Structural Change in an Open Economy
Kei-Mu Yi

Jing Zhang∗Federal Reserve Bank of Minneapolis

University of Michigan

May 17, 2011

Abstract
We develop a tractable, three-sector model to study structural change in a twocountry world. The model features an endogenous pattern of trade dictated by comparative advantage. We derive an intuitive expression linking sectoral employment
shares to sectoral expenditure shares and to sectoral net export shares of total GDP.
Changes in productivity and in trade barriers affect expenditure and net export
shares, and thus, employment shares, across sectors. We show how these driving
forces can generate the hump-shaped pattern that characterizes the manufacturing
employment share as a country develops, even when manufacturing is the sector withthe highest productivity growth.
JEL: F20, F40, O13, O41
Keyword: structural transformation, international trade, sectoral labor reallocation∗

Yi: Kei-Mu.Yi@mpls.frb.org, Zhang: jzhang@umich.edu. We thank George Alessandria, Roc Ar-

menter, Satyajit Chatterjee, Daniel Green, Ayhan Kose, Dirk Krueger, Andrei Levchenko, Kim Ruhl,
Nancy Stokey, Linda Tesar and seminar participants at Midwest Macro conference, SED conference, Philly
Fed brown bag, U. of Toronto RMM conference, Michigan State, Michigan, Columbia, Harvard, Missouri,
SUNY-Albany, Princeton, HKUST, and the Minneapolis Fed brown bag for helpful comments. Mohan
Anand, Daniel Green, Behzad Kianian, and Tim Uy provided excellent research assistance.

1

Introduction

Two of the most important developments affecting the world’s economies in the past halfcentury have been globalization, particularly in international trade, and the emergenceof a hump-shaped pattern in manufacturing employment shares for many upper-income
countries. Employment shares in manufacturing were previously thought to be increasing
monotonically, like services employment, as countries develop. But, we now know thatfor many countries, structural change — the evolution of sectoral employment and output
shares over time — involves three distinct patterns: agriculture declines, services rise, andmanufacturing follows a hump-shaped pattern.
Integration between developed and emerging market economies is often blamed for the
decline in manufacturing in most developed countries. Moreover, some of the emerging
market economies that joined the global trading system, such as South Korea and Taiwan,
have themselves experienced a hump-shaped pattern in manufacturing employment. It isnatural to wonder, then, if these two important developments are linked in some way. Afterall, the fundamental role of international trade is to facilitate specialization via an efficient
reallocation of employment and other factors of production across sectors.
The purpose of this paper is to develop an open economy model of structural change,
and to use it to understand the channels by which trade can affect structural change, particularly the hump-shaped pattern in the manufacturing employment share. To illustrate
clearly these channels, we employ a simple and tractable framework building on Eaton andKortum (2002). There are two countries and three sectors, two of which engage in international trade. Trade is motivated by Ricardian comparative advantage: relative productivity
differences across countries and goods determine patterns of specialization. Each country
runs a net export surplus in its sector of comparative advantage. We show that a sector’s
employment share equals the sum of the sector’s expenditure share and the sector’s net
export share of total GDP — there is a direct link between trade and structural change.

1

Trade also affects relative prices, which affect sectoral expenditure and employment shares.
We then develop two scenarios in which the presence of trade can generate a humpshaped pattern in the manufacturing employment share. For simplicity, consider a worldin which there is no structural change in the absence of trade.1 In the first scenario, thecountry with a comparative advantage in manufacturing — call it the “home” country —experiences both relative and absolute productivity growth in manufacturing over time.
Because of the relative productivity growth, the home country’s net export surplus in
manufacturing increases, leading to a rise in manufacturing employment initially. As time
passes, the home country will supply the entire world market for manufactured goods. After
this point, the continuing increase in absolute manufacturing productivity growth enables
the home country to supply world demand with fewer workers in each period. Hence, theinitial increases in manufacturing employment is followed by an eventual decline.
In the second scenario, the primary driving force is declining trade costs over time. As
trade costs decline, each country’s comparative advantage is increasingly revealed, and there
is increased specialization. This leads to a rising manufacturing employment share in the
country with a comparative advantage in manufacturing (again, the “home” country). If thehome country is small enough initially, over time its relative wage will increase, because thegains from specialization and trade are larger for smaller countries. The increase in home’s
relative wage reduces the relative purchasing power of the foreign country, which reduces
the amount of home country labor needed to satisfy foreign demand for manufactured
goods. As long as the home relative wage continues to increase, this relative purchasing
power effect will eventually dominate the employment effects from the increasing net export
surplus. Hence, the home manufacturing employment share will peak and then decline.
The above two scenarios seem plausible in which the “home” country is South Korea
or Taiwan. What happens to manufacturing in the larger, foreign country? Relative to au1

This would arise, for example, if the elasticity of substitution across sectors and the sectoral income
elasticities of demand are all one.

2

tarky, the foreign country will experience a faster decline in its manufacturing employment
share. The key reason is because an increasing share of its demand for manufactured goods
is being supplied from abroad. Countries like the United States could plausibly fit into thiscategory. Thus, our model can explain the recent manufacturing employment patterns indeveloped countries, as well as emerging market countries.
Most existing theoretical work on structural change has focused on closed economy
models and relies on one of two broad mechanisms. The first mechanism, which has been
the dominant one in the literature, operates on the demand side and draws from Engel’s
Law. Sectors differ in their income elasticities of demand; in particular, agriculture andfood have an income elasticity that is less than one, while the other sectors, on net, have an
income elasticity that exceeds one. A notable recent contribution in a three sector model isKongsamut, Rebelo, and Xie (2001). The second mechanism operates more on the supply
side and draws from the Baumol effect. Sectors differ in their productivity growth andelasticities of substitution between sectors are less than one. Then, employment sharesfall in sectors with high productivity growth. Both mechanisms can generate the observed
patterns of structural change in a closed economy setting, but both require special featuresin order to generate the hump-shaped pattern in manufacturing. For example, in Ngai and
Pissarides (2007) manufacturing must have below average productivity growth initially andthen above average productivity growth later.2
To highlight our transmission channels most clearly, our model employs the Baumol
assumptions, as in Ngai and Pissarides (2007). A closed economy version of our model cancapture the declining manufacturing employment shares present in most advanced nations.
But, it cannot explain the increasing manufacturing employment shares, let alone a humpshaped pattern, in emerging market nations for which manufacturing productivity growthis consistently above average. A framework allowing for international trade breaks the tight2

Ngai and Pissarides solve for the balanced growth equilibrium; average productivity growth changes
over time, even though sectoral productivity growth is constant, owing to composition effects.

3

link between sectoral production and sectoral expenditure, which facilitates changes in the
structure of production that are independent of changes in domestic demand. The presenceof international trade transforms the process of structural change.
Until recently, the main contributions in open economy models of structural change wereby Matsuyama (1992, 2009). The latter paper and Coleman (2007) are the most closely
related to ours.3 Matsuyama (2009) employs a simple Ricardian model to demonstratethat high manufacturing productivity growth need not lead to a decline in manufacturing
employment. Coleman (2007) uses a multi-country Heckscher-Ohlin-Ricardo framework to
study the effect of a large emerging market country on other countries’ GDPs and welfare.
Neither paper addresses the conditions under which productivity growth and declining tradebarriers can generate the hump-shaped pattern of manufacturing employment shares.
The rest of the paper is organized as follows. Section 2 shows some evidence to motivate
studying structural change in an open economy. Section 3 presents the benchmark model,
and Section 4 analyzes the autarky version of the model. Section 5 presents the mainderivations and discusses the two scenarios that generate the hump-shaped pattern in the
manufacturing labor share. Section 6 shows that our findings hold in the presence of nonhomothetic preferences, intermediate goods, and capital goods. Section 7 concludes.

2

Motivating Evidence

The reallocation of labor and output across broad economic sectors is one of the mostprominent features of development. The early empirical research by Clark (1957), Kuznets
3

Echevarria (1995) is also an early contribution to open economy models of structural change. She
employs a small open economy. Caselli and Coleman (2001) is effectively an open economy model withlabor mobility and human capital. It argues that changes in the relative supply of factors of production arenecessary to explain changes in both quantities and prices in the US structural change. However, its focus ison agriculture and non-agriculture; it does not highlight manufacturing. Other recent open economy modelsof structural change include Galor and Mountford (2008), Stefanski (2009), Teignier-Bacque (2009), Ungor(2009), and Betts, Giri, and Verma (2011). The latter four papers conduct quantitative studies involving
structural change in China, India, and/or South Korea. Galor and Mountford (2008) study the effect oftrade on fertility and population growth, and on human capital acquisition.

4

(1957, 1966), and Chenery and Syrquin (1975), among others, documented that the agriculture shares of output and employment decline, while the industry and services shares of
output and employment rise, as a country develops. In light of these patterns, most models of structural change developed at that time were two sector models.4 In more recent
years, Maddison (1991), Buera and Kaboski (2008), and others have shown that there arethree distinct sectoral allocation patterns: agriculture declines, services rises, and manufacturing follows a hump-shaped pattern, first rising, then falling, as Figure 1 shows for
the United States and South Korea.5 The hump-shaped pattern in manufacturing may be
one of the most important new facts about structural change in the past three decades. As
a consequence, three-sector models have become more prevalent in recent years, including
Kongsamut, Rebelo, and Xie (2001) and Ngai and Pissarides (2007).6
Figure 1: Hump in Manufacturing Labor Share30

25
United States

Percent

20

15
South Korea
10501870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
Year

We motivate studying structural change in an open economy by providing two empirical relationships. The first is the relation between the change over time in a country’s
4

The sectoral divisions were often agriculture and non-agriculture, agriculture and industry (manufacturing), or capital-intensive and labor-intensive. For recent examples of these divisions, see Caselli and
Coleman (2001), Laitner (2000), and Acemoglu and Guerrieri (2008). Also, Desmet and Rossi-Hansberg(2009) develop and calibrate a spatial model of structural change in which geography influences the shift
between services and manufacturing.
5
Data sources are International Historical Statistics (United States, 1870–1960), OECD Statistics(United States, 1963–2005) and GGDC cross-country database (South Korea, 1963–2005).
6
Also, see Buera and Kaboski (2008, 2009), Duarte and Restuccia (2009), Echevarria (1997), Foellmi
and Zweimuller (2008), Rogerson (2008), Herrendorf, Rogerson and Valentinyi (2009), Restuccia, Yang,
and Zhu (2008), and Verma (2008). Also, see Ju, Lin and Wang (2009) for an n-sector model.

5manufacturing net exports as a share of total GDP and the change in its manufacturing
employment share. Our sample of countries includes the 19 countries in the Groningen
Growth and Development Centre (hereafter, GGDC) 10-sector database, as well as 19
OECD countries covered by the OECD’s Annual Labor Force Statistics (hereafter, ALFS),
rev. 2, database. The GGDC 10-sector database includes Japan and emerging market
countries in South and Central America and East and South Asia; for each country, a fairly
long time series of sectoral data exists. Details on the construction of the variables andon the data sources are given in Appendix A1. Figure 2 shows that countries with larger
increases in their manufacturing net export share of GDP tended to have larger increases
in their manufacturing employment share.7 The correlation coefficient is 0.57.8
Figure 2: Manufacturing Net Exports and Manufacturing Employment
Change in Manu
ufacturing Labor Share, 1962‐2005,
Percentage Points

25%
20%
15%

TWN
THA

10%
BOL

5%

‐5%

IDN
CRI

MEX
IND

0%

MYS
KOR

BRA
COL PHL
PER
PRT
ITA
JPN
CHL
ESP
CAN

VEN

‐10%
FRA
NZL
USA
AUS

‐15%

FIN

BEL
AUT DEN
NLD
ARG
NOR
ISL
GER SWE
CHE

‐20%

GBR

‐25%
‐15%

‐10%

‐5%

0%

5%

10%

15%

20%

25%

30%

Change in Manufacturing Net Exports/GDP, 1962‐2005, Percentage Points

The second empirical relationship looks at the services sector. We run a regressionof the services employment share on per capita GDP and on openness, as measured by
the trade share of total GDP. Specifically, we examine 37 of the 38 countries, excluding
Taiwan. The time period covers 1960 to 2005. To reduce the effects of business cycles, weconstruct four-year non-overlapping averages for each of the three main variables. Details
7

We exclude Hong Kong and Singapore from the figure as they are essentially city-states and are outliers.
All countries but Japan, South Korea and Taiwan are either on one side of the hump or are notexperiencing a sharply defined hump. We re-did the plot including only those years for which Japan, South
Korea and Taiwan were on the increasing part of the hump. The correlation in that case is 0.63.
8

6

about construction of the variables and the data sources are given in Appendix A2. We
run the following regression:

list = β0 + β1 tradeit + β2 gdppcit + γi + it ,where list is the employment share in the services sector for country i in time period t,
tradeit is exports+imports as a share of GDP, and gdppcit is PPP GDP per capita inconstant 2005 international dollars. Per capita income is included to allow for an income
elasticity of demand for services that exceeds one. To control for country-specific factors,
such as the effects of geography and institutions on the services employment share, we also
include country fixed effects in the regression. The estimation results are given in Table 1.
Table 1: Trade and Services Labor Share
Services labor sharea

Trade0.0801

Income per capita
1.23e-5Constant
0.369(0.0289)(1.12e-6)(0.0251)

R2
0.67

Observations
379

a : Country fixed effects are included. The standard errors reported in parentheses are robust to heteroskedasticity.

The estimated coefficients β1 and β2 are statistically significant at the 1 percent level.
The coefficient on trade indicates that a 10 percentage point increase in the export (as wellas import) share of GDP is associated with a 1.6 percentage point increase in the services
employment share. This suggests the possibility of spillover from international trade to
structural change even in the (relatively) non-traded sector. Both empirical relationships
suggest the importance of the open economy for structural change, and are consistent, as
we will show, with the implications of our model.

3

Model

Our model builds on Ngai and Pissarides (2007, hereafter, NP) and Eaton and Kortum(2002). As discussed in the introduction, the driving force in NP is sector-biased produc7

tivity growth. A natural extension of NP to an open economy setting is one emphasizing
productivity differences as the motive for international trade, the Ricardian trade model.
We adopt the Eaton and Kortum (2002) Ricardian setting. To highlight the role of tradein structural change clearly, our model has one factor of production, two countries, andthree sectors: agriculture, manufacturing and services. The agriculture and manufacturing
goods are tradable and the services good is non-tradable. Preferences are homothetic. (Werelax the homotheticity assumption and also introduce intermediate goods or capital goods
to production in Section 6.) Productivity and trade costs change at different rates acrosssectors and countries; these forces drive structural change. Trade is balanced each period.
The model is thus static; we omit the time subscript unless needed.

3.1

Technologies

There is a single non-tradable good in the services sector (s). The agriculture (a) andmanufacturing (m) sectors each consist of a continuum of tradable goods along the [0, 1]
interval. Each country possesses technologies for producing all the goods in all sectors.
The production function for the services sector good of country i is

Yis = Ais Lis ,(1)

where Yis and Lis denote output and labor devoted to services, and Ais denotes exogenous
productivity of producing the services good.
The production function for tradable good z ∈ [0, 1] in sector q ∈ {a, m} of country i isyiq (z) = Aiq (z)liq (z),(2)

where yiq (z) and liq (z) denote output and labor devoted to this tradable good, and Aiq (z)denotes exogenous productivity of producing this tradable good.

8

Productivity Aiq (z) is the realization of a random variable Ziq drawn from the cumulative distribution function Fiq (A) = P r[Ziq ≤ A]. Following Eaton and Kortum (2002), we−θ

assume that Fiq (A) is a Fréchet distribution: Fiq (A) = e−Tiq A , where Tiq > 0, θ > 1, andq ∈ {a, m}. The parameter Tiq governs the mean of the distribution; a larger Tiq implies
that a high efficiency draw for any good z is more likely. The larger is θ, the lower theheterogeneity or variance of Ziq .9 We assume that the productivity is drawn each period.10
When agriculture or manufacturing goods are shipped abroad, they incur trade costs,
which include tariffs, transportation costs, and other barriers to trade. We model thesecosts as iceberg costs. Specifically, if one unit of manufacturing good z is shipped from1
units arrive in country i. Similarly, τija is the gross trade cost incurredcountry j, then τijm

from shipping one unit of the agriculture good from country j to country i. We assume
that trade costs within a country are zero, i.e., τiia = τiim = 1. In the case of free trade,
trade costs across countries are also zero, i.e., τ12a = τ21a = 1 and τ12m = τ21m = 1.

3.2

Preferences

Period utility of the representative household in country i is given by:1
U (Cia , Cim , Cis ) = (ωa Cia+ ωm Cim+ ωs Cis )  ,(3)

where Cia , Cim , and Cis are consumption of the composite agriculture good, the composite
manufacturing good, and the services good, respectively,  < 1, ωa , ωm , ωs > 0 and1ωa + ωm + ωs = 1. The elasticity of substitution across sectoral goods is 1−. If  ∈ [0, 1),

the elasticity of substitution exceeds or equals one; the sectoral goods are substitutes. If
 < 0, the elasticity of substitution is less than one; the sectoral goods are complements.
√
1/θ
Ziq has geometric mean eγ/θ Tiq and its log has a standard deviation π/(θ 6), where γ is Euler’s
constant.
10
Alternatively, we could assume that the productivity is drawn once in the initial period, and as the
T ’s change over time, the productivity relative to T remains constant.
99

The composite good in agriculture or manufacturing is an aggregate of the individual
goods as follows:
Ciq =

R

1
c (z)η dz
0 iq

 η1

,

(4)

where ciq (z) is the use of good z by country i to make the composite sectoral good q ∈{a, m}, and η < 1.
The representative household maximizes his/her utility (3) and (4) subject to the following budget constraint in each period:

Pia Cia + Pim Cim + Pis Cis = wi Li ,

(5)

Z 1
Piq Ciq =piq (z)ciq (z)dz,

for q ∈ {a, m},(6)0where wi , Pia , Pim and Pis denote the wage rate, and the prices of the agriculture composite
good, the manufacturing composite good, and the services good, respectively, and piq (z)denotes the price of good z in tradable good sector q ∈ {a, m}. The household supplies Li
inelastically and spends all labor income on consumption. The budget constraints (5) and(6) ensure that balanced trade holds period-by-period.

3.3

Equilibrium

In a Ricardian model, trade is determined by comparative advantage, based on relative
productivity differences and relative trade costs across countries. All factor and goods
markets are characterized by perfect competition. Labor is perfectly mobile across sectors
within a country, but immobile across countries. The following factor market clearing
conditions hold in each period in each country i

Li = Lis + Lim + Lia ,

10

(7)

where Lim =R10lim (z)dz and Lia =R10lia (z)dz.

We denote the actual trade costs that the household in country i pays for sector q ∈{a, m} good z by diq (z). Specifically, diq (z) is 1 if good z is produced domestically and isτijq , j 6= i, if good z is produced abroad. The following goods markets clearing conditions
hold in each period in each country i:

Yis = Cis ,y1a (z) + y2a (z) = d1a (z)c1a (z) + d2a (z)c2a (z),y1m (z) + y2m (z) = d1m (z)c1m (z) + d2m (z)c2m (z),(8)∀z ∈ [0, 1],(9)∀z ∈ [0, 1].

(10)

We define a competitive equilibrium of our model economy with country-specific andexogenous labor endowment processes {Li }, trade cost processes {τija , τijm }, productivity
processes {Tia , Tim , Ais } and structural parameters {σ, , η, β, θ} as follows.
Definition 1. A competitive equilibrium is a sequence of goods and factor prices {pia (z),pim (z), Pia , Pim , Pis , wi } and allocations {lia (z), lim (z), Lia , Lim , Lis , yia (z), yim (z), Yis ,cia (z), cim (z), Cia , Cim , Cis } for z ∈ [0, 1] and i = 1, 2, such that given prices, the allocations solve the firms’ maximization problems associated with technologies (1)-(2) and thehousehold’s maximization problem characterized by (3)-(6), and satisfy the market clearing
conditions (7)-(10).
Our model economy has a unique competitive equilibrium. We start the characterizationof this equilibrium with the prices. Goods prices equal marginal costs. Specifically, theservices good price in country i is given by Pis = Awisi . For tradable goods, the marginal costs
include the trade costs. The price that a consumer in country i pays to purchase one unitτw

jof good z in sector q ∈ {a, m} produced in country j is given by pijq (z) = Aijq
. The actual
jq (z)

price that the consumer in country i pays for this good is piq (z) = min {pi1q (z), pi2q (z)}.

11The price of the composite sector good q ∈ {a, m} is given by

Piq =

R
1

η

p (z) η−1 dz
0 iq

 η−1
η

,

and the aggregate price index Pi is given by
 1
 −1

1

1


1−
−1
1−
−1
1−
−1
Pi = ωa Pia + ωm Pim + ωs Pis.

(11)

We next characterize the household’s optimal consumption allocation. According to
the first order optimality conditions, the consumption expenditure share, Xiq =Piq Ciq, in
Pi Ci

sector q ∈ {a, m, s} of country i is given by
1
1−



Xiq = ωq

Piq
Pi


 −1

,

(12)

and the consumption expenditure share, Xiq (z), for good z in tradable sector q is given by
Xiq (z) =piq (z)
Piq

η
 η−1

Xiq .

The sectoral expenditure shares are determined by relative prices and the preference parameter . When the elasticity of substitution across sectors is one, i.e.,  = 0, the sectoral
expenditure shares are independent of the relative prices. When this elasticity of substitution is less than one, i.e.,  < 0, the higher is the sector-q relative price, the higher is theexpenditure share of sector q.
The model generates both inter-sector and intra-sector trade based on comparative advantage. Within a sector, which goods are exported or imported is determined by theidiosyncratic productivity draws in conjunction with the trade costs. Given our productivity distribution assumption, as long as trade costs are not prohibitively high, there will besome goods within a sector that a country will be able to produce more cheaply than the12other country; hence, in each sector in each country, some goods will be imported. Eachcountry will run a net export surplus in one sector and a net export deficit in the othersector. The relative wage endogenously adjusts to ensure that the balanced-trade condition is satisfied. Labor is allocated across sectors to meet local demand for the non-traded
services good and a portion of world demand for the traded goods. We fully characterize
the trade pattern and the labor allocation in the next two sections.

4

Structural Change under Autarky

We begin our analysis of the model by developing the pattern of structural change in aclosed economy or under autarky.11 Under autarky, all goods are produced domestically.
We focus on the sectoral allocation of employment. The results developed here will allow
us to highlight the contribution of international trade on structural change, which we study
in the following section.
We start with sectoral prices. We use the superscript c to denote the corresponding
variables in the closed economy. It is straightforward to show for country i and each period,
1
Piac
=
,
c
wi
Aia
1

c
1
Pim
=
,
c
wi
Aim

1

1
Pisc
=
,
c
wi
Ais

(13)

η−1

η 1
θ
, γ = (Γ(1 − 1−η)) η , and Γ is the Gamma function.12
where Aia = γ −1 Tiaθ , Aim = γ −1 TimθThus, the continuum of goods in the agriculture or manufacturing sector can be essentiallyreduced to one composite good with productivity Aia or Aim .
The feasibility conditions imply that the sectoral labor share equals the sectoral expen11

We use “autarky” and “closed” interchangeably. Autarky is a special case of our model in which thetrade costs are infinitely high. The autarky implications are similar to those in Ngai and Pissarides (2007).
112< 1 + θ to have a well-defined price index. Under this assumption, theWe need to assume 1−ηparameter η, which governs the elasticity of substitution across goods within a sector, can be ignored
because it appears only in the constant term γ.

13diture share:cliq=

wic Lciq
Piqc Ciqc
Lciq
= c
= c
= Xiqc ,
Li
wi Li
wi Li

(14)

for each sector q ∈ {a, m, s}.13 The sectoral labor shares depend on relative prices in thesame way as the sectoral expenditures shares in (12). When the elasticity of substitution
across sectors is less than one, the higher the sectoral relative price — owing to lower sectoral
relative productivity — the higher the sectoral expenditure and labor shares. When theelasticity is one, the sectoral labor shares are independent of the relative prices.14
Turning to dynamics, let Ẑ denote the log growth rate of variable Z. Then, we have,for any q ∈ {a, m, s} and any period tˆlc = X̂ c =iqt
iqt
where P̂itc =Pc(P̂iqt− P̂itc ),
−1

(15)

c
c
q∈{a,m,s} Xiqt P̂iqt . Thus, the elasticity of substitution links changes in sectoralcclabor shares ˆliqt
to changes in sectoral relative prices P̂iqt− P̂itc . When the elasticity of

substitution across sectors is less than one, i.e.,  < 0, a sector with declining relative
prices experiences declining expenditure and labor shares over time. In the Cobb-Douglas
case, i.e.,  = 0, there is no structural change: sectoral expenditure and labor shares areconstant over time.
The growth rate of sectoral labor shares can be expressed in terms of the growth rates
of sectoral productivities using (13):ˆlc = X̂ c =
iqt
iqt


(Âiqt − Âcit ),1−where the weighted average productivity growth Âcit =

P

(16)

c
q∈{a,m,s} Xiqt Âiqt . When the elas-

13
The sectoral labor share will equal the sectoral expenditure share even in a framework with capital andwith intermediate goods, as long as the coefficient on labor in the production function is identical acrosssectors, and similarly for capital.
14
When the elasticity is greater than one, higher sectoral relative prices imply lower sectoral expenditureand labor shares.

14

ticity is less than one, sectors with relatively high productivity growth experience declines in
employment shares. Labor moves from high productivity growth sectors to low productivity growth sectors. If the manufacturing sector has the fastest productivity growth among
the three sectors, the manufacturing labor share declines overtime. In many developing
countries, the manufacturing sector often experiences the fastest growth in productivity
and a rising labor share.

5Structural Change in an Open Economy

We now analyze the patterns of structural change in an open economy. We first examine
the impact effect of an open economy, that is, how sectoral relative prices, expenditure
shares, and labor shares change in the period in which a closed economy becomes open.
We then study the ensuing dynamics in the open economy relative to those in the closed
economy. We highlight two plausible scenarios that can generate a hump-shaped pattern
in manufacturing employment shares. One scenario involves a country with a comparativeadvantage in manufacturing, and with relative manufacturing productivity growth risingover time. The second focuses on declining trade costs in the manufacturing sector. Owing
to our two-country framework, relative wages, the terms of trade, and relative country sizes
are endogenous; these variables play a key role in the model dynamics, as we show below.

5.1

Impact of International Trade

We begin by defining sectoral comparative advantage. Country i has a comparative advantage in manufacturing if and only if
Aia /τjia
Aim /τjim
>
.
Ajm
Aja

15

Our definition is thus the traditional definition augmented by trade costs.15 If country i
has a comparative advantage in manufacturing, we will say it has a comparative disadvantage in agriculture, and vice versa. In the presence of trade costs, however, if country 1
has a comparative advantage in manufacturing, it is not necessarily true that country 2
has a comparative advantage in agriculture. We restrict our attention to cases in which
one country has a comparative advantage in manufacturing and the other country has acomparative advantage in agriculture, which is a restriction that trade costs cannot be too
different across sectors and countries.
5.1.1

Trade Patterns

We start our analysis with the trade patterns implied by comparative advantage. Expenditures on tradable goods are divided between domestic goods and imported goods. Under
the Fréchet distribution of productivities, the share of country i’s expenditure on sector q
goods from country j, πijq , captures intra-sector trade and is given by

πijq =(τijq wj /Ajq )−θ=(τijq wj /Ajq )−θ + (wi /Aiq )−θ1+(

1
wi /Aiq)−θτijq wj /Ajq

.

(17)

Equation (17) shows how a lower average cost of production, inclusive of trade costs, incountry j translates into a greater sectoral import share by country i. The import sharealso depends on the parameter θ; a higher θ implies a smaller dispersion of productivity
draws, which strengthens the effect of comparative advantage on intra-sector trade. Sectoral
spending that is not on imports is on domestic goods: πiiq = 1 − πijq .
If country i has a comparative advantage in manufacturing and country j has a comparative advantage in agriculture, equation (17) implies that πijm < πija and πiim > πiia .
The share of country i’s manufacturing spending that is on imports is less than the share
15

Hence, it is possible for a country to have a relative disadvantage in manufacturing from the productivities alone, but, owing to sufficiently small manufacturing trade costs, an overall comparative advantage
in manufacturing. See Deardorff (2004) for further discussion on the topic of comparative advantage in thepresence of trade costs.

16

of country i’s agriculture spending that is on imports. Intuitively, a greater share of spending is on domestic goods in the comparative advantage sector relative to the comparative
disadvantage sector. Lemma 1 summarizes this discussion.16
Lemma 1. (Intra-Sector Trade) If country 1 (2) has a comparative advantage in manufacturing (agriculture), then π12m < π12a and π21a < π21m .
We now characterize the patterns of international trade. Country i’s exports of sector
q goods are given by EXiq = πjiq Xjq wj Lj . It is the product of country j’s expenditure
devoted to sector q goods, Xjq wj Lj , and the fraction of that expenditure that is on imports,
πjiq . Similarly, country i’s imports of sector q goods are given by IMiq = πijq Xiq wi Li . Thus,
country i’s net exports of sector q goods is given by N Xiq = EXiq − IMiq . The balanced
trade condition implies that inter-sectoral trade sums to zero, i.e., N Xim + N Xia = 0. We
NX

denote the sectoral net export share of total GDP, wi Liqi , by Niq . We demonstrate laterthat the sectoral net export share is a key determinant of sectoral labor allocations.

5.1.2

Relative Prices and Expenditure Shares

We now examine the impact of trade on relative prices and expenditure shares in eachcountry. In order to facilitate comparisons with the autarky case, we normalize prices by
the wage rate. For the services good in country i, its price relative to the wage rate isPis= A1is , which is the same as under autarky. For the tradable composite good q, we have:
wi

"

Piq
1
1+
=
wi
Aiq



τijq wj /Ajq
wi /Aiq

−θ #− θ1

1
θ
πiiq
=
.
Aiq

(18)

Comparing equation (18) to (13), one can see that the price relative to the wage is lower
with trade than under autarky because πiiq < 1. The lower the trade cost or foreign
wage, or the higher the foreign technology, the lower is the sectoral expenditure share
16

Proofs are omitted unless specifically stated otherwise.

17

on domestic goods, and the lower is the sectoral price under trade relative to autarky.
Lemma 2 implies that the price gap between trade and autarky is larger in the sector ofcomparative disadvantage. Trade essentially allows each country to enlarge its effective
state of technology in the tradable sectors, thus leading to lower prices; moreover, the gainin effective technology is larger in the sector of comparative disadvantage.
The impact of trade on prices relative to the wage rate has direct implications for
welfare. The aggregate price level relative to the wage rate wPii is lower in the open economy
compared to autarky.

wiPimeasures the real purchasing power of each country’s income;hence, we have the well-known result from classical trade theory that opening up to tradeleads to a rise in welfare in both countries.
We next examine sectoral prices relative to the aggregate price level in the open economy
compared to autarky. From the above, it is clear that PPisi is higher in the open economy
in both countries; also, for the sector in which country i has a comparative disadvantage,
its price relative to the aggregate price is lower in an open economy. On the other hand,in the comparative advantage sector, the sectoral price relative to the aggregate price may
or may not be lower in the open economy than under autarky. Lemma 2 summarizes our
results for relative prices.
Pc

Lemma 2. (Open Economy Relative Prices) In both countries, Pwiai < wiac , Pwimi <
i

c
Pim
,
wic

Pc
Pc
Pc
Pis
= wisc , wPii < wic , and PPisi > Pisc . Moreover, if country 1 (2) has a comparative advantage
wi
i
i
i
Pc

Pc

1

2

< P2m
in manufacturing (agriculture), then PP1a1 < P1ac and PP2mc .
2
The impact of trade on sectoral relative prices determines the impact of trade on expenditure shares. Consider, for example, the case of an elasticity of substitution across sectorsthat is less than one. Because the relative services price PPisi is higher in the open economy
in both countries, the services expenditure share is also higher in the open economy inboth countries. If country i has a comparative disadvantage in sector q, the expenditure
share Xiq is lower in the open economy than in the closed economy. We cannot sign the18expenditure share of the sector in which country i has a comparative advantage. Lemma 3
summarizes our results for expenditure shares.
Lemma 3. (Open Economy Expenditure Shares) Assume that  < 0. Then, Xis > Xisc inboth countries. Moreover, if country 1 (2) has a comparative advantage in manufacturingcc(agriculture), then X1a < X1aand X2m < X2m
.

5.1.3

Labor Allocations

We now study the impact of trade on sectoral labor allocations. Because the services good
is non-tradable, the market clearing condition requires that Cis = Ais Lis = Xis wi Li /Pis .17
Thus, we have
lis =

Lis
= Xis .
Li

In an open economy, the non-tradable sector’s labor share equals its expenditure share —just as in the closed economy. This does not mean that trade has no impact on the services
labor share, because expenditure shares are affected by trade, as shown in Lemma 3.
Using the expression for Xis in equation (12), Pi in equation (11), and relative prices
in equation (18), we can write the service labor share as
1

1



θ −1
−1
lis
= ωa1− πiia



Ais
Aia


 −1

1
1−

1 
θ −1



+ ωm πiim

Ais
Aim


 −1

1

+ ωs1− .

(19)

The corresponding expression for the services labor share in autarky is given by
1

−1
lis
= ωa1−



Ais
Aia


 −1

1
1−

+ ωm



Ais
Aim


 −1

1

+ ωs1− .

When the elasticity of substitution is less than one, which we call the “Baumol” case, theservices labor share is higher in the open economy than under autarky. Moreover, the lower
17

We have not yet discussed value-added output shares. As should be clear by now, our simple framework
implies that each sector’s value-added output share equals its employment share.

19the sectoral expenditure on domestic goods, or the more a country imports from abroad,the higher is the labor share relative to autarky. This implication is consistent with theregression evidence presented in Table 1; even though services are non-traded, trade affects
this sector’s labor share through general equilibrium effects on relative prices.
We next examine the tradable sector labor shares. Country 1’s income from sector
q equals expenditures of both countries on its sector-q goods: w1 L1q = π11q P1q C1q +π21q P2q C2q . This implies

l1q =

w2 L2
L1q
= π11q X1q + π21q X2q
.
L1
w1 L1

(20)

Three forces determine the share of country 1’s labor devoted to sector q. It depends on the
expenditure share of each country on sector q goods, X1q and X2q . In addition, it depends
on the extent of specialization, i.e., the share of each country’s spending on sector q goods
that is on goods produced by country 1, π11q and π21q . Finally, it depends on the relative
size of the two economies. The smaller is country 1, the more its labor share is determinedby country 2’s demand. These three forces drive the dynamics of structural change in ourmodel, as we will see in sections 5.2 and 5.3.
Substituting 1 − π12q for π11q , we can rewrite (20) as follows:

l1q = X1q +π21q X2q w2 L2 − π12q X1q w1 L1= X1q + N1q .
w1 L1

(21)

Country 1’s labor share in sector q equals its sectoral expenditure share plus its sectoral net
export share of total GDP. Thus, the tight link that binds sectoral demand and productionin the closed economy does not hold in the open economy. The net export channel, N1q ,captures the direct contribution of international trade to structural change. In addition,
Lemma 3 tells us that trade contributes indirectly to structural change through the expenditure channel, X1q . For example, in the Baumol case, the expenditure share on the20

comparative disadvantage sector is lower in the open economy. Lemma 4 summarizes theeffects of trade on the sectoral labor allocations.
Lemma 4. (Open Economy Labor Allocations) In an open economy, the labor share of the
tradable sector q ∈ {a, m} is given by liq = Xiq + Niq , and the labor share of the nontradable
sector is given by lis = Xis . Specifically, the service labor share is given by equation (19).
The simplest way to see the direct contribution of trade to the sectoral labor shares is with
the Cobb-Douglas case, i.e.,  = 0. In this case, the services labor share is ωs under both
autarky and the open economy. The labor share of sector q ∈ {a, m} is ωq under autarky
and is ωq + Niq in the open economy. Niq is exactly the impact of international trade on
structural change.
Continuing with the Cobb-Douglas case, we now derive a natural, but important, implication of the model: a country will experience a net export surplus in its comparativeadvantage sector. Assume that country 1 has a comparative advantage in manufacturing,and country 2 has a comparative advantage in agriculture. The trade balance of sector q
in country 1 is given by

N X1q = π21q ωq w2 L2 − π12q ωq w1 L1 ,where the expenditure share is ωq in both countries. The pattern of comparative advantages
implies π21m > π21a and π12m < π12a . Thus, if country 1 ran a trade deficit in the manufacturing sector, it would also have to run a trade deficit in the agriculture sector. This
would violate the balanced trade condition. Hence, it must be the case that N X1m > 0 and
N X1a < 0, and that N1m > 0 and N1a < 0. Hence, when a country opens up to trade, labor
moves from its comparative disadvantage sector to its comparative advantage sector. We
can also establish this result under CES preferences and free trade. Lemma 5 summarizes
our results for inter-sector trade.18
18

It is often noted that the effect of opening up to international trade is similar to the effect of a21

Lemma 5. (Inter-Sector Trade) Assume  = 0 or free trade. If country 1 (2) has acomparative advantage in manufacturing (agriculture), then N1m > 0 and N1a < 0.
Proof: See Appendix B.

5.2

Dynamics of Structural Change

We now study the dynamics of structural change in an open economy. The growth rateof the services labor share in country i equals the growth rate of the services expenditure
share:
ˆlist = X̂ist .
As discussed above, while this is the same expression as in the closed economy, trade affects
the growth rate of the services labor share through its effect on the growth rates of theservices relative price and the services expenditure share.
The growth rate of the labor share of tradable sector q in country i is given by:ˆliqt = Xiqt X̂iqt + Niqt N̂iqt
liqt
liqt

(22)

This is clearly different from (15). Structural change dynamics in an open economy involve
changes in both the expenditure and net export channels. Note that in the Cobb-Douglas
case, i.e.,  = 0, there will be structural change as long as the net export channel evolves
over time. We summarize these two results in Proposition 1.
productivity shock in a closed economy. By facilitating a reallocation of resources, openness to trade leads
to an increase in overall output, even though overall inputs have not changed. For the effect of an open
economy on the expenditure shares, this logic is useful, as the productivity shock interpretation for the
tradable sectors helps us understand why agriculture’s expenditure share falls and services’ expenditure
share rises (when the elasticity of substitution is less than one). This logic, however, does not offer acomplete picture for thinking about structural change, because in an open economy, sectoral employment
is also determined by foreign demand for domestic goods. In addition, comparative advantage typicallywill imply that one tradable sector experiences an increase in employment owing to trade, while the othersector experiences a decrease, even though both experience a boost in effective productivity.

22

Proposition 1. (Structural Change Dynamics with Trade) In an open economy, (i) if
Niqt
Xiqt
Niqt
 = 0, ˆliqt = liqt
N̂iqt ; (ii) if  < 0, ˆliqt = liqt
X̂iqt + liqt
N̂iqt .

To understand better the dynamics of structural change, we consider the Cobb-Douglas
case and free trade, and we study how changes in the net export channel are linked to the
dynamics of comparative advantage. Assume that country 1 has a comparative advantage
in manufacturing, i.e., N1mt > 0. Comparative advantage is an ordinal concept. However,to economize on language we will refer to an increase in the ratio of country 1’s relative
productivity in manufacturing to country 1’s relative productivity in agriculture as growthin country 1’s comparative advantage. Our model predicts that if country 1’s comparativeadvantage grows sufficiently fast, it will experience a rise in the manufacturing net export
share and labor share. A necessary condition for N̂1mt > 0 is Âmt > Âat , and the sufficientcondition is:Âmt > Âat

L2t π12at + θ(wt L1t + L2t )π12at π12mt,
L2t π12mt + θ(wt L1t + L2t )π12at π12mt

(23)

1qt
w1t
where wt = w
and Aqt = A
for q ∈ {a, m}.19 As long as country 1’s growth in its
A2qt
2t

comparative advantage is sufficiently high, N̂1mt will be positive and its manufacturinglabor share will grow.
We now show how trade can generate a hump-shaped pattern for the manufacturing
employment share even when the manufacturing sector has the fastest productivity growth.
Suppose that all sectoral productivity growth rates are constant over time, with manufacturing having the fastest growth in both countries. Country 1’s manufacturing employment
share is given by
l1mt = ωm π11mt

wt L1t + L2t
wt L1t,which is a simplified version of equation (20). The above expression illustrates how changes
in the net export channel are tied to changes in specialization, π11mt , and to changes in
19
For details, see Appendix B2. The fraction on the right hand side of equation (23) is larger than one
because country 1’s comparative advantage in manufacturing implies that π12at > π12mt . An endogenous
mechanism to generate growth in comparative advantage over time would be learning by doing.

23

relative country-size,

wt L1t +L2t
wt L1t. Assume that Âmt and Âat satisfy equation (23) initially.

Thus, l1mt rises initially. Over time, π11mt increases as each country purchases a greater
fraction of its manufactured goods from country 1. In addition, if Âat > 0, then wt rises over2t
declines as country 1 becomes larger relative to country 2. As long as thetime, and wt Lw1tt L+L
1tincrease in specialization dominates the change in relative country-size, the manufacturinglabor share continues to increase. The increase in specialization diminishes over time,
however, because there are smaller further gains to employment from productivity growth.
In the limiting case in which π11mt reaches 1, there are no further increases in employment
from this channel. The adverse employment effects of changes in relative country-size,
however, continue over time. Thus, the country-size dynamics will eventually dominate thespecialization dynamics, and country 1’s manufacturing labor share will begin to decrease.20
We summarize the above discussion formally in Proposition 2.
Proposition 2 (Hump in Manufacturing Labor Share) Assume free trade,  = 0, constantlabor endowments, and constant sectoral productivity growth rates. If country 1 has acomparative advantage in manufacturing, the relative productivity growth rates Âa and Âmsatisfy equation (23) initially, and Âa > 0, then its manufacturing labor share l1mt displays
a hump-shaped pattern over time.
Proof: See Appendix B.
We briefly discuss the Baumol case. Now, changes in the expenditure channel affect20

Another way to write the manufacturing employment share in country 1 is
l1mt =1+

1 − ωs


ωa
ωm

π11at
π11mt



Using this expression, it can be seen that one implication of the hump-shaped pattern is that country 1
grows sufficiently large that eventually π11a increases at a more rapid rate than π11m . There are two reasonscountry 1 eventually buys an increasing fraction of its agricultural goods from local firms. First, country
1 becomes so efficient at producing manufactured goods that it eventually needs less labor to satisfy world
manufacturing demand, so additional labor is available for agricultural production. Second, the demand
for agricultural goods rises in country 1 as it gets richer, and country 2 eventually becomes too small tosatisfy this demand.

24

structural change dynamics. Trade can still generate a hump-shaped pattern in the manufacturing labor share. The story is similar to that described above. Initially, with highproductivity growth, and a comparative advantage in manufacturing, changes in the net
export channel contribute positively to the manufacturing labor share. Labor shifts towards the manufacturing sector to produce goods to satisfy increased global demand. This
inflow of labor into manufacturing more than offsets the outflow of labor owing to a declining expenditure share. Over time, changes in the net export channel, while remaining
positive, diminishes, as discussed above. At some point in time — likely before complete
specialization occurs — changes in the expenditure channel will dominate changes in the
net export channel, and the manufacturing labor share will begin to decline. Owing to theexpenditure channel dynamics, the peak of the hump will occur earlier in time comparedto the Cobb-Douglas case.
To provide further intuition, we illustrate the workings of the model with an example offree trade. One country is small, and one country is large: country 1’s labor endowment is
one-tenth of country 2’s. The initial sectoral productivity levels are identical in per-capita
terms across countries.21 Manufacturing total factor productivity (TFP) grows 2 percent
per year in country 1, and 1 percent per year in country 2. Agriculture TFP grows 1 percent
per year in country 1, and 2 percent per year in country 2. Thus, over time, country 1
develops an increasingly large comparative advantage in manufacturing, and similarly forcountry 2 in agriculture. In both countries, services TFP is constant over time. The
elasticity of substitution across sectors is set at 0.5, i.e., we implement the Baumol case.
In addition, ωq is set at 1/3 for each sector, and θ is set at 4.22 Table 2 summarizes therelevant parameters.
Figure 3 illustrates structural change in country 1 for both the closed and open economy
21

In a one-sector Eaton-Kortum model, the relative wage rate will be one if the two countries havethe same per-capita productivity. In our multi-sector environment, the relative wage rate depends on the
expenditure shares across sectors and across countries, in addition to the relative per-capita productivity.
In this example, the initial relative wage rate turns out to be close to, though not exactly, one.
22
The parameters σ, η, and β are irrelevant for this example.

25

Table 2: Parameter Values
Preferences
ωa = ωm = ωs = 1/3
Labor Endowment
L20 = 10
Sectoral Productivities
A1a0 = A1m0 = A1s0 = 1.0
Â1mt = Â2at = 0.02

 = −1.0
L10 = 1
θ = 4.0Â1at = Â2mt = 0.01

L̂1t = L̂1t = 0.0
1

20 θ
A2a0 = A2m0 = A2s0 = ( L
L10 )Â1st = Â2st = 0.0

cases. The closed economy is shown in dotted red lines: the agriculture and manufacturinglabor shares decline, while the services labor share increases, over time. This is because
the relative price of the composite agriculture and manufactured goods both decline overtime, which, with an elasticity of substitution less than one, implies declining expenditureand labor shares in these two sectors.
Figure 3: Structural Change in Country 1
0.7
0.6

Exp & labor share, closed
Exp share, open
Labor share, open

0.5

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.4

0.3

0.3

0.3

0.2

0.2

0.2

0.1

0.1

0.1

0
0

20

40

60

(a) Agriculture

80

100

0
0

20

40

60

80

(b) Manufacturing

100

0
0

20

40

60

80

100

(c) Services

For the open economy case, the expenditure shares are shown in dashed blue lines andthe labor shares are shown in solid black lines. Panel (a) shows the expenditure and laborpatterns in agriculture. Country 1 has a comparative disadvantage in agriculture thatgrows over time; hence, a greater fraction of spending on agricultural goods is on relatively
inexpensive imports. This drives down the relative price of the composite agricultural
goods, and hence, agriculture’s expenditure share. After 100 periods, the expenditure
share is less than half of the closed economy expenditure share. The increased reliance on
imports shows up on the production side as a sharp drop in agriculture’s employment share.
26

The gap between the expenditure share and the employment share is the net imports ofagriculture goods as a share of total GDP.
Panel (b) of Figure 3 shows the expenditure and labor shares for manufacturing. The
time path of the manufacturing expenditure share is quite similar to that of the closed
economy. The manufacturing labor share follows a hump-shaped pattern. The increasing
comparative advantage in manufacturing over time generates initially a positive contribution to manufacturing employment from increases in the net export channel. This positive
contribution initially more than offsets the negative contribution to manufacturing employment from changes in the expenditure channel, and the manufacturing labor share
increases. However, the increases in the net export channel diminish over time, and is
eventually dominated by the decreases in the expenditure channel. The interplay of thesetwo channels is the source of the peak and then subsequent decline in the manufacturinglabor share. Further understanding of this interplay comes from panel (a). Country 1 essentially stops producing agricultural goods at some point; after that time, labor in country
1 is allocated to only two sectors, services and manufacturing. As the services sector is
growing in terms of both expenditure and labor shares, owing to its increasing relative
price, the manufacturing sector must be shrinking.
Figure 4 presents the structural change patterns for country 2. Because country 2 islarge, the open economy patterns are similar to the closed economy patterns. However, themanufacturing sector shows a steeper decline, and the agriculture sector shows a slower
decline in the open economy than in the closed economy. Even relatively small economies
can impact the pace of structural change of large economies. The manufacturing patternsin Figures 3 and 4 are consistent with the data in Figure 2. We can interpret the changes
in Figure 2 as analogous to what happens when the global economy goes from autarky totrade. Then panel b in Figures 3 and 4 show that in one set of countries the manufacturinglabor share and net export share both increase, while in the other set of countries, bothshares decrease.
27

Figure 4: Structural Change in Country 2
0.5

0.5

0.5

0.4

0.4

0.3

0.3

0.3

0.2

0.2

0.2

0.4

0.1
0

Exp & labor share, closed
Exp share, open
Labor share, open

20

40

60

80

100

0.1
0

(a) Agriculture

20

40

60

80

100

0.1
0

20

(b) Manufacturing

40

60

80

100

(c) Services

Figure 5 illustrates the import shares. The import shares of the smaller country 1 arehigh initially. Over time, owing to the increasing comparative advantage in manufacturing
and disadvantage in agriculture, country 1 imports fewer manufactured goods and moreagriculture goods. In the latter sector, as mentioned above, eventually, almost all agriculture goods are imported. Figure 5 shows that country 2 imports an increasing share of its
manufactured goods expenditure over time. However, its expenditure share on manufactured goods is declining over time; hence, at some point, total manufactured imports fromcountry 1 diminish, which contributes to the declining manufacturing labor in country 1.
Figure 5: Import Shares
1.1

0.25

0.2

1

0.15

Agriculture
Manufacturing

0.9

0.1
0.8

0.7
0

0.05

20

40

60

80

100

(a) Country 1

0
0

20

40

60

80

100

(b) Country 2

Finally, Figure 6 addresses welfare implications. Panel (a) plots wages, where country
1’s wage is the numeraire. Country 1’s wage relative to country 2’s rises over time. To
28

understand this, it is useful to note that, owing to symmetry in the parameters, if the twocountries were the same size, the relative wage would be constant. When each country’s
comparative advantage sector experiences increasing comparative advantage over time, they
produce more of the same good (intensive margin) and more goods (extensive margin). The
rise in the intensive margin tends to lower the wage more than the rise in the extensive
margin. Because country 2 initially produces almost all the goods owing to its size, its
intensive margin increases faster than the extensive margin. By contrast, the extensive
margin rises faster than the intensive margin in country 1. This explains why country 1’s
relative wage rises over time.
Figure 6: Wages and Welfare
1.1

1.6

1

1.4

0.9

1.2

0.8

1

0.7
0.6

0.8
1 Open2 Open

0.6

0.5
0.4
0

1 Open2 Open1 Closed
2 Closed

0.4
20

40

60

80

100

0.2
0

(a) Wages

20

40

60

80

100

(b) Welfare

Panel (b) illustrates the welfare effects over time. Welfare is measured as the wage rate
divided by the overall price level. The two dashed lines illustrate the closed economy case.
They grow at the same rate. This is a result of the symmetry between the two countries
between agriculture and manufacturing. The two solid lines illustrate the open economy
case. Note that opening up to trade provides a large boost to country 1, because it now has
access to country 2’s goods. By contrast, country 2 does not receive as much of a boost,
owing to country 1’s small size, and hence, fewer opportunities for importing inexpensive
goods. Over time, country 1 narrows the welfare “gap” with country 2 by about 0.2 percent
per year.
29

5.3

Dynamics with Declining Trade Costs

We now present an alternative way of generating structural change: declining trade barriers.
To highlight the effect of changing trade costs on structural change, we eliminate sectorbiased TFP growth. Specifically, we assume that both countries have identical and constantproductivities growth across sectors and over time, i.e., Âiqt = ga for all i ∈ {1, 2}, q ∈{a, m, s} and t. Initially, A1m0 = A2a0 > A2m0 = A1a0 , which implies that country 1 would
have a comparative advantage in manufacturing in the absence of trade costs. To focus on
the dynamics of the net export channel, we again study the Cobb-Douglas case. We also
assume ωa = ωm , and both countries have identical and constant labor over time: Lit = L.
Trade costs in each sector are identical across the countries. Moreover, the net trade costof both sectors, τqt − 1, declines at a constant rate of τ̂ , which implies that τ̂qt = τqtτqt−1 τ̂ .
Thus, as the net trade cost approaches zero over time, τ̂qt also approaches zero.
Because changes in the net export channel are the only source of structural change
dynamics, we need only derive country 1’s manufacturing net export share over time.
Given the symmetry across the two countries, the equilibrium relative wage rate wt =w1t
w2t

= 1 in every period t. Thus, country 1’s manufacturing net export share is N1mt =

A1mt
A2mt
ωm (π21mt − π12mt ), where π21mt = [1 + ( A2mt)−θ ]−1 and π12mt = [1 + ( A1mt)−θ ]−1 .
τmt
τmt

Because A1mt > A2mt , it must be the case that π21mt > π12mt and N1mt > 0. The dynamics
of N1mt are given byN̂1mt =

θ[π12mt (1 − π12mt ) − π21mt (1 − π21mt )]τ̂mt.
π21mt − π12mt

The necessary and sufficient condition for N̂1mt > 0 given τ̂mt < 0 is A1mt > A2mt . Thus,
country 1’s manufacturing labor share and net export share rise as trade costs decline.
When τ̂mt approaches zero over time, both N̂1mt and ˆl1mt approach zero.
To further illustrate the impact of changing trade costs on dynamics of structuralchange, we present a numerical example with more general assumptions on the prefer30

ences and labor supply. The parameter values, except the productivities, are the same as
the ones in Table 2. In particular, we continue to employ the Baumol elasticity. Initially
1

1

20 θ
) , A2m0 = 1.5( LL20
) θ and A1s0 = A2s0 = 1.0. The
A1a0 = 1.5, A1m0 = 2.0, A2a0 = 2.0( LL10
10

productivities remain constant over time in all sectors and all countries. The trade costdeclines from 2.5 at a rate of 3% per period in both sectors and countries.
We present the dynamics of structural change of country 1 in Figure 7. The closed
economy sectoral labor shares are shown in dotted red lines. Owing to the Cobb-Douglas
assumption, there is no structural change in the closed economy. The open economy sectoral
expenditure shares and labor shares are shown in dashed blue lines and solid black lines,
respectively. The figure shows that as trade costs decline, each country’s comparativeadvantage is increasingly revealed, and there is increased specialization. Panel (a) showsthat the agriculture expenditure share declines rapidly in the open economy. Declining
trade costs allows this sector, which is country 1’s comparative disadvantage sector, toimport more inexpensive goods from abroad. The relative price of the agriculture composite
good falls rapidly, leading to the rapid decline in the expenditure share. The increased
reliance on inexpensive imports also shows up as an agriculture labor share that declines
even faster than the agriculture expenditure share. Again, the gap between the labor shareand the expenditure share represents agriculture net exports as a share of total GDP.
Figure 7: Impact of Changing Trade Costs in Country 1
0.4

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0.3

0.2

Exp & labor share, closed
Exp share, open
Labor share, open

0.1

0
0

10

20

30

(a) Agriculture

40

0

10

20

30

(b) Manufacturing

40

0
0

10

20

30

40

(c) Services

Panel (b) shows that country 1’s manufacturing labor share first rises and then declines
31

in the open economy. Because the manufacturing expenditure share changes little overtime, most of the labor share dynamics are from changes in the net export channel. As
trade costs decline, both countries increase their import and export shares in each sector
owing to increased specialization. This contributes to increased manufacturing labor incountry 1. If the labor endowments were the same across countries, the relative wage
would be constant at one over time. But, because country 1 is smaller, under a constantrelative wage, the increase in its total exports would exceed the increase in its total imports.
1t
must riseThus, the balanced trade condition implies that the relative wage rate wt = w
w2tover time. In other words, the purchasing power of country 2, in terms of country 1 labor,
falls over time. All else equal, this would imply less country 1 labor is needed to satisfy
manufacturing demand from country 2. Initially, the rise in the net manufacturing exports
arising from increases in specialization dominates the decline in net manufacturing exports
arising from country 1’s increasing size, and the manufacturing net export share of GDP
and the manufacturing labor share rises. As the increase in specialization diminishes overtime, the effect of country 1’s increase in size becomes more important, and eventuallyleads to a reversal in the trend of net manufacturing exports. The manufacturing net
export share of GDP and the manufacturing labor share begin to decline.
Country 2’s structural change in the tradable sectors is the opposite of those in country
1, qualitatively. The quantitative impact of declining trade costs on country 2 is muchsmaller owing to its large size. In both countries, the services labor share rises over timeand converges to the level attained when trade is frictionless.

6

Extensions

We now extend the model in each of three directions. We consider non-homothetic preferences, we allow for intermediate goods, and we introduce capital goods. We show that our
main results continue to hold.

32

6.1

Non-homothetic Preferences

The most common way that structural change has been modeled in the past is by using
preferences that capture Engel’s law, the fact that the food share of consumption diminishes
as a country develops. In other words, the income elasticity of demand for food is less thanone, and for at least one other sector, it is greater than one. The following non-homothetic
preference specification encompasses Engel’s law:

U (Cia , Cim , Cis ) = ωa log(Cia − Li c̄a ) + ωm log(Cim − Li c̄m ) + ωs log(Cis − Li c̄s ).

If c̄q > 0, we interpret c̄q as a per-capita subsistence requirement for sector q goods. This
will generate an income elasticity of demand less than one. If, on the other hand, c̄q < 0,then the income elasticity of demand for the sector q good is larger than one.
We maintain the CES functional form for aggregating individual goods into the composite sectoral goods; the expressions for the prices of these composite goods are the same
as before.23 The consumption expenditure share for sector q = {a, m, s} is given by

Xiq = ωq +c̄a Pia + c̄m Pim + c̄s Pis
Piq c̄q
− ωq
.
wi
wi

(24)

In the closed economy, the labor shares equal the expenditure shares. Given the relationshipbetween prices and productivities, we have

liq = Xiq = ωq +

c̄q
c̄a
c̄m
c̄s
− ωq (++).
Aiq
Aia Aim Ais

For much of the analysis below, we will take c̄a > 0, c̄m = 0, and c̄s < 0. This
formulation is similar to that in Kongsamut, Rebelo, and Xie (2001). Thus, because c̄a > 0
and c̄s < 0, the agriculture labor share is greater than ωa , but decreases as productivities
rise and countries get richer. The services labor share is always lower than ωs , and increases
23

However, the price index for the aggregate consumption good will be different from equation (11).

33

as productivities rise and countries get richer. The manufacturing labor share is ambiguous
and depends on the relative magnitude of Ac̄aia and Ac̄sis . When countries become sufficiently
rich, all labor shares converge to the appropriate ωq . Thus, non-homothetic preferences
produce structural change in the closed economy, even when the elasticity of substitution
across sectors is one.
We now turn to the open economy. As mentioned above, the expressions for prices of thecomposite sectoral goods are the same as before. Moreover, the effect of the open economy
on these prices is the same, e.g., the agriculture and manufacturing prices relative to thewage rate are lower compared to autarky. Then, from (24), we can see that expenditures on
agriculture are lower, and the manufacturing and services expenditure shares are higher, inthe open economy than in the closed economy. Finally, the expression for labor shares is still
given by equation (21). Thus, trade still affects labor allocations through an expenditurechannel and a net export channel.
Now consider the dynamics of labor allocations in the open economy under free trade.
Assume that country 1 has a comparative advantage in manufacturing. An increase in theextent of its comparative advantage in period t will lead to a higher π21m , and a lower
π21a , as before. These changes tend to increase manufacturing net exports and agricultural
net imports, which then tends to increase the manufacturing labor share and decrease theagriculture labor share.
Specifically, consider a case in which the only variable that changes between periodst − 1 and t is A1mt > A1mt−1 . We show in Appendix B3 that the relative wage w1t /w2t mustrise to preserve trade balance. As a result, in period t, the expenditure share of agriculture
declines, while that of manufacturing rises in country 1, and the opposite happens in country
2. Thus, the increase in the expenditure channel contributes positively to the manufacturinglabor share in country 1. Turning to the net export channel, we can show that an increasein country 1’s comparative advantage still leads to an increase in Nimt if the underlying
productivities, parameters and labor supplies are such that π12at−1 < θπ21at−1 holds in34period t − 1.24 Thus, while non-homothetic preferences are an additional mechanism forstructural change, a hump-shaped pattern in the manufacturing labor share is still possible.

6.2

Intermediate Goods

To introduce intermediate goods in a tractable way, we assume that each sector’s output
is produced from labor and intermediates, and the sector’s output is either consumed
or used as an intermediate to produce that sector’s goods. The production function forservices is given by Yis = ψAis Lαis Mis1−α , where ψ = α−α (1 − α)α−1 . Output Yis is used for
consumption or as an intermediate to produce services. The services market equilibrium
condition is Yis = Cis + Mis .
In each tradable sector, there is a composite intermediate good that has the samefunctional form as the composite final good:
Z 1

η

1/η

miq (z) dz

Miq =

.

0

The production function for good z in sector q is yiq (z) = ψAiq (z)liq (z)α Miq (z)1−α , where
Miq (z) is the use of the composite intermediate good Miq to make good z. The goods
market equilibrium condition for any z ∈ [0, 1] is given by:

y1q (z) + y2q (z) = d1q (z) (c1q (z) + m1q (z)) + d2q (z) (c2q (z) + m2q (z)) .
1

The prices of the sectoral goods in country i are given by: Pis = wi /Aisα and
"
Piq =
24

wiα
Aiq

−θ


+

For details see Appendix B3.

35

τijq wjα
Ajq

−θ #− αθ1.

The share of country i’s expenditure on sector q goods from country j, πijq , is given by

πijq =(τijq wjα /Ajq )−θ.
(τijq wjα /Ajq )−θ + (wiα /Aiq )−θ

We now turn to the labor allocations. It is easy to show that the labor share in services is the same as in the benchmark model: lis = Xis . The equilibrium condition forthe manufacturing sector in country 1 implies that w1 L1m = α(π11m P1m (C1m + M1m ) +π21m P2m (C2m + M2m )). Simplifying yields the same expression for the labor share as in thebenchmark model:

l1m = L1m /L1 = π11m X1m + π21m X2m w2 L2 /(w1 L1 ).

With identical expressions for labor shares, introducing intermediate goods does not change
our results from before. This is because, while intermediate goods leads to a distinction
between gross output and value-added, the share of consumption spending in total output
equals the share of value-added in gross output.

6.3

Capital

We now introduce capital as an input into the production of each good and consider capital
accumulation over time. Capital is perfectly mobile across sectors, but is immobile acrosscountries. The production function for the services sector good of country i in period tαis Yist = Aist Kist
L1−αist , where Kist denotes capital devoted to services, and α denotes thecapital share. The production function for tradable good z ∈ [0, 1] in sector q ∈ {a, m} of
1−ααcountry i in period t is yiqt (z) = Aiqt (z)kiqt(z)liqt(z), where kiqt (z) denotes capital devoted

to this tradable good.
The key assumption in this section is that the capital share α is the same across goods,

36sectors, and countries. This preserves the Ricardian trade features of the model.25 The
first-order optimality conditions of the firms’ problem imply the static allocation of inputs
across sectors and goods:
kimt (z)Kist
αwitkiat (z)===,liat (z)limt (z)List(1 − α)rit
where wit and rit denote the wage rate and the rental price of capital, respectively.
The representative household in country i maximizes his/her intertemporal utility,
which is given by
∞
X
t=0

βt

Cit1−σ − 1,1−σwhere Cit is final consumption, given by U (Ciat , Cimt , Cist ) in equation (3). The household
supplies Lit inelastically and faces the following budget constraint in each period t:

Pit (Cit + Iit ) = wit Lit + rit Kit ,where Iit and Kit denote aggregate investment and the capital stock, respectively.
The law of motion for capital is Iit = Kit+1 − (1 − δ)Kit , where δ is the depreciation
rate of capital. The aggregate investment good is a composite of the sectoral goods; thefunctional form for the aggregator is the same as for the consumption aggregator:1
Iit = (ωa Iiat
+ ωm Iimt+ ωs Iist) ,where Iiqt is the composite sector-q good used to produce the investment good.
The household’s optimal consumption and investment allocations are characterized by
25

Otherwise, the model would have Heckscher-Ohlin features.

37

the intertemporal Euler equation:−σ
Cit−σ = βCit+1




rit+1
+1−δ .
Pit+1

Given final demand Qit = Cit + Iit , the expenditure share Xiqt =

 −1
1 
P
.
first order optimality conditions: Xiqt = ωq1− Piqt
it

Piqt Qiqt
Pit Qitis given by the

In autarky, the feasibility conditions imply that the sectoral labor share equals thesectoral expenditure share:

liqt =

wit Liqt(1 − α)Piqt Qiqt
Liqt==
= Xiqt ,Lit
wit Lit(1 − α)Pit Qit

for each sector q ∈ {a, m, s}. This implies that our benchmark results for the autarky
dynamics of structural change are robust to the introduction of capital.
In the open economy, the trade patterns are similar to those in our benchmark model:

πijqt =

(τijqt Vjt /Ajqt )−θ,(τijqt Vjt /Ajqt )−θ + (Vit /Aiqt )−θ

where in each country i, the unit cost Vit = α−α (1 − α)−(1−α) ritα wit1−α replaces the wage rate
wit in our benchmark model. The same is true for the relative prices. For the services goodin country i, its price relative to the unit cost is PVist= A1ist . For the tradable composite
it
P

π

1/θ

good q, Viqt
= Aiiqt. Thus, Lemmas 1, 2 and 3 are robust to the introduction of capital.
it
iqt
Turning to the sectoral labor allocations, again, the services sector’s labor share equals
its expenditure share:

list =

List
wit List(1 − α)Pist Qist==
= Xist .
Lit
wit Lit(1 − α)Pit Qit

For tradable sector q, country 1’s income from sector q equals expenditures of both countries

38

on its sector-q goods:
w1t L1qt= π11qt P1qt Q1qt + π21qt P2qt Q2qt .
1−α
As in our benchmark model, we can derive each tradable sector’s labor share:

l1qt =

L1qt
P2t Q2t= π11qt X1qt + π21qt X2qt
= X1qt + N1qt .
L1t
P1t Q1t

Thus, with the inclusion of capital, the model still delivers the same expressions for thesectoral labor shares. Thus, Lemma 4, Lemma 5 and Proposition 1 also continue to hold.

7

Conclusion

International trade provides a mechanism by which sectoral output can exceed sectoral
expenditure or vice versa. In a neoclassical trading environment, comparative advantage
interacts with global sectoral demand to determine patterns of expenditure, trade, production, and employment. We develop a model highlighting these themes to study the effects
of an open economy on structural change. Our model draws from the closed economy structural change models based on biased sectoral productivity growth; these models naturally
extend to a dynamic Ricardian trade model in an open economy.
While our framework is simple, it yields rich intuition on the role of trade in structuralchange. We trace through two scenarios in which a country with a comparative advantage
in manufacturing can experience a hump-shaped pattern in manufacturing employment.
In the first scenario, if manufacturing’s productivity growth is sufficiently high, the gains
to employment from an increasingly large surplus in manufacturing net export are larger
than the losses to employment owing to declining manufacturing expenditure shares. The
gains to employment will diminish over time, however, owing to the country’s increasing
size, as well as smaller increases in specialization. Eventually, either the decreases in man39

ufacturing employment arising from the expenditure channel will dominate the increases
arising from the net export channel, or the net export channel alone will contribute to
decreases in employment; in both cases, employment in manufacturing will decline. In
the second scenario, if trade barriers in manufacturing decline sufficiently rapidly, then,again, manufacturing employment will rise. However, once free trade is reached or once
trade costs stop declining, the dynamics of the expenditure channel will dominate the now
non-existent dynamics of the net export channel. The main results hold up in the presenceof non-homothetic preferences, intermediate goods, and capital goods and investment.
Matsuyama (2008) states that “the central question [on structural change in an interdependent world] is whether structural change in one country will slow down or speed up
structural change in other countries.” Our framework addresses this question. In our firstscenario from above, the small emerging market economy with a comparative advantage
in manufacturing experiences relatively high productivity growth in that sector, and thelarge advanced economy with a comparative advantage in non-manufacturing experiences
relatively high productivity growth in that sector. From that starting point, we show thatin the advanced economy, the manufacturing sector will decline at a faster rate, and theservices sector will grow at a faster rate, in an open economy relative to the closed economy.
Our framework can be applied to other scenarios, as well.
It is important to quantitatively assess the importance of international trade in the
structural change experiences of emerging market countries, as well as of advanced countries.26 As mentioned above, Buera and Kaboski (2009) demonstrate that neither of thetwo core closed economy models of structural change — those that emphasize Stone-Geary
preferences and those that emphasize biased sectoral productivity growth — can quantitatively explain the recent experience of the United States. We are currently pursuingresearch to assess the extent to which trade can explain the gap between the data and theclosed economy models.
26

Stefanski (2009), Ungor (2009), and Teignier-Bacque (2009) are recent research along these lines.

40Appendix A
A.1 Data Sources and Variable Construction for Figure 2
Manufacturing employment share: This variable is constructed primarily from twodata sources, the GGDC 10-sector database (Timmers and de Vries, 2007), and the OECD
ALFS, rev. 2, database. The data for Hong Kong is supplemented by data from the 1971
Hong Kong Census. Some of the OECD data required interpolations, as well as imputations
using ALFS rev. 3, as well as the OECD STAN database. For Portugal, STAN was theprimary source. Exact calculations are available from the authors on request.
Manufacturing net exports share of total GDP: Manufacturing exports and imports
data for all countries except Taiwan are downloaded from the United Nations COMTRADE
database. We use SITC rev. 1 because this allows us to examine data from 1962 forward.
For some countries and time periods, there are gaps in the SITC rev. 1 data; we then use
SITC rev. 2 COMTRADE data.27 Data for Belgium was combined with Luxembourg prior
to 1999. For years after 1999, we add the two countries’ trade data for consistency. West
Germany data was used for 1962-1990, and Germany afterwards. For Taiwan, we use the
NBER-UN World Trade data set for 1962-2000, and sourceOECD for 2001-2005. Details
on how these data are concorded and spliced are available from the authors on request.
Manufacturing is defined in a way to ensure compatibility with the definition in the
GGDC 10-sector database. The SITC rev. 1 codes for manufacturing are: 012, 013, 022,
032, 046, 047, 048, 053, 055, 061, 062, 081, 091, 099, 1, 251, 26, 332, 4, 5, 6, 7, 8.
GDP in U.S. dollars was drawn from the IMF’s International Financial Statistics (IFS)(August 2008 CD). GDP in national currency was converted to U.S. dollars using period average exchange rates (Data downloaded from August 2008 IFS). For Venezuela,
end of period exchange rate were used for 1960-1963. Data for Taiwan GDP is fromhttp://61.60.106.82/pxweb/Dialog/statfile1L.asp. These data are available for all years inwhich manufacturing employment and net export data were available.
Countries and years covered (1962-2005, unless otherwise noted): Australia (19662005), Austria (1969-2005), Belgium, Canada (1970-2005), Denmark (1969-2005), Finland(1970-2005), France, Germany, Iceland (1964-2005), Italy (1970-2005), Netherlands (19702005), New Zealand (1964-2005), Norway, Portugal (1970-2005), Spain, Sweden (19632005), Switzerland, United Kingdom (1963-2005), United States, Hong Kong, Indonesia(1971-2005), India (1975-2004), Japan (1962-2003), Singapore (1970-2005), South Korea(1963-2005), Peru, Philippines (1971-2005), Thailand, Taiwan (1963-2005), Venezuela, Bolivia (1962-2003), Brazil, Chile, Colombia, Costa Rica (1965-2005), Mexico, Malaysia (19752005), Argentina. Changes over the entire period were computed and plotted in Figure 2.
A.2 Data Sources and Variable Construction for Table 1
Trade Openness: Trade openness is equal to the sum of total exports and total imports
divided by GDP, with all variables in U.S. dollars. Total imports equal total primary imports plus total manufacturing imports, and similarly for total exports. The data sources
27

We used the concordance tables in http://cid.econ.ucdavis.edu/usixd/wp5515d.html.

41

are the same as those listed above for manufacturing net exports. Primaries and manufacturing are defined in a way to ensure compatibility with the definitions of primaries andmanufacturing in the GGDC database. The SITC rev. 1 codes for primaries are: 00, 011,
023, 024, 025, 031, 041, 042, 043, 044, 045, 051, 052, 054, 07, 2, 32, 331, 34, 35, MINUS
251, MINUS 26. The SITC rev. 1 codes for manufacturing are same as in A.1 above.
Countries and years covered (1962-2005, unless otherwise noted): Argentina, Bolivia,
Brazil, Chile, Colombia, Costa Rice (1965-2005), Hong Kong, India (1975-2005), Indonesia (1967-2005), Japan, Malaysia (1964-2005), Mexico, Peru, Philippines, South Korea,
Singapore, Thailand (1962-2005, except 1988), Venezuela, Australia (1963-2005), Austria(1963-2005), Belgium-Luxembourg, Canada, Denmark, Finland (1963-2005), France, Germany, Iceland, Italy, Netherlands, New Zealand (1964-2005), Norway, Portugal, Spain,
Sweden, Switzerland, United Kingdom, and the United States.
The data sources for GDP are the same as those listed above for manufacturing net
exports share of GDP. These data are available for all years in which trade data wasavailable.
Services Labor Share: The data sources are the same as those listed above for the
manufacturing employment share. Countries and years covered (1960-2005, unless otherwise noted): Argentina, Bolivia (1960-2003), Brazil, Chile, Colombia, Costa Rica, Hong
Kong, Indonesia (1961, 1971-2005), India (1960-2004), Japan, South Korea (1963-2005),
Mexico, Malaysia (1975-2005), Peru, Philippines (1971-2005), Singapore (1970-2005), Thailand, Taiwan (1963-2005), Venezuela, Australia (1966-2005), Austria (1969-2005), Belgium, Canada, Denmark (1960, 1965, 1967, 1969-2005), Finland, France, Germany, Iceland(1964-2005), Italy (1970-2005), Netherlands (1970-2005), New Zealand, Norway, Portugal (1970-2005), Spain, Sweden (1963-2005), Switzerland, United Kingdom (1963-2005),
United States.
Income per capita: Our income per capita variable is chained GDP per capita, PPP inconstant 2005 international dollars from the Penn World Tables 6.3, RGDPCH series. The
data run from 1960-2005. Note: data for Belgium is for Belgium only. The following datais missing: Germany (1960-1969).
Four-year non-overlapping averages (except for 1960-1965) are created for each of the
3 variables. The periods are: 1960 (or earliest starting year)-1965, 1966-1969, ..., 20022005. Some 4-year periods contained less than four years of data. All periods with lessthan two years were excluded in the regression reported in the table. (As a sensitivity
analysis, we ran another regression that excluded the 17 country-period observations forwhich the 4-year period contained less than four years of data. The estimation results weresimilar. For example, the coefficient on trade openness was 0.0738 compared to 0.0805 in
the benchmark regression.)

Appendix B
Proof of Lemma 5: We first consider the case with the log preferences. In tradable
sector q of country 1, exports are π21q X2q w2 L2 , and imports are π12q X1q w1 L1 . Under aunit elasticity of substitution, two countries have identical sectoral expenditure shares:
42

X1q = X2q = ωq . We can write net exports of country 1 in the manufacturing sector andthe agriculture sector as:
N X1a = ωa (π21a w2 L2 − π12a w1 L1 ) ,N X1m = ωm (π21m w2 L2 − π12m w1 L1 ) .
The pattern of comparative advantages implies π21m > π21a and π12m < π12a . Thus, if
N X1m < 0, it must be the case that N X1a < 0. This would violate the balanced tradecondition. Hence, it must be the case that N X1m ≥ 0 and N X1a ≤ 0. Equivalently, we
have N1m ≥ 0 and N1a ≤ 0.
We then consider the case with the CES preferences and free trade. We prove bycontradiction. Assume that N X1m < 0. That is, π21mt X2mt w2t L2t < π12mt X1mt w1t L1t .
Plugging in the expression for the expenditure shares and simple algebra give
π21mt
π12mt



P2mt
P1mt


 −1


<

P2t
P1t


 −1

w1t L1t.
w2t L2t(25)

Under free trade, we have P2mt = P1mt and P2at = P1at . Given the comparative advantage in country 1, we also have π21mt > π21at and π12at > π12mt . This implies that
π21at
π12at



P2at
P1at


 −1

π21mt
<
π12mt



P2mt
P1mt


 −1

.

(26)

From inequality (25) and (26), we have
π21at
π12at



P2at
P1at


 −1


<

P2t
P1t


 −1

w1t L1t.
w2t L2t

Using again the expression for the expenditure shares, we have π21at X2at w2t L2t < π12at X1at w1t L1t .
Thus, we show that if N X1mt < 0, then N X1at < 0. For the balanced trade condition tohold, it must be the case that N X1mt > 0 and N X1at < 0. Q.E.D.
Proof of Proposition 2: From the balanced-trade condition, the equilibrium wage ratio
w1t
solves:wt = w2t
wt L1 + L2
[ωm π21mt + ωa π21at ]= ωa + ωm .
(27)
wt L1
Totally differentiating equation (27), we haveωm π21mt π̂21mt + ωa π21at π̂21at
L2−
ŵt = 0,ωm π21mt + ωa π21at
wt L1 + L2
where π̂21mt = θπ12mt (Âm − ŵt ) and π̂21at = θπ12at (Âa − ŵt ). Solving for ŵt yields:ŵt =ψmt Âm + ψat Âa,ψlt + ψmt + ψat43

m π12mt π21mt
a π12at π21at, and ψat = ωmθωπ21mt. Since Âa and Âmwhere ψlt = wt LL12+L2 , ψmt = ωθω+ωa π21at
m π21mt +ωa π21at
are both positive, we have ŵt is positive, which implies that the relative size of country 1
in the world economy keeps rising.
ihwt L1 +L2
The manufacturing labor share in country 1 is given by l1mt = ωm π21mt wt L1 . Again
totally differentiating, we have:


L2
L2
ˆl1mt = −ŵt + π̂21mt = −+ θπ12mt ŵt + θπ12mt Âm .
wt L1 + L2
wt L1 + L2

We then plug in the equation for ŵt and simplify. The necessary and sufficient conditionfor ˆl1mt > 0 is equation (23):Âm > Âa

L2 π12at + θ(wt L1 + L2 )π12at π12mt≡ Âa ξt ,L2 π12mt + θ(wt L1 + L2 )π12at π12mt

where ξt > 1, because Lemma 1 establishes π12at > π12mt under the pattern of comparativeadvantage.
Under the assumption that initially Âm and Âa satisfy equation (23), ˆl1mt > 0, i.e., themanufacturing labor share in country 1 initially rises over time. It also implies that Âm >φlt +φat (Âm −Âa ))< 0.
Âa given that ξt > 1. Moreover, π̂12mt = θπ21mt (ŵt − Âm ) = − θπ21mt (Âψltm+ψ
mt +ψatThus, π12mt declines over time to zero, or π21mt rises over time to one.
ih
2
When π21mt approaches one over time, l1mt starts to decline because l1mt = ωm π21mt wtwLt1L+L
1
2
always declines over time. This completes the characterization of the humpand wtwLt1L+L
1shaped pattern of l1mt .
Q.E.D.

B.3 Consider the case with free trade and non-homothetic preferences: c̄a > 0, c̄m = 0 andc̄s < 0. Assume that the underlying productivities, parameters and labor supplies are suchthat π12at−1 < θπ21at−1 , N1at−1 < 0 and N1mt−1 > 0 in period t − 1. If the productivities
and labor stocks remain constant in period t except A1mt > A1mt−1 , then N̂1mt−1 > 0.
Proof: We normalize w1t to be one in each period. Under free trade, we have P1qt = P2qt foreach tradable sector q. As A1mt rises from A1mt−1 while the other underlying parameters
remain unchanged, the wage rate w2t must be lower than w2t−1 to balance the trade inperiod t, i.e., ŵ2t < 0. Otherwise, in net country 1 will export more manufacturing goods
in period t than period t − 1 but export the same amount of agriculture goods in both
periods, which leads to a trade surplus in period t. As a result, P1at and P2at decline fromtheir period-t levels, i.e., P̂2at = P̂1at < 0. In particular,P̂2at = π12at ŵ2t > ŵ2t .
Now consider the agricultural net exports in country 1: N X1at = EX1at − IM1at , where
EX1at = π21at X2at w2t L2t and IM1at = π12at X1at w1t L1t . As w2t declines, π21at declinesand π12at rises since country 2 lowers its marginal cost of agriculture production relative
to country 1. Also, X1at declines and X2at rises according to the expenditure shares in44

equation (24). Let’s first look at X̂2at , which is given by
X̂2at = ξ2 (P̂2at − ŵ2t ) = −ξ2 π21at−1 ŵ2t > 0,c̄a (1−ωa )∈ (0, 1). This implies that X̂2at + ŵ2t = ŵ2t (1 − ξ2 π21at−1 ) < 0.
where ξ2 = P2at−1
w2t−1 X2at−1
ˆ 1at = π̂21at + X̂2at + ŵ2t < 0. We next study X̂1at , which is given byThus, EXX̂1at = ξ1 P̂1at = ξ1 π12at−1 ŵ2t < 0,c̄a (1−ωa )where ξ1 = P1at−1∈ (0, 1). Also we have π̂12at = −π21at−1 θŵ2t > 0. Under the
w1t−1 X1at−1
ˆ 1at = X̂1at +π̂12at > 0. Since the agricultural
assumption that π12at−1 < θπ21at−1 , we have IM
exports decline while the agriculture imports rise, the agriculture trade deficit rises, which
implies that the manufacturing trade surplus rises, i.e., N̂1mt > 0.

45

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