NBER WORKING PAPER SERIESTARIFF REDUCTIONS, ENTRY, AND WELFARE:
THEORY AND EVIDENCE FOR THE LAST TWO DECADES
Lorenzo Caliendo
Robert C. Feenstra
John Romalis
Alan M. Taylor
Working Paper 21768
http://www.nber.org/papers/w21768

NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
December 2015

Financial support from the National Science Foundation and the Sloan Foundation is gratefully acknowledged.
We thank Federico Esposito and Mingzhi Xu for excellent research assistance. For their helpful comments
we thank Kyle Bagwell, Fernando Parro, Stephen Redding, Esteban Rossi-Hansberg, Ina Simonovska,
and seminar participants. The usual disclaimer applies. The views expressed herein are those of theauthors and do not necessarily reflect the views of the National Bureau of Economic Research.
NBER working papers are circulated for discussion and comment purposes. They have not been peerreviewed or been subject to the review by the NBER Board of Directors that accompanies official
NBER publications.
© 2015 by Lorenzo Caliendo, Robert C. Feenstra, John Romalis, and Alan M. Taylor. All rights reserved.
Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided
that full credit, including © notice, is given to the source.

Tariff Reductions, Entry, and Welfare: Theory and Evidence for the Last Two Decades
Lorenzo Caliendo, Robert C. Feenstra, John Romalis, and Alan M. Taylor
NBER Working Paper No. 21768
December 2015
JEL No. F10,F11,F12,F13,F15,F17,F60,F62
ABSTRACT
Tariffs have fallen significantly around the globe over the last two decades. Yet very little is known
about the trade, entry, and welfare effects generated by this unprecedented shift in trade policy. We
use a heterogeneous-firm quantitative trade model to study the effects of observed changes in trade
policy. Importantly, in our model, tariffs affect the entry decision of firms across markets, a channel
that has been unduly overlooked in the literature. We first show how trade policy influences entry
and selection of firms into markets. We then use a new tariff dataset, and apply a 189-country, 15-sector
version of our model, to quantify the trade, entry, and welfare effects of trade liberalization over theperiod 1990–2010. We find that the impact on firm entry was larger in Advanced relative to Emerging
markets; that more than 90% of the gains from trade are a consequence of the reductions in MFN tariffs(the Uruguay Round); that PTAs have not contributed much to the overall gains from trade; and that,with the exception of a few Emerging and Developing countries, most countries do not gain much(and some lose) from a move to complete free trade under zero tariffs.

Lorenzo Caliendo
Yale University
School of Management
135 Prospect Street
New Haven, CT 06520
and NBER
lorenzo.caliendo@yale.edu

John Romalis
The University of Sydney
School of Economics
H04 - Merewether
NSW 2006 Australia
and NBER
jromalis@gmail.com

Robert C. Feenstra
Department of Economics
University of California, Davis
One Shields Avenue
Davis, CA 95616
and NBER
rcfeenstra@ucdavis.edu

Alan M. Taylor
Department of Economics andGraduate School of Management
University of California
One Shields Ave
Davis, CA 95616-8578
and CEPR
and also NBER
amtaylor@ucdavis.edu

1Introduction

After six postwar decades of relentless progress, in recent years world trade
growth, and world trade liberalization, have both now seemingly ground to halt.
Globally, trade grew twice as fast as GDP in the 25 years prior to 2007, but at
a rate below GDP since late 2011. The multilateral rounds of tariff negotiations
under the World Trade Organization (WTO) have stalled, possibly to the pointof no return, and the 2001 Doha Round—hailed as a “development round” butconcluded with a few face-saving proposals—failed in its primary goal of lowering tariffs for developing countries. With trade growth stagnant, little to show fora decade of WTO talks, and substantial roadblocks even standing in the way ofsmaller-scale deals like TPP and TTIP, should we conclude that tariff liberalization
aimed at furthering gains from trade has largely run its course, and compared tothe past has much less of a role to play in the world today?
We will argue that the answer could be yes for most, if not all, countries. To
make this case convincingly, however, we need to extend the leading current trademodels, and we need to take the application and calibration of these models to a
global level using data of a scope not seen before.
From a theoretical perspective, we not only build upon the most up-to-datemodel in international trade—with heterogeneous firms in the tradition of Melitz(2003) and Chaney (2008)—but also extend this model to incorporate tariffs andthe kind of input-output structure that is realistic for modern economies, following Caliendo and Parro (CP, 2015). With these more general model foundations,
we find that firm entry decisions can have meaningful impacts on trade and welfare, in ways not captured hitherto in many current-generation trade models.1
From an empirical perspective, we then go well beyond recent quantitative
exercises in expanding the data universe to build a tariff dataset that includes
not just the usual sample of Advanced (e.g., OECD) economies, but also a large
subsample of Emerging and Developing economies, using newly collected data
going back to the 1980s.2 Our work therefore permits a broader and more realistic
1 The importance of the input-output structure has been made clear in recent work by Costinot
and Rodrı́guez-Clare (2014). They used stylized, uniform tariff cuts to show how the gains fromtrade are systematically larger when the input-output structure is taken into account. Here are
echoes of an earlier trade literature on distortions due to high effective rates of protection, andmore recent empirical trade and growth papers highlighting the damaging effects of tariffs on
inputs (Goldberg et al. 2010; Estevadeordal and Taylor 2013).
2 We unify tariff schedules from five different sources. With more than 1 million observations per
year in the 1980s, rising to 2 million by the 2000s, with our tariff data we can perform tariff policy
experiments which could not be explored before now.

1

computation of the retrospective, and prospective, gains from trade liberalizationin both rich and poor nations, a step we think is crucial since it is in the poorer
countries that trade liberalization has proceeded most rapidly since 1990, and inwhich there yet may be still significant scope for further tariff reductions.
To sum up, our paper develops new theoretical results about tariffs, and theireffects on trade, entry, and welfare; it builds a new tariff dataset, uses data fromhigh- and low-income countries to calibrate the model; and it uses the model toperform policy experiments to evaluate the gains from actual past trade liberalization and possible future gains yet to be realized.
We implement three policy experiments. First, we quantify the effects for 189
countries and 15 sectors of, allegedly, the most successful GATT/WTO process,the Uruguay Round.3 We do so by evaluating the economic effects of the observedchange in Most Favored Nations (MFN) tariffs for countries at the product levelfrom the year 1990 to 2010. We then go beyond Uruguay Round and evaluate
the impact of all observed changes in tariffs, namely MFN and preferential tariffs,
during the same period. With this, we evaluate the effects of what we refer to
Uruguay Round + Preference. Finally, we ask if there are any further gains in theworld today by zeroing all tariffs, what we refer as Free Trade.
We find that the Uruguay Round had a profound impact. Almost all of thegains from tariff elimination result from the Uruguay Round. We find the effects
from additional tariff reductions, namely PTAs, have not contributed much tototal world trade and welfare. In fact, as a result of PTAs relative to MFN wefind, on average, a tiny increase on average trade share (measured as imports toincome ratio), whereas on its own the Uruguay Round doubled this average share.
In terms of welfare, Uruguay Round generated an average increase in welfare of
5.6% while the additional effect in welfare from PTAs is 0.3%.
When looking at countries by income group, we find that both the Advanced
and the Emerging and Developing economies gained most from Uruguay Roundtariff elimination relative to PTAs. We also find that the distribution of gains
across these two groups are quite different. For the Advanced economies, mostcountries gain and the gains do not vary widely. However, for Emerging and Developing economies, not all countries win, but the ones that do gain substantially.
We also go beyond trade and welfare effects and evaluate how commercial
3 Bagwell and Staiger (2010) survey recent economic research on trade agreements, with special
focus on the GATT/WTO. For earlier research on the impact of trade agreements, see, inter alia,
Anderson and van Wincoop (2002), Baier and Bergstrand (2007; 2009), Deardorff (1998), Redding
and Venables (2004), Rose (2004), Subramanian and Wei (2007), Trefler (1993; 2006).

2

policy has affected the entry and exit of firms across markets. We find that tariffs affect firm entry in very different ways across countries. For instance, thereductions in tariffs as a consequence of the Uruguay Round generated considerable changes in entry and exit of firms across industries in Advanced economies,
while there was a much smaller effect on Emerging economies. This differential
effect on entry, driven by international trade, is one of the reasons which may
explain why welfare effects can vary so much across income groups.
The results are striking when we consider moving to a world without tariffs.
Our results show that there may be extra gains for some Emerging economies.
This is a very different picture compared to the case of Advanced economies
where, according to our calculations, they appear not to gain much more frommoving to a world with no tariffs. Therefore, our results indicate that the Uruguay
Round of negotiation accomplished an awful lot for the Advanced economies,
with gains left on the table mainly for the Emerging and Developing economies.
The remainder of the paper is structured as follows. In Section 2 we briefly
recap the current generation of trade models, their treatment of tariffs and entry,
and how these relate to gains from trade; then, introducing the main departures
we take in this paper, we stress the critical role played by assumptions on tariffstructures, iceberg versus tariff frictions, input-output structure, and the possibility of firm entry (that is, as distinct from firm selection). In Section 3, we present
the quantitative model. In Section 4, to develop intuition, we present some key results with the aid of a simplified two-sector symmetric model. Section 5 describes
the new tariff dataset and the rest of the data sources that we use in order tocalibrate the 189 countries, 15 sector version of the model. Section 6 explains how
we take the model to the data, and section 7 presents the empirical results whichquantify the gains from tariff liberalization in the last 20 years, and the potential
remaining gains from tariff liberalization going forward. Section 8 concludes.

2

Tariffs, Icebergs, Entry, and Welfare

The recent work of Melitz and Redding (2015) shows how, in a Melitz (2003)
model, after relaxing the assumption of a Pareto distribution of firm productivities
assumed in Chaney (2008), changes in iceberg trade cost impact entry and welfare.
A major contribution of this paper is to clearly explain how tariffs affect entry, andultimately welfare, in a Melitz (2003) model, even without relaxing the maintained
assumption of a Pareto distribution of firm productivities.

3

We believe that the potential for tariffs to impact entry has been largely overlooked in the literature. One reason for this is that iceberg transport costs do
not affect entry in a Melitz-Chaney model, as shown most clearly by Arkolakis,
Costinot, and Rodrı́guez-Clare (ACR, 2012). One of their “macro” assumptions—which they label R2—is that aggregate profits in any country i (Πi , measured
gross of the entry fee) are a constant share of aggregate revenue (Ri ), and thatassumption is indeed satisfied in the special case of a Pareto distribution on productivity draws. In the further special case of a symmetric, one-sector, one-factor
model, revenue equals the factor supply (Li ), since without loss of generality we
can normalize wages wi = 1. In turn, revenue is fixed, aggregate profits are also
fixed, and since these equal the number of entrants N times the fixed costs ofentry f iE , it follows that Ni = Πi / f iE ∝ Ri / f iE = Li / f iE , which in turn is also thenfixed. Therefore, changes in iceberg transport costs have no impact on entry inthis case.4
The first paper to introduce ad valorem tariffs into a Melitz-Chaney model that
we are aware of is the important contribution of Balistreri, Hillberry, and Rutherford (2011). They note that entry is no longer necessarily fixed when either (i) ad
valorem “revenue” tariffs are imposed rather than iceberg transport costs, or (ii)there are multiple sectors. Their quantitative model is based on GTAP and models
the heterogeneous-firm sector as a single, aggregate manufacturing sector, withadditional constant-returns sectors in the economy. Our approach makes further
advances in several respects. We use a similarly simplified structure to analyticallysolve for the impact of ad valorem tariffs on entry in a 2-country symmetric version of our model, while in our more general quantitative model we use multiple
heterogeneous-firm sectors. In addition, our tariff data are much more detailed
than Balistreri et al. (2011), who consider a 50% tariff cut rather than the actual
impact of the Uruguay Round.5
Two more recent contributions have also sought to consider ad valorem tariffs
as opposed to iceberg transport costs in a Melitz-Chaney model: these are theworks by Felbermayr, Jung, and Larch (FJL, 2013, revised 2015) and Costinot andRodrı́guez-Clare (CR, 2014).6 In a working paper, FJL (2013) focus on a one4 In a multi-sector model, however, the factor supply to each sector is not fixed so it is quitepossible that changes in iceberg transport costs will affect entry, as ACR (section IV.A) note.
5 Another difference is that Balistreri et al. (2011) estimate all the fixed costs in their model from
GTAP data. In contrast, we use the “hat” algebra (Dekle, Eaton, and Kortum 2008) to solve forchanges in the key variables, which avoids the need to estimate fixed costs.
6 Contemporaneous work continues on this theme. Bagwell and Lee (2015) consider tariffs andentry in the Melitz-Ottaviano (2008) model. Hsieh et al. (2015), adopt a Melitz and Redding (2015)4

sector model with the ad valorem tariffs modeled as “revenue tariffs”—meaningthat the taxes are applied to full import revenue (covering all production costs,
fixed and variable, and profits, and hence fully inclusive of markups). In contrast,
CR focus in their main text on the case of ad valorem tariffs as so-called “costtariffs”—meaning that taxed are assumed only to the variable production costsof imports (without the markup, and without fixed costs or profits).7 CR also
introduce multiple sectors and traded intermediate inputs. Both papers allow for
only a fraction (including zero or one) of tariff revenue to be rebated to consumers.
Building on CR’s treatment, the in-press version of FJL (2015) allows for bothrevenue tariffs and cost tariffs within a one-sector version of the Melitz-Chaneymodel, and then uses CR’s multi-sector quantitative model in their simulations.
Naturally, the reader may worry that cost tariffs are less appealing as a descriptionof reality, and arguably no more tractable, an issue we will return to.
In their working paper, FJL (2013) are clear that they believe assumption R2
continues to hold in a one-sector model, while using revenue tariffs with fractional
rebate. As a result, they argue, entry is fixed. In the in-press version, FJL (2015)
do not explicitly refer to R2, but make the stronger claim that entry is fixed witheither cost or revenue tariffs and regardless of the rebate: “there are no entry effects
associated with changes in iceberg costs and tariffs as innovation fixed costs are
assumed to arise in terms of domestic labor” (p. 6). We believe that the impact oftariffs on entry in the one-sector model is much more subtle than recognized by
FJL (2015), as we now explain (with full details given in Appendix A).
Consider first the case of cost tariffs, with no rebate to consumers. The government instead wastes the tariff revenue. Assume labor in country i is the numeraire, with wi = 1. Using a tilde to denote the consumer price—inclusive offreight and tariffs (if any)—and the corresponding consumer quantity, the firm incountry i selling to country j solves the profit-maximization problem
πij ( ϕ) = maxpeij ( ϕ)≥0p̃ij ( ϕ) q̃ij ( ϕ) −τij (1 + tij )q̃ij ( ϕ)− f ij ,ϕ(1)

where q̃ij ( ϕ) is the quantity chosen by consumers at the price p̃ij ( ϕ) , the firm’s
marginal costs inclusive of iceberg costs τij and the ad valorem cost tariff tij areτij (1 + tij )/ϕ, and f ij are the fixed operating costs. We assume CES demand withiceberg structure, and empirically examine the selection effect on firms due to the Canada-U.S. free
trade agreement, which occurred just prior to our sample period.
7 The case of ad valorem tariffs as revenue tariffs is briefly discussed in the online Appendix to
CR, who refer to these two types of tariffs as “cost-shifters” and “demand-shifters.”

5elasticity σ and a Pareto distribution, G ( ϕ) = 1 − ϕ−θ , for the firm productivities, with ϕ ≥ 1. Then it can be shown by evaluating the integrals below thatassumption R2 of ACR holds, namely:
Z ∞
ϕij∗

|

πij ( ϕ) dG ( ϕ) ={z

Πij ≡ profits from j

Z ∞

σ−1
σθ

}

ϕij∗

p̃ij ( ϕ) q̃ij ( ϕ) dG ( ϕ) ,

|

{z

(2)

}

e ij ≡ revenue paid by consumers in jR

where ϕij∗ is the zero cutoff profit level of productivity at which πij ( ϕij∗ ) = 0. Now,
summing over all destination markets j, denoting the mass of entrants by Ni andthe sunk costs of entry by f iE , and using the free-entry condition and equation (2),
−1 e
Ri =
our Appendix A shows that it is straightforward to obtain Ni f iE = Πi = σσθσ −1
Li , where Li is the labor earnings in this one-sector economy coming fromσθ
the aggregate revenue of firms. It immediately follows that entry

Ni =

σ−1
σθ



1
Li
f iE

(3)

is fixed and does not vary with iceberg trade costs or with unrebated cost tariffs.
In comparison, now consider the case of revenue tariffs with full rebate of thetariff to consumers. In this case, the tariff-inclusive price p̃ij ( ϕ) must be dividedby (1 + tij ) to obtain the net price pij ( ϕ) = p̃ij ( ϕ) /(1 + tij ) earned by the firm,
which is used to compute net revenue of the firm. Profits of the the firm are thenπij ( ϕ) = max

pij ( ϕ)≥0xi
pij ( ϕ) q̃ij ( ϕ) − τij q̃ij ( ϕ) − f ij .
ϕ(4)

Direct calculation of the integrals below shows that the analogous expression
for R2, but now in the presence of revenue tariffs, becomes
Z ∞
ϕij∗

|

πij ( ϕ) dG ( ϕ) ={z

Πij ≡ profits from j

}

Z ∞

σ−1
σθ

ϕij∗

|

pij ( ϕ) q̃ij ( ϕ) dG ( ϕ) .
{z

(5)

}

Rij ≡ revenue earned by firms from je ij paid
A clear difference between (2) and (5) is that the former uses revenue R
by consumers, whereas the latter uses revenue Rij earned by firms, and thesediffer when ad valorem revenue tariffs are used.8 This difference is immaterial,
8 In contrast, with iceberg trade costs then c.i.f. revenue paid by consumers (at c.i.f. prices butwith quantity net of iceberg costs) equals the f.o.b. revenue earned by firms (at lower f.o.b. prices
but with quantity gross of iceberg costs).

6

Table 1: Operation of the entry margin under different forms of trade costs
No rebate
Icebergs

No:

Rebate−1 1 LNi = σσθfE i

Not applicable−1 1 LNi = σσθ
fE i

Yes:

−1 1
Ni = σσθ(wi Li + Ti )
w fE

No:

−1 1 LNi = σσθfE i

iCost tariffs

No:i

Revenue tariffs

Yes:

−1 1
Ni = σσθ(wi Li − Ti )wi f Eii iiNote: The table shows whether the entry margin is operative or not for each combination of trade
costs and rebates in a one-sector model with Pareto productivity draws. See text and Appendix A.

however, when the tariff revenue is fully rebated. In that case the labor earnings
paid by the firm are still Li , equal to the labor endowment. Then summing overdestination markets j, firm revenue net of tariffs is Ri = Li . It follows that entry is−1−1
determined by Ni f iE = Πi = σσθLi , which is again fixed as in (3).
Ri = σσθYet, as the reader may anticipate, a careful re-examination of these two cases
shows that entry is not fixed under alternative assumptions on the tariff rebate.
For example, with full rebate of the revenue under cost tariffs, we would obtaine i in country i is at tariff-inclusive
Ni = σ−1 1 E R̃i . The consumer expenditure Rσθ wi f ie i = wi Li + Ti , which depends on the collected tariff revenue
prices is given by R
Ti . Therefore entry depends on the tariff, and is given by
Ni =

σ−1 1
(wi Li + Ti ) .
σθ wi f iE

Alternatively, with no rebate under revenue tariffs, then country i tariff rev−1 1
R , where
enue Ti is wasted. It follows that in this case we have that Ni = σσθw fE ii i

Ri = wi Li − Ti . Therefore entry again depends on the tariff, and is given by
Ni =

σ−1 1
(wi Li − Ti ) .
σθ wi f iE

Table 1 summarizes all of the above results, which apply to the benchmark caseof the one-sector model with Pareto productivity draws. It is worth emphasizing
an important and novel insight from these results, which is that the existence ofa revenue effect coming from a tariff rebate is neither necessary nor sufficient togenerate changes in entry.
As the table shows, given the variety of possible trade cost formulations any
analysis of the impact of tariffs on entry and welfare could in principle consider
7

all four hypothetical tariff/rebate configurations. But in this paper we focus exclusively on ad valorem tariffs applied to the revenue of imports. This choice ismade for two reasons. First, we feel that these tariffs are much more realistic,since the alternative cost-based tariffs in CR and FJL (2015) are applied only tothe variable costs of an import, and not to their fixed operating costs. We do notbelieve that such a distinction between variable and fixed costs is made when thecustoms value of an import shipment is claimed at the border.9 But the second,
more important reason, comes from our finding above that entry is fixed in the
one-sector model when using revenue tariffs. This is a very convenient, and conservative, starting point for our broader analysis of tariffs, that now builds out
from the earlier literature.
To move beyond the one-sector case, suppose now that tariffs are applied to
the revenue of imports in a tradable heterogeneous-firm sector, but that there isanother, nontaxed sector in the economy (say, nontraded goods). The impact on
entry and on welfare will depend on the size of the nontaxed sector and also on
the extent of the (traded) intermediate inputs. Indeed, paradoxically, if these arehigh enough, we will show analytically that, conditional on the level of trade, thead valorem tariffs can result in lower welfare than iceberg transport costs, despite
the fact that the iceberg costs are thrown into the ocean whereas the tariffs arerebated to consumers! In other words, our analytical results will show quite
different—and potentially much greater—effects of revenue tariffs as comparedto iceberg trade costs in a two-sector model, depending on the importance of thenontaxed sector and intermediate inputs.
We present our general model next, and then derive analytical results from asymmetric, two-sector, two-country version of the model. Following that, we turnto the major quantitative part of the paper. Like Balistreri et al. (2011) and CR, wecalibrate our model to the input-output structure found in actual economies, but
we go beyond these authors: we include input-output data for a greater numberof developed and developing countries; we also include more low-income countries with large tariff distortions; we use actual multilateral tariff reductions in
the 1980s–2010s period (including the Uruguay Round), with highly disaggregate
tariffs, to capture the actual changes in trade policy.
9 Under the rules of the World Trade Organization, ad valorem tariffs are applied to the ”cus-toms value” of an import product, which is intended to reflect the price paid between unrelated parties. Such a price should, obviously, not exclude fixed costs or markups/profits. See:
http://www.wto.org/english/tratop e/cusval e/cusval info e. htm.

8

3

Model

The schematic production structure of the model is shown in Figure 1; it follows
CP, and was also adopted by CR. We consider a world with M countries, indexedby i and j. There are S sectors, producing final or intermediate goods, indexed bys and s0 . There is a mass Li of identical agents in each economy. Agents consume
nontradable final goods from all sectors. The final goods in turn are producedwith intermediate goods from different sources, either traded or nontraded. Finalgoods are also used as materials, i.e., inputs, for the production of intermediate goods, along with raw labor. Intermediate goods producers in each sector s
have heterogenous productivities ϕ. Upon entry, for which it pays a fixed cost,a firm’s ϕ is drawn from the known distribution of productivities Gs ( ϕ), where
we assume that Gs ( ϕ) = 1 − ϕ−θs follows a Pareto distribution with coefficientθs > 0. We further impose the standard condition that θs + 1 > σs , where σs isthe elasticity of substitution of intermediate varieties defined later, so as to ensurethat average aggregate productivity under constant elasticity of substitution (CES)
aggregation is well defined.
In addition to fixed entry costs, the intermediate goods producers face fixed
operating costs, and costs of trading, in all markets. As regards trading costs,
traded intermediate goods are subject to two types of bilateral trade frictions: an
ad valorem tariff tij,s applied to the revenue cost of imports from i to j, and an iceberg
trade cost of ad valorem form τij,s − 1 > 0 of shipping goods from i to j, where weassume tii,s = 0 and τii,s = 1 for all i, s. Intermediate goods producers decide
how much to supply to the domestic market and how much to supply abroad.
Intermediate producers in sector s and country i pay a fixed operating cost f ij,s inorder to produce goods for market j, and we make the standard assumption thathome operation is less costly than export operation, so that f ii,s < f ij,s for all j 6= i.
As a result of these fixed costs, less efficient producers of intermediate goods do
not find it profitable to supply certain markets, and some do not operate even in∗ the cutoff or threshold productivity level
the home market. We denote by ϕij,s∗ are not active
such that all firms in each sector s and country i with ϕ < ϕij,sin exporting to country j, or not active in the home market, in the case where∗ .
ϕ < ϕii,sDenote by Nj,s the mass of entering firms in equilibrium in each sector s andcountry j. By virtue of the Pareto distribution, the number of firms/products
actually sold in sector s, from country j, into market i is the the total number

9Figure 1: Schematic production structure of the model

Labor (Li)

goods
Exported

Intermediate goods
qi , 2 (M )Intermediate goods
qi ,1 (M )Composite
intermediate good 1

Composite
intermediate good 2

Qi,1Q
Qi,i2,2

goods
Imported

Households
DD

Ui (Ci ) C i,1 i C i,2 210

of entering firms
times
h
 the
imass of firms above the relevant threshold, which is= Nj,s ϕ∗ji,s −θs .

given by Nj,s 1 − Gs ϕ∗ji,s3.1

Households

Assume that agents consume only domestically produced nontraded final goods
with preferences given byS

Ui (Ci ) = ∏ (Ci,s )αi,s ,

(6)

s =1

where Ci,s is the consumption of a final good type with sector index s and produced in country i, and the αi,s are standard expenditure shares.10
Demand is then given by
Ci,s =

αi,s Ri
,
P̃i,s

(7)

where Ri represents the income of the agents in country i, and P̃i,s is the priceof final good s in country i. Note that we use a tilde to denote consumer prices,which are inclusive of tariffs (and iceberg costs). Agents derive income from twosources, labor income and rebated tariff revenue, as explained below; firm profits
will be equal to zero by free entry.

3.2

Final goods producers

Assume final goods are assembled from tradable intermediates using no labor.
Specifically, final goods are produced with a CES production function with elasticity of substitution equal to σs > 1 using only intermediate varieties as inputs.11
The cost minimization problem of the final good producers in each sector s
and country i is thenMmin

∑ Nj,s{q̃ ji,s ( ϕ)}≥0 j=1Z∞p̃ ji,s ( ϕ) q̃ ji,s ( ϕ) gs ( ϕ) dϕ,

ϕ∗ji,s10 The final goods are inherently nontraded by assumption, e.g., due to prohibitive iceberg costs.
11 Intermediate good producers are heterogeneous in their productivity levels and since a partic-

ular variety is related to a particular productivity throughout the paper we will abuse notation anddenote by ϕ both the productivity level and variety of the firm.

11subject toM ∑ Nj,s
j =1Z∞

 σ σ−s 1sq̃ ji,s ( ϕ)

σs −1
σs


gs ( ϕ) dϕ

≤ Qi,s ,ϕ∗ji,swhere q̃ ji,s ( ϕ) is the demand by country i and sector s of an intermediate variety ϕ from country j with the tariff-inclusive price p̃ ji,s ( ϕ), gs ( ϕ) is the densityof Gs ( ϕ), Qi,s is the total quantity of final goods produced, and Nj,s is the number of entering firms in country j and sector s. As
h noted above,
i the numberof firms/products actually sold to market i is Nj,s 1 − Gs ϕ∗ji,s= Nj,s ϕ∗ji,s −θs .
Note that q̃ ji,s ( ϕ) > 0, and the good is produced by j for i, if and only if ϕ ≥ ϕ∗ji,s .
Otherwise q̃ ji,s ( ϕ) = 0, which accounts for the lower limit of the integral.
From the standard solutions to this CES problem we find that the demand forintermediate goods of variety ϕ sold in sector s from j to i is given byq̃ ji,s ( ϕ) =p̃ ji,s ( ϕ)

−σs

P̃i,s

Yi,s
,
P̃i,s

(8)

where Yi,s = P̃i,s Qi,s is the value of output of the final good s in i, and P̃i,s is theaggregate price index for sector s in i (CES, over all varieties) inclusive of tariffs,
which is given byMP̃i,s =  ∑ Nj,s
j =1

3.3

Z∞

 1−1σsp̃ ji,s ( ϕ)1−σsgs ( ϕ) dϕ.

(9)ϕ∗ji,sIntermediate goods producers

Denote the quantity produced by a tradable intermediate goods producer in sector
s in country i with variety ϕ by q̃i,s ( ϕ). In order to produce, the intermediate
goods producer employs labor and uses materials from all sectors and combinesthem using the following constant returns to scale production functionSq̃i,s ( ϕ) = ϕli,s ( ϕ)γi ,s ∏ mi,s0 s ( ϕ)γi,s0 s ,(10)s 0 =1

where ϕ is productivity, li,s ( ϕ) is labor demand, mi,s0 s ( ϕ) is the quantity of materials used from sector s0 , γi,s ≥ 0 is the share in output of value added (here,
labor costs), and γi,s0 s ≥ 0 is the share in output of the cost of inputs from sector s012

used by sector s (input-output coefficients). We assume that the cost shares sum
to unity, ∑Ss0 =1 γi,s0 s + γi s = 1.
Cost minimization

We solve the problem of the tradable intermediate variety

producer in two stages. First, we determine the minimum cost of producing agiven quantity. The solution to this problem is the cost function of the firm.
Second, we solve for the profit maximization problem of the firm using the costfunction derived in the first stage.
The cost minimization problem of the tradable intermediate good of variety ϕin country i is given byC q̃i,s ( ϕ) ; wi , { P̃i,s0 }Ss0 =1 =S

min(li ( ϕ),{mi,s0 s ( ϕ)}Ss0 =1 )≥0

wi li,s ( ϕ) + ∑ P̃i,s0 mi,s0 s ( ϕ) ,s 0 =1subject to (10), where wi denotes the wage in country i.
From the first order conditions of this problem, the demand for labor in the
production of variety ϕ in each sector s is given byli,s ( ϕ) = γi,sxi,s q̃i,s ( ϕ),wiϕand the demand for intermediate inputs is given by
mi,s0 s ( ϕ) = γi,s0 sxi,s q̃i,s ( ϕ),ϕP̃i,s0where in the last expression we introduce a newly-defined term
xi,s ≡ wi /γi,s

γ

S

i,s

∏

s 0 =1P̃i,s0 /γi,s0 s

γi,s0 s,(11)

and we refer to this price index xi,s as the cost of the input bundle or more simply
as the input cost index. The input cost index contains information on prices fromall sectors in the economy and, clearly, the input cost directly affects production
decisions in all sectors. This is one key distinction of our model as compared to a
one-sector model or a multi-sector model without input-output linkages.
The solution to the cost minimization problem yields the following (variable)

13

cost function for each producer of variety ϕ in country i and sector s:C (q̃i,s ( ϕ) ; xi,s ) =xi,sq̃i,s ( ϕ) .
ϕ

(12)The marginal cost of each producer is then given by
MCi,s (q̃i,s ( ϕ) ; xi,s ) =

xi,s
.
ϕ

(13)

Profit maximization We now solve for the profit maximizing quantity of theintermediate variety producer assuming monopolistic competition. Producers incountry i pay a sector-specific fixed operating cost to sell into each market j,denoted by f ij,s . For simplicity we suppose that this cost is paid in units of labor.
Note that since the production technology is linear we can solve the profit
maximization problem for each individual market separately. Consider the profit
maximization problem of supplying goods to market j. Profits are given by
πij,s ( ϕ) = max

pij,s ( ϕ)≥0

xi,sqij,s ( ϕ) − wi f ij,s ,pij,s ( ϕ) q̃ij,s ( ϕ) −
ϕ
p̃

(14)

( ϕ)

subject to (8). The control variable in this problem is pij,s ( ϕ) = 1ij,s+tij,s , the net-oftariff price received by the exporting firm.
As we can see, this price differs from the tariff-inclusive price p̃ij,s ( ϕ) paid by
the importer, and means that the sales revenue p̃ij,s q̃ij,s is divided by the tariff factor
1 + tij,s in order to obtain producer revenue in (14). Note that the quantity soldby the firm is qij,s ( ϕ) = τij,s q̃ij,s ( ϕ) because of the iceberg trade costs. So the costsof production ( xi,s /ϕ)q̃ij,s are multiplied by the iceberg trade costs τij,s to obtain thecosts in (14).
These are subtle but very important details. This discussion shows how thetariffs and iceberg trade costs enter the profit equation in slightly different ways,
and follows from our reality-based assumption that the ad valorem tariff is applied
to the sales revenue. In contrast, if the tariff was applied to only the costs of theimported product then the costs ( xi,s /ϕ)q̃ij,s would be multiplied by the productof the iceberg trade costs and the tariff factor, τij,s (1 + tij,s ) in (14), so that the
tariffs and iceberg costs would enter the firm’s problem symmetrically.12
We will see that this distinction between how tariffs and iceberg costs are
12 For clarity, the profit maximization equation in the case where the tariff was applied to firm
revenue for the imported product (i.e., the net-of-tariff, post-markup) price would be as in (14), and14

modeled makes an important difference to the zero-profit-cutoff productivity that
we solve for below.
The first order conditions of this CES producer problem can be solved forthe quantity sold and price charged, as follows, making use of the CES demand
function at (8). As in the standard solution, price charged is the usual markup overunit cost pre-tariff (input cost index, adjusted for productivity, and also scaled by
the iceberg factor since it is a destination pre-tariff price). The quantity demandedis then a function of this price plus the tariff, relative to the price index of allintermediates in sector s in destination market i.
σs τij,s xi,sσs − 1 ϕσs xi,s τij,s.
σs − 1 ϕq̃ij,s ( ϕ) =pij,s ( ϕ) =−σs P̃σs −1 Y
j,s
j,s
σ ,
1 + tij,s s

(15)
(16)

Using these two expressions, we can then multiply to get the revenues for
sector s in country i from selling to market j as given by
rij,s ( ϕ) = pij,s ( ϕ) q̃ij,s ( ϕ) =σs xi,s τij,sσs − 1 ϕ1−σs P̃σs −1 Y
j,s
j,s
σ .
1 + tij,s s

The profits for sector s in country i from selling to market j are given by themarkup minus one, times unit cost pre-tariff, times output, less fixed costs:
1
πij,s ( ϕ) =σs − 1xi,s τij,s q̃ij,s ( ϕ)− (σs − 1) wi f ij,s .
ϕ(17)

we can scale that up by a factor (1 + tij,s ) to getxi,s(1 + tij,s )πij,s ( ϕ) = maxp̃ij,s ( ϕ) q̃ij,s ( ϕ) −τij,s (1 + tij,s )q̃ij,s ( ϕ) − wi f ij,s (1 + tij,s ) ,ϕpij,s ( ϕ)≥0
and where the tariff was applied to only the firm cost for the imported product would be
xi,sπij,s ( ϕ) = maxp̃ij,s ( ϕ) q̃ij,s ( ϕ) −τij,s (1 + tij,s )q̃ij,s ( ϕ) − wi f ij,s ,ϕpij,s ( ϕ)≥0
where in both expressions we use the firm’s destination price p̃ij,s and quantity sold q̃ij,s , to makefor comparability. From these two equations, viewed side-by-side, it is obvious that in the lattercase the effect of cost tariffs and icebergs are totally symmetric, entering as τij,s (1 + tij,s ), and setting
aside the income effects arising for the cost tariff rebate which are absent in the case of icebergs. It
is this feature that has been exploited to simplify matters in the previous literature, but it is a path
not taken in this paper.

15

3.4

Selection and Entry

Zero cutoff profit condition As usual, following Melitz (2003), the first-stage
E in each sector s and country i are assumed to be covered
fixed costs of entry f i,sby a lump-sum mutual-fund arrangement which pays out to all firms that enter,
whether they are non-operators, domestic operators, or export operators. This
scheme operates in the background, and ensures ex ante expected profits are zeroat the first-stage decision, which governs the entry of firms. This leaves only thesecond-stage fixed costs of operation f ij,s for each sector s and exporter-importer
pair ij to be considered, which govern the the selection of firms into non-operators,
domestic operators, or export operators according to another set of zero expected
profit conditions.
Given the presence of fixed operating costs, there exits a threshold level ofproductivity such that a firm in a given sector makes zero profit. We can characterize the threshold or cut-off level of productivity of operating firms by looking
at the profits of the marginal firm producer. In particular, the zero cutoff profit(ZCP) level of productivity is determined by
∗
πij,s ϕij,s= 0.
Using the equilibrium conditions for prices and quantities derived before, theZCP level of productivity in sector s is given by
∗
ϕij,s
=



σs
σs − 1

σs wi f ij,sYj,s σ 1−1s σsxi,s τij,s 1 + tij,s σs −1
P̃j,s

.

(18)

The threshold level of productivity is a function of the elasticity of demand,
fixed operating costs, the cost of the input bundle, the price index, total expenditure and trade costs. The larger are the fixed or variable costs of exporting and thecost of the input bundle, the larger is the ZCP level of productivity to enter into
the export market. Expansions in market j, captured by a larger Yj,s , or increases
in the price index, P̃j,s lower the threshold level of productivity. Note that there
is a ZCP condition for each sector in the economy and that they are all related by
the input-output linkages presented on the cost of the input bundle. Changes intrade cost of one good will affect the input bundle and in turn change the ZCPlevel of productivity on another sector. The extent to which sectors are related,namely the interconnections presented in the input-output table will determine
the extent to which changes in trade costs in one sector will impact other sectors.
16

Note that a reduction in the tariff level affects the ZCP condition in a waythat is different from a reduction in iceberg trade costs. This follows from ourassumption that tariffs are applied to the sales value of the import, as discussed
above. In practice, this means that a reduction in actual tariffs acts in the ZCP
condition very similarly to a joint reduction in iceberg trade costs an in fixed costs.
To see this, we can rearrange (18) in the following way

∗
ϕij,s
=



σs
σs − 1σs wi f ij,s 1 + tij,sYj,s ! σs1−1xi,s τij,s 1 + tij,s
P̃j,s


.

(19)

This equation makes clear that changes in the ad valorem tariff tij,s act in the samemanner as a joint change in f ij,s and τij,s .
We remark that, in contrast, if tariffs are applied only to the costs of imported
products, then they would have exactly the same effect on the zero-cutoff-profit
condition as do iceberg trade costs τij,s , and would appear only as multiplying
those trade costs above (i.e., as in the final term). Still, as we argue in Appendix
A, ad valorem tariffs applied to the costs of imports will have an impact on theentry of firms, in contrast to iceberg transport costs. Under our maintained assumption that tariffs are applied to the sales revenue, they have the “extra” impactof effectively reduced fixed costs, too. The gains from tariff reduction will take
into account this implicit reduction in fixed costs, which will act so as to encourage the entry of exporters and increase export variety, as we show below.
E in each sector, in units of labor, inFree entry Firms pay a fixed cost of entry f i,sorder to allow them to take a draw from the known distribution of productivities
Gs ( ϕ). Free entry implies that expected profits of firms have to be equal to entry
costs at each market s,
M

∑

Z∞

E
πij,s ( ϕ) gs ( ϕ) dϕ = wi f i,s.

j =1 ∗
ϕij,sUsing the equilibrium conditions (17) and (18) and given the assumption of
Pareto distribution of productivities we end up with the following equilibrium
condition

M

∗ −θ
=
∑ fij,s ϕij,ssj =1

θs − σs + 1 E
f i,s ,σs − 1(20)

that relates the ZCP levels of productivities to the fixed operating and entry costs.
17

3.5

Price index

We define the average productivity in sector s of intermediate goods in market isourced from market j asϕ̃ ji,s =! σ 1−1Z ∞sϕϕ∗ji,sσs −1µ ji,s ( ϕ) dϕ

,

(21)

h

i
is the conditional distribution of prowhere µ ji,s ( ϕ) = gs ( ϕ) / 1 − Gs ϕ∗ji,sductivities (conditional on the variety ϕ being actively produced for this {i, j, s}
combination). Then using the equilibrium conditions (9), and (16), we obtainM

σs x j,s τji,s 1 + t ji,sσs − 1ϕ̃ ji,sP̃i,s =  ∑ ϕ∗ji,s −θs Nj,sj =1

 !1−σs  1−1σs

,

(22)

h

i
where ϕ∗ji,s −θs = 1 − Gs ϕ∗ji,s is the probability that an entering firm in country
j is actually selling to market i, so that the number of products actually sold are
Nji,s ≡ ϕ∗ji,s −θs Nj,s .

3.6

Trade balance and market clearing

Two steps remain to close the model, the first being to ensure that all entities obey
their budget constraints, markets clear, and trade is balanced.
Expenditure shares Recall that Yi,s = P̃i,s Qi,s is the value of the output of the
final good s in country i, which is produced entirely from intermediate goods,
these being either imported or produced domestically. Hence, this value of output
equals the total expenditure on those intermediate goods.
Let λ ji,s denote the share of country’s i total expenditure in sector s on intermediate goods from market j. In this share, integrating over sales of all varietiesof s from j to i yields the numerator, and summing over all markets j gives thedenominator:
Nj,sλ ji,s =Z ∞ϕ∗ji,sp̃ ji,s ( ϕ) q̃ ji,s ( ϕ) gs ( ϕ) dϕ

I

Z ∞

n =1

ϕ∗ni,s∑ Nn,s.

(23)p̃ni,s ( ϕ) q̃ni,s ( ϕ) gs ( ϕ) dϕ

Using the equilibrium conditions (16) and (22) we can obtain the following ex-

18

pression for the expenditure share!1−σsσs τji,s x j,s 1 + t ji,s 1.
ϕ̃ ji,sσs − 1P̃i,sλ ji,s = ϕ∗ji,s −θs Nj,sSectoral trade flows(24)

We now solve for sectoral exports and imports and impose

balanced trade.
Consider sector s imports first. The total expenditure by country i on country jintermediate goods is given by λ ji,s Yi,s . Due to the presence of tariffs not all of thisexpenditure reaches producers in country j. The tariff-adjusted expenditure in
λcountry j on goods produced in country i, or exports from i to j, is Eij,s ≡ 1+ij,stij,s Yj,s .
Of course, that term is identical to imports arriving in j from i. Therefore, totalexports from country i, not including goods that are sold domestically, are givenbyλij,sYj,s ,
1 + tij,sj 6 =iEi,s ≡ ∑ Eij,s = ∑j 6 =i(25)

and total imports are given by
λ ji,s∑ Eji,s = ∑ 1 + t ji,s Yi,s .
j 6 =i(26)

j 6 =iAfter defining sectoral trade flows we now define the trade balance conditionSS
λ ji,sλij,sY=∑ ∑ 1 + t ji,s i,s ∑ ∑ 1 + tij,s Yj,s .
s =1 j 6 = i
s =1 j 6 = i(27)

Goods Market Equilibrium We can also define sectoral, Ti,s , and total, Ti , tariff
revenue as

S

S

s =1

s =1 j 6 = i

Ti = ∑ Tis = ∑ ∑ t ji,s Eji,s .

(28)With that, the expenditure on final goods from sector s by households in country
i is given by αi,s Ii , where Ii is total expenditure consisting of labor income plus
this redistributed tariff revenue, Ii = wi Li + Ti .
The total value of gross production of all intermediate goods in sector s incountry i is given by σsσ−s 1 ∑ jM=1 1+ij,stij,s Yj,s ; namely, the net-of-tariff value of secλtor s goods that are sold locally and abroad adjusted by markups. Given the
input-output coefficients, a share γi,s0 s of this gross production is then spent on

19intermediate inputs from sector s0 . Therefore, the materials from sector s0 demanded in sector s for the production of intermediate goods is then given by
γi,s0 s σsσ−s 1 ∑ jM=1 1+ij,stij,s Yj,s .
λWe can then obtain the total demand for the final good in sector s of countryi, which must equal total supply where we sum the demand from consumers for
final goods and demand for intermediate use (the term here in braces):(Yi,s = αi,s (wi Li + Ti ) +S

σs0 − 1 M λij,s00γ∑ i,ss σs0 ∑ 1 + tij,s0 Yj,s0
j =1
s 0 =1),(29)

We refer to this condition as the goods market equilibrium.

3.7

Firm Entry and Product Variety

The final step to close the model tackles selection and entry, solving for the mass
∗ for the varieties produced.
of firms Ni,s entering and the productivity cutoffs ϕij,sTo solve for product variety, we first rewrite (18) as
σs xi,s τij,s 1 + tij,s∗σs − 1P̃j,s ϕij,s !1−σs=

σs wi f ij,s 1 + tij,s
Yj,s

!
.

(30)

∗ by
We note that the average value ϕ̃ij,s is related to the cutoff ϕij,sϕ̃ij,s =! σ 1−1

Z ∞
∗
ϕij,s

s

ϕ

σs −1

∗
= ϕij,sµij,s ( ϕ) dϕ1θs + 1 − σs

 σ 1−1s,(31)

by the properties of the Pareto distribution. Substituting these last two equations∗
into (24) we can obtain an equation governing the cutoffs ϕij,s∗ −θs
λij,s = ϕij,sNi,sσs wi f ij,s 1 + tij,s
Yj,s

! 

1
θs + 1 − σs


.

(32)


Next, multiplying by Yj,s / 1 + tij,s , summing over j and making use of (25)and (20), we obtainM

Eii,s + Ei,s = ∑

j =1

∗ −θs
Ni,s
ϕij,s



σs wi f ij,s
θs + 1 − σs

20



E
= Ni,s wi f i,sσsσs − 1,(33)

from which we obtain an equation governing the mass of entrants Ni,s
Ni,s = ( Eii,s + Ei,s )E
wi f i,sσsσs − 1


.

(34)

It may appear surprising that total domestic plus international sales of intermediate inputs (Eii,s + Ei,s ) is so tightly linked to the mass of entrants Ni,s . But recall
the condition from ACR that aggregate profits in an economy, which equal entry
times the fixed costs of entry, are proportional to the labor force: therefore, entry
is fully determined by the labor force in each country. Equation (33) is the analogous result here: entry times fixed costs of entry is proportional to domestic sales
plus exports in each sector. But exports depend on ad valorem tariffs, as is clear
from (25) and the share equations in (24).

4Illustrative Two-Sector Symmetric Equilibrium

To illustrate some properties of the model by means of a simple example, andto obtain a closed-form solution for comparative statics, we study the special
case where countries are all identical and there are two sectors. This analysis is
explored in more detail in Appendix B.
Having just two sectors will allow us to enrich the input-output structure. The
first sector will be just as we have assumed above, with traded intermediate inputs
and a nontraded output good that is consumed and is also used as an intermediate input domestically. So this sector has both backward or forward linkages.
The second sector is much simpler and consists of purely nontraded consumer
services (e.g., haircuts), which are produced with labor and which neither use nor
are used as intermediate inputs. In other words, this residual sector has no backward or forward linkages. This second sector plays a role mainly on the demandside where it has a taste share of 1 − α, while the first sector has a taste share of α.
The condition (29) applies to the first sector only, and for clarity we drop thesummation over sectors s in (29); in fact, furthermore, we can drop the sector
subscript altogether. We let γ ≡ γi,ss denote the single nonzero term in the inputoutput matrix for the first sector in each country, with 0 < γ < 1. We assume thatthe ad valorem tariffs are equal across countries, tij,s = t for i 6= j, while tii,s = 0.
Output in the Two-Sector, Symmetric Equilibrium Rewriting (29), we knowthat in a symmetric equilibrium Yi = Yj , so that λij = λ ji and therefore ∑ jM=1 λij =21

λ(1− λ )ji
∑ jM=1 λ ji = 1. Notice that tariff revenue becomes Ti = tEji = t 1+t Yi = t 1+tii Yi .
Now, without loss of generality, we set wages as the numeraire, and with symme-

try wi = w j = 1, so that (29) becomesYi 1 − γ̃

1 + λii t
1+t(1 − λii )− αt= αLi .
1+t

(35)

1
where γ̃ is given by 0 < γ̃ ≡ γ σ−σ < 1.

Totally differentiating this expression and simplifying, we can obtain

dYi
Yi

= ∆


where ∆ ≡ 



1 − λii
1 + λii t

α − γ̃




dt
t
−
dλii ,
1+t
1 + λii tt(1−λii )(1−α)
1+− γ̃1+λii t < 1.

(36)(37)

To interpret this result, notice that when evaluated at the neighborhood of thefree trade equilibrium (t ' 0) then a reduction in tariffs will lead to a fall in thevalue of gross shipments unless ∆ < 0. For α < 1 we see that ∆ < 1 in general,
while for α < γ̃ then ∆ < 0. Thus, it is possible that the reduction in tariffs
raises gross shipments of the first good, which after all makes use of the cheaper
imported inputs. That outcome occurs in particular when the share parameter on
the first (differentiated) sector α is sufficiently small, in which case the fall in tariff
revenue and hence demand falls mainly on the second sector.
Entry in the Two-Sector, Symmetric Equilibrium

We will now explore howthese changes affect firm entry and product variety. To solvefor entry, notethat

domestic sales plus exports are Eii + Ei = ∑ jM=1 1+ijtij Yj = Yi λii + 11−+λtii , which
λfollows
 from symmetry across countries. The final expression is further simplified
tλii
as Yi 1+, and so from (34) we obtain1+ t
λλii Yi + ∑ j6=i 1+ijt Yj
σ−1

=
Ni =
σ
E
f i σ −1
σ f iE

1 + λii t
1+t


Yi ,

(38)

where we continue to normalize the wage at unity and suppress sector subscripts.
Then totally differentiating this expression and substituting the change in gross22

shipments from (37) and cancelling common terms, we arrive atdNi= ( ∆ − 1)Ni

1 − λii
1 + tλii



dt
−
1+t



t
1 + tλii


dλii .

(39)

Two contrasting local properties about tariffs and entry now follow. First,
consider a reduction in tariffs around the free trade equilibrium. Here, with t ' 0
and dt < 0, then it is ready seen that N̂i > 0 because ∆ < 1. So a small decrease in
the tariff leads to greater firm entry. But away from the free trade equilibrium thenit is quite possible that tariff reductions will inhibit entry. With a tariff reduction
we expect that the share of expenditure on home products falls, dλii < 0, which
will offset the induced entry. But because dλii is multiplied by t, then this term
is second order for small t, whereas the direct effect of the tariff reduction in
encouraging entry is of the first order. Therefore: for positive but small tariffs,
decreasing the tariff in the symmetric equilibrium will induce entry.
Second, consider starting from a situation with prohibitive tariffs. Here we get
the opposite result. Under autarky with λii = 1 the first term in brackets on theright of (39) clearly vanishes as tariff revenue disappears. Now suppose we makea small increase in the tariff to just reach λii = 1; this means that dλii > 0, so thesecond term in brackets on the right is negative, and with ∆ < 1, we see now that:
Near autarky, increasing the tariff in the symmetric equilibrium will induce entry.
Furthermore, we claim a global result: that the level of entry Ni will be thesame in the free trade equilibrium (with zero tariffs) and in the autarky equilibrium (with prohibitive tariffs). A bit of intuition for this result is that the autarky
equilibrium with prohibitive tariffs is isomorphic to an equilibrium with prohibitive iceberg transport costs, and because entry Ni is independent of iceberg
costs, it will therefore be the same as under free trade.
To see the result formally, equation (35) shows that Yi is the same whether
t = 0 or λii = 1, and then from (38), we quickly conclude that Ni is the same
whether t = 0 or λii = 1. Indeed, at both extremes, Yi = αLi / (1 − γ̃).
We can summarize and sharpen these results for the two-sector symmetricequilibrium as follows:
Theorem 1 The mass of entering firms Ni is the same under free trade and prohibitive
tariffs. If and only if α < 1, then: a) near the free trade equilibrium reducing the tariff
will increase entry; b) near the prohibitive tariff, reducing the tariff will decrease entry; c)entry is lower at all intermediate tariff levels than under free trade or prohibitive tariffs.

23

Proof. Part a) and b) have been shown already, except for the final claim partc). The latter can be seen to follow from (35) and (38), as follows. Normalizing
wages at unity, from (35) we see that Yi = αLi / (1 − γ̃) when t = 0 or λii = 1. It
follows from (38) that Ni = (σ − 1)αLi /[(1 − γ̃) σ f iE ] when t = 0 or λii = 1. Then
Ni ≤ (σ − 1)αLi /[(1 − γ̃) σ f iE ] at all other tariff equilibria provided that for t > 0
and λii < 1,


1 + tλii
1+t




1 − γ̃

1 + λii t
1+t




1
(1 − λii )
.
− αt
<
1+t
(1 − γ̃)Straightforward but tedious algebra shows this condition is satisfied for α < 1.
We think it is important to step back and understand what this result implies.
It says that, for this class of models: there must be a nontraded sector present in orderfor import tariffs to influence entry. Notice that without such a nontraded sector wehave α = 1 and hence ∆ = 1 in (37), and then we would necessarily have fixedentry with dNi = 0 in (39).
To go a little further, we can turn to numerical simulations of the two-sector
symmetric model to see more clearly how entry is affected by tariffs in different
configurations of the model. Figure 2 shows how the level of firm entry Ni andthe domestic share λii varies as the tariff level t changes over the range from free
trade to autarky, for different values of the traded sector share α.
Entry is the same under free trade and autarky. Entry is also constant when the
nontraded sector is absent and α = 1. Otherwise, starting close to free trade entry
falls as tariffs increase from zero, before then rising again in a ∪-shape after somepoint as tariffs approach prohibitive levels. The ∪-shape is more pronounced as
the nontraded sector grows in size (i.e., as α falls further below 1).
Welfare in the Two-Sector, Symmetric Equilibrium

We next obtain a closed-

form expression for the change in welfare in the simple model in the presence oftariffs and input-output linkages.
So far, we have not had to be explicit about the structure of the second sector,
which provides consumer services produced with labor alone. For simplicity, let
us now suppose that the second sector is competitive and that, without loss ofgenerality, productivity is unity so that the price of a unit of service equals thewage. Already the wages in each country are normalized at unity, so that theservice price is also constant and equal to one in both countries.

24

Figure 2: Entry effects of tariffs changes in the two-sector symmetric model
NFT

A87

N W)

N

D=1
D = 3/4
D = 1/2
D = 1/4
0.5

0.6

0.7

O(W,W)

0.8

0.9

1

Note: This figure shows how the level of firm entry Ni and the domestic share λ = λii vary as
E
V=2, forT=4,different
fD = fX =values
f =1, of the traded sector share α ∈ {1, 0.75, 0.5, 0.25}, withthe tariff Parameters:t = tij changes,t ∈ (0, ∞) and no iceberg costs, τ = 1. The other model parameters are σ = 2, θ = 4, f D = f ii =1, f X = f ij = 1, and f iE = 1.

It then follows that the change in welfare from (6) and (7) is given by
dUi
d P̃
dTi
= −α i +,Ui
wi Li + Ti
P̃i

(40)

where P̃i is the price index for the differentiated good that used traded inputs,
and Ri = wi Li + Ti is consumer’s income inclusive of tariff revenue.
The first term on the right of (40) is the change in the price index, which canbe computed from (22) as




d P̃i
1 dλii
1
1
1
1
∆
dNi
=
−
+
−
.
1 − γ θλii1−γ θ
σ − 1 θ ∆ − 1 Ni
P̃i

(41)

The first term on the right looks familiar: it is just how the price index changes
based on the implied change in the domestic share dλii . The second term is new:25

it reflects the entry margin we have introduced. This term, which depends on thechanging entry of firms in the differentiated sector, does not arise when evaluating
the welfare gains from reducing icebergs because entry does not change.
Combining these last two expression, the change in welfare is given by
dUi
Ui

=

α dλii−1 − γ θλii
{z
}
|

+

entry

trade volume

where ξ = 1−α γ

1

θ +

1
1
σ −1 − θ



∆
∆ −1



dNi
ξ
N
| {z i}+dTi.
w L +T| i i{z i}(42)tariff rebate. Now, as the reader may have grasped fromour earlier discussion of icebergs, cost tariffs, and revenue tariffs, this general
expression for welfare gains would inevitably vary if model assumptions werechanged. Most clearly, we know that in the simplest model of pure icebergs withno tariffs, there will be no change in entry, as we noted before, and there is no
tariff rebate, by construction; thus, the second and third terms disappear, and wewould be left with the first term on the right of (42), and this formula echoes theresult in ACR. In a different model framework, if non-Pareto productivity draws
were introduced, we know it is possible for the entry margin to become activein the second term under icebergs, but still with the third term at zero with notariff rebate; here this formula echoes the result in Melitz and Redding (2015).13
However, in the setting we study in this paper—with iceberg costs and revenue
tariffs present, and even with Pareto draws—all three terms in this expression
become nonzero, leading us naturally into a discussion of the signs and relative
magnitudes of these three different components of welfare change.14
A natural place to start the discussion of these subtleties is in the neighborhoodof what we call a free trade equilibrium (FT), which is to say where tariffs are zero(t = 0), but icebergs may be set at any arbitrary level (τ ≥ 1). In many simple oldand new trade models, a very standard result is that for a small, first-order changein (rebated) tariffs near free trade, welfare losses will be second-order small, whilst
for a small, first-order change in iceberg costs (or, say, nonrebated tariffs), welfare
losses will be first-order small. This often amounts to the difference between thearea of a Harberger triangle versus size of the tax revenue rectangle.
13 Of course, the elasticity of welfare with respect to entry is not constant, in general, in the Melitz

and Redding (2015) framework.
14 FJL (2015, Proposition 1) include a tariff revenue term in their expression for welfare, but not anentry term, which they are treating as fixed in their one-sector model. CR (2014, note 25, p. 227) also
include a tariff revenue term in their expression for welfare in the Armington model, where entry isagain fixed. A more general expression for welfare is provided in their online Appendix (equation
21), which allows for entry, although its connection to tariff changes is not explicitly solved for.

26

We now show that the same intuition can carry through in our setting but only
in a very special case: we have to be in the one sector model, that is, when α = 1
and all goods are traded; for simplicity we consider the case with no intermediates
present, γ = 0. Otherwise, both losses become first order.15 The result is stated in
the following theorem.
Theorem 2 Consider an economy near a free trade (FT) equilibrium, t = 0 and τ > 1.
Restrict attention to the case γ = 0 (no intermediates). Then for small increases in trade
frictions dt and dτ the formula for welfare changes becomes
dU FT
U

,

dt
α (1 − α )=−(1 − λii )1+t( σ − 1)

and

dU FT
U

,

dτ
= −α (1 − λii ) .
τEquivalently, in terms of implied changes in the trade share dλii /λi , we can write:
dUi /Ui FT
dλii /λii

=−
dτ =0

α (1 − α )θσ − σ + 1

anddU/U FT
dλii /λii

dt=0

α
=− .
θ

(43)

Thus, in the case α = 1 (one sector model) welfare losses are of the second order fortariffs since the terms on the left of the above expressions equal 0, and of the first-order for
icebergs. In all other cases with α < 1, both welfare losses are in general of the first order.
Proof. See Appendix B.
The proof of this theorem comes from solving for all three of the endogenouschanges on the right-hand side of (42) in terms of exogenous changes in the advalorem tariff and in iceberg costs, as done in Appendix D. The finding that thewelfare cost of changes in the tariff is of the first-order in more realistic settings(α < 1, γ > 0) demonstrates how the welfare implications of changes in trade
frictions in this model can depart from those seen in simpler settings. Note thatthe first-order effect of tariff changes must come from the second term on the rightof (42), i.e., the change in entry, since when α = 1 then entry is fixed and the first
and third terms in (42) still result in a second-order cost of tariffs. This resultiiclearly show that using the formula − 1−α γ dλθλii does not capture the welfare gains

from trade as we change tariffs in our model.
For illustration, Figure 3 shows how welfare and the domestic share change
globally with icebergs and tariffs. The figure considers two simple cases with no
15 In Appendix B we characterize the welfare effects in the neighborhood of the free trade equi-

librium when γ > 0. For this case, changes in tariff generate first-order welfare losses due to thepresence of intermediate goods but this is purely a consequence of the presence of markups.

27

Figure 3: Welfare effects of tariff and iceberg changes in the one-sector two-sector
symmetric model without intermediates

Note: This figure shows how the level of welfare U = Ui (relative to autarky equals 1) and thedomestic share λ = λii vary as the tariff t = tij changes with t ∈ (0, ∞) and τ = τij = 1 (blue paths)
or as the iceberg cost τ changes with τ = τij ∈ (1, ∞) and t = tij = 0 (red paths). The dotted lines
correspond to α = 1 and the solid lines α = 0.5. There are no intermediates, γ = 0. The othermodel parameters are σ = 5, θ = 10, f D = f ii = 1, f X = f ij = 2, and f iE = 1.

intermediate goods (γ = 0) and in which α = 1 or α = 0.5. As we can see, near
the free trade equilibrium changes in icebergs have always a first order effect onwelfare, while for the case of tariff changes this depends on α.
In light of Figure 3, let us now move away from results local to the freetrade equilibrium, and, in search of solutions that apply globally, we solve for thesecond and third terms on the right of (42) due to changes in ad valorem tariffs andin iceberg costs. Here we are interested in determining how and why the welfarechange dUi /Ui can deviate more generally from the expression − (1−αγ)θ dλii /λii .
We find that, according the structure of the economy, in some cases dUi /Ui >− (1−αγ)θ dλii /λii while in others dUi /Ui < − (1−αγ)θ dλii /λii , which can lead toseemingly paradoxical outcomes. To see this, recal that ∆ < 1 and that θ > σ − 1.
Then, the coefficient ξ on the entry term in (42) is guaranteed to be positive if∆ < 0, though it can also be positive for some values of ∆ > 0 that are not too
28

large. If the term is positive, then any increase in entry that accompanies a tariff
reduction will further reduce the price index in (41) and will further increase the resulting welfare gains. The magnitude of this welfare gain is sensitive to the valueof γ, which indicates the extent to which the differentiated products are used asiiintermediate inputs: as γ is larger, just as the gains via trade volumes (− 1−α γ dλθλii )

get larger, so too do the gains from entry correspondingly increase. Linkages
boost gains from trade via this channel too.
The welfare impact of a change in the tariff also depends on the change intariff revenue, the final term on the right of (42). From (26) we obtain imports(1−λii )1+t Yi , and then multiplying by the tariff t we obtain tariff revenue Tit(1−λii )1+t Yi . The change in tariff revenue is then

of

dTi
tdλii
=−
+
Yi
1+t



1 − λii
1+t=t (1 − λii ) dYi
dt
+
.
1+t
1+t
Yi

Notice that a reduction in the tariff directly lowers tariff revenue in the second
term, and also lowers revenue in the third term if gross output Yi falls, as occurs
precisely when ∆ < 0. In other words, the same condition that ensures a welfare
gain from increased entry in (42) now leads to an offsetting fall in tariff revenue.
Thus, summing the entry and tariff-revenue terms in (42) to get the overall
impact on welfare reveals a subtle balance of potential gains and losses in our
setting. We pursue this analysis further in Appendix B and, in particular, identify
a condition on parameters needed to ensure that dUi /Ui > − (1−αγ)θ dλii /λii , sothat the welfare impact of entry due to a tariff reduction leads to an “extra” rise
in welfare over and above that attributable to iceberg reductions. These results
are summarized as follows.
Theorem 3 (a) In regions where entry is rising (dNi > 0) due to a reduction in the tariff,
a necessary and sufficient condition to have dUi /Ui > − (1−αγ)θ dλii /λii regardless of thevalues of t ≥ 0 and 0 ≤ λii ≤ 1 is thatγ̃ ≡ γ

σ−1
σ





> 1−

2−α
σ + 1 − [(σ − 1)/θ ]



> 0.

(44)

When entry falls, the same condition implies that dUi /Ui < − (1−αγ)θ dλii /λii .
(b) If γ = 0 (no intermediate goods) then condition (44) cannot hold, so it follows thatdNi
dUi
1 α dλii
Ui ≶ − θ 1−γ λii as Ni ≷ 0

Proof. See Appendix B.
29

For example, if the differentiated sector has share α = 0.2, and σ = θ = 4, thencondition (44) become γ > 0.77. If we raise the share α for the differentiated sector
to α = 0.3, then the condition becomes γ > 0.8, so intermediate inputs must be
even more important. From this we get a clear sense that the differentiated sector
subject to the import tariff must be of modest size, while the role of intermediate
inputs must be substantial, in order for the increased entry to result in welfare
gains larger than − (1−αγ)θ dλii /λii . These results reinforce our discussion above,
where we found that a higher value of the intermediate share γ leads to greater
gains due to entry, but that a low value of α, such as α < γ̃ so that ∆ < 0, isneeded to ensure such entry occurs.
To develop some deeper intuition about welfare impacts, and to explore how
the nuanced implications of our model may diverge from prior analyses, we canagain turn to numerical simulations. We can then see more clearly how welfare
is affected in different configurations of the model and how the conclusions candiffer substantially from the results in models without entry.
Figure 4 shows how the level of country welfare Ui and the domestic share λii
varies either as the tariff level t changes or as the iceberg cost τ varies, over therange from free trade to autarky. Four different cases are studied corresponding
to different values of the traded sector share α and the intermediate share γ. The
figures may be compared qualitatively: since the model parameters vary widely,
the maximal gains from trade differ in each case, and the welfare scale on thevertical axis in not the same in each panel.
A benchmark case is shown in the lower-left panel of the figure, with no nontraded sector as α = 1, and a small intermediate share γ = 0.1. Welfare increases
from autarky as we move toward free trade. In the case of pure iceberg costs thegains as we reduce them from prohibitive levels are such that at any given level ofthe domestic share the gains are lower than when we liberalize pure tariffs costs,
and the reason for this is due to the dominant effect of the iceberg costs being
lost or wasted; in contrast, tariff revenue is rebate, so higher welfare results. The
resulting diagram, like Figure 3, takes on a “rugby ball” shape, with welfare levels
identical icebergs and tariffs in the cases of free trade and of autarky, but divergent in between. But as the other three cases in the figure show, this configurationof results is not guaranteed.
Moving from the lower-left to upper-left panel, we increase the intermediateshare from γ = 0.1 to γ = 0.9. As we know, this stronger input-output linkage
in the traded sector can dramatically increase the potential maximal gains from30

Figure 4: Welfare effects of tariff and iceberg changes in the two-sector symmetricmodel

Note: This figure shows how the level of welfare U = Ui (relative to autarky equals 1) and thedomestic share λ = λii vary as the tariff t = tij changes with t ∈ (0, ∞) and τ = τij = 1 (dotted/blue
paths) or as the iceberg cost τ changes with τ = τij ∈ (1, ∞) and t = tij = 0 (solid/red paths).
The four panels correspond to different values of the nontraded sector share α ∈ {1, 0.1} and theintermediate share γ ∈ {0.1, 0.9}. The other model parameters are σ = 5, θ = 10, f D = f ii = 1, f X =f ij = 2, and f iE = 1.

trade, as is clear from the change in range on the vertical axis (35% versus 3.5%).
However, this change also affects the marginal or incremental gains from tariff
liberalization or iceberg costs changes in all the equilibria shown. Notice thatthe “rugby ball” is now much thinner. The slopes of the dotted/blue lines andsolid/red lines are now much more similar and this reflects the entry mechanism
being more powerfully at work. Close to the free trade equilibrium, the entry
effect is positive and this raises the gains from tariff reductions, so the dotted/blueline is therefore steeper, and is closer in slope to the solid/red line. Close to theautarky equilibrium the opposite is true.
Moving from the lower-left to lower-right panel, we decrease the traded sector
share from α = 1 to α = 0.1, and this increase in nontraded share again has the31effect of making the the entry mechanism more powerful once again, and the“rugby ball” is again much thinner. It also, of course, makes the absolute gains
from trade smaller in this case as compared to the benchmark (0.3% versus 3.5%).
Finally, moving to the upper-right corner we consider the case where simultaneously both parameter changes occur: we decrease the traded sector share from
α = 1 to α = 0.1 and we increase the intermediate share from γ = 0.1 to γ = 0.9.
In the four cases in this entire figure, only this case corresponds to the condition
in expression (44) being satisfied. Now, compared to the benchmark the effects ofentry on welfare are turbocharged, and the result is dramatic. The “rugby ball”
flips over completely, and the dotted/blue path (welfare under changing tariffs)
sits below the solid/red path (welfare under changing icebergs).
Now in this final, perverse case the seemingly intuitive and common-sense
qualitative conclusions of more simple trade models, those which lack our entry
margin, can potentially be turned upside down. In this case, for a given level ofthe domestic share, agents would be better off living in a world of iceberg costs(where the costs are totally wasted) than in a world of tariffs (where tariff revenue
is rebated). This is because the effect of tariffs, when levied on revenue cost, notproduction cost, can distort the entry decision so much—under particular but
potentially realistic configurations with both large nontraded sectors and large
intermediate shares—that the welfare losses in the iceberg case end up smaller
than in the tariff case. Putting this finding another way, if such a world is more
realistic, then the gains from tariff liberalization can be much, much larger than
we might have previously thought when using models without entry.

5

Data Description

Our goal is to quantify the effects of actual tariff reductions over the last quarter
century. In order to do so, we need detailed information on tariff changes aswell as on production and trade flows for a large set of countries. In particular,
we are interested on understanding how developed and developing countries are
impacted by changes in trade policy and this can only be done if the data coverboth set of countries. We start by first describing the sources and the way weobtain tariff data and later on move to explain the source for production andtrade flow data.

32

5.1

New Tariff Data

This study builds a new comprehensive annual tariff dataset for the early 1980s
on. We obtain tariff schedules from five primary sources: (i) raw tariff schedules
from the TRAINS and IDB databases accessed via the World Bank’s WITS website
as far back as 1988 for some countries; (ii) manually collected tariff schedules
published by the International Customs Tariffs Bureau (BITD), some dating backas far as the 1950s;16 (iii) U.S. tariff schedules from the U.S. International Trade
Commission from 1989 onwards (Feenstra, Romalis, and Schott 2002); (iv) U.S.
tariff schedules derived from detailed U.S. tariff revenue and trade data from1974 to 1988 maintained by the Center for International Data at UC Davis; and(v) the texts of preferential trade agreements primarily sourced from the WTO’s
website, the World Bank’s Global Preferential Trade Agreements Database, or
the Tuck Center for International Business Trade Agreements Database. For the
U.S., specific tariffs have been converted into ad valorem tariffs by dividing by
the average unit value of matching imported products. Due to the difficulties
of extracting specific tariff information for other countries and matching it toappropriate unit values, only the ad valorem component of their tariffs are used.
The vast majority of tariffs are ad valorem. Switzerland is a key exception here,with tariffs being specific. We proxy Swiss tariffs with tariffs of another EFTA
member (Norway). We aggregate MFN and each non-MFN tariff program to the
4-digit SITC Revision 2 level by taking the simple average of tariff lines withineach SITC code.17
Tariff schedules are often not available in each year, especially for smaller
countries. Updated schedules are more likely to be available after significant tariff changes. Rather than replacing “missing” MFN tariffs by linearly interpolating
observations, missing observations are set equal to the nearest preceding observation. If there is no preceding observation, missing MFN tariffs are set equal to thenearest observation. Missing non-MFN tariff data (other than punitive tariffs applied in a handful of bilateral relationships) are more difficult to construct for two
reasons: (i) they are often not published in a given tariff schedule; and (ii) preferential trade agreements have often been phased in. To address this we researched
the text of over 100 regional trade agreements and Generalized System of Prefer16 Most tariff schedules can be fairly readily matched to the SITC classification.
17 Multiple preferential tariffs may be applicable for trade in a particular product between two

countries. Since the most favorable one may change over time, we keep track of each potentiallyapplicable tariff program.

33

ences (GSP) programs to ascertain the start date of each agreement or programand how the typical tariff preference was phased in. To simplify our constructionof missing preferential tariffs we express observed preferential tariffs as a fraction of the applicable MFN tariff. We fill in missing values of this fraction basedon information on how the tariff preferences were phased in. Preferential tariffs
are then constructed as the product of this fraction and the MFN tariff. We keep
the most favorable potentially applicable preferential tariff. Punitive non-MFN
tariff levels tend not to change over time (though the countries they apply to dochange). We replace missing observations in the same way we replace missing
MFN tariff observations.
An overview of the new tariff data is presented in Figures 5 to 9. These data
show, with country coverage and disaggregated detail of a kind we have havenever seen before, the remarkable impacts of the Uruguay Round on the levels
and dispersion of tariff rates around the world from the 1980s to the 2010s.
To start, Figure 5 plots the average (mean) ad valorem tariff rates, both MFN
and Preferential, across all countries and all goods at the SITC 4-digit goods level,in each year from 1984 to 2011, for the full sample, the Advanced economies, andthe Emerging and Developing economies. At the start of the period shown, in
the 1980s, the typical sample size for the calculations of these statistics is about 1
million distinct tariff lines. By the late 2000s, at the end of the period shown, thesample size in a given year is well over 2 million distinct tariff lines. It is clearthat both types of tariffs fell over the period, by about 9 percentage points, withessentially all of the reductions concentrated after 1990.
Given the similar trends, we focus henceforth on MFN tariffs in this section.
Figure 6 plots the median MFN ad valorem tariff rate across all goods at the SITC
4-digit level, in each year, for the full sample, the Advanced economies and theEmerging and Developing economies. It also plots ten percentiles from 5th, 15th,
25th, . . . to 95th in each year to give an idea of the dispersion of tariff rates.
This figure shows very clearly that the Uruguay Round was followed by a dramatic reduction in both the levels and dispersion of tariff rates, with these trends
being particularly concentrated in the subsample of Emerging and Developing
economies. In part this reflects the fact that these countries started with higher
levels and dispersion to begin with, and so had more scope for these kinds ofpolicy adjustments. In contrast, the Advanced countries had made much greater
progress in this direction during earlier GATT rounds going back to the 1940s.
Figure 7 uses histograms and kernel density plots to show the distributions of

34

0

5

Ad valorem tariff (%)
10
15

20

Figure 5: Average MFN and Preferential ad valorem tariff rates

1985

1990

1995

MFN tariffs, mean

2000

2005

2010

Preferential tariffs, mean

Note: Averages are taken over all 4-digit SITC level good, all countries, by year 1984–2011.

ad valorem tariff rates across countries and goods, for two snapshot years that wewill use for our policy experiments: a pre-Uruguay 1990 sample year and a postUruguay 2010 sample year. The histograms are truncated at the 50% tariff level;a small number of tariffs over this level (some well over 100%) appear in both
sample years for a few unusual goods and countries, but this right tail is not very
representative. Within the range shown, tariff peaks at certain round numbers areclearly visible (0, 5, 10, 15, etc.), as one would expect. However, looking past thosepeaks, we can clearly see again the impacts of changes in tariff policy over thisperiod. The spike at zero rises, as more zero-tariff rates appear across goods andcountries, and in the strictly positive region mass is shifted from the above-20%
region and into the below-20% region.
Finally, Figures 8 and 9 provides sectoral detail for tariffs aggregated up to
the level of 10 tradable sectors which we use in our calibrated model. This figure
shows clearly that the Uruguay Round did not have a peculiar compositional
impact across sectors. It lowered average tariffs pretty much across the board
in all sectors, and was not just confined to some limited areas of the tradable
35

Figure 6: Distributions of MFN ad valorem tariff rates

198519901995200020052010

20

40

60

80

Emerging/Developing

0

20

40

60

80

Advanced

0

0

20

40

60

80

All countries

198519901995200020052010

198519901995200020052010

Note: We use data for all 4-digit SITC level good, in 3 samples, by year 1984–2011 (percentiles
5/10/25/50/75/90/95).

economy. And again, the figure clearly shows the much larger scope for tariff
reductions in the Emerging and Developing sample, given the relatively hightariff rates they had at the start of the period in all sectors as compared to the
Advanced economies.

5.2

Production and Trade Data

To obtain production and trade data, we relied on the Eora MRIO multi-region
IO database. This dataset, to our knowledge, is the most comprehensive dataset
available that contains information on production, trade flows and input–output(IO) tables for 189 countries.18 Six sources are used to construct the multi-region
IO table. The sources are are: 1) input–output tables and production data fromnational statistical offices, 2) IO from Eurostat, IDE-JETRO, and OECD, 3) the
UN National Accounts Main Aggregates Database, 4) the UN National Accounts
Official Data, 5) the UN Comtrade international trade database, and 6) the UN
18 Please refer to http://worldmrio.com/ for more information.

36

Figure 7: Distributions of MFN ad valorem tariff rates, 4-digit SITC goods, allcountries, in 1990 and 2010
2010

0

.1

.2

.3

1990

0

5

10 15 20 25 30 35 40 45 50

0Density5

10 15 20 25 30 35 40 45 50

kdensity MFN_Tariff

Observations in 1990 = 1,119,930. Observations in 2010 = 2,724,754. Truncated to values <=50.

Figure 8: MFN ad valorem tariff rates, 10 sectors, all countries, in 1990 and 2010All
Agriculture and Fishing : 01
Mining and Quarrying : 02
Food & Beverages : 03
Textiles and Wearing Apparel : 04
Wood and Paper : 05
Petro., Chem. and Non-Met. Minerals : 06
Metal Products : 07
Electrical and Machinery : 08
Transport Equipment : 09
Other Manufacturing and Recycling : 10

0

10

20

Trade-weighted tariff (%) in sector s, averaged over pairs ij, by type of importer
1990

2010

37

30

Figure 9: MFN ad valorem tariff rates, 10 sectors, all countries, in 1990 and 2010
Advanced
Agriculture and Fishing : 01
Mining and Quarrying : 02
Food & Beverages : 03
Textiles and Wearing Apparel : 04
Wood and Paper : 05
Petro., Chem. and Non-Met. Minerals : 06
Metal Products : 07
Electrical and Machinery : 08
Transport Equipment : 09
Other Manufacturing and Recycling : 10

0

10

20

30

Trade-weighted tariff (%) in sector s, averaged over pairs ij, by type of importer
1990

2010

Emerging/Developing
Agriculture and Fishing : 01
Mining and Quarrying : 02
Food & Beverages : 03
Textiles and Wearing Apparel : 04
Wood and Paper : 05
Petro., Chem. and Non-Met. Minerals : 06
Metal Products : 07
Electrical and Machinery : 08
Transport Equipment : 09
Other Manufacturing and Recycling : 10

0

10

20

Trade-weighted tariff (%) in sector s, averaged over pairs ij, by type of importer
1990

2010

38

30

Servicetrade international trade database. For further information, refer to Lenzen
et al. (2012, 2013). We use Eora to obtain data on value added shares (γi,s ), shareof intermediate inputs in production (γi,s0 s ), gross output (GOi,s ), and total exports(Ei,s ).
A key advantage of this database, compared to others, is the fact that it contains information for a large set of countries (develop and developing countries)
and for early years. In particular we use the 1990 multi-region table with 25-sector
harmonized classifications. As a reference point, in comparison with the WIOD
database, we have more than three times the number of countries and account fora number of developing countries, some of them quite small. Moreover, there is
no WIOD for the year 1990, the period immediately before the Uruguay Roundtariff cuts. Having data for the 90’s allows us to take the model to the data andevaluate the effects of every single tariff reform after that period.
With our new tariff data we have greatly increased the disaggregation of the
trade and tariff data, however, from 13 aggregate merchandise sectors to 800 disaggregate SITC goods. This increase in the number of countries and traded goods
has come at the cost of aggregating the sectors to only about one-half as many as
included in the WIOD, and in particular, have only five broad nontraded service
sectors. We view this aggregation of the nontraded services as quite harmless toour question of studying the impact of the Uruguay Round tariff cuts. The large
number of countries and very large number of traded goods raises the question,
however, of how we solve the model: that would be a formidable task if all goods
were treated as distinct industries. Instead, we argue in the next sections that it ispossible to consistently aggregate over the traded goods at the SITC level to obtainaggregate tariffs.

6

Taking the Quantitative Model to the Data

There are two issues that we need to deal in order to take the model to the data.
First, we need to find a way to infer a large set of unobservable parameters.19
Second, we need to deal with the fact that trade is imbalanced and that our static
model cannot accommodate this. The way we solve the first issue is by expressing
the equilibrium conditions of the model in relative changes. By doing so, this19 Several parameters from our model are directly observable, like value added shares and inputoutput coefficients. However, there are a large number of parameters, like fixed entry, production,and exports costs, that are not observed. Yet, we will show how to solve the model without needing
to estimate fixed costs.

39

allows us to condition on an observed allocation in a given base year and solve themodel without needing estimates of fixed costs and other parameters which are
not directly observable.20 The way we solve the second issue is by first calibrating
the model with trade deficits as a residual and then use the model to net out the
deficits.

6.1

Equilibrium conditions of the model in relative form

To gain traction with the model when taking it to the data, we express the equilibrium conditions in relative terms using hat notation for the ratio of after-versusbefore levels for a given perturbation. After a lot of tedious manipulation (seeAppendix C) one can show that the corresponding equilibrium conditions of themodel are given byS b̃ 0 γi,s0 s ,bi )γi,s ∏ P
xbi,s ≡ (w
i,s

(45)

s 0 =1

M∑ λ ji,s

b̃ =
P
i,s

h

j =1

 i −θsb
τ ji,s xbj,s 1\+ t ji,sÂ ji,s

! −1θ

s

,

  −θsb+ t ji,sτ ji,s xbj,s 1\λ̂ ji,s = Â ji,s ,
b̃
P

(46)



(47)

i,s

0
Yi,s
=

0
λij,s
0

M

S

0
0 0
0
γ̃i,ss0 ∑∑0 Yj,s0 + αi,s wi Li + Ti ,
1
+
t
0
0

s =1
S

M

∑ ∑ 1 + t0

s =1 j =1

ji,sÂ ji,s ≡ N̂j,sŵ j (1\+t ji,s )
Ŷi,s

S

M

0
Yi,s
=∑∑

N̂i,s =
where

(48)

ij,s

j =1

λ0ji,s

0
1 + tij,ss =1 j =1\
λij,s∑ jM=1 1+tij,s Yj,sŵi

! σsσ−1−−1θs
s

and

0
λij,s

S

,

0
Yj,s
,

(49)

(50)

t0

σs −1
0 ; γ̃
Ti0 = ∑ ∑ 1+ji,st0 λ ji,s Yi,si,ss0 ≡ γi,ss0 σs .
s =1 j 6 = iji,s20 This idea was first advanced by Dekle, Eaton, and Kortum (2008) in the context of a Ricardian
trade model. CP and Ossa (2014) show that one can use this method to analyze the effects oftariff policy. CR refer to this as the exact hat algebra and show how it works for a variety of trademodels, including a multi-county, multi-industry Melitz model similar to the one we use here. The
key difference is that they show how it works for the case of cost tariffs while we use it for the caseof revenue tariffs.

40

Table 2: Elasticities
σs θs
σs −1 − 1θsσsAgriculture and Fishing (1 sector)

9.11

8.6

6.7

Mining and Quarrying (1 sector)

13.53

13.0

9.7

Manufacturing Sectors (all 8 sectors)

5.55

5.1

4.4

—

2.7

2.8

Sector(s)Nontraded services (all 5 sectors)

As we can see, by expressing the model in this way we can analyze the effectsof tariff changes without needing information of fixed entry and operating costs
which are, in general, difficult to estimate in the data, especially at the necessary
disaggregation. The only identification restriction we will impose is that these
fixed have not changed over time.
The above system of equations can then be used to study the impact of achange in iceberg costs, b
τ , as well as tariffs 1\
+t .
ji,s

6.2

ji,s

Trade Elasticity

We need to specify how we obtain estimates the elasticity of substitution and thePareto parameter. We use CP’s estimate of the trade elasticity. They show thatby triple differencing the gravity equation one can identify the elasticities using
tariff policy variation. In the context of our model the elasticity that is estimatedis given by 1 − σσss−θs1 .
In order to separately identify θs from σs we rely on estimates from the literature to obtain σsθ−s 1 . The two most used studies to deal with this issue are Chaney(2008) and Eaton, Kortum, and Kramarz (2011). Chaney (2008) obtains the coefficient by regressing the log of the rank of US firms according to their sales in
the United States on the log of sales using Compustat data on US listed firms.
Eaton, Kortum, and Kramarz (2011) who use a different procedure and data on
the propensity of French firms to export to multiple markets. Chaney (2008) findsthat σsθ−s 1 ≈ 2, while Eaton, Kortum, and Kramarz (2011) find σsθ−s 1 ≈ 1.5. We takethis latter estimate and apply it to our sectoral elasticities estimated using CP. For
the case of services we use a value of σs = 2.8
The values for the elasticities that we obtain are presented in Table 2. Notethat these values imply that σs are 6.7, 9.7, and 4.4 respectively. These numbers
are clearly within the range of values estimated by Broda and Weinstein (2006)41

where they find that the simple average of the elasticity of substitution are 17 at
a seven-digit (TSUSA), 7 at the three-digit (TSUSA), 12 at a ten-digit (HTS) and 4
at a three-digit (HTS) goods disaggregation.

6.3

Tariff aggregation, expenditure and final goods shares

Finally, using the information on tariffs, trade flows, production and with theestimated trade elasticities we can now solve for the model domestic sales, expenditure shares and final good shares.
6.3.1

Domestic Sales

To calculate domestic sales (Eii,s ) by country and sector, we need data on grossλproduction (GOi,s ), and total exports (Ei,s ≡ ∑ j6=i Eij,s = ∑ j6=i 1+ij,stij,s Yj,s ). Recall thatgross production in sector s is given by σsσ−s 1 ∑ jM=1 1+ij,stij,s Yj,s . We want to solve forλEii,s = λii,s Yi,s . Therefore, domestic sales are given by
Eii,s =
6.3.2

σs
GOi,s − Ei,s .
σs − 1

Expenditure Shares

Denote by Yij,s the total expenditure of country j on sector s goods from countryi. Total expenditure includes tariffs, therefore in order to calculate Yij,s we take
imports and multiply by tariffs. We do this at the sectoral level, namely Yij,s =Eij,s 1 + tij,s . Note that Yii,s = Eii,s . We then calculate expenditure shares as
λij,s = Yij,s / ∑i Yij,s ,(51)

where ∑i Yij,s = Yj,s is total expenditure.
6.3.3

Final goods consumption shares

To calculate final consumption share, αi,s we take the total expenditure of sectors goods, subtract the intermediate goods expenditure and divide by total final
absorption. Namely
αi,s =

Yi,s − ∑Ss0 =1 γi,ss0 GOi,s0,
wi Li + Ti

where wi Li is total value added and Ti tariff revenue which we calculate as Ti =∑Ss=1 ∑ j6=i t ji,s Eji,s .
42

6.3.4

Tariff aggregation from the good level

An important task is to find a model consistent procedure to aggregate goodslevel tariffs at a fine level to the correct sectoral-level equivalent at a coarser level.
We make the assumption that in country j and sector s there are Gj,s goods
indexed by g. Our goal is to solve for a sectoral tariff t ji,s such that the change inthis sectoral tariff (1 + t ji,s ) is equivalent to the effect of the observed changes intariffs at a goods level 1 + t ji,s ( g), g = 1..., Gj,s .
We calculate λij,s ( g), namely the expenditure share on g goods as
λij,s ( g) = Eij,s ( g) 1 + tij,s ( g) / ∑i Yij,s .

(52)

Note that the expenditure share from country i on all Gi,s goods from country j
has to equal to the total expenditure on sector s goods from country j, therefore
Gj,s∑ λ ji,s ( g) = λ ji,s .

g =1

Then the trade balance condition (27) can be re-written by adding the summation
over goods g as
Gj,s

Gi,s
S
λ ji,s ( g)λij,s ( g)∑ ∑ ∑ 1 + t ji,s ( g) Yi,s = ∑ ∑ ∑ 1 + tij,s ( g) Yj,s .
s =1 j 6 = i g =1
s =1 j 6 = i g =1
S

(53)

In order for (53) to be equivalent to (27), it is apparent that the tariffs must satisfyGj,sλ ji,s ( g)λ ji,s≡ ∑.
1 + t ji,s
1 + t ji,s ( g)
g =1

(54)

Using (51) , (52) and some manipulation we obtain a tariff aggregation formula:Gj,s∑ Eji,s ( g) 1 + t ji,s ( g)

1 + t ji,s =Gj,s∑ Eji,s ( g) t ji,s ( g)



g =1

⇐⇒

Gj,s

∑ Eji,s ( g)t ji,s =

g =1

Gj,s

(55)

∑ Eji,s ( g)

g =1

g =1

In other words, when aggregating over a finer set of goods g to a coarse sector

43

level, the sectoral aggregate tariff factor 1 + t ji,s should be computed as a tradeweighted mean of the tariff factors across the various goods g. The analogous
condition must hold for computing 1 + t0ji,s in the new equilibrium, evaluating theshares λ0ji,s ( g)/λ0ji,s in this new equilibrium. Clearly, if there is a uniform change
in the goods-level tariffs 1 + t ji,s ( g) then the new shares would equal their initialvalues λ ji,s ( g)/λ ji,s , and in that case it is obvious from the above that the change
in 1 + t ji,s ( g) would equal the change in 1 + t ji,s , i.e., the change in the sectoral
tariff just equals the uniform change in the goods-level tariffs.

7

A Quantitative Assessment of the Uruguay RoundIn this section we evaluate the trade, entry, and welfare effects of the observedchange in trade policy over the years 1990 to 2010.
We take as our initial baseline is the levels of tariffs in the year 1990, the year
before tariffs started falling as a consequence of the Uruguay Round. We willthen aim to quantify the economic effects of tariff changes by performing threedifferent exercises, as follows.
• We first impose on the model the actual changes in MFN tariffs from the year
1990 to the year 2010, holding fixed the preferential tariffs (PTA) in place inthe year 1990. This exercise we think of as informative on the effects ofchanges due to multilateral negotiations, so we label this case the “Uruguay
Round” experiment.21• We then go beyond the Uruguay Round effects on MFN tariffs, and aim toquantify the effects from all tariff changes, MFN together with any preferential PTA tariffs in place in the year 2010. We refer to this last exercise as
the “Uruguay Round + Preference” experiment.
• Finally, we explore whether there are any extra gains from tariff changes
by moving to a world with zero tariffs, what we refer as the “Free Trade”
experiment.
We then compare the gains between these three exercises, namely the gains
from Uruguay Round, Uruguay Round + Preference, and Free Trade.
21 Specifically, we set the 2010 tariff equal to minimum of the 1990 preference tariff and the 2010
MFN tariff.

44

Figure 10: Trade effects from tariff changes, world, histograms, 1990–2010
Trade

0

5

Density

10

15

Distribution of Trade/GDP across countries, by trade policy

0

.1

.2

.3

.4

.5

Trade/GDP
1990 Baseline

Uruguay Round

Uruguay Round + Preference

Free Trade

We first start by showing the trade effects from the change in tariffs from ourthree experiments. We calculate the share of total expenditure in each country
on foreign goods, a model counterpart of the trade share of GDP. Figure 10 uses
smooth histograms, or kernel density plots, to show the effects on the trade shareof GDP in all countries in the world in the baseline and 3 experiments. The results
are stark, Uruguay Round tariff reductions generate considerable trade effects.
The distribution of trade shares in 1990 had its mass concentrated in the 0%–
10% region. After the Uruguay Round experiment this mass is more spread out
in the 0%–20% region. There is little difference between the three experiments,suggesting that most of the impact that could have been achieved by a movetowards free trade was achieved by the Uruguay Round experiment; still, the Free
Trade case shows some extra trade might be generated by the removal of all tariffs.
Figure 11 shows the effects on the trade share of GDP for the case of Advancedand Emerging countries. The results are stark, Uruguay Round tariff reductions
generate considerable trade effects. The world, on average, became more openwith a roughly twofold increase in the median trade share in both subsamples.
Interestingly, the median level of openness increases slightly more for Advanced
economies relative to Emerging and Developing economies. The trade effects for45

Trade - Emerging/Developing
Trade/GDP: all countries, median, and 10 deciles (5-95), by trade policy
0.50

HKG
HKG

HKG

MUS

MUS

0.40

0.40

Trade - Advanced
Trade/GDP: all countries, median, and 10 deciles (5-95), by trade policy
0.50

Figure 11: Trade effects from tariff changes, subsamples, detail, 1990–2010

SGP
SGP
MDA
BGD

ISL
MLT
FRA

PRT
MLT
FRA

LUX

PER
MYS
SUD
THA

0.30

ISL
MLT
PRT

SUD

SDS

SDS
KOR
VEN
TWN
NGA
PAK
HUN
NAM
GIN
KEN
SYC
SWZ
TUR

MDA

BRA
JOR

JOR
SDS
HUN
PAK
TWN
KEN
SWZ
KOR
VEN
BGR
NGA
NAM
GIN
TUR
SYC

BGD
MDA
SGP
THA
MYS
PER
IND
VEN
SUD
BLZ
SVN
PAK
KEN
MUS
KOR
EGY
SYC
CIV
JOR
NGA
ECU
SDS
BRA

LKA

0.20

PRT

Trade/GDP relative to 1990 baseline

0.30

ISL

0.20

Trade/GDP relative to 1990 baseline

LUX

BGD
MDA
MYS
PER
SUD
THA

BLR
SGP

HKG
MYS

NLD
MLT

SYR
BLZ
TWN
SVK
SVN
LBN
VNM
MUS
THA
BRN
EST
LKA
LVA
MDV
KWT
JOR
CZE

NZL
JPN
NZL
GRC
AUS

NZL
GRC
AUS

0.10

0.10

BEL

GRC
AUS

USA
JPN
AUS

1990 Baseline

0.00

0.00

NER
BIH
NPL
COD
ARG
BRA
IRQ
SMR
SOM
TCD
MMR
KHM
BDI
PRK
AFG
GEO
MNE
GUY
ETH
LIE
MCO
SRB
ARM
USR

Uruguay Round Uruguay Round + Preference

Free Trade

1990 Baseline

RUS
NER
AFG
AND
SOM
CAF
BDI
TCD
COG
PSE
KHM
SMR
BIH
MMR
COD
ETH
GEO
PRK
MNE
GUY
LIE
MCO
SRB
USR
ARM

BFA
SOM
AFG
AND
CAF
BDI
PSE
TCD
KHM
SMR
BIH
COG
MMR
ETH
COD
GEO
MNE
PRK
GUY
LIE
MCO
SRB
USR
ARM

Uruguay Round Uruguay Round + Preference

ERI
AZE
TJK
ETH
BDI
KHM
COD
AND
PSE
KAZ
RUS
MMR
SOM
IRQ
SMR
BIH
PRK
GUY
GEO
MNE
LIE
MCO
SRB
USR
ARM

Free Tradethe latter are very dispersed. Some countries, like Hong Kong and Singapore
display a substantial increase in trade share, even from an initial high level, while
for other countries the trade share remain almost constant.
The second takeaway from both of figures is that Uruguay Round + Preference
does not generate a large increase in world trade relative to Uruguay Round only.
This is clearly seen by comparing the median change in openness for Advancedand Emerging and Developing countries as we move from the Uruguay Roundcase to the Uruguay Round + PTA. The line is flat, as it is at almost all marked
deciles. The histogram makes the same point. Finally, note that moving to zero
tariffs generates considerable trade share effects for Emerging economies, but little in the way of extra trade share effects for Advanced economies. This result
unmasks the asymmetrical impact of further reducing tariffs for Emerging andDeveloping countries. However, as we will see soon, this extra increase in trade
may not generate substantial positive welfare effects, unlike the Uruguay Round.
We now discuss our findings on firm entry. Figure 12 presents the distributionof changes in entry across all countries and sectors by trade policy relative to the1990 baseline (normalized to 1). Concretely, we are showing the change in entry,
namely N̂i,s . The histogram in Figure 12 shows that the entry margin is very active46

Figure 12: Entry effects from tariff changes, world, histograms, 1990–2010
Entry

0

1

Density2

34

Distribution of entry across countries/sectors, by trade policy.51
Entry (Nhat)
Uruguay Round

1.5
Uruguay Round + Preference

Free Trade
Truncated to [0.5,1.5]

and heavily impacted by the changes in tariffs. As we can see, there is mass in bothtails reflecting that in some country-sector cases entry goes up, while in others it
falls. As we compare experiments it is evident that both Uruguay Round and
Uruguay Round + Preference generate very similar entry effects, while moving toFree trade affects entry a little bit more. In particular, it tends to reduce entry on
average, in part, as a consequence of increased import competition.
Figure 13 separates the distribution of entry effects in the Advanced versus
Emerging and Developing countries. The left hand side panel shows the distribution of the change in entry for Advanced economies while the right hand sidepanel presents the distribution of the change in entry for Emerging markets. As
we can see, trade policy impacts firm entry across these types of countries in very
different ways. In particular, we find that firm entry reacts more in Advanced
economies (where tariff changes were smaller) relative to Emerging economies(where tariff changes were bigger): for all three experiments the results on firm
entry are very concentrated for Emerging markets while this is not the case forAdvanced economies. These results show clearly that entry is impacted by tariffs
not only theoretically, as we discussed several times in the paper, but that it is also
affected in a quantitatively significant way to a change in trade policy.

47

Figure 13: Entry effects from tariff changes, subsamples, histograms, 1990–20103
Density
2
1
0

0

1

Density2

3

4

Entry - Emerging/Developing
Distribution of entry across countries/sectors, by trade policy

4

Entry - Advanced
Distribution of entry across countries/sectors, by trade policy.51
Entry (Nhat)
Uruguay Round

1.5

.5

Uruguay Round + Preference

1
Entry (Nhat)
Uruguay RoundFree Trade

1.5
Uruguay Round + Preference

Free Trade

Truncated to [0.5,1.5]

Truncated to [0.5,1.5]

Figures 14 and 15 presents the welfare effects for the world, namely the change
in welfare relative to the base year 1990 (normalized to 1) for each of our threeexperiments. Here, the Uruguay Round accounts for most of the welfare effects
from tariff changes, with little further difference made by the other two experiments. In fact, the average gains across countries in our sample are +5.6% for
the Uruguay Round, +5.9% for Uruguay Round + Preference, and +5.9% for Free
trade. Yet there is substantial heterogeneity in terms of winners and losers, as thehistogram makes very clear, even if most countries are winners. And if anything,
the distribution of welfare changes shifts slightly left under Free Trade relative to
Uruguay Round, at least below the median, indicating that in our model the moveto zero tariffs and full free trade might have little welfare upside and quite a bitof downside. The bottom line here is that there may be little additional welfare
gain from a move towards zero tariffs from the position we find ourselves in after
the Uruguay Round, and which built on the previous 40 years of GATT-driven
tariff reductions which started after 1945. These findings are reinforced when we
split the sample according to Advanced and Emerging economies, as we can see
in Figure 16.

48

Figure 14: Welfare effects from tariff changes, world, histograms, 1990–2010
Welfare0

Density5

10Distribution of welfare changes across countries, by trade policy

.8

1

1.2
WelfareUruguay Round

1.4

1.6

Uruguay Round + Preference

Free Trade

8

Conclusion

In this paper we study the trade, firm entry, and welfare effects arising from actualchanges in trade policy in the last two decades. We do so with a multi-sector
heterogeneous firm model that incorporates tariffs, traded intermediate goods,
and an input-output structure that is realistic for modern economies.
First, we show that trade policy impacts firm entry and exit, a channel that has
not been fully explored before. We provide a theoretical characterization of theconditions under which tariffs affect firm entry and, ultimately, welfare. We showthat in a range of models the forces driving firm entry are inoperative only underrestrictive assumptions about the tradability of goods, the production structure,or the way tariffs are modeled.
Next, we present a new comprehensive annual tariff dataset starting in the
1980s that allows us to measure how MFN and PTA tariffs have changed overtime at a very disaggregated level. With these new data we can perform trade
policy experiments which could not be explored before now, something that weleave for future research.
49

Figure 15: Welfare effects from tariff changes, world, detail, 1990–2010

WelfareFor individual countries, median, and 10 deciles (5-95), by trade policy

1.6

MUS
MUS

MUS
MDA
TWN

TWN
TWN
KOR
MDA
SGP

SGP
HKG
NAM

HKG
NAM
BGD

SWZ

SWZ

HKG
MYS
PAK
NAM

1

1.2

MDA

IRN

.8

Welfare relative to 1990 baseline

1.4

BGD

1990 Baseline

Uruguay Round

50

Uruguay Round + Preference

Free TradeWelfare - Advanced

Welfare - Emerging/Developing

For individual countries, median, and 10 deciles (5-95), by trade policy

For individual countries, median, and 10 deciles (5-95), by trade policy

1.6

1.6

Figure 16: Welfare effects from tariff changes, subsamples, detail, 1990–2010

MUS
MUS

1.4

MDA
TWN
TWN
KOR

SGP
HKG
NAM

MDA
SGP
HKG
NAM
BGD

SWZ

SWZ

MDA

HKG
MYS
PAK
NAM

1.2

Welfare relative to 1990 baseline

MUS
TWN

1

1.2
1

Welfare relative to 1990 baseline

1.4

BGD

1990 Baseline

.8

.8

IRN

Uruguay Round Uruguay Round + Preference

Free Trade

1990 Baseline

Uruguay Round Uruguay Round + Preference

Free Trade

Finally, with our model and our data, we then go beyond gains-from-trade estimates based largely on advanced economies, and use an 189-country, 15-sector
version of our model to quantify the effects of trade liberalization over the period
1990–2010, including the greatest round of global tariff elimination, the Uruguay
Round. We find that the actual reductions in MFN tariffs in this period generated
large trade, entry, and welfare effects. We also find that the effects from preferential tariff reductions have not contributed much to total world trade and welfare,and that gains from future liberalization may remain on the table only for somedeveloping countries.

51

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STICERD - Economics of Industry Papers No. 41, Suntory and Toyota International
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53

A

Cost and revenue tariffs with and without rebate

A.1

Cost tariffs

Consider first the case cost tariffs. In a slight abuse of notation as compared to the main
text, we denote the solution to problem (1) bywi τij (1 + tij )q̃ij ( ϕ)− wi f ij ,ϕπij ( ϕ) = p̃ij ( ϕ) q̃ij ( ϕ) −(56)

where q̃ij is the quantity chosen by consumers at the optimal pricep̃ij ( ϕ) =

σ
σ−1



wi τij (1 + tij )
.
ϕ

(57)

Defining the expected value of firm revenues by R̃i , and the expected revenues per
entrant from country j by R̃ij , we have
M

M

Z ∞

j =1

j =1

ϕij∗

R̃i ≡ ∑ Ni R̃ij ≡ ∑ Nip̃ij ( ϕ) q̃ij ( ϕ) dG ( ϕ),where ϕij∗ is the cutoff productivity at which πij ( ϕij∗ ) = 0. As in the main text, we assume
a Pareto distribution, G ( ϕ) = 1 − ϕ−θ , for the firm productivities, with ϕ ≥ 1. We also σassume CES demand with elasticity σ, which implies that q̃ij ( ϕ) = q̃ij ϕij∗
ϕ/ϕij∗ .
Then combining the above equations, we obtain!σwi τij (1 + tij )  ∗  ϕq̃ij ϕijθ ϕ−θ −1 dϕ∑ Ni ϕ∗
∗
ϕ
ϕ
ij
ij
j =1
 

 w τ (1 + t )q̃ ϕ∗ Z ∞ σ−θ −2
M
i ij
ij ij
ij
θσ
ϕ
dϕ
∑ Ni σ − 1∗∗∗
ϕϕij ( ϕij )σ−1
ij
j =1
 
∞

 M
∗
w
τ
(
1
+
t
)
q̃
i ij
ij ij ϕij
θσ
ϕ σ − θ −1
Ni
σ − 1 j∑ϕij∗ (σ − θ − 1)
( ϕij∗ )σ−1 ∗
=1
ϕij
 

 M
wi τij (1 + tij )q̃ij ϕij∗
θσNi
( ϕij∗ )−θσ − 1 j∑ϕij∗ (θ − σ + 1)
=1

 M
θσ
Ni wi f ij ( ϕij∗ )−θ ,θ − σ + 1 j∑
=1
M

ei
R

=

=

=

=
=

Z ∞

σ
σ−1



(58)

where we assume θ > σ − 1 and the last line follows from πij ( ϕij∗ ) = 0 in (56).
In an analogous fashion, defining the expected value of firm profits by Π̃i , and the
expected profits per entrant from country j by Π̃ij , we have54M

Πi ≡ ∑ Ni Πij

M

≡

j =1

=

Z ∞ wi τij (1 + tij )q̃ij ( ϕ) − wi f ij dG ( ϕ)
ϕ
ϕij∗
j =1


Z ∞ 
Mwi τij (1 + tij )
1
q̃
ϕ
−
w
f
N
(
)
ij
i ij dG ( ϕ ),∑ i ϕ∗
σ−1
ϕ
ij
j =1

∑ Ni

p̃ij ( ϕ) −where the second line follows by using (57). Using the above equations, we obtain

Πi

M

=

=

=
=
=



Z ∞  wi τij (1 + tij )q̃ij



ϕij∗



!σ




ϕ
− wi f ij θ ϕ−θ −1 dϕ
∗

ϕ
ij
ij
j =1
 
∞

 w τ (1 + t )q̃ ϕ∗
M
i ij
ij ij
ij
θ
ϕ σ − θ −1−θ+ wi f ij ϕ
∑ Ni σ − 1
ϕij∗ (σ − θ − 1)
( ϕij∗ )σ−1
j =1
ϕij∗
 

 M
wi τij (1 + tij )q̃ij ϕij∗
θN
( ϕij∗ )−θ − wi f ij ( ϕij∗ )−θi∗ ( θ − σ + 1)
σ − 1 j∑
ϕ
ij
=1


 M
θ
− 1 ∑ Ni wi f ij ( ϕij∗ )−θ
σ−1
j =1

 M
σ−1
Ni wi f ij ( ϕij∗ )−θ ,θ − σ + 1 j∑
=1

∑ Ni ϕ∗ ( σ − 1) ϕ(59)

where the second-to-last line follows again from πij ( ϕij∗ ) = 0 in (56).
By combining these results we obtain
σ−1
R̃ .
σθ i

(60)

Πi = Ni wi f iE ,

(61)

Πi =
Free entry then implies

and therefore the mass of entrants is given byNi =σ − 1 R̃i.
σθ wi f iE

(62)

Given that R̃i = Yi , we get that the mass of entrants is given byNi =σ − 1 Yi.
σθ wi f iE

55

(63)

A.1.1

Entry with tariff revenue rebate

Consider the case in which tariff revenue is rebated to consumers. In this case
Yi = wi Li + Ti ,(64)

and therefore, we get that entry is given by
Ni =

A.1.2

σ−1 1
(wi Li + Ti ) .
σθ wi f iE

(65)

Entry without tariff revenue rebate

Consider the case in which tariff revenue is not rebated to consumers (consumed by thegovernment, i.e., disposed), thenYi = wi Li ,(66)
and then entry is fixed and given by
Ni =

A.2

σ−1 1
L.
σθ f iE i(67)

Revenue tariffs

Now consider the case of revenue tariffs. Again in a slight abuse of notation as comparedto the main text, we denote the solution to problem (4) by
πij ( ϕ) = pij ( ϕ) q̃ij ( ϕ) −wi τij q̃ij ( ϕ)− f ij ,ϕ(68)

where the optimal price charged by the firm to consumers is still as shown in (57), while
the firm earns pij ( ϕ) = peij ( ϕ) /(1 + tij ).
Defining the expected value of firm revenues at the net-of-tariff price by Ri , and the
expected revenues at the net-of-tariff price per entrant from country j by Rij , we have
M

M

Z ∞

j =1

j =1

ϕij∗

Ri ≡ ∑ Ni Rij ≡ ∑ Ni

pij ( ϕ) q̃ij ( ϕ) dG ( ϕ),where ϕij∗ is the cutoff productivity at which πij ( ϕij∗ ) = 0 in (68). This cutoff can differ
from that obtained from πij ( ϕij∗ ) = 0 in (56). Combining the above equations, we obtain
M

Ri

=

=
=

Z ∞

wi τij  ∗  ϕq̃ ϕij∑ Ni ϕ∗
ϕ ij
ϕij∗
ij
j =1
 

 M
w
τ
q̃
ϕij∗
i
ij
ij
θσ
N
( ϕij∗ )−θi ∗σ − 1 j∑
ϕ
(
θ
−
σ
+
1
)
ij
=1

 M
θσ
Ni wi f ij ( ϕij∗ )−θ ,θ − σ + 1 j∑
=1
σ
σ−1



56

!σ
θ ϕ−θ −1 dϕ(69)where the intermediate steps are analogous to those shown in (58), but without the cost
tariff (1 + tij ) that appears there, and once again the last line follows from πij ( ϕij∗ ) = 0 in
(68).
We can also define expected profits in this case asM

Z ∞ 

M

Πi ≡ ∑ Ni Πij

≡

j =1

=



wi τij∑ Ni ϕ∗ pij ( ϕ) − ϕ q̃ij ( ϕ) − wi fij dG( ϕ)
ij
j =1



Z
M
∞
wi τij
1
q̃
ϕ
−
w
f
N
(
)
i ij dG ( ϕ ),∑ i ϕ∗
σ−1
ϕ ij
ij
j =1

where the second line follows by using (57) with pij ( ϕ) = peij ( ϕ) /(1 + tij ). Using theabove equations, we obtain

Πi

M



Z ∞  wi τij q̃ij

∑ Ni ϕ∗ 

=

j =1



=

ϕij∗



( σ − 1) ϕ

ij

σ−1
θ−σ+1



ϕ
ϕij∗

!σ

− wi f ijθ ϕ−θ −1 dϕ M∑ Ni wi fij ( ϕij∗ )−θ ,

(70)

j =1

where once again the intermediate steps are analogous to those in (59), but without thecost tariff (1 + tij ) that appears there, and we use πij ( ϕij∗ ) = 0 from (68).
By combining the definition of Πi and Ri , we obtain
σ−1
R.
σθ i

(71)

Πi = Ni wi f iE ,

(72)

Πi =
Free entry then implies

and therefore the mass of entrants is defined byσ − 1 Ri.
σθ wi f iE

(73)

σ−1 1
(Y − Ti ) .
σθ wi f iE i

(74)

Ni =
Then entry is given by
Ni =

A.2.1

Entry with tariff revenue rebate

Consider the case in which tariff revenue is rebated to consumers. In this case
Yi = wi Li + Ti ,

57

(75)

and therefore, we get that entry is fixed
Ni =

A.2.2

σ − 1 Li.
σθ f iE(76)

Entry without tariff revenue rebate

Consider the case in which tariff revenue is not rebated to consumers (consumed by thegovernment, i.e. disposed), thenYi = wi Li ,(77)
and then entry is given by
Ni =

B

σ−1 1
(wi Li − Ti ) .
σθ wi f iE

(78)

Symmetric, two-sector, two-country equilibrium

In the main body of the text we present a closed-form solution for the comparative statics
of a two sector model. These equilibrium conditions are obtained assuming that countries
are identical. One of the sectors has traded intermediate inputs and makes a nontraded“manufacture” good that is consumed and also used as an intermediate input domestically. The second sector is consists of a nontraded final “service” good produced withlabor and consumed by households. We normalize the price of this good to one and thisensures that w = 1. The taste share of the service good is given by 1 − α, while the manufacture sector (the one with traded intermediates) has a taste share of α. We let γ ≡ γi,ssdenote the single term in the input-output matrix for the first sector in each country, with1
0 < γ < 1. We denote by γ̃ = σ−σ γ. We assume that the ad valorem tariffs (i.e., revenue
tariffs) are equal across countries, tij = t for i 6= j, while tii = 0, and the same assumption
for iceberg costs τij = τ for i 6= j, while τii = 1. We also assume that fixed costs are equal
across countries f ii = f jj = f D , f ij = f ji = f X , f iE = f jE = f E .
To simplify the notation we denote by Yi , P̃i , λii the expenditure, price index, andexpenditure share in country i of sector one goods. By symmetry we can further simplify
to repress subscripts, and define Yi = Yj ≡ Y, P̃i = P̃j ≡ P̃, λii = λ jj ≡ λ, λij = λ ji ≡ 1 − λ,Ni = Nj ≡ N, ϕii∗ = ϕ̄ii ≡ ϕ∗D , and ϕij∗ = ϕ∗ji ≡ ϕ∗X .
The equilibrium conditions for this model are then as follows
ϕ∗D =

ϕ∗X =





σ
σ−1

σ
σ−1





σ fD
Y

σ fX
Y

 1

σ −1

P̃

 1

σ −1

1
1− γ ,στ ( 1 + t ) σ −1
1− γ ,P̃

θ−σ+1 Ef ,σ−11 + λtt (1 − λ )Y 1 − γ̃−α= αwL,
1+t
1+t
f D ϕ∗D −θ + f X ϕ∗X −θ =

58

(79)

(80)

(81)
(82)

P̃ =

ϕ∗D −θ Nσ P̃γσ − 1 ϕ̃ D 1− σ

θ
+ ϕ̄−
X N



σ P̃γ τ (1 + t)
σ−1
ϕ̃ X

σ
1
1− γ
σ − 1 P̃ϕ̃ D

λ = ϕ∗D −θ N

1−σ ! 1−1 σ
,

(83)

!1− σ
,

(84)


 1
σ −1
where ϕ̃ j = ϕ∗j θ +11−σ
for j = { D, X }.
The endogenous variables to solve for are ϕ∗D , ϕ∗X , P, Y, λ, and N. We now proceed toshow how to solve for all these variables as a function of trade costs.
From (79) and (80) we can solve for ϕ∗X as a function of ϕ∗D ,ϕ∗X = F̃ (τ, t) ϕ∗D ,
1

(85)

σ

where F̃ (τ, t) = ( f X/f D ) σ−1 τ (1 + t) σ−1 . Note that in order to have an equilibrium withϕ∗X > ϕ∗D we assume f X > f D which implies that F̃ (τ, t) > 1. Using this last condition
together with equilibrium condition (81) we can solve uniquely for ϕ∗D (τ, t) as a functionof parameters and trade costs,ϕ∗D (τ, t) =



θ−σ+1
σ−1

− 1

!− 1

fE

θ

θ

,

f D + f X F̃ (τ, t)−θ(86)from which the solution for ϕ∗X (τ, t) follows immediately from (85).
After obtaining these two expressions for the entry thresholds we can solve for prices
as a function of the mass of entrants using equilibrium condition (83),1P̃1−γ = N (1−σ) G (τ, t) ,

(87)

where
σ
G (τ, t) =σ−1ϕ∗D (τ, t)−θ



1
ϕ̃ D

 1− σ+ ϕ∗X (τ, t)−θ

τ (1 + t )ϕ̃ X1−σ ! 1−1 σ,and ϕ∗X (τ, t) = F̃ (τ, t) ϕ∗D (τ, t).
We can then solve for λ using (84), and (87)λ = ϕ∗D (τ, t)−θ



σ1
σ − 1 G (τ, t) ϕ̃ D (τ, t) 1− σ,and after some algebra we obtain λ (τ, t), that is to say, an expression for λ only as afunction of parameters and trade costs (τ, t),λ (τ, t) =1
1 + F̃ (τ, t)

σ −1− θ(τ (1 + t))1−σ

.

(88)

To solve for an expression for N, note that substituting ϕ̃ D into (84) and using (79), we59

(1+ t )obtain λ = Y1 θ +1σ−σ ϕ∗D −θ f D N. Similarly, we can solve for 1 − λ = Y ϕ∗X −θ f X N θ +1σ−σ .
Now adding these expressions for 1 − λ and λ and using (81) we obtain
N=

σ−1
σ



1 + λt
1+t



Y
.
fE

(89)

Finally we note that using (82) together with (89) we can solve for the equilibrium
mass of firms N and gross output Y as a function of parameters and trade costs. In
particular,αwL 11++λtt
σ−1 1

.
σ f E 1 − γ̃ 1+λt − α t(1−λ)

N=

1+ t

(90)

1+ t

We can clearly see that in autarky we reach the limit λ = 1 and entry is given by N AUT =1 1 αwLN | λ =1 = σ −σ f E 1−γ̃ . It is also striking that firm entry takes this very same value aswell as in a model with no tariffs, when we reach the limit t = 0, since then we have
1 1 αwLN FT = N |t=0 = σ−σ f E 1−γ̃ . This last formula is independent of τ and this immediately
implies that in a model with no tariffs, entry is not affected by changes in iceberg costs.
In general we have that the change in the mass of entrants as we vary t and move form
autarky to an open economy with tariffs is given by(1 − γ̃)N̂ = 



1+λt
1+ t



t (1− λ )1 − γ̃ 11++λtt − α 1+t,and this expression collapses to N̂ = 1 when t = 0.

B.1

Change in welfare for a change in icebergs versus tariffs

In the two-sector symmetric model, start from equation (88),λ=1
1 + F̃ (τ, t)

σ − θ −1(τ (1 + t))1−σ

totally differentiating this expression, we obtaind F̃ (τ,t)
dtF̃ (τ, t)σ−θ −1 (τ (1 + t))1−σ (σ − θ − 1) F̃(τ,t) + (1 − σ) dττ + (1+ t )dλ = −
2
1 + F̃ (τ, t)σ−θ −1 (τ (1 + t))1−σd F̃ (τ, t)dτdtdλ= − (1 − λ ) ( σ − θ − 1)
+ (1 − σ )+.
λτ(1 + t )F̃ (τ, t)Note thatF̃ (τ, t)σ−θ −1 (τ (1 + t))1−σ =

60

1−λ
λ

(91)



Therefore,
dλ
=
λ
or

F̃ (τ, t)=d F̃ (τ, t)F̃ (τ, t)

=



fX
fD

 1

σ −1

σ

τ ( 1 + t ) σ −1


dτ
σ
dt
.
+
τ
σ − 1 (1 + t )




dτ
σ
dt
− (1 − λ ) 1 − θ(1 − λ ) θτ
σ−1 1+t

dλ
λ
|{z}

dτ
(1 − λ ) θ
|
{z τ}

=

change in domestic sharefrom change in icebergs

 dt+ (1 − λ) θ̃ − 1
1+t
|
{z
}
from change in tariffs

σwhere θ̃ = θ σ−1 .
Finally, using the expression for the change in welfare, we can obtain
dU
α dλ
dN
=−
+ (φ1 − φ2 ),U
1 − γ θλ
N
where
 

α
1
σ − 1 − ∆θ,
1 − γ θ ( σ − 1) (1 − ∆ )




σ −1
α  1−γ σ 1 + λt ,1 1+λt1 − α 1 − γ σ−1+t
σ 1+ t#"α − γ̃
.
t(1−λ)(1−α)
− γ̃
1+
1+λt


and

φ1

=

φ2

=

∆

=

Now we use the last expression and the following expressiondN= ( ∆ − 1)
N



tλ dλ
(1 − λ) t 1 dt−
1 + λt 1 + t t
1 + λt λ

to derive
dU
U



=

α 1
tλ
−
− (φ1 − φ2 ) (∆ − 1)1−γθ
1 + λt(1 − λ) t 1 dt
+ (φ1 − φ2 ) (∆ − 1),
1 + λt 1 + t t



dλ
λ

and finally
dU
U



=
+


α 1
tλ
dτ
−
− (φ1 − φ2 ) (∆ − 1)
(1 − λ ) θ1−γθ
1 + λtτ
α 1 − θ̃tλ(1 − λ )+ (φ1 − φ2 ) (∆ − 1) 1 − θ̃
dt.
1−γ θ
1 + λt
1+t

61

(92)

Proof of Theorem 2

B.2

Theorem 2 Consider an economy near a free trade (FT) equilibrium, t = 0 and τ > 1. Restrict
attention to the case γ = 0 (no intermediates). Then for small increases in trade frictions dt anddτ the formula for welfare changes becomes
dU FT
U

,

dt
α (1 − α )=−(1 − λii )1+t( σ − 1)

dU FT
U

and

,

dτ
= −α (1 − λii ) .
τEquivalently, in terms of implied changes in the trade share dλii /λi , we can write:
dUi /Ui FT
dλii /λii

=−
dτ =0

α (1 − α )θσ − σ + 1

dU/U FT
dλii /λii

and

dt=0

α
=− .
θ

(93)

Thus, in the case α = 1 (one sector model) welfare losses are of the second order for tariffs since
the terms on the left of the above expressions equal 0, and of the first-order for icebergs. In all othercases with α < 1, both welfare losses are in general of the first order.
Proof. Consider an economy near a free trade equilibrium (τ ≥ 1, t = 0). We focus on
the case in where γ = 0, no intermediate goods. Note that in this case we have that
φ1 =

1
α
(1 − ∆)(1 − γ) θ


1−

∆θ
σ−1


φ2 =

,

α
,
1−α

and

∆=



α − γ̃
1 − γ̃

.

After substituting these into (92), we get that the change in welfare near a free trade (FT)
equilibrium is given by
1 − λ dτα1 − ∆ γ − γ̃
dt
dU FT
= −α
−
+
.
(1 − λ )U1−γ τ(1 − γ ) σ − 1
1 − γ̃
(1 + t )Therefore, near a free trade equilibrium we have that
dU FT
U

,

dt
= −α
1+t



1−λ
1−γ



1 − ∆ γ − γ̃+
σ−11 − γ̃


and

dU FT
U

,

dτ
= −α
τ



1−λ
1−γ


.

Thus, near a free trade equilibrium, we can see that both welfare changes are first order
for a small change
 in icebergs or tariffs, provided that α < 1 so ∆ < 1, or that γ > 0 sothat γ̃ = γ

σ −1
σ

< γ.


 dt dτσEquivalently, using dλ
=
1
−
λ
θ
−
1
−
λ
1
−
θ
(
)
(
)
τ
σ−1 1+t , we can restate thisλresult as:
Fixing τ ≥ 1, varying t:

dU/U FTα=−dλ/λ(θ̃ − 1)(1 − γ)

Fixing t = 0, varying τ:

dU/U FTα=−,dλ/λθ (1 − γ )

1 − ∆ γ − γ̃+
σ−11 − γ̃

, (94)
(95)




σ
σ −1
where we remind the reader that θ̃ = θ σ−
while
γ̃
=
γ
. In the case α = 0 and
1σ
γ = 0, the expressions reduce to the formulae shown in the theorem (with ∆ = α).

62

B.3

Proof of Theorem 3

Theorem 3 (a) In regions where entry is rising (dNi > 0) due to a reduction in the tariff, anecessary and sufficient condition to have dUi /Ui > − (1−αγ)θ dλii /λii regardless of the values oft ≥ 0 and 0 ≤ λii ≤ 1 is thatγ̃ ≡ γ

σ−1
σ





> 1−

2−α
σ + 1 − [(σ − 1)/θ ]


.

(96)

When entry falls, the same condition implies that dUi /Ui < − (1−αγ)θ dλii /λii .
dNi
1 α dλiii(b) If γ = 0 (no intermediate goods) then dU
U ≶ − θ 1−γ λ if and only if N ≷ 0
i

ii

i

Proof. Part (b) follows as an immediate corollary, so it remains to prove (a).
We start by obtaining a closed-form expression for welfare in the symmetric twosector, two-county model. Welfare for a change in tariffs in the model is given by thechange in real income
dTi
d P̃
dUi
= −α i +.
Ui
wi Li + Ti
P̃i
We know Ti =t(1−λii )1+t Yi , and hence

tdλii
dTi
=−
+
Yi
1+t



1 − λii
1+t

i
We can than use the fact that w LY+
T =
i i

i

α
dUi
d P̃


= −α i +UiP̃i
1 − σ−1 γ 1+λii t
σ



1+ t



dt
t (1 − λii ) dYi
.
+
1+t
1+t
Yi

α

1+λii t , whereby
11− σ −σ γ1+ t

1 − λii dttt (1 − λii ) dYi−
dλii +
1+t 1+t 1+t
1+tYi

Now, to develop this change in welfare expression, from the main text we havedNi
= ( ∆ − 1)
Ni




t
1 − λii dt−
dλii ,
1 + λii τ 1 + t 1 + λii tfrom (37), and also
dYi
=∆
Yi




1 − λii dtt−dλii ,
1 + λii τ 1 + t 1 + λii tfrom (38), so that
1 dYi
1 dNi
=
,
∆ Yi
∆ − 1 Niand thus the change in welfare expression can be written





dUi
d P̃i
α 
1 + λii t dNi


= −α
−
.
Ui
1 − α 1 − γ σ−1 1+λii t
1 + t Ni
P̃i


1−γ
σ

63

σ −1
σ

1+ t


.

Then usingd P̃i
1 dλii1=−
1 − γ θλii
1−γ
P̃i



1
+
θ



1
1
−
σ−1 θ

∆
∆−1





dNi
,
Ni

from (22), it follows that,
dUi
Ui

 


1
σ − 1 − ∆θα dλiiαdNi−+
1 − γ θλii
1 − γ θ (σ − 1) (1 − ∆) Ni

 

σ −1
1
−
γ
σ
α 
 1 + λii t dNi .
−1 − α 1 − γ σ−1 1+λii t
1 + t Ni

=

1+ t

σ

α dλiii
In the case where we have dNi > 0 by assumption, we will have dU
Ui > − 1−γ θλii if
and only if,





α
1−γ


 

σ −1


1
σ − 1 − ∆θα  1−γ σ 1 + λii t .
>
1
+
λ
t
σ
−
1
ii
θ σ − 1 − ∆ ( σ − 1)
1−α 1−γ
1+t
σ

1+ t



α − γ̃
1 − γ̃

(97)

Now recall that

∆≡



α − γ̃
1+t(1−λii )(1−α)− γ̃
1+λii t =⇒ ∆ ≤
.

In order for (97) to hold for all values of t ≥ 0 and 0 ≤ λii ≤ 1, we replace the righthand side by its maximumvalue of α/(1 − α), and we replace its left-hand side by its
minimum value when ∆ =becomes

α−γ̃
1−γ̃





α
1−γ

, both obtained when t = 0 or λii = 1, so the condition


 

α−γ̃
α
1  σ − 1 − 1−γ̃ θ 


>
.
−α
θ
1−α
(σ − 1) 11−
γ̃

(98)

Cross-multiplying terms and simplifying, we can rewrite (98) asDividing by

1−α
1 − γ̃



1− α
1−γ̃



[(1 − α) − (1 − γ)(σ − 1)] > (1 − α)( θ − σ + 1).
θ

> 0, the condition becomes
1 − γ̃ (θ − σ + 1)
(1 − α ) 1 −> (1 − γ)(σ − 1).
1−αθSimplifying this condition, we obtain (96), which is (44) in the main text. The result
for the case where we have dNi < 0 follows directly.

64

C

Equilibrium conditions of the model in relative terms

E , γ , and γ 0 , subject to the
The parameters of the model are αi,s , σs , f ii,s , τij,s , θs , δ, f i,s
i,ss
i ,s

constraints ∑Ss=1 αi,s = 1 and ∑Ss0 =1 γi,ss0 + γi,s = 1. The equilibrium conditions to solve
the model are then as follows: M × M × S ZCP conditions (18),
∗
ϕij,s
=



σs
σs − 1

σs wi f ij,s
Yj,s

! 1

σs −1

 σs
xi,s τij,s 1 + tij,s σs −1
P̃j,s

;

M × S goods market equilibria (29),Yi,s =

λij,s0σs − 1 S
M
Y 0 + αi,s (wi Li + Ti ) ;0 =1 γi,ss0 ∑ j =1∑s
σs
1 + τij,s0 j,s

M × S sectoral prices (22),MP̃i,s = ∑ j=1 ϕ∗ji,s −θs Nj,sσs τji,s x j,s 1 + t ji,sσs − 1ϕ̃ ji,s !1−σs  1−1σs;

M × M × S expenditure shares (24),
λ ji,s = ϕ∗ji,s −θs Nj,sσs τji,s x j,s 1 + t ji,sσs − 1P̃i,s ϕ̃ ji,s

 !1−σs;

M × S free entry conditions (20),
M

∗ −θs
=
∑ fij,s ϕij,sj =1

θs − σs + 1 E
f i,s ;σs − 1

M × S input bundle costs (11),xi,s ≡ wi /γi,s

γ

S

i,s

∏
0

s =1



P̃i,s0 /γi,s0 s

γ 0

i,s s

;

and M trade balances (27),SM

λ ji,s

S

M

λij,s

∑s=1 ∑ j=1 1 + τji,s Yi,s = ∑s=1 ∑ j=1 1 + τij,s Yj,s .
We now show how we can express the model in relative changes. Consider the impactof a change in iceberg costs τ ji,s and/or tariffs t ji,s . Denote equilibrium prices and allocations under policy vector (τ, t), by the vector y and equilibrium prices and allocations
under policy vector (τ 0 , t0 ), by the vector y0 . In the hat notation, we let ŷ = y0 /y denote
the relative change in equilibrium prices and allocations after a change
in policy,
for any


 
\
0
0
element y of the vector y. Similarly, bτ = τ /τ and 1 + t
= 1+t
/ 1+t
.
ji,s

ji,s

65

ji,s

ji,s

ji,s

ji,s

Using input bundle costs (11) before and after a change in policy, we can easily obtain(45). We then proceed to solve for the change in sectoral prices. First we solve for prices
after a change in policy using equation (22), 1−σs  1−1σs
0 x0
0
τ
1
+
t
ji,s j,sji,s M0  σs0.
P̃i,s= ∑ j=1 ϕ∗ji,s 0−θs Nj,s0σs − 1ϕ̃ ji,s

Next we use the definition of expenditure shares before the change in policy (24), andmultiply and divide each expression in the summation by (24),
0
P̃i,s
=



∑

M
c∗ σs −1−θs N̂j,sλ ϕji,sj=1 ji,sbτ ji,s x̂ j,s 1\+ t ji,s

1−σs

P̃i,s

1−σs

 1

1−σs

,

(99)

c∗ = b̃where we use the fact that ϕ
ϕ ji,s . Now solve for the ZCP conditions (18) in relative
ji,schanges,! 1
 σsσ−s 1
σs −1
\
ŵ j
x̂ j,s bτ ji,s 1 + t ji,s
c∗ =
ϕ
,
(100)
ji,s
b̃
Ŷi,s
P
i,s

and substitute it into (99) to obtainMhb̃ = 
+ t ji,sτ ji,s x̂ j,s 1\P ∑ λ ji,s bi,s i−θsN̂j,s + t ji,sŵ j 1\

j =1

Ŷi,s

 1−1σs

 σs −1−θs
σs −1




b̃
P
i,s

θs −σs +1

,and after combining terms we obtain (46)

b̃ =
P
i,s

∑

M
λ
j=1 ji,shb+ t ji,sτ ji,s x̂ j,s 1\

where we defineÂ ji,s ≡ N̂j,s ŵ j 1\+ t ji,s
Ŷi,s

i−θs

 1
Â ji,s−θs,

 σs −1−θs
σs −1



.

Expenditure shares in relative changes are solved in a similar way. Start from solving
for the expenditure share after a change in policy using (24) 1−σs
0 x0
0
τ
1
+
t
ji,s j,sji,s0  σs
λ0ji,s = ϕ∗ji,s 0−θs Nj,s,00σs − 1P̃i,s ϕ̃ ji,stake the ratio of this expression relative to the expenditure share before the change in66

policy, 1−σs
\
b
τ
x̂
1
+
t
ji,s

c∗ σs −1−θs N̂j,s  ji,s j,s
.
=ϕ
ji,s
b̃
λ ji,sPλ0ji,si,sNow use the ZCP condition in relative changes (100) and combine terms to obtain the
expenditure shares in relative changes (47),λ̂ ji,s = N̂j,s ŵ j 1\+ t ji,sŶi,s −θs  σsσ−s1−−1θs bτ ji,s x̂ j,s 1\+ t ji,s



,
b̃
P
i,s

 −θsbτ ji,s x̂ j,s 1\+ t ji,sÂ ji,s .
λ̂ ji,s = 
b̃
P


i,s

The goods market equilibrium conditions (48) and the trade balance equilibrium conditions (49) are given by (27) and (29) at policy (τ 0 , t0 ).
Finally, to solve for the change in entry, note that, from the free entry condition (20)and imposing trade balance (27), we obtain
Ni,s =

Eii,s + Ei,s

,
σs
E
wi f i,sσs −1and expressing this in relative terms we end up with (50).

67