parity condition.
From the definition of real effective interest rates, (12) may also be written
(16)

et =

1 + it* it*+1 1 + it +1
et +1 .
1 + it 1 + it*+1 it +1

This equation reveals that the current exchange rate is closely associatedwith the expected exchange rate, current and expected interest rates in thehome and foreign countries. When the foreign current expected interest
rates are higher than the home current and expected rates of interest, theexpected exchange rate is bound to be lower than the current rate. Given
the current and expected interest rates, the current exchange rate moves directly in proportion to the expected rate. Given the expected exchange rate,
the current rate rises immediately in response to a rise in the foreign current and expected interest rate relative to the home current and expectedinterest rates. These results seem to fit in with recent experiences in international financial markets.
The representative consumer in each country is assumed to prepare
money at the beginning of period t in order to pay for its consumption in
the same period as described by (9) and (14). For simplicity, each country’s output is supposed to be at the full employment level and correctly
anticipated by firm and consumers. We simplify the world by assuming
away capital investment and depreciation.
3. General Equilibrium
The major concern of the present paper is to clarify the determinants ofthe exchange rate and the dynamics of current account adjustment in a two-country monetary model of international trade and finance where eachcountry’s currency is used only for transaction purposes. In this section,
we introduce money as a medium of exchange and formulate the monetary
equilibrium of the model. We first consider the general equilibrium of the
7. Real exchange rates deviate from purchasing power parity in the short run, but
a number of recent studies have shown that they tend toward it in the long run. See
Rogoff (1996) for a survey of empirical literature on purchasing parity.

231

Balance of Payment Adjustment under Capital Mobility

world in which international capital movements are prohibited by somereason or another (e.g. by government decree) and then formulate that of
the world under perfect capital mobility. The analysis of the model underalternative assumptions will be postponed to the next two sections.
3.1. The World without International Capital Movements
In the absence of any risks with regard to the repayment of loans, no
one will be induced to hold a country’s currency for the store-of-value purposes as long as the rate of nominal interest denominated in the currency
becomes positive. We assume that this is indeed the case. Capital transactions are assumed to be free inside the country. In the absence of international lending or borrowing, however, the consumer in each country uses
money only for purchasing her country’s product. To put it differently, theequilibrium condition in the domestic capital market implies
ptCt = Mt.

(17)

The present model becomes extremely simple in the absence of capital mobility. Since there is no international lending or borrowing, we can simplify (6) by setting BHt−1 = BFt−1 = 0. The home consumer’s budget constraint then reduces to
(18)

Ct +

M
1 ~
1
Ct +1 = t +M t +1 .
rt
pt rt pt

We may write the home country’s consumption function as
(19)

⎛M
⎞
1
Ct = ρ ⎜ t +M t +1 ⎟ .
⎝ pt rt pt +1⎠

In the world without international capital movements, the domestic commodity market must be equilibrated in every period so that(20)

Ct = Yt,

where Yt denotes the output of the national product in period t. Combinedwith (17), this implies the quantity-of-money equation(21)

ptYt = Mt.

Let us also assume that a similar relationship is expected to hold in periodt + 1, or

232

(22)

Michihiro Ohyama

pt+1 Yt+1 = Mt+1,

where Yt+1 denotes the expected output in period t + 1. Substituting (19),(21) and (22) into (20), we get
(23)

rt =

ρ Yt +1.
1 − ρ Yt

In equilibrium the home country’s real effective interest rate is thus equal
to the product of the consumer’s time preference rate ρ /(1 − ρ ) and the
expected growth factor Yt+1/Yt. In the stationary state where the growth factor is unity, the real effective interest rate is exactly equal to the time preference rate. The equilibrium in the domestic capital market implies thehome country’s current account equilibrium.
We can stipulate similar relationships for the foreign country as well.
Thus
(24)
(25)

rt* =

ρ * Yt *+1,
1 − ρ * Yt *"pt!Yt! Mt!.

In general there is no reason to expect that the home and foreign real effective interest rates coincides with each other. The home and foreign pricelevels are also determined independently of each other. We can express theexchange rate as
(26)

et =

Yt * M t,
Yt M t*by virtue of purchasing power parity condition, (15).
3.2. The World with Perfect Capital Mobility
Let us turn to the case where international capital movements are completely free. The equilibrium condition in international capital market iswritten(27)

BHt + BHt* = 0,(28)

BFt + BFt* = 0.

Using (1) and its counterpart for the foreign country and recalling that**
BHt−1 + BHt−1= 0 and BFt−1 + BFt−1= 0, we can rewrite (27) and (28) as

233

Balance of Payment Adjustment under Capital Mobility

pt Ct + et p *t C *t = Mt + et M *t ,(29)which means that the home and foreign supply of money in period t must
be used for the purchase of world product in the same period. The equilibrium condition in the world commodity market, together with purchasing
power parity (15), implies
Ct + et p *t C *t = Yt + et p *t Y *t .

(30)

We assume that the national currency of each country is used as an indispensable means of payment in purchasing the good produced in thatcountry. Also suppose that the consumers in each country prefer to buy
domestically produced good as long as it is available. The monetary equilibrium condition for the home currency is then given by[]min( pt Ct , pt Yt ) + max et pt (Ct* − Yt * ), 0 = M t ,(31)

and the corresponding condition for the foreign currency by⎤⎡pmin( pt*Ct* , pt*Yt * ) + max ⎢ t (Ct − Yt ), 0⎥ = M t* .
e
⎦
⎣ t

(32)

Provided that the world capital market is in equilibrium, we have Ct > Yt
or Ct < Yt according as C *t < Y *t or Ct > Yt as is clear from (29). For definiteness, let us suppose for the moment that Ct
Yt and C *t
Y *t in theneighborhood of equilibrium. This means that the home country runs a
deficit, and the foreign country a corresponding surplus, in its trade account. In this case, (31) becomes

"

(33)

!

pt Yt = Mt,

which, combined with (29), (30) and (31), yields
p *t Y *t = M *t .

(34)

!

"

It should be clear that these quantity equations also obtain when Ct
Yt
and C *t
Y *t in the neighborhood of equilibrium. Substituting (9) and (14)into (30), we get(35)1− (1 − ρ ) pt Yt + (1 − ρ *et pt*Yt * )rt*= ( ρ − ρ * ) (1 + it −1 ) BHt −1 + (1 + it*−1 )et BFt −1 .

( λ t ρpt Yt +1 + ρ *et pt*Yt *+1 )

[

[

]

]

234

Michihiro Ohyama

Quantity equations (33) and (34), together with the equilibrium condition
for the world commodity market (35), ensures monetary equilibrium inboth countries.
Under the assumption of uncovered interest parity, (3) and (4), asset
holders become indifferent as to the choice of bonds denominated in thehome currency and those denominated in the foreign currency. Thus thecomposition of their portfolio becomes indeterminate in every period. To
avoid arbitrariness, we henceforth assume that international credit is heldin the form of bonds denominated in the foreign currency, or(36)

BHt = BHt−1 = 0.

This may be interpreted to mean that the foreign currency serves as the
key currency in international lending and borrowing.8
In what follows, let us concentrate on the system of equations (15), (33),(34) and (35) describing the general equilibrium of international economies.
*
Given ρ , ρ *, λ t, it−1, i *t−1, Yt, Yt+1, Yt*, Yt+1
, BFt−1 and BHt−1, these four equa*tions contain six “unknowns,” rt , et, pt, pt*, Mt and Mt*. We obtain alternative interpretations of the system depending on which variables we choose
as ultimate unknowns. We shall consider two basic interpretations of thesystem pertaining to the regime of flexible exchange rates in the next two
sections.
4. Adjustment by Interest Rate
The orthodox interpretation of the model of international economies under capital mobility set out in the preceding section is that the world capital market is cleared by the adjustment of interest rate in every period.
4.1. Short-Run Equilibrium
In this subsection we consider the short-run international equilibrium inwhich the interest rate is adjusted to clear the world capital market withmoney supply exogenously given in each country. In this case, there are
four endogenous variables, pt, pt*, et, and rt*, to be determined by four
equations (15), (33), (34) and (35). The values of pt, pt*, and et are determined in the same fashion as in the world without international capital
movements considered in the preceding section. For instance, substituting
8. Recall the assumption that a country’s product can be purchased only by its
currency. In light of this it may seem natural that the country with a deficit in her
current account issues bonds denominated in the currency of the country with acorresponding surplus. As noted in the text, however, the choice of denominating
currency is immaterial as long as one can freely trade currencies in the foreign exchange market.

235

Balance of Payment Adjustment under Capital Mobility(33) and (34) into (15), we obtain the expression of the exchange rate:
et =

(37)

M t Yt *,M t* Yt

which is identical to (26). Thus international capital mobility exerts no influence whatsoever on the determination of national price levels and theexchange rates under the present interpretation of the system.
It is the rate of interest which plays a major role in the equilibration ofinternational capital market in the present system. The substitution of (33)
and (34) into (35), together with (15) and (36), yields9

(38)

rt* =

ρYt +1 + ρ *Yt *+1.
(1 − ρ )Yt + (1 − ρ )Yt * + (1 + it*−1 )( ρ − ρ * ) BFt −1 pt**

The denominator of the left-hand side of this equation may be assumed to
be positive. Note that λ t = 1 and rt = rt* by virtue of (15). In the special
case in which the home and foreign consumers’ rates of time preference
are identical, or ρ = ρ *, (38) simplifies to
(39)

rt* =

ρ Yt +1 + Yt *+1.
1 − ρ Yt + Yt *This is the weighted average of the home and foreign interest rates in theworld without international capital movements.
More interesting is the case where the home and foreign consumers have*,different time preference rates. In this case, the term, ( ρ −ρ *)BFt−1/pt−1
plays a role to determine the equilibrium rate of interest. In view of (38),an increase in (ρ −ρ *)BFt−1/pt*, lowers (resp. raises) the real effective rate ofinterest in period t if (ρ −ρ *)BFt−1 is positive (resp. negative). For concreteness, suppose that (ρ −ρ *)BFt−1/pt* > 0. If ρ > ρ * and BFt−1 > 0, an increasein BFt−1/pt*, then means an increase in the real indebtedness of the homecountry whose rate of time preference is higher than that of the foreigncountry, or an international transfer of real wealth from the former to thelatter. This in turn suppresses the world’s propensity to consume thereby
lowering the equilibrium rate of intrerest. If ρ < ρ * and BFt−1 < 0, a decrease in BFt−1/pt*, or an increase in its absolute value means an increase in
the real indebtedness of the foreign country whose rate of time preferenceis higher than that of the home country, or an international transfer of real
wealth from the former to the the latter. Thus we obtain the same conclu9. With the purchasing power parity condition prevailing in every period, we
have λ t = 1, or rt = rt*. (See (13) and (15))

236Michihiro Ohyamasion. Genarally, we have
Proposition 1. (International indebteness and interest rate): An increase in
the real indebtedness of a country with higher (resp. lower) rate of time
preference than that of its trading partner lowers (resp. raises) the equilibrium real interest rate.
There are some noteworthy implications of this proposition. First, recall
that an increase in the money supply of the foreign country raises the foreign price level and decreases the real indebtedness of the foreign country
in the same period (seibniorege effects). Thus Proposition 1 implies thatthe money supply of the key-currency country is generally not neutral to
the real structure of the international economy. In contrast, an increase in
the home country’s money supply merely gives rise to a proportionate risein the home price level and the nominal exchange rate leaving all the realvariables unaffected. Second, note that a deficit in a country’s current account will, ceteris paribus, increase its real external debt thereby affecting
the world interst rate over time. For instance, a deficit in the home country’s current account is bound to lower (resp. raise) the world equilibrium
interest rate in the course of time if its rate of time prefence is higher (resp.
lower) than that of the foreign country. Third, an increase in the rate of interest in a period increases the real indebtedness of the home country andlowers (resp. raises) the rate of interest in the next priod if the home residents have a higher (resp. lower) rate of time preference than the foreigners.
4.2. Current Account and Interest Rate Dynamics
The general equilibrium of the system considered in the foregoing analysis is temporary in nature. As noted above, each country’s external indebtedness changes through time to affect the equilibrium of the system aslong as its current account is out of balance. At this point, let us consider
the dynamic adjustment process of current account imbalances. To simplify
matters, we assume here that all exogenous variables are stationary, or*Mt = M , Mt* = M *, Yt = Yt+1 = Y , Yt* = Yt+1
= Y * and rt = rt* = it.
With these simplifying assumptions, we may write the inter-periodical
change in the home country’s net external debt as(40)

BFt − BFt−1 = p *(Ct − Yt) + it−1BFt−1 = p *(Yt* − Ct*) + it−1BFt−1.

The first term of the right-hand side signifies the home country’s deficit intrade account, and the second its deficit in service account. The substitution of (9) and (14) into (40) yields

237

Balance of Payment Adjustment under Capital Mobility⎡
1 ⎤BFt − BFt −1 = ⎢1 − ρ (1 + ) ⎥( − p *Y + it −1 BFt −1 )
it ⎦
⎣
⎡
1 ⎤
= ⎢1 − ρ * (1 + ) ⎥( p *Y * + it −1 BFt −1 ).
i
t ⎦
⎣

(41)
If ρ = ρ *, (38) reduces to

it =

(42)

ρ
ρ*
=
,
1− ρ 1− ρ*in the present setting. Therefore, we have BFt = BFt−1 in view of (41). In
words, the interest rate is equalized to the common rate of time preference
and the current account is balanced every period.
Generally, (38) and (41) yield

(43)

it =

(1 − ρ ) * ρp *Y + (1 − ρ ) ρ * p *Y *.
( ρ − ρ * ) BFt + (1 − ρ )(1 − ρ * ) p * (Y + Y * )Note that the rate of interest is negatively (resp. positively) correlated withthe current value of the home country’s net external debt if ρ > ρ *(resp.
ρ < ρ *). Thus the dynamics of interest rate is directly related to the dynamics of home net external debt. Substituting (43) into (41) and rearranging terms, we get
BFt − BFt −1 =
(44)

=

[

]

( ρ − ρ * ) (1 − ρ ) p *Y * − ρBFt −1 I t*(1 − ρ ) ρp Y + (1 − ρ ) ρ p Y *

[

*

*

*

] ,

( ρ * − ρ ) (1 − ρ * ) p *Y + ρ * BFt −1 I t*
*

*

*

*

(1 − ρ ) ρp Y + (1 − ρ ) ρ p Y*

where It and It* represent the home and foreign national incomes measured
in the unit of the foreign currency in period t, i.e.,(45)

It = p *Y − it−1BFt−1,(46)

It* = p *Y *+ it−1BFt−1.

This is a first-order non-linear difference equation in BF. The stationary
state solutions of (44) are given by

238

Michihiro Ohyama(1 − ρ * ) p *Y
,
ρ*

(47)

BF =

(48)

BF = −(1 − ρ ) p *Yρ*!"provided that ρρ *.
Figure 1 illustrates the dynamic adjustment process of the current account balance for the case ρ > ρ *. The curve BB is the graph of (43). It
has a positive intercept on the vertical axis and cuts the 45 degree line
through the origin at two points, E and F , signifying the stationary statesolutions of (44). Of these stationary equilibria, E is stable, but F is unstable. Starting from any initial value between BF and ABF , the home country’s net external debt monotonically increases and converges to BF as time
tends to infinity. The polygonal line with arrows exemplifies a possible adjustment path along which the current account imbalance decreases throughtime. From (43), it should be clear that the rate of interest decreases monotonically and converges to the corresponding stationary value.
BFt

E
B

45°

B0

O

BFt-1

F
B

Figure 1. External Debt under Interest Adjustment

At the stable stationary equilibrium, the home country becomes a net
debtor, and the foreign country a net creditor due to the assumption ρ >ρ *meaning that the home consumer’s time preference is stronger than the foereigner’s. The inspection of (41) reveals

(49)

it =

ρ*
ρ
<
,
*
1− ρ
1− ρ

239

Balance of Payment Adjustment under Capital Mobility

in the stationary state. Thus the rate of interest is equalized to the foreign
consumer’s time preference rate in the long run. These results are reversedin the case ρ < ρ *. Now, BF is the stable stationary value of the foreigncountry’s net external debt. The home country becomes a net creditor, andthe foreign country a net debtor in the long run. The rate of interest converges to the home consumer’s time preference rate as time tends to infinity. I have established
Proposition 2. (Stability of Interest Rate Dynamics): The current accountimbalances are automatically adjusted through time and the country withweaker time preference than the rest of the world is bound to be a net
creditor setting the international interest rate in line with its time preference rate in the long run.
It should be noted here that the net debtor has to pay out the sum of interest amounting to the entire value of its output in the stationary statewith no purchasing power left for its consumption. This point can be readily confirmed by substituting (47) (or (48)) into (45) (or (46)) with
it−1 = (1−ρ )/ ρ and BFt−1 = BF (or it−1= (1−ρ *)/ ρ * and BFt−1 = BF). This result may be referred to as the “tragedy of a cicada” in analogy to the wellknown story of a cicada and ants in the Fables of Aesop.
Proposition 3. (Tradgedy of a Cicada): In the long-run stationary state thecountry with lower time preference consumes everything produced in theworld leaving nothing for the country with stronger time preferece. 10
5. Adjustment by Money Supply
In the foregoing section we assumed that the rate of interest plays a keyrole in the equilibration of the world capital market. This interpretation of
the basic model leads to the orthodox conclusion that international current
account disequilibrium tends to be dissolved over time through the international transfer of wealth from the country with deficit to the country withsurplus. It also implies that the country with stronger time preference than
the rest of the world tends to accumulate external debt and impoverishedto the point of starvation in the long run. It is, however, possible to view
the world market as the place where the home currency is exchanged forthe foreign currency and regard the exchange rate or, more basically, thekey currency country’s money supply, as the key adjusting factor for themarket. This view turns out to be relevant to the situation in which the
10. The myopic behavior, or the bounded rationality of the consumer is not responsible for this seemingly absurd result. For instance, a similar result obtains in
the general equilibrium model of international trade with perfectly informed rational consumers discussed by Helpman and Razin (1982).

240

Michihiro Ohyamahome and foreign time preference differ from each other and the monetary
authority adjusts money supply so as to keep the world real interest rate ata certain target level. The tragedy of a cicada may be avoided in such asituation by the appropriate monetary policy of the key-currency country.
5.1. Short-Run Equilibrium
In the model of the preceding section, the exchange rate is determinedby the purchasing power parity condition (15) and quantity equations (33)
and (34) in the same fashion as in the case where there are no international
capital transactions. Thus international capital mobility exerts no influenceon its equilibrium value. Moreover, given the home and foreign money
supplies, exchange rate is kept constant throughout the current account adjustment process described above. This conclusion is apparently at variancewith recent experiences in the foreign exchange markets. In reality, the exchange rate appears to get more volatile both in the short run and in thelong run when less restrictions are imposed on international capital transactions. This observation suggests that money supplies, together with the exchange rate, play some role in international adjustment. In the present section, we therefore consider an alternative interpretation of our system, i.e.,
according to which the key currency country’s money supply is adjusted toclear the international money market.
We assume that the foreign country, or the key currency country, adjusts
its money supply so as to fix the rate of interest at a certain predetermined
level and the home country keeps its money supply at a given level. In thisregime, we have four endogenous variables, et, pt, pt*, and Mt*, to be determined by four equations (15), (33), (34) and (35) given the values of allother variables. To be more precise, pt is trivially determined by (33).
Given rt* and pt, (34) may be solved for et to give

(50)

[

]

[

]

ρYt +1 + ρ *Yt *+1 rt* − (1 − ρ )Yt + (1 − ρ * )Yt *
et
=
,
pt
(1 + it*−1 )( ρ − ρ * ) BFt −1!"

provided that (ρ −ρ *) BFt−1
0. Given pt and et, (15) and (34) determine
pt* and Mt*. In view of the purchasing power parity condition (15), the present regime is viable only if the foreign country, or the key currency country, adjusts its money supply, or its price level in conformity with (50).
The present regime is viable only if the home and foreign consumers
have different time preferences, or ρ
ρ * with some international indebtedness in the preceding period, or BFt−1
0. Otherwise, the present regime
would become meaningless. Furthermore, the target range of interest rate is
restricted if the equilibrium exchange rate is to be positive. To be more
precice, let us define the critical rate of interest as

!"
!"

241

Balance of Payment Adjustment under Capital Mobility

r~ * =(51)

ρYt +1 + ρ *Yt *+1,(1 − ρ )Y1 + (1 − ρ * )Yt *which is the weighted average of the home and foreign equilibrium rates
of interest in the world without capital mobility. (See (23) and (24) above).
The target rate of interest must be set above (resp. below) this critical level
if (ρ −ρ *) BFt−1 < 0 (resp. > 0), orr * ≤ r~ * according as ( ρ − ρ * ) BFt −1 ≥ 0.

(52)This short-run equilibrium is potentially unstable under the usual Walrasianadjustment process if the exchange rate is regarded as the adjusting factor
in money market. To see this point, suppose that the home country runs a
deficit and the foreign country a corresponding surplus in the trade account.
From equations (9), (14), (34) and (35), the excess demand for the foreign
currency may be written,pt( ρYt +1 + ρ *Yt *+1 )rt*− (1 − ρ ) pt Yt + (1 − ρ * ) pt Yt * − (1 + it*−1 )( ρ − ρ * ) BFt −1et .
pt Ct + et pt*Ct* − pt Yt − et pt*Ct* =

(53)

[

]

If (ρ −ρ *) BFt−1 < 0, a rise in et, or a fall in the external value of the foreign currency will increase the excess demand for the foreign currency ensuring the local stability of the foreign exchange market. In contrast, if(ρ −ρ *) BFt−1 > 0, the equilibrium becomes unstable.11 This outcome may
not be relevant, however, to the present regime in which the foreign government is supposed to adjust its money supply so as to achieve the target
interest rate.12
Let us consider the determinants of exchange rate under the present regime. The exchange rate is here dependent on diverse factors: the target
rate of interest, the current output levels, the expected future output levels,
the home and foregn rates of time preference, the home country’s money
supply and the home country’s net external debt. Comparing (50) with (36),
it should be clear that the exchange rate is likely to be more volatile under
11. If the home country runs a surplus and the foreign country a corresponding
deficit in the trade account, the left-hand side of (53) divided by et may be interpreted as the excess demand for the home currency, and the equilibrium is also apparently stable if and only if (ρ −ρ *)BFt−1 < 0.
12. In fact, it may be equally plausible here to regard the exchange rate as theadjusting factor in achieving the purchasing power parity condition, (15), and theforeign money supply as the adjusting factor in achieving money market equilibrium, (32).

242

Michihiro Ohyama

adjustment by money supply than under adjustment by interest rate because of its dependency on additional factors such as international indebtedness and future (expected) output levels.
Some of comparative statical results depends on whether the short-run
equilibrium is stable in the sense mentioned above, i.e., whether the signof (ρ −ρ *)BFt−1 is negative or positive. For instance, a rise in the foreign
target rate of interest leads to a depreciation of the home currency and afall in the foreign price level and money supply if (ρ −ρ *)BFt−1 < 0 but
would lead to opposite results if ( ρ −ρ *)BFt−1 > 0. Similarly, an increase in
the expected future output (expected income growth) will bring about anappreciation of the home currency if and only if (ρ −ρ *)BFt−1 < 0. In contrast, an increase in the home money supply will result in a proportionate
rise in the home price level and a corresponding depreciation of the homecurrency irrespective of the sign of (ρ −ρ *)BFt−1.
The dynamic effects of current account imbalance on the equilibrium exchange rate differs depending on whether the home country is currently a
net borrower or a net lender in the world capital market. Suppose that thehome country runs a deficit in its current account in period t − 2. It would
increase its net indebtedness in period t + 1. Alternatively put, it would increase the absolute value of Bt−1 if Bt−1 > 0, but decrease the absolute valueof Bt−1 if Bt−1 < 0. In view of (50), we obtain
Proposition 4. (Current Account Imbalances and Exchange Rate ): If a
country runs a deficit in its current account, it will undergo an depreciation (resp. appreciation) of its currency over time if it is a net lender (resp.
borrower) in the world capital market.
5.2. Current Account and Money Supply Dynamics
At this point, let us investigate the adjustment process of the current account under the present setup. For simplicity, all the exogenous variables
are assumed to be stationary through time, or that Yt = Yt+1 = Y ,*Yt* = Yt+1
= Y *, Mt−1 = Mt = M and so on. The foreign money supply andthe foreign price level are endogenously determined, but the foreigners assumed to have static expectations with respect to the price level so that rt= rt* = i *.
With these assumptions, we can express the inter-periodical change inthe foreign net external debt as

(54)

1 ⎤
⎡
BFt − BFt −1 = ⎢1 − ρ * (1 + * ) ⎥( − pt*Y + i * BFt −1 )i ⎦⎣1 ⎤ * * *⎡= ⎢1 − ρ (1 + * ) ⎥( pt Y + i Bt −1 ).
i ⎦
⎣

243

Balance of Payment Adjustment under Capital Mobility

From (15) and (50),

(55)

pt* =

( ρ − ρ * )(1 + i * )i * BFt −1[ρ − (1 − ρ)i ]Y + [ρ − (1 − ρ )i ]Y
*

*

*

*

*

.

Substituting (55) into (54), we get[ρ − (1 − ρ)i ][ρ − (1 − ρ )i ](Y + Y ) ) B[ρ − (1 − ρ)i ]Y + [ρ − (1 − ρ )i ]Y*(56)

BFt = (1 −

*

*

*

*

*

*

*

*

*

Ft −1

.

The monetary authority of the key-currecy country can convert any initialstate into a stationaty state of this adjustment process by setting the target
rate of interest at a unique level depending on the sign of (ρ −ρ *)BF0. In
view of (52), it is given by

(57)

⎡ ρ
ρ* ⎤
i * = max ⎢,,*⎥⎣1 − ρ 1 − ρ ⎦when ( ρ −ρ *) BF0 < 0, and by

(58)

⎡ ρ
ρ* ⎤
i * = min ⎢,,*⎥⎣1 − ρ 1 − ρ ⎦when ( ρ −ρ *)BF0 > 0.
Starting from any initial state, the monetary authority can reduce international indebtedness indefinitely through time by appropriately choosing thetarget rate of interest. Here again, the range of the appropriate target interest rates depend on the sign of (ρ −ρ *)BF0.
First, suppose that (ρ −ρ *)BF0 < 0. In view of (50), (51), (52) and (55),
BFt then decreases monotonically over time and converges to zero if andonly if(59)⎡ ρρ* ⎤ * ~*,>i >r .
max ⎢*⎥⎣1 − ρ 1 − ρ ⎦This condition also ensures that the exchange rate and foreign price levelremain positive throughout the process. If the current account imbalances
are to be adjusted through time, the target interest rate must be set at a

244Michihiro Ohyama

level not lower than the rate of time preference of either country.
Turn to the case where ( ρ −ρ *)BF0 > 0. In light of (50), (51), (52) and(55), the range of appropriate target interest rates relevant to this case is⎡ ρ
ρ* ⎤i * < min ⎢,.
*⎥⎣1 − ρ 1 − ρ ⎦(60)

The automatic adjustment of current account imbalances is possible only if
the target interest rate is set at a level intermediate between the minimumof the two country’s rates of time preference and lower than the criticallevel which ensures the existence of meaningful equilibrium.
In summary, we can state
Proposition 5. (International Adjustmentby Money Supply): International
current account imbalances may be adjusted to avoid the tragedy of a cicada if the key-currency country set the target rate of interest appropriately and adjusts its money supply comformably so as to equilibrate money
market continuously.
Figure 2 illustrates the stable adjustment process for the case where
BF0 > 0 and the target interest rate is chosen from the relevant appropriate
range. The home country’s current account remains always in surplus sothat the home external debt, together with its current account surplus, decreases monotonically through time and converges to zero as time tends toinfinity. The home currency appreciates against the foreign currency andthe foreign price level and money supply rise throughout the process of adjustment.
BFt

B

45°

O

B0

BFt-1

B

Figure 2. External Debt under Money Supply Adjustment

245

Balance of Payment Adjustment under Capital Mobility

6. Summary and Conclusion
In this paper we have analyzed the long-run adjustment of current account imbalances of two countries under the regime of flexible exchange
rate with perfect international capital mobility. Our analysis of international
adjustment is based on the view of money circulating from producers to
consumers and then from consumers to producers serving on the way only
as a means of payment. Specifically, we have considered two possible factors in international adjustment, i.e., the interest rate and the key-curency
country’s money supply (or exchange rate) in the context of a simple cashin-advance model of international trade payments.
In the case of adjustment by interest rate, the exchange rate is determined by the money supplies and real national incomes of the two countries independently of international indebtedness and national time preferences. The current account imbalances are basically adjustable through international specie-flow mechanism in this case. The country with time
preference stronger than elsewhere tends to run a surplus in its current account, while the rest of the world tends to accumulate net external debt until it uses up all the non-interest income in interest payment. The case ofadjustment by money supply gives rise to drastically different performances of the system. The equilibrium value of exchange rate becomes sensitive to changes in international indebtedness and national time preferences. The current account imbalances may be adjusted over time only if
the target interest rate is set at an appropriate level depending on the keycurrency country’s initial state of external indebtedness and time preference relative to the rest of the world.
Let us briefly mention some qualifications of the present model. First, it
is assumed that the home and foreign countries produce one and the samecommodity. This assumption hinders us from considering the determinationof the real exchange rate and its implications for international adjustment.
It is, however, not difficult to extend the analysis of the temporary equilibrium to the case where there are two or more commodities. Such an extension is interesting in its own right, but would not affect the major conclusions of the present study substantially. Second, national currencies aresupposed to function entirely as a means of payment, and not as a store ofvalue, in the present model. This assumption serves to focus our attention
on the important aspect of money, but it may be unrealistic in the uncertain world where money is used as store of value to hedge exchange andcountry risks. The asset market approach to exchange rate determinationemphasizes this function of money. It should be considered, however, as acomplement (rather than a substitute) to the formulation adopted here.

246

Michihiro Ohyama

References
Helpman, E. and A. Razin. 1982. Dynamics of Floating Exchange Rate Regime.
Journal of Political Economy 90: 728-754.
Lucas, R. E. 1982. Interest Rates and Currency Prices in a Two-Country World.
Journal of Monetary Economics 10: 335-359.
Metzler, L. A. 1948. The Theory of International Trade. In A Survey of Contemporary Economics, chapter 6, ed. H. S. Ellis. Philadelphia: Blakiston Co: 210-254.
Obstfeld, M. and K. Rogoff. 1996. Foundations of International Macroeconomics.
Cambridge, Massachusetts: The MIT Press.
Robinson, J. 1937. Essays in the Theory of Employment. London: Macmillam, 2nded., 1947.
Rogoff, K. 1996. The Purchasing Power Parity Puzzle. Journal of International
Economics, Journal of Economic Literature 34: 647-668.
Sohmen, E. 1961. Flexible Exchange Rate. Chicago: University of Chicago Press,
Revised ed., 1969.
Svensson, L. E. O. 1985. Currency Prices, Terms of Trade, and Interest Rate: A
General Equilibrium Asset-Pricing Cash-in-Advance Approach. Journal of International Economics 18: 17-41.
Tsiang, S. S. 1959. The Theory of Forward Exchange and Effects of Government
Intervention on the Forward Exchange Market. IMF Staff Papers 7: 75-106.

12Technology, Geography, and Trade
Jonathan Eaton and Samuel Kortum*

1. Introduction!

"

Theories of international trade have not come to grips with a number ofbasic facts: trade diminishes dramatically with distance; prices varyacross locations, with greater differences between places farther apart;factor rewards are far from equal across countries； countries’ relative
productivities vary substantially across industries. The first pair of facts indicate that geography plays an important role in economic activity. The
second pair suggest that countries are working with different technologies.
Various studies have confronted these features individually, but have notprovided a simple framework that captures all of them.
We develop and quantify a Ricardian model of international trade (onebased on differences in technology) that incorporates a role for geography.1
The model captures the competing forces of comparative advantage promoting trade and of geographic barriers (both natural and artificial) inhibiting it. These geographic barriers reflect such myriad impediments as transport costs, tariffs and quotas, delay, and problems with negotiating a deal
from afar.
The model yields simple expressions relating bilateral trade volumes,
first, to deviations from purchasing power parity and, second, to technology and geographic barriers.2 From these two relationships we can estimate
the parameters needed to solve the world trading equilibrium of the modeland to examine how it changes in response to various policies.

$#* A previous version circulated under the title ”Technology and Bilateral Trade,”
NBER Working Paper No. 6253, November, 1997. Deepak Agrawal and Xiaokang
Zhu provided excellent research assistance. We gratefully acknowledge the helpfulcomments of Zvi Eckstein and two anonymous referees as well as the support of
the National Science Foundation.
1. Grossman and Helpman (1995) survey the literature on technology and trade
while Krugman (1991) provides an introduction to geography and trade.
2. Engel and Rogers (1996) and Crucini, Telmer. and Zachariadis (2001) explore
the geographic determinants of deviations from the law of one price.
247

248

Jonathan Eaton and Samuel Kortum

Our point of departure is the Dornbusch, Fischer, and Samuelson (1977)
two-country Ricardian model with a continuum of goods. We employ aprobabilistic formulation of technological heterogeneity under which themodel extends naturally to a world with many countries separated by geographic barriers. This formulation leads to a tractable and flexible framework for incorporating geographical features into general equilibrium
analysis.
An additional feature of our model is that it can recognize, in a simple
way, the preponderance of trade in intermediate products. Trade in intermediates has important implications for the sensitivity of trade to factor
costs and to geographic barriers. Furthermore, because of intermediates, location, through its effect on input cost, plays an important role in determining specialization.3
Table 1. Trade, Labor, and Income Data

Country

Australia
Austria
Belgium
CanadaDenmark
FinlandFranceGermany
GreeceItaly
Japan
Netherlands
New Zealand
NorwayPortugal
Spain
SwedenUnited Kingdom
United States

Imports Imports from Sample as% of Mfg.
% ofSpending
All Imports
23.8
40.4
74.8
37.3
50.8
31.3
29.6
25.0
42.9
21.3
6.4
66.9
36.3
43.6
41.6
24.5
37.3
31.3
14.5

75.8
84.2
86.7
89.6
85.2
82.2
82.3
77.3
80.8
76.8
50.0
83.0
80.9
85.2
84.9
82.0
86.3
79.1
62.0

Human-Capital Adj. Mfg.
Mfg.
Mfg.
Mfg. Labor’s
Wage
Wage
Labor % Share(U.S.=1) (U.S.=1) (U.S.=1) of GDP
0.61
0.70
0.92
0.88
0.80
1.02
0.92
0.97
0.40
0.74
0.78
0.91
0.48
0.99
0.23
0.56
0.96
0.73
1.00

0.75
0.87
1.08
0.99
1.10
1.10
1.07
1.08
0.50
0.88
0.91
1.06
0.57
1.18
0.32
0.65
1.11
0.91
1.00

0.050
0.036
0.035
0.087
0.020
0.022
0.205
0.421
0.015
0.225
0.686
0.043
0.011
0.012
0.033
0.128
0.043
0.232
1.000

8.6
13.4
13.2
10.5
11.5
12.5
12.6
20.6
6.1
12.4
14.4
11.0
9.6
8.7
10.7
11.6
14.2
14.7
12.4

Note: All data except GDP are for the manufacturing sector in 1990. Spending on manufactures is gross manufacturing production less exports of manufactures plus imports of manufactures. Imports from the other 18 excludes imports of manufactures from outside our sample of countries. To adjust the manufacturing wage and manufacturing employment for human capital. we multiply the wage in country i by e −0.06Hi，and employment in country i by
e 0.06Hi，where Hi，is average years of schooling is country i as measured by Kyriacou (1991).
See the Appendix for a complete description of all data sources.

3. Hummels, Rapoport, and Yi (1998) document the importance of trade in intermediates. Yi (2003) discusses how trade in intermediates, which implies that agood might cross borders several times during its production, can reconcile thelarge rise in world trade with relatively modest tariff reductions. Krugman and
Venables (1995) also provide a model in which, because of trade in intermediates,
geography influences the location of industry.

249

Technology, Geography, and Trade

We estimate the model using bilateral trade in manufactures for a crosssection of 19 OECD countries in 1990.4 The parameters correspond to:each country’s state of technology, governing absolute advantage， theheterogeneity of technology, which governs comparative advantage, andgeographic barriers. We pursue several strategies to estimate these parameters using different structural equations delivered by the model and data on
trade flows, prices, geography, and wages.
Our parameter estimates allow us to quantify the general equilibrium of
our model in order to explore numerically a number of counterfactual situations:
We explore the gains from trade in manufactures. Not surprisingly, allcountries benefit from freer world trade, with small countries gaining
more than big ones. The cost of a move to autarky in manufactures ismodest relative to the gains from a move to a “zero gravity” world
with no geographic barriers.
We examine how technology and geography determine patterns of specialization. As geographic barriers fall from their autarky level, manufacturing shifts toward larger countries where intermediate inputs tend
to be cheaper. But at some point further declines reverse this pattern assmaller countries can also buy intermediates cheaply. A decline in geographic barriers from their current level tends to work against the largest countries and favor the smallest.
We calculate the role of trade in spreading the benefits of new technology. An improvement in a country’s state of technology raises welfare
almost everywhere. But the magnitude of the gains abroad approach
those at home only in countries enjoying proximity to the source andthe flexibility to downsize manufacturing.
We analyze the consequences of tariff reductions. Nearly every country
benefits from a multilateral move to freer trade, but the United States
suffers if it drops its tariffs unilaterally. Depending on internal labormobility, European regional integration has the potential to harm participants through trade diversion or to harm nonparticipants nearby
through worsened terms of trade.
With a handful of exceptions, the Ricardian model has not previously
served as the basis for the empirical analysis of trade flows, probably because its standard formulation glosses over so many first-order features ofthe data (e.g., multiple countries and goods, trade in intermediates, andgeographic barriers).5 More active empirical fronts have been: the grav-

"

!
#

!

"

#
$

!

4. We think that our model best describes trade in manufactures among industrial
countries. For most of these countries trade in manufactures represents over 75 percent of total merchandise trade. (The exceptions are Australian exports and Japanese imports.) Moreover, the countries in our sample trade mostly with each other,as shown in the second column of Table 1.
5. What has been done typically compares the export performance of only a pairof countries. MacDougall (1951, 1952) is the classic reference. Deardorff (1984)
and Leamer and Levinsohn (1995) discuss it and the subsequent literature. Choudhri and Schembri (2002) make a recent contribution.

250

Jonathan Eaton and Samuel Kortum!

ity modeling of bilateral trade flows， computable general equilibrium(CGE) models of the international economy, and factor endowments or
Heckscher-Ohlin-Vanek (HOV) explanations of trade.
Our theory implies that bilateral trade volumes adhere to a structure resembling a gravity equation, which relates trade flows to distance and to
the product of the source and destination countries’ GDPs. Given the success of the gravity model in explaining the data, this feature of our modelis an empirical plus.6 But to perform counterfactuals we must scratch beneath the surface of the gravity equation to uncover the structural parameters governing the roles of technology and geography in trade.7
In common with CGE models we analyze trade flows within a generalequilibrium framework, so we can conduct policy experiments. Our specification is more Spartan than a typical CGE model, however. For one thing,
CGE models usually treat each country’s goods as unique, entering preferences separately as in Armington (1969).8 In contrast, we take the Ricardian approach of defining the set of commodities independent of country, with specialization governed by comparative advantage.
Our approach has less in common with the empirical work emanatingfrom the HOV model, which has focussed on the relationship between factor endowments and patterns of specialization. This work has tended to ignore locational questions (by treating trade as costless), technology (by assuming that it is common to the world), and bilateral trade volumes (since
the model makes no prediction about them).9 While we make the Ricardianassumption that labor is the only internationally immobile factor, in princi-"

5. What has been done typically compares the export performance of only a pairof countries. MacDougall (1951, 1952) is the classic reference. Deardorff (1984)
and Leamer and Levinsohn (1995) discuss it and the subsequent literature. Choudhri and Schembri (2002) make a recent contribution.
6. Deardorff (1984) reviews the earlier gravity literature. For recent applications
see Wei (1996), Jensen (2000), Rauch (1999), Helpman (1987), Hummels and Levinsohn (1995), and Evenett and Keller (2002).
7. We are certainly not the first to give the gravity equation a structural interpretation. Previous theoretical justifications posit that every country specializes in aunique set of goods, either by making the Armington assumption (as in Anderson(1979), and Anderson and van Wincoop (2003) or by assuming monopolistic competition with firms in different countries choosing to produce differentiated products (as in Helpman (1987), Bergstrand (1989), Redding and Venables (2001)). An
implication is that each source should export a specific good everywhere. Haveman
and Hummels (2002) report evidence to the contrary. In our model more than one
country may produce the same good, with individual countries supplying different
parts of the world.
8. Hertel (1997) is a recent state-of-the-art example.
9. Leamer (1984) epitomizes this approach, although Leamer and Levinsohn(1995) admit its failure to deal with the obvious role of geographic barriers. The
literature has begun to incorporate roles for technology, introducing factoraugmenting technological differences, as in Trefler (1993, 1995) and industryspecific technological differences, as in Harrigan (1996). Trefler (1995) recognizes
geography by incorporating a home-bias in preferences. Davis and Weinstein(2001) strive to incorporate more general geographic features.

251

Technology, Geography, and Tradeple one could bridge the two approaches by incorporating additional immobile factors.
To focus immediately on the most novel features of the model and how
they relate to the data we present our analysis in a somewhat nonstandard
order. Section 2, which follows, sets out our model of trade, conditioning
on input costs around the world. It delivers relationships connecting bilateral trade flows to prices as well as to geographic barriers, technology, andinput costs. We explore empirically the trade-price relationship in Section
3. In Section 4 we complete the theory, closing the model to determine input costs. With the full model in hand, Section 5 follows several approaches to estimating its parameters. Section 6 uses the quantified model
to explore the counterfactual scenarios listed above. Section 7 concludes.
(The Appendix reports data details.)
2. A Model of Technology, Prices, and Trade Flows
We build on the Dornbusch, Fischer, Samuelson (1977) model of Ricardian trade with a continuum of goods. As in Ricardo, countries havedifferential access to technology, so that efficiency varies across commodities and countries. We denote country i’s efficiency in producing goodj ∈ [0, 1] as zi(j).
Also as in Ricardo, we treat the cost of a bundle of inputs as the sameacross commodities within a country (because within a country inputs aremobile across activities and because activities do not differ in their input
shares). We denote input cost in country i as ci. With constant returns toscale, the cost of producing a unit of good j in country i is then ci/zi(j).
Later we break ci into the cost of labor and of intermediate inputs,
model how they are determined, and assign a numeraire. For now it suffices to take as given the entire vector of costs across countries.
We introduce geographic barriers by making Samuelson’s standard andconvenient “iceberg” assumption, that delivering a unit from country i tocountry n requires producing dni units in i. 10 We set dii = 1 for all i. Positive geographic barriers mean dni > 1 for n ≠ i. We assume that crossborder arbitrage forces effective geographic barriers to obey the triangle inequality: For any three countries i, k, and n, dni dnk dki.
Taking these barriers into account, delivering a unit of good j producedin country i to country n costs:

!

(1)

⎛ c ⎞
pni ( j ) = ⎜ i ⎟ d ni ,⎝ zi ( j) ⎠10. Krugman (1995) extols the virtues of this assumption. Most relevant here isthat country i’s relative cost of supplying any two goods does not depend on thedestination.

252

Jonathan Eaton and Samuel Kortum

the unit production cost multiplied by the geographic barrier.
We assume perfect competition, so that pni(j) is what buyers in country
n would pay if they chose to buy good j from country i. But shopping
around the world for the best deal, the price they actually pay for good jwill be pn(j), the lowest across all sources i:(2)pn(j) = min{pni(j); i = 1,..., N },where N is the number of countries.11
Facing these prices, buyers (who could be final consumers or firms buying intermediate inputs) purchase individual goods in amounts Q (j) tomaximize a CES objective:(3)

U = ⎡ Q( j )
⎢⎣ 0

∫

1

(σ −1) / σ

dj ⎤
⎥⎦

σ / (σ −1),

where the elasticity of substitution is σ > 0. This maximization is subject
to a budget constraint that aggregates, across buyers in country n, to Xn,
country n’s total spending.
Dornbusch, Fischer, and Samuelson work out the two-country case, but
their approach does not generalize to more countries.12 Extending themodel beyond this case is not only of theoretical interest, it is essential toany empirical analysis of bilateral trade flows.
2.1. Technology
We pursue a probabilistic representation of technologies that can relate
trade flows to underlying parameters for an arbitrary number of countries
across our continuum of goods. We assume that country i’s efficiency in
11. Bernard, Eaton, Jensen, and Kortum (2003) extend the analysis to allow forimperfect competition to explain why exporting plants have higher productivity, as
documented in Bernard and Jensen (1999). With Bertrand competition each destination is still served by the low-cost provider, but it charges the cost of the second cheapest potential provider. The implications for the aggregate relationships we examine below are not affected.
12. For two countries 1 and 2 they order commodities j according to the countries’ relative efficiencies z1(j)/z2(j). Relative wages (determined by demand and labor
supplies) then determine the breakpoint in this “chain of comparative advantage.”With more than two countries there is no such natural ordering of commodities.
Wilson (1980) shows how to conduct local comparative static exercises for the N country case by asserting that zi(j) is a continuous function of j. Closer to ourprobabilistic formulation, although with a finite number of goods and no geographic barriers, is Petri (1980). Neither paper relates trade flows or prices to underlying parameters of technology or geographic barriers, as we do here.

253

Technology, Geography, and Trade

producing good j is the realization of a random variable Zi (drawn independently for each j) from its country-specific probability distribution
Fi(z) = Pr[Ziz]. We follow the convention that, by the law of large
numbers, Fi(z) is also the fraction of goods for which country i’s efficiency is below z.
From expression (1) the cost of purchasing a particular good from country i in country n is the realization of the random variable Pni = cidni/Zi,
and from (2) the lowest price is the realization of Pn= min{Pni; i= 1,..., N }.
The likelihood that country i supplies a particular good to country n is theprobability π ni that i’s price turns out to be the lowest.
The probability theory of extremes provides a form for Fi(z) that yields
a simple expression for π ni and for the resulting distribution of prices. We
assume that country i’s efficiency distribution is Fréchet (also called theType II extreme value distribution):!

Fi (z ) = e − Ti z ,−θ(4)where Ti > 0 and θ > 1. We treat the distributions as independent acrosscountries. The (country-specific) parameter Ti governs the location of the
distribution. A bigger Ti implies that a high efficiency draw for any good j
is more likely. The parameter θ (which we treat as common to all countries) reflects the amount of variation within the distribution. A bigger θ
implies less variability. Specifically, Zi (efficiency) has geometric mean1#
! and its log has standard deviation π
6 Here γ = .577...
e r #!Ti(Euler’s constant) and π = 3.14.... (We use γ and π differently below.)13
The parameters Ti and θ enable us to depict very parsimoniously aworld of many countries that differ in the basic Ricardian senses of abso-

!# ""
#!

13. Kortum (1997) and Eaton and Kortum (1999) show how a process of innovation and diffusion can give rise to this distribution, with Ti reflecting a country’s
stock of original or imported ideas. Since the actual technique that would ever beused in any country represents the best discovered to date for producing each good,it makes sense to represent technology with an extreme value distribution. The distribution of the maximum of a set of draws can converge to one of only three distributions, the Weibull, the Gumbell, and the Fréchet (See Billingsley (1986)). Only
for the third does the distribution of prices inherit an extreme value distribution,
which is why we use it. As for our independence assumption, for our analysis here
an observationally equivalent joint distribution that embeds correlation across countries isρ⎧⎪ ⎡ N1/ ρ ⎤ ⎫⎪F z 1 ,..., z N = exp ⎨− ⎢Ti z i−θ ⎥ ⎬,⎦ ⎪⎭⎪⎩ ⎣ i =1

(

"

)

∑(

)

where 1
ρ > 0. Correlation decreases as ρ rises, with ρ = 1 implying independence. See, e.g., Small (1987). All that we do in this paper stands, with Ti reinterpreted as T1/i ρ and θ as θ / ρ .

254

Jonathan Eaton and Samuel Kortum

lute and comparative advantage across a continuum of goods. We will refer to the parameter Ti as country i’s state of technology. In a trade context
Ti reflects country i’s absolute advantage across this continuum.
The parameter θ regulates heterogeneity across goods in countries’ relative efficiencies. In a trade context θ governs comparative advantage
within this continuum. As we show more formally below, a lower value ofθ , generating more heterogeneity, means that comparative advantage exerts a stronger force for trade against the resistance imposed by the geographic barriers dni.14
2.2. Prices
What do these assumptions imply about the distribution of prices in different countries? Substituting the expression for Pni into the distribution ofefficiency (4) implies that country i presents country n with a distributionof prices Gni(p) = Pr[Pnip] = 1−Fi (cidni/p) or:!

(5)

Gni ( p) = 1 − e−[ Ti ( ci d ni )

−θ

] pθ

.

!

The lowest price for a good in country n will be less than p unless eachsource’s price is greater than p. Hence the distribution Gn(p) = Pr[Pn p]
for what country n actually buys is
Gn ( p) = 1 −N∏[1 − G ( p)].
ni

i =1

Inserting (5), the price distribution inherits the form of Gni(p):(6)

Gn ( p) = 1 − e−Φ n pθ,

where the parameter Φ n of country n’s price distribution isN(7)Φ n = ∑ Ti (ci d ni ) .
−θ

i =1

The price parameter Φ n is critical to what follows. It summarizes how!

14. Our results translate nicely into the two-country world of Dornbusch, Fischer,and Samuelson(1997). They represent technology by a function A(x), where x is
the fraction of goods for which the ratio of home (country 1) to foreign (country 2)
efficiency is at least A. Using a result on the distribution of the ratio of independent Type II extreme value random variables, our model delivers A(x) = (T1/T2)1 / θ((1 − x)/x)1 / θ . It shifts up if the foreign state of technology T1 rises relative tohome’s T2.

255

Technology, Geography, and Trade!

states of technology around the world， input costs around the world, andgeographic barriers govern prices in each country n. International tradeenlarges each country’s effective state of technology with technology available from other countries, discounted by input costs and geographic barriers. At one extreme, in a zero-gravity world with no geographic barriers(dni = 1 for all n and i), Φ is the same everywhere and the law of one
price holds for each good. At the other extreme of autarky, with prohibitive geographic barriers (dni → ∞ for n ≠ i), Φ n reduces to Tn cn!!, country n’s own state of technology downweighted by its input cost.
We exploit three useful properties of the price distributions:(a) The probability that country i provides a good at the lowest price incountry n is simply"

T (c d )π ni = i i ni
Φn

(8)

−θ

,

i’s contribution to country n’s price parameter.15 Since there are a continuum of goods, this probability is also the fraction of goods that country n buys from country i.
(b) The price of a good that country n actually buys from any country i
also has the distribution Gn(p).16 Thus, for goods that are purchased,conditioning on the source has no bearing on the good’s price. A sourcewith a higher state of technology, lower input cost, or lower barriers exploits its advantage by selling a wider range of goods, exactly to thepoint at which the distribution of prices for what it sells in n is the same
as n’s overall price distribution.
(c) The exact price index for the CES objective function (3), assumingσ < 1 + θ , ispn = γ Φ n−1/θ .

(9)⎡ ⎛ θ + 1− σ ⎞ ⎤Here, γ = ⎢Γ ⎜
⎟⎥
⎠⎦
θ
⎣ ⎝

1/(1−σ ),15. We obtain this probability by calculating

[

]

[

]

πni = Pr Pni ( j ) ≤ min{ Pns ( j ); s ≠ i} = ∫ ∏ 1 − Gns ( p) dGni ( p).
∞

0

s ≠i

16. We obtain this result by showing thatGn ( p) =1
π ni∫ ∏ [1 − G (q )]dG (q ).
p

0

ns

s ≠i

ni

256

Jonathan Eaton and Samuel Kortum

where Г is the Gamma function.17 This expression for the price index
shows how geographic barriers, by generating different values of the priceparameter in different countries, lead to deviations from purchasing power
parity.
2.3. Trade Flows and Gravity
To link the model to data on trade shares we exploit an immediate corollary of Property (b), that country n’s average expenditure per good does
not vary by source. Hence the fraction of goods that country n buys fromcountry i, π ni, from Property (a), is also the fraction of its expenditure on
goods from country i:
X ni Ti (ci d v )
=
Xn
Φn

(10)

Ti (ci d ni )−θk =1 knk−θ=∑ T (c d )
N

k

−θ

,

where Xn, is country n’s total spending, of which Xni is spent (c.i.f.) on
goods from i.18 Before proceeding with our own analysis, we discuss how
expression (10) relates to the existing literature on bilateral trade.
Note that expression (10) already bears semblance to the standard gravity equation in that bilateral trade is related to the importer’s total expenditure and to geographic barriers. Some manipulation brings it even closer toa gravity expression. Note that the exporter’s total sales Qi are simply
N

Qi =

N

d mi−θ X v∑ X = Tc ∑ Φ
mi

m=1

−θ
i i

m=1

.

m

17. The moment generating function for x = −lnp is E (e tx) = Φ t / θ Г (1−t/ θ ).
(See, e.g., Johnson and Kotz (1970)). Hence E [p −t]−1/t = Г (1 − t/ θ )−1/tΦ −t/θ . The
result follows by replacing t with σ − 1. While our framework allows for the possibility of inelastic demand (σ1), we must restrict σ < 1 +θ in order to have awell defined price index. As long as this restriction is satisfied, the parameter σ
can be ignored, since it appears only in the constant term (common across countries) of the price index.
18. Our model of trade bears resemblance to discrete-choice models of market
share, popular in industrial organization (e.g., McFadden (1974), Anderson, dePalma, and Thisse (1992), and Berry (1994)): our trade model has a discrete
number of countries whereas their consumer demand model has a discrete numberof differentiated goods; in our model a good’s efficiency of production in different countries is distributed multivariate extreme value whereas in their’s a consumer’s preferences for different goods is distributed multivariate extreme value;in our model each good is purchased (by a given importing country) from only
one exporting country whereas in their model each consumer purchases only one
good; we assume a continuum of goods whereas they assume a continuum of
consumers. A distinction is that we can derive the extreme value distribution fromdeeper assumptions about the process of innovation.

!

"

#

$

!

257

Technology, Geography, and Trade

Solving for Tici!!, and substituting it into (10), incorporating (9), we get(11)⎛ d ni ⎞⎜ ⎟⎝ pn ⎠

X ni =∑−θXn⎛ d mi ⎞m=1 ⎜ p ⎟
⎝ m⎠
N

Qi .

−θ

Xm

Here, as in the standard gravity equation, both the exporter’s total sales Qi
and, given the denominator, the importer’s total purchases Xn enter withunit elasticity. Note that the geographic barrier dmi between i and any importer m is deflated by the importer’s price level pm: Stiffer competition inmarket m reduces pm, reducing i’s access in the same way as a higher geographic barrier. We can thus think of the term (dmi /pm)−θXm as the market
size of destination m as perceived by country i. The denominator of theright-hand side of (11), then, is the total world market from country i’s
perspective. The share of country n in country i’s total sales just equals
n’s share of i’s effective world market.
Other justifications for a gravity equation have rested on the traditional
Armington and monopolistic competition models. Under the Armington assumption goods produced by different sources are inherently imperfect
substitutes by virtue of their provenance. Under monopolistic competition
each country chooses to specialize in a distinct set of goods. The more
substitutable are goods from different countries, the higher is the sensitivityof trade to production costs and geographic barriers. In contrast, in ourmodel the sensitivity of trade to costs and geographic barriers depends on
the technological parameter θ (reflecting the heterogeneity of goods in
19. The expressions for bilateral trade shares delivered by the Armington andmonopolistic competition models make the connections among these approaches
explicit. For the Armington case define ai as the weight on goods from country i in
CES preferences. Country i’s share in country n’s expenditure is then
X ni
=
Xn

aiσ −1 (ci d ni )− (σ −1)( )∑ a (c d )N

σ −1
k =1 kk− σ −1.

nk

In the case of monopolistic competition with CES preferences define mi as thenumber of goods produced by country i. Country i’s share in country n’s expenditure is then
− (σ −1)mi (ci d ni )
X ni
=
.
N
− (σ −1)Xn
mk (ck d nk )

∑

k =1

Returning to equation (10), the exporter’s state of technology parameter Ti in ourmodel replaces its preference weight ai"!1 (in Armington) or its number of goods
mi (under monopolistic competition). In our model the heterogeneity of technology
parameter θ replaces the preference parameter σ − 1 in these alternatives. (Thestandard assumption in these other models is that all goods are produced with thesame efficiency, so that ci reflects both the cost of inputs and the f.o.b. price ofgoods.)

258

Jonathan Eaton and Samuel Kortum

production) rather than the preference parameter σ (reflecting the heterogeneity of goods in consumption). Trade shares respond to costs and geographic barriers at the extensive margin: As a source becomes more expensive or remote it exports a narrower range of goods. In contrast, in models
that invoke Armington or (with some caveats) monopolistic competition,
adjustment is at the intensive margin: Higher costs or geographic barriers
leave the set of goods that are traded unaffected, but less is spent on each
imported good.19
3. Trade, Geography, and Prices: A First Look
Our model implies a connection between two important economic variables that have been analyzed extensively, but only in isolation: tradeflows and price differences. To establish this link we divide (10) by theanalogous expression for the share of country i producers at home, substituting in (9), to get
−θ

(12)

⎛ pd ⎞
X ni / X nΦ= i d ni−θ = ⎜ i ni ⎟ .
X ii / X iΦn⎝ pn ⎠We refer to the left-hand-side variable, country i’s share in country n relative to i’s share at home, as country i’s normalized import share in country
n. The triangle inequality implies that the normalized share never exceeds
one.20As overall prices in market n fall relative to prices in market i (as reflected in higher pi /pn) or as n becomes more isolated from i (as reflected
in a higher dni), i’s normalized share in n declines. As the force of comparative advantage weakens (reflected by a higher θ ), normalized importshares become more elastic with respect to the average relative price andto geographic barriers. A higher value of θ means relative efficiencies are
more similar across goods. Hence there are fewer efficiency outliers that
overcome differences in average prices or geographic barriers.21
The relationship between normalized trade share and prices in equation(12) is a structural one whose slope provides insight into the value of ourcomparative advantage parameter θ . Before using this relationship to estimate θ we first exploit it to assess the role played by geographic barriers
20. Since a purchaser in country n can always buy all her goods in i at a priceindex pidni, pn cannot be higher.
21. To obtain further intuition into expression (12) recall that the prices of goods
actually sold in a country have the same distribution regardless of where they comefrom. Hence the price index of producers in country i selling at home is pi. The
subset of i producers who also sell in n have a price index in country n of pn. (Thetriangle inequality ensures that anyone in i able to sell in n is also able to sell ini.) But to get into country n, country i producers have to overcome the geographic
barrier dni. Hence, the price index at home of these exporters is pn /dni. Of the set of
producers able to compete in a market with price index pi, the fraction who would
survive in a market with price index pn/dni < pi, is (pidni /pn )−θ .

259

Technology, Geography, and Tradein trade.
We measure normalized import shares, the left-hand side of equation(12), with data on bilateral trade in manufactures among 19 OECD countries in 1990, giving us 342 informative observations (in which n and i aredifferent).22 Normalized import shares never exceed 0.2, far below the levelof one that would hold in a zero-gravity world with all dni = 1. Furthermore, they vary substantially across country-pairs, ranging over four ordersof magnitude.

Figure 1. Trade and Geography

An obvious, but crude, proxy for dni in equation (12) is distance. Figure
1 graphs normalized import share against distance between the corresponding country-pair (on logarithmic scales). The relationship is not perfect,and shouldn’t be. Imperfections in our proxy for geographic barriers aside,
we are ignoring the price indices that appear in equation (12). Nevertheless,the resistance that geography imposes on trade comes through clearly.
Since we have no independent information on the extent to which geographic barriers rise with distance, the relationship in Figure 1 confounds
the impact of comparative advantage (θ ) and geographic barriers (dni) on
trade flows. The strong inverse correlation could result from geographic
barriers that rise rapidly with distance, overcoming a strong force of com22. When i = n the equation degenerates to a vacuous identity. We use country
n’s manufactured imports from country i to obtain Xni and country n’s absorptionof manufactures from all countries of the world to obtain Xn, defined as gross
manufacturing production less exports plus imports of manufactures. The Appendix
describes our sources of data.

260

Jonathan Eaton and Samuel Kortum

parative advantage (a low θ ). Alternatively, comparative advantage might
exert only a very weak force (a high θ ), so that even a mild increase ingeographic barriers could cause trade to drop off rapidly with distance.
To identify θ we turn to price data, which we use to measure the term
pidni/pn on the right-hand side of equation (12). While we used standard
data to calculate normalized trade shares, our measure of relative prices,and particularly geographic barriers, requires more explanation. We workwith retail prices in each of our 19 countries of 50 manufactured products.23 We interpret these data as a sample of the prices pi(j) of individualgoods in our model. We use them to calculate, for each country-pair n and
i and each good j, the logarithm of the relative price, rni(j)=lnpn(j)−lnpi(j).
We calculate the logarithm of pi /pn, as the mean across j of −rni(j). To get
at geographic barriers dni we use our model’s prediction that, for any commodity j, rni(j) is bounded above by lndni with this bound attained forgoods that n imports from i. (For goods that n does not buy from i, rni(j)is below lndni.) Every country in our sample does in fact import fromevery other. We take the (second) highest value of rni across commodities
to obtain a measure of lndni.24 In summary, we measure ln(pidni /pn) by theterm Dni defined as

(13)

Dni =

{

}

max 2 j rni ( j )∑ [r ( j )] / 50
50

j =1

,

ni

(where max2 means second highest).25
The price measure expDni reflects what the price index in destination nwould be for a buyer there who insisted on purchasing everything from
23. The United Nations International Comparison Program 1990 benchmark
study gives, for over 100 products, the price in each of our countries relative to theprice in the United States. We choose 50 products that are most closely linked to
manufacturing outputs.
24. We used the second highest (rather than highest) value of rni(j) to mitigate
the effect of possible measurement error in the prices for particular commodities.
Indeed, the second order statistic correlates more with the trade data than the first,
and more than higher order statistics. Office and computing equipment is often an
outlier. An alternative strategy is just to drop this sector from the calculation anduse the highest value of the remaining rni(j) to measure lndni. The correlation is almost identical to the one in the scatter. While direct measures of the cost of transporting goods exist (see, e.g. Hummels (2002), they fail to capture all the costs involved in buying things from far away, such as delay and the difficulty of negotiation across space.
25. Our prices are what domestic consumers pay (including taxes and retailmarkups) rather than what domestic producers receive. But to the extent that factors specific to individual countries but common to all goods drive the deviation
between consumer and producer prices, the resulting errors in this expression cancel.

261

Technology, Geography, and Trade
Table 2. Price Measure Statistics
Foreign Sources

Foreign Destinations

Country

Minimum

Maximum

Minimum

Maximum

Australia(AL)Austria (AS)Belgium (BE)Canada (CA)Denmark(DK)
Finland(FI)France(FR)Germany(GE)Greece(GR)Italy(IT)Japan(JP)Netherlands(NE)New Zealand(NZ)
Norway(NO)Portugal(PO)Spain(SP)Sweden(SW)United Kingdom(UK)
United States(US)NE (1.44)
SW (1.39)
GE (1.25)
US (1.58)
FI (1.36)
SW (1.38)
GE (1.33)
BE (1.35)
SP (1.61)
FR (1.45)
BE (1.62)
GE (1.30)
CA (1.60)
FI (1.45)
BE (1.49)
BE (1.39)
NO (1.36)
NE (1.46)
FR (1.57)

PO
NZ
JP
NZ
PO
PO
NZ
NZ
NZ
NZ
PO
NZ
PO
JP
JP
JP
US
JP
JP

BE (1.41)
UK (1.47)
GE (1.35)
AS (1.57)
NE (1.48)
DK (1.36)
BE (1.40)
BE (1.25)
NE (1.48)
AS (1.46)
AL (1.72)
DK (1.39)
AL (1.64)
SW (1.36)
SP (1.59)
NO (1.51)
FI (1.38)
FR (1.52)
CA (1.58)

US (2.03)
JP (1.97)
SW (1.77)
US (2.14)
US (2.41)
US (2.87)
JP (2.40)
US (2.22)
US (2.27)
JP (2.10)
US (3.08)
NZ (2.01)
GR (2.71)
US (2.31)
JP (3.25)
JP (3.05)
US (2.01)
NZ (2.04)
SW (2.70)(2.25)(2.16)(2.02)(2.57)(2.21)(2.61)(2.42)(2.28)(2.71)(2.19)(3.25)(2.17)(2.08)(2.84)(2.56)(2.47)(2.70)(2.37)(3.08)

Note: The price msasure Dni is defined in Equation(13). For destination country n, the minimum Foreign Source is mini !
"n expDni. For source country i, the minimum Foreign Destination is minn !
"i expDni.

source i, relative to the actual price index in n (the price index for a buyerpurchasing each good from the cheapest source). Table 2 provides someorder statistics of our price measure. For each country we report, from its
perspective as an importer, the foreign source for which the measure islowest and highest. We then report, from that country’s perspective as anexporter, the foreign destination for which the measure is lowest and highest. (In parentheses we report the associated values of expDni.) France, forexample, finds Germany its cheapest foreign source and New Zealand its
most expensive. A French resident buying all commodities from Germany
would face a 33 per cent higher price index and from New Zealand a 142
per cent higher price index. A resident abroad who insisted on buying everything from France would face the smallest penalty (40 per cent) if shewere in Belgium and the largest (140 per cent) if she were in Japan. Note
how geography comes out in the price data as well as in the trade data:
The cheapest foreign source is usually nearby and the most expensive far
away. Note also, from column 4, that large countries would typically suffer
the most if required to buy everything from some given foreign source.
Figure 2 graphs our measure of normalized import share (in logarithms)
against Dni. Observe that, while the scatter is fat, there is an obvious negative relationship, as the theory predicts. The correlation is −0.40. The rela-

262

Jonathan Eaton and Samuel Kortum

tionship in Figure 2 thus confirms the connection between trade and prices
predicted by our model.
Moreover, the slope of the relationship provides a handle on the valueof the comparative advantage parameter θ . Since our theory implies a zerointercept, a simple method-of-moments estimator for θ is the mean of theleft-hand-side variable over the mean of the right-hand-side variable. The
implied θ is 8.28. Other appropriate estimation procedures yield very similar magnitudes.26 Hence we use this value for θ in exploring counterfactuals. This value of θ implies a standard deviation in efficiency (for a given
state of technology T ) of 15 percent. In section 5 we pursue two alterna-

Figure 2. Trade and Prices
26. A linear regression through the scatter in Figure 2 yields a slope of −4.57
with an intercept of −2.17 (with respective standard errors 0.6 and 0.3). The factthat OLS yields a negative intercept is highly symptomatic of errors in variables,
which also biases the OLS estimate of θ toward zero. (The reasoning is that inFriedman’s 1957 critique of the Keynesian consumption function.) There are manyreasons to think that there is error in our measure of pidni /pn. Imposing a zero intercept, OLS yields a slope of −8.03, similar to our method-of-moments estimate.
(Instrumental variables provide another way to tackle errors in variables, an approach we pursue in section 5, after we complete the general equilibrium specification of the model.) We also examined how the three components lnpi, lnpn, andlndni, contributed individually to explaining trade shares. Entering these variables
separately into OLS regressions yielded the respective coefficients −4.9, 5.5, −4.6
(with a constant) and −9.0, 6.4, −6.8 (without a constant). All have the predicted
signs. For 42 of our 50 goods similar price data are available from the 1985
Benchmark Study. Relating 1985 trade data to these price data yields very similar
estimates of θ .

263

Technology, Geography, and Tradetive strategies for estimating θ , but we first complete the full descriptionof the model.
4. Equilibrium Input Costs
Our exposition so far has highlighted how trade flows relate to geography and to prices, taking input costs ci as given. In any counterfactual experiment, however, adjustment of input costs to a new equilibrium is crucial.
To close the model we decompose the input bundle into labor and intermediates. We then turn to the determination of prices of intermediates,
given wages. Finally we model how wages are determined. Having completed the full model, we illustrate it with two special cases that yield simple closed-form solutions.
4.1. Production!

We assume that production combines labor and intermediate inputs, withlabor having a constant share .27 Intermediates comprise the full set ofgoods combined according to the CES aggregator (3). The overall price index in country i, pi, given by equation (9), becomes the appropriate index
of intermediate goods prices there. The cost of an input bundle in country iis thus(14)

ci = wiβ pi1− β ,where wi is the wage in country i. Because intermediates are used in production, ci depends on prices in country i, and hence on Φ i. But throughequation (7), the price parameter Φ i depends on input costs everywhere.
Before turning to the determination of price levels around the world, we
first note how expression (14), in combination with (9), (7), and (10), delivers an expression relating the real wage (wi /pi) to the state of technology
parameter Ti and share of purchases from home π ii:

(15)

⎛T ⎞
wi
= γ −1/ β ⎜ i ⎟pi⎝ π ii ⎠1/ βθ

.

27. We ignore capital as an input to production and as a source of income, although our intermediate inputs play a similar role in the production function. Baxter (1992) shows how a model in which capital and labor serve as factors of production delivers Ricardian implications if the interest rate is common across countries.

264

Jonathan Eaton and Samuel Kortum

Since in autarky π ii = 1, we can immediately infer the gains from tradefrom the share of imports in total purchases. Note that, given import share,
trade gains are greater the smaller θ (more heterogeneity in efficiency)and (larger share of intermediates).

!

4.2. Price Levels
To see how price levels are mutually determined, substitute (14) into (7),applying (9), to obtain the system of equations:

(16)

−θ ⎤
⎡N
pn = γ ⎢ Ti d ni wiβ pi1− β ⎥⎦⎣ i =1

∑ (

)

−1/θ

.

The solution, which in general must be computed numerically, gives priceindices as functions of the parameters of the model and wages.
Expanding equation (10) using (14) we can also get expressions for
trade shares as functions of wages and parameters of the model:
−θ

(17)

⎛ γ d w β p1− β ⎞X ni= π ni = Ti ⎜ ni i i ⎟ ,
Xn
pn
⎝
⎠

with the pi’s obtained from expression (16) above.
We now impose conditions for labor market equilibrium to determine
wages themselves.
4.3. Labor-Market Equilibrium
Up to this point we have not had to take a stand about whether ourmodel applies to the entire economy or to only one sector. Our empirical
implementation is to production and trade in manufactures. We now show
how manufacturing fits into the larger economy.
Manufacturing labor income in country i is labor’s share of country i’s
manufacturing exports around the world, including its sales at home. ThusN

(18)

wi Li = β∑π X ,ninn =1

where Li is manufacturing workers and Xn is total spending on manufactures.
We denote aggregate final expenditures as Yn with α the fraction spent
on manufactures. Total manufacturing expenditures are then265

Technology, Geography, and Trade

Xn =

(19)

1− β
β

wn Ln + αYn ,where the first term captures demand for manufactures as intermediates by
the manufacturing sector itself. Final expenditure Yn consists of valueadded in manufacturing YnM = wnLn plus income generated in nonmanufacturing YnO . We assume that (at least some of) nonmanufacturing output canbe traded costlessly, and use it as our numeraire.28
To close the model as simply as possible we consider two polar casesthat should straddle any more detailed specification of nonmanufacturing.
In one case labor is mobile. Workers can move freely between manufacturing and nonmanufacturing. The wage wn is given by productivity in nonmanufacturing and total income Yn is exogenous. Equations (18) and (19)combine to giveN

(20)

wi Li =∑ π [(1 − β )w L + αβY ],
ni

n

n

n

n =1

determining manufacturing employment Li.
In the other case labor is immobile. The number of manufacturing workers in each country is fixed at Ln. Nonmanufacturing income YnO is exogenous. Equations (18) and (19) combine to formN

(21)

wi Li =∑ π [(1 − β + αβ )w L + αβY ],
ni

n

n

0
n

n =1

determining manufacturing wages wi.
In the mobile labor case we can use equations (16) and (17) to solve forprices and trade shares given exogenous wages before using (20) to calculate manufacturing employment. The immobile labor case is trickier in that
we need to solve the three equations (16), (17), and (21) simultaneously
for prices, trade shares, and manufacturing wages.
In the case of mobile labor, our model has implications not only for
intra-industry trade within manufacturing, but for specialization in manufacturing. The technology parameter Ti then reflects not only absolute advantage within manufactures, but comparative advantage in manufacturing
relative to non-manufacturing. In the immobile case labor specialization isexogenous, and Ti is reflected in manufacturing wages. In either case θgoverns specialization within manufacturing.
28. Assuming that nonmanufactures are costlessly traded is not totally innocuous,as pointed out by Davis (1998).

266

Jonathan Eaton and Samuel Kortum

4.4. Zero-Gravity and Autarky
While, in general, the rich interaction among prices in different countries
makes any analytic solution unattainable, two special cases yield simple
closed-form solutions. We consider in turn the extremes in which geographic barriers disappear (zero gravity), meaning that all dni = 1, andgeographic barriers are prohibitive (autarky), meaning that dni → ∞ forn ≠ i.
With no geographic barriers the law of one price holds. In either themobile or immobile labor cases the condition for labor market equilibrium
reduces to!

wi ⎛ Ti / Li ⎞=⎜⎟wN ⎝ TN / LN ⎠

(22)

"

1/ (1+θβ ).

Since prices are the same everywhere this expression is also the relative
real wage.
When labor is mobile this expression determines the relative amounts of1!"!.
manufacturing labor in each country, which are proportional to Ti /wi
The country with a higher state of technology relative to its wage will specialize more in manufacturing. When labor is immobile the expression
gives relative wages, which depend on the state of technology in per
worker terms. Given Ti, as Li increases workers must move into productionof goods in which the country is less productive, driving down the wage.
Suppose manufacturing is the only activity so that α = 1 and Yi = wiLi.
The wage must adjust to maintain trade balance. Real GDP per worker(our welfare measure) is then Wi = (Yi /Li)/p = wi /p. Manipulating (22) and
(16),

(23)

Wi = γ −1/ β Ti (1/ 1+θβ )⎤⎡ N 1/(1+θβ )( Lk / Li )θβ /(1+θβ ) ⎥⎢ Tk⎦⎣ k =1∑1/θβ,which increases with technology Tk anywhere. An increase at home confers
an extra benefit, however, because it raises the home wage relative towages abroad. How much country i benefits from an increase in Tk depends on k’s labor force relative to i’s. If the labor force in the source
country k is small, wk rises more, diminishing the benefits to others of its

267

Technology, Geography, and Trade

more advanced state of technology.29
We can solve for a country’s welfare in autarky by solving (23) for a
one-country world or by referring back to (15) setting π ii = 1. Doing so,
we get(24)

Wi = γ −1/ β Ti 1/θβ .

Note, of course, that there are gains from trade for everyone, as can beverified by observing that we derived (24) by removing positive terms
from (23).30
While these results illustrate how our model works, and provide insight
into its implications, the raw data we presented in Section 3 show how far
the actual world is from either zero-gravity or autarky. For empirical purposes we need to grapple with the messier world in between, to which we
now return.

5. Estimating the Trade Equation
Equations (16) and (17), along with either (20) or (21), comprise the fullgeneral equilibrium. These equations determine price levels, trade shares,
and either manufacturing labor supplies (in the mobile labor case) or
manufacturing wages (in the immobile case). In section 6 we explore howthese endogenous magnitudes respond to various counterfactual experiments. In this section we present the estimation that yields the parametervalues used to examine these counterfactuals.

29. If we plug these results for zero gravity into our bilateral trade equation (10),we obtain a simple gravity equation with no “distance” term:
X ni =

YnYi
βY

W

.

Bilateral trade equals the product of the trade partners’ incomes, Yi and Yn, relative
to world income, Y W, all scaled up by the ratio of gross production to value added.
Note that this relationship masks the underlying structural parameters, Ti and θ .
30. Note also that trade has an equalizing effect in that the elasticity of real GDP
with respect to one’s own state of technology Ti is greater when geographic barriers are prohibitive than when they are absent. The reason is that, with trade, thecounty that experiences a gain in technology spreads its production across a wider
range of goods, allowing foreigners to specialize in a narrower set in which they
are more efficient. The relative efficiency gain is consequently dampened. Under
autarky, of course, every country produces the full range of goods.

268

Jonathan Eaton and Samuel Kortum

5.1. Estimates with Source Effects
Equation (17), like the standard gravity equation, relates bilateral tradevolumes to characteristics of the trading partners and the geography between them. Estimating it provides a way to learn about states of technology Ti and geographic barriers dni.
Normalizing (17) by the importer’s home sales delivers
X ni Ti ⎛ wi ⎞= ⎜ ⎟X nn Tn ⎝ wn ⎠

(25)

−θβ

⎛ pi ⎞⎜ ⎟⎝ pn ⎠−θ (1− β )d ni−θ .

We can use equation (17) as it applies to home sales, for both country iand country n, to obtainpiw ⎛T⎞= i ⎜ i⎟pn wn ⎝ Tn ⎠−1/θβ

⎛ X i / X ii ⎞⎜⎟⎝ X n / X nn ⎠

−1/θβ

.

Plugging this expression for the relative price of intermediates into (25)and rearranging gives, in logarithms:

(26)

ln

X ni′
w
1 T
= −θ ln d ni + ln i − θ ln i ,
X nn
T
w
′
β
n
n

!!

where lnXni! ≡ lnXni − [(1 − )/ ] ln(Xi /Xii). By defining
Si ≡

(27)

1
β

ln Ti − θ ln wi ,this equation simplifies to:

(28)

ln

X ni′
= −θ ln d ni + Si − Sn .
X nn′

We can think of Si as a measure of country i’s “competitiveness,” its stateof technology adjusted for its labor costs. Equation (28) forms the basis of

269Technology, Geography, and Trade

our estimation.31
We calculate the left-hand side of (28) from the same data on bilateral
trade among 19 countries that we use in Section 3, setting β = .21, the average labor share in gross manufacturing production in our sample. As in
Section 3, this equation is vacuous as it applies to n = i, leaving us 342
informative observations. Since prices of intermediates reflect imports fromall sources, Xn includes imports from all countries in the world. In other respects this bilateral trade equation lets us ignore the rest of the world.
As for the right-hand side of (28), we capture the Si as the coefficientson source-country dummies. We now turn to our handling of the dni’s.
We use proxies for geographic barriers suggested by the gravity literature.32 In particular, we relate the impediments in moving goods from i to
n to proximity, language, and treaties. We have, for all i ≠ nlndni = dk + b+ l + eh + mn + δ ni,(29)

where the dummy variable associated with each effect has been suppressed
for notational simplicity. Here dk (k = 1,...,6) is the effect of the distance
between n and i lying in the kth interval, b is the effect of n and i sharing
a border, l is the effect of n and i sharing a language, eh (h = 1, 2) is theeffect of n and i both belonging to trading area h, and mn (n = 1,...,19) isan overall destination effect. The error term δ ni captures geographic barriers arising from all other factors. The six distance intervals (in miles) are:[0,375); [375,750); [750,1500); [1500,3000); [3000,6000); and [6000,maximum]. The two trading areas are the European Community (EC) and theEuropean Freer-Trade Area (EFTA).33 We assume that the error δ ni is orthogonal to the other regressors (source country dummies and the proxies
for geographic barriers listed above).
31. Iftion:!= 1 and S = lnY , equation (28) is implied by the standard gravity equa-"

X ni = κd ni−θ YY
i n,

where is a constant. But from equation (11) our theory implies that S should reflect a country’s production relative to the total world market from its perspective:
Given the geographic barrier to a particular destination, an exporter will sell more
there when it is more remote from third markets.
32. An alternative strategy would have been to use the maximum price ratios introduced in Section 3 to measure dni directly. The problem is that country-specificerrors in this measure are no longer cancelled out by price level differences, as
they are in (13).
33. An advantage of our formulation of distance effects is that it imposes little
structure on how geographic barriers vary with distance. We explored the implications of the more standard specification of geographic barriers as a quadratic function of distance. There were no differences worth reporting.

270

Jonathan Eaton and Samuel Kortum

To capture potential reciprocity in geographic barriers, we assume thatthe error term δ ni consists of two components:

δ ni = δ 2ni + δ 1ni .
The country-pair specific component δ ni2 (with variance σ 22) affects twoway trade, so that δ ni2 = δ in2, while δ in1 (with variance σ 12) affects one-way
trade. This error structure implies that the variance-covariance matrix ofδ has diagonal elements E ( δ niδ ni ) = σ 12 + σ 22 and certain nonzero offdiagonal elements E (δ ni δ ni) = σ 22.
Imposing this specification of geographic barriers, equation (28) becomes

(30)

ln

X ni′
= Si − Sn − θmn − θd k − θb − θl − θeh + θδ 2ni + θδ 1ni ,X nn′which we estimate by generalized least squares (GLS).34
Table 3 reports the results. The estimates of the Si indicate that Japan is
the most competitive country in 1990, closely followed by the UnitedStates. Belgium and Greece are the least competitive. As for geographic
barriers, increased distance substantially inhibits trade, with its impact
somewhat attenuated by a shared language, while borders, the EC, andEFTA do not play a major role. The United States, Japan, and Belgium are
the most open countries while Greece is least open.35 Note that about aquarter of the total residual variance is reciprocal.

34. To obtain the parameters of the variance-covariance matrix for GLS estimation we first estimate the equation by OLS to obtain a set of residuals ε̂ ni ε̂ ni. We
2then estimate θ 2 22 by averaging ε̂ niε̂ in and θ 2 σ 22 + σ 12 by averaging (εˆ ni ) .
35. Our finding about the openness of Japan may seem surprising given its low
import share reported in Table 1. Analyses that ignore geography (for example, thefirst part of Harrigan (1996)), find Japan closed. Once geography is taken into account, however, as (implicitly) later in Harrigan, it no longer appears particularly
closed. (Eaton and Tamura (1994) find Japan relatively more open to U.S. exports
than European countries as a group.) As equation (10) reveals, our concept of acountry’s openness controls for both its location and its price level (as reflected byits price parameter Φ ). Not only is Japan remote, its competitiveness as a manufacturing supplier implies a high Φ , making it a naturally tough market for foreigners to compete in. At the other extreme, our finding that Greece is quite closed(even though it has a high import share) controls for both its proximity to foreign
manufacturing sources and its own inability to export much anywhere else.

!

(

)

271

Technology, Geography, and Trade

Table 3. Bilateral Trade Equation
Variable

est.

s.e.

−3.10
−3.66
−4.03
−4.22
−6.06
−6.56
0.30
0.51
0.04
0.54

(0.16)(0.11)(0.10)(0.16)(0.09)(0.10)(0.14)(0.15)(0.13)(0.19)

Distance [0, 375)
Distance [375, 750)
Distance [750, 1500)
Distance [1500, 3000)
Distance [3000, 6000)
Distance [6000, maximum]
Shared border
Shared language
European CommunityEFTA− θ d1− θ d2− θ d3− θ d4− θ d5− θ d6
−θ b
−θ l
−θ e1
− θ e2

Country

Source-Country

Destination-Country

est.
0.19
−1.16
−3.34
0.41
−1.75
−0.52
1.28
2.35
−2.81
1.78
4.20
−2.19
−1.20
−1.35
−1.57
0.30
0.01
1.37
3.98

est.
0.24
−1.68
1.12
0.69
−0.51
−1.33
0.22
1.00
−2.36
0.07
1.59
1.00
0.07
−1.00
−1.21
−1.16
−0.02
0.81
2.46

Australia
Austria
Belgium
CanadaDenmark
FinlandFranceGermany
GreeceItaly
Japan
Netherlands
New Zealand
NorwayPortugal
Spain
SwedenUnited Kingdom
United States
Total Sum of Squares
Sum of squared residuals
Number of observations

S1
S2
S3
S4
S5
S6
S7
S8
S9
S 10
S 11
S 12
S 13
S 14
S 15
S 16
S 17
S 18
S 19
2937
71
342

s.e.
(0.15)−θ m1(0.12)−θ m2(0.11)−θ m3(0.14)−θ m4(0.12)−θ m5(0.12)−θ m6(0.11)−θ m7(0.12)−θ m8(0.12)−θ m9(0.11)−θ m10(0.13)−θ m11(0.11)−θ m12(0.15)−θ m13(0.12)−θ m14(0.12)−θ m15(0.12)−θ m16(0.12)−θ m17(0.12)−θ m18(0.14)−θ m19Error Variance:
2 2
Two-way( 2 )One-way( 2 12 )

!"
!"

s.e.
(0.27)(0.21)(0.19)(0.25)(0.19)(0.22)(0.19)(0.19)(0.20)(0.19)(0.22)(0.19)(0.27)(0.21)(0.21)(0.19)(0.22)(0.19)(0.25)
0.05
0.16

Note: Estimated by generalized least squares using 1990 data. The specification is
given in equation (30) of the paper. The parameters are normalized so that19
19
i !1 Si = 0 and
i !1 mn = 0. Standard errors are in parentheses.

!

!

On their own, the competitiveness measures and the coefficients on theproxies for geographic barriers reflect a combination of underlying factors.
Below we use estimates of θ to extract from them the parameters that weneed for our counterfactuals. We now provide two alternative estimates ofθ to the one from Section 3.
5.2. Estimates Using Wage Data
One approach brings data on wages to bear in estimating (26). The coefficient on relative wages in the bilateral wage equation provides the first272

Jonathan Eaton and Samuel Kortum

alternative estimate of θ . This approach no longer allows us to absorb thetechnology parameter Ti into a source country effect. Instead, based on
Kortum (1997) and Eaton and Kortum (1996), we relate technology to national stocks of R&D and to human capital as measured by years ofschooling. Table 4 presents the data. (Again, see the Appendix for a description.) Using our estimates of Si from the previous section we estimate⎛ 1⎞
Si = α 0 + α R ln Ri − α H ⎜ ⎟ − θ ln wi + τ i ,⎝ Hi ⎠
where Ri is country i’s R&D stock, Hi is average years of schooling, andτ i the error. The wage wi is adjusted for education.
Table 4. Data for Alternative Parameters
Research

Years ofLabor Force

DensityCountry

Stock

Schooling(HK adjusted)(pop/area)

Australia
Austria
Belgium
CanadaDenmark
FinlandFranceGermany
GreeceItaly
Japan
Netherlands
New Zealand
NorwayPortugal
Spain
SwedenUnited Kingdom
United States(U.S.=1)
0.00870.00630.01510.02990.00510.00530.11080.16830.00050.04450.24920.02780.00100.00570.00070.00840.02060.14231.0000(years/person)
8.7
8.6
9.4
10.0
6.9
10.8
9.5
10.3
8.4
9.1
9.5
9.5
9.3
9.2
6.5
9.7
9.6
8.5
12.1

(U.S.=1)
0.054
0.024
0.029
0.094
0.017
0.019
0.181
0.225
0.025
0.159
0.544
0.043
0.010
0.015
0.026
0.100
0.031
0.186
1.000

(U.S.=1)
0.08
3.43
12.02
0.10
4.47
0.55
3.88
9.50
2.87
7.16
12.42
13.64
0.47
0.49
4.01
2.88
0.71
8.76
1.00

Note: Research stocks, in 1990, are from Coe and Helpman (1995). Average years ofschooling Hi, in 1985, are from Kyriacou (1991). Labor forces, in 1990, are from Summers
and Heston(1991).They are adjusted for human capital by multiplying the country i figure
by e 0.06Hi．
See the Appendix for complete definitions.

Labor-market equilibrium suggests that a country’s wage will increase
with its level of technology, introducing a positive correlation between lnw
and τ . As suggested by our model, we use the total workforce and population density as instruments: Given its technology Ti, a country with moreworkers has a lower wage. Population density proxies (inversely) for pro-

273

Technology, Geography, and Tradeductivity outside manufacturing. Table 5 reports the results.
Both the OLS and 2SLS estimates of θ are significant and of the correct sign, but lower than suggested by the trade-price relationship. As expected, accounting for the endogeneity of wages raises our estimate of θ ,from 2.86 to 3.60.
Table 5. Competitiveness Equation

Constant
Research stock, lnRi
Human capital, 1/Hi
Wage, lnwi
Total Sum of Squares
Sum of squared residuals
Number of observations

αR
−αH
−θ

Ordinary

Two-Stage

Least Squares

Least Squares

est.
3.75
1.04
−18.0
−2.84
80.3
18.5
19

s.e.
(1.89)(0.17)(20.6)(1.02)

est.
3.82
1.09
−22.7
−3.60
80.3
19.1
19

Note: Estimated using 1990 data. The dependent variable is the estimates
cuntry competitiveness shown in Table 3. Standard errors are in parentheses.

s.e.
(1.92)(0.18)(21.3)(1.21)! of sourcei

5.3. Estimates Using Price Data
The second alternative is to estimate the bilateral trade equation (28) using our measure of ln(pidni /pn), Dni, defined in expression (13), instead of
the geography terms in (29), along with source and destination effects. The
coefficient on Dni provides yet another estimate of θ . (The estimatedsource effects reflect the price level terms in Dni as well as technology andwages, making them harder to interpret.)
OLS estimation yields θ = 2.44 (with a standard error of 0.49). A potential objection is the errors-in-variables problem with our Dni measurediscussed in Section 3. We address this problem by using the observable
geography terms in (29) as instruments for Dni. Doing so we obtain a 2SLS
estimate of θ = 12.86 (with a standard error of 1.64). The increase inmagnitude supports the errors-in-variables interpretation.
5.4. States of Technology and Geographic Barriers
For each of our estimates of θ we derive estimates of the states of technology Ti and geographic barriers as follows:
Following equation (27), we strip the estimates of Si in Table 3 down to
Ti using data on wages (adjusted for education) and an estimate of θ . Table 6 shows the results. Note, for example, that, while our estimates of Si
imply that Japan is more “competitive” than the United States, we find that
her edge is the consequence of a lower wage rather than a higher state of274

Jonathan Eaton and Samuel Kortum

technology. At the other end, our low estimate of Belgium’s competitiveness derives in large part from the high wage there.
Table 6. States of Technology
Estimated

ImpliedCountry

Source-Country

States of Technology

Australia
Austria
Belgium
CanadaDenmark
FinlandFranceGermany
GreeceItaly
Japan
Netherlands
New Zealand
NorwayPortugal
Spain
SwedenUnited Kingdom
United States

Competitiveness
0.19
−1.16
−3.34
0.41
−1.75
−0.52
1.28
2.35
−2.81
1.78
4.20
−2.19
−1.20
−1.35
−1.57
0.30
0.01
1.37
3.98

θ =8.28
0.27
0.26
0.24
0.46
0.35
0.45
0.64
0.81
0.07
0.50
0.89
0.30
0.12
0.43
0.04
0.21
0.51
0.49
1.00

θ =3.60
0.36
0.30
0.22
0.47
0.32
0.41
0.60
0.75
0.14
0.57
0.97
0.28
0.22
0.37
0.13
0.33
0.47
0.53
1.00

θ 12.86
0.20
0.23
0.26
0.46
0.38
0.50
0.69
0.86
0.04
0.45
0.81
0.32
0.07
0.50
0.01
0.14
0.57
0.44
1.00

!

Note: The estimates of source-country competitiveness are the same shownin Table 3. Forˆan estimated parameter i, the implied state of technology is Ti =（e S i wi!）β . States of technology are normalized relative to the U.S. value.

Dividing the coefficients on geographic proxies in Table 3 by θ and exponentiating gives the percentage cost increase each imposes. Column twoof Table 7 reports the results. For θ = 8.28, a typical country in the closest distance category faces a 45 percent barrier relative to home sales, rising to 121 percent in the farthest distance category. Sharing a border reduces the barrier by 4 percent while sharing a language reduces it by 6
percent. It costs 25 percent less to export into the United States, the mostopen country, than to the average country. At the high end it costs 33 percent more to export to Greece than to the average country.36 Moving to al36. Wei (1996) obtains very similar results from a gravity model making theArmington assumption that each country produces a unique set of commodities. He
does not estimate the elasticity of substitution between goods from different countries, but picks a value of 10 as his base. As discussed, the Armington elasticity
plays a role like our parameter θ . Hummels (2002) relates data on actual freightcosts for goods imported by the United States and a small number of other countries to geographical variables. His finding of a 0.3 elasticity of cost with respect todistance is reflected, roughly, in our estimates here.

275

Technology, Geography, and Tradeternative values of θ affects the implied geographic barriers in the opposite direction. Even for our high value of θ , however, geographic barriersappear substantial.

Table 7. Geographic Barriers
Source of Barrier
Distance [0, 375)
Distance [375, 750)
Distance [750, 1500)
Distance [1500, 3000)
Distance [3000, 6000)
Distance [6000, maximum]
Shared border
Shared language
European Community
EFTA
Destination country:
Australia
Austria
Belgium
CanadaDenmark
FinlandFranceGermany
GreeceItaly
Japan
Netherlands
New Zealand
NorwayPortugal
Spain
SwedenUnited Kingdom
United States

Estimated
Geography
Parameter
−3.10
−3.66
−4.03
−4.22
−6.06
−6.56
0.30
0.51
0.04
0.54
0.24
−1.68
1.12
0.69
−0.51
−1.33
0.22
1.00
−2.36
0.07
1.59
1.00
0.07
−1.00
−1.21
−1.16
−0.02
0.81
2.46

ImpliedBarrier’s % Effect on Cost
θ =8.28
θ =3.60
θ =12.86
45.39
136.51
27.25
55.67
176.74
32.97
62.77
206.6536.85
66.44
222.7538.82
108.02439.0460.25
120.82518.43
66.54
−3.51
−7.89
−2.27
−5.99
−13.25
−3.90
−0.44
−1.02
−0.29
−6.28
−13.85
−4.09
−2.81
22.46
−12.65
−7.99
6.33
17.49
−2.61
−11.3932.93−0.86−17.43−11.42
−0.80
12.85
15.69
14.98
0.30
−9.36
−25.70−6.35
59.37−26.74−17.42
15.15
44.88
−5.90
−24.2792.45−1.97−35.62−24.33
−1.83
32.06
39.82
37.85
0.69
−20.23−49.49

−1.82
13.94
−8.34
−5.22
4.03
10.94
−1.69
−7.49
20.11
−0.56
−11.60
−7.51
−0.52
8.10
9.84
9.40
0.19
−6.13
−17.40Note: The estimated parameters governing geographic barriers are the same as those shownin Table 3. For an estimated parameter dˆ , the implied percentage effect on cost is 100
ˆ(e !d "!−1).

Our simple method-of-moments estimator of θ = 8.28 from Section 3lies very much in the middle of the range of estimates we obtain from ouralternative approaches, θ = 3.60 using wage data and θ = 12.86 using
price data. Hence, except where noted, we use it (and the consequent val-

276

Jonathan Eaton and Samuel Kortum

ues of Ti and dni) in the analysis that follows.37
6. Counterfactuals
The estimation presented in Section 5 provides parameter values that allow us to quantify the full model, enabling us to pursue an analysis ofcounterfactuals. Given that the model is highly stylized (we have, for example, suppressed heterogeneity in geographic barriers across manufacturing goods), these counterfactuals should not be seen as definitive policy
analysis. But regardless of how indicative they are of actual magnitudes,
they do provide insight into the workings of the model.
To complete the parameterization we calculate α = 0.13, the average demand for final manufactures as a fraction of GDP.38 Table 8 summarizes
the structural parameters of the model, their definitions, the values we assign to them, and where we got these numbers.

Table 8. Summary of Parameters
Parameter

Definition

Value

Sourceθcomprative advantage

8.28(3.60,12.86)

Section 3(Section 5.2, Section5.3)

αmanufactuing share

0.13

production and trade dataβlabor share in costs

0.21

wage costs in gross output

Tistates of technology

Table 6source effects stripped of wages

dni

geographic barriers

Table 7

geographic proxies adjusted for θ

We can examine counterfactuals according to a number of different criteria. One is overall welfare in country n, measured as real GDP:Wn = Yn / pn!. (Since nonmanufactures are numeraire, the price level in
37. Our estimates of θ , obtained from different data using different methodologies, differ substantially. Nonetheless, they are in the range of Armington elasticities for imports used in computable general equilibrium models. See, for example,
Hertel (1997).
38. Specifically we solve for α from the relationshipX nn + IMPn = (1 − β )( X nn + EXPn ) + αYn ,"summed across our sample (with= .21) in 1990. Here IMPn is manufacturing
imports and EXPn is manufacturing exports, and Yn is total GDP, each translated
from local currency values into U.S. dollars at the official exchange rate.

277Technology, Geography, and Tradecountry n is pn!. Since we hold labor supplies and populations fixed
throughout, there is no need to distinguish between GDP and GDP per
worker or GDP per capita.) Decomposing the change in welfare into income and price effects gives
ln

Wn′
Y′
p ′ ⎛ w′ − wn ⎞ wn Ln
p′= ln n − α ln n ≈ ⎜ n− α ln n .
⎟WnYnpn ⎝ wn ⎠ Yn
pn

(Here x′n denotes the counterfactual value of a variable xn.) In the case ofmobile labor, of course, only the price effect is operative. Aside from looking at welfare, for the case of mobile labor, we ask about manufacturing
employment while, for the case of immobile labor, we look at the manufacturing wage wn. We also investigate how trade patterns change.
Since we have data on both manufacturing employment and manufacturing wages, we can look at our model’s implications for each given data on
the other. Our fit is not perfect since we impose a common manufacturing demand share α across countries and ignore sources of manufactures from outside our sample of 19 OECD countries.
We wish to distinguish the effects of any of the counterfactuals we examine in the next section from the initial misfit of our model. We therefore
compare the various counterfactuals that we examine with a baseline inwhich wages are calculated to be consistent with equations (16), (17), and(20), given actual manufacturing employment and GDP. Comparing thesebaseline wages with actual data the root mean square error is 5.0 percent.39
In performing counterfactuals we proceed as follows: With mobile labor
we treat total GDP and wages as fixed. We set GDPs to their actual levels
and wages to the baseline. With immobile labor we treat nonmanufacturing
GDP and manufacturing employment as fixed. We set manufacturing employment to its actual level and nonmanufacturing GDP to actual GDP lessthe baseline value for labor income in manufacturing (actual employment
times the baseline wage).

!

"

6.1. The Gains from Trade
We first consider the effects of raising geographic barriers to their autarky levels (dni → ∞ for n ≠ i). We then perform what turns out to be
the more extreme exercise of asking what would happen in a zero-gravity
39. Our model overstates the Canadian wage by 21 percent, but otherwise predictions are quite close. With our estimated parameters, Equation (30) predicts
much more trade between Canada and the United States than actually occurs. Since
U.S. purchases loom large in Canada, its labor market equilibrium condition (18)
implies more demand for Canadian manufacturing labor than there really is.

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Jonathan Eaton and Samuel Kortum

world with no geographic barriers (with all dni = 1).40
Table 9 shows what happens in a move to autarky for each of our 19
countries. The first column reports the welfare loss in the case of mobilelabor. The costs of moving to autarky range from one quarter of a percent
for Japan up to ten percent for Belgium.41 While these costs appear modest,
it should be remembered that they reflect the effects of shutting down
trade only in manufactures and hence understate the loss from not trading

Table 9. The Gains from Trade: Raising Geographic BarriersCountry
Australia
Austria
Belgium
CanadaDenmark
FinlandFranceGermany
GreeceItaly
Japan
Netherlands
New Zealand
NorwayPortugal
Spain
SwedenUnited Kingdom
United States

Welfare
−1.5
−3.2
−10.3
−6.5
−5.5
−2.4
−2.5
−1.7
−3.2
−1.7
−0.2
−8.7
−2.9
−4.3
−3.4
−1.4
−3.2
−2.6
−0.8

Percentage Change from Baseline to Autarky
Mobile Labor
Immobile Labor
Mfg. Prices Mfg. Labor Welfare Mfg. Prices Mfg. Wages
11.1
48.7
−3.0
65.6
54.5
24.1
3.9
−3.3
28.6
4.5
76.0
2.8
−10.3
79.2
3.2
48.4
6.6
−6.6
55.9
7.6
40.5
16.3
−5.6
59.1
18.6
18.1
8.5
−2.5
27.9
9.7
18.2
8.6
−2.5
28.0
9.8
12.8
−38.7
−3.1
−33.6
−46.3
24.1
84.9
−7.3
117.5
93.4
12.7
7.3
−1.7
21.1
8.4
1.6
−8.6
−0.3
−8.4
−10.0
64.2
18.4
−8.9
85.2
21.0
21.2
36.8
−3.8
62.7
41.4
32.1
41.1
−5.4
78.3
46.2
25.3
25.1
−3.9
53.8
28.4
10.4
19.8
−1.7
32.9
22.5
23.6
−3.7
−3.2
19.3
−4.3
19.2
−6.0
−2.6
12.3
−6.9
6.3
8.1
−0.9
15.5
9.3

!"

Note: All percentage changes are calculated as 100ln(x′/x) where x′is the outcome underautarky yatarky (dni → ∞ for n i ) and x is the outcome in the baseline.

40. For simplicity, we ignore any tariff revenues that geographic barriers might
generate. We consider the effect of reducing tariff barriers, taking revenue effects
into account, in Section 6.4 below.
41. In the mobile labor case (with total GDP and the manufacturing wage fixed)
the only welfare effect is from the decline in the manufacturing price level, which
affects welfare with an elasticity α . As a consequence we can use expression (15)to obtain a simple analytic formula for the welfare effect of moving to autarky:
ln

Wn′ α
=
ln π nn .
Wn θβ

It follows that the gains from trade vary inversely with θ . The implied gains fromtrade more than double, for example, using our lower estimate of θ = 3.60.

279

Technology, Geography, and Tradeat all.42 Manufacturing labor, shown in column three, rises everywhere except in Germany, Japan, Sweden, and the United Kingdom. That manufacturing employment shrinks in these four when trade is shut down could beseen as indicating their overall comparative advantage in manufactures.
The remaining columns consider the effects of moving to autarky withimmobile labor. Column four reports the welfare loss. The effect on welfare
is more negative than when labor is mobile, but usually only slightly so.
The net welfare effects mask larger changes in prices and incomes. In
all but the four “natural manufacturers” (Germany, Japan, Sweden, theUnited Kingdom), the price rise is greater when manufacturing labor is immobile. (In Germany and Japan manufacturing prices actually fall.) But
these greater price changes lead to only slightly larger effects on welfare
because they are mitigated by wage changes (reported in column six): The
wage in manufacturing rises in all but the four “natural manufacturers.”43
Three of the four countries we have identified as “natural manufacturers,” where manufacturing shrinks in moving to autarky, are quite large. A
question is whether these countries’ manufacturing prowess results fromtheir state of technology relative to the cost of labor, or because of theirsize and location. In the first case a total elimination of geographic barriers
would continue to favor these countries. In the second the elimination ofgeographic barriers would remove their advantage. Table 10 shows, in its
first three columns, what our model says would happen in a zero-gravity
world (setting all dni = 1). Looking at manufacturing employment in thecase of mobile labor (column three), Germany and Japan experience large
drops while Sweden continues to gain. Little happens in the United Kingdom. At the same time smaller, peripheral countries all experience expansion.
Our welfare measure indicates that we are very far from a world of zerogravity. Furthermore, world trade would be about five times its current
42. Since most trade is in manufactures, we could try to argue that we have captured most of the gains from trade. But trade volume may be a poor indicator of
the gains from trade in other sectors relative to manufacturing. Since productivity
in agriculture or mining is likely to be much more heterogeneous across countries,
applying our model to trade in these goods could well deliver a much lower valueof θ . An implication is that eliminating what trade does occur would inflict much
more damage.
43. How much labor force immobility exacerbates the damage inflicted by autarky depends on the extent of specialization in manufacturing. A move to autarky
raises the manufacturing wage the most in Greece, with the smallest manufacturing
share. But since its share of manufacturing labor income (reported in Table 1) is sosmall, the overall welfare effect is swamped by the large increase in manufacturing
prices. In Germany, with the largest manufacturing share, a move to autarky lowers
the manufacturing wage. But since the share of manufacturing is so large, the welfare cost of this loss in income is not offset by the drop in manufacturing prices.
For countries that are less specialized (in or away from manufactures), labor mobility makes less difference for overall welfare.

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Jonathan Eaton and Samuel Kortum

level in such a world. The last three columns of Table 10 report an experiment closer to reality: What happens if geographic barriers fall to 69 percent of their baseline levels across the board, leading to a doubling ofworld trade?44 Welfare rises by 1 to 3 percent as the price of manufactures
falls by 10 to 20 percent. These effects are of the same order of magnitude
as the costs of moving to autarky, but with less variation around the mean.
We already see the United States and Japan losing their size-based edge inmanufactures from this more modest drop in geographic barriers, while
manufacturing in most small countries rises.
Table 10. The Gains from Trade: Lowering Geographic BarriersCountry
Australia
Austria
Belgium
CanadaDenmark
FinlandFranceGermany
GreeceItaly
Japan
Netherlands
New Zealand
NorwayPortugal
Spain
SwedenUnited Kingdom
United States

Percentage Changes in the Case of Mobile Labor
Baseline to Zero Gravity
Baseline to Doubled Trade
Welfare Mfg. Prices Mfg. Labor Welfare Mfg. Prices Mfg. Labor
21.1−156.7
153.2
2.3
−17.1
−16.8
21.6
−160.3
141.5
2.8
−20.9
41.1
18.5
−137.2
69.6
2.5
−18.6
68.8
18.7
−139.0
11.4
1.9
−14.3
3.9
20.7
−153.9
156.9
2.9
−21.5
72.6
21.7
−160.7
172.1
2.8
−20.9
44.3
18.7
−138.3
−7.0
2.3
−16.8
15.5
17.3
−128.7
−50.4
1.9
−14.3
12.9
24.1
−178.6
256.5
3.3
−24.8
29.6
18.9
−140.3
6.8
2.2
−16.1
5.7
16.6
−123.5
−59.8
0.9
−6.7
−24.4
18.5
−137.6
67.3
2.5
−18.5
65.6
22.2
−164.4
301.4
2.8
−20.5
50.2
21.7
−161.0
195.2
3.1
−22.9
69.3
22.3
−165.3
237.4
3.1
−22.8
67.3
20.9
−155.0
77.5
2.4
−18.0
−4.4
20.0
−148.3
118.8
2.7
−19.7
55.4
18.2
−134.8
3.3
2.2
−16.4
28.5
16.1
−119.1−105.1
1.2
−9.0
−26.2

Note: All percentage changes are calculated as 100ln (x′/x) where x′is the outcome underlower geographic barriers and x is the outcome in the baseline.

6.2. Technology vs. Geography
Our discussion of the gains from trade has already brought up the question, raised in the economic geography literature, of the roles of geography
and technology in determining specialization. To allow specialization tovary, we consider the case in which labor is mobile. With zero gravity thefraction of a country’s labor force devoted to manufacturing is then pro1!"!, so depends only on the state of technology per
portional to (Ti /Li)/wi
44. We find an elasticity of trade volume with respect to overall geographic barriers of around 2 to 3.

281

Technology, Geography, and Tradeworker and the wage. When geographic barriers are prohibitive the fraction
is simply α, the share of manufactures in final demand, so that not eventechnology matters. But in neither case is geography relevant.
How do technology and geography compete in determining comparativeadvantage in between these extremes? Looking at what happens to thefraction of labor devoted to manufacturing as geographic barriers fall, twobasic patterns emerge. For smaller countries manufacturing shrinks as geographic barriers diminish from their autarky level. Production shifts tolarger countries where inputs are cheaper. As geographic barriers continue
to fall, however, the forces of technology take over, and the fraction of thelabor force in manufacturing grows’ often exceeding its autarky level. The
results for Denmark, depicted in Figure 3, illustrate this pattern nicely. For

Figure 3. Specialization, Technology, and Geography

the largest countries in our sample, Germany, Japan, and the United States,
the pattern is reversed. Their manufacturing sector at first grows and thenshrinks as geographic barriers fall. Germany, also depicted in Figure 3, illustrates the pattern most starkly.
Extant geographic barriers place the world near a transition between one
where the effects of geography dominate and one where technology governs comparative advantage. The results suggest a decline in barriers would
lead to specialization more along Ricardian lines, with large countries start-

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Jonathan Eaton and Samuel Kortum

ing to lose their edge.45
6.3. The Benefits of Foreign Technology
With geographic barriers as high as they are, how much does tradespread the benefit of a local improvement in technology? We increase thestate of technology Ti by 20 percent, first for the United States and thenfor Germany. Table 11 reports what happens to welfare in different countries of the world as a percentage of the effect locally. Other countries always gain through lower prices. With labor mobile there is no additional
income effect, so the net welfare effect is always positive. When labor isTable 11. The Benefits of Foreign Technology
Country
Australia
Austria
Belgium
CanadaDenmark
FinlandFranceGermany
GreeceItaly
Japan
Netherlands
New Zealand
NorwayPortugal
Spain
SwedenUnited Kingdom
United States

Welfere Consequences of Improved Technology
Higher U.S. State of Technology Higher German State of Technology
Mobile Labor
Immobile Labor
Mobile Labor
Immobile Labor
27.1
14.9
12.3
4.4
9.3
2.9
61.8
5.4
13.2
3.0
50.7
4.8
87.4
19.9
9.3
1.3
12.2
6.2
62.5
7.1
11.3
4.3
37.5
3.0
10.1
4.2
39.2
3.0
9.7
−11.6
100.0
100.0
14.0
18.3
38.9
8.0
9.7
3.9
38.4
3.0
6.6
−0.8
5.9
−0.2
12.8
6.8
63.5
8.3
33.8
13.5
15.6
3.9
13.2
11.7
43.8
6.1
14.3
8.6
39.6
4.7
9.6
7.0
27.3
3.3
12.8
1.1
42.7
2.3
14.6
0.5
38.3
1.6
100.0
100.0
9.7
1.4

Note: All numbers are expressed relative to the percentage welfare gain in the country
whose technology expands. Based on a counterfactual 20 percent increase in the state oftechnology for either the United States or Germany.

45. Whether a further decline in geographic barriers (defined in the iceberg sensehere) is in the works is an open question. Recent increases in trade volumes relative to output may have created a perception that technical progress in communication and transport is feeding an inexorable trend toward lower geographic barriers.
Our model illustrates how, in order to increase trade, the rate of progress in international transactions must exceed that in production. A proportional increase in allstates of technology Ti has no effect on trade shares. The reason is that technicalprogress implies a proportional reduction in the cost of delivering goods to any
destination, whether at home or abroad, so does not affect the margin at which
goods are imported or produced locally.

283

Technology, Geography, and Tradeimmobile, foreign countries also experience a negative income effectthrough lower wages in manufacturing. Hence the overall welfare effect isgenerally lower when countries cannot downsize their manufacturing labor
forces.46 Germany and Japan, with large manufacturing shares, actually suffer welfare losses in response to technological improvements elsewhere.
The percentage benefits decay dramatically with distance and size. With
labor mobile the gain in nearby countries approaches that where the improvement occurred. Canada, for example, benefits almost as much as theUnited States from a U.S. technological improvement. Germany’s smallerneighbors experience more than half the gain from an improvement in German technology as Germany itself. At the other extreme, Japan, which isboth distant and large, gets little from either Germany or the United States.
The results point to the conclusion that trade does allow a country tobenefit from foreign technological advances. But for big benefits two conditions must be met. First, the country must be near the source of the advance. Second, the country needs to be able to reallocate its labor to activities outside of manufacturing.
6.4. Eliminating Tariffs
In our analysis so far we have ignored, for simplicity, any revenues generated by geographic barriers, treating them as entirely natural. Our framework can, however, readily incorporate revenue-generating barriers. We assume that country n’s imports from country i are subject to an ad valorerm tariff tni (on the c.i.f. price). Geographic barriers then decompose
into their tariff 1 + tni and natural dni! components, so that dni = (1+tni) dni!.
We augment income Yn by tariff revenue TRn, where
TRn =

t ni

∑ 1+ t X .
i ≠n

ni

ni

We calculate a baseline world in which countries impose a uniform 5
percent tariff on all imports.47 We then ask what happens when: allcountries remove tariffs， the United States removes its tariff unilaterally,
and members of the European Community (as of 1990) drop tariffs
against each other.

#

"

!

46. The exception is Greece. In the case of immobile labor the added benefit oflower wages in suppliers nearby more than offsets the reduction in the wages
earned by its own small fraction of workers in manufacturing.
47. This figure corresponds roughly to average statutory rates among the OECD.
See, e.g., Hertel (1997).

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Jonathan Eaton and Samuel Kortum

6.4.1. General Multilateral Tariff Elimination
Welfare rises almost everywhere if all 19 countries collectively remove
tariffs. The benefits are substantially greater with mobile labor, varying
from a high of 1.31 percent for Belgium to a low of 0.21 percent for Japan,
with most countries gaining around one percent. With immobile labor thegains never exceed half a percent. Germany actually experiences a 0.05
percent loss (losing more in tariff revenue than its gain from lower prices
and a slightly higher wage in manufacturing).
6.4.2. U.S. Unilateral Tariff Elimination
If the United States removes tariffs on its own, everyone benefits except
the United States, which, for standard optimal tariff reasons, suffers a welfare loss of 0.005 percent with mobile labor (0.13 percent with immobilelabor). The biggest winner is Canada, which enjoys a welfare gain of 0.5
percent with mobile labor (1.1 percent with immobile labor).
With mobile labor, the percentage gains for other countries roughly equalor exceed the U.S. loss. The results point to the importance of pursuing
freer trade multilaterally, since the benefits to the rest of the world of U.S.
liberalization far exceed the cost to the United States.
6.4.3. Trade Diversion in the European Community
Table 12 reports some effects of eliminating tariffs within the 1990
European Community. Who gains and who loses depends very much on
the mobility of labor. As the second column reports, with immobile labor
the major losers are nonmembers nearby, whose manufacturing wages must
fall in order for them to remain competitive suppliers to the EC. Membersof the EC consequently benefit from lower external prices and a greater
premium placed on their own manufacturing workers.
With mobile labor, however, the losers (as reported in the first column)
are the northern EC members. In this scenario workers in nonmember
states move to other activities rather than suffer wage cuts. Northern EC
members divert imports from these nonmember states to less efficientsouthern EC sources.
Note from the third and fourth columns that with market integration,
intra-EC trade expands substantially, especially when labor is mobile.
Moreover, in the mobile labor case, EC market share elsewhere generally
expands: By making inputs cheaper, market integration provides EC countries a cost advantage outside.

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Technology, Geography, and Trade
Table 12. The European Community: Welfare and Trade

Country
Australia
Austria
Belgium*
CanadaDenmark*
FinlandFrance*Germany*
Greece*Italy*Japan
Netherlands*
New Zealand
NorwayPortugal*Spain*
SwedenUnited Kingdom*
United States

Effect of Removing a all Tariffs on Intra-EC Trade
Aggregate Welfare
Imports the EC
Mobile Labor
Immobile Labor
Mobile Labor
Immobile Labor
0.13
0.11
27.7
2.8
0.32
−0.07
−1.9
−3.4
−0.91
0.54
61.3
26.3
0.01
0.01
28.0
2.2
−0.27
0.18
49.9
30.8
0.28
−0.02
4.6
−2.9
0.08
0.05
46.3
33.7
−0.03
−0.03
58.5
41.9
0.28
0.13
30.8
24.0
0.14
0.04
44.9
36.4
0.07
−0.01
32.4
2.3
−0.58
0.33
56.3
26.9
0.14
0.09
24.1
1.9
0.34
0.05
3.2
−2.9
0.03
0.10
44.0
32.8
0.21
0.05
43.7
34.3
0.31
−0.10
2.0
−3.3
−0.02
0.02
51.9
36.1
0.10
0.03
27.8
2.2

Note: All numbers are percentage changes from the baseline. In the baseline all trade is subject to a 5 percent tariff. The counterfactual is to remove tariffs between members (as of1990) of the EC (appearing with a*). Each pair of columns shows the results of peforming
the counterfactual first for the case of mobile labor and then for the case of immobile labor.

7. Conclusion
Comparative advantage creates potential gains from trade. The extent towhich these gains are realized, however, is attenuated by the resistance imposed by geographic barriers. We have developed a Ricardian model that
captures these two forces quite parsimoniously. The model delivers equations relating bilateral trade around the world to parameters of technology
and geography. We use data on bilateral trade flows, prices, and geography
to estimate the parameters.
While the gravity literature has recognized the importance of geographic
barriers in curtailing trade flows, formal models of international trade havetypically ignored them. The exceptions are models in which specialization
is preordained by product differentiation, via either the Armington assumption or monopolistic competition. In contrast, our framework allows geographic barriers as well as technology to determine specialization. It also
connects trade flows to the deviations from the law of one price that geographic barriers generate.

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Jonathan Eaton and Samuel Kortum

A Data Appendix
Our analysis uses data for manufacturing in 1990 for the 19 OECD
countries listed in Table 1.
A.1. Trade Data
Our dependent variables are transformations (discussed in the text) of bilateral manufacturing imports. Country i’s imports from home are gross
manufacturing production less manufacturing exports. Its total manufacturing expenditures are home purchases plus imports from everywhere else.
These measures are reported by the STAN database in local currencies(OECD, 1995). We calculate imports from each of the other 18 countries,
as a fraction of total manufactured imports, based on the United NationsStatistics Canada bilateral merchandise trade data by 4-digit SITC, as described in Feenstra, Lipsey, and Bowen (1997).48 All import measures arec.i.f. Since our dependent variables normalize imports either by home sales
or by total expenditures, no exchange rate translation is required.
The first column of Table 1 shows that imports typically represent lessthan half of spending on manufactures, the exceptions being Belgium, theNetherlands, and Denmark. The second column shows that most of the imports of our sample of 19 OECD countries are purchased from one of theother 18 countries in the sample.
A.2. Price Data
Prices in 1990 for over 100 GDP categories in each of our 19 countries
are from World Bank (1993). We use the 50 items identified by Hooper
and Vrankovich (1995) as corresponding to either: textile, apparel, andleather products， machinery, equipment, and fabricated metal products,
or other manufactured products. We dropped the many items related tofood and chemicals since we thought their prices would be unduly influenced by proximity to natural resources and taxes on petroleum products,
two factors absent from our model.

#

"

!

A.3. Proxies for Geographic BarriersDistances between countries serve as a determinant of geographic barriers. The distances are in thousands of miles measured between central cities in each country. (A list of the cities is in Eaton and Tamura, 1994.)
48. We used the concordance of Maskus (1991) to determine those SITC codes
corresponding to manufactures. Using the concordance in Feenstra, Lipsey, andBowen made virtually no difference.

287

Technology, Geography, and Trade!

Language groups are: English (Australia, Canada, New Zealand, United
Kingdom, United States)， French (Belgium and France), and German(Austria and Germany).

"#

A.4. Manufacturing Employment and Wages
Since we use the model itself to solve for the price of intermediates, theonly input costs entering our empirical trade equations are manufacturing
wages. Annual compensation per worker in manufacturing (which includes
employers’ compulsory pension and medical payments) is reported by theOECD (1995) in local currency. We translate into U.S. dollars at the current exchange rates to obtain measured compensation compi, reported in
the third column of Table 1.49 We then adjust by worker quality, setting
wi = (compi)e !gH i , where Hi is average years of schooling and g is the return to education. Column four of Table 1 reports the human-capital adjusted wage (human-capital adjusted manufacturing employment is shownin column five). We set g = .06, which Bils and Klenow (2000) suggest is
a conservative estimate. Years of schooling is from Kyriacou (1991), as
shown in Table 4.
A.5. Aggregate Income
In our counterfactuals we require total income in 1990. We use localcurrency GDP in 1990 (from OECD (1997)) translated into U.S. dollars at
the 1990 exchange rate. The last column of Table 1 shows manufacturinglabor income as a percentage of total income.
A.6. Data for Alternative Parameters
Table 4 shows the data used to pursue our alternative estimate of θ , asdescribed in Section 5.2. The first column shows stocks of research Ri foreach country, from Coe and Helpman (1995). They use the perpetual inventory method (assuming a depreciation rate of five percent) to add up
real R&D investment by business enterprises. The second column shows
the human capital measure Hi, for which we use average years of schooling in 1985 from Kyriacou (1991).
We use two variables to instrument for wage costs. The first is aggregate workforce worki, from Summers and Heston (1991, version 5.6),
shown in the third column of Table 4. As with wages, we adjust for education setting Li = (worki)e gH i . The second instrument is density, defined as
the aggregate workforce divided by a country’s land area, shown in thelast column of Table 4.
49. We used the official rather than the purchasing power exchange rate since it
determines differences in costs of production. In our model, differences in purchasing power arise endogenously.

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Jonathan Eaton and Samuel Kortum

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13

Bilateral Trade Patterns andWelfare: An Egypt-EU Preferential
Trade Agreement
Denise Konan and Keith Maskus*

1. Introduction
In recent years, computable general equilibrium (CGE) models havebeen used to analyze the impact of preferential trade liberalization for several countries. A standard approach is to rely on a model of a single, pricetaking country where goods are differentiated by region of production andconsumption follows the Armington assumption. An important parameterin determining the welfare implications of preferential trading arrangements (PTAs) is the pre-liberalization volume share of trade with the proposed partner. Yet, conventional theory has not examined the role of tradeshares in this typical CGE modeling framework. This paper examines therole of the volume of partner country trade in determining the outcome of
a PTA in a small-country CGE model where products are differentiated ona regional basis.
The traditional approach is characterized in Lipsey’s (1970) model
where a PTA between countries that already trade in large volumes with
one another is less likely to be trade-diverting as the potential partner is already a low-cost supplier of the imported good. In contrast, the models of
Panagariya (1996), Bhagwati and Panagariya (1996) and Schiff (1996)
show that if a country is large (that is, able to influence the terms of trade)
relative to the potential partner but is a small price taker in the rest of theworld, then the smaller is the initial partner import share the lower are
trade diversion (and overall) losses. In a partial-equilibrium, differentiated* We appreciate the insights of James Cassing, Edward Leamer, Raymond Riezman, Keith Head, Neil Vousden, Rodney Tyers, Brian Copeland and participants at
Australian National University and Kobe University. Research for this paper was
supported in part by the World Bank. The analysis and opinions in this paper are
those of the authors and do not necessarily represent those of the World Bank.
293

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Denise Konan and Keith Maskus

products model, Konan and Maskus (2000a), we show that an ambiguous
relation exists between trade shares and gains from a PTA. For small levels of initial partner trade share, increases in that share are negatively related with welfare gains from a PTA. When initial trade volumes with thepartner are relatively high, a positive relation exists between partner tradeshare and welfare gains.
The Bhagwati and Panagariya result relies on two key assumptions： that
tradable products are homogeneous and that the domestic offer curve has
finite elasticity. As de Melo and Robinson (1989) explained, however, thisframework is not satisfying for single-country CGE model for several reasons. First, the homogeneity assumption is not consistent with the two-way
trade, which is generally observed in aggregated trade statistics. Second,
homogeneity implies that small price changes from liberalization lead to
extreme and unrealistic specialization in production when products are notdifferentiated. Third, especially for most developing countries, it is reasonable to assume that international terms of trade will not be significantly influenced by domestic trade reform. De Melo and Robinson have shownthat the assumption of a price-taking, general equilibrium economy is theoretically consistent with that of product differentiation by region (the Armington assumption) when multi-sector models are not heavily disaggregated.
To illustrate these issues, we employ a CGE model of Egypt.1 The European Union (EU) is in the process of negotiating bilateral EuroMediterranean Agreements (EMAs) with several nations of the Middle Eastand North Africa (MENA) region (Hoekman and Djankov (1996)). The
EU has already reached agreements with Turkey and Tunisia. The case of
Egypt is particularly interesting as its trading pattern is much less focusedon the EU than are those of some of its African neighbors. In this paper
we consider the potential for Egypt to gain from participation in the EMA
initiative and the importance of Egypt’s share of trade with the EU in determining such gain. Given actual Egyptian trade patterns, the direct trade
impact of an EMA is negative. Welfare may rise overall as trade liberalization interacts with the domestic tax structure to enhance efficiency, a process that we describe in detail in a companion paper (Konan and Maskus(2000b)).
2. Trade Creation and Trade Diversion with Differentiated Products
We extend the Vousden (1990, chapters 9 and 10) model of a small
country to demonstrate the importance of partner trade shares.2 While simple in dimension, this model provides our basic definitions and analytical
1. Our CGE model of Egyptian trade liberalization is established in the literature(Hoekman and Konan (2000), Hoekman, Konan, and Maskus (1998), Konan and
Maskus (1997, 2000b), Maskus and Konan (1997)).
2. See also Harrison, et al. (1993).

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Bilateral Trade Patterns and Welfare

results. It also illustrates important features of the more complicated CGE
model that is described in the next section.

Ｅ

Ｆ

Ｇ

Ｈ

Ａ
k
m
B

n

C

Figure 1. Import Markets

Assume that a small country (A) trades with two regions, a potential
partner (B) and the rest of the world (R). Country A’s importable goods
are differentiated by region of origin, with imports labeled MB and MR.
These imports are imperfect substitutes and are purchased at exogenous
prices. Initially, suppose that imports face no domestic competition. The
basic implications of a PTA with B are illustrated in Figure 1. At an initial!
non-discriminatory ad valorem tariff of t = (PiA /Pi −1) within a sector i,11country A imports quantities MB and MR . Suppose that A moves to a
PTA that eliminates the tariff on B but maintains the tariff on ROW. Consumer surplus in A’s market for the B good increases by the area
PBA ACPB! while tariff revenues fall by PBA ABPB , resulting in a net welfare
gain of area ABC , which may be defined as import trade creation. However, because imports from B and ROW are imperfect substitutes, the fallin the price of the B good engenders a fall in country A’s demand for MR,
1
2
shown as a shift in Hicksian demand from DR to DR . The revenue loss ofarea EFGH may be defined as import trade diversion.
The net welfare effect in the import market, measured as the area ABC EFGH , depends on three key parameters： the own-price elasticity of compensated demand for MB, the elasticity of substitution between B and ROW
imports, and the share of total import expenditures originating from B initially.
The import analysis is complicated when there is substitutability in consumption between imports and a domestically produced good. The fall in
the price of country B’s imports reduces the demand for (and the price of)A’s substitute good. The demand for ROW imports declines also as the12prices of B and A goods fall, represented by the shift from DR to DR in296

Denise Konan and Keith Maskus

Figure 1, resulting in trade-diversion welfare losses of area EFGH .3 De1
2
mand for the B import also falls from DB to DB in response to the lower!
A and ROW prices. While consumer surplus increases by area PBA knPB ,!
Atariff revenues on B imports fall by PB ABPB , resulting in an ambiguouschange in welfare of area mBn minus area kAm. The greater is the elasticity of substitution between the domestic good and imports, the greater isthe follow-on decline in import demand, the lower is trade creation, andthe greater is trade diversion.
While the partner import share remains an important determinant of
PTA effects, it is impossible to derive expressions for trade creation (TC)and trade diversion (TD) as closed-form functions of that parameter. Numerical simulations for a PTA between Egypt and the EU, reported later inthe paper, reveal that both processes are concave and non-monotonic functions of EU’s share of Egyptian imports. However, in this case economic
welfare continuously increases in that share.
3. An Application Using a Computable General Equilibrium Model of
Egypt
In this section we summarize our CGE model of a small country (Egypt)
to demonstrate the importance of initial trade shares in the formation of a
PTA. The basic framework extends the applied general equilibrium model
developed by Maskus and Konan (1997).
We model Egypt as a small open economy (SOE) in which household
and production decisions follow standard neoclassical assumptions of optimization. Of particular interest are the regional and sectoral aspects of
Egypt’s international trade. In the model, bilateral trade flows with the EU(including Turkey) and the rest of the world (ROW) are distinguished foreach of 38 sectors (three in agriculture, two in mining and quarrying, 21 in
manufacturing, and 12 in services).
Final demand by a representative agent (RA) is determined by a nested
utility function for given prices and budget constraint.4 In the first stage ofthe multi-level budgeting problem, the RA decides on aggregate purchases
per sector according to a Cobb-Douglas subutility function. Given the firststage allocation of income per sector, the RA decides how much to spend
on domestic and imported goods of each sector according a CES subutility
function. Egyptian importables in each sector are further differentiated byregion of origin： the EU and ROW. These imports are imperfectly substitutable and are purchased at exogenous prices.
3. In general the shift in ROW demand would be different in this case than in
the prior case but to avoid cluttering the diagram we use the same shift to depict
both cases.
4. We assume that this demand structure also characterizes government consumption and investment spending.

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Bilateral Trade Patterns and Welfare

Note that, computationally, Armington differentiation is not inconsistent
with assuming Egypt faces fixed foreign prices. De Melo and Robinson(1989) demonstrated that the assumption of a price-taking, general equilibrium economy is theoretically consistent with that of product differentiation by region when multi-sector models are not extensively disaggregated.
The Armington assumption implies that the components of a composite
Egyptian vegetable product, for example, differ from those of the EU or
ROW composite. Yet Egypt does not have price-setting power in the aggregate market for tomatoes. Moreover, to assume alternatively that goods
are homogeneous would not be consistent with two-way trade, which is
generally observed in aggregated trade statistics.
The model is static and requires two closure rules. First, to achievesaving-investment balance we assume that the aggregate capital stock isexogenously fixed at the benchmark level and financed by consumer savings that act as a lump-sum transfer. The interest rate of capital is endogenously determined by factor-demand conditions. Second, the currentaccount balance is exogenously fixed in real terms at its benchmark deficit
level. As external prices are fixed, Egypt’s real exchange rate, which we
define as the shadow price of a foreign-currency index, will adjust to
maintain the deficit as domestic prices and trade quantities vary.
Regarding the agent’s budget constraint, she receives income from supplying the labor and capital endowments. Supplemental income is obtained
through foreign borrowing via the current-account deficit. In addition to
consumption, the agent must pay for government borrowing and investment. Domestic price indexes are CES aggregates across home prices andimported prices and are functions of producer prices, a consumption tax,
and tariffs.
Production in each sector exhibits constant returns and requires production labor, non-production labor, capital, and intermediate inputs. Primaryfactors are assumed to be perfectly mobile across sectors but internationally immobile.5 Firms maximize profits under perfectly competitive conditions. Intermediate goods and value added combine to produce final goods
under a Leontief technology, with value added depending on labor andcapital in a CES production function. The composite intermediate good is
a CES aggregate of domestic and imported intermediates. Imported intermediates are further disaggregated into a CES nest of EU and ROW imports. Production costs depend on prices of factors and intermediate goods,
tariffs and non-tariff barriers on intermediate inputs, and a tax on capitaluse. Production is sold into domestic and export markets using a constantelasticity of transformation (CET) nest, while exportables are further transformed into EU-bound and ROW-bound exports in a subsequent Arming5. Maskus and Konan (1997) also consider models with sector-specific capital in
all sectors or selected resource-constrained sectors.

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Denise Konan and Keith Maskus

ton CET nest. Market-clearing conditions in each product and factor market are included.
As trade reform will directly alter tax collections, a detailed treatment of
Egyptian public finance is critical. We assume that the public sector consumes a fixed bundle of goods and services evaluated at endogenous prices.
The government maintains a fixed real budget deficit and endogenously
adjusts domestic tax instruments to counteract the revenue effects of tariffreforms. The primary replacement tax mechanism is assumed to be a goods
and service tax (GST) which acts as a sales tax on final consumption. In
practice the government also taxes capital usage, with capital defined here
as operating surplus less depreciation. Capital taxes vary substantiallyacross sectors and these rates are held fixed in the counterfactual simulations.
To implement the model empirically, we develop an Egyptian data set
consisting of a Social Accounting Matrix (SAM) and a variety of policy,
trade, and technology parameters for the year 1990. Relationships for intermediate demand, final demand, and valued added are defined by the 1989/
90 Input-Output (IO) table for Egypt (CAPMAS 1994a, b). To account forrecent reform activities in Egypt we update policy parameters to a second
benchmark year 1994. Thus, 1994 provides the benchmark for the ensuing
simulations.
Major Egyptian import sectors include machinery, food processing,vegetable foodstuffs, and chemicals, while export flows are dominated bytransportation (largely the Suez Canal), oil, and textiles. On a regional basis, Egypt provides an interesting case study as its trade structure isstrongly diversified. According to 1994 trade data, less than half of all
merchandise import and export trade is with the EU and these shares varyconsiderably across products. Egypt’s trading relations are much less focused on the EU than are those of other North African countries, such as
Morocco (Rutherford, Tarr and Rutström 1997). In the absence of regional
data on services trade, we assume that the EU’s initial shares are equivalent to its total merchandise import and export shares. Among the most important Egyptian production sectors are vegetable food products, animal
products, food processing, trade, transport, social services, construction,and cotton textiles. Of these, services employ a disproportionate share of
the labor force, while capital tends to be concentrated in agricultural sectors.
The IO Table is supplemented with data on government policy parameters. We apply effective rates of capital taxation calculated by the WorldBank (1995) for 1990. There are no taxes levied on agriculture, an approximate 18% tax on manufactures (including mining and crude oil sectors), and approximately a 23% tax on services. By 1993 Egypt had phasedin a goods and services tax and phased out indirect production taxes andmost subsidies (World Bank, 1995). The GST is applied on the sales of299

Bilateral Trade Patterns and Welfare

goods and services, with rates that vary across industries. We treat the
GST as a tax on domestic final demand (excluding government purchases).
Import-weighted tariff rates are computed from information on 1994
trade and tariff collections data by 8-digit Harmonized System classification. Currently, tariffs are levied on an MFN basis. We aggregate these tariff rates to the IO sectors by developing import weights consistent with aconcordance constructed by the authors. Various tariff exemptions imply
that Egypt does not collect full revenue on its legal tariff rates, forcing us
to scale the weighted rates down by approximately 20% to be consistent
with 1994 revenues. It is difficult to obtain information on trade barriers in
Egyptian services. Conversations with Egyptian experts indicate that theservice sector is largely closed to foreign competition. A conservative implicit service tariff rate of 15% is assumed in the benchmark.
There are no formal empirical estimates of various Egyptian elasticitiesof domestic substitution and transformation. A survey of previous Egyptian
elasticity assumptions is provided by Lofgren (1994) and we select benchmark parameters consistent with his reported ranges. The elasticity of substitution between labor and capital is assumed to vary across sectors, as
taken from Harrison et al. (1993). The various trade elasticities correspondto the central cases in Rutherford, Tarr and Rutström (1997). They include
an Armington substitution elasticity between regional imports of 5.0 and
between imported and domestic consumption of 2.0, and a transformation
elasticity between regional exports of 8.0 and between domestic and exported output of 5.0.
4. Simulation Results
In this section we analyze various trade liberalization scenarios for
Egypt： one MFN reform and two preferential trade agreements. The resultsof baseline counterfactual experiments are described. To illustrate the importance of initial bilateral trade shares with discriminatory tariff reform,
we go on to perform detailed sensitivity analysis on trade shares.
4.1. Baseline Trade Liberalization Simulations
The baseline counterfactual experiments involve a set of trade liberalization exercises, the results of which are reported in Table 1. For comparison
purposes, in Column (1) we report the results of a unilateral removal of all
Egyptian tariffs, resulting in global free trade.6 The EU is assumed to provide no additional market access. This policy generates estimated welfare
gains (measured as Hicksian equivalent variation) of 0.81 percent over
6. Throughout the counterfactual simulations the beverage tariff is not changed
to reflect Egypt’s social policy for maintaining rigorous barriers on imported alcoholic beverages.

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Denise Konan and Keith Maskus

benchmark 1994 levels. The real exchange rate depreciates by 1.24 percent
in order to maintain the benchmark current-account deficit. Tariff elimination requires an offsetting rise in the consumption tax (GST) rates of 24
percent to sustain real government revenues.
Two possible outcomes of an EU partnership agreement are reported inColumns (2) and (3). Scenario EU_AT considers an agreement whereby
Egypt eliminates all tariffs on EU products while maintaining existing tariffs on ROW. The EU responds by providing improved access in agriculture and textiles and clothing. Based on the estimates of Harrison, et al.
(1989), the benefit of inclusion in the EU’s common agricultural policy
and greater access under its quotas on textiles and clothing is approximatedas an eight-percent price increase for Egyptian exports bound for the EU inthese sectors.
Any PTA would result in trade creation and trade diversion. As in ourearlier theoretical model, we compute import TC as the change in consumer surplus less tariff-revenue losses on imports arriving from the EU.7
As Egypt also experiences an improvement in its terms of trade with theEU, the TC measure further includes the net increase in producer surplus
for exporters to the EU. Trade diversion is computed as losses in tariff
revenues on imports from ROW. The model estimates TC gains from thisagreement of 500 million real Egyptian pounds and TD losses of 530 million pounds, implying a direct welfare loss of 30 million pounds. Thus, wefind that the direct impact of this form of PTA would be negative for
Egypt.
This direct measure of static welfare changes reflects the standard conception, in which TC and TD emerge against an idealized backdrop of anotherwise undistorted economy and no fiscal revenue target. However,other distortions exist in the Egyptian economy and interact with trade reform, while the government is constrained to offset changes in tariff revenues with altered tax rates. We find that in the context of this PTA, theEgyptian government could lower the GST by 3.4 percent while maintaining a fixed deficit, implying an added gain in welfare. That is, despite thepreferential lowering of tariffs, there is a reduction in the GST as resources and consumption flow into higher-taxed sectors in general equilibrium. Overall, EU_AT provides a 0.14 percent static gain in welfare. The
real exchange rate depreciates by 1.25 percent to maintain the benchmark
current-account imbalance.
In the second preferential trade agreement scenario, EU_TOT, the EU
offers the same concessions in textiles and agriculture described in EU_AT
and, in addition, recognizes Egyptian inspection practices and production
standards. We assume this generates a one-percent reduction in EU non7. Because preferences are homothetic, this measure is a monotonic transformation of Hicksian equivalent variation.

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Bilateral Trade Patterns and Welfare

tariff barriers on Egyptian exports, yielding an equivalent improvement in
Egyptian export prices across the board. Trade creation and trade diversion
estimates are comparable to those observed in the EU_AT scenario, with asmaller net welfare loss. Accounting for tax neutrality, the overall welfare
gains of 0.27 percent are double the gains available under the first case.
The GST is reduced by 3.59% and the real exchange rate depreciates by
0.95 percent.
Table 1. Baseline Trade Liberalization Scenarios (% change)

CREATION*
DIVERSION*
NET WELFARE
EXCHANGE
GSTWELFARE*GLOBAL
(1)

EU_AT
(2)

EU_TOT
(3)

1.24
24.03
0.81

0.50
0.53
−0.03
1.25
−3.39
0.14

0.51
0.52
−0.01
0.95
−3.59
0.27

Measured in billion Egyptian pounds (ELs).

SCENARIOSEU_AT is a PTA with the EU in which Egypt eliminates all tariffs on EU imports.
The EU provides improved access in agricultural goods and textiles and clothing,
resulting in an eight-percent rise in those Egyptian export prices to the EU.
EU_TOT extends scenario EU_AT. Egypt eliminates all tariffs on EU imports.
The EU provides more liberal access to domestic markets, resulting in a onepercent increase in all export prices to the EU, with an eight-percent price increasein agriculture and textiles.
GLOBAL involves unilateral tariff elimination by Egypt against all trading partners. The EU grants no concessions and export prices are unchanged.
VARIABLE ESTIMATES
CREATION is the real increase in GDP (in billion Egyptian pounds) due to tradecreation.
DIVERSION is the real decrease in GDP (in billion Egyptian pounds) due to trade
diversion.
NET WELFARE equals CREATION minus DIVERSION.
EXCHANGE is the percentage change in the real exchange rate, or shadow priceof foreign currency, necessary to maintain the benchmark current account imbalance.
GST is the percentage change in the consumer tax (or GST) required for government revenue neutrality.
WELFARE is the percentage change in real benchmark 1994 GDP measured inequivalent variation.

4.2. Analysis of Different Bilateral Trade Shares
The preceding analysis was based on observed benchmark EU tradeshares. Unlike the single-sector model in Section 2, these proportions vary

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Denise Konan and Keith Maskus

across products, complicating the analysis of TC and TD as the aggregate
EU trade shares change. To handle this problem, we simulate the impact of
discriminatory trade reform under the supposition that Egypt’s imports andexports are more or less concentrated with the EU than is actually observed. That is, a series of (fictitious) new benchmarks is created in which
sectoral European trade flows are assumed to range from 50 percent of observed imports and exports to 150 percent of actual flows. Sectoral ROW
trade flows are redefined as the residual of total imports (exports) lesssimulated EU imports (exports). Note that for trade multipliers exceeding
one it is possible for simulated EU imports (exports) to exceed total imports (exports) in some sectors. Trade in these cases is characterized as acorner solution whereby all benchmark imports (exports) are assumed tooriginate in (be destined to) the EU and ROW trade flows are set to zero.
The counterfactual experiments, EU_AT and EU_TOT, are run against thisbackdrop of contrived EU trade.
Consider the impact of the EU_AT tariff reform under the presumptionthat Egyptian trade flows with the EU are half the observed benchmark
levels. The results (not shown) are an estimated 329 million Egyptian
pounds in welfare gain from TC with the EU, while TD losses are approximately 483 million pounds. Thus, at our lowest partner trade shares, thenet welfare loss is −154 million pounds, or five times that using the observed shares.
Trade creation, trade diversion, net welfare and welfare (including tax
offsets) are graphed as functions of EU trade multipliers in Figure 2. Confirming our theoretical results, TC and TD are concave functions of partnertrade shares. Focusing purely on the difference between TC and TD, theeconomy stands to suffer a fall in net welfare unless benchmark trade isapproximately 1.11 times more heavily focused on the EU than that observed in our 1994 benchmark. Nonetheless, a larger simulated trade sharewith the EU appears to be associated with greater welfare gains (or smaller
welfare losses).
As discussed above, aggregate welfare changes depend also on offsettingchanges in tax rates for fiscal neutrality. Figure 2 also depicts aggregatechange in welfare in response to the EU_AT trade agreement. Although
they are highly correlated, aggregate welfare changes everywhere exceed
direct welfare impacts, implying that TC and TD interact positively withendogenous domestic tax changes. The PTA generally results in an estimated rise in aggregate welfare except with small partner trade multipliers.
Similar results pertain with sensitivity analysis of trade shares in the EU_TOT case, as shown in Figure 3. Both TC and TD are concave with respect to the EU multiplier. Both net and aggregate welfare increase as theshare of trade with the EU is scaled up. Direct welfare gains attributed directly to net trade creation are positive only for EU trade multipliers at or
above about 1.07.

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Bilateral Trade Patterns and Welfare

Figure 2. EU_AT Share Sensitivity Analysis

Figure 3. EU_TOT Share Sensitivity Analysis

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Denise Konan and Keith Maskus

5. Concluding Remarks
This paper considers the welfare implications of a discriminatory preferential trading arrangement in a general equilibrium model where imports
are differentiated by region of origin and terms of trade are fixed. The relationship between the initial (pre-reform) relative volume of trade with thepotential partner and welfare changes is theoretically ambiguous. Applied
general equilibrium analysis of Egyptian trade illustrates the issues with regionally differentiated trade flows. Our simulations indicate that potential
Egyptian welfare gains from a European PTA are modest. Experiments altering the composition of Egyptian trading patterns show that trade creation and diversion are non-monotonic, concave functions of the benchmark
share of trade with the PTA partner. Nonetheless, aggregate welfare gains
rise with the initial partner trade share. Thus, in the particular case considered here, the more focused Egypt’s trade patterns are on the EU, the more
the country would gain from a preferential trading arrangement.

References
Bhagwati, J. and A. Panagariya. 1996. Preferential Trading Areas and Multilateralism––Strangers, Friends, or Foes? In The Economics of Preferential Trade
Agreements, eds. J. Bhagwati and A. Panagariya. College Park, MD: The AEI
Press: 1-78.
CAPMAS. 1994a. Egypt: Consolidated Accounts, 1980-90. Cairo: Government
Planning Bureau.
CAPMAS. 1994b. Egypt: Input-Output Tables 1989-90. Cairo: Government Planning Bureau.
De Melo, J. and S. Robinson. 1989. Product Differentiation and the Treatment of
Foreign Trade in Computable General Equilibrium Models of Small Economies.
Journal of International Economics 27: 47-67.
Harrison, G. W., T. F. Rutherford and I. Wooton. 1989. The Economic Impact of
the European Community. American Economic Review 79: 288-294.
-------- . 1993. An Alternative Welfare Decomposition for Customs Unions. Canadian Journal of Economics 26: 961-968.
Hoekman, B. and S. Djankov. 1996. The European Union’s Mediterranean Free
Trade Initiative. The World Economy 19: 387-407.
Hoekman, B. and D. E. Konan. 2000. Rents, Red Tape, and Regionalism: E：
conomic Effects of Deeper Integration. In Catching up with the Competition:
Trade Policy Challenges and Options for the Middle East and North Africa, eds.
B. Hoekman and J. Zarrouk. Ann Arbor: University of Michigan Press: 171-206.
Hoekman, B., D. E. Konan and K. E. Maskus. 1998. Economic Incentives and Effects. In Building Bridges: An Egypt-US Free Trade Agreement, eds. A. Galal
and R. Lawrence. Washington D.C.: Brookings Institution Press: 79-109.
Konan, D. E. and K. E. Maskus. 1997. A Computable General Equilibrium Analysis of Egyptian Trade Liberalization Scenarios. In Regional Partners, Global
Markets: Limits and Possibilities of the Euro-Mediterranean Agreements, eds. A.

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Galal and B. Hoekman. London: Center for Economic Policy Research in Europe(CEPR) and Washington D.C.: Brookings Institute Press: 156-177.
–––– . 2000a. The Relation between Partner Trade Shares and Domestic Welfare in
a Preferential Trade Agreement with Differentiated Products. manuscript, University of Hawaii.
–––– . 2000b. Joint Trade Liberalization and Tax Reform in a Small Open Economy: The Case of Egypt. Journal of Development Economics 61(2): 365-392.
Lipsey, R. 1970. The Theory of Customs Unions: A General Equilibrium Analysis.
London: Weidenfelt and Nicolson.
Lofgren, H. 1994. Elasticity Survey. Cairo: Center for Egyptian Studies.
Maskus, K. E. and D. E. Konan. 1997. Trade Liberalization in Egypt. Review ofDevelopment Economics 1: 275-293.
Panagariya, A. 1996. The Free Trade Area of the Americas: Good for Latin America? The World Economy 19: 485-515.
Rutherford, T. F., D. G. Tarr and E. E. Rutstrom. 1997. Morocco’s Free Trade
Agreement with the EU: A Quantitative Assessment. Economic Modelling 14:
237-269.
Schiff, M. 1997. Small is Beautiful: Preferential Trade Agreements and the Impact
of Country Size, Market Share, and Smuggling. Journal of Economic Integration
12: 359-387.
Vousden, N. 1990. The Economics of Trade Protection. Cambridge: Cambridge
University Press.
World Bank. 1995. Egypt: Into the Next Century: Volume. 1, Macroeconomic
Framework. Washington: The World Bank.

14

Is Free Trade Goodfor the Environment?
Werner Antweiler, Brian R. Copeland,and M. Scott Taylor*

The debate over the role international trade plays in determining environmental outcomes has at times generated more heat than light. Theoretical work has been successful in identifying a series of hypotheses linking
openness to trade and environmental quality, but the empirical verificationof these hypotheses has seriously lagged. Foremost among these is the pollution haven hypothesis that suggests relatively low-income developing
countries will be made dirtier with trade. Its natural alternative, the simple
factor endowment hypothesis, suggests that dirty capital-intensive processes
will relocate to the relatively capital-abundant developed countries withtrade. Empirical work by James A. Tobey (1990), Gene M. Grossman andAlan B. Krueger (1993), and Adam B. Jaffe et al. (1995) cast serious
doubt on the strength of the simple pollution haven hypothesis because
they find that trade flows are primarily determined by factor endowment
considerations and apparently not by differences in pollution abatement
costs. Does this mean that trade has no effect on the environment?
This paper investigates how “openness” to international markets affects
pollution levels to assess the environmental consequences of international
trade. We develop a theoretical model to divide trade’s impact on pollution
into scale, technique, and composition effects and then examine this theory
using data on sulfur dioxide concentrations from the Global Environment* An earlier version of this paper was circulated under the title, “Trade and theEnvironment: Theory and Empirical Results” (August 1997). We express ourthanks to, without implicating, P. Beaudry, D. Green, H. Emery, G. Heal, K. Head,
K. Scholz, J. McGregor, seminar participants at numerous universities, the NBER
Summer Institute Workshop on Public Policy and the Environment, the NBER
Trade, Resources, and the Environment conference, and the Research Institute for
Economics and Business in Kobe, Japan. Financial support was provided by the
SSRHC, the Hampton Fund, and the NSF.
307

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Werner Antweiler, Brian R. Copeland, and M. Scott Taylor

Monitoring Project. The decomposition of trade’s effect into scale, technique, and composition effects has proven useful in other contexts [seeGrossman and Krueger (1993); Copeland and Taylor (1994, 1995)] andhere we move one step forward to provide estimates of their magnitude.
We find that international trade creates relatively small changes in sulfur
dioxide concentrations when it alters the composition, and hence the pollution intensity, of national output. Combining this result with our estimatesof scale and technique effects yields a somewhat surprising conclusion: if
trade liberalization raises GDP per person by 1 percent, then pollution concentrations fall by about 1 percent. Free trade is good for the environment.1
We obtain this conclusion by estimating a very simple model highlighting the interaction of factor endowments and income differences in determining the pattern of trade. Our approach, although relatively straightforward, is novel in four respects. First, by exploiting the panel structure ofour data set, we are able to distinguish empirically between the negativeenvironmental consequences of scalar increases in economic activity––thescale effect––and the positive environmental consequences of increases inincome that call for cleaner production methods––the technique effect. Thisdistinction is important for many reasons.2 Grossman and Krueger (1993)
interpret their hump-shaped “Kuznets curve” as reflecting the relative
strength of scale versus technique effects, but they do not provide separate
estimates of their magnitude. Our estimates indicate that a 1 percent increase in the scale of economic activity raises pollution concentrations by
0.25 to 0.5 percent for an average country in our sample, but the accompanying increase in income drives concentrations down by 1.25−1.5 percent
via a technique effect.
Second, we devise a method for determining how trade-induced changes
in the composition of output affect pollution concentrations. Many empirical studies include some measure of openness to capture the impact trade
has in altering the composition (and hence the cleanliness) of national output, but there is very little reason to believe that openness affects the composition of output in all countries similarly. Both the pollution haven hypothesis and the factor endowment hypothesis predict that openness totrade will alter the composition of national output in a manner that depends on a nation’s comparative advantage.
l. Free trade appears to lower sulfur dioxide concentrations for an average country in our sample, but may of course worsen the environment through other channels. Our evidence is specific to sulfur dioxide; however, sulfur dioxide emissions
are highly correlated with other airborne emissions.
2. For example, income transfers across countries raise national income but not
output, whereas foreign direct investment raises output more than national income.
To evaluate the environmental consequences of either we need separate estimatesof technique and scale effects.

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Is Free Trade Good for the Environment?

For example, under the pollution haven hypothesis, poor countries get
dirtier with trade, whereas rich countries get cleaner.3 As a result, simply
adding openness to trade as an additional explanatory variable for pollution(across a panel of both rich and poor countries) is unlikely to be fruitful.
Instead we look for trade’s effect by conditioning on country characteristics. We find that openness conditioned on country characteristics has ahighly significant, but relatively small, impact on pollution.
Third, we show how to combine economic theory with our estimates ofscale, composition, and technique effects to arrive at an assessment of theenvironmental impact of freer trade. Grossman and Krueger’s influential
study of NAFTA presented an argument based on the relative strength ofthese same three effects, but their estimate of the composition effect oftrade was obtained from methods and data unrelated to their complementary work estimating the relative strength of scale and technique effects.
Moreover, their evidence on composition effects was specific to the situation of Mexico. Here we estimate all three effects jointly on a data set
that includes over 40 developed and developing countries.
Finally, our approach forces us to distinguish between the pollution consequences of income growth brought about by increased openness fromthose created by capital accumulation or technological progress. We findthat income gains brought about by further trade or neutral technologicalprogress tend to lower pollution, whereas income gains brought about by
capital accumulation raise pollution. The key difference is that capital accumulation necessarily favors the production of pollution-intensive goods,
whereas neutral technological progress and further trade do not. One immediate implication of this finding is that the pollution consequences of
economic growth are dependent on the underlying source of growth.4
The theoretical literature on trade and the environment contains many
papers in which pollution policy differences across countries drive
pollution-intensive industries to countries with lax regulations.5 One criticism of these papers is that, although they are successful in predicting
trade patterns in a world where policy is fixed and unresponsive, their results may be a highly misleading guide to policy in a world where environmental protection responds endogenously to changing conditions.
Empirical work by Grossman and Krueger (1993) suggests that it is im3. That is, the composition effect of trade for poor countries makes them dirtier,whereas the composition effect for rich countries makes them cleaner. The full effect of trade may be positive even for poor countries, depending on the strength of
the technique and scale effects. See, for example, Proposition 2.
4. Another more speculative implication of our results is that pollution concentrations should at first rise and then fall with increases in income per capita, if
capital accumulation becomes a less important source of growth as development
proceeds.
5. For example, Rüdiger Pethig (1976), Horst Siebert et al. (1980), and Martin C.
McGuire (1982) all present models where the costs of pollution-intensive goods arelower in the region with no environmental policy.

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Werner Antweiler, Brian R. Copeland, and M. Scott Taylor

portant to allow policy to change endogenously with income levels, and in
our earlier work (Copeland and Taylor (1994, 1995)) we investigated how
income-induced differences in pollution policy determine trade patterns.
Although this earlier work produced several insights, it ignored the role
factor abundance could play in determining trade patterns.
In contrast, the model we develop here allows income differences andfactor abundance differences to jointly determine trade patterns. The model
contains as one limiting case the canonical Heckscher-Ohlin-Samuelson(HOS) model of international trade and as another limiting case a simple
pollution haven model. Considering these two motivations for trade is especially important in an empirical investigation because many of the mostpolluting industries are also highly capital intensive.6 Moreover, it allows
us to examine whether changes in dirty goods production brought about bytrade is better explained by factor abundance motives or by pollution haven motives arising from an unequal distribution of world income.
The empirical literature in this area has progressed in three distinct ways.
One influential group of studies asks: “How does economic growth affectthe environment?”. This literature was initiated by early work by Grossman
and Krueger (1993, 1995) and has since produced a sizable and fast growing empirical literature examining what has come to be known as the “Environmental Kuznets curve.”7 Many of these studies also investigate therole of trade by adding a measure of openness as an additional regressor.
The defining feature of this literature is its lack of explicit theory. Although the results from these studies are often interpreted within the context of scale, composition, and technique effects, they do not provide separate estimates of their magnitudes.
Our work is most closely related to this branch of the literature, but differs in that we employ an explicit theoretical model to guide our estimation; we present separate estimates of scale, composition, and techniqueelasticities; and we provide a methodology for adding up these effects toassess the environmental implications of freer trade. Despite the fact that
this earlier work lacks a formal theory, some of their conclusions receive
support in our work. Most notably, Grossman and Krueger’s (1993) studyof NAFTA had at its core the argument that technique effects offset scaleeffects––at least for Mexico––and that the composition effect created byfurther United States-Mexico trade was likely to be driven more by factor
endowment considerations than by differences in environmental regulation.
Our work supports these conclusions: income effects appear to be eco6. See Muthukumara Mani and David Wheeler (1997) and Werner Antweiler etal. (1998), Appendix Section B.l, for evidence linking capital intensity and pollution intensity.
7. Some authors refer to it as the Grossman-Krueger-Kuznets Curve. Other early
contributions to this literature are Thomas M. Selden and Daqing Song (1994) and
Nemat Shafik (1994).

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Is Free Trade Good for the Environment?

nomically and statistically significant, and the trade-induced composition
effects are not driven by differences in pollution regulations.
There is a second group of studies examining the link between the costsof pollution abatement cost and trade flows. This approach was pioneeredby Tobey (1990) and was employed in the context of the NAFTA agreement by Grossman and Krueger (1993).8 This branch of the literature asksa slightly different question: “How do environmental regulations affecttrade flows?”. Nevertheless some of their results are also relevant to ourwork. For example, a common result from these studies is that measures ofenvironmental stringency have little effect on trade flows. This result immediately casts doubt on the pollution haven hypothesis, which holds that
trade in dirty goods primarily responds to cross-country differences inregulations. Although our work is quite different in approach and method,
we too find little support for the pollution haven hypothesis. We do not infer from this, however, that the cost of regulations does not matter to tradeflows; instead, we suggest it is because other offsetting factors more thancompensate for the costs of tight regulation in developed economies.
Finally, there are those studies that employ either the U.S. Toxic Release
Inventory, U.S. emission intensity data, or simple rules to categorize goods
industries as dirty or clean, to construct measures of the toxic (or pollution) intensity of production and trade flows. Work along these lines includes Patrick Low and Alexander Yeats (1992), Robert E. B. Lucas et al.
(1992), and Mani and Wheeler (1997). The strength of this branch of theliterature is its broad cross-country coverage; its weakness is that this coverage arises from the construction of data under various assumptions regarding the similarity of emission intensities across countries. This literature typically asks: “How has the pollution intensity of exports or production changed over time?” By comparing the answer to this question acrosscountries differing in development level, income, or trade stance, theauthors hope to identify links between various policy options, country
characteristics, and environmental outcomes. Although this work is useful in documenting trends in the pollution intensity of output and trade, itcannot answer why these trends exist. Our work differs from this methodby using theory to identify those factors we believe to be crucial to environmental outcomes, and by using regression analysis to hold all else equal
when evaluating the links between country characteristics and environmental outcomes.
The overall impression one gets from this literature is that, even though
there are many interesting findings, a consensus view does not exist––andthe path to building such a consensus view is unclear. The unsettled natureof the literature arises, at least in part, because existing studies are ham8. Arik Levinson (1996) reviews this work.

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Werner Antweiler, Brian R. Copeland, and M. Scott Taylor

strung by the lack of a well-defined theory. This naturally makes inference
difficult. Additional difficulties arise because good data on pollution levels
are scarce, and even the best data reflect not only anthropogenic influences
but also the little-understood natural processes of dispersion and absorption.
As a consequence, our simple first-generation pollution and trade model
carries a heavy burden in providing us with the structure needed to isolate
and identify the implications of international trade. Although this is a concern, we suggest that earlier empirical investigations failed to find a strong
and convincing link between environmental outcomes and freer trade precisely because they lacked a strong theoretical under-pinning. With a more
complete theoretical framework to guide us, we are able to look in the“right directions” for trade’s effect. Moreover, our simple pollution
demand-and-supply model may play a useful role in focusing future efforts
in this area.
The rest of the paper is organized as follows. In Section 1 we develop a
relatively simple general equilibrium model of trade to determine how afall in trade barriers affects pollution levels. In Section 2 we then describe
our strategy for dealing with econometric difficulties and present our estimating equation. In Section 3 we present our empirical results. Section 4
concludes. Appendices A and B contain proofs of propositions and a description of our data. An additional Technical Appendix, available on request from the authors, contains further supporting materials.

1．
TheoryA. The Model
A population of N agents lives in a small open economy that produces
two final goods, X and Y, with two primary factors, labor L and capital K.
Industry Y is labor intensive and does not pollute. Industry X is capital intensive and generates pollution as a by-product. We assume constant returns to scale, and hence the production technology for X and Y can be
described by unit cost functions c X(w, r) and c Y(w, r). Let Y be the numeraire, and denote the relative price of X by p. Because countries differ
in their location, proximity to suppliers, and existing trade barriers, domestic prices will not be identical to world prices. Accordingly we write(1)p = β p w,

where β measures the importance of trade frictions and p w is the common
world relative price of X. Note β > 1 if a country imports X and β < 1 if

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Is Free Trade Good for the Environment?

a country exports X.9
Pollution Abatement.––We denote pollution emissions by Z. Pollution is
generated by X production, but firms have access to an abatement technology. Abatement is costly but uses the same factor intensities as all otheractivities in the X industry; hence, we simply treat units of X as inputs
into abatement. If a firm has a gross output of x units, and allocates xa
units to abatement, then its net output is xn = x(1 − θ ), where θ = xa/x isa measure of the intensity of abatement. If pollution is proportional to output and abatement is a constant returns activity, then we can write pollution emissions as(2)

z = e(θ ) x,

where e(θ ) is emissions per unit of X produced and is decreasing in θ .10
We assume abatement is worthwhile [e′(0) =−∞］，but with physical limits [e(1) > 0].
The government uses pollution emission taxes to reduce pollution. Given
the pollution tax τ , the profits π x for a firm producing X are given byrevenue less factor payments, pollution taxes, and abatement costs. Using(1) and our definition of θ , we may write profits succinctly as(3)π x = p Nx − wLx − rKx,

where p N= p(l −θ )−τ e(θ ) is the net producer price for gross output. Because of constant returns, the output of an individual firm is indeterminate,
but for any level of output, the first-order condition for the choice of θ
implies(4)p = −τ e′(θ ).

Hence, we have θ = θ (τ /p) with θ ′> 0 and we can write emissions perunit output as
9. For example, let v be the level of iceberg transport costs (that is, v < 1 is thefraction of the good that arrives at the destination when a unit is exported). Then if
the good is exported from home, we have p d = vp w, and if the good is imported,
we have p d = p w/v. Freer trade (an increase in v) raises p d if X is exported andlowers p d if X is imported.
10. When x units of gross output are produced, and xa units are devoted toabatement, emissions are given by E (xa, x). Given our assumptions, E is decreasing in xa, increasing in x, strictly convex in xa, and linearly homogeneous in x andxa together. Convexity in abatement inputs follows from diminishing returns to thevariable factor and implies increasing marginal abatement costs. Linear homogeneity follows from constant returns. Using the linear homogeneity of E , we thenwrite E (xa, x) = e(θ )x.

314

Werner Antweiler, Brian R. Copeland, and M. Scott Taylore = e(τ /p),(5)

where e′< 0. The production side equilibrium conditions are simply (2),(4), and the standard zero profit and full employment conditions:(6)p N = c X ( w, r ), 1 = cY ( w, r ),K = crX x + crY y , L = cwX x + cwY y.

Consumers.––For most of our analysis, consumers differ only in theirpreferences over pollution. There are two groups in society: N g Green consumers who care greatly about the environment (Greens); and N b= N −N g
Brown consumers (Browns) who care less about the environment. Eachconsumer maximizes utility, treating pollution as given. For simplicity, we
write the indirect utility function of a consumer in the ith group as(7)⎛G/ N⎞iV i ( p , G / N , z ) = u⎜
⎟ −δ z⎝ ρ ( p) ⎠!

for i = {g, b} and where δ g > δ b 0, G is national income (so G /N is per
is increasing and concave.
capita income), ρ (p) is a price index, andImplicit in (7) is the assumption of homothetic preferences over consumption goods. Pollution is a pure public bad, but Greens suffer a greater disutility than Browns. It is now convenient to define real per capita income as
I = [G /N ]/ ρ (p) and rewrite indirect utility as simply u(I ) − δ iz .

!

Government.––We model the policy process very simply. We assume
the government chooses a pollution tax to maximize a weighted sum ofeach group’s preferences. It solves
(8)

[

]

max N λV g + (1 − λ )V b ,τwhere λ is the weight put on Greens. λ may vary across governments.11
We introduce this formulation to allow for the realistic possibility that government behavior varies across countries (perhaps across Communist andnon-Communist countries), while allowing for an endogenous link between
pollution policy and economic conditions.
The optimal pollution tax maximizes the weighted sum of utilities in (8)subject to private sector behavior, production possibilities, fixed world
prices, and fixed trade frictions (see, however, Section 3, subsection E, for
11. For example, if the government is utilitarian, then λ = N g/N ; if the government is controlled by the Greens, λ = 1, and if controlled by Browns, λ = 0.

315

Is Free Trade Good for the Environment?

a consideration of optimal tariffs). Private sector behavior can be represented by a standard GNP function giving maximized private sector (net oftax) revenue as R (p N, K , L).12 Overall income is private sector revenue
plus rebated taxes G = R (p N, K , L) + τ z. The first-order condition yieldsu ′( I )dIdz− λδ g + (1 − λ )δ b
= 0.
dτ
dτ

[

]

With world prices fixed we have
dI
1 ⎡
dp N
dz ⎤
=
+z +τ
⎢Rp N
⎥
dτ Nρ( p) ⎣
dτ
dτ ⎦
=

τ dz
.
Nρ( p) dτ

Rearranging our first-order condition now yields an amended Samuelson
rule:
(9)

[

]

τ = N λMD g ( p, I ) + (1 − λ ) MD b ( p, I ) ,iwhere MD i(p, I ) = δ iρ (p)/u′
is marginal damage per person, and MD I > 0
given the concavity of the utility function. Simplifying allows us to rewrite(9) slightly as:
(10)

τ =T

!(p, I ).

We refer to T = λ N δ g + (1 − λ ) N δb as “country type” and Tφ (p, I ) as
effective marginal damage (MD). Pollution policy therefore varies witheconomic conditions and government type.
B. Pollution Demand and Supply
Our model yields a relatively simple reduced form linking pollution
emissions to a short list of (predetermined) economic factors. To isolate
the role of trade, it is important to understand how these different economic factors affect the demand for, and supply of, pollution. To do so,
we use the terminology of scale, composition, and technique effects. We
start by noting the private sector’s demand for pollution is implicitly defined by (2). To rewrite this demand in a more convenient form for empirical work, we define an economy’s scale as the value of national output at
12. See Avinash K. Dixit and Victor Norman (1980) and Alan D. Woodland(1982).

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Werner Antweiler, Brian R. Copeland, and M. Scott Taylor

base-year world prices. In obvious notation, our measure of scale S is(11)

S = p x0 x + p y0 y.

Choosing units so that base-year prices are unity, we now write pollution
emissions as(12)

z = ex = eϕS ,where is the share of X in total output. Equation (12) provides a simple
decomposition: pollution depends on the pollution intensity of the dirty industry e(θ ), the relative importance of the dirty industry in the economy ,and the overall scale of the economy S . In differential form,zˆ = Sˆ + ϕˆ + eˆ,(13)where hats denote percent change. The first term is the scale effect. It
measures the increase in pollution generated if the economy were simply
scaled up, holding constant the mix of goods produced and production
techniques e(θ ). For example, if all endowments of the economy grew by
10 percent, and if there was no change in the composition of output oremission intensities, then we should expect to see a 10 percent increase inpollution. The second term in (13) is the composition effect. If we hold thescale of the economy and emissions intensities constant, then an economy
that devotes more of its resources to producing the polluting good will pollute more. Fina1ly, we have the technique effect, captured by the last term.
All else constant, an increase in the emission intensity will increase pollution.
We will use a quantity index of output to measure the scale effect. Because a change in prices creates opposing composition and technique effects, however, it is necessary to divide each into its more primitive determinants. Using (6) we can solve for the share of X in total output as afunction of the capital/labor ratio κ = K /L, the net producer price p N andbase-year world prices (suppressed here). That is, the composition of output is = (κ , p N), and we have the composition effect given by(14)

ϕˆ = ε ϕKκˆ + ε ϕp pˆ N ,where the elasticity of with respect to κ and p N are both positive. Next
differentiate p N and employ (1) and (4) to find

(15)

(

)

pˆ N = βˆ + pˆ w (1 + a ) − aτˆ ,317

Is Free Trade Good for the Environment?

where a = e(θ )τ /p N. Similarly, using (1) and (5) we find()

eˆ = ε e , p / τ βˆ + pˆ w − τˆ ,(16)

where the elasticity of emission intensity with respect to p/ τ is positive.13
Combining (13)−(16) we obtain a decomposition of the private sector’s demand for pollution:

(17)

[

]

zˆ = Sˆ + ε ϕ , Kκˆ + (1 + a )ε ϕ , p + ε e , p / τ βˆ

[

]

[

]

+ (1 + a )ε ϕ , p + ε e , p / τ pˆ − aε ϕ , p + ε e , p / τ τˆ .
w

All elasticities are positive. If we draw this derived demand in {z, τ }space, then (17) shows that an increase in scale, capital abundance, or theworld price of dirty goods shifts the pollution demand curve to the right. A
movement of β toward 1 captures a reduction in trade frictions. However,
because β is greater than 1 for a dirty good importer this implies ˆ < 0;and because β is less than 1 for a dirty good exporter, a reduction in trade
frictions implies ˆ > 0. Therefore, a reduction in trade frictions shifts thepollution demand curve to the right for a dirty good exporter, but to theleft for a dirty good importer.
Increases in the pollution tax reduce the quantity demanded of pollution
through two channels. First they lower the demand for pollution by raisingabatement and lowering the emissions per unit of X produced. This is captured by the elasticity ε e, p/τ > 0. Second, higher pollution taxes lower the
producer price of X and induce a shift in the composition of output thatlowers X output for any given emissions intensity. The strength of this effect depends on the importance of pollution taxes in the net producer price(a) and the elasticity of with respect to a change in producer prices, ε !,p.
Pollution supply is in effect given by government policy that sets theprice for polluting. From (1) and (10) we obtain a decomposition of pollution supply:

!

!

(18)

τˆ = Tˆ + ε MD , p βˆ + ε MD , p pˆ w + ε MD , I Iˆ,

where ε MD, p > 0 and ε MD, I > 0. If we draw (18) in {z, τ } -space, then increases in real income, relative prices, or country type shift the pollution
supply curve upward. For example, if Greens are given a greater weight insocial welfare, or become a larger fraction of the population over time,then policy becomes more stringent and pollution supply shifts upward.
Similarly, an increase in real income will increase the demand for environ13. It is convenient to define elasticities so that they are positive. Note that e isdecreasing in τ /p, and therefore increasing in p/ τ .

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Werner Antweiler, Brian R. Copeland, and M. Scott Taylor

mental quality and shift up the pollution supply curve. An increase in theworld relative price of X makes consumption of market goods more expensive relative to environmental protection. This creates a pure substitution
effect toward more environmental protection, reflected in (18) by ε MD,p > 0.
As a result pollution supply shifts up. An identical substitution effect is atwork when trade frictions fall.
A Reduced Form.––Combining supply in (17) and demand in (18)yields a simple reduced form linking pollution emissions to a small set of
economic factors:(19)zˆ = π 1 Sˆ + π 2κˆ − π 3 Iˆ + π 4 βˆ + π 5 pˆ w − π 6 Tˆ ,where all π i are positive, and none of the right-hand-side variables are determined simultaneously with emissions. Two features of (19) warrant further comment. First, because a change in domestic prices shifts pollution
supply and demand in opposing directions, it is not obvious that π 4 and π 5
are positive. We evaluate this claim more formally in Proposition 1 below.
Second, we claim “a reduced form” links emissions to our economic factors, despite the fact that emissions and these same factors are clearly endogenous variables. In our framework, emissions are determined endogenously, but recursively. As a result, the factors on the right-hand side of(19) are not simultaneously determined with or by the level of emissions.14
This feature of our simple general equilibrium model has the benefit ofproviding us a simple, straightforward, and parsimonious reduced form
linking pollution emissions to economic determinants. We evaluate ourfirst claim below.
The Trade-Induced Composition EffectProposition 1．Consider two economies that differ only in their trade frictions: (i) if both countries export the polluting good, then pollution ishigher in the country with lower trade frictions; (ii) if both import the polluting good, then pollution is lower in the country with lower trade fric14. To see this, note that R (p N, K, L) + τ z = p(l − θ )x + y, which is independent of z. Next, note that (4), (6), and (10) solve for I , τ , and θ , given world
prices. With τ , θ , and p determined, p N is given. Outputs are determined by p N,
and z follows from z = e(θ ) x. This result follows for two reasons. First, a society
may decide to spend some of its potential income on improving environmental
quality and the remainder on consumption goods but higher pollution does notcause higher real income. Second, because marginal damage is independent of z,
the equilibrium level of emissions does not affect the pollution tax. As a result, achange in emissions does not cause second-order changes in the composition of
output or our measures of scale and income. As a result of these two features, real
income, scale, and the pollution tax are set simultaneously, whereas emissions are
set recursively.

!

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tions.
Proof
See Appendix A.
Proposition 1 isolates the trade-induced composition effect. The sign ofthis composition effect differs across countries. For an exporter of the polluting good, β rises with freer trade and this raises the relative price of thedirty good X. This shifts a dirty good exporter’s pollution demand curve tothe right and shifts its pollution supply curve up. Pollution demand shifts
out for two reasons: the composition of national output shifts toward X;
and emission intensities rise because abatement inputs are now more costly.
The shift in the pollution supply curve dampens this increase in pollution
as the pure substitution effect of the goods price increase leads the government to raise the pollution tax. However, the direct demand-side effects
swamp the substitution effect in supply, and pollution rises.15 Consequently,
holding all other determinants of pollution supply and demand constant,emissions must rise. This increase in emissions represents the tradeinduced composition effect for a dirty good exporter.
In contrast, β falls with freer trade for an importer of the polluting good.
This raises the relative price of the clean good Y, and again shifts both
pollution demand and supply. Demand-side determinants dominate andemissions fall. This reduction in emissions represents the trade-induced
composition effect for a clean good exporter.
Proposition 1 therefore implies that, if we look across all countries andhold other determinants of emissions constant, we should not expect tofind openness per se related in any systematic way to emissions. Although
Proposition 1 is useful, it is limited in two respects. First, although it isolates the trade-induced composition effect, any fall in trade frictions willalter the scale of output and income per capita of the liberalizing country
as well. Therefore to account for the full environmental impact of a fall intrade frictions we must also account for the accompanying scale and technique effects. Proposition 1 captures the partial effect of trade liberalization; an overall assessment needs the full effect. Second, the results fromthe proposition are conditional on trade patterns, but the proposition itself
is silent on the determinants of trade patterns. We treat each of these issues
in turn below.
The Full Impact of Openness.––To find the full impact of a change intrade frictions we must account for the change created in real incomes, thescale of output, and its composition. Differentiate (12) with respect to β ,15. To see this, note that the increase in τ is less than proportional to the increase in β , because the increase in τ induced by β is a pure substitution effect,
which is proportional to the share of X in consumption (which is less than one).
This ensures both that emission intensity e rises, and that the share of X in production rises. Details are in the Appendices.

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holding world prices, country type, and factor endowments constant, to
find
(20)

dz β
dS β
dI β
= π1
−π3
+ π 4.
dβ z
dβ S
dβ I

A fall in trade frictions produces a scale effect, a technique effect, and thetrade-induced composition effect, discussed previously. To understand how
these three effects interact to determine the environmental consequences oftrade, we employ Figure 1.
In the top panel of Figure 1 we depict the production response of a dirty
good exporter to a fall in trade frictions. In the bottom panel we depict thepollution consequences of these changes. Before the reduction in trade frictions, production is at point A, the world price is p w, and the net price isp N. We have assumed this country is an exporter of the dirty good andtherefore has consumption at a point to the northwest of A along the economy’s budget constraint (not drawn). Note that the value (in world prices)of domestic output at A measures this economy’s scale. In the bottom
panel we depict the equilibrium pollution level both before and after thefall in trade frictions. Recall that z = e(θ )x. Hence when production is at
A, and emissions intensity is e(θ A), pollution is given by z A.
When trade frictions fall the domestic price approaches the world priceand production moves to point C at the new producer price of p N. At C,
real income is higher and there is a change in the techniques of production.
The emissions intensity falls to e(θ C) and overall pollution falls to z C. Our
methodology divides the movement from z A to z C into three component
parts. First, holding both the scale of the economy and the techniques of
production fixed, trade creates a change in the composition of output givenby the movement from A to B. Corresponding to this movement is the in-

Figure 1. A Dirty Good Exporter

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Is Free Trade Good for the Environment?

crease in pollution from z A to z B in the bottom panel. This is the tradeinduced composition effect isolated in Proposition 1.
The movement in the top panel from point B to point C is the scale effect. The increase in pollution from z B to z S in the bottom panel gives thepollution consequences of this scale effect. Finally, note that the value of
output measured at world prices rises because of trade and this real income
gain (indirectly) creates the technique effect shown in the bottom panel.
The technique effect is the fall in pollution from z S to z C as producers
switch to cleaner techniques with lower emissions intensity.
In total the diagram shows that trade liberalization for a dirty good exporter leads to less pollution if the composition and scale effects are overwhelmed by the technique effect. Because this is only a possibility, andnot a necessity within our model, we formalize our results in Proposition 2.
Proposition 2. Consider a small reduction in trade frictions for our small
open economy, then:i if the small open economy exports the clean good, the full effect of thistrade liberalization is to lower pollution emissions;ii if the small open economy exports the dirty good and the elasticity of
marginal damage with respect to income is below one, then the full effect of this trade liberalization is to raise its pollution emissions;iii if the small open economy exports the dirty good and the elasticity of
marginal damage with respect to income is sufficiently above one, thenthe full effect of this trade liberalization is to lower its pollution emissions.

!
!
!

Proof
See Appendix A.
The first part of the proposition concerns dirty good importers. For dirty
good importers the trade-induced composition effect is negative and because X production falls, the sum of composition and scale effects mustalso be negative.16 Consequently, pollution emissions will fall for a dirty
good importer. For a dirty good exporter, both the trade-induced composition effect and the scale effect are positive. Pollution demand shifts rightfrom these two forces, and Proposition 2 indicates that if the policy response is sufficiently weak (an elasticity of marginal damage with respect
to income less than one) emissions will rise. That is, the upward shift inpollution supply is overwhelmed by the demand shifts. Alternatively, if theelasticity of marginal damage is sufficiently strong, then emissions will fallas the technique effect dominates. The full effect of a trade liberalization
16. This is a product of our two-good model. With many polluting goods thescale effect may dominate the composition effect, leading to a rise in pollution
from these two sources.

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differs from the partial effect because of two additional effects, and because these new effects can be strong enough to overwhelm the composition effect.
C. Adding up Scale, Composition, and Technique Effects
The amount of information required to implement an adding-up exercise
akin to (20) is great. In our empirical work we develop estimates for π 1,
π 3, and π 4. But even with these estimates in hand we are faced with disentangling the effects of trade liberalization on income growth from all otherpotential sources. Because attempts to link trade to growth and income levels are the subject of an already large and somewhat controversial literature,
we do not attempt to measure trade’s effect on GDP (dS/dβ ) or GNP perperson (dI/dβ ). Instead we employ economic theory to add up our estimated scale, composition, and technique effects. Taking factor endowments
as fixed, a lowering of transport costs or trade barriers raises the value ofdomestic output and real income in a small open economy. The value of
output and income rise by the same percentage and this creates both scale
and technique effects.17 Therefore, we can simplify (20) slightly and write

(21)

dz β
dI β
= [π 1 − π 3 ]+ π 4.
dβ z
dβ I

In some circumstances we can add up these three effects to come to an
overall assessment of trade without knowledge of trade’s effect on income
or scale. For example, consider a dirty good exporter. Note that dI/dβ is
positive because an increase in β represents lower trade frictions. If wefind π 1 > π 3 and π 4 > 0, then we conclude that trade liberalization raises
pollution for a dirty good exporter: scale effects dominate technique andthe trade-induced composition effect is positive. Under these same circumstances, trade liberalization would have an ambiguous effect on emissions
for a clean good exporter. Consequently, even to implement our more limited adding-up exercise, it is necessary to ask: who exports dirty goods andwhy?
Pollution Haven versus Factor Abundance Motives.––In our model comparative advantage is primarily a function of relative factor abundance andrelative incomes. Although limiting cases of our model reflect only pollution haven motives or pure factor endowment motives, in general we expect both determinants of comparative advantage to matter. To investigate
17. If GNP differs from GDP because of receipts or payments from abroad, thenwe would need to correct for the (generally small) share of these payments in GNP.

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Is Free Trade Good for the Environment?

further we solve for autarky prices. Let RD (p) denote the demand forgood X relative to good Y. Then the relative price of good X is determined by the intersection of the (net) relative supply and demand curves(22)

RD (p) = (1 − θ ) χ (κ , p N),

where χ = x/y is determined from (6), and net relative supply is (1 − θ )χ.
Totally differentiating, using (15), (16), and (18), and rearranging gives anexpression linking autarky prices to real income and endowments:

(23)

θ
⎡
⎤
ε MD , I ⎢aε χ , P N +ε θ ,τ / p ⎥ Iˆ − ε χ ,κ κˆ
1−θ
⎣
⎦
pˆ =
,
∆

where all elasticities and ∆ are positive. Equation (23) shows that in general, the pattern of trade is determined by both factor abundance andincome-driven differences in pollution policy. For example, unless both thedirty and clean sectors use identical factor proportions then εχ ,κ is not zeroand capital abundance matters to comparative advantage. Similarly, if theenvironment is a normal good, then ε MD,I is nonzero and real income matters as well.
The Role of Factor Endowments.––Standard factor endowment theories
predict capital abundant countries export capital-intensive goods. In ourmodel this need not be true because pollution policy can reverse this pattern of trade. Nevertheless, capital abundance is still a key determinant ofcomparative advantage in our model. Because X is relatively capital intensive, an increase in κ , holding all else constant, increases Home’s relative
supply of X, and lowers Home’s autarky relative price of X. Using (23)
we obtain p̂ < 0 because εχ ,κ > 0. All else equal, an increase in the abundance of the factor used intensively in the pollution-intensive sector increases the likelihood that a country will be an exporter of pollutionintensive goods. We can show that if the country is sufficiently capitalabundant, it must export the capital intensive (polluting) good:
Proposition 3. Suppose the world price p w is fixed. Then, for a given levelof real income I, there exists a κ such that if κ > κ , then Home exports
X. Moreover, for such a country, the trade-induced composition effect will
be positive.

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Werner Antweiler, Brian R. Copeland, and M. Scott Taylor

Proof
See Appendix A.
The Role of Income Differences.––An alternative theory of trade patterns
is the pollution haven hypothesis. According to this view, poor countries
have a comparative advantage in dirty goods because they have lax pollution policy, and rich countries have a comparative advantage in clean
goods because of their stringent pollution policy.18 This result can be obtained as a special case of our model: if all countries have the same relative factor endowments, but differ in per capita incomes, then richer countries will have stricter pollution policy and this will lead to a comparativeadvantage in clean goods. Using (23) we obtain p̂ > 0 whenever Iˆ > 0.
When countries differ in factor endowments and income levels, we canshow that if the country is sufficiently rich, it must export the laborintensive (clean) good.
Proposition 4. Suppose the world price p w is fixed and there exists an εsuch that ε MD,I > ε > 0. Then, for a given level of the capital/labor ratio
κ , there exists an I, such that if I > I, then Home exports Y. Moreover, forsuch a country, the trade-induced composition effect will be negative.
Proof
See Appendix A.
From Theory to Estimation.––Proposition 1 contains a very simple message: comparative advantage matters. If we compare countries with similar
incomes and scale, openness should be associated with higher pollution in
dirty good exporters and lower pollution in dirty good importers. Therefore
to isolate the trade-induced composition effect, we must condition on
country characteristics. This observation begs three questions: how are weto measure openness, what country characteristics should we use, and how
should we condition on these characteristics?
Various measures of “openness” exist. We need a measure with bothtime-series variation and a wide cross-country coverage. In our theory alowering of trade frictions brings domestic prices closer to world prices
and it does not matter whether this occurs because of a fall in transportand communication costs or (apart from revenue effects) because of a
GATT-inspired reduction in trade restrictions.19 However, because we do
not observe movements in β directly we must make use of an observableconsequence of heightened integration: increases in a country’s trade inten18. See Copeland and Taylor (1994) for a model that explores this issue.
19. See, however, Section 3，subsection E, on the tariff-substitution effect in alarge open economy.

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Is Free Trade Good for the Environment?

sity ratio (defined as the ratio of exports plus imports to GDP valued atworld prices). We formalize this link below.
Proposition 5. If preferences over consumption goods are homothetic,
trade intensity rises as β approaches 1.
Proof
See Appendix A.
Proposition 5 links unobservable trade frictions with observable trade intensity. Lower trade frictions means greater trade intensity, regardless of acountry’s comparative advantage. Therefore, in our empirical application
we replace unobservable trade frictions with observable trade intensity.20
To address our second question, interpret the hat notation in equation(23) as describing small differences across countries. With this interpretation, (23) links differences in autarky relative prices across countries to differences in their relative factor abundance and real income levels. If wetake the rest of the world as our small country’s partner in this exercise,then the strength and direction of country i’s comparative advantage will
depend on its capital abundance relative to a world average (denoted by
κ i), and its real income relative to a world average (denoted by ι i). Although other factors play a role in determining comparative advantage,
capital abundance and real income are the key country characteristics
within our model.
Finally, to condition on these characteristics we let Ψ be a function
measuring the partial effect of an increase in trade intensity on pollution.
Our theory tells us that we can write Ψ = Ψ(κ i, ι i), but does not give us
much more guidance in this regard. The interaction between factor abundance and pollution haven motives depends quite delicately on elasticities
of substitution, factor shares, and (unknown) third derivative properties ofour more basic functions. This is apparent from (23) because the elasticities in this expression are functions of prices, incomes, and, trade frictions.
Consequently, we adopt a flexible approach to capturing these influencesby adopting a second-order Taylor series approximation to Ψ in our empirical work. That is, we employ(24)

Ψi ≅ ψ 0 + ψ 1κ i + ψ 2κ i2 + ψ 3ι i + ψ 4ι i2 + ψ 5κ iι i ,20. If trade frictions are not exogenous, but are endogenously determined alongwith pollution policy, then our proxy (trade intensity) may be correlated with unmeasured determinants of pollution policy. In Section 3，subsection E, we discuss
the likely implications of such a link between trade and pollution policy.

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and then interact this measure with trade intensity to capture the tradeinduced composition effect.
This method has several advantages. It allows the impact of further
openness on pollution to depend on country characteristics. It does not dictate whether one or both motives are present in the data or how they interact. And we can evaluate Ψ using our estimates to provide some simple
reality checks. For example, does the pollution demand curve shift rightfor some countries and not for others (i.e., does Ψi vary in sign depending
on country characteristics)? For which countries does it shift right? Are
these countries poor countries as predicted by the pollution haven hypothesis, or are they capital abundant countries as predicted by the factor abundance hypothesis? Finally, the formulation is a relatively parsimonious andreasonably flexible method for estimating an unknown nonlinear function.
2．
Empirical Strategy
This section describes how we move from our theory to an estimating
equation. To do so we need to discuss our data, its sources and limitations(subsection A), and address the links between theory and our estimating
equation (subsection B).
A. Data Sources and Measurement Issues
A real-world pollutant useful for our purposes would: (1) be a byproduct of goods production; (2) be emitted in greater quantities per unitof output in some industries than others; (3) have strong local effects; (4)be subject to regulations because of its noxious effect on the population;(5) have well known abatement technologies available for implementation;and (6), for econometric purposes, have data available from a mix of developed and developing as well as “open” and “closed” economies. An almost perfect choice for this study is sulfur dioxide.
Sulfur dioxide (SO2) is a noxious gas produced by the burning of fossil
fuels. Natural sources include volcanoes, decaying organic matter, and sea
spray. Anthropogenic sources are thought to be responsible for somewhere
between one-third and one-half of all emissions (United Nations Environment Programme (1991); Kraushaar and Ristinen (1998)). SO2 is primarily
emitted as either a direct or indirect product of goods production and is notstrongly linked to automobile use. Because energy-intensive industries arealso typically capital intensive, a reasonable proxy for dirty SO2-creating
activities may be physical-capital-intensive production processes. Readily
available, although costly, methods for the control of emissions exist andtheir efficacy is well established. In addition, in many countries SO2 emissions have been actively regulated for some time.
The Global Environment Monitoring System (GEMS) has been record-

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Is Free Trade Good for the Environment?

ing SO2 concentrations in major urban areas in developed and developing
countries since the early 1970s. Our data set consists of 2,555 observations
from 290 observation sites located in 108 cities representing 43 countries
spanning the years 1971-1996. The GEMS network was set up to monitor
the concentrations of several pollutants in a cross section of countries using comparable measuring devices.21 The panel of countries includes primarily developed countries in the early years, but from 1976 to the early
1990s the United Nations Environment Programme provided funds to expand and maintain the network. The coverage of developing economies
grew over time until the late 1980s. In the 1990s coverage fell with datafrom the United States only for 1996. The World Health Organization(1984) reports that until the late 1970s data comparability may be limited
as monitoring capabilities were being assessed, many new countries wereadded, and procedures were being developed to ensure validated samples.
Accordingly, we investigate the sensitivity of our findings to the time period.
The GEMS data are comprised of summary statistics for the yearly distribution of concentrations at each site. In this study we use the log of median SO2 concentrations at a given site, for each year, as our dependent
variable. We use a log transform because the distribution of yearly summary statistics for SO2 appears to be lognormal (WHO (1984)). Previous
work in this area by the WHO and others has argued that a lognormal distribution is appropriate because temperature inversions or other special pollution episodes often lead to large values for some observations. In contrast,
even weather very helpful to dissipation cannot drive the level of the pollutant below zero.
In addition to the data on concentrations, the GEMS network also classifies each site within a city as either city center, suburban, or rural in land
type, and we employ these land-type categories in our analysis. A list of
the cities involved, the years of operation of GEMS stations, and the number of observations from each city along with a frequency distribution of
SO2 emissions is given in our Technical Appendix (available upon request).
In moving from our theoretical model to its empirical counterpart weneed to include variables to reflect scale, technique, and composition effects. As well, we have to include site-specific variables to account for meteorological conditions. Our estimations will require the use of data on real
GDP per capita, capital-to-labor ratios, population densities, and various
measures of “openness.” The majority of the economic data were obtained
from the Penn World Tables 5.6. The remainder was obtained from several
sources. A description of data sources and our methods for collection are
21. The range of sophistication of monitoring techniques used in the network
varies quite widely, but the various techniques have been subject to comparability
tests over the years. Some stations offer continuous monitoring, whereas othersmeasure only at discrete intervals.

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Werner Antweiler, Brian R. Copeland, and M. Scott Taylor

provided in Appendix B together with a table of means, standard deviations, and units of measurement for the data.
B. The Estimating Equation
In moving from our theoretical model to estimation we face several issues. Here we discuss three: identification, excluded variables, and functional form.
Identification.––The private sector’s demand for pollution, written indifferential form, is given by (17). The pollution supply curve is given by(18). A problem arises because most measures of the scale of economic activity that shifts pollution demand (for example real GDP or real GDP perperson) will be highly or perfectly correlated with real income per capita
that shifts pollution supply.
We address this problem by exploiting three different sources of variation in our data. First, we note that changes in the scale of output musthave contemporaneous effects on pollution concentrations, whereas pollution policy is likely to respond slowly, if at all, to changes in income levels. Consequently, we use as our proxy for income a one-period lagged,
three-year moving average of income per capita, but link pollution concentrations to a contemporaneous measure of economic activity. To the extent
that there is significant variation over time in activity measures, this sourceof variation will help in our identification.22
Second, the scale of economic activity should be measured by economic
activity within a country’s borders (i.e., GDP), whereas the income relevant to the technique effect should reflect the income of residents wherever
it is earned (i.e., GNP). Therefore, we can exploit the difference between
GDP and GNP measures to separate technique from scale effects. Even
though the gap between these two figures is not large for most economies,
it is significant for some. This cross-country variation will be useful inseparating scale from technique.
Finally, we measure the scale of economic activity S at any site by anintensive measure of economic activity per unit area. This intensive measure is GDP per square kilometer. Lacking detailed data on “Gross City
Product,” we construct GDP per square kilometer for each city and eachyear by multiplying city population density with country GDP per person.
22. For example, we expect that a significant recession would drive down concentrations (a scale effect) but not lead to a rewriting of pollution control laws (i.e.,a technique effect). This source of variation in pollution data has been exploited
before. See Kenneth Y. Chay and Michael B. Greenstone (1999).

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Is Free Trade Good for the Environment?

As a result, scale is now measured in intensive form, as is our dependent
variable.23 To explain concentrations of pollution we need a measure ofscale reflecting the concentration of economic activity within the samegeographical area. Other possible measures of scale fail this test. Moreover,since we assume pollution policy is determined by national averages forincome per capita and the number of exposed individuals, we are in effectfixing the pollution supply curve for all cities within a given country. This
“allows” us to employ the within-country variation in scale across cities toseparate the influence of scale from that of technique.
Unobservable Variables: Fixed or Random Effects? ––Several variables
relevant to our theory are unobservable. To account for these exclusions
we estimate an individual effects model for ε ijkt given by(25)

ε ijkt = ξ t + θ ijk + vijkt ,where ξ t is a time-specific effect, θ ijk is a site-specific effect, and vijkt is an
idiosyncratic measurement error for observation station i in city j in country k in year t.
Our common-to-world but time-specific effect is included to capturechanges in knowledge concerning pollution, changes in the world relative
price of dirty goods, and improvements in abatement technologies. Although proxies for some of these variables could be constructed, choosing
proxies will of course introduce new issues of data quality, coverage, andso forth. Instead we note that, because each of these variables affects all
countries in a similar way, a preferred method may be to treat them as unobservable. For example, a rise in the world price of dirty goods affects all
countries in a similar way. Accordingly, we capture these common-toworld excluded variables with a set of unrestricted time dummies.
θ ijk is a site-specific effect representing excluded site (or countryspecific) variables such as excluded economic determinants or excluded
meteorological variables. For example, country type T appears in (19) but
is virtually unobservable in that it relies on both knowledge of the weight
governments apply to Greens and Browns in their economy and the shareof each in the overall population. Because the panel is relatively short foralmost all countries, we take these country-type and distribution parameters
as fixed over time. As well, there are unmeasured topographical and mete23. This is admittedly a rough measure of economic activity, and the quality ofthis proxy may vary systematically with a country’s development level. To investigate this concern we have allowed the scale effect to vary across countries divided
by income category, by allowing for nonlinearities in the response to scale, and by
excluding the perhaps most troubling rural observations. Our results are similar to
those reported for our simpler specification. For one such sensitivity test see
Table 2.

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Werner Antweiler, Brian R. Copeland, and M. Scott Taylor

orological features that undoubtedly affect the dissipation of pollution ateach site. Finally, we allow for an idiosyncratic measurement error vijkt.
Two sources of this error would be machine error in reading concentrations and human error in calculation or tabulation.
Throughout we present both fixed- and random-effects estimates forevery model. Whereas random-effects estimation is in theory more efficient,
it is unclear whether excluded country-specific effects subsumed in our error term are uncorrelated with our regressors. Although fixed-effects estimation is preferable in just these cases, fixed effects limits the crosssectional variation we can exploit for separating scale from technique effects.
Functional Form.––Our model predicts emission levels but our data areon concentrations. Meteorological models mapping emissions from a (single) stack into measured concentrations at a receptor are functions of emission rates, stack height, the distance to the receptor, wind speed, temperature gradients, and turbulence. Much of this information is not presently
available. In view of these limitations we adopt a linear approximation tomeasured concentrations by writing concentrations at site ijk, at time t asC
Zijkt
= X ′jkt α + Yijkt′ γ + ε ijkt

(26)

X ′jkt α = α 0 + α 1 SCALE jkt + α 2 KLkt + α 3 INCkt + α 4 Ψkt TI kt
Ψkt = ψ 0 + ψ 1 REL. KLkt + ψ 2 REL. KL2kt + ψ 3 REL. INCkt+ ψ 4 REL. INCkt2 + ψ 5 REL. KLkt REL. INCkt ,where SCALE is city-specific GDP/km2, KL is the national capital-to-laborratio, INC is a one-period-lagged three-year moving average of GNP/N, TI
is the trade intensity (X+M)/GDP, REL.KL is country k’s capital-to-laborratio measured relative to the world average, and REL.INC is country k’s
real income measured relative to the world average (see Appendix B for
further details). Note that world price and country-type variables are captured in (25), and trade intensity has replaced trade frictions in (19), as discussed previously. Y contains site-specific weather variables and sitespecific physical characteristics (discussed below), and ε ijkt is a site-specificerror reflecting unmeasured economic and physical variables. We refer toequation (26) as Model A in our estimations.
Model A follows from our reduced form if we assume linearity in the
response to scale, technique, and composition variables. This linearity assumption is, however, somewhat at odds with our theory. In theory, theimpact of capital accumulation on pollution depends on the techniques of
production in place. But when countries differ in income per capita, they
will also differ in producer prices and hence their techniques of production.

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Is Free Trade Good for the Environment?

Consequently, the Rybczyinski derivatives embedded in (26) will differ
across countries. As well, the impact of capital accumulation on the composition of output is not a linear function of KL. Similarly, the impact ofincome gains on pollution depends on the existing composition of output
and hence the existing capital-to-labor ratio and income per capita. To account for these possibilities we amend Model A by adding the squares ofincome per capita (INC2kt ) and the capital-to-labor ratio (KL2kt ) as well as
their cross-product (INCkt KLkt ). We refer to this amended form of (26) as
Model B. As a consequence, the impact of factor accumulation can now
differ across countries and over time in closer accord with our theory. Finally, we consider a further nonlinearity by adding SCALE2kt to Model B.
A nonlinearity in the impact of scale could arise from nonhomotheticities
in production or consumption. We refer to this slightly amended model as
Model C.
Models A, B, and C differ from those previously estimated in several regards. For example, empirical work within the Environmental Kuznets
curve tradition employ measures only of site-specific attributes and income
per capita as regressors, leaving out a role for factor endowments or scale
to play independent effects. Grossman and Krueger (1993, 1995) are themost prominent examples of this approach, but there are many others. Lewis Gale and Jose A. Mendez (1998) add measures of factor endowments
to a Kuznet’s curve regression, but their (one-year) cross-sectional analysis
cannot distinguish between constant-over-time site attributes and scale effects. Empirical work using (constructed) cross-country emission data oremission intensity data has tried to link country characteristics (factor endowments, growth in income, fuel use, etc.) to environmental outcomes,
but these studies always fail to condition the impact of openness on country characteristics. For example, see Low and Yeats (1992) and Lucas et al.
(1992). As a result, we are not aware of even one study where the impactof trade is conditioned on those country characteristics determining comparative advantage, despite the fact that the trade-induced composition effect should vary across countries according to comparative advantage.

3．
Empirical Results
A. Main Results
Table 1 presents the main results from our estimations. We present estimates from Models A, B, and C in Table 1 using both random and fixed
effects.

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Werner Antweiler, Brian R. Copeland, and M. Scott Taylor
Table 1. Alternative Hypotheses Tests

Estimation method:
Model specification:
Variable/column:
Intercept
City economic intensity GDP/km2(City economic intensity)2/1,000
Capital abundance(K/L)(K/L)2Lagged per capita income(Income)2(K/L)×(I )Trade intensity TI=(X +M )/GDP
TI×REL.K/L
TI×(REL.K/L)2
TI×REL.INC
TI×(REL.INC)2
TI×(REL.K/L)×(REL.INC)
Suburban dummy
Rural dummyCommunist country(C.C.)dummy
C.C.dummy×income
C.C.dummy×(income)2
Average temperature
Precipitation variation:
Helsinki Protocol:
Observations
GroupsR2
Log-likelihood
LR test/χ 2(df)Hausman test/Wald χ 2(df)Scale elasticity
Composition elasticity
Technique elasticity
Trade intensity elasticity

Random effects
A
(1)

B
(2)

Fixed effects
C(3)−2.865*** −3.279*** −3.311***0.042*** 0.058*** 0.070***−0.2440.102**
0.293**
0.286*
0.014
0.013−0.982*** −1.248*** −1.312***0.708*** 0.669***−0.309*** −0.285***−0.915−0.488−0.510−0.462−1.952*−1.828*0.018−0.230−0.2480.470
1.056*
1.011*
0.118−0.308*−0.285*−0.1650.870*** 0.822***−0.299−0.435*−0.422*−0.623−0.674−0.6310.312−0.252−0.257−0.2834.569*
4.641*−5.755** −5.788**−0.055*** −0.052*** −0.052***
3.446
5.860
6.158
−0.232*−0.092−0.114
2,555
2,555
2,555
290
290
290
0.33950.3737
0.374
−2550
−2523
−2522
55.596*** 1.604
65.761** 15.158
53.7890.192*** 0.265*** 0.315***
0.583**
0.948*** 0.993***−0.905*** −1.577*** −1.577***−0.436*** −0.388*** −0.394***

A
(4)

B
(5)

C
(6)

−2.506*** −4.324*** −4.299***0.024*
0.058*** 0.089*−0.3400.165**
0.461**
0.437*
0.006
0.008−1.326*** −0.096−0.2280.559*** 0.578***−0.381*** −0.386***−3.677*** −3.142** −3.216**
0.159−2.252*−2.121−0.168−0.123−0.1762.128**
2.687***
2.614***−0.108−0.595** −0.584**−0.2800.900**
0.924**

1.170−0.060*8.599−0.1792,555
290
0.2483−3964
118.42**9.621**−8.931***−0.057*10.810*
0.016
2,555
290
0.131
−3906
2.035

9.639**−8.806**−0.056*10.716*
0.016
2,555
290
0.1499−3905

0.112*
0.266*** 0.398**
0.945**
1.006**
0.975*−1.222*** −1.153** −1.266**−0.641*** −0.864*** −0.882***

Notes: To conserve space, no standard errors or t-statistics are shown.The dependent variable
is the log of the median of SO2 concentrations at each observation site. Model A follows directly from our empirical implementation, whereas model B allows for additional interaction
between capital abundance and income. In addition to model B, model C allows for nonlinearity in our scale variable. All model specifications use time-fixed effects. Elaticities are evaluated at sample means using the Delta method.
*Significance at the 95 percent confidence level.
**Significance at the 99 percent confidence level.
***Significance at the 99.9 percent confidence level.

Scale, Composition, and Technique Effects.––Consider our core variables representing scale, composition, and technique effects. In all columnsof Table 1 we find a positive and significant relationship between the scaleof economic activity as measured by GDP/km2 and concentrations. From

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Is Free Trade Good for the Environment?

the bottom of Table 1 we see that the coefficient estimates imply a samplemean elasticity of concentrations to an increase in scale somewhere between 0.1 and 0.4. The scale elasticity estimates increases in magnitude as
we move from Model A through to Model C, although the estimates differ
only slightly across random and fixed effects. Because the models arenested, we can test the restrictions imposed in Models A and B via a likelihood ratio (LR) test. It appears there is little gained in moving to theslightly more general Model C from Model B; conversely, the restrictions
imposed by Model A are rejected by the data as shown by the significant
LR test statistics in columns (1) and (4). These empirical results together
with our knowledge of theory suggest that less emphasis be placed on theestimates from Model A.
Next consider the impact of a nation’s capital-to-labor ratio. In all columns of Table 1, we find a positive composition effect arising from an increase in capital-to-labor ratios. The estimated effect is typically quite large.
With the exception of column (1), we find a 1 percent increase in a nation’s capital-to-labor ratio––holding scale, income, and other determinants
constant––leads to perhaps a 1 percent-point increase in pollution. Our success in finding a link between factor endowments and pollution may appear surprising given the universal difficulties researchers have had in finding a strong link between factor endowments and trade flows. We would
note, however, that the production side of the HOS model has received
some support (see especially Harrigan (1995, 1997)), and our model focuses on a highly aggregate relationship between overall pollution intensive output and factor endowments.
The estimates in Table 1 also predict a strong and significantly negative
relationship between per capita income levels and concentrations. The elasticity of concentrations to an increase in income is typically quite large andis always significant. Using the estimates from Table 1, the technique elasticity varies between −0.9 and −1.5. This technique effect seems surprisingly strong, but the result appears to be robust. Alternative specifications(discussed below) lead to somewhat different conclusions, although theelasticity is almost universally estimated to be greater than −1 in magnitude, suggesting a strong policy response to income gains.
The Trade-Induced Composition Effect.––Next consider the estimates forthe trade-induced composition effect. In all columns we reject the hypothesis that the terms reflecting the trade-induced composition effect are jointly
zero.24 Although the sign and significance of some individual coefficientsvary across specifications, the results from Model B and Model C in bothrandom and fixed effects are very similar. At the sample mean, the overall
elasticity of concentrations to an increase in trade intensity is relatively
constant, ranging from approximately −0.4 to −0.9. Therefore, for an aver24. This is in contrast to the case where trade intensity appears alone or is replaced by other measures of “openness.” We investigated this issue more fully in
Antweiler et al. (1998 Table 2 p. 29).

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Werner Antweiler, Brian R. Copeland, and M. Scott Taylor

age country in our sample the trade-induced composition effect is negative.
Considering the individual coefficients, it is clear that country characteristics describing both relative income and abundance are important, but it isdifficult to evaluate the relative strength of pollution haven and factor
abundance motives. We present several methods of evaluation below.
Site-Specific and Country-Type Considerations.––Because income gains
may not equally translate into policy responses we note it is important todistinguish between Communist and non-Communist countries. The Communist country interactions with income and income squared in Models B
and C suggest that the technique effect is very small or nonexistent inCommunist countries. For example, using the fixed-effects results fromcolumn (6), we cannot reject the hypothesis of a zero technique effect inCommunist countries! In the random-effects case in column (3), the technique elasticity is fully one-third of that for our average, non-Communist
country.25 We investigated other country-type effects by including adummy variable for those years a country was bound by the Helsinki protocol on acid rain. Our results indicate this variable has little explanatory
power. The results, however, do indicate that site-specific land use andweather variables have a bearing on concentrations as expected. Higher
temperatures both dissipate pollution faster and reduce the need for homeheating; precipitation highly concentrated in one season reduces the abilityof rain to wash out concentrations.
B. Discussion and Evaluation
Although the results in Table 1 appear to be supportive of our theory, it
is important to go beyond sign and significance tests to investigate whether
the magnitude of these estimates are in some sense plausible. We pursue
several of these reality checks below.
To start note that the implied scale, composition, and technique elasticities are not implausibly high, and all are significantly different from zero.
Together these elasticities provide some simple reality checks. For example,
suppose our average economy experienced neutral technological progressof 1 percent, raising both GDP and GNP per person by 1 percent. According to our estimates from Table 1, the positive scale effect from thisgrowth will always be dominated by the negative technique effect.26 Al25. The technique elasticity in the random-effects case is much smaller −0.50 but
is significantly different from zero; the technique elasticity in the fixed-effects caseis −0.062 with a 95 percent confidence interval of [−0.90, 0.78].
26. Holding input use constant (capital, labor, and pollution), neutral technological progress raises output in our model. Each unit of pollution is more productive
than before, and this via a scale effect argues for more pollution. Because real incomes are now higher, however, pollution may in fact fall from a technique effect.
Whether we have more or less pollution in equilibrium after the shock therefore depends on the relative strength of these two effects.

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Is Free Trade Good for the Environment?

though the estimates differ across columns, in all cases our results indicate
neutral technological progress lowers pollution concentrations. Alternatively, when an increase in income and production is fueled entirely bycapital accumulation, the picture is far less favorable to the environment. If
we assume a share of capital in output of 1/3, then the full impact of capital accumulation working through scale, composition, and technique effects
is to raise pollution concentrations.27 Even though these two exercises are
not tests of our theory, the results are reassuringly close to what we may
have expected ex ante.
To assess the plausibility of our trade intensity elasticity, we calculated
the trade intensity elasticity for all countries in our sample. From Proposition 1 we note that the sign of the trade-induced composition effect shouldreflect a country’s comparative advantage in clean versus dirty goods.
Therefore it is not plausible that all countries in the world have negativetrade intensity elasticities. Although we have only a sample of countries it
seems reasonable to expect both positive and negative elasticities.
As a check on our theory we present in Figures 2 and 3 below a plot ofcountry-specific elasticities against relative income using estimates from

Figure 2. Country-Specific Trade Elasticities [Model B, Random Effects,
Corresponding to Table 1 Column(2)]27. Take, for example, the estimates from column (6). Then our estimates indicate that a 1 percent increase in the capital-to-labor ratio raises concentrations byperhaps 1 percent, all else equal. However, an increase in the capital-to-labor ratio
will have accompanying impacts on the scale of economic activity and on real incomes. If we make a back-of-the-envelope calculation by taking capital’s share in
the value of domestic output at 1/3, then capital accumulation leading to a 1 percent increase in the capital-to-labor ratio creates a 1/3 percentage-point increase in
GDP per capita and GDP/km2. Therefore, capital accumulation also creates an induced technique effect of approximately −1.2/3 = −0.4 and an induced scale effectof perhaps 0.13 = 0.39/3. Adding the direct composition effect to these estimatessuggests that economic growth fueled entirely by capital accumulation raises pollution concentrations.

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Werner Antweiler, Brian R. Copeland, and M. Scott Taylor

Model B in columns (2) and (5) of Table 1. Although there are more positive elasticities in Figure 2 than 3, in both there is a distribution of elasticities around zero. Our inference is simply that some countries’ pollution demand shifts right with a fall in trade frictions and some shift left because
countries differ in their comparative advantage. 28 For example, from either
Figure 2 or Figure 3 we would conclude a small trade liberalization in
Canada, all else equal, shifts its pollution demand curve to the right. The
inference is that, despite Canada’s relatively high income, its comparativeadvantage lies in capital-intensive dirty products. Alternatively, we would
conclude a small trade liberalization in India shifts its pollution demand
curve to the left, the inference being that, despite its relatively low income,its comparative advantage lies in labor-intensive and relatively clean goods
production. Although these two countries estimates may accord well with
our intuition, other country-specific elasticities are harder to explain [e.g.,
why is Malaysia’s elasticity (MYS) so negative and Switzerland’s (CHE)
so positive?]. Because our country-specific estimates do vary across specifications, we caution the reader from drawing too strong an inference fromany one of them.

Figure 3. Country-Specific Trade Elasticities [Model B, Flxed Effects,
Corresponding to Table 1 Column(5)]28. The random-effects implementation in Figure 2 has more positive point elasticities than the fixed effects in Figure 3, but relatively minor changes in specifications moves the entire set of fixed-effects estimates upward.

337

Is Free Trade Good for the Environment?

Pollution Haven and Factor Abundance Motives.––The second featureof note in Figures 2 and 3 is that the elasticity estimates increase with relative income. Note that if the simple pollution haven hypothesis were literally true and the sole determinant of trade in dirty products, we would expect just the opposite––a strong negative correlation between relative income and the magnitude of our country-specific elasticities. This is because, under the pollution haven hypothesis, poor countries specialize indirty goods and rich countries specialize in clean goods. A small movement toward free trade would shift the pollution demand curve inward fora rich country and outward for a poor country. In fact, as shown in the figures, the relationship is definitely nonnegative and, in fact, slightly positive.29 It appears that if anything, high-income countries have a comparative advantage in dirty capital-intensive products.
In total, although changes in trade intensity seem to matter, the magnitude of the induced change in pollution concentrations appears relatively
small. In Figure 2 the vast majority of countries have trade intensity elasticities less than 1 in absolute value; in Figure 3 the majority of countries
also satisfy this requirement.
One explanation for these findings is simple: low-income countries typically have both low incomes per capita and low capital-to-labor ratios. The
pollution haven hypothesis suggests that a low-income economy should bemade dirtier by trade, but if pollution-intensive industries are also capitalintensive then, whatever benefits accrue from lax pollution regulation
could be largely undone by the relatively higher price of capital in thiscapital-scarce country. As a result, further openness to trade will have avery small effect on the pollution intensity of output for low-income countries. Similarly, high-income countries have both high income and highcapital-to-labor ratios. The former argues in favor of trade lowering thepollution intensity of output, whereas the latter argues in favor of traderaising it.
Judging from Figure 2 and 3 it appears that, if anything, factor endowment motives are offsetting tighter pollution policy in relatively rich countries. This may explain why other investigations have failed to find a significant relationship between the strictness of pollution regulations and decreased trade in capital-intensive dirty goods. It may also explain why previous researchers have found it quite difficult to find pollution haven effects in the data. It is not that the (ceterus paribus) pollution haven hypothesis is wrong, or that the (ceterus paribus) factor endowment driven
basis for trade is absent. But rather, because these two partial theories
work against each other, the net result of the potentially very large composition effects predicted by either theory turn out to be rather small in practice.
29. Even excluding the strongly negative elasticities of Malaysia (MYS) and Iraq
(IRQ), the relationship is significantly positive in both Figures 2 and 3.

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Werner Antweiler, Brian R. Copeland, and M. Scott Taylor

C. An Environmental Assessment of Freer Trade
Taking factor endowments as fixed, a lowering of transport costs ortrade barriers raises the value of domestic output and real income in asmall open economy. The value of output and the value of income rise by(approximately) the same percentage, and this creates both scale and technique effects. Using the estimates from either Model B or Model C in Table 1, the net effect of a 1 percent change in income created by trade is a0.8-0.9 percent fall in emissions: that is, using (21) we have π 1 − π 3 < 0.
The composition effect of trade for our average country is also negative;that is, from (21) we have π 4 < 0. Therefore, for an average country in our
sample, the full impact of further openness to international trade––throughscale, technique, and composition effects––will be a reduction in SO2 concentrations!
Similar results follow from all of our specifications: the scale elasticity
is dominated by the technique elasticity, whereas the trade-induced composition effect of trade is typically small in magnitude.30 How large a reduction any one country reaps from a fall in trade frictions will, of course, depend on country characteristics, the impact further trade has on domestic
income and output, and how the ongoing process of globalization is affecting country characteristics elsewhere in the world. Given that countries
will differ somewhat in their particular elasticities, some may indeed bemade dirtier from a reduction in trade frictions, but we expect that trade’s
effect––whether positive or negative––will be small.31 After all, the estimated impact of even a large trade liberalization on GDP is small, andwhen this small increase in GDP is filtered through our estimated scale
and technique elasticities, the net effect is likely to be smaller still. Although, in theory, trade’s impact on the pollution intensity of output canbe large, in practice our estimates suggest a much more muted response.
These conclusions, however, rely on our assumption that factor endow30. In the Technical Appendix we investigate a two-equation two-stage leastsquares (2SLS) fixed-effects model where our city scale measure and pollution aredetermined simultaneously. We find a scale elasticity in excess of 1, but also amuch larger technique elasticity (approaching −2). As a result, our conclusion on
their relative magnitude remains unchanged.
31. Averaging across countries and years, the average trade intensity is 41 percent with a standard deviation of 32 percentage points. A one-standard-deviation
change in trade intensity is then equal to a 79 percent change in trade intensityfrom its average value, whereas a one-standard-deviation change in pollution concentrations is equivalent to a 203 percent change from its average value. Using our
fixed-effects estimate of the trade intensity elasticity from Table 1, column (6), a
79 percent increase in trade intensity amounts to a 69 percent reduction in pollution
concentrations, or about one-third of a standard deviation of pollution concentration.
Using the random-effects estimate from column (3) in Table 1, the same onestandard-deviation change in trade intensity amounts to a change of less than onesixth of the standard deviation in pollution concentration.

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Is Free Trade Good for the Environment?

ments and technology remain fixed when trade frictions fall. If further
trade spurs capital accumulation or brings knowledge spillovers and hastens technological progress, then other calculations must come into play.
Whether these trade-induced changes bring about a net improvement in theenvironment will depend on their estimated size because they have opposing effects on pollution concentrations. There is a burgeoning empirical literature linking openness to growth and technology adoption and we havenothing new to add here. But clearly our estimates, together with input
from these other sources, might provide another method for assessing
trade’s full impact.
D. Alternative Specifications
The results from Table 1 and Figures 2 and 3 suggest that our approachof dividing the determinants of pollution into scale, technique, and composition effects is fruitful. It is, however, important to investigate whether our
results are robust to reasonable changes in specification, time period, andso forth. We have conducted numerous sensitivity tests of our specification
and report four alternatives in Table 2. Additional results are available in
our Technical Appendix, available upon request from the authors. In allcolumns we amend our full Model C from Table 1 to include other determinants, investigate other time periods, or adopt more flexible specifications.
In columns (1) and (5) we have restricted the time period of our analysis
to the years 1976-1991. Before 1976 only a few countries participated andafter funding ceased in 1991 country coverage is reduced. To allow forpossible data quality and sample selection problems we consider thisshorter time period. This shortened period has 489 fewer observations, although as shown in columns (1) and (5) the results are similar both interms of elasticity estimates and significance levels. Our overall conclusions regarding the relative strength of scale versus technique effects remains, as does the muted response to changes in trade intensity.
In columns (2) and (6) we investigate the importance of other factor endowments. In our parsimonious model of pollution demand and supply“factor endowments” enter directly only through the inclusion of thecapital-to-labor ratio. Other potential factor endowments were excluded because, even though they are undoubtedly relevant to income levels, there islittle reason to believe that they have an independent effect on either thedemand for a clean environment or the derived demand for pollution emissions; however, local abundance either in clean or dirty fuels may affectemissions. We investigate this possibility by adding in columns (2) and (6)country-specific measures of hard and soft coal deposits per worker. Over-

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Werner Antweiler, Brian R. Copeland, and M. Scott Taylor
Table 2. Sensitivity Tests

Estimation method:
Model specification:
Variable/column:
Intercept
City economic intensity GDP/km2(City economic intensity)2/1,000
Capital abundance(K/L)(K/L)2Lagged per capita income(Income)2(K/L)×(I)
Trade intensity TI=(X +M )/GDP
TI×REL.K/L
TI×(REL.K/L)2
TI×REL.INC.
TI×(REL.INC.)2
TI×(REL.K/L)×(REL.INC.)
Suburban dummy
Rural dummy
Inward FDI stock/capital stock
FDI/K×poor countries
FDI/K×rich countries
Communist country(C.C.)dummy
C.C.dummy×income
C.C.dummy×(income)2
Average temperature
Precipitation variation
Hard coal (per worker)
Soft coal (per worker)
Helsinki Protocol
Observations
GroupsR2
Log-likelihood
Hausman test/Wald χ 2(df)Scale elasticity(all/middle)
Scale elasticity(poor countries)
Scale elasticity(rich countries)
Composition elasticity
Technique elasticity
Trade intensity elasticity
FDI elasticity(poor countries)
FDI elasticity(middle)
FDI elasticity(rich countries)

Random effects
Time
(1)

Factors(2)−2.545***0.068***−0.054−0.1150.036**−1.771***0.585***−0.147*−2.466***0.934−0.876**1.344**−0.2280.333−0.284−0.519−3.141***0.075***−0.2750.289*
0.012−1.629***0.717***−0.276***−0.671−1.758*−0.252
1.167*−0.309*0.803***−0.424*−0.620−0.971*
7.785***−8.683***−0.061***8.867*−0.242*2066
274
0.3243−2030
94.211***0.314***

0.985***−1.425***−0.266**FDI(3)−3.650***0.070***−0.2310.439***−0.002−1.451***0.660***−0.255***−0.198−2.879**0.304
1.518**−0.308*0.519−0.445*−0.6550.039
4.736−0.362−0.326−0.1104.602*
4.201−5.683* −5.677*−0.056*** −0.051***
5.859
7.633
−0.6902.998*−0.157−0.092
2555
2525
290
284
0.37790.3684−2519−2496
55.53684.269***0.333*** 0.318***

Fixed effects
Scale
(4)

Time
(5)

Factors
(6)

FDI
(7)

Scale
(8)

−3.635*** −1.697
0.154*** 0.091*−0.2540.279* −0.077
0.010
0.032
−0.852* −3.109**
0.611*** 0.512*−0.278*** −0.041−0.501−7.161***−1.890*1.699−0.142−1.043**1.212*
4.495***−0.354** −0.742**
0.784** 0.164−0.490**−0.730*−4.679***0.087*−0.3290.426*
0.008−0.4280.757***−0.401***−3.333**−2.281*−0.131
3.097***−0.723***0.922**−4.679***0.092*−0.3730.754***−0.024−0.9810.563***−0.297***−3.747***−2.737*0.811
2.720**−0.3600.092−4.345***0.029−0.4755.668** 16.809*** 11.751***−7.127** −14.13*** −10.84***−0.052*** −0.072* −0.055*
5.882
14.298** 10.893*
4.217
4.120
−0.094−0.173−0.054
2555
2066
2555
290
274
290
0.389
0.16770.0605
−2512
−2982
−3900
59.331*0.499*** 0.414*
0.388*
0.643***
0.537***
1.008*** 1.026*** 0.803*** 1.442** 0.864*−1.740*** −1.551*** −1.218*** −2.220*** −1.230**−0.351*** −0.364** −0.292** −0.543** −0.791***
0.091
0.004
−0.0390.489**
0.006−0.0520.564***−0.400***−2.964**−2.541*−0.1122.677***−0.617**
0.993**

1.234*
6.314−0.82810.271**−8.840**−0.04913.972**9.819**−9.039***−0.062*
11.471*

0.036
2525
284
0.1577
−3858

0.035
2555
290
0.1337−3899

0.412**

0.094
0.355*
0.598***
1.150** 1.056**−1.505*** −1.204**−1.189*** −0.899***
0.143
0.121*
0.049

Notes: No standard errors or t-statistics are shown. The dependent variable is the log of themedian of SO2 concentrations at each observation site. All model specifications use time fixed
effects. Elasticities are evaluated at sample means using the Delta method. Model “Time” includes only the years 1976-1991 of the primary GEMS phase; model “Factors”introduces factor endowment-related variables; and model “FDI” allows for an an inward foreign direct investment stock relative to the overall capital stock, interacted with income. The terms richcountries and poor countries refer to the top and bottom 30 percent of countries in the Penn
World Tables with respect to per capita GDP.
*Significance at the 95 percent confidence level.
**Significance at the 99 percent confidence level.
***Significance at the 99.9 percent confidence level.

341

Is Free Trade Good for the Environment?

all the results support our earlier conclusions.
Although a greater endowment of high sulfur soft coal leads to moreconcentrations, at least in the random-effects implementation in column (2),this effect disappears in the fixed-effects estimation in column (6). These
results are not surprising: an abundance of soft coal means that countries
like China will have higher concentrations, all else equal, but because mineral endowments have very little time series variation they will be well
captured by country fixed effects. Consequently, although abundance ofhigh sulfur coal surely adds to emissions, its explicit inclusion has very little effect on our results.
In columns (3) and (6) we investigate the impact foreign direct investment may have on our results. If multinational corporations have common
production methods in both developed and developing countries for engineering, quality control, or other reasons, then the pollution intensity of
their production will be determined by the income per capita of the source
country. As a result, a larger multinational presence in a poor country may
mean it is cleaner, all else equal; however, there is an alternative hypothesis working in the other direction. If multinationals locate in poor countries
because of their lax environmental protection, then we may instead find apositive relationship between foreign direct investment (FDI) and pollution.
To investigate this issue we have calculated for each year and country in
our sample the ratio of its inward stock of FDI to its overall capitalstock.32 We refer to this as FDI intensity: it measures the share of the domestic capital stock that may have cleaner than expected techniques of
production. We then interact this measure with a categorical variable representing a country’s income per capita to allow the multinational effect todiffer across rich and poor countries. The results from this exercise are
mixed. In the fixed-effects estimation, there is a slight positive relationshipbetween FDI and concentrations for poor, middle-income, and rich countries. Only the middle-income relationship is statistically significant. Moreover, the coefficient estimates imply that a 10 percentage point increase in
the ratio of the FDI stock to K stock would raise concentrations by about
1 percent. This is a small effect on pollution concentrations arising from avery large change in FDI. In the random-effects estimation, none of the coefficients is significantly different from zero. Overall, we find little relationship between the extent of FDI in an economy (even a poor one) andits pollution level. Again our elasticity estimates are changed only slightly
from our earlier specification.
Finally, in columns (4) and (8) we investigate whether our scale effectdiffers significantly across countries categorized by income per capita lev32. In theory we may want to distinguish between acquisitions of brownfields,
capacity expansions, and greenfield investments because greenfield investors areperhaps more likely to bring their own plant-specific technology to the foreigncountry.

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Werner Antweiler, Brian R. Copeland, and M. Scott Taylor

els. If there were important nonhomotheticities in production or consumption, or if our method of constructing scale was more appropriate for someincome categories than others, this may show up when we allow for disaggregation. The results in column (4) indicate that, whereas separate estimation of scale across income categories tends to raise the overall elasticity
estimates to approximately 0.5 or 0.6, the results are very similar to thosepresented earlier. In column (8) we find similar results for the poor andrich categories, but the middle-income group has a much lower elasticity
and it is not precisely estimated. The middle-income group results may be
a consequence of the exclusive reliance of fixed effects on the (nowsmaller) within-group variation for estimation. Despite these caveats, theelasticity estimates, although different across classes, are not significantly
different from each other.33
E. Alternative Theories: Tariff Substitution and Distributional Motives
In our framework, governments use pollution policy only to target pollution, and not for other purposes, such as to influence the terms of trade or
to redistribute income. As a result, the pollution tax is always equal to effective marginal damage, and changes in openness affect our pollution supply curve only through its impact on real income and relative prices. Moregenerally, pollution policy and openness may be linked through otherchannels if governments use pollution policy for other purposes. To examine this possibility further we need to specify the potential theoretical links
involved and then ask what variation in the data such a link would create.
There are (at least) two reasons why trade and environmental policies may
be linked. Each of these links is probably deserving of a paper-length
treatment of both theory and further empirical work, but here our goal ismerely to sketch two possibilities and identify their probable impact on ourempirical results.
Tariff Substitution.––The first link arises from market power. If countries were large and had complete discretion in setting both trade and pollution policy, then both instruments would be targeted: the tariff would be
set at its optimal level according to the inverse elasticity rule, and the pollution tax would equal effective marginal damage as in our small open
economy case. But if tariff choices are constrained by international agreements, then governments may find it useful to substitute environmental
33. In our random-effects implementation we can go further and divide the components of our scale measure into population density and contemporaneous GDP/N.
Doing so yields an elasticity of concentrations to population density of 0.57; anelasticity with respect to contemporaneous GDP/N of 0.25; and an overall scaleelasticity of 0.65. We cannot reject our restriction that both population density andcontemporaneous GDP/N share the same elasticity.

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Is Free Trade Good for the Environment?

policy for trade policy. We will refer to this as the tariff substitution motive. To proceed further consider the optimal pollution tax for a large open
economy:(27)

1 ⎞ dp /dτ⎛τ = Tφ ( p, I ) + pE *p ⎜ t − * ⎟,⎝ ε ⎠ d z / dτwhere ε * is the elasticity of foreign export supply, Ep! is the price derivative of foreign export supply, and t is the ad valorem tariff. To highlightthe tariff substitution motive, rewrite (27) to obtain the gap between thepollution tax and effective marginal damage:(28)

1 ⎞ dp /dτ⎛τ − Tφ ( p, I ) = pE *p ⎜ t − * ⎟.
⎝ ε ⎠ d z /dτThis gap reflects the tariff substitution motive. Consider first a dirty good
importer. When the tariff is set at its optimal level, the right-hand side of(28) is zero: each instrument is targeted and there is no tariff substitution
motive. If the tariff is constrained to be below its optimal level, then theright-hand side of (28) is negative and a dirty good importer sets the pollution tax below marginal damage to substitute for the tariff. Increased openness therefore induces a loosening of pollution policy that was not accounted for in our empirical work.34 For a dirty good exporter, a similarargument works in reverse as trade restrictions are reduced below their optimal level, there is an incentive to tighten pollution policy because pollution taxes can be used as a substitute for an export tax. Increased openness
in this case leads to a tightening of pollution policy not accounted for in
the empirical work.
The Redistribution Motive.––Even if countries are small in world markets, governments may adjust pollution taxes to try to undo the redistribution of income caused by increased openness. We refer to this as the redistributive motive. To illustrate this motive, retain our small open economy
framework, but now assume Greens and Browns differ in factor ownership,with Browns having greater capital per person than Greens; for simplicity,
let u (I ) = ln(I ). Then given the government’s weight λ on Greens, thepollution tax will be used both to target pollution and also to influence the34. We know that the gap is zero when tariffs are optimal and is negative whentariffs are zero, so “on average” we expect an increase in openness to widen thegap. However, it should be noted that because the right-hand side of (28) includes
the elasticity of foreign export supply, world prices and so forth, the gap between τand marginal damage may not increase monotonically as tariffs fall.

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Werner Antweiler, Brian R. Copeland, and M. Scott Taylor

income distribution. This again yields a gap between the pollution tax andeffective marginal damage:(29)

τ − Tφ ( p, I ) =

λ−s
dp/dτ
G
,
s(1 − s) d z /dτwhere s is the share of Greens in national income. Note that if the weight
given to Greens exceeds their current share of national income, then thepollution tax is higher than marginal damage. This is because higher pollution taxes lower the producer price of X and raise the real return to labor.
Alternatively, if the weight given to Browns is greater than their current
income share, the right-hand side of (29) is negative: the pollution tax is
set below marginal damage to raise the real return to capital.
Consider the effects of increased openness, starting from the position
where λ = s. In this case, the pollution tax in a dirty good exporting
country rises above marginal damage to compensate for the Greens loss inincome.35 Increased openness hurts workers in this case, and the government cushions the blow by tightening the pollution tax to raise wages. Fora dirty good importer, the result is reversed: increased openness leads to aloosening of pollution policy to compensate for Browns’ loss in income.
Implications of the Theories.––Each theory adds a country-specific unmeasured factor to our simpler determinants of pollution. The factor is acountry-type effect, and it is relevant to both a country’s degree of openness and its pollution supply curve. In the large-country case, the unmeasured country type is described by its trade pattern and market power; andin the redistributive theory, by its preferred and actual income distribution.
The impact these country-type effects have on our empirical results depends on whether they are time varying. If the country differences are simple level effects and do not vary over time, then our fixed-effects implementation is appropriate, even if country type is correlated with otherright-hand-side regressors. If country type is uncorrelated with the righthand-side variables, then our random-effects estimation is more efficientand still unbiased. On average, countries of different types would have different pollution levels, but they would respond similarly to changes inopenness, scale, and so forth. Given that the panel is quite short for many
countries, this constant-over-time country-type assumption may be appropriate.
If these country-type effects are time varying, then they will be corre35. Let Γ = τ − Tφ (p, I ). Then, evaluating at λ = s, we have d Γ/dβ = −sβ G |sτ |![|z |s(1 − s)] > 0, because s < 0 (an increase in openness reduces workers’ shareτ

of income).

β

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Is Free Trade Good for the Environment?

lated with our measure of openness. Consequently, our results concerning
the effects of further openness and income on pollution may be undermined. To assess whether these motives could be responsible for our results, consider what is left out by our simpler specification. Start with tariff
substitution. When tariffs are reduced and openness rises, tariff substitution
creates an unaccounted-for upward shift in pollution supply for a dirty
good exporter. This leads to less pollution than our model would predict.
Alternatively, tariff substitution produces an unaccounted-for downward
shift in pollution supply for a dirty good importer. In this case, tariff substitution leads to more pollution than our model would predict. In bothcases, unaccounted-for shifts in supply work against the shift in pollution
demand created by further openness. Similarly, the redistributive motive
shifts the pollution supply curve up for a dirty good exporter and down fora dirty good importer in response to increased openness. Again, we findthat this additional potential determinant of pollution tends to dampen thecomposition effect created by further openness.
Could tariff substitution or redistribution motives be responsible for thelarge technique effects we find? Both of these alternative theories lead toan unmeasured positive relationship between pollution and openness forsome countries. Therefore, it is difficult to see how the omission of eitherof these two additional determinants would manifest itself in a stronger
measured negative relationship between income and pollution.
These two alternative theories, however, do suggest a smaller (than wewould otherwise predict) change in the composition of output created by afall in trade frictions. As such, another interpretation of our findings of asmall trade-induced composition effect is that governments may be simultaneously dampening the impact of increased openness on pollution withcompensating changes in pollution taxes. To disentangle the additional
shifts in pollution supply suggested by either theory from the other effects
in our data would require us to obtain information on changes in both tariff levels and pollution regulations over time for many countries in our
sample; or employ knowledge about the preferred and actual income distribution in many countries over time. But good cross country and timeseries data on pollution regulations and trade protection are unavailable,
and the preferred income distribution is unobservable. These two alternative theories are perhaps best examined within a single country context
where data on regulations, tariffs, and income distribution are available.36

36. We discuss here the extreme case where pollution policy is the only available instrument. There are many other instruments (such as production subsidies),
which are a better substitute for a tariff; and similarly there are many other instruments (such as income transfers), which can redistribute income. To the extent thatthese other instruments are available, then the dampening shift in pollution supply
that we find above will be less relevant.

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Werner Antweiler, Brian R. Copeland, and M. Scott Taylor

4．
Conclusions
This paper investigates how openness to trading opportunities affects
pollution concentrations. We started with a theoretical specification highlighting scale, technique, and composition effects and then showed how
this theoretical decomposition is useful in thinking about the relationshipbetween openness to international markets and the environment. In our empirical section we adopted a specification directly linked to our earlier theory. We then estimated this specification, paying special attention to thepotentially confounding influences introduced by the panel structure of ourdata set. Our results consistently indicate that scale, technique, and composition effects are not just theoretical constructs with no empirical counterparts; rather, these theoretical constructs can be identified and their magnitude measured. Moreover, once measured they can play a useful role in determining the likely environmental consequences of technological progress,
capital accumulation, or increased trade. These estimates may also be useful in aggregate CGE modeling of the effects of various free trade agreements and other trade reforms (see, e.g., Michael J. Ferrantino and Linda
A. Linkins (1996)).
Our work is distinguished by the endogeneity of pollution policy and theclose connection we have tried to draw between theory and empirical estimation. Although it represents a useful first step toward answering our title’s question, it is clearly not the last. The benefits of our approach aretransparency, simplicity, and explicitness. We have presented an explicit
model of trade and pollution and we have moved from theory to empiricalestimation in a transparent manner. Transparency immediately leads to suggestions for extension along both theoretical and empirical lines. Simplicity
means additional questions can be addressed within our framework. And
the benefit of presenting an explicit pollution demand-and-supply model isthat researchers should now be drawn to deeper questions concerning endogeneity, omitted variables, and sample selection. We view this paper’s
attempt at integrating theory with empirical work as its major contribution
to ongoing research in this area.
Several extensions seem natural. One cost of reduced-form estimation isthat structural parameters remain hidden. Reduced-form estimation was essentially forced on us by the lack of data on regulations in many developing countries. If we adopt similar methods but restrict the sample to industrialized countries, we could then employ measures of pollution stringency
as proxies for pollution regulations. With data on both the quantity and“price” of pollution, the identification of structural parameters seems possible. A shift to a narrower set of countries with more detailed data may also
allow us to examine the tariff substitution and redistributive motives we
discussed, but did not estimate, here. Finally, our method for adding up
scale, composition, and technique effects could be enhanced by direct esti-

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Is Free Trade Good for the Environment?

mates of the income gains brought about by trade liberalization, and improved by explicit consideration of foreign direct investment and technology transfer.
As with any empirical exercise some questions remain unanswered, but
overall our estimates indicate that increases in a country’s exposure to international markets create small but measurable changes in pollution concentrations by altering the pollution intensity of national output. Although
our estimates indicate that greater trade intensity creates only relatively
small changes in pollution via a composition effect, economic theory andnumerous empirical studies demonstrate that trade also raises the value ofnational output and income. These associated increases in output and incomes will then exert an impact on pollution concentrations via our estimated scale and technique effects. Our estimates of the scale and techniqueelasticities indicate that, if openness to international markets raises both
output and income by 1 percent, pollution concentrations fall by approximately 1 percent. Putting this calculation together with our earlier evidence
on composition effects yields a somewhat surprising conclusion with regard to sulfur dioxide: freer trade is good for the environment.
Appendix A. Proof of Propositions
Proof of Proposition 1
Use (17) and (18), and hold T, S, I, K/L, and p w constant:

[

] [
+ε
)(1 − ε]zˆ = (1 + a )ε ϕ , p + ε e , p /τ βˆ − aε ϕ , p + ε e , p /τ τˆ[(= ε ϕ , p + aε ϕ , p

e , p /τMD , p)]βˆ .

Using Roy’s identity, we can show that ε MD,p is equal to the share of x in
consumption (note that when calculating this elasticity, real income I isheld constant, and so we obtain a pure substitution effect). Hence,
ε MD,p < 1, and z rises as β rises. For a dirty good exporter, increased
openness corresponds to an increase in β , and hence all else equal, a reduction in trade frictions raises pollution. For a dirty good importer, a reduction in trade frictions lowers β , and pollution falls.
Proof of Proposition 2
Note z = −Rτ (where Rτ = −eRp and Rττ > 0). ThenN[

dz = − Rττ dτ + p w (1 − θ ) Rτp N dβ⎤
⎡ dτ
= Rττ ⎢ p w
dβ − dτ ⎥,⎥⎦⎢⎣ dp z]

348

Werner Antweiler, Brian R. Copeland, and M. Scott Taylor

where the last step follows from differentiating z = −Rτ , holding z constant.
Next eliminate dτ by differentiating (10), noting that I = G /(Nρ ) and thatdG = p w(1 − θ ) Rp d β + τ dz. Rearranging and converting to elasticity
form yieldsNdz ⎡ p dτ
pM ⎤=⎢− ε MD , p + ε MD , I
⎥ H,
G ⎥⎦
dβ ⎢⎣ τ dp z
where M is imports of X and H is a positive expression. From the proofof Proposition 1, ε MD,p < 1. But (p/ τ )(dτ /dp)|z > 1 because z = ex and e isdecreasing in τ /p. (An increase in p raises x, and so to keep z constant,
we need τ /p to rise.) Hence, if M > 0, then dz /dβ > 0 and so increased
openness reduces pollution for a dirty good importer (β falls). For a dirty
good exporter, M < 0 and β rises when openness rises. From the proof of
Proposition l, ε MD,p is the share of X in consumption, and so with
ε MD,I 1, we have!

d z ⎡ p dτ
px ⎤
>⎢
−
⎥ H > 0,dβ ⎢⎣ τ dp z G ⎥⎦!

where px/G < 1 is the share of X in output at domestic prices. So pollution rises for a dirty good exporter if ε MD,I
1. Finally, if ε MD,I is sufficiently large, the sign of dz /dβ is reversed for a dirty good exporter andpollution falls as openness rises.
Proof of Proposition 3
For a given p and I , Home’s relative demand RD (p) is fixed. For given
p and I , the unit input coefficients given in (6) are fixed, and hence χ approaches infinity as κ rises. Consequently, there exists a κ such that forκ > κ , χ exceeds relative demand, and Home exports X . The increase inpollution via the trade-induced composition effect follows from Proposition
1.
Proof of Proposition 4
The relative producer price of X is p N < p(l − θ )−τ e(1), where e(l) > 0.
Because ε MD,I > ε > 0, τ increases without bound as income rises given(18). Moreover, θ rises from (4), and hence there exists some I for whichp N falls to 0, in which case X output is 0. The relative demand for X is,
however, independent of income. Hence for sufficiently large I , Home
must import X and export Y . The fall in pollution from the trade-induced
composition effect follows from Proposition 1.

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Is Free Trade Good for the Environment?

Proof of Proposition 5
Define trade intensity as the value of exports plus imports at world
prices (excluding transportation services). Using the trade balance constraint,
TI = 2 p w

Mxp w (1 − θ ) x + y,where Mx is imports of X . Consider first an importer of X (Mx > 0). Let
G w = p w(1 − θ ) x + y, and G = β p w(1 − θ ) x + y. By homotheticity, we
can write the demand for X as D x = h(p)G . Letting δ x = p wD x/G w, and= p w(1 −θ ) x/G w, we have TI = 2(δ x − ). With some rearranging, we
can write[]δ x = p w h 1 + ( β − 1)ϕ .
Then
1 ∂TI ∂δ x ∂ϕ
=
−
2 ∂β
∂β ∂β

( p ) ⎡⎢ ∂D
=
w 2

x

G w ⎢⎣ ∂p u

−

⎤
∂D x
M x ⎥ + p w h( β − 1) − 1 ϕ β < 0,
∂G
⎥⎦

[

]

! !

where we have used the Slutsky decomposition. Note that the substitution
effect in demand is negative ( D x/ p|u < 0) and the income effect( D x/ G ) is positive, so the bracketed term involving demand changes isnegative. As well, p wβ h < 1 from the consumer’s budget constraint, and
β > 0 (an increase in β shifts production toward X ) and so the last term
is negative as well. Thus TI/ β < 0 for an importer of X . Hence a fall inβ (a movement toward 1) increases trade intensity. For an exporter of X ,one can proceed most simply by replacing |p wMx| with imports of Y , My in
the definition of trade intensity and following a similar analysis as earlier
to conclude that an increase in β (a movement toward 1) raises trade intensity.

! !

! !

Appendix B. Data Set Description
The dependent variable in our study is the concentration of sulfur dioxide at observation sites in major cities around the world as obtained
through the GEMS/AIR data set supplied by the World Health Organization. Measurements are carried out using comparable methods. Each obser-

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Werner Antweiler, Brian R. Copeland, and M. Scott Taylor

vation station reports annual summary statistics of SO2 concentrations suchas the median, the arithmetic and geometric mean, as well as 90th and 95
th percentiles.
We have chosen to use a logarithmic transformation of the median SO2
concentration as our dependent variable. The distribution of concentrations
is highly skewed toward zero when viewed on a linear scale. As waspointed out in the WHO (1984) report about the GEMS/AIR project, concentrations are more suitably described by a lognormal distribution with anumber of observations concentrated at the measurement threshold of themeasurement devices. There is also an ambient level of SO2 in the air thathas natural causes.
A large share of observations were from the United States because ofthis country’s extensive network of air quality measurement stations. Other
large contributor countries were China, Canada, and Japan. Many of theother observation stations provided short or discontinuous streams of data
while participating in the GEMS/AIR project. All in all, our analysis isbased on over 2,600 observations from 293 observation stations in 109 cities around the world; these cities are located in 44 countries.
The primary source for our data is the AIRS Executive International Database that contains information about ambient air pollution in nations thatvoluntarily provide data to the GEMS/AIR program sponsored by theUnited Nations World Health Organization.37 We had problems with theidentification of several observation stations. The longitude and latitude information provided in one of the ancillary files was in some cases incorrect and was corrected case by case based on the description of the location.
Additional data sources for our regressors include the Penn World Tables 38 for macroeconomic data, the World Investment Report 39 for inward
FDI stock data, the CIESIN Global Population Distribution Database 40 for
37. This package is available from the United States Environmental Protection
Agency (US-EPA) at http://www.epa.gov/airs/aexec.html. The US-EPA kindly provided a much more complete version of this data set that included not only averages but also median and other percentiles of SO2 concentrations. We would like toexpress our gratitude to Jonathan Miller of the US-EPA for providing additional
GEMS/air data not contained in the public release of the data base, and for patiently answering our numerous technical questions.
38. Robert Summers and Alan Heston, “The Penn World Table (M5): Expanded
Set of International Comparisons, 1950-1988.” Quarterly Journal of Economics,
May 1991, 106(2), 327-68. Available in revision 5.6 from the Center for International Comparisons at the University of Pennsylvania at http://pwt.econ.upenn.edu/.
39. United Nations Centre on Transnational Corporations, 1992 and 1999 volumes.
40. This data set from the Consortium for International Earth Science Information Network (CIESIN) is available only for 1990. It can be obtained freely fromthe United Nations Environmental Programme server maintained by the U.S. Geological Survey at http://grid2.cr.usgs.gov/globalpop/ l-degree/description.html.

351

Is Free Trade Good for the Environment?

population density data, the World Resources Institute World Resources
Database 41 for natural resources and physical endowments, and data fromthe Global Historical Climatology Network 42 (GHCN) for weather conditions at the observation stations. Yet more time series were obtained fortariff and nontariff trade barriers43 and educational attainment.44
Summary statistics for the major variables appear in Table B1. Some ofthe variables warrant further explanation. First, our scale measure of economic activity GDP per square kilometer is calculated by multiplying acountry’s real per capita GDP ($/person) with each city’s population density (people/km2). Extrapolations for per capita GDP were carried out for
the years past 1993 based on real growth rates obtained from the IMF/IFS
statistics. Population densities were available only for 1990.
Table B1. Summary Statistics
Variable
Log of SO2
City economic intensity
GDP per capita(current)
Population density
Capital abundance(adjusted)
Capital abundance(unadjusted)
Education attainment
GNP per capita, 3-yr average
Communist country(C.C.)
C.C.× income
Trade intensity(X +M )/GDP
Relative(K /L)(adjusted)
Relative income
Inward FDI stock/capital stock
Average temperature
Precipitation coefficient of variation
Hard coal reserves
Soft coal reserves

Dimension

Number ofobservations

Mean

SD

Min

Max

log10(ppm)$m per km2$10k
1,000 people/km2$10K/worker$10K/worker
0-1 range
$10k
［ ］
$10k
［ ］
World=1.00
World=1.00
［ ］
℃
［ ］
GJoule/worker
GJoule/worker

2,555
2,555
2,555
2,555
2,555
2,555
2,555
2,555
2,555
319
2,555
2,555
2,555
2,555
2,555
2,555
2,555
2,555

−2.112
0.790
1.478
0.063
5.612
3.207
0.540
1.396
0.125
0.302
0.409
1.357
2.500
0.106
14.689
0.011
0.040
0.038

0.481
0.878
0.862
0.055
2.497
1.763
0.226
0.815
0.331
0.208
0.322
0.605
1.392
0.250
5.600
0.006
0.043
0.052

−3.000
0.010
0.109
0.001
0.829
0.130
0.088
0.111
0.000
0.127
0.088
0.203
0.221
0.001
2.617
0.001
0.000
0.000

−0.939
5.934
2.718
0.276
17.189
7.750
0.799
2.635
1.000
0.716
2.617
4.174
4.138
2.193
28.967
0.054
0.146
0.348

!
!

!
!

Notes: All monetary figures are in 1995 U.S. dollars. The interaction term for income with
the Communist countries dummy shows the case only where the dummy is equal to 1; thus
the mean for this line is the mean for the Communist countries only.

41. World resources 1998-1999: A guide to the global environment, Oxford: Oxford University Press, 1998.
42. Information is available on monthly average temperatures, monthly precipitation, and atmospheric pressure. The raw data and description file are available fromthe National Climatic Data Center of the U.S. National Oceanic and Atmospheric
Administration at ftp://ftp.ncdc.noaa.gov/pub/data/ghcn/.
43. See Jeffrey D. Sachs and Andrew M. Warner: “Economic Convergence andEconomic Policies.” National Bureau of Economic Research (Cambridge, MA)
Working Paper No. 5039, February 1995.
44. These figures were obtained from Robert J. Barro and Jong-Wha Lee’s(1994) study, available from the NBER website at http://www.nber.org/pub/barro.
lee/ZIP/.

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Werner Antweiler, Brian R. Copeland, and M. Scott Taylor

The capital abundance (K/L) of countries was obtained from the physical capital stock per worker variable in the Penn World Tables. We haveadjusted this series for human capital by applying a 0-1 average educationindex (in which 1 represents 16 years of schooling) obtained from theBarro/Lee data set. Relative capital abundance is obtained by dividing eachcountry’s capital abundance by the corresponding world average for the
given year, where “world average” is defined by all the countries in the
Penn World Tables.
Our income (I ) variable is the three-year average of lagged GNP per
capita. This addresses two problems. First, contemporaneous income andthe level of pollution may be determined simultaneously. Lagged income,however, is exogenous. Second, it is reasonable to assume that incomechanges translate only slowly into policy changes. We therefore smoothout some of the variation introduced through business cycles and include
three years of data. (We also experimented with longer lags, without mucheffect on our results.) More concretely, for a given year t we compute
It = (yt−1 + yt−2 + yt−3)/3. Relative income is constructed in the same fashion
as our relative capital-abundance measure. GNP figures were obtained byadjusting GDP figures with a GNP/GDP correction factor obtained fromthe International Monetary Fund’s International Financial Statistics. However, such correction factors were unavailable for the former Czechoslovakia, Egypt, Hong Kong, Iraq, Peru, Poland, and the former Yugoslavia.
Unadjusted GDP figures were used in these cases.
The data on foreign direct investment (FDI) were obtained as percentages of the stock of inward FDI relative to GDP, and interpolated where
necessary. These figures were then divided by GDP to capital stock ratios
obtained from the Penn World Tables to obtain the percentage of inward
FDI stock relative to a country’s entire capital stock.
The suburban and rural location type dummy variables are from theoriginal GEMS/AIR data set. The third (default) location type is central
city. Our trade intensity measure is calculated as the sum of exports andimports expressed as a percentage of gross domestic product. The Communist country dummy used in our study identifies the following countries:
China, Czechoslovakia, Poland, and Yugoslavia. The country dummy for
the Helsinki Protocol identifies Austria, Belgium, Bulgaria, Canada,
Czechoslovakia, Denmark, Finland, France, Germany, Hungary, Italy, Luxembourg, The Netherlands, Norway, and Switzerland, in the years after1985.
For the purpose of calculating sample-mean elasticities we used averagesof the relevant variables calculated as follows. An average country value
for variable X is calculated by first averaging X ’s values over time foreach country, and then averaging across countries. This procedure gives
equal weight to all countries.

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Is Free Trade Good for the Environment?

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Shafik, N. 1994. Economic Development and Environmental Quality: An Econometric Analysis. Oxford Economic Papers Supp. 46: 757-773.
Siebert, H., J. Eichberger, R. Gronych and R. Pethig. 1980. Trade and the Environment: A Theoretical Enquiry. Amsterdam: Elsevier/North-Holland.
Tobey, J. A. 1990. The Effects of Domestic Environmental Policies on Patterns ofWorld Trade: An Empirical Test. Kykios 43(2): 191-209.
United Nations Environment Programme. 1991. Urban Air Pollution. Nairobi:
UNEP.
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North-Holland.
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and the World Health Organization.

Acknowledgements to the Publishers

The editors and publisher wish to thank the following publishers andauthors who have kindly given permission for the use of copyright material.

The American Economic Association for the article: Werner Antweier,
Brian R. Copeland and M. Scott Tayler. “Is Free Trade Good to the Environment?”. American Economic Review vol.91, no.4, 877-908, Sep.
2001.
The Econometric Society for the article: Jonathan Eaton and Samuel Kortum. “Technology, Geography, and Trade”. Econometrica vol.70, no.5,
1741-1779, Sep. 2002.
Delhi School of Economics for the article: Ronald Jones. “Trade, Technology, and Income Distribution”. Indian Economic Review, vol.32, no.2,
129-140, July-Dec. 1997.
The Japanese Economic Association for the article: Tatsuo Hatta. “Whynot Set Tariffs Uniformly Rather than Optimally”. The Economic Studies
Quarterly, vol.45, no.3, 196-212, Sep. 1994.
Blackwell Publishers Ltd for the articles: Wilfred Ethier. “Unilateralism ina Multilateral World”. Economic Journal vol.112, no.479, 266-292,
April 2002.
: Henrik Horn and James Levinsohn. “Merger Policies and Trade Liberalization”. Economic Journal vol.111, no.470, 244-276, April 2001.
: Satya Das. “Trade and Personal Distribution of Wealth and Income:Beyond the Stolper-Samuelson Theorem”. Pacific Economic Review
vol.6, no.1, 1-23, Feb. 2001.
Elsevier Science for the article: Alan Deardorff. “Fragmentation in Simple
Trade Models”. North American Journal of Economics and Financevol.12, no.2, 121-137, July 2001.
J.C.B. Mohr (Paul Siebeck) Verlag for the article: Wolfgang Mayer. “Endogenous Corrections of Economic Policies under Majority Voting”. Finanzarchiv Neue Folge, vol.55, no.1, 41-58, 1998.
Kluwer Academic Publishers for the article: Michihiro Ohyama. “International Adjustment under Capital Mobility”. In Global Competition andIntegration, eds. R. Sato, R. V. Ramachandran and K. Mino. 329-354,
1998.

355

RIEB KOBE Conference on“Recent Developments in International Trade:Theoretical and Empirical Investigations”
ProgramMarch 22-24, 1998
Kobe University, Kobe
8:45-9:00

Welcome Address
Seiichi Katayama, Organizer (Kobe University)
Opening Address
Ken-ichi Ishigaki, Director of RIEB (Kobe University)

Session 1.

Sunday, March 22, 1998 9:00-12:15
Chair: Yasuhiro Sakai (Tsukuba University)

9:00-9:55

Satya Das (Indian Statistical Institute)“Trade and Personal Distribution of Wealth and Income:Beyond the Stolper-Samuelson Theorem”
Discussant: Shunpei Takemori (Keio University)

10:10-11:05

Sajal Lahiri (University of Essex and Osaka)“Export-Oriented Foreign Direct Investment and Local
Content Requirement”
Discussant: Kotaro Suzumura (Hitotsubashi University)

11:20-12:15

Tatsuo Hatta (Osaka University)“A Theory of Optimum Tariff under Revenue Constraint”
Discussant: Takashi Fukushima (Tokyo Metropolitan University)

12:15-2:15

Lunch BreakSession 2.

Sunday, March 22, 1998 2:15-5:30
Chair: Michihiro Ohyama (Keio University)

2:15-3:10

Brian Copeland (University of British Columbia)“Trade and the Environment: Theory and Empirical Results”

357

358

The Conference Program

Discussant: Makoto Tawada (Nagoya City University)
3:25-4:20

James Levinsohn (University of Michigan)“Merger Policies and Trade Liberalization”
Discussant: Fumio Dei (Kobe University)

4:35-5:30

Jonathan Eaton (Boston University)“Technology and Bilateral Trade”
Discussant: Keith Maskus (University of Colorado)

Session 3.

Monday, March 23, 1998 9:00-12:15
Chair: Tadashi Inoue (Hosei University)

9:00-9:55

Michihiro Ohyama (Keio University)“International Adjustment under Capital Mobility”
Discussant: Yoshiyasu Ono (Osaka University)

10:10-11:05

Carsten Kowalczyk (Tufts University)“Trade, Transfers, Developing Countries, and the Core”
Discussant: Noritsugu Nakanishi (Kobe University)

11:20-12:15

Keith Maskus (University of Colorado)“Is Small Beautiful? Trade Shares and Trade Creation
with Differentiated Products”
Discussant: Brian Copeland (University of British Columbia)

12:15-2:15

Lunch BreakSession 4.

Monday, March 23, 1998 2:15-5:30
Chair: Kotaro Suzumura (Hitotsubashi University)

2:15-3:10

Wilfred Ethier (University of Pennsylvania)“Unilateralism in a Multilateral World”
Discussant: Koji Shimomura (Kobe University)

3:25-4:20

Alan Deardorff (University of Michigan)“Fragmentation in Simple Trade Models”
Discussant: Makoto Yano (Keio University)

4:35-5:30

Ronald Jones (University of Rochester)“Trade, Technology, and Income Distribution”
Discussant: Michihiro Ohyama (Keio University)

359

The Conference Program

5:45-7:30

Conference Party
Second Floor of New Kanematsu Building
Rokkodai Campus, Kobe University

Session 5.

Tuesday, March 24, 1998 9:00-12:15
Chair: Kazuo Nishimura (Kyoto University)

9:00-9:55

Yuka Ohno and Kaz Miyagiwa (Rice University andKobe University)“Nuclear Bombs and Sanctions”
Discussant: Jota Ishikawa (Hitotsubashi University)

10:10-11:05

Ngo Van Long (McGill University)“Protection, Lobbying, and Market Structure”
Discussant: Sajal Lahiri (University of Essex and Osaka)

11:20-12:15

Wolfgang Mayer (University of Cincinnati)“Endogenous Corrections of Economic Policies under Majority Voting”
Discussant: Motoshige Ito (University of Tokyo)
Closing Address
Kaz Miyagiwa, Co-organizer (Kobe University)

KOBE ECONOMIC & BUSINESS RESEARCH SERIES

No.1 (1962)

History of the Yen

Hiroshi SHINJO

No.2 (1963)

Production Theory of International Trade
Hikoji KATANO

No.3 (1970)

Monetary Factors in Japanese Economic Growth
Edited by Jiro YAO

No.4 (1970)

Macro-economic Theory of Take-off Process
Hikoji KATANO

No.5 (1977)

Accounting Measurement under Uncertainties
Isao NAKANO

No.6 (1978)

Japan’s Direct Investment to ASEAN Countries
Hikoji KATANO et al.

No.7 (1979)

Economic Analysis of ShippingFreight
Tetsuji SHIMOJO

No.8 (1981)

Japanese Enterprises in ASEAN Countries −Statistical
Outlook
Hikoji KATANO

No.9 (1984)

Essay in Some Topics of Modern Economic Theory
Kazuo SHIMOMURA

No.10 (1989)

A Quantitative Analysis of Educational Policy in Postwar
Japan
Yasuo KONISHI

No.11 (1992)

Innovation and Business Dynamism in Japan and Korea
Edited by Kenji KOJIMA

No.12 (1993)

Essays on the Economic Analysis of Labour Union
Kazuo SHIMOMURA

No.13 (1997)

Economic Relations and Developments in Asia and Pacific:
Collected Papers of International Cooperation Studies
Edited by Kazuhiro IGAWA

No.14 (1997)

Japanese Corporate Governance: An International
Perspective
Kenji KOJIMA

No.15 (2000)

Commitments and Contests: A Game-theoretic
Perspective on Japanese Vertical Relationships
Kenji KOJIMA