metadata: authors: 0: author: Ju, Jiandong
1: author: Lin, Justin Yifu
2: author: Wang, Yong
count: World
docna: 0: docna: Endowment structures, industrial dynamics,
            and economic growth
docty: Policy Research Working Paper
subtopic: Economic Theory & Research,Industrial Economics,Construction Industry,Common Carriers Industry,Food & Beverage Industry,General Manufacturing,Pulp & Paper Industry,Plastics & Rubber Industry,Coastal and Marine Resources,Economic Growth,Energy and Natural Resources,Business Cycles and Stabilization Policies,Global Environment
teratopic: Private Sector Development,Macroeconomics and Economic Growth,Finance and Financial Sector Development
abstracts: cdata!: This paper develops a dynamic general
            equilibrium model to explore industrial evolution and
            economic growth in a closed developing economy. The authors
            show that industries will endogenously upgrade toward the
            more capital-intensive ones as the capital endowment becomes
            more abundant. The model features a continuous
            inverse-V-shaped pattern of industrial evolution driven by
            capital accumulation: As the capital endowment reaches a
            certain threshold, a new industry appears, prospers, then
            declines and finally disappears. While the industry is
            declining, a more capital-intensive industry appears and
            booms, ad infinitum. Explicit solutions are obtained to
            fully characterize the whole dynamics of perpetual
            structural change and economic growth. Implications for
            industrial policies are discussed.
repnme: repnme: Endowment structures, industrial dynamics,
            and economic growth
display_title: Endowment structures, industrial
            dynamics, and economic growth
listing_relative_url: /research/2009/09/12589199/endowment-structures-industrial-dynamics-economic-growth
topicv3: Economic Growth m1326241 471,Natural Resources m1326446 1979,Manufacturing Sectors m1326521 1281,Environment, Natural Resources and Blue
            Economy m1327391 566,Industry Policy m1327403 1075
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Private Sector Development,Macroeconomics and Economic Growth,Finance and Financial Sector Development
no_of_pages: 43
model_extractions: WPS5055 Policy Research Working Paper 5055 Endowment Structures, Industrial Dynamics, and Economic Growth _Jiandong Ju Justin Yifu Lin Yong Wang_ The World Bank Development Economics Vice Presidency September 2009
Policy Research Working Paper 5055

# **Abstract**

This paper develops a dynamic general equilibrium model to explore industrial evolution and economic growth in a closed developing economy. The authors show that industries will endogenously upgrade toward the more capital-intensive ones as the capital endowment becomes more abundant. The model features a continuous inverseV-shaped pattern of industrial evolution driven by capital accumulation: As the capital endowment reaches a certain threshold, a new industry appears, prospers, then declines and finally disappears. While the industry is declining, a more capital-intensive industry appears and booms, ad infinitum. Explicit solutions are obtained to fully characterize the whole dynamics of perpetual structural change and economic growth. Implications for industrial policies are discussed.

This paper—a product of the Development Economics Vice Presidency—is part of a larger effort in the World Bank to contribute to a better understanding of the economic and social development process. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at research@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Endowment Structure, Industrial Dynamics, and Economic Growth

Jiandong Ju<sup>�</sup> , Justin Yifu Lin<sup>y</sup> , Yong Wang<sup>z�</sup> This version: October 20, 2009 Abstract This paper develops a dynamic general equilibrium model to explore industrial evolution and economic growth in a closed developing economy. The authors show that industries will endogenously upgrade toward the more capital-intensive ones as the capital endowment becomes more abundant. The model features a continuous inverse-V-shaped pattern of industrial evolution driven by capital accumulation: As the capital endowment reaches a certain threshold, a new industry appears, prospers, then declines and ...nally disappears. While the industry is declining, a more capital-intensive industry appears and booms, ad in...nitum. Explicit solutions are obtained to fully characterize the whole dynamics of perpetual structural change and economic growth. Implications for industrial policies are discussed.

Key Words: Endowment, Industrial Dynamics, Economic Growth, Structural Change JEL Codes: L50, O14, O40

> �University of Oklahoma, Email address: jdju@ou.edu; yWorld Bank, Email address: justinlin@worldbank.org; zHong Kong University of Science and Technology, Email address: yongwang@ust.hk. For detailed comments and helpful discussions, we would like to thank Philippe Aghion, Jinhui Bai, Gary Becker, Veronica Guerrieri, Chang-Tai Hsieh, Aart Kraay, Kala Krishna, Norman Loayza, Francis T. Lui, Erzo Luttmer, Rachel Ngai, Paul Romer, Harald Uhlig, Danyang Xie, as well as many other seminar participants in several institutions. Ju and Wang thank the World Bank for the hospitality and ...nancial support. All remaining errors are our own.

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"The growth of GDP may be measured up in the macroeconomic treetops, but all the action is in the microeconomic undergrowth, where new limbs sprout, and dead wood is cleared away." –World Bank Commission on Growth and Development (2008, pp.2-3)

# 1 Introduction

The main goal of this paper is to develop a formal model to explain the industrial dynamics along the path of economic growth in developing countries. We show how the optimal leading industries are structurally di¤erent at di¤erent development stages, depending mainly on the economy’s endowment structure and its evolution. Sustained economic development from a low-income status to high-income status in countries in modern times is characterized by continuous technological innovation and industrial upgrading (see Chenery (1960), Kuznets (1966), Maddison (1980), Chenery, Robinson, and Syrquin (1986), Hayami and Godo (2005)). Beneath the GDP growth, the products or major industries in the manufacturing sector of these economies are continuously changing over time. First labor-intensive goods such as textiles and shoes are produced, then those industries decline and are gradually replaced by the more capital-intensive industries such as machinery and electronics, which also decline later while even more capital-intensive industries arise such as cars and aircraft, and so forth. Such a pattern, as shown in Figure 1, was referred as the ‡ying geese pattern of economic development by Akamatsu (1962) in the 1930s and further developed by Kojima (2000).

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transformation driven by the externality of human capital. Buera and Kaboski (2009) focus on the expansion of the service sector. Some other works strive to match Kuznets facts, which state that development is typically a process of a decline in agriculture, a rise in services, and a hump-shaped change in industry. In addition, that literature mainly focuses on the long-run (balanced or asymptotic) growth rate (or steady state) without explicitly and completely characterizing the whole dynamics for the structural change per se. Moreover, in those models the structural changes are driven either by the demand shift in the consumption goods as people get richer (see Laitner (2000), Caselli and Coleman (2001), Kongsamut, Rebelo, and Xie (2001), Gollin, Parente, and Rogerson (2002)), or by the di¤erent productivity growth across di¤erent sectors as ...rst suggested by Baumol (1967), and further developed by Hansen and Prescott (2002) and Ngai and Pissarides (2007). In this paper, we argue that the inverse-V-shaped industrial dynamics in a developing country is driven mainly by the change in its endowment structure. The endowments are given at any given time and changeable over time. One of the key di¤erences between a developed and developing country is the di¤erence in the relative abundance of capital in their endowment structures. The economic development process in a developing country is characterized by the continuous upgrading of its endowment structure from relatively scarce in capital and relatively abundant in labor or natural resources to relatively abundant in capital and relative scarce in labor/natural resources. Lin (2003, 2009) argues that the optimal industrial structure in an economy at a given time should be consistent with the given endowment structure at that time: as capital accumulates and becomes relatively cheaper, the industries should optimally upgrade toward more capital-intensive ones accordingly. Motivated by Lin’s argument, our model will show that the driving force for the ‡ying-geese pattern of industrial upgrading in the development process of a developing country is the continuous capital deepening in the endowment structure.

Acemoglu and Guerrieri (2008) have examined how the capital deepening has an 3
asymmetric impact on the sectors with di¤erent capital intensities, but their main objective is to study how the elasticity of substitution between two sectors with di¤erent capital shares a¤ects the long-run asymptotic aggregate growth rate. Moreover, their model has two sectors and is thus unable to explain the ‡ying-geese pattern of repetitive inverse-V-shaped industrial upgrading dynamics.

It is very important to understand the widely observed inverse-V-shaped industrial dynamics in the process of economic development. What type of industry should we expect to dominate at a certain stage of development? Would it be optimal for the government in a low-income country to support the development of certain industries that prevail in high-income countries? To answer these questions, it is not enough to merely recognize the long-run structural change among the primary, secondary, and tertiary sectors or in the rural-urban transformation.

In what follows, we develop a growth model featuring this inverse-V-shaped industrial dynamics along the development path. The major force driving the structural change is the increase in the capital-labor ratio (or alternatively, endowment structure). As capital becomes more abundant and relatively cheaper, the more capital-intensive industrial goods are produced, because the more capital-intensive industry products are not only more a¤ordable but also more desirable for the consumers. At the same time, the more labor-intensive goods are gradually displaced. As capital becomes even more abundant, goods with an even higher capital intensity become more desirable to produce and consume. This generates the endless inverse-V-shaped industrial dynamics. Our model underscores the key role played by the changes in endowment structure rather than productivity increase. This might be reasonable because our model is mainly geared toward developing economies where industrial upgrading relies mainly on borrowing existing technologies from developed countries (Hayami and Goto (2005)), in contrast to the developed economies where huge research and development expenditure is required for technology innovation and industrial upgrading.

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To highlight the industrial dynamics, we deviate from the standard practice in the growth literature, which typically only focuses on the steady state or the long-run (balanced or asymptotic) growth rate. Instead, we obtain the explicit solution for the whole dynamics in the structural changes, even though we are considering a dynamic economy with an in...nitely dimensional commodity space and an in...nite time horizon.<sup>3</sup> We decompose this seemingly complicated structural analysis into two steps. First, along the time dimension, the representative household simply decides the allocation of capital for producing consumption goods and savings. The household’s capital allocation determines the evolution of capital endowment and the intertemporal use of capital in production. Then, along the cross-section dimension, the capital allocated for production determines the production structures (industrial choices) as if it were a static model. Ultimately, the mathematical problem is reduced to dynamic optimization with switching state equations. This approach, which we call a dynamic structural analysis, can tremendously simplify the analysis of perpetual industrial upgrading with long-run growth.

Our paper is related to the literature of quality-ladder growth models because in our model di¤erent industrial goods are modelled as perfect substitutes and are produced with di¤erent technologies. Aghion and Howitt (1992) emphasize that the ...rm’s incentives to earn monopolistic rents justify its endeavor to undertake risky and costly R&D, which ultimately causes the creative destruction (also see Grossman and Helpman, 1991a). Our model is methodologically closest in spirit to Stokey (1988), who characterizes how the learning-by-doing keeps the band of the produced commodities moving toward higher and higher qualities. The main goals of that literature, however, are to generate sustained economic growth at the aggregate level instead of trying to explain the inverse-V-shaped industrial dynamics. More

> 3 There may be a technical reason why the well-recognized fact of industrial dynamics has rarely been formalized in growth models. Closed-form solutions for transitional dynamics are typically very hard to obtain even in most of the two-sector growth models, but the aforementioned inverse-V-shaped industrial dynamics is by nature the transitional dynamics per se, so the industrial upgrading with an in...nite-dimensional commodity space appears even more unwieldy.

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importantly, all these papers try to emphasize the role of technological advancement or knowledge accumulation with stable industries while our paper stresses the role of capital accumulation and industrial upgrading. In addition, this literature, like other growth models, also mainly studies the long-run balanced growth path while leaving the transitional dynamics aside. The industrial climbing result in Stokey (1988), for example, is obtained essentially through comparative statics rather than the full-blown dynamic model. By contrast, we are able to provide the closed-form solutions for all the dynamics.

Simple comparative statics in our static model shows how the change in the endowment structure determines the changes in industrial structures, a result similar to the Heckscher-Ohlin model with multiple diversi...cation cones (see Leamer (1987), Schotter (2003)). However, there is a nontrivial di¤erence. These multiple diversi...cation cone models mainly consider open economies where the production structure of a country is determined by international specialization. By contrast, in our closed economy model, the households and ...rms select endogenously which set of products to consume and produce. More importantly, our dynamic model enables us to obtain explicit solutions to characterize the whole inverse-V-shaped dynamics of the in...nite industrial upgrading, while H-O models with multiple diversi...cation cones are mostly static. To highlight the direct impact of endowment change on the industrial dynamics, we purposefully ignore the e¤ect of international specialization according to comparative advantage and only consider a closed economy in this paper.<sup>4</sup> We suspect that our main proposition, namely, the change in endowment structures drives the change in industrial structures, will be only strengthened

> 4 Notice that in our paper a developing country is implicitly assumed to be able to freely borrow the technology knowhow of more capital intensive industries from the developed countries. The main conclusions of the model are expected to hold in an open economy model. Moreover, except in an extremely small economy, the domestic market plays a major role in economic development. For example, Chenery, Robinson, and Syrquin (1986) ...nd that expansion in the domestic demand accounted for a 72%-74% increase in domestic industrial output in those countries with population larger than 20 million, and that even for small and manufacturing-oriented countries with population less than 20 million, domestic demand expansion accounts for a 50%-60% increase in the total industrial output. See Murphy, Shleifer and Vishy (1989) for more argument.

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in an open economy, as predicted by standard H-O trade models.<sup>5</sup> Our model characterizes the ...rst-best scenario in which the industrial structures evolve optimally in a perfectly competitive and frictionless economy. In such an ideal world, no government intervenes and the market itself can identify and support the right industries at each development stage. But what if the government pursues a wrong development strategy and pushes the economy to develop some inappropriate industries? We show in this paper that such policy mistakes may sometimes cause the economy to fall into a poverty trap such that long-run growth becomes impossible without foreign help. The markets are far from perfect in the real world, so it may be desirable for the government to have an industrial policy which will help to provide ...rms with information, coordinate ...rms’investments and compensate for externalities produced by pioneer ...rms (Murphy, Shleifer, and Vishny (1989), Lin (2009)). However, the prerequisite for a successful industrial policy is to identify what type of industries should be supported at each di¤erent development stage. Our ...rst-best characterization sets a theoretical benchmark that may potentially help us think further about these issues.

The paper is organized as follows: Section 2 presents the static model. The dynamic model is analyzed in Sections 3 and 4. Welfare consequences of the mistakes in industrial choices are discussed in Section 5. Section 6 concludes. Technical proofs and derivations are put in the Appendix.

# 2 Static Model

## 2.1 Setup

Consider a closed developing economy with a unit mass of identical households. Each household is endowed with L units of labor and E units of capital, which

> 5 Ventura (1997) shows theoretically how factor-price-equalization driven by international trade can explain the rapid catching-up growths of several export-oriented East Asian economies. Krugman (1979) constructs a North-South trade model to explore how the catching up process depends on whether the rich country’s innovation speed exceeds the poor country’s imitation speed.

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conceptually consists of both tangible physical capital and intangible capital. For parsimony purpose, we will narrowly interpret this "composite capital" as physical capital from now on in this qualitative investigation. The given commodity space has in...nite dimensions. Let cn denote the consumption of good n = 0; 1; 2; ::. In particular, good 0 may be interpreted as a household product, and good n for n � 1 may be interpreted as “industrial”product. De...ne the aggregate good as where the quality coe¢ cient for good i is �n.<sup>6</sup> We require cn � 0 for any n: The representative household’s utility function is CRRA: All the production technologies exhibit constant returns to scale. In particular, good 0 is produced with labor only. One unit of labor produces one unit of good 0. For any industrial good n = 1; 2; 3; :::; both labor and capital are required and the production functions are Leontief:<sup>7</sup>

> 6 This assumption is quite standard in the vertical innovation growth literature. The speci...cation is also mathematically isomorphic to the following alternative economic interpretation: C is the ...nal good while all the cn; n = 0; 1; 2; ::: are intermediate goods, so �n should be interpreted as the "productivity" for good n. It is not unusual in growth literature to assume perfect substitutability for the output across di¤erent production activities. For example, the agricutural Malthus production and the modern Solow production are two linearly additive components for the total output in Hansen and Prescott (2002) and Lucas (2009). A further discussion will be devoted to this "perfect substitutability" assumption later.

> 7 This assumption drastically simpli...es the dynamic strucutral analysis partly by giving us a lot of linearities. In the Appendix, we show that the main results remain valid with Cobb-Douglass function, but the dynamic analysis will be much more complex. Houthakker (1956) shows that Leontief production functions with Pareto-distribution heterogenous paratermers can aggregate into Cobb-Douglass production functions. Lagos (2006) constructs another distribution that can aggregate heterogenous Leontief functions into CES production functions. These may be helpful in understanding how ...rm heterogeneities may a¤ect our results, which is a very interesting research direction.

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where an is the capital intensity of producing one unit of good n: All the markets are perfectly competitive. Let pn denote the price of good n. Let r denote the rental price of capital and w denote the wage rate. Thus, ...rm’s zero pro...t function implies that p0 = w and pn = w + anr for n = 1; 2; 3; ::.

We assume Therefore, a higher-index good has a higher quality but is more capital intensive. The last inequality in (4) not only rules out the trivial case that only the highest quality good is produced in any equilibrium, but also simpli...es our analysis, as will be clear shortly.

The household problem is to maximize (1) subject to the following budget constraint Set up the Lagrangian with the multiplier denoted by �, and we obtain the following optimality condition for consumptions:

# 2.2 Market Equilibrium

The market equilibrium is determined by the endowment structure (capital per capita),<sup><u>E</u></sup> L<sup>: In the Appendix, we show that at most two goods are produced simultaneously</sup> in the equilibrium and that these two goods have to be adjacent in capital intensities. The intuition is the following: Suppose goods n and n + 1 are produced for some 9
n � 1. From consumer’s maximization problem, we immediately have which implies that Obviously, MRSj;j+1 > pjp+1j<sup>whenever</sup> w<sup><u>r</u>></sup> a<sup>j</sup> <u>�(a��1�)</u><sup>; and MRSj;j�1></sup> pjp�j 1<sup>whenever</sup> wr<sup><</sup> a<sup>j�</sup> <u>�</u><sup>1</sup> �(a1��)<sup>foranyj= 1; 2; ::.Therefore,when</sup> w<sup><u>r</u>=</sup> a<sup><u>n</u></sup> <u>�(a��1�)</u><sup>,goodn + 1mustbe</sup> strictly preferred to good n + 2; because the marginal rate of substitution is larger than their relative price. This means that cj = 0 for all j � n + 2. Using the same logic, we can also verify that cj = 0 for all 1 � j � n � 1. In addition, condition (4) ensures that good 0 will not be produced, as can be veri...ed by simply comparing the marginal rate of substitution between good n and good 0 and their price ratio. Similarly, when goods 0 and 1 are produced, we can show that good 1 is strictly preferred to any good n � 2: The market clearing conditions for labor and capital are 10
<!-- Start of picture text --> E<br>a n + 1<br>W '<br>B '<br>a n<br>W<br>B<br>a n − 1<br>A ' A<br>0 L<br><!-- End of picture text --> Figure 2. How Endowment Stucture Determines Optimal Industries The market equilibrium can be illustrated graphically in Figure 2, where labor and capital are represented by horizontal and vertical axes, respectively. O represents the origin for the country. Lines Oa<sup>n</sup> = (1; a<sup>n</sup> ) cn and Oa<sup>n+1</sup> = �1; a<sup>n+1�</sup> cn+1 are the vectors of factors used in producing cn and cn+1 in the equilibrium. Let point W = (L; E) be the factor endowment of the country. If W = a<sup>n</sup> L; only good n is produced. Similarly, if W = a<sup>n+1</sup> L; only good n + 1 is produced. When a<sup>n</sup> L < W < a<sup>n+1</sup> L; both goods n and n+1 are produced. The factor market clearing conditions, (8) and (9), determine the usages of labor and capital in industries n and n + 1; which are represented by vector OA and vector OB in the parallelogram OAWB, respectively. If the capital endowment increases from W to W<sup>0</sup> ; the new equilibrium becomes parallelogram OA<sup>0</sup> W<sup>0</sup> B<sup>0</sup> so that cn decreases but cn+1 increases.

More precisely, the equilibrium output of each commodity cn, the relative factor prices w<sup><u>r</u>; and the corresponding aggregate output Care summarized in the following</sup> table.

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Table 1: Static Equilibrium The whole static equilibrium is summarized verbally in the following proposition.

Proposition 1 In a closed economy, the static market equilibrium is determined by the endowment structure, <u>EL</u><sup>:Generically,onlytwogoodsadjacentincapital</sup> intensities are produced in equilibrium. As capital per capita increases, every commodity exhibits an inverse-V-shaped life cycle. A good enters the market, prospers (its output increases) and then declines, and ...nally is fully replaced by another product with a higher capital intensity. The ratio of the interest rate to the wage rate declines as<sup><u>E</u></sup> L<sup>increases.</sup> Figure 3 shows that the relative factor prices w<sup><u>r</u>, which declines in a stair- shaped</sup> fashion as E increases. This discontinuity results from the Leontief production assumption but the ‡at part is more general: During the structural change, resource reallocation occurs without changes in relative prices.

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<!-- Start of picture text -->
*<br>r<br> <br> <br>w<br> <br>λ− 1<br>a<br>λ− 1<br>a ( a − λ )<br>λ− 1<br>a 2( a − λ )<br>λ− 1<br>a 3( a − λ )<br>0<br>aL a 2 L a 3 L E<br><!-- End of picture text -->

Figure 3. How Relative Factor Price Ratios Depend on Endowment Structure It is straightforward to compute the capital share in the total output, which <u>(</u><sup><u>�</u></sup> <u>a�</u><sup>�</sup> <u>1</u><sup><u>1)E</u></sup> equals <u>�a��11</u><sup>E+ an</sup> a<sup><u>(</u></sup> �<sup>a�</sup> 1<sup>�)</sup> L<sup>whenE2[anL; an+1L]foranyn�1.</sup> So the capital share monotonically increases with capital during each diversi...cation cone and then suddenly drops to<sup><u>(�</u></sup> a�<sup>�</sup> 1<sup>1)astheeconomyentersadi¤erentdiversi...cationcone,butit</sup> always falls into the following interval [<sup><u>�</u></sup> a�<sup>�</sup> 1<sup><u>1</u>;</sup><sup><u>(</u></sup> (<sup>�</sup> a�<sup>�</sup> 1)<sup>1)</sup> �<sup>a]foranydevelopmentstagewith</sup> n � 1. This result is consistent with the Kaldor fact that the capital share is fairly stable over time (see Barro and Sala-i-Martin (2004) for more discussions on the robustness of Kaldor facts).

How cn changes has already been encoded in Figure 2 but its inverse-V-shaped pattern can be more intuitively seen in Figure 4. When capital endowment E reaches threshold value a<sup>n</sup> L; good n + 1 enters the market, and its output increases as E increases up to the point E = a<sup>n+1</sup> L and then it declines. At the point E = a<sup>n+2</sup> L; good n + 1 exits from the market while a new good with a higher quality (n + 3) appears.

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<!-- Start of picture text -->
*<br>c n<br>L<br>0<br>aL a 2 L a 3 L a 4 L E<br>* * * *<br>c 0 : c 1 : c 2 : c 3 :<br><!-- End of picture text -->

Figure 4. How Each Industry Depends on the Endowment The above equilibrium in our closed economy model turns out to be very similar to the H-O trade model with multiple diversi...cation cones. However, the main mechanisms are totally di¤erent. Leamer (1987) and other papers in this literature mainly consider (small) open economies where the production structure of a country is determined by international specialization and each good has to be consumed. In our closed-economy general equilibrium model, which set of goods should be consumed and produced is an endogenous decision, depending solely on the domestic demand and endogenous relative factor prices, which are mainly dictated by the endowment structure.

# 3 Dynamic Model

In this section, we will develop a dynamic model to capture the complete industrial dynamics along the path of economic growth. The key idea is to break down the evolution analysis of production structures into two steps. Along the time dimension, the representative consumer decides her intertemporal consumption ‡ows of the aggregate good C and makes the saving and investment decisions. This dynamic decision determines the evolution of endowment structure<sup><u>K</u></sup> L<sup>and the optimal capital</sup> 14
expenditure<sup><u>E</u></sup> L<sup>ateverytimepointt:Inthecrosssectiondimension,thecapital</sup> expenditure<sup><u>E</u></sup> L<sup>thendeterminestheproductionstructures,exactlythesameasin</sup> the static model.

By the second Welfare Theorem, we can characterize the competitive equilibrium by resorting to the following social planner problem: subject to where � is the time discount rate. K(t) is the amount of working capital at t. At each time, the old capital can be transformed into new working capital using the standard AK model technology and � is the exogenous technology parameter net of the depreciation rate. All the new working capital can be used to either produce the consumption good or to save/invest. E(C(t)) is the total capital used to produce the aggregate consumption C(t). All the consumption goods are non-storable. The total labor endowment L is constant over time.<sup>8</sup> To ensure positive consumption growth, we assume � � �> 0. To exclude the explosive solution, we also assume � <u>� �</u><sup>Puttingthemtogether,weassume</sup> �<sup>(1 ��) < �.</sup> From Table 1, we know that E(C) is a strictly increasing, continuous, piece-wise linear function of C. It is not di¤erentiable at C = �<sup>i</sup> L, for any i = 0; 1; :::. Therefore, the above dynamic problem may involve changes in the functional forms

> 8 It is straightforward to examine how exogenous changes in the “e¤ective labor”(for example, let L(t) = L0e<sup>�t</sup> for some �> 0) may a¤ect economic dynamics.

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ck, éK < < <AL éK — A < <A > 2 DN 2 <!-- Start of picture text -->
-—O _ _ pt -—O _ _ pt<br>—_—oOo —_—oOo<br>ék <<<br>EK < <<br>gk — << 2<br><!-- End of picture text -->

<!-- Start of picture text --> <<<br>_a — _dA r _—Xr<br><!-- End of picture text --> <!-- Start of picture text --> <<<br><!-- End of picture text -->
<< < < ~~=~~ pt _ ” ck 5 ¢ A — ¢ —X n¢¢ N— > —-\ > ~~et~~ —o —pt _ ~~a~~ Mo ~~yay~~ Ss ¢ ¢ —X ¢ > -r > n ~~—_——_~~ _ -n &. A L,A ¢ ¢ —o —pt _ a ~~|~~
can be decomposed into two multiplicative terms: The marginal utility of capital �n;n+1 and the marginal capital requirement for each additional unit of aggregate consumption �<sup><u>ann+1+1�</u></sup> �<sup><u>a</u></sup> �<sup>nn(seeTable1).Takinglogofbothsidesofequation(15)and</sup> di¤erentiating with respect to t; we have: for tn � t � tn+1 for any n � 0. The strictly concave utility function implies that the optimal consumption ‡ow C(t) must be continuous and su¢ ciently smooth (with no kinks) throughout the time, hence from (16) we obtain: Following Kamien and Schwartz (1991), we have two additional necessary conditions at t = tn+1: Substituting equations (18) and (19) into (12), we can verify that K<sup>�</sup> (tn+1) = K<sup>+</sup> (tn+1). In other words, K(t) is indeed continuous.

Observe that C(t0)e <u>��� �</u><sup>(tn�t0)</sup> = C(tn) = �<sup>n</sup> L, so tn = log C<sup><u>�</u></sup> <u>(</u><sup>n</sup> t�0)<sup><u>L</u></sup> �<sup>+</sup> <u>�</u><sup><u>��</u></sup> �<sup><u>�</u>t0</sup> . De...ne � mn � tn+1 � tn, which measures the length of the period when both good n and n + 1 are produced. It is easy to see that This result is summarized in the following proposition, where the goods at di¤erent 18
levels should be interpreted as di¤erent industries.<sup>9</sup> These industries di¤er in the capital intensities of their production technologies.

Proposition 2 The duration of each diversi...cation cone for goods n and n + 1is identical for all n � 1. The speed of industrial upgrading (measured by m1<sup>)strictly</sup> increases with the e¢ ciency of the production of capital goods, �; and intertemporal elasticity of substitution, �<sup><u>1</u>,butstrictlydecreaseswiththequalitygap�andtime</sup> discount rate �: The intuition is the following: when the household is more impatient (larger �), it will consume more and save less, causing the industrial upgrade to slow down. When the quality gap is larger (larger �), the marginal utility of the current goods are bigger, therefore it pays to stay longer. When the production of the capital good becomes more e¢ cient (�), capital can be accumulated faster, so the upgrade speed is increased. When the aggregate consumption is more substitutable across time, the household is more willing to sacri...ce the current consumption so long as the aggregate consumption in the future can get su¢ ciently larger, which requires quicker industrial upgrading.

# 4 Industrial Dynamics

We are now ready to derive the industrial dynamics for the entire time period. The industrial dynamics depends on the initial capital stock, K(0): We show in the

> 9 To obtain closed-form solutions for the whole dynamics with in...nite dimensional commodity space, we make the strong assumption that di¤erent industrial goods are perfectly substitutable so that some industries can die out. However, we believe this assumption is not crucial for our main result in industrial dynamics, depending on how the model is interpreted. For example, we may alternatively interpret each good n as a composite of several imperfectly substitutable industrial goods (such as food, clothes, electronics, etc.) similar to Acemoglu and Guerrieri (2008). The quality of the goods in each of these industries will improve over time, and the capital intensity of their technologies will also increase over time, which is re‡ected in the properties of the aggregate good n. We conjecture that the aggregate output of each industry (weighted sum over all the goods of di¤erent qualities in the same industry) will maintain the inverse-V-shaped dynamic pattern, although no industries will vanish (but some goods at certain quality levels will). We will leave this for future research.

19
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<!-- Start of picture text --> ék -| se AA = |x h A ><br>a B w 4 & ><br>a -(~—)*= » -rA\}) € —<br>° ~(5 =x) fe e9<br>\~ (Se -e) & -<br>os spe e a _<br>; f-p<br>— ><br>Xr —xr A- a”<br>==<br>* f-p<br>~ 2 AL<br>r»A -r A-<br>* NS<br><!-- End of picture text -->
This can be illustrated in the following inverse-V-shaped time pattern of industrial dynamics: <!-- Start of picture text -->
*<br>c n<br>L<br>0<br>t<br>t 1 t 2 t 3 t 4<br>* * * *<br>c 0 : c 1 : c 2 : c 3 :<br><!-- End of picture text -->

Figure 5. How Industries Evolve over Time when K0 2 (#0; #1) The above mathematical results can be read as follows: Proposition 3 There exist a strictly increasing and non-negative sequence of threshold values for capital stock, f#ig<sup>1</sup> i=0<sup>, which are all independent of the initial capital stock,</sup> such that the economy starts to produce good n when its capital stock K(t) reaches #n�1: K(t) evolves following the equation (23), while the total consumption C(t) remains constant at L until t0, after which it grows exponentially at the constant rate<sup><u>���</u>When</sup> �<sup>: The output of each industry evolves in an inverse-V-shaped pattern:</sup> capital stock K(t) reaches #n�1; good n enters the market and its output grows approximately at the constant rate<sup><u>��</u></sup> �<sup><u>�</u></sup> until capital stock K(t) reaches #n; its output then declines approximately at the constant rate<sup><u>��</u></sup> �<sup><u>�</u>;andexitsfromthemarketat</sup> the time when K(t) reaches #n+1:<sup>10</sup> 10 � <u>L</u> More rigorously, the sum of the good n’s output and a constant, cn<sup>(t) +</sup> ��1<sup>;growsatthe</sup> constant rate<sup><u>��</u></sup> �<sup><u>�</u>;andthenc�</sup> n<sup>(t) �</sup> ��L�1<sup>declinesattheconstantrate</sup><sup><u>��</u></sup> �<sup><u>�</u>:</sup> 22
# 5 "Mistakes" in Product Selection and Consequences

Our previous analysis characterizes the ...rst-best industrial dynamics in a frictionless economy. The evolution of optimal production structure is determined by the change of capital per capita, K(t)=L; which evolves following equation (23). In this section, we will brie‡y discuss the welfare consequences if the goods chosen to produce are not the ...rst-best ones. These “selection mistakes” may happen in real life for a variety of reasons. For example, the government in a developing economy may, for some political reasons, pursue a catching-up development strategy by prematurely pushing the economy to produce what is produced in the much more developed economies, which is too capital intensive (see Lin 2003, 2008), that is, the economy is urged to produce good n + s when good n is the ...rst best for some s � 1. Or the market itself may fail to choose optimal products, due to incomplete information or ...rms’monopoly behavior, etc. Due to space limitations, we will focus our analysis on the ex-post welfare consequences per se while remaining agnostic about what causes those deviations from the ...rst-best industrial selections.

<!-- Start of picture text --> K ( t )<br>E ( t ), K ( t )<br>K 1 M ( t )<br>θ n K n M EnM + 1 E 2 ME (( tt ))<br>K En M K n + 1 M E 1 M ( t )<br>a n + s L<br>A<br>aE n L B K 2 M ( t )<br>0 t n t n + 1 T t<br><!-- End of picture text --> Figure 6. What Happens if Wrong Industrial Choice is Made The optimal evolution of capital stock K(t); and capital expenditure E(t) are represented by curve KK(t) and EE(t) in Figure 6, respectively. At time tn; 23
K(tn) = #n and E(tn) = a<sup>n</sup> L. It is optimal for the economy to start producing good n + 1 so that both good n and good n + 1 should be produced at time interval (tn; tn+1). Now suppose, for some unexpected and exogenous reasons, the economy starts to produce goods n+s and n+s+1 during the period [tn; tn+1] for some s > 0: s measures the magnitude of the industrial deviation. So at time tn; instead of using E(tn) = a<sup>n</sup> L; now suppose the economy chooses the expenditure E(tn) = a<sup>n+s</sup> L and maintains the same consumption growth rate<sup><u>��</u></sup> �<sup><u>�</u></sup> during this period. We use the superscript “M ” to denote all the variables after the economy is unexpectedly hit by this “mistake.”What will the welfare consequence be?

Obviously at time tn, the aggregate consumption jumps from C(tn) to C<sup>M</sup> (tn). Capital expenditure E<sup>M</sup> (t) now evolves as follows: for any t 2 [tn; tn+1]. It is represented by curve En<sup>ME</sup> n<sup>M</sup> +1<sup>inFigure6.Di¤erent</sup> from equation (22), the transition equation of capital now becomes If s is su¢ ciently large, the capital expenditure E<sup>M</sup> (t) exceeds �K<sup>M</sup> (t) and therefore K<sup>M</sup> (t) declines in time period [tn; tn+1]: In that case, capital stock evolves along the curve Kn<sup>MK</sup> n<sup>M</sup> +1<sup>whichisnotonlybelowthe...rst-bestpathKK(t)butalso</sup> decreasing. At time tn+1; K<sup>M</sup> (tn+1) < #n+1: Let us assume #h � K<sup>M</sup> (tn+1) � #h+1 for some 0 < h < n: Suppose at time t = tn+1 the government (or agents) in the economy suddenly realizes that it made mistakes during the period [tn; tn+1]. What should it do? There are two scenarios: In Scenario 1, let us assume there is no adjustment cost to rectify the mistake. The economy can freely re-optimize everything at t = tn+1 at given capital stock 24
K = K<sup>M</sup> (tn+1). Since #h � K<sup>M</sup> (tn+1) � #h+1, the economy will immediately downgrade its production structure and start producing goods h and h + 1. The corresponding capital expenditure E<sup>M</sup> (t<sup>+</sup> n+1<sup>)mustbebetweenahLandah+1L,and</sup> the economy will then follow the optimal path as if it began with K = K<sup>M</sup> (tn+1): The evolution paths for K<sup>M</sup> and E<sup>M</sup> are represented by KKn<sup>MK</sup> n<sup>M</sup> +1<sup>K</sup> 1<sup>M(t)and</sup> EAEn<sup>ME</sup> n<sup>M</sup> +1<sup>BE</sup> 1<sup>M(t); respectively.Consumers enjoy the goods with qualities higher</sup> than the optimal, n + s and n + s + 1; in time period [tn; tn+1]; but have to adjust the economy at a much lower level thereafter. The consumer’s life utility following the mistaken path KKn<sup>MK</sup> n<sup>M</sup> +1<sup>K</sup> 1<sup>M(t)certainlyislowerthantheoptimumandcan</sup> be computed. Similarly, if the country saves more capital than the optimum, and produces goods n � s and n � s + 1 in [tn; tn+1]; the country will re-optimize and start to produce goods j and j +1 for some j � n +1 after t = tn+1; that also lowers consumer’s lifetime total utility.

In Scenario 2, let us assume that the production structure can not be reversed and maintain the full employment assumption. That is, when the economy starts to produce good m; it can not produce any good with the quality lower than m in the future. Full employment implies that the quantity of total consumption can not decrease either. The industrial irreversibility may be due to the fact that the physical capital used to produce high quality goods can not be reversed to produce lower quality goods, or consumers who are used to consuming high-quality goods are simply addicted to their consumer behavior, or political groups in current industries may lobby against the structural adjustment. Under this assumption, the optimal choice is to produce the lowest quality good constrained by the downward rigidity constraint n � h + s + 1. Therefore, at each time point after t = tn+1 capital expenditure E must always equal a<sup>h+s+1</sup> L. As too little capital is saved, K<sup>M</sup> (t) continues to decline after tn+1 and will be exhausted at time T: The evolution paths for K<sup>M</sup> and E<sup>M</sup> in Scenario 2 are represented by KKn<sup>MK</sup> n<sup>M</sup> +1<sup>K</sup> 2<sup>M(t)and</sup> EAEn<sup>ME</sup> n<sup>M</sup> +1<sup>E</sup> 2<sup>M(t)T;respectively.</sup> Due to the adjustment rigidity, a short-term 25
mistake in production selection hurts the economy permanently by fully exhausting all capital stock. The economy falls into a poverty trap without any growth and can only a¤ord to produce good 0 forever after time T , if that is allowed after T .

Scenarios 1 and 2 provide two extreme cases for the e¤ect of mistakes in production selection. Without adjustment cost, one period mistake to produce products above the optimum lowers social welfare and postpones future product upgrading. When the production structure is not reversible, however, one period over-expenditure in capital may permanently degenerate the economy and destroy the hope for growth. We can impose the same downward adjustment rigidity constraint on the economy analyzed in the previous two sections, but nothing changes because this adjustment constraint is simply not binding.

An intermediate adjustment cost function between Scenarios 1 and 2 may be more realistic, but also more complicated to analyze. For example, we may assume that right after time tn+1; capital stock K(t<sup>+</sup> n+1<sup>)=�([h �(n + 1)])K(tn+1)where</sup> �(:) is the adjustment cost function. �(0) = 1, 0 � �(:) � 1, and �(:) becomes larger if the absolute value of [h � (n + 1)] increases. If the economy maintains its current production structures, there will be no adjustment cost. Otherwise, a more radical adjustment incurs a higher adjustment cost. Scenario 1 represents the case that �(:) � 1. For Scenario 2, it simply refers to the case that �(:) � 0 if h�(n+1) < 0. When �(:) is intermediate, the economy may not immediately adjust her production structures to the optimal products h and h +1. Instead, the country may gradually downgrade its production structure to the optimal one determined by its endowment structure. A thorough formal exploration is beyond the scope of this paper, but studies of such optimal adjustment in production structures seem very interesting, although quite limited in the literature.

In the real world, we observed successful examples of industrial upgrading in Japan, South Korea, and Taiwan from the 1950s to the 1980s. That may be partly attributed to the fact that the government in those economies pursued the 26
right industrial development policies that were consistent with their endowment structures. However, there are many examples of less successful development with “non-optimal”industrial dynamics in developing economies including China, India, Russia, and many other Eastern European and Latin American countries during various historical periods. These countries all erroneously pursued development strategies that de...ed their comparative advantages by naively trying to quickly mimic the production structure of the developed economies and, hence, prematurely built too many heavy industries that were inconsistent with the economy’s endowment structure. That ultimately resulted in serious economic stagnation and caused huge welfare loss. Just as predicted by our above analysis, the welfare consequence is even worse when the industrial adjustment is more costly. Indeed, we frequently observe prolonged di¢ cult periods of adjustment in many economies undertaking reforms. For instance, it has been more than 15 years since the regime switched in Russia and the country’s endowment structure also dramatically deteriorated. Nevertheless, military and some other heavy industries are still the main supporting industries in that country (Lin 2003, 2009).

Serious welfare consequences may result from the government’s failure to recognize that the optimal industries are actually endogenous to the development stage (capital endowment). Such important policy implications, although indirectly derived from this model, may not be obvious from the standard one-sector or multi-sector growth models.

# 6 Conclusion

We have developed a tractable in...nite-horizon general-equilibrium model to analyze the optimal industrial structure and its dynamics in a closed developing economy. Explicit solutions are obtained to fully characterize the whole economic dynamics (including the transitional dynamics), although the commodity space is in...nitely 27
dimensional. Our model generates an inverse-V-shaped dynamic pattern of industrial change, which is widely observed in the real world but rarely, if ever, formalized in growth models. The engine that drives this continuous structural change is the increasing relative abundance of capital in the endowment structure. In a closed economy, capital keeps accumulating because the capital goods are produced with Arrow’s AK model technology, which can be interpreted as learning-by-doing in the capital production. This endogenous technological change in the capital good production gives us the sustained and constant economic growth in the aggregate good consumption. However, since the industries are upgrading in a waxing-and-waning fashion all the time, the growth rates of each individual industrial good are shown to be changing along the process. We highlight the endogeneity of the industrial structures and its dynamics: The optimal industrial choice and industrial dynamics are dictated by the economy’s endowment structure and its change.

Economic growth and industrial upgrading are two crucial and integrated aspects of sustained economic development. On the quantitative side, sustained economic development requires the sustainable growth of per capita income; on the structural side, sustainable economic development typically entails the continuous upgrading and transformation of industries. Most existing growth models postulate the same aggregate production function (with changing inputs and productivity) for all the countries at di¤erent development stages, and, thus, naturally focus on the quantitative side of economic aggregates, which have been guiding economists to conduct many insightful policy studies such as how to boost human and physical capital accumulation and how to enhance technological improvement, and so forth. However, the structural side is largely ignored by these models. This perhaps accounts for the more serious shortage of academic and policy research related to structural changes in development: How to help the economy identify the optimal products and industries to develop at each di¤erent development stage, which kind of ...nancial institutions can best serve the corresponding industrial structures at di¤erent stages, how to 28
facilitate the structural transformation in the process of labor and capital reallocation across industries, how openness may a¤ect a country’s industry upgrading, and, consequently, what the optimal industrial, ...nancial, trade, and many other macroeconomic policies should be at di¤erent development stages, so on and so forth. We hope the model developed in this paper may serve as a useful starting point to address all these fundamental issues.

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