essays on structural transformation, trade, and economic growth
TRANSCRIPT
ESSAYS ON STRUCTURAL TRANSFORMATION,
TRADE, AND ECONOMIC GROWTH
Zongye Huang
Department of Economics
McGill University
Montreal, Quebec
May 2015
A thesis submitted to McGill University in partial fulfillment of
the requirements of the degree of Doctor of Philosophy
c© Zongye Huang 2015
DEDICATION
This thesis is dedicated to my wife, Zhang Li,and my son, Huang Cheng-Min.
ii
ACKNOWLEDGMENTS
First and foremost, I want to express my grateful and sincere thanks to my advisers,
Professor Ngo Van Long and Professor Markus Poschke. It has been a great honor to
be their Ph.D. student. Without their valuable guidance and generous support, this thesis
would never have been completed.
Professor Ngo Van Long, one of Canada’s leading economists, is a fabulous adviser.
Professor Long has conducted excellent research across a wide range of topics. His great
energy and enthusiasm for doing research inspired me and kept me motivated. He has
provided me with incredible insight and wisdom, and encouraged me to try different ap-
proaches and not be afraid of being silly. I appreciate all his encouragement, understanding,
and support.
Professor Markus Poschke is a wonderful mentor. He is smart and helpful. He is always
able to point out the weakness in my work and teaches me a rigorous approach to deal with
problems.
I am also grateful to a number of faculty members in the Department of Economics
including Professor Francisco Alvarez-Cuadrado, Professor Jagdish Handa, Professor John
Galbraith, Professor Franque Grimard, Professor Sonia Laszlo, and Professor Victoria
Zinde-Walsh, who have offered excellent courses in the department. Thanks to Angela
Fotopoulos, Elaine Garnham, Lisa Stevenson, Judy Dear, Mylissa Falkner and Jackie Gre-
gory for their administrative assistance.
I would also like to thank Enrique Calfucura, Meng-Cheng Chien, Xin Liang, Qing
Liu, Yan Song, Tingting Wu, Lei Xu, Huijun Zhang, and other students at McGill for their
friendship and helpful discussions on my research topics.
Finally, my deepest appreciation is expressed to my parents, my family, and friends, for
their love, encouragement, and support.
Zongye Huang
May 6, 2015
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ABSTRACT
This thesis intends to address questions that are related to structural transformation,
trade, and economic growth. The following three essays sequentially investigate three in-
teresting topics that involve these themes.
The first essay investigates the structural transformation in the United States from 1950
to 2005. In particular, we emphasize the role of trade in this process. We develop and cali-
brate a three-sector model to evaluate the contributions of various factors. It shows that, in
addition to traditional explanations, such as non-homothetic preference and sector-biased
productivity progress, international trade is another major source of structural change and
is able to explain about 35.5 percent of the overall labor share decrease in American manu-
facturing. A further decomposition exercise estimates that inter-sector trade makes a mod-
erate contribution, while trade imbalances dominate the trade channel and account for the
recent contraction of employment in the U.S. manufacturing sector. This result supports
the argument that persistent trade deficits have a substantial impact on labor allocations.
The second essay analyzes the connection between two key variables, the manufactur-
ing employment share and the investment rate, during economic development. Empirical
observations document that both of them exhibit a hump-shaped pattern as income in-
creases. Following the recent research on agricultural technology adoption, I propose that
the modernization of agriculture is the primary mechanism that forms these two hump-
shaped patterns simultaneously, thus, unbalanced technology growth is unnecessary to de-
rive such a hump-shaped pattern. This simple cause helps to explain the similarity of struc-
tural transformation processes across countries. The long-run equilibrium of our model is
on a generalized balanced growth path as defined by Kongsamut, Rebelo, and Xie (2001).
In the third essay, we explore the interaction between trade and growth. In particular,
we assume that the information of advanced technology is embodied within high-quality
capital goods, which are produced by developed economies. Thus, international technology
diffusion goes through the channel of trading high-quality capital goods, which establishes
a direct causal linkage from trade to growth. The capital import is subject to the balance
of payments constraint and must be financed by exports. We develop a formal two-country
model, characterize the steady states, and discuss their dynamic features. Our model could
shed light on several stylized facts.
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ABRÉGÉ
Cette thèse se propose d’aborder les questions qui sont liées à la transformation struc-
turelle, le commerce et la croissance économique. Les trois essais qui suivent se proposent
d’examinersuccessivement trois sujets intéressants qui impliquent ces thèmes.
Le premier essai étudie la transformation structurelle aux États-Unis de 1950 à 2005.
Nous insistons tout particulièrement sur le rôle du commerce dans ce processus. Nous
développons et étalonnons un modèle à trois secteurs pour évaluer les contributions de
divers facteurs. Il montre que, en plus des explications traditionnelles, comme la préférence
non-homothétique et le progrès de la productivité du secteur polarisée, le commerce in-
ternational est une autre source importante de changement structurel et est en mesure
d’expliquer environ 35,5 pour cent de la diminution globale de la part du travail dans le
secteur manufacturier américain. Un autre exercice de décomposition estime que le com-
merce inter-secteur apporte une contribution modérée, alors que les déséquilibres commer-
ciaux dominent le canal de commerce et représentent la contraction récente de l’emploi
dans le secteur manufacturier américain. Ce résultat s’appuie sur le faitque les déficits
commerciaux persistants ont un impact considérable sur les allocations de travail.
Le deuxième essai analyse le lien entre deux variables clés, la part de l’emploi manu-
facturier et le taux d’investissement, au cours du développement économique. Les obser-
vations empiriques indiquent que les deux présentent un motif en forme de bosse au fur et
à mesure que le revenu augmente. Après la recherche récente sur l’adoption de la technolo-
gie agricole, je propose que la modernisation de l’agriculture soit le principal mécanisme
qui forme ces deux modèles en forme de bosse en même temps, donc, la croissance de la
technologie asymétrique n’est pas nécessaire pour obtenir un tel motif en forme de bosse.
Cette cause simple permet d’expliquer la similitude des procédés de transformation struc-
turelle entre les pays. L’équilibre à long terme de notre modèle se trouve sur une trajectoire
de croissance équilibrée généralisé tel que défini par Kongsamut, Rebelo, et Xie (2001).
Dans le troisième essai, nous explorons l’interaction entre le commerce et la croissance.
En particulier, nous supposons que l’information de la technologie de pointe est intégrée
dans les biens d’équipement de haute qualité, qui sont produits par les économies dévelop-
pées. Ainsi, la diffusion de la technologie internationale passe par le canal du commerce
des biens d’équipement de haute qualité, qui établit un lien de causalité direct du com-
merce à la croissance. L’importation de capital est soumise à une contrainte de balance des
v
paiements et doit être financé par les exportations. Nous développons un modèle formel à
deux pays, caractérisons les états stables, et discutons de leurs caractéristiques dynamiques.
Notre modèle pourrait faire la lumière sur plusieurs faits stylisés.
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Contents
1 Introduction 1
2 A Brief Review of Literature 52.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Structural Change and Unbalanced Growth Path . . . . . . . . . . . . . . 6
2.3 Understanding Structural Transformation . . . . . . . . . . . . . . . . . . 8
2.3.1 Non-homothetic Preference . . . . . . . . . . . . . . . . . . . . . 8
2.3.2 Production Technology . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.3 Agriculture Modernization . . . . . . . . . . . . . . . . . . . . . . 10
2.3.4 Factor Accumulation . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3.5 Open Economy and Trade . . . . . . . . . . . . . . . . . . . . . . 13
3 Structural Transformation and Trade Imbalances 153.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Related Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3 Structural Change in the United States, 1950-2005 . . . . . . . . . . . . . 20
3.4 The Model of Structural Change . . . . . . . . . . . . . . . . . . . . . . . 24
3.4.1 Economic Environment . . . . . . . . . . . . . . . . . . . . . . . . 25
3.4.2 Economic Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4.3 Trade-balance-augmented Model . . . . . . . . . . . . . . . . . . 34
3.5 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5.1 Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5.2 Closed Economy Model . . . . . . . . . . . . . . . . . . . . . . . 38
3.5.3 Trade-augmented Model . . . . . . . . . . . . . . . . . . . . . . . 40
3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
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3.6.1 Technology Slowdown and Rising Capital Intensity . . . . . . . . 41
3.6.2 Decomposition of the Structural Transformation . . . . . . . . . . 43
3.6.3 Value-added Trends . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.6.4 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.6.5 Model with Only Non-homothetic Preference . . . . . . . . . . . . 47
3.7 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.8 Technical Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.9 Data Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4 Agriculture Modernization and Structural Transformation 534.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2 Facts and Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.3.1 Economic Environment . . . . . . . . . . . . . . . . . . . . . . . . 63
4.3.2 Market Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.4 Four Stages of Economic Growth . . . . . . . . . . . . . . . . . . . . . . . 66
4.4.1 GBGP Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.4.2 Traditional Economy . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.4.3 Mixed Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.4.4 Convergent Economy . . . . . . . . . . . . . . . . . . . . . . . . 72
4.5 A Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.5.1 Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.5.2 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.5.3 Uniqueness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.5.4 Dynamic Path of kt and ct . . . . . . . . . . . . . . . . . . . . . . 82
4.5.5 Change of Manufacturing Employment . . . . . . . . . . . . . . . 83
4.6 Empirical Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.6.1 Investment and Structural Change: an Empirical Analysis . . . . . 84
4.6.2 Other Suggestive Evidence . . . . . . . . . . . . . . . . . . . . . . 87
4.7 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.8 Mathematical Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.9 Data Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
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5 Quality Upgrading and Capital Good Import 985.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.2 A Simple Two-country Model . . . . . . . . . . . . . . . . . . . . . . . . 102
5.2.1 Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.2.2 Preference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.2.3 Trade Balance and Market Clearing Conditions . . . . . . . . . . . 107
5.3 Economic Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.3.1 Foreign Country’s Problem . . . . . . . . . . . . . . . . . . . . . . 109
5.3.2 Home Country’s Problem . . . . . . . . . . . . . . . . . . . . . . 110
5.4 Balanced Growth Paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.4.1 Balanced Growth Path with Q = 1 . . . . . . . . . . . . . . . . . . 112
5.4.2 Balanced Growth Path with Q < 1 . . . . . . . . . . . . . . . . . . 113
5.4.3 The Dynamics of Q . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.5.1 Import Share of Investment . . . . . . . . . . . . . . . . . . . . . . 120
5.5.2 Trade Balance and Exchange Rate Reversal . . . . . . . . . . . . . 121
5.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.7 Mathematical Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6 Conclusion 129
Bibliography 131
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List of Tables
3.1 Model details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Common parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3 Case-specific parameter values . . . . . . . . . . . . . . . . . . . . . . . . 38
3.4 Statistics in the data and the models . . . . . . . . . . . . . . . . . . . . . 43
3.5 Decomposition of the structural transformation in U.S. manufacturing . . . 44
3.6 Robustness analysis of the structural change model . . . . . . . . . . . . . 47
3.7 Robustness of relative contributions in manufacturing . . . . . . . . . . . . 47
4.1 Summary of the key variable movements . . . . . . . . . . . . . . . . . . 74
4.2 Calibration parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.3 Investment rate and structural change in a sample of 34 countries . . . . . 86
4.4 Manufacturing employment and investment rate in a sample of 34 countries 86
4.5 Moments with peak manufacturing employments . . . . . . . . . . . . . . 89
5.1 The interaction of balance of payments constraint and optimal capital im-
port . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.2 Common parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.3 Case-specific parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.4 Investment share (% of imported final expenditure) . . . . . . . . . . . . . 121
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List of Figures
3.1 U.S. sectoral employment shares, 1950-2005 . . . . . . . . . . . . . . . . 21
3.2 Labor income share in manufacturing . . . . . . . . . . . . . . . . . . . . 22
3.3 Trade balance/GDP ratio (through H-P filter) . . . . . . . . . . . . . . . . 23
3.4 Closed economic models vs U.S. data . . . . . . . . . . . . . . . . . . . . 39
3.5 Trade-augmented model vs U.S. data . . . . . . . . . . . . . . . . . . . . . 41
3.6 Case 5 (TFP slowdown) vs Case 2, with U.S. data . . . . . . . . . . . . . . 42
3.7 Relative contributions on structural change . . . . . . . . . . . . . . . . . 44
3.8 Case 4 model vs U.S. data in terms of value-added shares . . . . . . . . . 46
4.1 Manufacturing employment shares in 34 countries . . . . . . . . . . . . . 61
4.2 Investment rate across income and country . . . . . . . . . . . . . . . . . 61
4.3 Investment rates in Indonesia, India, Japan, and Korea . . . . . . . . . . . 62
4.4 Investment rates in Malaysia, Singapore, and Thailand . . . . . . . . . . . 62
4.5 Capital/labor ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.6 Investment rate (%) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.7 Output growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.8 Agriculture employment shares (%) . . . . . . . . . . . . . . . . . . . . . 80
4.9 Employment shares of the three sectors (%) . . . . . . . . . . . . . . . . . 80
4.10 Uniqueness of dynamic paths . . . . . . . . . . . . . . . . . . . . . . . . 82
4.11 Dynamic path for kt and ct . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.12 Changes of manufacturing employment shares . . . . . . . . . . . . . . . 84
4.13 Manufacturing employment shares for China 1952-2010 . . . . . . . . . . 88
4.14 Peak manufacturing employment shares with per capita income . . . . . . 90
4.15 Agricultural employment shares before and after the peak year of manu-
facturing employment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
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5.1 The balance of payments constraint for quality improvement (BOP) . . . . 114
5.2 The optimal capital import (OCI) locus . . . . . . . . . . . . . . . . . . . 115
5.3 Zero Q equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.4 One Q steady state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.5 Investment share of import (data vs model prediction) . . . . . . . . . . . 122
5.6 Real exchange rate dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.7 Government debt and quality improvement . . . . . . . . . . . . . . . . . 124
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Chapter 1
Introduction
Broadly speaking, this thesis intends to address the interactions between structural trans-
formation, trade, and economic growth. More specifically, our focus is on answering three
specific questions. The first question is how international trade affects the process of struc-
tural transformation. The second question is why investment rates exhibit a hump-shaped
pattern during economic growth and how they affect structural transformation. And the last
question is what explains the Asian economic growth.
Before we proceed to address these questions one by one, in chapter 2, we briefly
review existing research that has investigated structural transformation and economic de-
velopment.
In the literature on structural transformation, even though the U.S. economy is often
used as a benchmark for calibration, the traditional models cannot account for the steep
decline in manufacturing and rise in services in the United States since the late 1970s
(Buera and Kaboski, 2009). Chapter 3 intends to solve this puzzle. By revisiting a few
stylized facts of structural change in the United States from 1950 to 2005, we find that
the timing of the recent movements of labor from the manufacturing sector to the service
sector coincide with the increase in trade deficits and globalization. Therefore, we argue
that international trade might be a plausible candidate that has been missing in most of
the previous studies on structural change. Trade can influence the process of structural
transformation through two direct channels, inter-sector trade and trade imbalance, and
one indirect channel through which trade could affect productivity growth and industry
structure. However, since we don’t have enough information for the indirect channel, we
1
focus on the two direct channels. We construct and calibrate a three-sector model that
accounts for both traditional factors and two direct channels of trade to estimate their impact
on employment share movements in the manufacturing sector. Our quantitative results
indicate that the trade imbalances alone can explain up to 30 percent of the total decline
in manufacturing employment, and the inter-sector trade effect explains about 5 percent,
while the unbalanced productivity progress might account for about 34 percent. A key
implication of these results is that persistent trade deficits have substantial impacts on labor
allocations. The economic intuition is very straightforward: since we are enjoying imported
manufacturing goods, we are using our resources elsewhere.
The structural transformation process is often summarized by three distinct patterns of
labor movements in three broad sectors: the agriculture sector declines; the service sec-
tor rises; and the manufacturing sector follows a hump-shaped pattern, whereby it first
expands and then declines. Bah (2011) and Herrendorf, Rogerson, and Valentinyi (2014)
show that countries that successfully join the high-income group share similar patterns of
structural change. Another stylized fact of growth is that investment rates (measured by in-
vestment/output ratio) also exhibit hump-shaped patterns along with income growth: first,
in low-income countries, on average, the investment rate increases as income rises (Laitner,
2000; Hsieh and Klenow, 2007); second, for high-income countries, the investment rate de-
creases as per capita income increases. Since the expenditure on capital goods is skewed
towards manufactured goods, these two hump-shaped patterns are somehow interrelated.
However, in a model where all sectors share an identical neoclassical production function,
the manufacturing sector remains stable, while the agriculture sector declines and the ser-
vice sector increases, and the investment rate is also constant (Kongsamut, Rebelo, and Xie,
2001). Therefore, most models rely on assuming unbalanced sectoral productivity growth
to generate the hump-shaped pattern of employment in the manufacturing sector. In these
models, the role of investment is either unimportant or ignored. Although the different
rates of technology improvements have significant contributions on structural transforma-
tion, which have been well-documented in the literature both theoretically and empirically,
we would like to emphasize that the rise and fall of investment can affect the demand for
capital goods, thus affecting the structural transformation consequently.
In chapter 4, following the literature that stresses the role of agriculture modernization
in economic growth (Hansen and Prescott, 2002; Gollin, Parente, and Rogerson, 2007;
2
Yang and Zhu, 2013), we derive that the modernization of the agriculture sector, the transi-
tion from a traditional sector that relies on labor-intensive technology into a modern sector
that adopts capital-intensive technology, can generate a hump-shaped pattern for invest-
ment. And the employment and output share of the manufacturing sector will be affected
correspondingly. There are two channels through which agriculture modernization affects
demand for capital goods. The adoption of modern technology requires a certain level of
capital inputs, which directly causes the investment rate to rise. In addition, the modern
agriculture sector needs less labor inputs, thus it further releases excess workers into other
modern sectors, who have to accumulate capital goods to settle down. This second chan-
nel represents an indirect impact on investment from agriculture modernization. Since the
majority of capital goods comes from the manufacturing sector, the high demand of cap-
ital goods is transformed into demand for manufactured products. Thus, our framework
can generate these two hump-shaped patterns along with income increases simultaneously
without assuming unbalanced sectoral technology improvements. In addition, our model is
an extension of the framework of Kongsamut, Rebelo, and Xie (2001), implying that the
long-run equilibrium will be on a generalized balanced growth path that is consistent with
the Kaldor facts.
In chapter 5, we explore the linkage between trade and economic growth. This idea
is motivated by the experience of Asian economic growth, which involves intensive capi-
tal accumulation, industry catching up, export-orientated policy, and chronic trade surplus.
In order to consolidate existing evidences, we consider a specific channel of international
technology diffusion that directly connects trade with growth. We assume that the infor-
mation of advanced technology is embodied within high-quality capital goods produced
by developed economies. And by importing foreign capital goods, developing countries
can gradually upgrade their domestic capital stock and improve product quality. However,
since trade is subject to the balance of payment constraint, the volume of import has to
be financed by export. As a result, we argue that the paradigm of Asia’s growth is more
appropriately called “trade-led” growth, rather than “export-led” growth. We develop a
two-country model that features quality upgrading with complex insights of trade. A qual-
ity index is introduced to represent the development of technology and the quality of out-
put, which allows us to mimic the empirical findings that rich economies tend to consume
more high-quality goods from other developed economies (Hallak, 2006). Using a stan-
3
dard phase diagram analysis, we demonstrate the properties of two types of steady states
and characterize their dynamic features.
Finally, we summarize our findings and briefly discuss future research in chapter 6.
4
Chapter 2
A Brief Review of Literature
2.1 Introduction
The one-sector growth model has become the workhorse of modern macroeconomics that is
able to capture the essence of modern economic growth with a simplest structure. However,
by virtue of being a minimalist structure, the one-sector model necessarily abstracts from
several important features. Structural transformation, which is the reallocation of economic
activities across different sectors during economic growth, is one of them.
Kuznets (1966) considered structural change as one of the most prominent features of
development. If we observe the economic growth in three broad sectors, there are three
distinct sectoral patterns: agriculture declines, services rise, and the manufacturing sector
follows a hump-shaped pattern.1 Following Kuznets (1971), the structural transformation
during economic development can be divided into two phases. In the beginning of the de-
velopment process, an economy allocates most of its resources to the agriculture sector. As
the economy develops, resources are reallocated from agriculture into manufacturing and
services. This substantial reallocation of resources out of agriculture to the modern sectors
is known as “industrialization”, which is the key feature of the first phase of structural trans-
formation. In the second phase, only the service sector continues to expand and resources
from both agriculture (already relatively small) and industry move into services. This “de-
industrialization” process has been observed in both developed and middle-income coun-
1For empirical studies that document these general patterns, see Chenery and Syrquin (1975), Maddison(1991), Echevarria (1997), and recently, Bah and Brada (2009), Bah (2011), Mcmillan and Rodrik (2011),and Herrendorf, Rogerson, and Valentinyi (2014), among many others.
5
tries. In the end, the majority of employment and value-added are generated in the service
sector.
The objective of this chapter is to briefly review selected research that has been con-
ducted on structural transformation and economic growth. In section 2.2, we will discuss
the balanced growth path in the context of structural change. Section 2.3 presents the vari-
ous theoretical approaches that have been put forward to explain structural transformation,
including non-homothetic preference, biased technology growth, agriculture moderniza-
tion, factor accumulation, and trade.
2.2 Structural Change and Unbalanced Growth Path
The balanced growth path plays a prominent role in the standard one-sector exogenous
growth model. However, when we look at models that incorporate structural transforma-
tion, the standard balanced growth path does not exist in most cases. Many features in a
multi-sector growth model would prevent the economy from having key variables to grow at
a constant rate, for example, the non-homothetic preference, unbalanced sectoral productiv-
ity growth, and different capital income shares in production functions. To our knowledge,
only Kongsamut, Rebelo, and Xie (2001) and Ngai and Pissarides (2007) have successfully
defined concepts that are similar to the balanced growth path in structural change models.2
Kongsamut, Rebelo, and Xie (2001) were the first to present a model consistent with
both the dynamics of sectoral labor reallocation and the Kaldor facts of constant growth
rate, capital-output ratio, real rate of return to capital, and input shares in national income.
They constructed a three-sector economy in a continuous-time general equilibrium frame-
work with a common rate of exogenous technological progress and non-homothetic pref-
erences. The preference is specified as the income elasticity of demand being less than
one for agricultural goods, equal to one for manufacturing goods, and greater than one for
services. They also defined the concept of a generalized balanced growth path on which
the real interest rate is constant whereas the sector shares are permitted to grow differen-
tially and qualitatively fit empirical observations. In particular, the employment share of
agriculture shrinks, the employment share of services rises, while the employment share of
2Their results have been summarized by proposition 3.1 in chapter 3.
6
manufacturing remains constant. A weakness of the model is that the generalized balanced
growth path requires the validity of a knife-edge condition for its existence.
Ngai and Pissarides (2007) presented a purely technological explanation of structural
change. In their multi-sector growth model with many final consumption goods, sec-
tors have identical production functions but differential exogenous rates of technological
progress. For the case of low substitutability between final goods, employment is shifted
away from sectors with high rates of technological progress along the balanced growth path.
This result again parallels the main finding of Baumol (1967). Along the balanced growth
path, employment in the sector with the lowest rate of technological progress expands and
employment in the other sectors is either monotonically declining or hump-shaped.
However, it turns out that these conditions under which one can simultaneously gen-
erate balanced growth and structural transformation are rather strict and are not able to
fit empirical observations by ruling out many interesting features in the growth context.
Herrendorf, Rogerson, and Valentinyi (2014) argued that the literature on structural trans-
formation has possibly placed too much attention on requiring exact balanced growth, and
models with approximate balanced growth might possess better features that are able to ac-
count for many salient features of structural transformation. Several models incorporated
non-homotheticity of preference converge to steady states asymptotically. For example, in
the models developed by Echevarria (2000) and Dolores Guilló, Papageorgiou, and Perez-
Sebastian (2011), key variables approach and get infinitely close to the balanced-growth
path.
In this thesis, we do not restrict ourselves to any definitive long-run growth path. In-
stead, we use different concepts based on the dynamic properties of each model. For exam-
ple, in chapter 3, we define a static growth path to approximate the growth path and quan-
titatively evaluate contributions of various factors on the structural change in the United
States from 1950 to 2005. In chapter 4, by imposing a few strict assumptions on pa-
rameters, the economy is able to grow along the generalized balanced growth path as in
Kongsamut, Rebelo, and Xie (2001).
7
2.3 Understanding Structural Transformation
In the literature, various factors have been put forward to explain why the sectoral allo-
cations of economic activities have to undergo a common pattern of structural change.
Summarized by Kuznets (1973) in his Nobel lecture, the non-homothetic preference of the
consumption demand and different technological innovations in the production sectors are
the two central causes of structural change, which are still relevant in the most recent theo-
retical literature on the topic. In addition, recent research has stressed other channels, such
as technology switch, factor accumulation, and international trade.
2.3.1 Non-homothetic Preference
The non-homothetic preference mimics the evolution of consumption expenditures during
economic growth. Since the proportion of income spent on food falls as income rises, as
summarized by Engel’s law, the income elasticity of demand for food is set to be less than
that of other goods. The decline of the food consumption share is consistent with one key
feature of structural change: the inevitable decline of the agriculture sector, in terms of both
employment and value-added, during economic development. The subsistence demand of
agriculture products plays a central role to model the structural transformation.3
In addition, the expenditure on services continues to rise. Buera and Kaboski (2012)
emphasize that the growth of service consumption is driven by the demand for skill-
intensive services, which coincides with a period of rising relative wages and quantities
of high-skilled labor.
2.3.2 Production Technology
Baumol (1967) discussed the idea that different rates of production innovation can also
lead to structural transformation. He divided the economy into two sectors, a “progressive”
one that uses new technology and a “stagnant” one that uses labor as the only input. If
the production costs and prices of the stagnant sector rise indefinitely, labor should move
in the direction of the stagnant sector. Ngai and Pissarides (2007) formalized the idea of
3See, for instance, Echevarria (1997), Laitner (2000), Kongsamut, Rebelo, and Xie (2001), Gollin, Par-ente, and Rogerson (2007), Restuccia, Yang, and Zhu (2008), Duarte and Restuccia (2010), and Alvarez-Cuadrado and Poschke (2011).
8
“Baumol’s cost disease” and showed that a low (below one) elasticity of substitution across
final goods leads to shifts of employment shares to sectors with low productivity growth.
The results of Baumol (1967) and Ngai and Pissarides (2007) suggest that de-
industrialization in advanced economies4 is not necessarily an undesirable phenomenon,
but is essentially the natural consequence of the industrial dynamism exhibited in these
economies. In most advanced economies, labor productivity has typically grown much
faster in manufacturing than it has in services. Thus, given the similarity of output trends
in the two sectors, lagging productivity in the service sector results in this sector absorbing
a rising share of total employment, while rapid productivity growth in manufacturing leads
to a shrinking employment share for this sector. Dolores Guilló, Papageorgiou, and Perez-
Sebastian (2011) showed that this biased technical change hypothesis finds most support
in the U.S. data, while Iscan (2010) presented quantitative results that suggest that non-
homothetic preferences have a larger weight in structural transformation.
If the sectoral production functions have different factor proportions, Acemoglu and
Guerrieri (2008) found that capital deepening, the increase in the capital-labor ratio, pro-
motes the output of the capital intensive sector, while the relative prices move against it and
encourage the reallocation of labor to other sectors.
Alvarez-Cuadrado, Long, and Poschke (2014) explored a general framework that en-
compasses the two mechanisms as special cases and emphasizes an additional channel, the
different degree of capital-labor substitutability. They argued that the fraction of labor al-
located to the sector with high elasticity of substitution between capital and labor would
decrease as the economy grows. In addition, this mechanism emphasizes that structural
change is driven by changes in the relative price of factors, rather than changes in the rela-
tive price of outputs.
In most papers, the technology innovation happens exogenously. Dolores Guilló, Papa-
georgiou, and Perez-Sebastian (2011) used an overlapping-generations endogenous growth
model with a common production function to evaluate two of the traditional explanations of
structural change: sector-biased technical change and non-homothetic preferences. Their
numerical simulations found that, in a closed economy framework, the biased technical
change hypothesis got most support.
4Rowthorn and Ramaswamy (1999) and Rowthorn and Coutts (2004) documented the secular decline inthe share of manufacturing in national employment in selected OECD countries, and briefly discussed andquantified some of the factors that are responsible for such a structural change.
9
2.3.3 Agriculture Modernization
Technology switch, rather than technology growth, has been stressed as a new channel to
explain the structural change process. The modernization of agriculture production has
received most of the attention. In low-income countries, the agriculture sector is the largest
and dominant sector because people have to meet food constraint to survive. However,
the food production in low income countries are significantly different from the agriculture
production in rich countries. By constructing a 43-country data set with sector-specific
physical capital and human capital, Priyo (2012) revealed that cross-country variations in
capital per worker in the agriculture sector are larger than the variations in non-agriculture
sectors. Therefore, the modernization of agriculture, which is a technology switch, could
be the key mechanism to understand long-run economic development.
In a seminal paper, Hansen and Prescott (2002) provided powerful insights into the
transition from stagnation to growth. In their two-sector model, the single final good can
be produced by using two types of technology. The traditional technology is land inten-
sive, while the modern technology is capital intensive. If only land-intensive technology is
profitable to operate, the economy would be trapped in the Malthusian regime. Because of
the diminishing return to labor, the wage decreases or becomes stagnate as the population
grows, and the living standard remains the same. As the productivity of the modern sector
continues to increase and surpasses certain threshold, the adoption of a capital-intensive
technology begins and gradually transfers the economy into a Solow-type growth, where
standard of living can improve continuously.
Gollin, Parente, and Rogerson (2007) emphasized the food problem and the importance
of modern agricultural technology on growth. They considered three types of technology:
a traditional technology, an intensification of traditional agriculture with exogenous pro-
ductivity index, and a modern technology using manufactured capital goods. However, the
timing of technology adoption was selected by calibration to the data rather than endoge-
nously determined by the economic agent in the model.
Yang and Zhu (2013) considered a two-sector, two-good model, and focused on the role
played by agricultural modernization in the transition from stagnation to growth. If food
consumption relies on traditional technology, industrial development has a limited effect
on per capita income because most labor has to remain in farming. Growth is not sus-
tainable until this relative price drops below a certain threshold, thus inducing farmers to
10
adopt modern technology that employs industry-supplied inputs. Once agricultural mod-
ernization begins, per capita income emerges from stasis and accelerates toward modern
growth.
Both Hansen and Prescott (2002) and Yang and Zhu (2013) proposed that industrial
development is a necessary precondition for the modernization of the agriculture sector.
Alvarez-Cuadrado and Poschke (2011) confirmed this assertion and showed that improve-
ments in industrial technology (industry pull) mattered more in countries in early stages of
economic development and structural transformation.
2.3.4 Factor Accumulation
As defined by Syrquin (1988), factor accumulation refers to the use of resources to increase
the productive capacity of an economy. Indicators of accumulation include rates of saving;
investment in physical capital, in research and development, and in the development of hu-
man resources (health, education); and investment in other public services. In this section,
we focus on aggregate saving/investment patterns. Most of the long-run results reported
below apply to both savings and investment.
Investment, or capital accumulation, is a crucial factor for economic development. De
Long and Summers (1991) found that machinery and equipment investment has a strong
association with growth. Blomstrom, Lipsey, and Zejan (1996) confirmed the correlation
and found technology growth causes capital accumulation. Podrecca and Carmeci (2001)
examined the linkage between investment and growth and identified two-direction Granger
causality. And Bond, Leblebicioglu, and Schiantarelli (2010) found a positive relationship
between investment as a share of gross domestic product (GDP) and the long-run growth
rate of GDP per worker. To understand the Asian economic growth miracle, Young (1994,
1995) argued that a large share of the output growth can be explained by rapid factor ac-
cumulation of both capital and labor, while the growth of total factor productivity is not
extraordinarily high. However, the role of investment is often ignored in the literature of
structural transformation, since it brings complicated dynamic features into models.
In the time series data, we observe two distinct patterns for saving/investment rates at
different income levels. First, for countries at low levels of income, as the per capita income
increases, the saving rate rises. Second, for high-income countries, there is a trend that the
11
saving rate decreases. Thus, the saving rate exhibits a hump-shaped pattern during the full
cycle of economic growth.5
Echevarria (2000) and Laitner (2000) explained the first fact as a consequence of the
non-homothetic preference satisfying Engel’s law. The non-homothetic preference used
by Echevarria (2000) implies the investment rates increase with the level of income as
the economy approaches the steady state. Increasing investment rates imply a positive
correlation between growth rates and the level of income, at low levels of income.
Laitner (2000) argued that the increase in saving/investment rate is simply determined
by the way that saving is measured. He analyzed an economy consisting of two sectors:
agriculture and manufacturing. For the agricultural sector, land is an important factor of
production as is capital for the manufacturing sector. Since the size of farmland is fixed
in agricultural production, any extra return from technological progress and population
expansion would be represented by the appreciation of land price, which is not recorded
as savings by the national income account. However, the stock of reproducible capital
would increase as the marginal productivity of capital rises, which is recognized as national
saving. Therefore, as labor moves out of agriculture, land becomes less important, and
capital accumulation becomes more important. As a result, the saving rate would rise.
The decline of saving rate for middle-income and high-income countries is also closely
related to structural transformation and growth. There are two possible explanations. One
is the slowdown of productivity growth for middle to high income economies as they have
to make innovations by themselves rather than mimic the existing production process.6 The
other one is that the high saving/investment rate during economic development is associated
with the fixed capital formation process. One consequence of economic growth is urbaniza-
tion. As a country develops, the process of structural transformation from agriculture into
manufacturing and services involves a shift of labor out of rural areas and into urban ones.
Urbanization triggers a huge demand on public infrastructure and residential construction.
As the structural transformation completes, this construction demand decreases.
5This pattern is more distinct for countries that have been able to achieve persistent growth. We illustratethe investment rates of a set of Asian countries in Figures 4.3 and 4.4.
6This can be viewed as converging to the steady state in Solow and Ramsey models. On the steady state,the investment rate is constant.
12
2.3.5 Open Economy and Trade
In a closed economy, domestic supply and demand have to be equal. However, when we
include international trade, the domestic production for tradable goods can deviate from
domestic demand. Therefore, if an economy would like to take the gain from trade and
continue to specify production following comparative advantages, the distribution of sec-
toral economic activities would be affected as well. In the literature, this inter-sector trade,
especially the agriculture-manufacturing trade, has been evaluated in various papers.
Echevarria (1995) discussed the impact of trade in the context of the Ricardian trade
model: a country should specialize in producing either agricultural goods or manufactured
products, depending on their comparative advantages in the world market. The service
sector is set to be non-tradable. If the country is good at producing agriculture goods, trade
helps growth at low levels of income, but trade slows the country’s growth at higher levels,
while in the country that produces manufactured products trade has no substantial effect on
growth.
Yi and Zhang (2010) used a three-sector, two-country model to study structural change
in which all goods are produced with labor only. They provided examples for which the
country with higher productivity growth in manufacturing experiences an inverted-U shape
in the shares of manufacturing employment and value added while the other country expe-
riences a downward sloping shape in the shares of manufacturing labor and value added. In
a following paper, Uy, Yi, and Zhang (2013) applied their three-sector, two-country model
to conduct a quantitative assessment on the structural change of South Korea. They cap-
tured the major part of evolution of employment shares in agriculture and service, but only
the rising part of the hump-shape in manufacturing.
Betts, Giri, and Verma (2011) studied the role of international trade in Korea’s indus-
trialization in a two-country model with three sectors. They found that international trade
played a crucial role for the rapid rise in the manufacturing value added and employment
shares, but that it did not play much of a role for the decline of Korean agriculture. Such a
story is consistent with various accounts regarding the importance of trade in the develop-
ment of Korea.
Teignier (2011) quantitatively evaluated the structural change of the United Kingdom
and Korea, and argued that low-income countries can gain significantly from adopting the
strategy of producing manufactured products to exchange for agricultural goods.
13
Mao and Yao (2012) also studied structural change in a small open economy that has
two tradable sectors, agriculture and manufacturing, and one non-tradable sector, services.
They assumed the relative price between the agriculture sector and the manufacture sector
is given by the world price and trade is always balanced. They calibrated the economy of
South Korea between 1970 and 2009 and showed that the simulated structural transforma-
tion can fit the historical data. They focused on two countervailing effects: the productiv-
ity effect and the Balassa–Samuelson effect, which represent the unbalanced productivity
growth and non-homothetic preference. They argued that the productivity effect dominates
in the early stage of development and is gradually replaced by the Balassa-Samuelson ef-
fect.
One drawback of these studies that focus on the agriculture-manufacturing trade is that
the trade for food mechanism has seldom worked in practice. Gollin, Parente, and Rogerson
(2007) showed that food imports and food aid only supplied around 5% of total calorie
consumption in low-income countries in 2000. Therefore, importing agriculture goods is
not a major source of food at the macro level for poor countries.
Swiecki (2013), following Yi and Zhang (2010), built a model that can include four
forces of structural transformation: sector-biased technological progress, non-homothetic
preference, international trade, and changing wedges between factor costs across sectors.
The results show that non-homothetic preferences can account for movement of labor out of
agriculture in poor economies, while sector-biased technological growth is overall the most
important mechanism for understanding experiences of developed countries. In addition, it
shows that trade factor also has significant contributions.
Kehoe, Ruhl, and Steinberg (2013) focused on the direct impact of U.S. borrowing
(saving glut) on the decline in goods-sector employment between 1992 to 2012. They
found that the saving glut is only responsible for the boom in construction employment
during this period and the faster productivity growth in the goods sector is responsible for
most of the shift in employment away from the manufacturing sector.
14
Chapter 3
Structural Transformation and TradeImbalances
3.1 Introduction
The economics literature has documented structural transformation during the industrial-
ization process, which involved a massive reallocation of labor from the agriculture sector
into the manufacturing and service sectors.1 Kuznets (1966) considered structural change
as one of the most prominent features of development.
The literature that develops models of economic growth and development consistent
with such structural changes typically starts by positing two assumptions in a closed econ-
omy. One is the non-homothetic preference for households, emphasized as the demand-side
reason. This allows for changes in the marginal rate of substitution between different goods
as an economy grows, and it generates results that are consistent with Engel’s law, leading
directly to a pattern of uneven growth between sectors. Another assumption, first proposed
by Baumol (1967), is sector-biased technological progress on the supply side. Ngai and
Pissarides (2007) showed that with a low (less than one) elasticity of substitution across
final goods and identical production functions across sectors, employment shifts to sectors
with relatively lower Total Factor Productivity (TFP) growth. Later, Acemoglu and Guer-
rieri (2008) found that if there are different factor proportions in the production functions,
1For empirical works that document the historical sectoral allocations, see Maddison (1991), Echevarria(1997), Rogerson (2008), and recently Buera and Kaboski (2011), among many others.
15
the increase in the capital-labor ratio promotes the output of the capital intensive sector,
while the relative prices move against it and encourage the reallocation of labor to other
sectors.
In order to evaluate the performance of these models, a prevalent exercise is to replicate
the structural transformation in the United States. Bah (2008) and Buera and Kaboski
(2009) found that the predictions of traditional structural change models cannot account
for the steep decline in manufacturing and rise in services in the recent data.
The traditional structural change literature, which focuses on the long-term industrial-
ization process, often makes the assumption that the economy is in autarky. However, this
assumption is unlikely to hold when we investigate the postwar United States. As the world
economic leader, the United States has been actively involved in international trade, sup-
ported the globalization process, and experienced a soaring trade deficit since the 1970s,
eventually reaching 6 percent of the GDP in 2005. In addition, the timing of the recent in-
tensive labor movements from the manufacturing to the service sectors in the United States
follows the increase of trade deficits quite closely.
Our goal in this chapter is to provide quantitative evidence of the U.S. experience of
structural change and evaluate how much of the employment share movements can be
linked to trade factors. We emphasize that there are two channels in which structural trans-
formation can be affected by trade.
The first one is inter-sector trade, which is associated with the Ricardian theory of com-
parative advantage between sectors. If an economy is relatively more efficient in producing
manufactured goods, it can export the product of the manufacturing sector for other goods,
such as agriculture products and services, while keeping the overall trade balanced.
The other trade factor is the large and persistent trade imbalances, in particular the trade
deficits of the United States. The dominant type of trade, within developed economies and
between emerging and developed economies, is the exchange of manufactured products. If
we account for the inter-sector trade, national trade deficits reflect net imports of manufac-
tured goods, which should contribute to the allocation of labor across different sectors in
the United States.
To evaluate these factors, we first develop a three-sector economy model to conduct
quantitative evaluations. This model inherits features from the traditional literature, in-
cluding the non-homothetic preference, sector-biased technological progress, and hetero-
16
geneous capital intensities in sectoral production functions. The quantitative calibration
results of this closed economy model can reproduce the labor movements from 1950 to the
late 1970s, but show noticeable deviations from the data in the recent period.
For the two trade effects, the inter-sector trade, despite its popularity in theory, has
been playing a minor role in the United States. The calibration results show the sectoral
trade balances can explain roughly 4.5 percent of the total decline during the sample pe-
riod, while the trade imbalance effect explains up to 31 percent of the total manufacturing
employment share decline.
These results quantitatively fit the historical trends in the data and are robust to various
parameter values and alternative measures of structural change. In addition, these findings
are in line with the implications of Sachs and Shatz (1994) and Bernard, Jensen, and Schott
(2006), which support the argument that international competition and trade balances have
significant impacts during structural transformation.
The rest of this chapter is organized as follows. In section 3.2, we first briefly review
the literature that is related to structural change and trade, and also, in particular, the struc-
tural transformation of the United States. Section 3.3 documents some historical evidence
of the U.S. economy from 1950 to 2005. Section 3.4 presents the economy model and
characterizes the equilibrium properties. Section 3.5 calibrates the model to evaluate its
performance. Section 3.6 discusses several relevant issues and checks the robustness of the
results. Finally, section 3.7 concludes.
3.2 Related Literature
In the literature of structural transformation, only a few studies have investigated the link-
age between trade and structural change. And most of them have focused on the role of
inter-sector trade.
Echevarria (1995) considered a Ricardian model to study the impact of trade on struc-
tural transformation in which a country could make use of its comparative advantages and
specialize in producing either agricultural goods or manufactured products. The model
shows that for countries whose economies depend on the manufacturing and services sec-
tors, trade does not have a substantial effect on growth, while country specializes in pro-
17
ducing primary commodities could grow faster at low levels of income, but would grow
slower at high levels of income.
Recent research has argued that international trade plays an indispensable role in struc-
tural change. Teignier (2011) showed that for a small country with low agricultural pro-
ductivity, international trade can stimulate growth and structural change, since trade allows
imported agricultural goods to reduce agricultural employment. However, the trade bal-
ances of South Korea might not support this idea. Since 1960, South Korea continued to
import food and had persistent trade deficits in the agriculture sector. But the trade balances
of the manufacturing sector were also deficits from 1960 to 1981.2 It seems that the import
of agricultural products helped the economic growth of South Korea, but it is not clear if
the import had been financed by the export of manufactured goods.
Yi and Zhang (2010) constructed an Eaton-Kortum trade model and argued that changes
in productivity and in trade barriers affect employment shares across sectors, and the trade
pattern can generate the hump-shaped pattern of the manufacturing employment share as a
country develops. But, in their two-country model, if country 1 is able to have the hump-
shaped manufacturing employment pattern, country 2 might not be able to achieve a similar
pattern. This feature cannot explain why the hump-shaped pattern is relatively common
across countries. In a following paper, Uy, Yi, and Zhang (2013) conducted a quantitative
assessment of the role of international trade in structural change for South Korea, which
is able to capture the major part of the evolution of employment shares in agriculture and
service, but only the rising part of the hump-shape in manufacturing.
Swiecki (2013), following Yi and Zhang (2010), built a model that can include four
forces of structural transformation: sector-biased technological progress, non-homothetic
preference, international trade, and changing wedges between factor costs across sectors.
For poor countries, non-homothetic preferences can account for the movement of labor
out of agriculture, while sector-biased technological growth is overall the most important
mechanism for understanding the experiences of developed countries. The estimate of the
United States shows that trade is the second most important factor to explain structural
change.
There is another large body of literature that directly focuses on the impact of trade
on the number of workers employed in the U.S. manufacturing sector. Sachs and Shatz
2The overall trade balances of South Korea were deficits before 1985.
18
(1994) estimated the impact of trade on manufacturing employment and found that “the
increase in net imports between 1978 and 1990 is associated with a decline of 7.2 percent
in production jobs in manufacturing and a decline of 2.1 percent in non-production jobs in
manufacturing”. They also found that the international competition drove out the positions
of low-skill workers and promoted industries with higher skill requirement.
Sviekauskas (1995) studied the impact of trade on U.S. employment for two sub-
periods: 1977–1982 and 1982–1985. The trade deficit was stable during the first period,
from $37 billion to $38 billion. But the trade deficit increased from $38 billion to $134
billion, in the second period. Sviekauskas (1995) estimated that trade contributed 77,000
jobs in 1977 and 486,000 in 1982, but resulted in a loss of 2.5 million jobs in 1985. So on
a net basis, trade cost the economy 3 million jobs during the period 1982-1985.
Bivens (2004) estimated that the rising trade deficit in manufactured goods accounted
for about 58% of the decline in manufacturing employment between 1998 and 2003 and
34% of the decline from 2000 to 2003. U.S. domestic output was about 76.5% of domestic
demand, nearly 14% less than the average between 1987 and 1997.
On the other hand, several authors believed that international trade has played a minor
role in the contraction of U.S. manufacturing. Krugman and Lawrence (1994) noted that
the share of the U.S. labor force employed in manufacturing and the share of U.S. output
accounted for by value added in manufacturing have both been falling since 1950. They
looked at several trends in the U.S. data and they argued that foreign competition has played
a minor role in the contraction of U.S. manufacturing. However, in a recent paper, Krugman
(2008) reconsidered the connection between trade and wages. He found out that developing
countries appeared to be able to vertically integrate into the value-added supply chain. He
suggested that such vertical fragmentation of production means that growing trade with
developing countries may have a larger impact on wage inequality in developed countries
than traditional micro-factor content studies indicate.
Lindsey (2004) claimed that international trade contributed only modestly to this fre-
netic job turnover. Between 2000 and 2003, manufacturing employment dropped by nearly
2.8 million, yet imports of manufactured goods rose only 0.6 percent. And Kehoe, Ruhl,
and Steinberg (2013) focused on the direct impact of U.S. borrowing (saving glut) on the
decline in goods-sector employment between 1992 to 2012. Their numerical results show
19
that the recent loss of jobs in the goods-producing sector can be clearly explained by the
saving glut hypothesis (Kehoe, Ruhl, and Steinberg, 2013, Figure 6).
The decline of the manufacturing sector in the U.S. is also related to the recent literature
on “job polarization”. Autor, Katz, and Kearney (2009), and Goos, Manning, and Salomons
(2009) found that the share of employment in occupations in the middle of the skill distri-
bution, such as well-paid middle-skill jobs in manufacturing and clerical occupations, has
declined rapidly in the U.S. and Europe. Goos, Manning, and Salomons (2014) claim that
they can explain much of job polarization by routine-biased technological change and off-
shoring. Autor, Dorn, and Hanson (2013) estimated that import competition from China
could explain one-quarter of the contemporaneous aggregate decline in U.S. manufactur-
ing employment. In industries that are more trade-exposed, transfer benefits payments for
unemployment, disability, retirement, and healthcare also rise sharply.
3.3 Structural Change in the United States, 1950-2005
This section documents the process of structural transformation; the total factor productiv-
ity (TFP) growth in agriculture, manufacturing, and service sectors; and the trade balances
in the United States from 1950 to 2005. The sectoral employment shares during the pe-
riod come from the Groningen Growth and Development Centre (GGDC) 10-sector and
Historical National Accounts databases for numbers of workers and hours worked. For
productivity, data sources include Jorgenson (1991), the United States Department of Agri-
culture (USDA), the Bureau of Labor Statistics (BLS), and the EU KLEMS Growth and
Productivity Accounts Timmer and Vries (2008). The labor income shares were estimated
using various release of the GDP-by-industry accounts from the Bureau of Economic Anal-
ysis (BEA). The U.S. trade data comes from the BEA and the United Nation Commodity
Trade (UN COMTRADE) database. More details of the data series are listed at the end of
this chapter.
Figure 3.1 reveals the trend of structural change over the period in terms of number
of workers and hours worked. Both data series display the same qualitative properties:3
the employment share is steadily decreasing in the goods sectors, including agriculture
and manufacturing, and is steadily increasing in the service sector. This is consistent with3The deviations between the two time series since the 1960s are due to the change of working hours,
especially the shorter working time per worker in the service sector.
20
the process of structural transformation as first described by Kuznets (1966): as a coun-
try becomes more productive, resources are reallocated from goods-producing sectors to
services-producing sectors.
1950 1960 1970 1980 1990 20000
10
20
30
40
50
60
70
80
90
100
Labo
r S
hare
s (%
)
Number of WorkersHours Worked
Service
Manufacture
Agriculture
Figure 3.1: U.S. sectoral employment shares, 1950-2005
A puzzling feature of the postwar U.S. economy is the rapid decline of the manufac-
turing labor employment share since the late 1970s. Buera and Kaboski (2009) argued that
the traditional models of structural change have failed to match the data in this period. In
the following sections of this paper, several possible factors that might contribute to labor
reallocation will be evaluated individually.
The first factor is sector-biased productivity growth. As Ngai and Pissarides (2007) and
Duarte and Restuccia (2010) proposed, if the elasticity of substitution across final goods
is less than one, labor allocation will shift from high-productivity growth sectors to the
sectors with lower TFP growth. Therefore, the structural transformation noted above might
come from the faster growth of manufacturing productivity (Brauer, 2004).
The Bureau of Labor Statistics reported that the productivity growth in agriculture was
higher than in the non-farm sector, from 1948 to 2005, the average annual TFP growth was
21
at 1.7 percent in the farm sector, compared to 1.2 percent in the non-farm sector.4 How-
ever, within the non-farm sector, the TFP growth rates of manufacturing and services are
not directly reported. Jorgenson (1991) estimated relatively a low TFP growth rate in man-
ufacturing at 0.6 percent, compared to 0.9 percent in the service sector5 from 1950 to 1977.
The EU KLEMS Growth and Productivity Accounts reported that TFP has been growing at
1.03 percent and 0.5 percent on average in manufacturing and services, respectively, since
1977. In addition, Englander and Mittelstadt (1988), Jorgenson and Gollop (1992), and the
Bureau of Labor Statistics reported a slowdown of TFP growth in the non-farm sector in
the early 1970s, from 1.5 percent during 1950-1970 to 0.8 percent during 1971-2005.
1950 1960 1970 1980 1990 20000.6
0.62
0.64
0.66
0.68
0.7
0.72
0.74
0.76
0.78
0.8
Labo
r In
com
e S
hare
Manufacturing H−P filterManufacturing Labor Share
Figure 3.2: Labor income share in manufacturingSource: Bureau of Economic Analysis (BEA), Industry Economic Accounts.
Second, while different factor income shares across sectors might play an important role
in structural transformation, they have received less attention in the literature. Acemoglu
and Guerrieri (2008) showed that factor proportion differences and capital deepening across
sectors will lead to a factor reallocation. Valentinyi and Herrendorf (2008) found that agri-
culture has the highest capital share, followed by manufacturing and the service sectors.4See Jorgenson (1991), Jorgenson and Stiroh (2000), and more recently, Alvarez-Cuadrado and Poschke
(2011) for the estimations of total factor productivity growth.5I use industry value-added weights to generate the sector TFP growth rates for this paper.
22
Moreover, as shown in Figure 3.2, from 1950 to 2005, we have observed significant move-
ments on the manufacturing labor income share: it increased from 0.68 to a peak over 0.72
around 1972 and declined to 0.64 in the early 2000s.6 Models that consider labor as the
only factor of production or that assume constant and identical capital share across sec-
tors, such as those of Ngai and Pissarides (2007), Buera and Kaboski (2009), Duarte and
Restuccia (2010), and Uy, Yi, and Zhang (2013), are incapable of handling these issues.
1950 1960 1970 1980 1990 2000−7
−6
−5
−4
−3
−2
−1
0
1
Tra
de B
alan
ce/G
DP
Rat
io (
%)
National Trade BalanceAgriculture Trade BalanceManufacturing Trade BalanceService Trade Balance
Figure 3.3: Trade balance/GDP ratio (through H-P filter)
The third, and probably most ignored, factor is international trade. The traditional
models of structural transformation are often restricted to a closed economy, which is an
inappropriate assumption for the postwar U.S. economy. Figure 3.3 illustrates the historical
trends of the trade balances. The aggregate trade balance shifted from surplus to deficit in
the early 1970s and continued to deteriorate, reaching 6 percent of the GDP in 2005.
Trade can influence the process of structural transformation in two direct channels and
an indirect channel. First, inter-sector trade might play an important role in structural
change. As Mann (2002) documented, the trade balance of the United States for the man-
ufacturing sector has been persistently and increasingly negative, and the trade balance
6This is calculated by the author using the Industry Economic Accounts from Bureau of Economic Anal-ysis (BEA). The data is trended using the Hodrick–Prescott filter with a smoothing parameter of 100.
23
for the service sector has been persistently positive, while agriculture trade surplus has
remained but has become relatively insignificant.
The other channel refers to the chronic trade deficits in the United States since the late
1970s. As a persistent feature, rising trade deficits have attracted extensive attention. As
illustrated in Figure 3.3, after controlling for the sectoral trade balances, the net import
of manufactured goods dominates the trade deficit of the country. If we consider the net
import of manufactured products as a foreign replacement of domestic production, the trade
imbalances will contribute directly to the declining manufacturing employment.
There might be an indirect impact from trade to structural change. Sachs and Shatz
(1994) argued that international competition can drive out low-skilled positions and pro-
mote industries with higher skill requirements. They estimated that a substantial decline of
manufacturing employment could be associated with the increase of imports between 1978
and 1990, as firms were moving into relatively more capital intensive industries. Later,
Bernard, Jensen, and Schott (2006) found that plant survival and growth in U.S. manufac-
turing are negatively associated with industry exposure to imports from low-wage coun-
tries, implying that firms adjust their production according to trade pressure. Therefore,
the rising capital shares in the manufacturing sector might reflect this firm’s level response.
Since we cannot directly measure this factor, we put it into the discussion section.
In the following sections, a formal model of structural transformation will be con-
structed in order to evaluate these factors in turn.
3.4 The Model of Structural Change
This section develops a three-sector model of structural transformation that intends to repli-
cate sectoral employment compositions during long-term economic growth. Following the
literature of modeling structural change, the model adopts three features to achieve this out-
come: non-homothetic preference, sector-biased technological growth, and different factor
shares in production functions. In addition, we extend this model to include the contribu-
tion of international trade.
24
3.4.1 Economic Environment
Firms
There are three consumption goods produced by three sectors in the model: agriculture,
manufacturing, and service, denoted by letters a, m, and s, respectively. The manufactured
products are also used for investment,7 whereas the outputs of the other two sectors are
non-durable. Labor and capital are the two factors of production. At time t, the outputs
satisfy the following Cobb-Douglas production functions with constant return to scale:
Yi,t = Bi,tKαii,t L1−αi
i,t , (3.1)
where, for sector i (i ∈{a, m, s}), Yi,t is the output, Ki,t is the capital input, Li,t is the labor
employment, and {Ba,t , Bm,t , Bs,t} is the set of sectoral productivity at time t, which have
the following growth rates
γi,t =Bi,t
Bi,t. (3.2)
There is a continuum of homogeneous firms in each sector, while both goods and factor
markets are competitive. Labor and capital are mobile across sectors. Therefore, at period
t, a representative firm in sector i solves,
maxKi,tLi,t>0
Pi,tYi,t−wtLi,t− rtKi,t , (3.3)
where the price of the output Pi,t , wage wt , and interest rate rt are given for the firm.
Households
The economy is populated by an infinitely lived representative household of constant size
L. Each member of the household provides one unit of labor inelastically to the market
in every period. Therefore, the aggregate labor supply is L, which can be normalized to 1
without loss of generality. The household chooses consumption to maximize the following
7Kongsamut, Rebelo, and Xie (2001) reported manufacturing and construction sectors produced between90% and 93% of investment in the United States during the period of 1958 to 1987. This ratio, calculatedusing the World Input-Output Database Timmer (2012), was between 77% and 82% from 1996 to 2009.
25
lifetime utility:
Uh =∞
∑t=0
βtU(Ct) =
∞
∑t=0
βt C
1−σt −11−σ
, (3.4)
where σ > 0 is the intertemporal elasticity of substitution of consumption, and if σ =
1, U(Ct) = logCt , β is a discount factor, and Ct is a composite consumption with three
components: the consumption of agriculture goods, manufacturing, and service goods,
Ct =
(w
1θa (Ca,t−Ca)
θ−1θ +w
1θmC
θ−1θ
m,t +ws1θ (Cs,t−Cs)
θ−1θ
) θ
θ−1
, ∑i
wi = 1, (3.5)
where Ca > 0, is a subsistence level of agricultural consumption that introduces non-
homotheticity to the preference, which has a long tradition in the literature of develop-
ment,8 Cs 6 0 captures the home-produced services, and θ is the elasticity of substitution
across goods. In a recent empirical study, Herrendorf, Rogerson, and Valentinyi (2013)
calibrated utility function parameters to be consistent with the U.S. consumption data and
found that a Stone-Geary specification (θ = 1) fits the data well in terms of final consump-
tion expenditure, while a preference with low elasticity of substitution, for example, the
Leontief specification (θ = 0), fits the value-added sectoral consumption data well. Thus,
assuming θ ∈ [0, 1] is reasonable, and we will choose the appropriate value of θ in section
3.5.
The budget constraint of the household at time t is
∑i∈{a,m,s}
Pi,tCi,t +Pm,tSt = wtL+ rtKt , (3.6)
where St is saving and Kt is the total capital stock.
8It is not literally the “subsistence” food requirement in a modern economy, but this terminology is com-monly used to introduce non-homotheticity to the model. See, for instance, Echevarria (1997), Laitner (2000),Kongsamut, Rebelo, and Xie (2001), Gollin, Parente, and Rogerson (2007), Restuccia, Yang, and Zhu (2008),Duarte and Restuccia (2010), and Alvarez-Cuadrado and Poschke (2011).
26
Trade Balance and Market Clearing Conditions
The market clearing conditions for factor markets require that the demand for labor and
capital from firms is equal to the supply of labor and the current capital stock,
∑i∈{a,m,s}
Li,t = L, ∑i∈{a,m,s}
Ki,t = Kt . (3.7)
Given δ as the depreciation rate, the law of motion for capital is
Kt+1 = (1−δ )Kt + It , (3.8)
where It is the domestic investment, and satisfies the following market clearing conditions,
Yi,t = Ci,t +NXi,t i ∈ {a, s}
Ym,t = Cm,t + It +NXm,t , (3.9)
where NXi,t is the net export of sector i, and if NXi,t > 0, the sector has a trade surplus.
The aggregate trade balance of this economy, T Bt , is given by
T Bt = ∑i∈{a,m,s}
Pi,tNXi,t . (3.10)
As discussed in section 3.3, there are two direct channels of trade that influence the
domestic economy. First, inter-sector trade might play an important role, as discussed in
Yi and Zhang (2010) and Teignier (2011). To evaluate this factor, we calculate the net
export of manufactured products that is necessary to maintain a balanced trade for the
whole economy,
NXSectorm,t =−
Pa,tNXa,t +Ps,tNXs,t
Pm,t. (3.11)
NXSectorm,t represents the trade balance of the manufacturing sector, which is determined by
relative comparative advantages between home and foreign economies. This sectoral trade
imbalance reflects the gain from trade and might not cause any concerns. However, we also
want to look at the scenario when the international trade is not balanced. We calculate the
27
following sectoral trade balance component,
NXT Bm,t =
T Bt
Pm,t, (3.12)
where NXT Bm,t captures the impact that is linked to the aggregate trade position.
This decomposition exercise separates the two distinct factors of trade and allows us
to focus on the impact of the total trade imbalance. The distribution of trade imbalances
across sectors will not affect our results.9 And it is clear to find that
NXm,t = NXSectorm,t +NXT B
m,t .
The national saving, measured by manufacturing good, is given by
St = It−NXT Bm,t . (3.13)
For the sake of simplicity, we assume the trade balances are exogenously given. This
assumption certainly abstracts from several important features, but it is an important step
to start with. In addition, if we set all trade balances to zero, our model converges to the
closed economy model that has been extensively discussed in the literature, which can be
used as a benchmark case.
3.4.2 Economic Equilibrium
In this section, we start with a closed economy, where NXi,t = 0 and T Bt = 0. We can
define the following competitive equilibrium.
Definition 3.1. A competitive equilibrium is a sequence of prices {Pa,t , Pm,t , Ps,t}t>0,
household consumption {Ct(Ca,t , Cm,t , Cs,t)}t>0, labor allocations {L, La,t , Lm,t , Ls,t}t>0,
and capital stocks {Kt , Ka,t , Km,t , Ks,t}t>0, such that (i) given prices, firms employ labor
9It will be interesting to consider the distribution effects of trade imbalances. For example, given a nationaltrade deficits worth 6 percent of total output, if country A has 3 percent deficits in both manufacturing andservices sectors, while country B has balanced trade in services but 6 percent deficits in manufacturing, thetwo components for each country will be the following: country A has to maintain a 3 percent surplus tocompensate for its deficit in services as in equation (3.11), thus the second component will be 6 percent ofdeficits; for country B, the first component is zero while the second component will remain the same for theother country.
28
and capital to solve the firm’s problem in equation (3.3); (ii) given prices, a household
chooses {Ct(·)} to solve the intertemporal consumption problem in equation (3.4); and (iii)
the prices {Pa,t , Pm,t , Ps,t}t>0 make the markets clear: equation (3.7), (3.8), and (3.9) hold.
The balanced growth path
The key concept in the literature of economic growth is the balanced growth path where
important macroeconomics variables, such as output, consumption, and capital stock, grow
at constant but not necessarily common rates. In general, the balanced growth path is not
applicable in models with structural change where resources reallocate across sectors (Her-
rendorf, Rogerson, and Valentinyi, 2014). However, with a restrictive set of conditions,
structural change is consistent with balanced growth, which is characterized by the follow-
ing proposition.
Proposition 3.1. The closed economy with structural change is consistent with balanced
growth if and only if
(a) γi = γ , αi = α , and (Ca,t , Cs,t) 6= 0, ∑i PiCi = 0, the case of Kongsamut, Rebelo, and
Xie (2001);
(b) Ci,t = 0, αi = α , and γi 6= γ , for some i 6= j, thus pi,t 6= p j,t , the case of Ngai and
Pissarides (2007).
Proof. This proposition is similar to proposition 1 in Buera and Kaboski (2009), see section
3.8 for more details.
Proposition 3.1 shows that conditions for jointly having generalized balanced growth
and structural transformation become considerably very stringent. Herrendorf, Rogerson,
and Valentinyi (2014) argued that if we want to capture features in reality, the conditions
above are too restrictive to be satisfied. It is exactly the challenge of this paper, as we want
to capture the complex nature of the structural transformation process in the U.S. economy.
Therefore, the model has to be able to deal with different sources of structural change,
including non-homothetic preference, unbalanced technology growth, different production
functions, inter-sector trade, trade imbalances, and so on. With different capital intensi-
ties across sectors, the relative prices will change as the capital/labor ratio or productivity
change. Thus, as discussed in Acemoglu and Guerrieri (2008), the balance growth path is
not applicable in this model.
29
The household’s maximization problem can be broken down into two sub-problems.
First, the households have to solve the intertemporal optimization problem, making the
saving/investment decision. Second, the households will solve the static distribution prob-
lem to maximized consumption across sectors.
To simplify the analysis, instead of investigating an unbalanced growth path with com-
plex dynamic features, we adopt a static approach that focuses on studying a sequence of
steady states, which is defined as the following.
Definition 3.2. At a steady state, without productivity shock, household consumption and
capital stock remain constant.
Following an exogenous progress of productivity growth, the economy shifts from one
steady state to another. Thus, we can define the following static growth path.
Definition 3.3. The static growth path is a sequence of steady states determined by an
exogenous productivity sequence {Bi,t}t>0 with i ∈ {a,m,s}.
There are a few reasons why we adopt this static approach. The first advantage of this
static approach is that we do not have to take a stand on the exact nature of intertemporal
opportunities available to the household or to specify how expectations of the future are
formed. Thus, when we allow several factors to vary simultaneously,10 our static approach
can capture the main impacts of these factors, while it maintains a minimal structure. Sec-
ond, as we discussed during the calibration exercise in section 3.5, in the sample period,
the investment rates in the United States were roughly constant, thus this static approach
is appropriate to describe the U.S. economy. Therefore, our model is closer to a Solow
exogenous growth model, rather than a Ramsey growth model. However, every period,
households make consumption choices to maximize utility.
Our framework suffers from a few limitations. Since investment is assumed to replace
depreciation, the contribution of investment on structural change has been held to be con-
stant. This specification of investment is similar to Kongsamut, Rebelo, and Xie (2001),
and is consistent with the empirical fact that the United States have a roughly constant in-
vestment rate over the sample period, but it still ignores the crucial role of investment on
structural transformation. In addition, this approach is unable to study the the transition
dynamics, which is theoretically very important.10These factors include, but are not limited to, slowdown of productivity growth, rising capital income
share, and trade imbalances. They are set to be either exogenous or unexpected.
30
The factor markets
The first-order conditions of the firm’s problem imply that the marginal productivity of
labor must be equal to the wage rate, while the marginal productivity of capital is equal to
the interest rate. Assuming perfect factor mobility, the wage rates and interest rates must
be the same across sectors at any given time. If the capital labor ratio in sector i is defined
as ki,t =Ki,tLi,t
, it will satisfy the following equations:
ka,t = makm,t , ks,t = mskm,t , (3.14)
where ma =αa(1−αm)αm(1−αa)
, ms =αs(1−αm)αm(1−αs)
.11
Also, the wage rate and interest rate at time t are given by
wt = Pm,t(1−αm)Bm,tkαmm,t ,
rt = Pm,tαmBm,tkαm−1m,t . (3.15)
The relative prices, pa,t and ps,t , are determined by the relative productivity and capital
income shares, such as
pa,t =Pa,t
Pm,t=
Bm,t (1−αm)
Ba,t (1−αa)mαaa
kαm−αam,t ,
ps,t =Ps,t
Pm,t=
Bm,t (1−αm)
Bs,t (1−αs)mαss
kαm−αsm,t . (3.16)
Given relative prices as a function of km,t , the employment shares can be derived as
functions of {Kt , Ks,t , km,t}.
11Factor mobility implies that the factor prices must be equal across sectors,
rt = Pa,tBa,tαakαa−1a,t = Pm,tBm,tαmkαm−1
m,t = Ps,tBs,tαskαs−1s,t ,
wt = Pa,tBa,t(1−αa)kαaa,t = Pm,tBm,t(1−αm)k
αmm,t = Ps,tBs,t(1−αs)k
αss,t .
Therefore,wt
rt=
1−αi
αiki,t
implies ka,tkm,t
= αa(1−αm)αm(1−αa)
≡ mA, and similarly ks,tkm,t
= αs(1−αm)αm(1−αs)
≡ mS.
31
Proposition 3.2. The market equilibrium labor allocation {La,t , Lm,t , Ls,t} is determined
by {Kt , Ks,t , km,t}, namely the aggregate capital stock, the capital input in service sector,
and the capital labor ratio in domestic manufacturing, respectively.
Proof. See section 3.8.
Consumption
Capital accumulation is determined by the intertemporal decision of the household. The
first-order conditions for consumption imply the intertemporal Euler equation:(Ct+1
Ct
)σ
= βPt
Pt+1(rt+1 +1−δ ), (3.17)
where Pt is the price index satisfying,
PtCt = ∑i∈{a,m,s}
Pi,tCi,t . (3.18)
In general, of course, the non-homotheticity term in the consumption functions can
lead to corner solutions. However, this is not relevant for aggregate consumption in a
rich country such as postwar U.S. (Herrendorf, Rogerson, and Valentinyi, 2013). Looking
ahead, the calibration results in the following sections show that the household chooses
quantities that are far away from corners.
Then, assuming interior solutions, the composition of Ct in equation (3.5) implies that,
at time t,
Ca,t−Ca
Cm,t=
wa
wm
(Pm,t
Pa,t
)θ
, (3.19)
Cm,t
Cs,t−Cs=
wm
ws
(Ps,t
Pm,t
)θ
. (3.20)
Given the productivity set at time t, in order to reach the steady state, the intertemporal
Euler equation should satisfy the restriction that both consumption and capital stock are
constant, Ct = Ct+1 and Kt = Kt+1. This implies It = δKt , km,t = km,t+1, and therefore,
Pt = Pt+1. Equation (3.17) can be rewritten as rt+1 =1ρ+ δ − 1. Thus, the interest rate is
determined by the discount factor ρ and the depreciation rate δ .
32
Proposition 3.3. Assuming interior solutions exist, given productivity sequence {Bi,t}t>0,
if the discount factor β and the depreciation rate δ are held constant, the interest rates on
a static growth path are constant,12 as denoted by rss,
rss =1β+δ −1. (3.21)
Proof. If δ and β are time invariant, at any time t, the steady state interest rate rt+1 =1β+δ −1≡ rss is constant.
By solving the first-order conditions of firms, the marginal productivity of capital is
equal to the interest rate. Then, on the static growth path, the capital labor ratio in manu-
facturing is given by
km,ss,t =
(Pm,tBm,tαm
rss
) 11−αm
, (3.22)
where a productivity growth on Bm,t will trigger an increase of the capital/labor ratio in
manufacturing. This capital deepening will then lead to structural change along the static
growth path.
Labor allocations on the static growth path
First, without loss of generality, Pm,t can be normalized to one.13 Then, km,ss,t is solely
determined by Bm,t , the productivity level of the domestic manufacturing sector. Further,
the relative prices pa,ss,t and ps,ss,t are given by the productivity Ba,t , Bm,t , Bs,t , and km,ss,t ,
according to equation (3.16). The relative prices will help to estimate the consumption and
solve the capital stock Kss,t and capital input of the service sector Ks,ss,t . Therefore, when
the technology path is given, the model is able to simulate the labor movements on the
static growth path.14
12The constant return of capital along the economic growth process is supported by the cross-countryexamination by Caselli and Feyrer (2007).
13If Pm,t = 1, pi,t =Pi,tPm,t
= Pi,t , i ∈{a, s}.14One drawback of this approach is that the analysis of steady states might underestimate the employment
in manufacturing, since investment is restricted to replacing capital depreciation. However, in the U.S. data,the historical investment output ratio is roughly constant over the period. And our calibrated models quan-titatively fits the investment output ratio in the data. Further, even with this possible downward bias, thechallenge to the model is still the rapid decline of manufacturing shares. Therefore, it does not effect theconclusion.
33
3.4.3 Trade-balance-augmented Model
The previous section dealt with a closed economy. Hereafter, we will introduce the trade
balance effect into the model. The trade factors are considered as exogenous external sup-
ply15 to the economy.
Since the nominal trade balances reported in the data are not comparable with the real
sectoral net exports in the model, we have to transform the information of the data into the
model. The link we choose is the trade balance/GDP ratio, which can be calculated from
the data as follows
µi,t =nxi,t
gd pt, (3.23)
where tbi,t and gd pt are sectoral trade balances and nominal output in the data, respectively.
The gross domestic output in the model is given by
GDPt = ∑i∈{a,m,s}
Pi,tYi,t , (3.24)
which is a function of {Kt , Ks,t , km,t}.The trade balance16 in the model is determined by
NXi,t = µi,t ·GDPt . (3.25)
Using the market-clearing condition in equation (3.9), following the same algorithm,
we are able to solve the employment shares while the sectoral trade balances/GDP ratio are
fixed to their values in the data.
One potential drawback of this exercise is that it implicitly assumes that the value-
added shares in the data can be quantitatively transformed into the model. Both Buera and
Kaboski (2009) and Herrendorf, Rogerson, and Valentinyi (2014) found that traditional
15We do not want to address the endogenous mechanism that might determine this trade balances, espe-cially the huge trade deficits in the manufacturing sector. Despite the relative price dynamics in the domesticeconomy, a large portion of the net trade position depends on external exogenous sources, such as the termof trade shifts, the foreign currency devaluation, and so on. Therefore, we assume exogenous trade balancesand focus on the response of the domestic labor market.
16In the trade literature, the trade balance position will be endogenously determined by various factors oftrade, such as transportation cost, relative prices, trade barriers, international finance conditions, etc. Thisexogenous assumption in this model is only valid to evaluate the counter-factual response in the domesticlabor market.
34
models have difficulties in matching the similar, but distinctive, trends between employ-
ment shares and value-added shares. However, as part of the robustness check, we show
that this issue is negligible and does not change our main conclusion.
3.5 Calibration
In this section, the model presented above will be calibrated to match the postwar labor
movements and real economic growth in the United States from 1950 to 2005. The labor
allocation over the period is measured by the employment shares in the three sectors.17
Case 1 is our benchmark model, which includes a non-homothetic preference and differ-
ent capital income shares in production functions. The TFP growth rates are kept constant
over the whole period in all sectors, where the manufacturing and service sectors share the
same growth rate as reported by the Bureau of Labor Statistics. We, then, consider differ-
ent technology growth rates in the model, denoted as Case 2. The trade effects are divided
into the inter-sector trade effect and total trade balance effect. In Case 3 model, the trade
balances of agriculture and services are used to calculate the corresponding manufacturing
trade balance that is necessary to keep the total trade balance balanced. Case 4 model will
use data from all sectors, where the trade imbalance effect will be the net change on top of
Case 3.
Table 3.1: Model details
Model # FactorsCase 1 Differential capital shares, non-homothetic utilityCase 2 Higher TFP growth in manufacturingCase 3 Inter-sector trade effectsCase 4 Total trade effects
3.5.1 Parameter Values
The model period is 1 year. The measure of labor input in the model is the sectoral shares
of hours worked. The parameter values to determine are the sector capital intensity, αi; the
17The data has been filtered to focus on low-frequency time series, using the Hodrick–Prescott filter witha smoothing parameter of 100.
35
depreciation rate δ ; the preference parameter, β , θ , wa, wm, Ca, Cs;18 and the time series
of sectoral productivity Bi,t with sectoral TFP growth rates denoted by γi,t .
Multi-factor Productivity Growth
The United States Department of Agriculture has calculated the rate of total factor produc-
tivity growth in agriculture every year from 1948 to 2008, which provides the sequence of
{Ba,t}. The average TFP growth rate, γa, was 1.7 percent during the period from 1950 to
2005, as confirmed by Alvarez-Cuadrado and Poschke (2011).
Case 1 The Bureau of Labor Statistics reported a 1.2 percent TFP growth rate from 1950
to 2005 in the non-agriculture business sector, thus setting both γm and γs to be 1.2 percent.
Cases 2, 3, and 4 The TFP growth rates in the manufacturing and service sectors have
various estimates among different researchers. For example, based on the estimates of
industry-level TFP growth in Jorgenson (1991), the TFP growth rate was about 0.77 per-
cent in the manufacturing and 1.1 percent in the service sector from 1950 to 1970. These
estimates would be too low to explain the 1.5 percent aggregate growth rate in the non-
farm sector over the period, according to the Bureau of Labor Statistics. Therefore, we will
calibrate them jointly in order to match two targets: the average TFP growth rate in the non-
agriculture sector and the average growth rate of real GDP per capita. The corresponding
values are 2.5 percent in the manufacturing and 0.6 percent in the service sector.
Factor Intensities
The income shares of capital and labor are held constant in all three sectors at any moment
in the sample period. For agriculture, the EU KLEMS Growth and Productivity Accounts
estimated the capital income share to be 0.54 in the U.S. agriculture sector,19 which is
also confirmed by Valentinyi and Herrendorf (2008). Therefore, α is set at 0.54. The
manufacturing labor income share, as in Figure 3.2, provides two distinctive patterns: from
1950 to 1970, the labor income share in the manufacturing sector increased slightly with
an average around 0.705, and it has been decreasing monotonically since the early 1970s.
18The intertemporal substitution rate σ is not relevant for the calibration of the static growth path.19The EU KLEMS Growth and Productivity Accounts only cover the post-1977 period.
36
The service labor income share has been relatively stable, remaining at about 0.74 over the
periods. Thus, taking the average, the capital shares in the productivity function are set as
αm = 0.295 and αs = 0.26.
Depreciation Rate
In the model, the capital depreciation reflects the demand of capital for investment. Thus,
we use the investment/capital ratio to match the capital depreciation rate, δ . The Bureau of
Economic Analysis reports a roughly constant investment/capital stock ratio for the United
States at about 6.3 percent on average. It is consistent with the estimate of 6 percent from
McQuinn and Whelan (2007). Therefore, δ is set at 0.063.
Preference
The real consumption share in agriculture converges to wa in the long run. The value-added
share of agriculture goods in consumption was only 5.7 percent in 2009, while the average
value-added share of manufactured goods was about 14.5 percent.20 Since the agriculture
value-added share is continuously decreasing, wa should be less than 0.057, and is set to
0.01.21 And, the consumption share of manufacturing goods, wm, is set to 0.145.
Acemoglu and Guerrieri (2008), Herrendorf, Rogerson, and Valentinyi (2013), and oth-
ers have found the elasticity of substitution θ should be less than unity. I follow Buera and
Kaboski (2009) and set θ at 0.5. As part of the robustness check, various values of θ will
be evaluated in Section 3.6.4. The discount factor, β , is set at 0.97, similar to the value
used in Echevarria (1997).
The other parameters, Ca and Cs, are selected to match the initial employment shares in
1950.
Initial Parameters
The initial efficiency parameters Bi,0 affect the unit of measurement of the three goods. As
usual, these parameters are normalized to one and the units of the three goods are chosen
accordingly.
20These numbers are derived from the national table of the United States in the World Input-OutputDatabase from 1996 to 2009.
21This value is also used by Duarte and Restuccia (2010).
37
The set of parameters used is summarized in Table 3.2. The values of Ca and Cs are
calculated to match the initial labor employment shares in 1950, and the corresponding
values are in Table 3.3, which also summarizes other case specific parameters.
Table 3.2: Common parameters
Parameter Value Sourceβ 0.97 Echevarria (1997)δ 0.063 McQuinn and Whelan (2007) and BEAθ 0.5 Buera and Kaboski (2009)wa 0.01 World Input-Output Databasewm 0.145 World Input-Output Databaseαa 0.54 EU KLEMSαm 0.29 BEA Industry Economic Accountsαs 0.26 BEA Industry Economic Accountsγa 0.017 United States Department of AgricultureCa 0.35 Industry employment share in 1950Cs -0.27 Industry employment share in 1950Bi,0 1 Normalization
Table 3.3: Case-specific parameter values
Parameter Case 1 Case 2-4γm 1.2% 2.5%γs 1.2% 0.6%
3.5.2 Closed Economy Model
This section provides some insights on how well the model fits the data. Starting with a
closed economy, we use the calibrated model to compute the sectoral shares of employment
of the U.S. economy from 1950 to 2005 and compare them with the data series.
In the benchmark (Case 1) model, there are only modest structural changes predicted
by the model (Figure 3.4), which are mainly caused by the non-homothetic preference.
The employment share in manufacturing remains almost constant during the period, slowly
decreasing from 33 percent to 30 percent, while the service employment share increases
from 58 percent to 67.8 percent, mainly from the decline of employment in agriculture,
38
1950 1960 1970 1980 1990 20000
10
20
30
40
50
60
70
80
90
100
Data Employment SharesCase 1 Model (Benchmark)Case 2 Model (Unbalanced TFP)
Agriculture
Manufacturing
Service
Figure 3.4: Closed economic models vs U.S. data
down from 9 percent to just above 2 percent. Notice that even though the calibration only
targets the initial employment share in agriculture in 1950, the model implies a time path
of the equilibrium employment shares in agriculture that is close to the data. However,
it is clear that the above structural transformation cannot explain the trends in the non-
farm sectors, which reported 17.5 percent employment share in the manufacturing and 80.9
percent in services in 2005. One matter worth noting is that the real per capita GDP growth
rate is lower than the data in the benchmark case. According to equation (3.22), the capital
labor ratio in manufacturing is determined by the productivity Bm,t . The TFP growth in
the manufacturing sector not only increases the output at any given input, but also triggers
a capital accumulation process. Therefore, the results above imply that the productivity
growth rate might be underestimated in the benchmark case.
The Case 2 model is meant to explore the scenario when the manufacturing sector has
a relatively higher TFP growth rate. As illustrated in Figure 3.4, the model does a better
job on replicating the sectoral employment shares in the data, showing a steady decline in
the share of manufacturing employment from about 33 percent in 1950 to 25.2 percent in
2005 (17.5 percent in the data), whereas the share of workers in the service sector increases
from about 58 percent to 73.4 percent (80.9 percent in the data). Nevertheless, since 1980,
39
the model predictions have deviated from the data. A significant part of the employment
composition change, roughly a five-percent decline in manufacturing and a simultaneous
rise in services over the last three decades, still lacks a convincing explanation.22 These
calibration results are consistent with the findings of Bah (2008) and Buera and Kaboski
(2009).
3.5.3 Trade-augmented Model
As discussed earlier, persistent trade deficits could contribute to structural changes through
two direct channels: inter-sector trade effect and trade imbalance effect. We will consider
them in turn.
In the Case 3 model, we investigate the factor of inter-sector trade. If the trade sur-
plus in the agriculture and service sectors in the United States reflects comparative ad-
vantages in these sectors, the economy can have a corresponding trade deficit in manu-
facturing. This channel of structural change has been discussed in Yi and Zhang (2010)
and Teignier (2011). We estimate counter-factual manufacturing trade balances that can
keep the economy-wide trade balanced. And we solve for the employment shares, using
these sectoral trade balances as exogenously given. The numerical results of the Case 3
model, as reported in Figure 3.5, show only moderate contribution, compared to the Case 2
model. Numerically, the predicted manufacturing employment share in 2005 decreases by
1 percent to 24 percent, while the service share increases to 74.3 percent.
In the Case 4 model, actual sector trade balance/GDP ratios are used to evaluate the
total contribution of trade on the labor redistribution. Compared to the results in the Case 3
model, the predicted employment share for the manufacturing sector decreases by roughly
5 percent to 19.6 percent, while the employment share for the service sector increases 4.8
percent to 78.8 percent. These estimates lie between the two measures of employment
shares. The predicted manufacturing share (19.6 percent) is lower than the share in terms
of hours worked (20.3 percent in 2005), but higher than the share in terms of the number
of workers (17.5 percent in 2005).
Taking trade factors into account, the calibration exercises have explained a large por-
tion of labor movements in the sample period, where a significant part can be related to22We conduct another numerical exercise in which we want to find the sectoral productivity growth rates
that can fit the employment movements very well. The estimated TFP growth rate in the manufacturing sectoris quite high, γm = 4.5% and γs =−1%.
40
1950 1960 1970 1980 1990 20000
10
20
30
40
50
60
70
80
90
100
Labo
r S
hare
(%
)
Data Employment SharesCase 3 Model (Inter−sector Trade)Case 4 Model (Overall Trade)
Manufacturing
Agriculture
Service
Figure 3.5: Trade-augmented model vs U.S. data
the chronic trade deficits. This result provides some support for the argument that trade
imbalances have a substantial impact on the composition of employment.
3.6 Discussion
3.6.1 Technology Slowdown and Rising Capital Intensity
There are several facts in the data that are worth noting: a slowdown of productivity growth
in the early 1970s and a rising capital income share in manufacturing over the same period.
The recession during the 1970s put an end to the post-World War II economic boom.
The Bureau of Labor Statistics reported a sharp decline of TFP growth in the non-farm
business sector. The annual TFP growth rates dropped from 1.7 percent between 1950
and 1973, to 0.6 percent after 1973. If the slowdown had not been balanced between
the manufacturing and service sectors, it might have affected the structural transformation
process, as we have seen in the Case 2 model presented above.
Interestingly, around the same time, the manufacturing capital income shares stopped
a moderate decline from 1950 to 1973, and started to rise steadily. According to Sachs
41
and Shatz (1994) and Bernard, Jensen, and Schott (2006), the higher income share of cap-
ital in manufacturing is actually one of the consequences of international competition, as
low-skill (possibly more labor-intensive) manufacturing industries are more exposed to
competition.23 Thus, the rise of labor intensity and its impact on labor allocation might be
indirectly linked to trade factors.
To consider the TFP slowdown in 1973, we calculate the sectoral productivity from
1977 to 2005 to be 1.03 percent for the manufacturing sector and 0.5 percent for the service
sector by using the estimate of the EU KLEMS project. This model, denoted as Case 5,
does not account for trade balances and is directly comparable to the Case 2 model.
On top of the TFP slowdown in Case 5, in the Case 6 model, we allow the capital
intensities in the manufacturing sector to vary, which increased from 0.29 in 1970 to 0.47
in 2005.
1950 1960 1970 1980 1990 20000
10
20
30
40
50
60
70
80
90
100
Labo
r S
hare
s (%
)
Data Employment SharesCase 2 ModelCase 5 Model (TFP Slowdown)
Manufacturing
Service
Agriculture
Figure 3.6: Case 5 (TFP slowdown) vs Case 2, with U.S. data
Figure 3.6 illustrates the calibration results of the Case 5 model. As we predicted, the
relatively larger drop of TFP growth in the manufacturing sector leads to a higher employ-
23Another explanation of the capital income share change comes from the limitation of the Cobb-Douglastype production function. Alvarez-Cuadrado, Long, and Poschke (2014) provided a more general discussionon elasticity of substitution and structural change process by using the CES type of production functions.
42
ment share compared to the Case 2 model. Quantitatively, the manufacturing employment
share predicted by the Case 5 model is around 27.4 percent in 2005, 2.2 percent higher than
the 25.2 percent reported by the Case 2 model.
In Case 6, after adding the rising capital share to our numerical exercise, the calibrated
manufacturing employment share returns to 25 percent. Therefore, productivity slowdown
and higher capital share have opposite contributions with equivalent magnitudes. These
two factors do not change any of the above conclusions.
In addition, the Case 6 model can explain an interesting feature in the data. From 1950
to 1979, the output per worker in the manufacturing sector increased at 2.4 percent and
the multifactor productivity in non-farm business grew at 1.46 percent. Since 1980, the
annual progress of multifactor productivity was around 0.75 percent, while the output per
worker in the manufacturing sector increased at 3.8 percent every year. This shows that
per worker output in the manufacturing sector grew relatively slowly during the period of
rapid technology improvement in the 1950s and 1960s, but has increased quickly since
1980, when the TFP growth slowed down. When we take the rising capital intensity in
the manufacturing sector into consideration, we find that industry that is becoming more
capital intensive can increase per worker output through capital deepening. Thus, even
when technology growth has slowed down, the overall output growth can be maintained.
3.6.2 Decomposition of the Structural Transformation
Table 3.4 shows some statistics of both the data and the models. In general, the models
have been able to mimic several key aspects of the U.S. economy.
Table 3.4: Statistics in the data and the models
Statistics, average 1950-2005 Data Case 1 Case 2 Case 3 Case 4Per capita GDP growth gate 2.15% 1.67% 2.15% 2.14% 2.12%Capital to output ratio 3.21 3.20 3.15 3.16 3.156Investment to output ratio 20.2% 19.2% 18.9% 18.9% 18.9%
The analysis in the previous sections has proved that a structural change model in the
open economy context can explain labor movements across sectors, especially the recent
rapid decline in manufacturing employment. On the basis of the different constructions of
43
Table 3.5: Decomposition of the structural transformation in U.S. manufacturing
Model # Net∆ Cumulative∆ SourcesCase 1 3.7 % 3.7 % Differential capital shares, non-homothetic utility24
Case 2 4.8 % 8.5 % Unbalanced TFP growth ratesCase 3 0.7 % 9.2 % Inter-sector trade effectCase 4 5 % 14.2 % Trade imbalance effectData 16 % The decline of employment share from 1950 to 2005
the models, the postwar structural transformation in the United States can be separated into
different sources that have been discussed in the literature, as summarized in Table 3.5.
The key driver that contributes most to structural change is the trade imbalance effect,
which accounts for 5 percentage points in the model. And taking the inter-sector trade
effect into account, which adds another 0.7 percentage points, the trade-related factor can
explain about 5.7 percentage points, or 35.5 percent (5.7 out of 16) of the employment
share decline in the U.S. manufacturing sector. Therefore, international trade has become
the most important factor that contributes to the structural transformation of the postwar
U.S. economy.
Figure 3.7: Relative contributions on structural change
44
The relative contributions of these factors have been evolving over time, as illustrated
in Figure 3.7.25 The traditional motivations, such as the non-homothetic preference and
different capital intensities across sectors, and the unbalanced productivity growth were the
key drivers in the early periods. However, the relative shares have been decreasing since
the late 1960s. The contributions of trade-related factors changed significantly and became
more and more important. Inter-sector trade, most of the time, contributes positively to
the decline of U.S. manufacturing as the trade surplus in the agriculture and service sector
reflect some of the comparative advantages of the U.S. economy. The impact from trade
imbalances provides a more compelling trend, as it turned from being a dragging factor to
one of the most important driving factors to push down manufacturing employment.
These results are in line with the findings of Sachs and Shatz (1994) and Bernard,
Jensen, and Schott (2006). However, because of the identification problem, the causality
relationship during the whole process is unclear. As mentioned by Krugman and Lawrence
(1994), the structural change process, including trade balance deterioration, could come
from the slowdown of the technology change. Therefore, the correlation found in the model
between trade balance and labor movement might be caused by unknown shocks. There
are still many issues that need to be clarified to fully understand the structural change in
the United States, especially the extraordinary decline in the manufacturing sector since the
early 1980s.
3.6.3 Value-added Trends
The structural transformation across sectors can be also measured in terms of value-added
shares. However, it seems that the traditional models have difficulty matching the two
trends simultaneously. Buera and Kaboski (2009) argued that their model exhibits large
deviation between value-added shares and employment shares, and Herrendorf, Rogerson,
and Valentinyi (2014) argued that using common production functions across sectors they
can either connect the production measures to the data in terms of employment shares or
in terms of value-added shares. However, in our model, since the manufacturing sector is
considered to be more capital intensive, the relative price of service will increase as the
country becomes richer.
25The Y axis is the accumulative employment share change in the United States from 1950 to 2005, whichhas been normalized to 1.
45
1950 1960 1970 1980 1990 20000
10
20
30
40
50
60
70
80
90
100
Val
ue−
adde
d S
hare
s (%
)
Data Value−added ShareCase 4 Model (Value−added)
Manufacturing
Service
Agriculture
Figure 3.8: Case 4 model vs U.S. data in terms of value-added shares
Figure 3.8 reports the value-added share of the Case 4 model. Qualitatively, the model,
which is only set to fit the employment share in 1950, makes a plausible prediction for the
trends of value-added shares. Even though we are using a static approach to approximate
the long-run growth path, by using production functions with different capital intensities
across sectors, we can partially capture the change of relative prices.
3.6.4 Robustness
The calibration exercises depend on the assumption of household preferences and the
choice of parameter values. One core parameter worth revisiting is the elasticity of substitu-
tion between the manufacturing and service sectors, denoted by θ . In the main body of the
calibration, we use a relative low elasticity of substitution (θ= 0.5) across industry goods,
following Buera and Kaboski (2009). But Herrendorf, Rogerson, and Valentinyi (2013)
found that a Leontief utility (θ= 0) fits the value-added sectoral consumption data for U.S.
households.26 Therefore, robustness checks on the values of θ , especially a preference
close to the Leontief specification, would be crucial for the calibration.
Table 3.6 summarizes the model (Case 4) predictions with different values of θ and
the elasticity of substitution between manufacturing products and services, and compares
26Buera and Kaboski (2009) also reported that Leontief preference provides a better fit in their model.
46
those results with the employment share change in the data. We keep other parameters
untouched. It shows that a smaller θ leads to larger labor movements across sectors. For
example, the employment share increase in the service sector will be 18 percent for θ =
0.75, 21.2 percent for θ = 0.5, and will reach 23.5 percent if θ = 0.01, which is close
to the Leontief preference. In addition, we break down the employment share change in
the manufacturing sector to identify the relative contributions of different factors when the
preference parameters are adjusted.
Table 3.6: Robustness analysis of the structural change model
Employment Share Case 4 ModelChange in Data θ = 0.75 θ = 0.5 θ = 0.01
Agriculture -7 % -6.9 % -7 % -7 %Manufacturing -16 % -11.2 % -14.2% -16.5 %
Service 23 % 18% 21.2 % 23.5 %
Table 3.7 shows that as the rate of substitution across sectors decreases, the different
growth rates of productivity become more and more important. However, trade factors are
still one of the key drivers behind the structural transformation in the United States, among
which the trade imbalance channel dominates.
Table 3.7: Robustness of relative contributions in manufacturingθ = 0.75 θ = 0.5 θ = 0.01
Preference & capital intensity 29.3% 26.0% 23.8%Unbalanced TFP growth 23.3% 34.0% 43.2%Inter-sector trade effect 7.1% 4.7% 3.5%
Trade imbalance 40.2% 35.3% 29.5%
3.6.5 Model with Only Non-homothetic Preference
The benchmark model, Case 1 model, includes both non-homothetic preference and differ-
ent capital intensities across sectors. If we want to only have non-homothetic preference,
we have to choose different initial parameter values to match the initial employment shares
in 1950. This model is incomparable with other cases. For example, if we assume com-
mon capital intensity in production functions(αA =αM =αS = 0.35), balanced productivity
47
growth, and no trade, the model only predicts a 0.7 percentage decline in the manufacturing
sector. It shows that for a developed country at 1950, the model with only non-homothetic
preference cannot explain a significant portion of the labor movements over the sample
period. This result is consistent with the finding of Swiecki (2013) that the non-homothetic
preference is more relevant for the movement of labor out of agriculture in developing
countries.
3.7 Concluding Remarks
According to Buera and Kaboski (2009), the steep decline in manufacturing employment
shares cannot be explained by traditional theories of structural change. Therefore, in this
paper, we intend to answer the following quantitatively motivated question: how much
could a unified model of structural change with trade factors explain the contraction of the
manufacturing employment shares in the United States?
The first contribution of this chapter is to introduce trade factors to the traditional mod-
els of structural change. International trade provides a channel through which sectoral
expenditures can deviate from the sectoral output, or vice versa. We mainly focus on two
channels, inter-sector trade and trade imbalances.
Second, our model quantifies the roles of different factors on the composition of la-
bor employment, especially the decreasing manufacturing employment share. The results
show that, in addition to traditional explanations, such as a non-homothetic preference and
sector-biased productivity progress, international trade is another key driving force of struc-
tural change. The calibrated models show that about 35.5 percent of the overall share of
employment decrease in American manufacturing from 1950 to 2005 can be linked to trade
factors. We estimate that inter-sector trade makes only a moderate contribution, while trade
imbalances dominate the recent contraction of the manufacturing employment share.
These findings are consistent with those of Sachs and Shatz (1994) and Bernard, Jensen,
and Schott (2006) that international trade have a significant impact on the production sector
of tradable goods: firms either move to more capital-intensive industries or close their
plants sooner because of the competition. The labor market responds accordingly. As a
result, labor moves out of the sectors of tradable goods, such as manufacturing, and into
the non-tradable sectors, such as services.
48
The model and related calibration exercises provide a better understanding on the cur-
rent structural problem in the United States. For example, in our quantitative exercise,
persistent trade deficits can explain 31 percent of the recent contraction of the manufactur-
ing sector, or roughly 5 percent of total employment. As many economist have argued,27
this trade balance position cannot be maintained forever. When the trade deficits shrink,
the U.S. economy will need some of these manufacturing jobs back again. However, this
renaissance of American manufacturing might take a longer time to restore, since a por-
tion of job-specific human capital could have been destroyed during the last two or three
decades. This might be one of the reasons to explain the sluggish recovery from the recent
great recession. In addition, the model shows that countries that have trade deficits will
achieve a slightly lower growth rate, while countries that can maintain a trade surplus can
enjoy a higher rate of economic growth. Although the magnitude of this loss/benefit is not
large, it can accumulate over time.
3.8 Technical Details
Proposition. 3.1 The closed economy with structural change is consistent with balanced
growth if and only if
(a) γi = γ , αi = α , and (Ca,t , Cs,t) 6= 0, ∑i PiCi = 0, the case of Kongsamut, Rebelo, and
Xie (2001);
(b) Ci,t = 0, γi 6= γ ,αi = α , for some i 6= j, thus pi,t 6= p j,t , the case of Ngai and Pis-
sarides (2007).
Proof. (a) Using ∑i PiCi = 0, the budget constraint in equation (3.6) rewrites as
∑i∈{a,m,s}
Pi,t(Ci,t−Ci)+ Pm,tIt = ∑i∈{a,m,s}
Pi,tYi. (3.26)
Plugging the market clear conditions and law of motion for capital to the budget con-
straint,
Kt +δKt +Cm,t + Pa,t(Ca,t−Ca)+ Ps,t(Cs,t−Cs) = Bm,tKαt , (3.27)
27See, for example, Feldstein (2008).
49
or
Kt +δKt +Cm,t + Pa,t(Ca,t−Ca)+ Ps,t(Cs,t−Cs)
B1
1−α
m,t
=
Kt
B1
1−α
m,t
α
. (3.28)
As Bm,t increases at a constant rate γ , the whole economy is able to evolve at a constant
rate, γ
1−α. For more details about this generalized balance growth path, see Kongsamut,
Rebelo, and Xie (2001).
(b) See Ngai and Pissarides (2007) Proposition 4.
Proposition. 3.2 The market equilibrium labor allocation {La,t , Lm,t , Ls,t} is determined
by {Kt , Ks,t , km,t}, namely the aggregate capital stock, the capital input in service sector,
and the capital labor ratio in domestic manufacturing, respectively.
Proof. According to equation (3.7) and (3.14), first get Ls,t =Ks,t
mskm,t, then, Ka,t +Km,t +
Ks,t = Kt can be written as,
makm,tLa,t + km,t(L−La,t−Ks,t
mskm,t) = Kt−Ks,t
Therefore, the labor employment shares across sectors are given by
La,t =Ks,t−Kt + km,t
(L− Ks,t
mskm,t
)km,t(1−ma)
Lm,t = L−La,t−Lm,t (3.29)
Ls,t =Ks,t
mskm,t
which depend on a three-variable set, {Kt , Ks,t , km,t}, the aggregate capital stock, the capital
stock in the service sector, and the capital-labor ratio in domestic manufacturing, respec-
tively.
50
3.9 Data Sources
Share of Employment by Sector
The shares of sectoral hours worked and the price of services relative to manufacturing are
from the Groningen Growth and Development Centre (GGDC) 10-sector and Historical
National Accounts databases28 where the economy is disaggregated into 10 sectors.
We aggregate those sectors into the three sectors used throughout this paper. The agri-
culture sector includes agriculture and fishery; manufacturing includes mining, manufac-
turing, utilities, and construction; and service sector covers the remaining industries. For
the United States, both the employment shares in terms of number of workers and hours
worked are available for the whole sample period. The value-added of each sector is given
in both constant and current prices.
Production Function and Productivity
The Economic Research Service of the United States Department of Agriculture (USDA)
reported agriculture productivity from 1948 to 2009.29 For the the non-agriculture business
sector, the Bureau of Labor Statistics reported multifactor productivity growth rates from
1950 to 1976. And EU KLEMS provides detailed sectoral productivity estimates since
1977.
The sectoral labor/capital income shares are calculated using various releases of the
BEA’s GDP-by-industry accounts, tables in 72SIC, 87SIC, and 02NAICS. The labor in-
come shares are also available as Unit Labor Costs (ULC) in the OECD statistics since
1970. In addition, we refer to the estimates in Valentinyi and Herrendorf (2008).
National Income Accounts and Trade Balances
The real GDP per capita comes from the Penn World Table (version 6.3), while BEA re-
ported the investment to output ratio, and capital to output ratio.
28Data is available at http://www.ggdc.net.29http://www.ers.usda.gov/data-products/agricultural-productivity-in-the-us.aspx
51
Net export of goods and services are reported by the BEA since 1929. Within the
trade of goods, the United Nation Commodity Trade (UN COMTRADE) database provides
estimates from 1961.
52
Chapter 4
Agriculture Modernization andStructural Transformation
4.1 Introduction
The process of economic growth is always associated with a structural transformation,
which is the reallocation of economic activities across different sectors. As we divide the
economy into three broad sectors, three distinct employment patterns emerge: the agri-
culture sector declines; the service sector rises; and the manufacturing sector follows a
hump-shaped pattern, whereby it first expands with the service sector and then declines.
This hump-shaped pattern of employment in the manufacturing sector is a puzzling fea-
ture of structural transformation, since the manufactured goods can perform two different
roles simultaneously: they can be consumed as final goods or they can be used as capital
goods. If we consider manufactured products as consumption goods, in order to achieve the
hump-shaped pattern, we need to assume a low elasticity of substitution across final goods
with unbalanced productivity growth across sectors. This channel is backed by “Baumol’s
cost disease”, which predicts that labor should move in the direction of the sector with low
productivity growth since the costs and prices of this stagnant sector should rise indefi-
nitely. Ngai and Pissarides (2007) formalized this mechanism and provided a theoretical
framework.
In addition, expenditure on capital goods is skewed towards manufactured goods, such
as machinery and building materials. Kongsamut, Rebelo, and Xie (2001) documented that
53
about 90% to 93% of investment goods were produced by the manufacturing sector dur-
ing the period from 1958 to 1987 in the United States. The World Input-Output Database
provides a more detailed picture of the sources of capital goods for forty countries world-
wide.1 In developing countries, about 85% to 92% of investment goods are produced by
the manufacturing sector, while this ratio for developed countries is about 70% to 85%.
For example, in the year 2000, this ratio was 91% for China, India, and Mexico; 86% for
Brazil and Turkey; 85% for Taiwan; 82.5% for Japan; 80.5% for the United States; and
about 70% for France and Sweden.2 Therefore, investment demand is a key component of
the demand for manufactured products. A higher rate of investment will increase the share
of manufactured goods in total demand, and thereby raise the share of manufacturing in
employment and real output.
Empirical observations reveal that investment behavior shows another hump-shaped
pattern during economic growth: first, in low-income countries, on average, the investment
rate increases as income grows; second, for high-income countries, the investment rate
decreases as per capita income increases. Therefore, the evolution of investment should
somehow contribute to the structural transformation, it should especially affect the eco-
nomic activities in the manufacturing sector.
In this chapter, we focus on the second role of the manufacturing sector and turn to
explore the linkage between manufacturing employment share and investment rate. Our
model highlights the importance of agricultural modernization as a central mechanism of
the transition from traditional economy to modern growth, which could generate these
hump-shaped patterns simultaneously. In our model, the traditional agriculture sector re-
lies on a labor-intensive technology that doesn’t improve overtime. Therefore, in order to
satisfy the subsistence level of food consumption, the traditional agriculture sector has to
occupy a large portion of the labor force. In this economy, there also exists a modern agri-
culture technology that uses capital as a key input and has a productivity index improving at
an exogenous rate. After a certain threshold, the modern technology becomes more efficient
than the traditional one and is gradually adopted for agriculture production. This process is
called “agriculture modernization” and would affect capital goods demand (investment) in
1Timmer (2012) provided an overview of the contents, sources, and methods used in compiling the WorldInput-Output Database, which is available online at http://www.wiod.org.
2The declining share of manufactured product in investment might also contribute to the rise of the servicesector. However, this is beyond the scope of this chapter.
54
two ways. First, the adoption of modern technology requires capital inputs, which affects
investment demand directly. Second, this agriculture modernization has an indirect impact,
since it releases excess workers who have to accumulate capital goods to settle down in
other modern sectors. Both channels increase the demand for physical capital goods that
are produced in the manufacturing sector. Both investment rate and manufacturing em-
ployment increase. When the majority of workers in the traditional agriculture sector have
moved into other sectors, the demand for manufactured goods peaks and starts to decrease.
Later, the manufacturing employment share also begins to decrease. Therefore, agriculture
modernization establishes a linkage between these two hump-shaped patterns.
In our model, the modernization of agriculture is an endogenous choice by households,
and we investigate the timing and mechanisms of the transition process. We divide the
process of development into four different stages: traditional stage, mixed stage, convergent
stage, and generalized balanced growth path (GBGP) stage. Unique to our model is the
emphasis on the role of capital accumulation in such a process. Both the manufacturing
employment share and investment rate in our model generate hump-shaped patterns: they
first increase, then decrease and converge to their long-run growth path.
There are a few papers that have discussed the pattern of the investment rate during
structural change. Laitner (2000) observed the rise of the saving rate during economic
development and used structural transformation as an explanation. There are two sectors:
agriculture and manufacturing. For the agricultural sector, land is an important factor of
production. Since the size of farmland is given to be fixed, the benefit from technological
progress and population expansion is represented by the increase in land price, which is not
recorded as savings. For the manufacturing sector, reproducible capital is used as a factor
of production. The stock of capital increases following the technology growth. The capital
accumulation is recognized by the national income account as savings. During structural
change, the size of the agriculture sector decline. As a result, land becomes less important,
while capital becomes more important, and the recorded national saving/investment rate
rises. Therefore, the definition of saving in the national account leads to an increase in sav-
ing rates during economic development. Echevarria (2000) put non-homothetic preference
as the primary factor that causes the investment rate to rise with income level. A country
with a low level of income cannot save/invest much, as it is constrained by the subsistence
demand for food. As it gets richer, the saving rate rises. The simulation result shows that
55
the saving/investment rate in a closed economy increases and converges asymptotically to
a steady state. These two papers can account for the rise in investment rate during devel-
opment, but failed to address the drop in investment rate in higher stages of development.3
Our model owes a major intellectual debt to a burgeoning body of literature that stresses
the important role of a technology switch in the agriculture sector. Hansen and Prescott
(2002) constructed a two-sector model with one single final good to track the transition
out of a stagnant Malthusian economy. They argued that if only traditional land-intensive
technology is profitable to operate, the economy would be trapped in a Malthusian regime.
Because of the exogenous technology growth in the modern sector, the capital-intensive
technology gradually becomes profitable to households and firms. The adoption of modern
technology transfers the economy into a Solow type economy, where income and living
standards continue to improve. Gollin, Parente, and Rogerson (2007) examined the effects
of using three types of agricultural technologies to calibrate the experience of the United
Kingdom over the last 200 years. In addition to the traditional technology, they consider
two modern technologies: one is purely technical with an exogenous technology progress
and does not use capital or manufactured inputs (this approach is used to mimic some
features of the Green Revolution in developing countries); the other one includes capital
as a factor of production. The calibrated model is used to evaluated international income
differences. And they argued that food constraints can delay industrialization. Yang and
Zhu (2013) endogenized the decision of adopting technology in agricultural production,
which is similar to Hansen and Prescott (2002) but in a more general two-sector, two-good
model. They focused on the role played by agricultural modernization in the transition
from stagnation to growth. Instead of using capital as a factor of production, they intro-
duced intermediate goods supplied by the non-agricultural sectors in their modern type of
production function. They argued that development in the non-agricultural sectors has a
limited effect on per capita income if food consumption relies on traditional technology
and occupies a large share of the labor force. After the relative price of manufactured inter-
mediate goods drops below a certain threshold, farmers start to adopt modern technology
and start to enjoy modern growth.
Although each of these papers shares several features with ours, there are major dif-
ferences in the model proposed in this chapter. We are using agriculture modernization
3Echevarria (2000) reported that the saving/investment rate might decrease slightly before approachingthe steady state in models with trade. However, the downward trend is insignificant.
56
to explain the evolution of investment and manufacturing employment during economic
growth. Echevarria (2000) and Laitner (2000) recognized the rise of investment rate during
the industrialization process, but ignored the other half of the coin, the de-industrialization
process. Our four-sector, three-product model is different from the framework of Hansen
and Prescott (2002), which essentially uses two production technologies to produce one
single good, leaving no room to explore the implications of the subsistence food constraint
and the employment pattern for the manufacturing sector. Gollin, Parente, and Rogerson
(2007) evaluated the food problem and the importance of modern agricultural technology
on long-run growth, and included capital as one factor of production in one of their modern
technologies. However, they did not emphasize the role of capital accumulation in such
a structural transformation process. In their calibration excesses for the United Kingdom,
they found that the investment to output ratio increased over time, but they did not report if
their model is capable of predicting de-industrialization at high income levels. In addition,
technology adoption is arbitrarily set rather than endogenously determined by the economic
agent in the model. Similar to us, Yang and Zhu (2013) divided long-run economic devel-
opment into several stages and emphasized the importance of agriculture modernization.
Since they did not include physical capital in their production functions, they left no role
for capital accumulation to play.
The rest of this paper is organized as follows. Section 4.2 documents some stylized
facts for structural change including the difference of agriculture technologies at differ-
ent income levels, the employment pattern in the manufacturing sector, and the investment
shares. Section 4.3 presents the basic structures of the model and characterizes the equi-
librium properties. Section 4.4 explores the theoretical features of the model in each of the
four stages. In section 4.5, we present a numerical example to demonstrate the dynamic
features of this model. Section 4.6 provides some empirical evidence that supports the
mechanism that we propose in this chapter. And section 4.7 concludes this chapter.
4.2 Facts and Evidence
We document the following four facts based on empirical observations. Although none of
them is absolutely new, we believe that the setup of the model is based on the following
evidence.
57
Fact 4.1. In developing countries, the agriculture sector is often the largest and dominant
sector and it accounts for a large fraction of employment.
In 2000, the United Nations Food and Agriculture Organization (FAO) estimated that
agriculture accounted for 55 percent of employment for all developing countries. The
World Development Index organized by the World Bank reported in 2000 that in economies
with a per capita GDP less than one thousand dollars, about 49% of the employment share
is held by the agricultural sector. For many of the countries4 that are often considered to be
the poorest economies on earth, over 80% of workers are employed in agriculture. These
countries must produce the bulk of their own food to satisfy subsistence needs,5 presum-
ably because imports are prohibitively costly and because these countries have few goods
or resources to exchange for food.
Fact 4.2. The structure of the agriculture sector in developing countries is significantly
different from that in developed countries.
The agriculture sector in low-income countries (per capita income less than $500 in
2000) is quite different from that in high-income countries (per capita income higher than
$15,000). We estimate that the output per worker is only $200 in the agriculture sector and
$750 in the manufacturing sector. The same numbers in the rich countries are $14,300 and
$27,800 or 71 and 37 times that of poor countries, respectively. In terms of intermediate
product utilization, the fertilizer consumption of these rich countries is 22 times that of the
poor countries (418 verses 19 kilograms per hectare of arable land).
Recent work on estimating the sectoral capital stock revealed that the cross-country
difference of capital intensity is also larger in agriculture. For example, Priyo (2012) esti-
mated that, in his sample, capital per worker in non-agriculture sectors in the richest 10%
of the countries is 6.6 times that in the poorest 10%, whereas the ratio for the agricultural
sector jumps 30 times to 204.5 between the richest 10% and their poorest counterparts.
Moreover, as Caselli (2005) and Restuccia, Yang, and Zhu (2008) explained, differences
in labor productivity in the non-agricultural sector are much smaller than differences in
agricultural labor productivity.4We only consider agriculture employment shares reported since 2000. Thus these countries include
Burkina Faso, Ethiopia, Madagascar, Mozambique, and Tanzania, which are countries whose per capita GDPis less than 350 international dollars (2000).
5Gollin, Parente, and Rogerson (2007) found that agricultural land and labor are overwhelmingly devotedto food production in most poor economies, specifically to meet the subsistence needs of the population.
58
Based on these observations, it is evident that the agriculture sector in poor countries
possesses a very small capital stock and use very little fertilizer, but employ a large portion
of the labor force. We argue that we should separate this sector from other sectors, including
the modern farming industry, and consider it as a traditional subsistence sector.
Fact 4.3. The employment share in the manufacturing sector exhibits a hump-shaped pat-
tern during economic development.
The hump-shaped pattern of manufacturing employment has been well documented in
the literature.6 For example, Iscan (2010) documented that the manufacturing sector in the
United States employed less than 3% of the labor force around 1810. The employment
share gradually increased to above 10% in the 1840s and peaked right above 30% in the
1950s. After reaching 25-27% in the early 1980s, it began a precipitous decline, with
manufacturing accounting for slightly less than 10% of the workforce in recent years. All
other rich economies have gone through a similar cycle of industrialization followed by
de-industrialization (Herrendorf, Rogerson, and Valentinyi, 2014).
Figure 4.1 plots the historical time series of manufacturing employment shares in 34
countries from 1950 to 2005 based on the Groningen Growth and Development Centre 10-
sector data. The vertical axis is the share of employment, while the horizontal axis is the
log of GDP per capita in international dollars (2005) as reported by the Penn World Table
(PWT version 6.3).7 It shows that the employment shares of the manufacturing sector fol-
low a hump-shaped pattern: they increase at the early period of development, starting from
about 10% of employment; peak above 30%; and decrease thereafter. The solid line is used
to summarize the patterns of structural change in the data, which are calculated by using the
LOWESS (locally weighted scatter-plot smoothing) method. In the literature, linear regres-
sions are also very commonly used to explore the trends of structural change. For exam-
ple, Rowthorn and Ramaswamy (1999) and Rowthorn and Coutts (2004) used a quadratic
function of log per capita income and other factors to account for the change of manufac-
turing employment share, and more recently, Bah (2011) and Herrendorf, Rogerson, and
6Kuznets (1966, 1971, 1973) discussed the industrialization process in which labor leaves the agriculturesector and enters industry and services sectors. Rowthorn and Ramaswamy (1999) and Rowthorn and Coutts(2004) reviewed de-industrialization in the OECD countries. Bah (2011) discussed the paths of structuralchange for different groups of countries. And Herrendorf, Rogerson, and Valentinyi (2014) documented thetrend of employment shares using several different data sources.
7Data sources are listed in section 4.9.
59
Valentinyi (2014) regressed a cubic function to summarize these patterns. However, un-
necessary specification of regression function might generate implausible estimates. The
non-parametric regression method does not request such specification and is very flexible
to show the trajectory in the data.
Fact 4.4. During the process of development, the investment rate first increases with income
and then gradually decreases, following a hump-shaped pattern.
The pattern of investment rates is not as obvious as the pattern of employment shares,
since investment is more volatile and is directly affected by business cycles. Figure 4.2
reveals the investment rates across countries from 1960 to 2012 that were documented
by the World Bank. The solid line represents the derived trend for the investment rate at
different income level, which exhibits a hump-shaped pattern.
In order to be more specific, we investigate the long-term trend of investment rate in a
set of countries. Kuznets (1966, Table 5.5) documented the investment rate over a period
of approximately a century (1860–1960 in most cases), and the World Development Index
provides the investment shares measured by fixed capital formation since 1960. The ratio
of net investment to output evolved in Australia from 12% to 30% before hitting 22%; it
evolved in Denmark and Italy from 5% to more than 25% in the 1960s before dropping
to 20% in the 2000s, and in Canada from 7% to 25% and down to 20%; in Japan and
Korea, it evolved from 6% to 36% and then 23%, and from 6% to 40% and down to 30%,
respectively.
Figure 4.3 and Figure 4.4 display the pattern of investment rate during economic de-
velopment for seven Asian countries: Indonesia, India, Japan, Korea, Malaysia, Singapore,
and Thailand. The investment rate firstly increases as income growth peaks at a mid-income
level, and decreases thereafter. This pattern is more distinct in countries that have been able
to achieve sustained growth, such as Korea, Japan, Malaysia, Singapore, and Thailand.
4.3 The Model
We construct a four-sector model that produces three types of consumption goods. The
four sectors are traditional agriculture, modern agriculture, manufacturing, and services,
indexed by subscript 0 to 3. In order to maintain a structure that is as close as possible to
60
.1.2
.3.4
.5S
hare
in to
tal e
mpl
oym
ent
6 7 8 9 10 11Log of GDP per capita (2005 international $)
Figure 4.1: Manufacturing employment shares in 34 countriesSource: GGDC10-sector database, PWT6.3, and author’s calculations.
010
2030
4050
Inve
stm
ent r
ate(
%)
4 6 8 10 12Log of GDP per capita (2005 international $)
Data point Lowess trend
Figure 4.2: Investment rate across income and countrySource: World Development Index and author’s calculations.
61
1020
3040
50In
vest
men
t rat
e(%
)
6 7 8 9 10 11
Log of GDP per capita (2005 international $)
Indonesia IndiaJapan Korea
Figure 4.3: Investment rates in Indonesia, India, Japan, and Korea
1020
3040
50In
vest
men
t rat
e(%
)
7 8 9 10 116
Log of GDP per capita (2005 international $)
Malaysia SingaporeThailand
Figure 4.4: Investment rates in Malaysia, Singapore, and ThailandSource: World Development Index and author’s calculations.
62
standard growth models with structural change,8 we abstract from the presence of land and
the presence of international trade.9
4.3.1 Economic Environment
Preference
The economy is populated by an infinitely lived representative family. For simplicity, we
hold family size constant and normalized to one. Since each member of the household
inelastically provides one unit of labor to the market every period, we also normalize the
aggregate labor supply to one. Therefore, the labor movements across sectors are equivalent
to the time allocation of the representative agent.
We assume that preferences are time separable and include different income elasticities
in our utility specification:
U(Ci,t) =
C1,t if C1,t < C1,
C1 + γ logC2,t +(1− γ) log(C3,t +C3), if C1,t > C1,(4.1)
where C1 > 0 is a subsistence level of agricultural consumption that embeds our version of
Engel’s law. This utility function is very similar to the one used in Kongsamut, Rebelo, and
Xie (2001), except that we impose a more restrictive condition on agriculture consump-
tion that is constrained by an upper bound, C1.10 Households with a low living standard
only care about agricultural consumption, while households with a high standard of living
would become satiated with C1,t = C1 and devote their remaining expenditures exclusively
to goods from other sectors. C3 6 0 can be viewed as representing home-produced services.
Lifetime utility is given by∞
∑t=0
βtU(Ci,t), (4.2)
8For example, Kongsamut, Rebelo, and Xie (2001) used a similar model without the modernization of theagriculture sector.
9Food imports and food aid are not a major source of food at the macro level for poor countries. Usingthe United Nations Food and Agriculture Organization (FAO) data, Gollin, Parente, and Rogerson (2007)claimed that net imports of food supplied around 5% of total calorie consumption in 2000 for all low-incomecountries. They concluded that it is reasonable to view most economies as closed from the perspective oftrade in food. Therefore, most of the resources in agriculture are used domestically to meet domestic foodneeds.
10Laitner (2000) and Gollin, Parente, and Rogerson (2007) made similar assumptions in their two-sectormodels.
63
where β is the subjective time discount factor.
The budget constraint of the family is given by
∑i∈{0,1,3}
Pi,tYi,t +P2,t(C2,t + It) = wt + rtKt . (4.3)
Technology
There are two types of technologies that are potentially available for farm production. Tra-
ditional technology uses labor as the only input11 with a productivity index B0,t :
Y0,t = B0,tN0,t . (4.4)
Modern technology uses both labor and capital, which is similar to the other sectors:
Yi,t = Bi,t (φi,tKt)α (XtNi,t)
1−α , i = 1,2,3, (4.5)
where Bi,t and i ∈ {0,1,2,3} are relative productivity indexes. For simplicity of analysis,
we assume Bi,t is time invariant, Bi,t = Bi, and set B2,t ≡ 1. φi,t represents the capital
allocation for sector i at time t. And Ni,t are labor inputs. One thing worth noting is that
the labor employment of the agriculture sector is the sum of both traditional and modern
agriculture sectors, NA,t = N0,t +N1,t . Finally, variable Xt denotes the level of technological
progress, which is assumed to be labor augmenting and to increase at an exogenous rate g,
Xt+1
Xt= 1+g, and Xt > 0, g > 0. (4.6)
As shown in the household preference, if C1B0
> 1, only the traditional agriculture sector
exists. This economy will struggle to survive. However, a more interesting scenario would
include all three types of consumption goods, thus we make the following assumption.
Assumption. 4.1. C1B0
< 1.
Since the production functions exhibit constant returns to scale, we assume, for analyt-
ical convenience, that there is just one competitive firm operating in each sector. Given a
11Land is a key input in farming. However, since we have ignored population growth, quantity of arableland would be constant all the time.
64
wage rate (wt) and a capital rental rate (rt), the firm in sector i and i ∈ {0,1,2,3} solves
the following problem:
max{PiYi−wtNi,t− rtφi,tKt} , (4.7)
subject to the production functions above. Given δ as the depreciation rate, the capital
accumulation is usual,
Kt+1 = (1−δ )Kt + It .
If we let yi,t =Yi,t
XtNi,tand ki,t =
φi,tNi,t
KtXt
, equation (4.5) can be rewritten as
yi,t = Bi,tkαi,t , i = 1,2,3. (4.8)
Since capital and labor are freely mobile, an efficient allocation requires that the
marginal rate of transformation be equated across all production sectors, which implies
φi,t
Ni,t=
11−N0,t
, (4.9)
ki,t =Kt
1−N0,t≡ kt . (4.10)
The relative prices, pi,t , are determined by the relative productivity and capital income
shares, such as
p0,t =P0,t
P2,t=
B2
B0(1−α)kα
t Xt ,
pi =Pi,t
P2,t=
B2
Bi, i ∈ 1,2,3. (4.11)
Using these relative prices, the resource constraint of these two modern sectors is given
by
C2,t + It + p1Y1,t + p3Y3,t = B2 (Kt)α [(1−N0,t)Xt ]
1−α . (4.12)
4.3.2 Market Equilibrium
Definition 4.1. A competitive equilibrium is a sequence of relative prices {p0,t}t>0, factor
prices {wt , rt}t>0, household consumption {Ct(Ci,t)}t>0, labor allocations {Ni,t}t>0, capital
allocations {φi,t}t>0, and capital stock {Kt}t>0, such that the followings is true:
65
(i) Given the sequence of prices, firms employ labor and capital to solve the allocation
problem specified in equation (4.7);
(ii) Given the sequence of prices, the household maximizes equation (4.2) subject to
budget constraint, equation (4.3);
(iii) All markets clear:
Y0,t +Y1,t = C1,
Y2,t− It =C2,t ,
Y3,t =C3,t ,
∑i∈{0,1,2,3}
Ni,t = 1,
∑i∈{1,2,3}
φi,t = 1.
The competitive equilibrium for this economy characterizes the optimal allocation of
consumption across sectorsp3(C3,t +C3)
C2,t=
1− γ
γ, (4.13)
and the Euler equation is given by
C2,t+1
C2,t= β (rt+1 +1−δ ), (4.14)
where capital rental rate
rt = αB2kα−1t . (4.15)
4.4 Four Stages of Economic Growth
The following proposition summarizes the conditions of technology adoption in the agri-
culture sector.
Proposition 4.1. If we let Zt =(
B0(1−α)B1
) 1α
X− 1
α
t , in agricultural production, the firm
1) uses only traditional technology, if kt < Zt ;
2) uses only modern technology, if kt > Zt ;
3) and uses a mixed combination, if kt = Zt .
66
Proof. See section 4.8.
We assume X0 > 0 is small enough at the beginning of the analysis to ensure that the
traditional economy is feasible.12
Proposition 4.1 suggests that long-term economic growth can be divided into at least
three stages. In the following definition, we would like to treat the economic growth as a
four-stage process.
Definition 4.2. Four stages of economy growth.
Traditional Economy: agriculture production only uses traditional technology.
Mixed Economy: both traditional and modern technologies are equally efficient, agri-
culture production starts to adopt modern technology.
Convergent Economy: only modern technology exists in agricultural production, the
economy converges to a generalized balanced growth path through a capital accumulation
process.
GBGP Economy: the economy evolves along a generalized balanced growth path.
In the rest of this section, these four stages will be discussed in turn.
4.4.1 GBGP Economy
We start with the last stage, the fourth stage, where this economy performs in a way that
is close to the standard growth model. We will show that under certain assumptions, this
economy can grow along the generalized balanced growth path (GBGP), which is defined
by Kongsamut, Rebelo, and Xie (2001) as follows.
Definition 4.3. A generalized balanced growth path is a trajectory with a constant real
interest rate.
In addition, we make the following assumption to ensure the existence of a generalized
balanced growth path.13
12In order to ensure a positive production in the service sector all the time, X0 has to satisfy
X0 >B1B2
B23
γ
1− γ
C1[B2kα
0 − k0 (g+δ )](1− C1
B0).
13See Kongsamut, Rebelo, and Xie (2001) for more details.
67
Assumption. 4.2. C1C3
= B1B3
.
Proposition 4.2. Whenever assumption 4.2 holds, a generalized balanced growth path
exists. Relative prices, aggregate labor income share, and the growth rate of output and
capital are constant. The employment share declines in agriculture, rises in services, and
remains stable in manufacturing. The capital rental rate and capital/labor ratio are given
by
r =1+g
β+δ −1. (4.16)
k =
(αB2
r
) 11−α
(4.17)
Proof. See section 4.8.
The moment that the economy reaches its generalized balanced growth path is denoted
by G. Since the total demand of agriculture product is given by C1, the agriculture employ-
ment is
N1,t =C1
B1kαt Xt
, (4.18)
at time G, N1,G = C1B1kα XG
.
Similar to the result of Kongsamut, Rebelo, and Xie (2001), the dynamic reallocation
of labor across sectors is given by
N1,t+1−N1,t = − g1+g
C1
B1kαXt, (4.19)
N2,t+1−N2,t = 0, (4.20)
N1,t+1−N1,t =g
1+gC3
B3kαXt. (4.21)
Since N2,t is constant, N2,t = N2,G = γ + 1−γ
B2(g+δ )k. These equations show that along
the generalized balanced growth path, the share of labor in agriculture continues to decline,
the share in manufacturing remains constant, and the share in services expands. In the long
run, these rates converge to zero, as Xt continues to grow.
68
4.4.2 Traditional Economy
When only traditional technology is operated in the agriculture sector, the economy is in
the traditional stage. According to proposition 4.1, kt < Zt should be satisfied to ensure that
the traditional production technology is more cost-efficient than the modern technology in
food production.
The share of workers employed in the agriculture sector remains constant through the
traditional stage, such that
N0 =C1
B0. (4.22)
Since no firms use modern agriculture technology to produce outputs, the rest of labor,
1− N0, is employed by the manufacturing sector and the service sector. In addition, as we
assume the traditional agriculture sector only uses labor as inputs, the value-added share of
the agriculture sector would be lower than the employment share. 14
The following descriptions summarize key characteristics of this traditional economy.
The agriculture sector employs a large portion of the labor force to use traditional tech-
nology to satisfy the subsistence food demand. The value-added share of output of this
traditional agriculture sector is less than the employment share of workers. There is no
sign of industrialization in which workers leave the agriculture sector to join the modern
sectors.
4.4.3 Mixed Economy
Between the traditional economy and the GBGP economy, there are two interesting stages
that contain complex dynamic features. We start with the mixed economy, where a combi-
nation of traditional and modern agriculture technologies is used.
Starting with an economy in the traditional stage, as long as the exogenous technologi-
cal progress, Xt , continues to grow, the relative price of output produced by the traditional
agriculture technology rises correspondingly. A time will eventually come at which the
equality condition in proposition 4.1 holds and farmers start to adopt the modern tech-
nology for agricultural production. At that point, marked by subscript M, the economy
14As we assume C1B0
< 1, the other two sectors, manufacturing and services, will employ 1−N0. Given wage
rate wt , the value added per worker in the traditional agriculture sector is v0,t =p0,tC1
N0=B2 (1−α)kα
t Xt , whilethe value added per worker in the modern sectors is vi,t = B2kα
t Xt .
69
enters the mixed stage, since both technologies are operated simultaneously. We have
ZM =(
B0(1−α)XMB1
) 1α
= kM. Thus, continued industrial productivity growth, or a persis-
tent increase in the relative price of traditional agriculture products, eventually triggers the
transition from traditional agriculture production to modern agriculture production.
Throughout the duration of the mixed economy, the equality condition in proposition
4.1 has to be maintained, which determines the evolution of the capital/labor ratio, as char-
acterized in the following proposition.
Proposition 4.3. During the transition process of the mixed economy, for any time t > M,
if N0,t > 0, N1,t > 0, the capital/labor ratio is given by
kt =
[B0
B1(1−α)Xt
] 1α
, (4.23)
where kt satisfies kt =kt−1
(1+g)1/α< kt−1 6 kM.
Proof. Since both types of technology share the same relative price in the mixed economy,
for t > M, p0,t = p1 gives kt =[
B0B1(1−α)Xt
] 1α , where kt < kt−1 as Xt > Xt−1.15
Proposition 4.3 suggests that because the employment adjustment in the traditional agri-
culture cannot be completed immediately, the capital/labor ratio decreases. New workers
who leave the traditional agriculture demand capital goods to start. In addition, according
to equation (4.15), the capital rental rate would increase correspondingly.
Using the optimal consumption allocation, equation (4.13), and assumption 4.4.1, the
aggregate consumption is a function of C2,t , such as
p1C1 +C2,t + p3C3,t = C2,t + p3(C3,t +C3)
=C2,t
γ. (4.24)
Proposition 4.4 summarizes some dynamic features of employment share movements
across sectors.15With certain parameter values, for example, Nt is very small or g is large enough, the stage of mixed
economy can last less than one period, meaning that equation (4.23) does not hold even for kM+1. However,this issue is only caused by the modeling approach of discrete time with a fixed time interval. We can changethe unit of time interval, or rewrite these equations in continuous time, to deal with this problem. If theequation of N0,t is differentiable at any time t, and N0,M > 0, it will take time tM > 0 before N0,t reaches 0,during which equation (4.23) holds with Xt = g, and kt =− g
α.
70
Proposition 4.4. The movements of employment shares in the mixed economy exhibit the
following properties:
1) Total employment shares used to produce agriculture goods start to decline;
2) The size of the traditional agriculture sector, in terms of employment, is given by
G(N0,t+1)
G(N0,t)= β (αB2kα−1
t +1−δ ), (4.25)
where kt is given by equation (4.23) and G(N0,t+1) =C2,t satisfies
G(N0,t+1) ≡ −γ
[1−N0,t+1
(1+g)1−α
α
− (1−δ )(1−N0,t)
]ktXt
+γB2(1−N0,t)kαt Xt ; (4.26)
3) The employment shares in the manufacturing and service sectors are given by
N2,t = γ(1−N0,t)+1− γ
B2
[1−N0,t+1
(1+g)1−α
α
− (1−δ )(1−N0,t)
]k1−α
t , (4.27)
N3,t =1
B3kαt Xt
[1− γ
γ
G(N0,t+1)
p3−C3
]. (4.28)
Proof. See section 4.8.
Unfortunately, proposition 4.4 cannot make clear predictions on the movements of the
manufacturing employment share, which is the key variable that we care about most. How-
ever, based on the mechanism described in this stage, the switch of agriculture production
from traditional technology into modern technology causes a rapid decline of the agri-
culture employment share that should be shared by the manufacturing and the service
sectors. Equation (4.27) indicates that manufacturing employment has two components
on the right-hand side. The first component would increase as N0,t drops to zero. The
second component is associated with the demand for investment in this economy. There
are two opposite factors, k1−αt decreases since kt drops with Xt , while the direction for
(1−N0,t)(1
(1+g)1−α
α
−1+δ )− ∆N0,t+1
(1+g)1−α
α
is unpredictable. Because the lack of capital in this
stage drags down the capital/labor ratio to maintain the relative price for agriculture prod-
71
ucts, we argue that the second component in equation (4.27) should, in general, increase
with 1−N0,t . The numerical example in section 4.5 roughly confirms this prediction.16
Finally, we would like to show that the length of this mixed stage is finite, meaning that
the technology adoption process will complete and move on to the next stage. The reason
that the economy has to undergo the mixed stage is the adoption of modern technology
in the agriculture sector can not complete instantly, since both the technology adoption
and the release of worker to other sectors demand capital goods which has to be produced
gradually. Therefore, the capital-labor ratio represents the threshold capital requirement for
agriculture modernization and structural change. As we have shown in proposition 4.3 that
the capital/labor ratio decreases continuously in the mixed stage, meaning that it becomes
easier to adopt modern technology. Therefore, it will drive the economy to approach the
end of this mixed stage.
4.4.4 Convergent Economy
At the end of the mixed stage, the employment share in the traditional sector reaches zero.
Traditional technology becomes obsolete and all economic activities take place in modern
sectors. We claim that at this very moment, which is marked by subscript C, this economy
enters the era of a convergent stage with N0,C = 0. According to proposition 4.3, in the
mixed economy stage, the capital/labor ratio has been decreasing over time, thus kC < kM.
Therefore, we impose the following assumption that the capital/labor ratio at time C, kC is
less than k.
Assumption. 4.3. At moment C, kC < k.
Assumption 4.3, which seems a little arbitrary, has economic intuitions behind it. If
we assume kC > k, since kM > kC, kM is strictly larger than k, which implies rM < r. This
result is counter-intuitive, as on average the real interest rate is higher in countries with
lower incomes.17
Using the aggregate consumption, equation (4.24), we let ct =c2,tγ
=C2,tγXt
. And the
dynamic features of our model in this convergent stage are similar to a standard Ram-
sey–Cass–Koopmans growth model with a saddle path that converges to the steady states16See section 4.5.5 and Figure 4.12 for more details.17The World Development Index shows that the average real interest rate decreased as income level in-
creased in 2005.
72
with ct = kt = 0. The two key equations, therefore, are given by
ct+1
ct= β (αB2kα−1
t+1 +1−δ ), (4.29)
kt+1 =B2kα
t +(1−δ )kt− ct
1+g. (4.30)
The Euler equation implies that total consumption will increase at a rate higher than
g, for kt < k. And on such a saddle path, both kt and ct have to increase. However, as
kt approaches k, the growth rate of ct decreases and converges to g. In section 4.5, we
construct a numerical example to illustrate the dynamic features of our model. Figure 4.5
demonstrates the path of kt through the four stages. And Figure 4.11 illustrates the inter-
action between kt and ct , which provides the dynamic paths for both mixed and convergent
stages.
Sectoral employment shares, in this convergent stage, are given by
N0,t = 0,
N1,t =C1
B1kαt Xt
,
N2,t = γ +1− γ
B2
[(1+g)
kt+1
kαt− (1−δ )k1−α
t
], (4.31)
N3,t = 1−N1,t−N2,t .
The equation for N1,t shows that the agriculture employment share decreases as it is on
the generalized balanced growth path. The following proposition shows that manufacturing
employment share decreases in the convergent stage.
Proposition 4.5. In the convergent stage, the employment share of the manufacturing sec-
tor decreases. If kt converges along the saddle path to k, the manufacturing employment
share also goes to the size on the generalized growth path.
Proof. See section 4.8.
The main dynamic features of our model on sectoral employment shares, as discussed
above, are summarized by Table 4.1, where “TA” and “MA” represent “traditional agri-
culture” and “modern agriculture”, and “A”, “M”, and “S” stand for the three aggregate
73
sectors. We use “+”, “−”, “Const.”, and “0” to indicate if the parameter would increase,
decrease, remain constant, or remain at zero. If the trend of the variable is not clearly
predictable, we leave it blank.
Table 4.1: Summary of the key variable movements
StagesSectoral employment
kt InvestmentTA MA A M S
Traditional Const. 0 Const.Mixed − + − +∗ + − +#
Convergent 0 − − − + + −GBGP 0 − − Const. + Const. Const.
* Trend of manufacturing employment: we expect N2,t to increase in the mixed stage andreach its peak right before entering the convergent stage.# The investment rate first increases in the mixed stage. As most labor has left the tradi-tional agriculture sector, the investment rate begins to decrease.
Table 4.1 indicates that the agriculture employment share (both traditional and modern
agriculture) is constant in the traditional stage and continues to shrink since the mixed
stage, while the service sector expands. The size of the manufacturing sector is more
complicated to determine. However, based on our analysis and economic intuition, we
expect manufacturing employment to firstly increase in the mixed stage, then decrease in
the convergent stage, and eventually reach the steady state on the generalized balanced
growth path. Therefore, it implies a hump-shaped trend of manufacturing employment
during the structural transformation process. The peak moment is expected to be close to
the end of the mixed stage, since the size of the traditional agriculture approaches zero.
Although the main focus of this chapter is theoretical, in next section, we start with a
numerical example to illustrate the relevance of the mechanism highlighted by the model.
4.5 A Numerical Example
The structural change arises from a combination of multiple forces, of which the agriculture
modernization is only one. In addition, restrictive assumptions have been made to assure
the existence of the generalized balanced growth path in the long run. Therefore, our model
might not be flexible enough to replicate the actual patterns of structural transformation.
74
In this section, our goal is to numerically illustrate some key features of this model.
Computationally, we exploit the fact that at the limit the economy converges to the gener-
alized balanced growth path. Therefore, the full transition path can be simulated using a
backward induction algorithm.
Taking the initial size of the traditional agriculture sector, the values of preference pa-
rameters, and the growth rate of technology, we can compute the steady state on the general
balanced growth path. Next, we employ a shooting algorithm in which only a guess for the
value of kC is needed to compute the entire path of allocations for the economy, where C
represents the moment when the economy enters the convergent stage.
Given the status of the generalized balanced growth path and initial agriculture employ-
ment, N0, for a wide range of kC that satisfies certain feasibility conditions, the model can
generate a transition path for this economy. In short, with limited information, the transi-
tion dynamic path is not unique. In order to pin down certain kC, we have to impose further
boundary conditions, for example, the initial capital/labor ratio k0. We will discuss this
issue in section 4.5.3.
4.5.1 Parameter Values
We consider a sample economy that is characterized by the parameters in Table 4.2. Pro-
duction parameter, Bi, is normalized to 1.18 The manufacturing consumption share, γ , is
set at 0.15, which is consistent with a relatively low expenditure share on manufacturing
products in the long run. In several developed countries, the manufacturing consumption
shares are already lower than 15%. For example, in the United States, the manufacturing
products only consisted of about 14% to 15% of total consumption between 1996 and 2009.
In Japan, this ratio was between 12.9% and 14.2% over the same period.19 The subsistence
demand for food, C1, is set at 0.5 in order to match a initial agriculture employment share
at 50%. C3 is also set at 0.5, according to assumption 4.4.1. The household discount factor,
β , is set at 0.965, which is a typical value within the range of 0.96 to 0.98 that has been
commonly used in the literature.20 The capital income share is set at 0.5, which is higher
18These parameters only determine the relative price across sectors.19These numbers are calculated by the author using the World Input-Output database by Timmer (2012).20Echevarria (1997) used 0.9743 as the discount factor, and Gollin, Parente, and Rogerson (2007) used
0.96 in their calibration excessive.
75
than the estimate of Gollin (2002).21 However, the capital income share is a key parameter
to trigger the rapid decline of agriculture employment shares during the mixed economy
stage. In addition, a relatively high capital intensity helps to explain the size of the decline.
The role of this parameter will be discussed in more detail. The capital depreciation rate is
set to be 0.06, which is consistent with the estimate of McQuinn and Whelan (2007) on the
U.S. economy. The last component is the exogenous technology progress, which is set to
grow at 0.01.
Table 4.2: Calibration parameters
Parameter Value Comments/observationsPreference parametersγ Manufacturing consumption .15C1 Subsistence term .5 Initial agriculture employment at 50%C3 Home service production .5 Assumption 4.4.1β Discount factor .965 Real interest rate around 5%
Traditional agricultural sectorB0 Relative productivity 1 NormalizationN0 Initial employment share .50 Initial agriculture employment at 50%
Modern sector parametersα Capital income share .50g Exogenous technology growth .01δ Depreciation rate .06 Estimate of depreciation rate as in
McQuinn and Whelan (2007)B1 Relative productivity 1 NormalizationB2 Relative productivity 1 NormalizationB3 Relative productivity 1 Normalization
4.5.2 Numerical Results
Figure 4.5 reports the dynamic path of the capital/labor ratios. The solid line represents
the efficient labor adjusted capital/labor ratio, which is the key variable in this model. The
numerical simulation result confirms the predictions from the model in the previous section.
It implies that if the economy is expecting such an industrialization process, it would start
21Gollin (2002) estimated that the labor income shares across countries are within a range of 0.65 to 0.8.
76
M C G t
K
i,t/(X
t N
i,t)
Ki,t
/Ni,t
Mixed economy ConvergentTraditional GBGP
Figure 4.5: Capital/labor ratio
to accumulate capital before it enters the mixed economy. Then, the capital/labor ratio will
fall since labor leaves the traditional sector for modern sectors. As the transition completes,
the capital labor ration increases and converges to its generalized balanced growth path.
The per capita capital stock, Ki,tNi,t
, is represented by the dash line and exhibits a similar trend
as the capital/labor ratio but includes a time trend.
One thing worth noting is that the capital/labor ratio we used in the model is different
from the capital stock per capita that has been used in the growth literature. The capi-
tal/labor ratio in the model measure the capital intensity in the modern sector. Although
this capital/labor ratio might decrease in the mixed stage, the overall capital stock per capita
might still increase.
Along the capital/labor ratio path, we can derive the real interest rate (capital rental
rate) using equation (4.15), which determines the intertemporal consumption decision, ac-
cording to the Euler equation of consumption, as shown in equation (4.14). Then, we can
calculate the investment share in this sample economy, as shown in Figure 4.6. The hump-
shaped pattern for investment is consistent with the observation for the emerging economies
summarized in section 4.2.
The simulation also reports the growth rate of this economy, as illustrated in Figure
4.7. In general, the output growth rate exhibits a hump-shaped pattern. In the traditional
77
M C G t6
11
16
20
Mixed economy ConvergentTraditional GBGP
Figure 4.6: Investment rate (%)
M C G t
Mixed economy ConvergentTraditional GBGP
Figure 4.7: Output growth
78
stage, as the forthcoming industrialization is anticipated, the growth rate increases. As the
economy starts to modernize its agriculture production, the growth rate first experiences a
fall and then gradually increases and peaks during the mixed stage. For the rest of the mixed
stage and the full convergent stage, this output growth rate continues to fall and converges
to its long-run level along the generalized growth path. This pattern of economic growth
rate is qualitatively consistent with empirical evidence, for example, according to Table 9
in Ros (2001), over the period of 1965 to 1997, the economic growth rate of low-income
countries was between 2.6% and 3.1%, that of high-income countries was about 3.4% to
3.5%, while that of middle-income countries was about 4.5%.22
Next, we turn to look at the agriculture employment shares of the traditional sector,
the modern sector, and the aggregate share. As illustrated in Figure 4.8, in the traditional
agriculture stage, because of the subsistence food demand, traditional agriculture employ-
ment is stagnant and occupies a significant portion of the labor force. As the economy
enters the mixed stage, traditional technology is gradually replaced by modern technology,
meanwhile, the aggregate employment of the agriculture starts to decline. At the end of the
mixed stage, only the modern agriculture continues to operate and its employment share
will decrease further by following the exogenous technology progress.
Finally, Figure 4.9 summarizes the movements of sectoral employment in the sample
economy. In the traditional stage, 0 6 t 6 M, the manufacturing sector starts to increase
since households anticipate rapid industrialization in the near future, while the agricultural
employment occupies a large share (50% of total employment) and remains unchanged.
After moment M, the economy enters the mixed stage, agriculture modernization starts,
and the employment share of the agriculture decreases rapidly. At the same time, the sizes
of both the service sector and the manufacturing sector enlarge at similar rates. At mo-
ment C, traditional agriculture production becomes obsolete and is replaced by modern
technology. The employment share of the manufacturing sector reaches its peak and starts
to decline and converge to its long-run steady-state level. Therefore, in the mixed econ-
omy stage and the convergent stage, manufacturing employment exhibits a hump-shaped
pattern, which is a puzzling feature of structural change as discussed in section 4.2. In
the long run, the economy will evolve along the generalized balanced growth path as pro-
22Christiano (1989) and Easterly (1994) obtained a similar hump shape for the growth rate over timeseries. Easterly (1994) and Echevarria (1997) found a hump-shaped relationship between growth rates andinitial income.
79
M C G t0
10
20
30
40
50
60
Traditional Agriculture N0,t
Modern Agriculture N1,t
Agriculture Total Na,t
Mixed economy ConvergentTraditional GBGP
Figure 4.8: Agriculture employment shares (%)
M C G t15
25
35
45
55
Mixed economy ConvergentTraditional GBGP
Manufacturing
AgricultureService
Figure 4.9: Employment shares of the three sectors (%)
80
posed by Kongsamut, Rebelo, and Xie (2001), where the employment share declines in
agriculture, rises in services, and is stable in manufacturing.
Comparing manufacturing employment shares with the movements of investment rates
(Figure 4.6), each of these two variables shows a hump-shaped pattern and the investment
rate peaks early.
4.5.3 Uniqueness
The numerical exercise, in addition, reveals that the backward induction method has a
drawback: the solution to our model might not be unique if we only have the information
on the generalized balanced growth path.
In the traditional stage, even though the model can separate the traditional agriculture
sector from the modern sectors, the economy in the traditional stage might not be able
to converge to a steady state. As a result, given k on the balanced growth path, we lack
a second boundary condition to close the system. Even after fixing N0, the size of the
traditional agriculture sector, the dynamic path for kt is unclear. However, if the initial
capital/labor ratio, kM, is known, the dynamic path is solved.
Figure 4.10 illustrates the results of two simulations with identical k and N0. In ad-
dition, both simulations are using the same parameter value set in Table 4.2. The only
difference between the two models is the value of kC, and also the corresponding kM at
moment M. Since we care about the process of structural transformation since M, we only
simulated dynamic paths starting from moment M. The solid curves represent the transfor-
mation paths in the previous simulation, while the dash lines demonstrate the results of an
alternative simulation.
It shows that although the two sample economies have identical initial employment
shares in agriculture at moment M and they converge to the same generalized balanced
growth path in the long run, the paths of structural change are distinct. In addition, the
economy with the lower initial capital/labor ratio, kM, seems to evolve faster (dash lines)
and reaches the steady state several periods earlier with a higher peak manufacturing em-
ployment share. A possible explanation is that the rental interest rate is relatively higher in
this economy, which causes higher saving/investment.
We propose to set kM = k as an additional condition to pin down the dynamic path, as
shown by the dash lines in Figure 4.10. Since this kM is determined by k, the generalized
81
Em
ploy
men
t Sha
res
The same GBGP
Manufacturing
Service
Agriculture
M Time
Cap
ital/l
abor
rat
io
Benchmark simulation Unique path
kt=k
Figure 4.10: Uniqueness of dynamic paths
growth path, it is somehow “unique” in our model. This specific dynamic path is called k
path, or the unique path.
4.5.4 Dynamic Path of kt and ct
In a standard Ramsey-Cass-Koopmans growth model, it is very convenient to draw a phase
diagram to analyze the transition paths. Using equation (4.29) and equation (4.30), Figure
4.11 reports the dynamic path for kt and ct . It shows that starting from M, both consumption
and capital/labor ratio decreases in the mixed stage, then, at t =C−1, consumption jumps
down before entering the convergent stage, and finally, they move along a saddle path to
the steady state.
82
Capital/labor ratio kt
Con
sum
ptio
n c t
Mixed Stage
Convergent StageSaddle Path
t > GSteady State
t = M
t = C
Consumption Jump
Figure 4.11: Dynamic path for kt and ct
4.5.5 Change of Manufacturing Employment
In Figure 4.9, a simulated example shows that the manufacturing employment share fol-
lows a hump-shaped pattern during structural change with a peak moment around C. We
let ∆N2,t = N2,t −N2,t−1 to denote the change of employment share in the manufacturing
sector, and plot the trajectory of ∆N2,t in Figure 4.12. Starting from t = M, ∆N2,t remains
positive before t = C− 2, and then stays in the negative regime until reaching the gener-
alized balance growth path at G. This implies that the manufacturing employment share
first increases, peaks at C−2, and then decreases. The result from the simulated example
is consistent with our discussion back in section 4.4. In the mixed stage, the rise of the
manufacturing employment is associated with the decline of the traditional agriculture sec-
tor. As the economy approaches C, N0,t drops to zero. Therefore, the investment demand
for manufactured products starts to drop. As a result, the overall employment share of the
manufacturing sector peaks right before moment C.
83
M C G t−2.5
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2x 10
−3
Cha
nge
of e
mpl
oym
ent s
hare
∆
N2,
t
Figure 4.12: Changes of manufacturing employment shares
4.6 Empirical Evidence
The previous sections show that the agriculture modernization process have two impacts
on structural transformation and investment. First, it replaces traditional agricultural tech-
nology by modern technology that is more capital intensive. Second, it releases excessive
workers to other sectors who demand capital goods and infrastructures to settle down. As a
result, this modernization of agriculture raises demand for capital goods and causes invest-
ment rate to rise.
In this section, we begin with an empirical test to check the relationship between the
speed of agriculture modernization (the drop of agriculture employment share) and the
investment rates. And then, we turn to review some historical experiences of structural
change that are consistent with our framework.
4.6.1 Investment and Structural Change: an Empirical Analysis
The theoretical analysis and the numerical example discussed above have illustrated
how agriculture modernization would affect structural change, investment, and economic
growth: rapid decline of the agriculture sector leads to a strong demand for capital goods,
as a result, the investment rate would be high. Since capital goods are primarily produced
84
by the manufacturing sector, the manufacturing employment share tends to move along
with investment. Therefore, our theory can be schematically summarized as
Agriculture modernizationÀ⇒ Investment rate
Á⇒ Manufacturing employment
This section empirically investigates these two theoretical predictions. Our first hypoth-
esis implies that the agriculture modernization demands capital goods, affecting investment
rates. The basic regression model using panel data is specified as follows,
Invi,t = a ·∆Ai,t +b ·Zi,t + εt , (4.32)
where Invi,t is the investment share of GDP, ∆Ai,t = NA,i,t −NA,i,t−1is the change of em-
ployment share in the agriculture sector, Zi,t is a set of control variables that are included in
the regression as potential explanations, such as the manufacturing employment share, the
output growth rate, the real GDP per capita, country dummies, and time dummies. Thus,
this regression tests whether the change of agriculture employment affects investment rate,
after controlling these relevant explanatory variables. We expect a to be negative, mean-
ing that a more rapid decline in agriculture employment share is associated with a larger
demand for capital goods, leading to a higher level of investment.
Our second hypothesis is that the demand of capital goods, measured by investment
rate, can affect the employment share of the manufacturing sector. The regression model is
given by
N2,i,t = c ·∆Ai,t +d · Invi,t + e ·Zi,t + εt . (4.33)
We expect that the coefficent of investment, d, to be positive, implying that higher invest-
ment rates is correlated with higher manufacturing employment.
We construct a panel data covering 34 countries from 1950 to 2005. Most sectoral
employment shares are calculated using the GGDC 10-sector database, while the national
account data are from the Penn World Table (version 6.3).23
Table 4.3 presents the estimation results of equation (4.32) using the compiled panel
data covering 34 economies. The results confirm that there is a negative and significant
relationship between the decline of agriculture employment and investment, and the direc-
tion and magnitude of this coefficient is relatively stable as we add more control variables.
23Data sources are listed in section 4.9.
85
Table 4.3: Investment rate and structural change in a sample of 34 countriesDependent variable: Investment rate
(1) (2) (3) (4)
Change of agriculture employment-0.865*** -0.732*** -0.744*** -0.697***
(0.211) (0.207) (0.176) (0.182)
Manufacturing employment share0.238***(0.066)
Output growth rate0.142*** 0.140*** 0.136***(0.041) (0.043) (0.046)
Real GDP per capita0.065*** 0.046***(0.016) (0.016)
Country dummies Y Y Y YTime dummies Y Y Y YNo. of obs. 1350 1349 1349 1349Adj.R2 0.604 0.611 0.668 0.700
Notes: All regressions are OLS. Standard errors in parentheses. Robust standard errors areclustered at country level. * p < 0.1, ** p < 0.05, *** p < 0.01.
Table 4.4: Manufacturing employment and investment rate in a sample of 34 countriesDependent variable: Manufacture employment
(1) (2) (3) (4) (5)
Change of agriculture employment-0.291 0.256 0.210 0.143 0.130(0.239) (0.252) (0.254) (0.198) (0.195)
Investment rate0.527*** 0.533*** 0.407*** 0.409***(0.101) (0.104) (0.070) (0.073)
Output growth rate-0.054(0.075)
Real GDP per capita0.054* 0.096***(0.029) (0.035)
Real GDP per capita squared-0.002*(0.001)
Country dummies Y Y Y Y YTime dummies Y Y Y Y YNo. of obs. 1589 1350 1349 1350 1313Adj.R2 0.719 0.756 0.755 0.771 0.777
Notes: All regressions are OLS. Standard errors in parentheses. Robust standard errors areclustered at country level. * p < 0.1, ** p < 0.05, *** p < 0.01.
86
It implies that a larger the decrease of employment share in the agriculture sector is asso-
ciated with a higher share of resource to be invested. In addition, the regression results
show that the rapid economic growth and high-income level are associated with high rate
of investment. Finally, the manufacturing employment share is positively associated with
the investment rate, which has to be further investigated.
The main results for the determination of the investment ratio, shown in Table 4.4.
are as follows. The change of agriculture employment can not explain the movements in
manufacturing employment share. In contrast, the investment rate is positively correlated
with the employment share in the manufacturing sector, which is statistically significant at
1%. This result is stable for different sets of control variables. Therefore, we argue that the
implications from our model are supported by these empirical evidences.
4.6.2 Other Suggestive Evidence
Both the theoretical analysis and numerical example show that the peak of the manufac-
turing employment during economic development, which is a main feature of structural
transformation, can be a clear indicator for the adoption of modern agriculture technology.
The rising manufacturing sector is associated with industrialization, during which modern
society is transformed from agrarian societies as peasants became factory workers. Over-
time, manufacturing cedes its place to services.
Before we continue our analysis, we have to identify the peak moment for the manufac-
turing sector, which might not be very clear to determine. During economic development
the rise of the manufacturing employment share might not be single peaked, since it can be
interrupted by many factors, including world wars, business cycles, and severe economic
crises. For example, in Malaysia and Thailand manufacturing employment shares reached
all time highs in 1996 and 1997 before they met the Asian financial crisis. Malaysia experi-
enced a quick rebound after the crisis and almost went back to the peak employment share
in 2001, before it started to de-industrialize. In Thailand, the manufacturing employment
recovered slowly from the crisis, rose to the pre-crisis level in 2005, and has continued to
rise slightly since then. Therefore, in these cases, we recognize that Malaysia might have
reached its peak moment in 2001 (the second and last high employment share in manufac-
turing before the deindustrialization); and we treat Thailand as an emerging economy in
which the manufacturing employment share still has potential to increase. The same logic
87
510
2510
3020
Man
ufac
turin
g em
ploy
men
t sha
re %
1940 1960 1980 20001950 19901970 2010year
Figure 4.13: Manufacturing employment shares for China 1952-2010Source: The National Bureau of Statistics of China, China Statistical Yearbook (2011).
is applied to other developing countries. In a recent online column,24 Rodrik compared the
peak level of industrialization (measured by the manufacturing sector’s share of total em-
ployment) for early and late developers. However, there is an obvious mistake for the case
of China, which is asserted by Rodrik as being de-industrialized since 1996. This is ex-
actly an example of the identification problem for multiple peaks during economic growth.
Figure 4.13 depicts that the manufacturing employment share had reached a peak around
1996 before it dropped sharply as a result of the simultaneous Asian financial crisis and the
reform of state-owned enterprises. Since the year 2002, the manufacturing sector in China
has grown rapidly and employs about 30 percent of the labor force. As a result, China has
now surpassed the United States as the number one producer.
Using the above criterion, we identify the peaks of manufacturing employment shares
in 29 countries, as summarized in Table 4.5. We also use the following chart, Figure 4.14, to
illustrate the relationship between peak manufacturing employment and per capita income
in constant dollars in 2000. The results show the developed countries today have shared
a common experience of structural transformation: they reached a relatively higher share
of employment in the manufacturing sector at a rather high income stage. As indicated
24“On premature deindustrialization”, http://rodrik.typepad.com/dani_rodriks_weblog/2013/10/on-premature-deindustrialization.html.
88
Table 4.5: Moments with peak manufacturing employments
Country Code YearIncome Employments2000$ Agriculture Manufacturing
Developed countryAustralia AUS 1964 15061 0.103 0.399Austria AUT 1966 13260 0.205 0.413Canada CAN 1956 13200 0.164 0.347
Denmark DNK 1964 14642 0.155 0.370Spain ESP 1977 15377 0.187 0.354
Finland FIN 1975 16610 0.149 0.361France FRA 1973 17878 0.119 0.361
Hong Kong HKG 1976 9859 0.027 0.514Italy ITA 1975 16077 0.160 0.385Japan JPN 1973 17476 0.165 0.362Korea KOR 1991 12460 0.169 0.359
Netherlands NLD 1965 15608 0.082 0.373New Zealand NZL 1967 15534 0.132 0.384
Singapore SGP 1984 18187 0.013 0.387Sweden SWE 1965 16404 0.103 0.411Taiwan TWN 1987 11417 0.156 0.424
United Kingdom GBR 1955 11926 0.046 0.458United States USA 1953 14916 0.073 0.335
Developing countryArgentina ARG 1958 6145 0.223 0.336
Brazil BRA 1981 7381 0.326 0.243Chile CHL 1993 7002 0.169 0.265
Colombia COL 1995 5271 0.265 0.209Costa Rica CRI 1994 8158 0.231 0.289
India IND 2002 1980 0.610 0.169Mexico MEX 2000 10570 0.168 0.282
Malaysia MYS 1997 9730 0.155 0.379Peru PER 1974 5831 0.459 0.205
Philippines PHL 1997 2228 0.400 0.164Venezuela VEN 1978 11032 0.150 0.280
Sources: Groningen Growth and Development Centre (GGDC) 10-sector Historical Na-tional Accounts database.
89
ARG,1958
AUS,1964
AUT,1966
BRA,1981
CAN,1956
CHL,1993
COL,1995
CRI,1994
DNK,1964
ESP,1977FIN,1975FRA,1973
GBR,1955
HKG,1976
IND,2002
ITA,1975
JPN,1973KOR,1991
MEX,2000
MYS,2001NLD,1965NZL,1967
PER,1974
PHL,1997
SGP,1984
SWE,1965TWN,1987
USA,1953
VEN,1978.2
.3.4
.5P
eak
man
ufac
turin
g em
ploy
men
t sha
re
0 5000 10000 15000 20000Per capita income (2000$)
Figure 4.14: Peak manufacturing employment shares with per capita incomeSource: Various historical statistics, see section 4.9.
in Table 4.5, in our sample, developed countries have a peak manufacturing employment
share no less than that of the United States, 33.5%. Most of their agriculture employment
shares were already less than 20% at the peak. In addition, 11 economies out of 29 in our
sample had their agriculture share in the small range between 15% and 17%. And only 5
economies had less than 10% of workers in the agriculture sector before the employment
share of the manufacturing sector declined, including Netherlands, U.K., U.S., and two city
states, Hong Kong and Singapore. Thus, the structural transformation of the United States,
despite its popularity in the literature, is somehow an exception.
With the help of these estimated peak moments, we can break any structural transfor-
mation process into two sub-periods, before and after the manufacturing peak, which is set
to be a common moment across countries. Both the theoretical and numerical analysis in
the previous sections predict that the employment share of the agriculture sector decreases
faster before reaching the peak moment. Figure 4.15 shows that in selected countries, the
rate of decline for the agriculture sector does slow down after the manufacturing employ-
ment share has peaked.
90
0.1
.2.3
.4.5
Agr
icul
ture
Em
ploy
men
t
−20 0 20 40
Peak Year
Finland France Italy
0.2
.4.6
Agr
icul
ture
Em
ploy
men
t
−40 −20 0 20 40
Peak Year
Japan Korea Venezuela
Figure 4.15: Agricultural employment shares before and after the peak year of manufactur-ing employmentSource: Various historical statistics, see section 4.9.
91
4.7 Concluding Remarks
This paper studies the connection between the two hump-shaped patterns of economic de-
velopment: the investment share and the manufacturing employment share. We propose
that agricultural modernization is the key mechanism that causes these two patterns to oc-
cur simultaneously.
Following the burgeoning body of literature that stresses the important role of the
technology switch in the agriculture sector, i.e., Hansen and Prescott (2002), Gollin, Par-
ente, and Rogerson (2007), and Yang and Zhu (2013), we construct a four-sector, three-
product model to investigate dynamic features in capital/labor ratio and sectoral employ-
ment shares. We assume the traditional agriculture sector only uses raw labor input,
whereas modern agriculture production utilizes capital. Productivity improvement in the
modern sectors causes the relative price of traditional agriculture to rise and eventually trig-
ger the transition to adopt modern technology. During the process of technology adoption,
workers who leave the traditional sector temporally demand capital goods to adopt modern
technology. Since the labor movements cannot be completed immediately, the capital labor
ratio decreases, and the interest rate and investment ratio rise. At the end of the technology
adoption, the economy converges to a generalized balanced growth path in the long run.
We adopt a simulation approach to illustrate the dynamic features of our model. It
predicts that the peak moment of manufacturing employment is associated with the mod-
ernization of the traditional sector, which is supported by historical observations. Our
model, without unbalanced technology progress, is able to generate hump-shaped patterns
on manufacturing employment shares, on investment rates, and on economic growth rates.
These results provide a common mechanism to explain the common pattern of structural
transformation during long-term economic growth.
4.8 Mathematical Details
Proposition. 4.1 If we let Zt =(
B0(1−α)B1
) 1α
X− 1
α
t , in agriculture production, the firm
1) uses only traditional technology, if kt < Zt ;
2) uses only modern technology, if kt > Zt ;
3) and uses a mixed combination, if kt = Zt .
92
Proof. The cost of per unit of agriculture product using the traditional technology is given
by
Cost0,t =Wt
B0,t.
The modern technology gives the cost function as the following
Cost1,t =1
αα(1−α)1−α
Rαt
B1,t
(Wt
Xt
)1−α
.
If both technologies are equally cost efficient, we have the mixed production condition,
kt =
(B0,t
(1−α)XtB1,t
) 1α
,
where kt =Kt
(1−N0,t)Xtis the capital/labor ratio in the modern sector.
The food production uses only traditional technology if
kt 6
(B0,t
(1−α)XtB1,t
) 1α
;
and uses only modern technology if
kt >
(B0,t
(1−α)XtB1,t
) 1α
.
Proposition. 4.2 Whenever assumption 4.2 holds, a generalized balanced growth path
exists. The relative prices, aggregate labor income share, and growth rate of output and
capital are constant. The employment share declines in agriculture, rises in services, and
is stable in manufacturing. The capital rental rate and capital/labor ratio are given by
r =1+g
β+δ −1.
k =
(αB2
r
) 11−α
93
Proof. Assumption 4.4.1 yields p1C1 = p3C3. Thus, using the result of optimal consump-
tion, equation (4.13), we can we rewrite the resources constraint for the modern economy,
equation (4.12), as
B2kαt Xt = p1C1 + It +C2,t + p3C3,t ,
= It +C2,t + p3(C3,t +C3),
= It +C2,t
γ.
There exists a steady-state level of capital/labor ratio kt = k, which implies that the
left-hand side expands at a constant rate g. On the right-hand side, both investment (It) and
consumption aggregation (C2,tγ
) can also grow at rate g. The corresponding capital rental
rate r = 1+gβ
+δ −1. And k =(
αB2r
) 11−α .
The economy is on a generalized balanced growth path.
Proposition. 4.4 The movements of employment shares in the mixed economy exhibit the
following properties:
1) Total employment shares used to produce agriculture goods start to decline;
2) The size of the traditional agriculture sector, in terms of employment, is given by
G(N0,t+1)
G(N0,t)= β (αB2kα−1
t +1−δ ),
where kt is given by equation (4.23), and G(N0,t+1) =C2,t satisfies
G(N0,t+1) ≡ −γ
[1−N0,t+1
(1+g)1−α
α
− (1−δ )(1−N0,t)
]ktXt
+γB2(1−N0,t)kαt Xt .
3) The employment shares in the manufacturing and service sectors are given by
N2,t = γ(1−N0,t)+1− γ
B2
[1−N0,t+1
(1+g)1−α
α
− (1−δ )(1−N0,t)
]k1−α
t ,
94
N3,t =1
B3kαt Xt
[1− γ
γ
G(N0,t+1)
p3−C3
].
Proof. 1) In the mixed economy, kt = Zt , let n1 and n0 denote the labor inputs used to
produce one unit of agriculture goods, we have
n1 =k−α
t
B1Xt=
Z−αt
B1Xt=
1−α
B0<
1B0
= n0.
Therefore, the modern technology uses less labor input to produce one unit of agricul-
ture goods. Because the total consumption for agriculture goods is fixed at C1, the adoption
of modern production will release labor from the traditional sector and decrease the total
employment share in the agriculture sector.
2) Since kt = Zt , the relative price, equation (4.11), yields p0,t =B2B0
(1−α)kαt Xt =
B2B1
=
p1.
Investment function is given by
It = Kt+1− (1−δ )Kt
= [kt+1(1−N0,t+1)(1+g)− (1−δ )kt(1−N0,t)]Xt .
The resource constraint of this economy can be characterized by
B2kαt (1−N0,t)Xt = It +
C2,t
γ,
=
[1−N0,t+1
(1+g)1−α
α
− (1−δ )(1−N0,t)
]ktXt
+C2,t
γ. (4.34)
Equation (4.34) suggests that C2,t is a function of N0,t+1,
C2,t = γB2(1−N0,t)kαt Xt
−γ
[1−N0,t+1
(1+g)1−α
α
− (1−δ )(1−N0,t)
]ktXt ,
≡ G(N0,t+1).
95
Plugging in the intertemporal Euler equation, equation (4.14), the dynamic of this econ-
omy is given byC2,t
C2,t−1=
G(N0,t+1)
G(N0,t)= β (αB2kα−1
t +1−δ ).
3) Employment of the manufacturing sector is given by
N2,t =C2,t + ItB2kα
t Xt,
= γ(1−N0,t)+1− γ
B2
[1−N0,t+1
(1+g)1−α
α
− (1−δ )(1−N0,t)
]k1−α
t ,
N3,t =C3,t
B3kαt Xt
=1
B3kαt Xt
[1− γ
γ
G(N0,t+1)
p3−C3
].
Proposition. 4.5 In the convergent stage, the employment share of the manufacturing sec-
tor decreases. If kt converges along the saddle path to k, the manufacturing employment
share also goes to the size on the generalized growth path.
Proof. According to assumption 4.3, kC < k. kt evolves on a saddle path and converges to
the steady state, for t >C, we have kt+1 > kt .
For the manufacturing employment,
N2,t+1−N2,t =1− γ
B2
[(1+g)
(kt+2
kαt+1− kt+1
kαt
)+(1−δ )
(k1−α
t − k1−α
t+1)]
.
We rewrite the Euler equation
B2kα−1t+1 −
[kt+2kt+1
(1+g)− (1−δ )]
B2kα−1t −
[kt+1kt
(1+g)− (1−δ )] = β (rt+1 +1−δ )
1+g> 1,
which gives
(1+g)(
kt+2
kt+1− kt+1
kt
)< B2
(kα−1
t+1 − kα−1t)< 0.
Since k1−αt − k1−α
t+1 < 0, we have N2,t+1 < N2,t .
96
In the convergent stage, if kt rises along the saddle path toward k, from equation (4.31),
we have N2,t converge to
N2,G = γ +1− γ
B2(g+δ )k.
4.9 Data Sources
Our main source of data is the 10-sector database by Timmer and Vries (2008).25 It
covers 33 countries from 1950 to 2005. We add the sectoral employment shares for China
using the China Statistical Yearbook (2011). Therefore, our sample overall includes 34
countries.26 The latest update available for each country was used. Data for Latin American
and Asian countries came from the June 2007 update, while data for the European countries
and the United States came from the October 2008 update.
The three broad sectors are categorized as the following: the primary sector (agricul-
ture), which only includes agricultural production; the secondary sector (manufacturing),
which consists of mining, manufacturing, public utilities and construction; the tertiary sec-
tor (service), which covers wholesale, retail trade (including hotels and restaurants), trans-
port, storage, and communication finance, insurance, and real estate and community, social
and personal services, and government services.
The real GDP per capita comes from the Penn World Table (version 6.3), while BEA
reports investment to output ratio, and capital to output ratio. The ratio of investment to
output comes from Kuznets (1966) Table 5.5 and the World Development Index by the
World Bank.
25Available at http://www.ggdc.net/ databases/10_sector.htm26The complete country list includes, Argentina, Australia, Austria, Bolivia, Brazil, Canada, Chile, China,
Colombia, Costa Rica, Denmark, Spain, Finland, France, United Kingdom, Germany, Hong Kong, Indone-sia, India, Italy, Japan, Korea, Mexico, Malaysia, Netherlands, New Zealand, Peru, Philippines, Singapore,Sweden, Thailand, Taiwan, United States, and Venezuela.
97
Chapter 5
Quality Upgrading and Capital GoodImport
5.1 Introduction
Finding the secret recipe of economic growth has been an eternal request for economists.
“Once one starts to think about them, it is hard to think about anything else” (Lucas, 1988).
This chapter is primarily motivated by the experience of the East Asian growth miracle.
Since the 1950s, most of the countries have improved their income and reached middle-
income status, but only a few countries have become high-income economies. Agénor,
Canuto, and Jelenic (2012) show that only 13 out of 101 middle-income economies in 1960
became high income by 2008, of which 5 countries come from East Asia–Hong Kong SAR
(China), Japan, the Republic of Korea, Singapore, and Taiwan, China. In addition, main-
land China, the second-largest economy since 2010, has been the world’s fastest-growing
major economy, with growth rates averaging 10% over the past 30 years.
Three broad sets of explanations have been proposed for the “East Asia Growth” ex-
perience. The first set of explanations operates through the intensive factor accumulation,
including both physical and human capital. Young (1992, 1994, 1995, 2003) and Krugman
(1994) found that the main driver of the rapid economic growth is factor accumulation, and
the estimated total factor productivity growth rates were respectable but not outstanding
after taking into account the dramatic rise in factor inputs.
98
A second set of explanations focuses on the pattern of industrial upgrading. The indus-
tries started by producing labor-intensive goods (such as textiles and shoes), which declined
and were replaced by more advanced industries (such as machinery), which also declined,
to be later superseded by automobiles and electronics. This industry catching-up process is
referred to as the flying geese pattern of economic development (Akamatsu, 1962; Kojima,
2000).
The third set of explanations places heavy emphasis on export orientation growth strat-
egy and government interventions. For example, prior to the early 1960s, South Korea
and Taiwan followed import-substitution policies that were adopted by most other devel-
oping countries at the time, such as, import protection, multiple and overvalued exchange
rates, and repressed financial markets. However, these policies were gradually replaced by
export-oriented policies, including currency devaluation and export subsidization, which
greatly reduced the trade barriers and allowed them to specialize along their comparative
advantage and to benefit from trade expansion. Meanwhile, the learning-by-doing mecha-
nism fostered technological improvement.
Although each of these explanations captures a few features of the East Asian growth
experience, they are fragmented and incomplete.
First, if the rapid economic growth in East Asia is primarily caused by input accumula-
tion, particularly accumulating physical capital, it should be easily replicated by other de-
veloping countries. However, only a few Asian economies have successfully followed this
growth strategy. Chen (1997) challenged the factor accumulation explanation by comparing
the growth experience of Singapore to mainland China (prior to the reform). Borensztein
and Ostry (1996) found that the TFP growth of China was -0.7% between 1953 and 1978,
while Young (1995) estimated that the rate of total factor productivity growth in Singapore
averaged 0.2 percent a year from 1966 to 1990.1 Although both countries were found to
heavily rely on capital accumulation with insignificant TFP growth, the observed economic
performances were striking. Chen (1997) further argued that the contrast between the East
Asian growth miracle and the relatively insignificant TFP growth estimates indicated that
the predominant source of growth could be embodied capital. Thus, the whole concept of
TFP growth accounting should be questioned (Felipe, 1999; Felipe and McCombie, 2003).
1In a more recent study, Hsieh (2002) conducted a dual exercise and suggested that technological progressin Singapore’s growth was significant and comparable to other Asian economies.
99
Therefore, the observed factor accumulation might be the consequence of growth, rather
than the driving force.
Second, the mechanism of achieving continuous industrial upgrading is still unknown.
Ju, Lin, and Wang (2010) argued that a continuous inverse-V-shaped pattern of industrial
evolution could be driven by capital accumulation when the industry profitability depends
on capital endowment. However, their framework suffers from at least two drawbacks.
First, the persistent output growth in their model is caused by the AK technology, which is
only weakly associated with the industry dynamics. Second, empirical observations show
that the establishment of more advanced industries requires high-quality capital goods,
such as modern industry robots, rather than a large quantity of capital goods. Therefore,
the quality dimension of capital cannot be ignored.
Third, the causal relationship between export orientation and growth is problematic.
Rodrik, Grossman, and Norman (1994) found little causal evidence for the role of export
orientation in the economic growth in Korea and Taiwan since the early 1960s, because
exports were initially too small to have any significant impacts on aggregate economic
performance. Boltho (1996) investigated the rapid growth of Japan in three sub-periods
(1913-37, 1952-73, 1973-90) and found that the domestic forces propelled long-run growth.
Lawrence and Weinstein (1999) found that high import volumes were particularly benefi-
cial for Japan from 1964 to 1973 and stressed that learning from foreign rivals is an im-
portant conduits for growth. Therefore, a mechanism that could stress domestic force, in
particular the investment boom, might be more plausible. Since the domestic industry of
producing capital goods is poorly developed in an economy such as South Korea or Taiwan
in the 1960s, capital goods are mostly imported.2 Consequently, an increase in investment
becomes possible only through an increase in imports. But if the economy cannot borrow
freely from abroad, an increase in exports is required to pay for the imports. Therefore, the
outward orientation of the economy was the result of the increase in demand for imported
capital goods (Rodrik, 1997).
The model presented in this chapter intends to explore the interaction between trade
and growth. We assume that importing foreign capital goods can improve the quality
of domestic capital stock and product, because the information of advanced technology
is embodied within high-quality capital goods produced by developed countries. There-
2Eaton and Kortum (2001) have shown that most countries generally import equipments from a smallnumber of R&D-intensive countries.
100
fore, capital goods importing is an important channel of international technology diffusion,
which establishes a direct causal linkage from trade to growth.
This model consolidates existing evidences into one explanation. It shows that the
observed export expansion is used to finance the import of foreign capital goods to achieve
quality upgrading. And the industry upgrading process can be summarized by this process
of quality improvement. Since the output growth is primarily caused by the used of high-
quality capital goods with embodied technology, the standard growth accounting exercise
might overstate the role of capital accumulation in economic growth.
As trade pattern is subject to the balance of payments constraint, foreign demand, term
of trade, and trade balance can significantly affect economic growth. For developing coun-
tries, our framework indicates two barriers for economic growth. The first barrier is that
the feasibility of trade can be restricted by the low product quality, because high-quality
capital goods are only produced by a few rich countries who trade intensively with each
other (Eaton and Kortum, 2001; Hallak, 2006). Thus, in order to exchange sufficient cap-
ital goods, developing countries have to compete for the limited opportunities to export.
However, if a developing country decides to stimulate foreign demand through currency
depreciation, the second barrier arises, because the foreign capital might become too ex-
pensive to be imported for investment. As a result, our model shows that the condition for
economic growth can be very tricky. Depending on different trade patterns, both conver-
gence and divergence of income level could take place.
Our model is supported by several strands of literature. Our explanation of the export
expansion during economic growth coincides with the main idea of Rodrik (1997), though
the cause of import increase is different. In our model, importing foreign capital goods
plays as the primary channel of international technology diffusion, while Rodrik (1997)
argued that the profitability of domestic investment raises the demand for capital goods and
increases capital import consequently. Our emphasis on the balance of payments constraint
is distinct from the orthodox growth theory, which links us to the balance of payments
constrained growth models.3 Thirlwall (2011) claimed that “in the long run, no country
can grow faster than that rate consistent with balance of payments equilibrium on current
account unless it can finance ever-growing deficits which, in general, it cannot.” Therefore,
3See Thirlwall and Hussain (1982), Thirlwall (2011), and many others.
101
in our baseline model, a crucial condition for achieving sustainable growth is to maintain a
non-negative current account.
The role of imported capital goods on growth has strong empirical roots. Lee (1995)
used cross-country data for the period 1960 to 1985 and showed that the ratio of imported
capital goods to domestically produced capital goods in the composition of investment is
positively related with the per capita income growth rate. In a recent study, Herrerias and
Orts (2013) confirmed that the ratio of imported to domestic capital goods determined the
long-run growth rate and argue that the link between trade openness and long-run growth
operates mainly through imports.
We owe a major intellectual debt to the growing literature on product quality. Since
rich countries import more and consume more from countries producing high-quality goods
(Hallak, 2006), we assume that low product quality dampens demand. In addition, Feenstra
and Romalis (2014) found that the exports of rich countries tend to be of high quality,
whereas poor countries tend to have notably lower quality exports. Thus, in our model,
the primary channel of income convergence relies on product quality convergence. Henn,
Papageorgiou, and Spatafora (2013) found out that quality upgrading is particularly rapid
during the early stages of development, with quality convergence largely completed as a
country reaches upper middle-income status, and the quality upgrading was particularly
impressive in East Asia.
The rest of this chapter proceeds as follows. Section 5.2 presents the basic economic
environment of our two-country model, in which the primary channel of technology im-
provement is importing high-quality capital goods. We characterize the economic equilib-
rium in section 5.3 and define two types of balanced growth paths in section 5.4. Section
5.5 discusses two implications with an extension of the basic model. And section 5.6 con-
cludes.
5.2 A Simple Two-country Model
We start our analysis with a simple two-country model. Home country, H, is a low-income
country, while foreign country, F , is a developed country. In general, we will mark foreign
variables with asterisks.
102
5.2.1 Production
For the sake of simplicity, we assume that these two economies are very similar to each
other. Each country produces one product that can be used for both consumption and
investment, with the following production technologies
Yt = (Zt)α (Nt)
1−α , Y ∗t = (Z∗t )α (N∗t )
1−α , (5.1)
where Nt and N∗t are labor inputs, and Zt and Z∗t are capital stocks in terms of efficient
units, Zt = qtKt and Z∗t = q∗t K∗t . The capital stocks are described by two types of variables,
the quality indexes, qt and q∗t , reflect the production efficiency of capital goods, and Kt and
K∗t represent the quantities of capital goods. Therefore, the change of Zt can be divided
into changes in two dimensions: the change of capital quality, and the change of capital
quantity,Zt
Zt=
qt
qt+
Kt
Kt. (5.2)
The law of motions for the quantity of capital stock are given by
K∗t = I∗F,t−δK∗t , (5.3)
Kt = IH,t + IF,t−δKt , (5.4)
where IH,t , IF,t , and I∗F,t represent the capital goods used by the home country that are
produced by the home country, capital goods used by the home country that are produced
by the foreign country, and foreign-produced capital goods used by the foreign country,
respectively.4 Since they represent investment flows, they are assumed to be non-negative.
The quality improvement mechanisms are different across countries. Since the foreign
country is considered to be the leader of technology innovation on the frontier, the product
quality of the foreign country is assumed to improve at an exogenous constant rate g, which
can only be partially captured by the developing home country. However, the home country
can import foreign-produced capital goods to improve the quality of its capital stock. Thus,
4Here, we assume that the foreign capital goods and domestic capital goods are perfect substitutes interms of quantity, as the quality properties have been represented by q.
103
the quality improvement progress is given by
q∗t =q∗tq∗t
= g, (5.5)
qt = Qtg+φt(1Q−1), (5.6)
where Qt is defined as a relative quality index
Qt =qt
q∗t, and 0 < Qt 6 1, (5.7)
which measures the efficiency difference of capital stocks between the home country and
the foreign country. For Qt = 1, the production functions are the same for both countries,
and for Qt < 1, the home production is less efficient than the foreign production.
The first component on the right-hand side of equation (5.6) describes the benefit of
the home country from the foreign technology innovation as a spillover effect. However,
only a portion of the technology progress can be learned by them, since their relatively
low quality of capital stock and production limits their benefits. The second component
represents the channel of importing high-quality capital goods from the foreign country to
improve the quality of production. However, the foreign capital goods used in developing
countries are less efficient (in absolute term), since they have to cooperate with domestic
low-quality capital goods, and can be adversely affected by weak local institutions. The
quantity share of newly imported foreign capital goods in home countries capital stock is
given by
φt =IF,t
Kt. (5.8)
Without exogenous technology improvement (g = 0), we can show that our model is
equivalent to Hulten (1992)’s vintage investment model with embodies technical change.
The law of motion for capital stock in efficiency units5 satisfies
Zt = qtIH,t +q∗t IF,t−δZt ,
= qtIH,t +q∗t IF,t−qtδKt ,
= qt(IH,t + IF,t−δKt)+(q∗t −qt)IF,t .
5Hulten (1992) used Zt+1 = Ht +(1−δ )Zt to describe the law of motion for efficient capital stock, whereHt = qt IH,t +q∗t IF,t .
104
The growth rate for capital stock is given by
Zt
Zt=
qt(IH,t + IF,t−δKt)
qtKt+
(q∗t −qt)IF,t
qtKt,
=IH,t + IF,t−δKt
Kt+
(1Q−1)
φt ,
=Kt
Kt+
qt
qt.
5.2.2 Preference
Each economy is populated by an infinitely lived representative family. For simplicity, we
assume the family size grows at a constant rate n and N0 = N∗0 ,
Nt = N0ent . (5.9)
The representative family of country i maximizes their lifetime utility as the following
∞∫0
C1−σt −11−σ
e−ρtdt, (5.10)
where ρ is the rate of time preference (measure of impatience). And Ct is a comprehensive
consumption index that depends on quality-adjusted consumption goods from both home
and foreign countries,6
Ct =
γ
1η
H (CH,t)η−1
η +(1− γH)1η
(CF,t
QθHt
)η−1η
η
η−1
, (5.11)
C∗t =
[γ
1η
F (C∗F,t)η−1
η +(1− γF)1η
(QθF
t C∗H,t
)η−1η
] η
η−1
, (5.12)
where γH and γF represent domestic preference weight on domestically produced consump-
tion goods, we assume γF > γH > 12 . This assumption generates a home consumption bias.
6These two consumption indexes are based on their local product, respectively. In order to compare theabsolute consumption, we can easily transform them into indexes based on one common product, e.g. theforeign product.
105
The elasticity of substitution between domestically produced and imported consumption
goods is denoted by η , and we assume η > 1.7
In both countries, imported consumption goods are adjusted by the relative quality in-
dex Qt with non-negative parameters, θH and θF . The economic intuition of this quality
adjustment can be easily interpreted as we solve the household’s optimization problem to
derive the following consumption allocations
CF,t =1− γH
γH
(PH,t
PF,t
)η CH,t
QθH(η−1)t
= (1− γH)
(PF,t
Pt
)−η Ct
QθH(η−1)t
, (5.13)
C∗H,t =1− γF
γF
(P∗F,tP∗H,t
)η
QθF (η−1)t C∗F,t = (1− γF)
(P∗H,t
P∗t
)−η
QθF (η−1)t C∗t , (5.14)
where PH,t is the domestic price of home product in home country, P∗H,t is the foreign price
of home product in foreign country, PF,t and P∗F,t represents the prices of foreign product in
home and foreign countries, and Pt and P∗t are consumption-based aggregate price indexes
Pt =
[γHP1−η
H,t +1− γH
QθH(η−1)t
(PF,t)1−η
] 11−η
, (5.15)
P∗t =[γF(P∗F,t)1−η
+(1− γF)(P∗H,t)1−η QθF (η−1)
t
] 11−η
. (5.16)
Equations (5.13) and (5.14) describe the way that relative quality index affects con-
sumption demand. For example, Given foreign consumption index C∗t , equation (5.14)
shows that a small Qt leads to a weak foreign demand for the home country. Therefore,
QθF (η−1)t < 1 performs as a quality punishment factor on home country’s product, while
1QθH (η−1)
t> 1 represents a quality premium from consuming foreign product. It shows that,
given relative prices, households of foreign country prefer consumption variety, but only
a relatively small amount of low-quality consumption goods from the home country are
sufficient to make them satisfied. This implication is consistent with the empirical finding
of Hallak (2006) that rich countries import more from countries producing high-quality
goods.
7Obstfeld and Rogoff (2005, 2007) argued that, although the estimates of the trade elasticity cover a widerange, they typically include many values much higher than 2. Thus, they used 2 and 3 as representativevalues for aggregate trade elasticity. Examples of recent estimates can be found from Broda and Weinstein(2006).
106
The reason that the absolute quality levels, qt and q∗t , do not enter the consumption
index is that qt and q∗t measure the quality of capital goods rather than the quality of con-
sumption goods. Since they have already been used as efficiencies indexes in the production
functions, including them in the consumption index causes a double counting problem and
prevents us from solving the steady states.8
The resource constraint of the home country is given by
PH,t(CH,t + IH,t)+PF,t(CF,t + IF,t) =WH,tNt +RH,tZt . (5.17)
Similarly, the resource constraint of the foreign country is given by
P∗H,t(C∗H,t)+P∗F,t(C
∗F,t + I∗F,t) =W ∗F,tN
∗t +R∗F,tZ
∗t . (5.18)
5.2.3 Trade Balance and Market Clearing Conditions
The aggregate trade balance of home country, T Bt , is given by
T Bt = PH,tC∗H,t−PF,t (IF,t +CF,t) . (5.19)
We assume the law of one price holds in our model. The nominal exchange rate εt is
defined as the ratio of prices in home country to the prices in foreign country. Without trade
costs, we have PF,t = εtP∗F,t and PH,t = εtP∗H,t . Since we have defined price indexed based
on local product, we set PH,t = P∗F,t = 1, thus PF,t = εt and P∗H,t =1εt
. The exchange rate,
εt =PF,tPH,t
, is also the relative price between foreign product and home product, and the term
of trade for the foreign country. Pt and P∗t becomes price indexes that only depend on two
key variables, εt and Qt . For example, P(εt) =
[γH +(1− γH)
(εtQ
θHt
)1−η] 1
1−η
. And the
8Using absolute quality indexes, qt and q∗t , would cause a technical problem when we solve for steadystates. For example, if we consider the following preference,
Ct =
[γ
1η
H (qtCH,t)η−1
η +(1− γH)1η ((q∗t )CF,t)
η−1η
] η
η−1,
we can not normalized Ct by qα
1−α
t Nt to derive ct that satisfies the steady state condition.
107
real exchange rate is given by
RERt =εtP∗tPt
=
[γF (εt)
1−η +(1− γF)QθF (η−1)t
] 11−η
[γH +(1− γH)
(εtQ
θHt
)1−η] 1
1−η
. (5.20)
Using the optimal consumption conditions and relative prices, the balance of trade be-
comes
T Bt = (1− γF)
(1
εtP∗t
)−η
QθF (η−1)t C∗t − εt
[(1− γH)
(εt
Pt
)−η Ct
QθH(η−1)t
+ IF,t
]. (5.21)
In this basic model, we do not allow international lending and borrowing. Therefore,
the balance of payments constraint implies T Bt = 0, which endogenously determines the
exchange rate, εt .
The goods market of both economies should be clear, thus
YH,t = CH,t + IH,t +C∗H,t , (5.22)
YF,t = CF,t + IF,t +C∗F,t + I∗F,t . (5.23)
Before we proceed, let us introduce the following normalized variables, kt =Kt
qα
1−αt Nt
,
yt =Yt
qα
1−αt Nt
= kαt , ct =
Ct
qα
1−αt Nt
, iF,t =IF,t
qα
1−αt Nt
, iH,t =IH,t
qα
1−αt Nt
, which represent per capita
capital stock, output, consumption, and investments normalized by product quality index,
respectively. Similarly, we normalize foreign variables by (q∗t )α
1−α N∗t .
Therefore, using optimal consumption allocations and market clear conditions, we have
y∗t = (1− γH)
(Pt
εt
)η
ctQα
1−α−θH(η−1)
t + γF (P∗t )η c∗t + i∗F,t + iF,tQ
α
1−α
t , (5.24)
yt = (1− γF)(εtP∗t )η c∗t Q
θF (η−1)− α
1−α
t + γH (Pt)η ct + iH,t . (5.25)
In addition, the balance of payments constraint is given by
iF,t = (1− γF)(P∗t )η
εη−1t c∗t Q
θF (η−1)− α
1−α
t − (1− γH)(Pt)η
ε−η
t ctQ−θH(η−1)t . (5.26)
108
5.3 Economic Equilibrium
We now proceed to derive the macroeconomic equilibrium of this two-country system. We
start with the foreign country’s optimization. And later, we move on to the home country’s
problem.
5.3.1 Foreign Country’s Problem
For the foreign country, the intertemporal dynamic problem can be treated as a direct im-
plication of the standard Ramsey–Cass–Koopmans growth model, which is described by
the following two differential equations:
c∗tc∗t
=1σ
(r∗t −δ −n−ρ− α
1−ασg− P∗t
), (5.27)
k∗t = (k∗t )α −
(n+δ +
α
1−αg)
k∗t −P∗t c∗t . (5.28)
where P∗t = P∗tP∗t
is the change in price level.
Imposing steady state conditions, c∗t = k∗t = 0, we can solve for the steady state values
of capital and consumption as follows,
k∗t =
(δ +n+ρ
α+
σ
1−αg− P∗t
α
) 1α−1
, (5.29)
c∗t =1
P∗t
[(k∗t )
α −(
n+δ +α
1−αg)
k∗t
]. (5.30)
In the absence of price change, P∗t = 0, this set of solution is consistent with the steady
state solution of a standard Ramsey–Cass–Koopmans model, such that k∗t = κ and c∗t P∗t =
ζ , where
κ ≡(
δ +n+ρ
α+
σ
1−αg) 1
α−1
, (5.31)
ζ ≡[
κα − (n+δ +
α
1−αg)κ]. (5.32)
109
5.3.2 Home Country’s Problem
Because of the quality improvement mechanism, the home country has a complicated op-
timization problem. For an economic agent in home country, denoted by superscript i, the
consumption per capita and capital stock per capita are given by Cit =
CtNt
, Kit =
KtNt
. In ad-
dition, as we assume that the representative firms rent capital and employ labor from the
household, it is the agent in the representative household that chooses consumption and
investment composition to maximize the following life-time utility
max∞∫
0
(Ci
t)1−σ −11−σ
e−ρtdt,
which is subject to the following constraints9
RtqtKit +Wt = PtCi
t +PH,tIiH,t +PF,tφtKi
t ,
Kit = Ii
H,t +(φt−δ −n)Kit ,
qt =
(Qtg+
1−Qt
Qtφt
)qt .
The maximum principle can be used to handle such a problem.10 We define a standard
Hamiltonian, where µt and νt are called the costate variable, and λt is a Lagrange multiplier,
H(Ci
t , Kit , qt , φt , Ii
H,t , t)
=
(Ci
t)1−σ −11−σ
+λt(RtqtKi
t +Wt−PtCit −PH,tIi
H,t−PF,tφtKit)
+µt(IiH,t +(φt−δ −n)Ki
t)+νt
[(Qtg+
1−Qt
Qtφt
)qt
].
9The share of capital stock owned by agent i, Kit , has a quality measure, qi
t . Sine all economic agent areidentical, qi
t = qt . The law of motion for qit can be replaced by equation (5.6).
10Obstfeld and Rogoff (1996) discussed a general procedure to solve such a maximization problem on page748.
110
The first-order conditions (FOC) are given by
∂H
∂Cit
=(Ci
t)−σ −λtPt , (5.33)
ρ− µt
µt=
λt
µt(Rtqt−PF,tφt)+(φt−δ −n), (5.34)
ρ− νt
νt=
λt
νtRtKi
t +2Qtg−φt , (5.35)
∂H
∂φt= −λtPF,tKi
t +µtKit +νt
1−Qt
Qtqt , (5.36)
∂H
∂ IiH,t
= µt−λtPH,t , (5.37)
where PH,t = 1, PF,t = εt , and Pt =
[γH +(1− γH)
(εtQ
θHt
)1−η] 1
1−η
.
Equation (5.36) provides the first-order condition for φt . The first term represents the
cost of using the foreign capital goods, the second term stands for the cost of using domes-
tic capital goods, while the last term measures the quality benefit that comes from capital
import. In addition, equation (5.37) implies that µt = λt . Therefore, we can rewrite equa-
tion (5.36) as ∂H∂φt
= λtKit (1− εt)+νt
1−QtQt
qt , where λt > 0 and νt > 0. Thus, the optimal
choice of φt depends on the exchange rate. In addition, because of the linearity of the
Hamiltonian function with respect to the variable φt , it has a bang-bang solution. If εt < 1,
we have ∂H∂φt
> 0, as a result, the optimal value for φt should take the maximum value that
is available; if εt = 1, ∂H∂φt
= 0 implies νt = 0 or Qt = 1; if εt > 1 and Qt = 1, ∂H∂φt
< 0, thus
φt = 0; and if εt > 1 and Qt < 1, νt > 0. This interaction between quality upgrading and
exchange rate will be discussed in section 5.4.3.
The Euler equation and the law of motion for capital of the home country are given by
ct
ct=
1σ
[αkα−1
t −((εt−1)φt +δ +n+ρ + Pt
)]− α
1−αqt , (5.38)
kt = kαt −
[n+δ +
α
1−αqt +(εt−1)φt
]kt−Ptct . (5.39)
111
5.4 Balanced Growth Paths
We define a balanced growth path as being one along which key economic variables in these
two economies can grow at a constant rate. Equations (5.5) and (5.6) provide a necessary
condition for the balanced growth path in this two-country system, such that
q∗t = g = qt = Qtg+φt(1
Qt−1), (5.40)
which yields two solutions, Qt = 1, or Qt < 1 and φt = Qtg. As a result, in our model, there
are two potential balanced growth paths.
Proposition 5.1. Balanced Growth Paths. For Qt = Q = 1, or ∃ Q∈ (0, 1), Qt = Q, output
per capita, consumption per capita, and capital per capita in the two-country system can
grow along the balanced growth path at the constant rate, α
1−αg.
5.4.1 Balanced Growth Path with Q = 1
For Qt = Q = 1, we have qt = q∗t , which implies that both countries share the same quality
level. According to our discussion of equation (5.36), there are three distinct scenarios
that depend on the equilibrium exchange rate εt , which are summarized by the following
proposition.
Proposition 5.2. Balanced Growth Path with Q = 1. For Qt = Q = 1, the balanced of
payments constraint determines equilibrium exchange rate, ε , which characterizes three
equilibria with balanced growth path. And all major variables of these two economies can
grow at a constant rate, α
1−αg.
1. If ε = 1, we have Pt = P∗t = 1. Thus kt = k∗t = κ , ct = c∗t = ζ . And φ = (γH− γF)ζ
κ>
0. In particular, φ = 0 if and only if γH = γF .
2. If ε < 1, we have Pt < 1 < P∗t , kt > κ = k∗t and ct > ζ > c∗t . And φ = max{
0, iF,tkt
},
where
iF,t = (1− γF)(P∗t )η
εη−1c∗t − (1− γH)(Pt)
ηε−ηct .
3. If ε > 1, we have Pt > 1 > P∗t , kt = κ = k∗t , ct < ζ < c∗t , and φ = 0.
Proof. See section 5.7.
112
Although importing foreign capital goods does not affect the relative quality at Qt =
Q = 1, the choice of importing foreign capital goods to the home country still depends on
the following balance of trade condition,
(1− γF)(P∗t )η
εη−1t c∗t − (1− γH)(Pt)
ηε−η
t ct = 0, (5.41)
which directly comes from the trade balance equation with φt = 0. If the solution of equa-
tion (5.41) for εt provides that ε > 1, the Q steady state is a single point {Q = 1, εt = ε}; if
ε 6 1, the Q steady state is a set {Q = 1, ε 6 εt 6 1}, and every point that belongs to this
set is a steady state, where φ will be chosen to satisfies the trade balance condition, thus
εt = 0.
The Q steady state is a simple extension of the standard Ramsey model. The home
country and the foreign country are almost identical, and follow the same balanced growth
path to grow at rate α
1−αg. If this Q = 1 steady state is reached, we argue that the home
economy have caught up with the foreign economy.
5.4.2 Balanced Growth Path with Q < 1
Let us now return to the case that the home country is a less developed country with q0 < q∗0.
For any Qt ∈ (0,1), equation (5.6) implies that there exists φ(Qt) that satisfies q = g,
φ(Qt) = Qtg. (5.42)
This provides a necessary and sufficient condition for the home country to maintain a
constant relative quality with the foreign country. Therefore, in this case, importing high-
quality capital goods plays a key role in enabling the home country to keep up with the
foreign country. And the foreign country will always be the leading economy in this two-
country system.
Proposition 5.3. Balanced Growth Path with Q ∈ (0, 1) exists if and only if the solution to
the following equations of Qt and εt satisfies 0 < Qt < 1 and εt > 1,
(1− γF)(P∗t )η
εη−1t c∗t Q
θF (η−1)− α
1−α
t − 1− γH
QθH(η−1)t
(Pt)η
ε−η
t ct−Qtgkt = 0, (5.43)
113
n+δ +ρ + α
1−ασg
εt−11−Qt
Qt−ρ− α
1−ασg+
α
1−αg = 0, (5.44)
where kt =(
δ+n+ρ+(εt−1)Qtgα
+ σ
1−αg) 1
α−1< κ .
Proof. See section 5.7.
The first condition in proposition 5.3 is derived from the balance of payments constraint
for quality improvement, which establishes the boundary that the home country is able
to maintain a constant relative quality index with the foreign country. This is called the
balance of payments constraint for quality improvement locus, or simply BOP locus. For
any given ε , if Q is above this locus, the balance of trade constraint implies that iF,t >
φ(Qt)kt , thus Qt > 0, meaning that the balance of payments constraint is unbounded for
quality improvement and growth. This region is marked as “feasible”. If Q is below the
BOP locus, the balance of payments constraint implies that iF,t < φ(Qt)kt , thus, Qt < 0, the
home country diverges from the foreign country. This information is summarized in Figure
5.1, with arrows that illustrate the direction of motion for Q.
Figure 5.1: The balance of payments constraint for quality improvement (BOP)
The second condition in proposition 5.3 is derived from the first-order condition of
optimal capital import with φt = Qtg as the optimal solution, which establishes a direct
114
linkage between Qt and εt . Thus, for εt > 1, we have
Qt(εt) =n+δ +ρ + α
1−ασg
(εt−1)(1+ρ + α
1−ασg− α
1−αg)+n+δ +ρ + α
1−ασg
, (5.45)
which describes the locus of optimal capital import (OCI) for quality improvement that
satisfies Q = 0. For points to the right of this curve, the foreign capital goods are too
expensive to import for investment,11 thus, the optimal capital import share,φt , is less than
φ , thus, Q < 0. For points to the left of this OCI locus, the quality benefit that comes from
importing foreign capital goods overtakes the high foreign price, φt > φ , thus Q > 0. And
the latter region is marked as “optimal” for quality improvement, meaning that domestic
households prefer to import capital goods to improve Q. The directions of movement for
Q are displayed on the Q− ε plane by Figure 5.2.
Figure 5.2: The optimal capital import (OCI) locus
The interaction of the BOP locus and the OCI locus determines the dynamic features
of Q and ε on the Q− ε plane, as being summarized in Table 5.1. In particular, the steady
state of Q is determined by the intersection of these two curves.
• If an economy only satisfies the feasibility condition, the representative household is
feasible to choose a large sufficient level of capital import to improve Q, but chooses
11Recall that the first-order condition for φt , equation (5.36), for a larger εt , φt becomes smaller.
115
to not do so (not optimal), Q < 0. As a result, a relatively low capital import causes
the exchange rate to appreciate, ε < 0.
• If an economy only satisfies the optimality condition, the representative household
intend to choose a high capital import level that can not satisfies the balance of pay-
ments constraint with current exchange rate. Since international borrowing is not
allowed, this state is unstable, the exchange rate has to sharply depreciate to satisfies
the feasibility condition.
• If neither of these two conditions can be satisfied, we will have Q < 0. When this
low capital import choice is still bounded by the balance of payments constraint, we
will have ε > 0, otherwise, ε 6 0.
• If both feasibility and optimality conditions can be satisfied, we have Q > 0. How-
ever, the change of exchange rate is still determined by whether the balance of pay-
ments constraint is bounded.
Table 5.1: The interaction of balance of payments constraint and optimal capital import
BOP locusOCI locus
Above On Beneath
AboveFeasible, Not Optimal Feasible, - Feasible, Optimal
Q < 0, ε < 0 Q = 0, ε < 0 Q > 0, ε uncertain
On-, Not Optimal -, - -, OptimalQ < 0, ε < 0 Q steady state Unstable, ε > 0
BeneathNot Feasible, Not Optimal Not Feasible, - Not Feasible, Optimal
Q < 0, ε uncertain Unstable, ε > 0 Unstable, ε > 0
5.4.3 The Dynamics of Q
Following a standard phase diagram analysis, we can evaluate the existence of these two
types of steady states and characterize their dynamic features,
116
In our model, the steady state with Q is determined by the intersection of the BOP locus
and the OCI locus, while the steady state with Q = 1 is determined by the intersection of
trade balance condition at Q = 1, equation (5.41).12
For the sake of simplicity, we assume a minimum foreign demand structure for con-
sumption goods produced in the home country, and replace equation (5.14) by
c∗H,t = Γ(P∗H,t)−η QθF (η−1)
t , (5.46)
where Γ = (1− γF)(P∗t )η c∗t and we assume P∗t = 1. Therefore, the two-country model is
reduced to a small open economy model. We allow the foreign country to grow at a steady
state, where c∗ = ζ and k∗ = κ . Since c∗ is given as a constant, Γ is mainly affected by
parameter γF , the home bias parameter in the foreign country.
Table 5.2: Common parameters
Parameter δ g n α γH ρ σ η
Value 0.03 0.02 0.01 0.4 0.8 0.03 1 2
Table 5.3: Case-specific parameters
CaseParameter
θH θF γFFigure 5.3 (a) 3 3 0.95Figure 5.3 (b) 2 2 0.5Figure 5.4 (a) 1 1 0.8Figure 5.4 (b) 1 5 0.5
The following figures are simulated using various sets of parameters. Table 5.2 sum-
marizes the parameter values that are commonly used across models, including capital
depreciation rate δ , foreign quality improvement rate g, population growth rate n, produc-
tion function parameter α , home country consumption weight γH , preference parameter ρ
and σ , and the trade elasticity η . And Table 5.3 lists the case-specific parameters, such as
12Comparing equations (5.41) and (5.43), we know that the solution (ε) that satisfies the trade balancecondition at Q = 1 is to the left of the BOP locus.
117
quality adjustment parameters θH and θF , and foreign demand parameter Γ.13 One feature
worth noting is that these case-specific parameters do not enter equation (5.45), meaning
that the OCI locus is unaffected.
According to our proposition 5.1, Q = 1 is always a steady state, which is marked by
letter D, whereas the existence of steady state with Q ∈ (0, 1), marked by E, is uncertain.
Therefore, we discuss the following two cases, which are constructed based on the number
of intersections of the OCI locus and the BOP locus.
Zero Q Equilibrium
When the BOP locus and OCI locus have zero intersections in the interval of (0, 1) for Q,
the steady state with Q doesn’t exist. Figure 5.3 displays two possible scenarios, where the
arrows show the directions of movement for both ε and Q. On the ε−Q plane, these two
curves can be roughly parallel, or they can turn to intersect at Q > 1. The BOP locus can
be either above or beneath the OCI curve.
(a) (b)
Figure 5.3: Zero Q equilibriumNote: F, NF, O, NO stand for “Feasible”, “Not Feasible”, “Optimal”, and “Not Optimal”respectively. The steady state Q in panel (a) is given by ε = 1.57, while the steady state Qin panel (b) is given by 0.79 < εt 6 1.
13We do not stress the economic intuitions in these exercises, since we would like to cover most scenariosthat are theoretically possible.
118
Figure 5.3 panel (a) provides an example in which the BOP locus is above the OCI
locus. It shows that no points on the ε −Q plane could simultaneously satisfy the two
conditions in proposition 5.3. For any initial point, there is no dynamic path for the home
economy to catch-up with the technology frontier.
Panel (b) of Figure 5.3 illustrates a different case in which the BOP locus is beneath
the OCI locus. And steady state D (a set of steady states with Q = 1) appears to be stable.
There exists an optimal growth path lying between the BOP locus and the OCI locus and
passing a point that belongs to set D. Thus, panel (b) demonstrates a region wherein quality
upgrading and convergence would take place.
One Q Equilibrium
When the BOP locus intersects with the OCI locus only once within the interval of (0, 1)
for Q, we have one unique Q steady state, denoted by E. Figure 5.4 demonstrates two
examples.
(a) (b)
Figure 5.4: One Q steady stateNote: F, NF, O, NO stand for “Feasible”, “Not Feasible”, “Optimal”, and “Not Optimal”respectively. The steady state Q in panel (a) is given by ε = 1, while the steady state Q inpanel (b) is given by 0.59 < εt 6 1.
Panel (a) of Figure 5.4 illustrates the scenario wherein the BOP locus crosses the OCI
locus at point E from above. The arrows around point E indicate that this steady state is
locally stable. For an economy with initial quality index Q0 < Q, there is a dynamic path
119
that leads to point E. However, the equilibrium point D, in this case, is unstable. Thus,
point E is a dominant steady state. Since Q < 1, the quality upgrade in the home country
will prematurely stop at Q. Comparing this result with the example of Figure 5.3 panel
(b), we find that this is mainly caused by the relatively high home bias in the consumption
demand of the foreign country. This feature is consistent with the empirical finding of
Henn, Papageorgiou, and Spatafora (2013) that the quality convergence is particularly rapid
during the early stages of development and completes as a country reaches upper middle-
income status.
Figure 5.4 panel (b) depicts the scenario wherein the BOP locus crosses the OCI locus
from another direction. The intersection point E is a Q steady state, but it is unstable.
According to Table 5.3, one key difference arises: the quality punishment factor θF is
large, thus the foreign demand drops rapidly with lower product quality. As a result, this
equilibrium generates two contrary dynamic paths: for an economy with initial product
quality that is relatively close to the foreign leader (Q0 > Q), it could converge to the set of
steady state D, reaching Q= 1; for a poorer economy with low initial product quality (Q0 <
Q), in contrast, it is severely constrained by the balance of payment. This country cannot
simultaneously satisfy the feasibility and optimality conditions, and has to deteriorate to
the lower right corner of this ε −Q plane. Therefore, in this case, both convergence and
divergence of income would take place.
5.5 Discussion
In this section, we revisit a series of stylized facts and apply our model to shed light on the
underlying relationship between trade and economic growth.
5.5.1 Import Share of Investment
An important piece of empirical evidence that reveals the role of capital goods import
involves a trade-off between consumption and investment in a country’s imports. Based on
data from the World Input-Output Database (Timmer, 2012), Table 5.4 lists the percentage
of imports that is used for investment for ten countries during 1996 and 2009, and shows
that rapid developing economies spend larger shares of import on investment. For example,
the investment shares of import could be higher than 60 percent in China, India, Korea, and
120
Turkey, while they can be lower than 30 percent in developed countries like the United
Kingdom and Japan.
Table 5.4: Investment share (% of imported final expenditure)
1996 2000 2004 2009China 66.6 68.2 65.6 55.4France 30.5 32.0 29.6 32.7India 48.0 35.3 65.5 64.5Japan 27.9 32.5 31.5 27.8Korea 61.7 52.3 50.0 44.8
Mexico 44.9 49.0 44.5 39.7Taiwan 40.0 49.0 45.7 40.0Turkey 69.1 58.7 56.8 50.4U.K. 34.8 31.5 21.9 19.2U.S. 43.5 44.3 39.5 36.0
Source: Author’s calculation using World Input-Output Database, 1996-2009.
Since the United States is often referred as the world economic leader, we use the PPP
converted GDP per capita relative to the United States as an approximate indicator for
Q (Penn World Table version 7.1). Figure 5.5 illustrates a negative relationship between
capital goods import (for investment) and relative income to the United States.
This result is qualitatively consistent with the implication of our model. The dash line
in Figure 5.5 depicts the capital goods import shares along the OCI locus, which continu-
ously decreases as Q increases. When Q is lower, the benefit on quality improvement from
importing foreign capital goods is relatively large. As a result, individuals would spend a
larger portion of international trade revenue on high-quality foreign capital inputs. As Q
approaches to 1, importing foreign capital goods become less attractive, thus the investment
share drops and is gradually replaced by household consumption.
5.5.2 Trade Balance and Exchange Rate Reversal
One of the prevalent illusions of Asian economic growth is that the rapid economic ex-
pansions are associated with chronic trade surpluses. This phenomenon has been heavily
criticized as a “beggar-thy-neighbor” policy, which involves exporting unemployment to
other nations and influencing foreign labor market structures. In chapter 3, we show that
121
IND
IND
INDCHNCHNINDCHN
CHNTUR
TUR
TUR
TUR
MEXMEX
MEX
MEXKOR
KOR
KOR
KOR
TWN
TWNTWN
TWN
GBR
JPNFRAJPNFRAGBRJPNFRA
FRA
GBRGBR
JPN
USAUSA
USAUSA
020
4060
8010
0In
vest
men
t sha
re o
f im
port
(%
)
0 20 40 60 80 100Relative income/quality to the leader (%)
Data Model prediction
Figure 5.5: Investment share of import (data vs model prediction)Note: Parameter values are given by Table 5.2 and the case of Figure 5.4 panel (a).
U.S. trade deficits could account for about 30 percent of the overall employment share de-
crease in American manufacturing. Bernanke (2005) further argued that it is a primary
cause of the global current account imbalances.
The economic history tells a different story: major Asian economies did not develop
large trade surpluses in the early stage of development until they passed a certain threshold,
at which point their trade balances turned into surpluses. This trade balance reversion can
take several years to complete, during which the trade balances fluctuate up and down
between deficits and surpluses. This took place in Japan and Taiwan between 1965 to
1980, in South Korea between 1977 to 1996, and in China during the 1990s.
This trade balance reversal is associated with the dynamics of real exchange rate. Fol-
lowing Rodrik (2008), we use data from Penn World Tables 7.1 (Heston, Summers, and
Atina 2012) to calculate a “real” exchange rate (RER)
lnRERit = ln(
XRATit
PPPit
),
where i is an index for countries and t is an index for time periods. Exchange rates (XRAT )
and PPP conversion factors (PPP) are expressed as national currency units per U.S. dollar.
Figure 5.6 depicts the change of the real exchange rate of five economies during 1950-2010:
122
China, Japan, South Korea, Singapore, and Taiwan. It shows that China, South Korea, and
Taiwan shared a similar relationship between growth and real exchange rate adjustment,
which first depreciated, and then reversed to appreciate. In developing countries, real ex-
change rates significantly affect economic growth, as overvaluation hurts growth while
undervaluation facilitates it (Rodrik, 2008). This relationship is stronger for developing
countries, but disappears for advanced countries. Thus, it suggests that the real exchange
rate is associated with some fundamental factors in the process of economic convergence.0
12
34
Rea
l exch
an
ge
ra
te
4 6 8 10 12log real GDP
China Japan
Korea Singapore
Taiwan
Figure 5.6: Real exchange rate dynamics
Government Debt: an Extension of the Baseline Model
Since we assume no foreign capital flows in the basic model, the area that is “Not Feasible,
but Optimal” is actually inaccessible: the exchange rate has to depreciate sharply to ensure
the trade balance is zero. As a result, in the example that is illustrated by Figure 5.4 panel
(b), a low income country is unable to catch up with the foreign country. Therefore, it
would be interesting to investigate whether foreign aid is able to help.
We assume that the government in the home country is able to borrow in the capital
market to finance trade deficits, as long as the government debt is below the debt ceiling,
Bt 6 B, such that
T Bt = Bt+1−RB,tBt ,
123
where RB,t represents the interest rate of government bond. In addition, we assume the
adjustment of exchange rate is sluggish and depends on a function of trade balance, τ(·)
ε
ε= τ (tbt) , (5.47)
where tbt = (1− γF)(P∗t )η
εη−1t c∗t Q
θF (η−1)− α
1−α
t − (1− γH)(Pt)η
ε−η
t ctQ−θH(η−1)t − iF,t .
Following these two assumptions, the home economy that starts with an initial state that
is considered to be “Not Feasible, but Optimal” can catch up with the foreign economy,
while the exchange rate depreciates and foreign debts accumulate over time.
Figure 5.7: Government debt and quality improvement
Figure 5.7 illustrates the example of Figure 5.4 panel (b) with international borrowing.
It shows that if the government can borrow to finance the capital good import, a growth
strategy emerges: the home country can take a saddle path (dash arrow line) to reach equi-
librium point E. However, this stage of growth heavily relies on accumulating foreign debt
to finance persistent trade deficits, which makes the home economy more vulnerable to
external shocks and currency crisis. After passing point E, this economy becomes self-
reliance and has the option to reach the set of steady state D. An overview of the whole
process indicates that two patterns would reverse before and after passing point E: the
trade balances move from deficit to surplus and the exchange rate turns from depreciation
to appreciation.
124
5.6 Concluding Remarks
We have developed a growth model that features quality upgrading as the primary driver
of income convergence. As we assume that technology is embodied in high-quality capital
goods, the model emphasizes the import of foreign capital goods as the main channel of
international technology diffusion, which could be restricted by the balance of payments
constraint. We characterize the possible steady states and discuss their dynamic features.
Our model consolidates existing empirical evidence on the East Asian growth experi-
ence. Importing foreign capital goods improves the quality of domestic capital stock and
output through an intensive factor accumulation process, and consequently promotes in-
dustry upgrading (measured by quality improvement). Since import expansion is subject to
the balance of payments constraint, persistent export expansion is needed to finance rising
capital goods import, while better product quality ensures growing foreign demand. It sug-
gests that the factor accumulation, industry upgrade, and export orientation strategy can be
considered as three by-products of economic development.
The role of product quality is in keeping with the empirical findings by Hallak (2006)
and Feenstra and Romalis (2014) that rich countries import more and consume more from
countries producing high-quality goods. Thus, a potential barrier of growth is the low prod-
uct quality in developing countries. Our analysis shows that for a developing economy with
very poor product quality, it would be hurt badly by the balance of payments constraint,
since the foreign demand is very limited. It also implies that countries that are close to the
economic leader have better opportunities to catch-up to the frontier.
Our framework yields predictions about the dynamics of trade balance and exchange
rate. In an extension that allows government borrowing, our model demonstrates the sce-
nario with trade balance reversal and exchange rate reversal, which is consistent with the
empirical observations in a few Asian economies. One thing worth noting is that the ex-
change rate, generally speaking, appreciates along with quality improvements.
Finally, our framework is simple enough to allow for extensions and variations. For
example, it is straightforward enough to allow multiple sectors in our model to analyze
structural change. Then the model could quantitatively evaluate the economic growth and
structural transformation for a specific economy. We will pursue such an extension in our
ongoing research.
125
5.7 Mathematical Details
Proposition. 5.2 Balanced Growth Path with Q = 1. For Qt = Q = 1, the balanced of
payments constraint determines equilibrium exchange rate, ε , which characterizes three
equilibria with balanced growth path. And all major variables of these two economies can
grow at a constant rate, α
1−αg.
1. If ε = 1, we have Pt = P∗t = 1. Thus kt = k∗t = κ , ct = c∗t = ζ . And φ = (γH− γF)ζ
κ>
0. In particular, φ = 0 if and only if γH = γF .
2. If ε < 1, we have Pt < 1 < P∗t , kt > κ = k∗t and ct > ζ > c∗t . And φ = max{
0, iF,tkt
},
where
iF,t = (1− γF)(P∗t )η
εη−1c∗t − (1− γH)(Pt)
ηε−ηct .
3. If ε > 1, we have Pt > 1 > P∗t , kt = κ = k∗t , ct < ζ < c∗t , and φ = 0.
Proof. Let’s go over the three scenarios in turn. From equation (5.26), we have
ε2η−1t =
(1− γH)(Pt)η−1 ct
(1− γF)(P∗t )η−1 c∗t
,
which implies that the equilibrium exchange rate, ε , is determined by preference parameter
γH , γF , elasticity of trade η , and relative consumption.
1. ε = 1. Since PF,t = εt and P∗H,t =1εt, we have Pt = P∗t = 1. Equations (5.5) and (5.6)
are consistent with standard Ramsey–Cass–Koopmans model. Under these specific
configuration, we have
kt = k∗t = κ,
ct = c∗t = ζ .
According to the balanced trade condition, we have
φt = (γH− γF)ζ
κ> 0.
In particular, φt = 0 if and only if γH = γF .
126
2. ε < 1. Pt < 1 < P∗t .
kt =
(δ +n+ρ
α+
σ
1−αg− (1− ε)φt
) 1α−1
> κ = k∗t ,
ct =1Pt
{kα
t −[
n+δ +α
1−αg+(ε−1)φt
]kt
}>
1Pt
[κ
α − (n+δ +α
1−αg)κ]> ζ >
ζ
P∗t= c∗t
From equations (5.36) and (5.26), we have
ktφt = (1− γF)(P∗t )η
εη−1c∗t − (1− γH)(Pt)
ηε−ηct .
3. ε > 1. Pt > 1 > P∗t . Since ∂H∂φt
< 0, we haveφt = 0. Thus,
kt =
(δ +n+ρ
α+
σ
1−αg) 1
α−1
= κ = k∗t ,
ct =1Pt
ζ < ζ <ζ
P∗t= c∗t ,
Proposition. 5.3 Balanced Growth Path with Q ∈ (0, 1) exists if and only if the solution to
the following equations of Qt and εt satisfies 0 < Qt < 1 and εt > 1,
(1− γF)(P∗t )η
εη−1t c∗t Q
θF (η−1)− α
1−α
t − 1− γH
QθH(η−1)t
(Pt)η
ε−η
t ct−Qtgkt = 0,
n+δ +ρ + α
1−ασg
εt−11−Qt
Qt−ρ− α
1−ασg+
α
1−αg = 0,
where kt =(
δ+n+ρ+(εt−1)Qtgα
+ σ
1−αg) 1
α−1< κ .
Proof. According to the Hamiltonian, when εt > 1 and 0 < Qt < 1, we get νt > 0, meaning
that the constraint of quality improvement is binding, qt = g. Equation (5.38), the Euler
equation, implies that kt =(
δ+n+ρ+(εt−1)Qtgα
+ σ
1−αg) 1
α−1< κ .
127
Using an implication of the first-order conditions, such that λtνt=
1−QtQt
qt
(εt−1)Kit, we have
φt =λt
νtRtKi
t +2Qtg−ρ + νt
=
1−QtQt
qt
εt−1αkα−1
t
qt+2Qtg−ρ + νt
=1−Qt
Qt
αkα−1t
εt−1+2Qtg−ρ +
[λt + ˆ(εt−1)+ Ki
t − qt−ˆ(
1−Qt
Qt
)]
Since Cit = ct +
α
1−αqt , thus,
φt =1−Qt
Qt
αkα−1t
εt−1+2Qtg−ρ+
[−σ ct−
ασ
1−αqt− Pt + ˆ(εt−1)+ kt +
α
1−αqt− qt−
ˆ(1−Qt
Qt
)].
At steady state, we have φt = Qtg, qt =α
1−αg and ct = 0. Using αkα−1
t = n+δ +ρ +α
1−ασg+(εt−1)φt , we have
(1− 1−Qt
Qt
)φt =
1−Qt
Qt
n+δ +ρ + α
1−ασg
εt−1+2Qtg−ρ
+
[−σ ct−
ασ
1−αqt− Pt + ˆ(εt−1)+ kt +
α
1−αqt− qt−
ˆ(1−Qt
Qt
)]
2Qg−g = 2Qg−g+1−Qt
Qt
n+δ +ρ + α
1−ασg
εt−1−ρ− ασ
1−αqt +
α
1−αqt ,
n+δ +ρ + α
1−ασg
εt−11−Qt
Qt−ρ− ασ
1−αg+
α
1−αg = 0,
Qt(εt) =n+δ +ρ + α
1−ασg
(εt−1)(ρ + α
1−ασg− α
1−αg)+n+δ +ρ + α
1−ασg
.
128
Chapter 6
Conclusion
This thesis consists of three original research papers. Each of them covers an interesting
topic that is related to structural transformation, trade, and economic growth.
We start with a quantitative evaluation of the impact of trade balance on structural
change, using the postwar data of the United States. Similar to the results of Bah (2008)
and Buera and Kaboski (2009), we first show that a closed economy structural change
model runs into difficulties to account the decline of employment shares in the manufactur-
ing sector since the early 1980s. After taking into account for the sectoral trade pattern and
the overall trade balance, the unexplained structural transformation mostly disappears. As
we decompose the relative contributions of various factors in our benchmark calibration,
the trade imbalance can explain up to 30 percent of the total decline of the manufacturing
employment in the United States; other trade factors, such as the inter-sector trade effect,
cover about 5 percent; while the unbalanced productivity progress might account for about
34 percent. These quantitative results support the argument that international competition
and trade imbalances have significant impacts on domestic labor market and affect struc-
tural change.
The second essay explains the stylized fact that both the manufacturing employment
shares and investment rates exhibit some hump-shaped trends as income rises. Following
the recent research that stressed the role of the modernization process in the agriculture
sector, which gradually transfers a traditional Malthusian economy into a modern Solow
economy, we argue that the modernization of the traditional economic sector can simul-
taneously cause these two hump-shaped pattern. There are two channels through which
129
agriculture modernization can affect investment and structural change. The direct effect
comes from the replacement of traditional labor-intensive agriculture production technol-
ogy by a modern capital-intensive technology, which increases demand for capital goods.
As a result, agricultural labor demand decreases, which causes an indirect effect, since the
workers who leave the traditional agriculture sector require extra capital goods to settle
into the modern sectors. Overall, the agriculture modernization process temporally raises
the demand of capital goods, leading to high investment rates and high labor employment
in the manufacturing sector. We further show that the long-run equilibrium of our model
satisfies the condition for the generalized balanced growth path (Kongsamut, Rebelo, and
Xie, 2001). Our model yields predictions that agriculture modernization can cause the
hump-shaped patterns of manufacturing employment and investment rate simultaneously.
Therefore, the unbalanced technology growth is not necessary to derive a hump-shaped
pattern of structural transformation. It establishes a simple mechanism that helps us to
understand why the patterns of structural transformation across countries are very similar.
Finally, we explore the relationship between trade and growth in the third essay. We fo-
cus on a specific channel of international technology diffusion that developing country can
only improve productivity (measured by quality) through importing foreign capital goods,
which is subject to the balance of payment constraint. This mechanism consolidates the
three popular explanations into one plausible story: foreign capital import improves the
quality of domestic capital stock by factor accumulation and consequently promotes indus-
try upgrading (measured by quality improvement), while the continuous export expansion
ensures that this growth process is sustainable. Therefore, we prefer to use trade-led growth
rather than export-led growth to describe the Asian growth miracle. The predictions from
our model qualitatively fit empirical observations. For example, our framework shows that
the capital import share in final expenditure decreases as income increases, fitting the fact
that low income country tends to import more capital goods.
These models have great flexibility to allow for extensions and implications. For exam-
ple, the interaction between trade constraint and growth provides new insights for fighting
poverty and achieving sustainable growth, and understanding the structural transformation
process helps us to predict industry dynamics, labor market movements, and pollution and
energy consumption patterns, which could generate a large body of policy recommenda-
tions.
130
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