metadata: authors: 0: author: Ju, Jiandong
1: author: Lin, Justin Yifu
2: author: Wang, Yong
count: World
docna: 0: docna: Marshallian externality, industrial
            upgrading, and industrial policies
docty: Policy Research Working Paper
subtopic: Labor Markets
teratopic: Macroeconomics and Economic Growth,Industry,Water Resources,Rural Development
abstracts: cdata!: A growth model with multiple industries
            is developed to study how industries evolve as capital
            accumulates endogenously when each industry exhibits
            Marshallian externality (increasing returns to scale) and to
            explain why industrial policies sometimes succeed but
            sometimes fail. The authors show that, in the long run, the
            laissez-faire market equilibrium is Pareto optimal when the
            time discount rate is sufficiently small or sufficiently
            large. When the time discount rate is moderate, there exist
            multiple dynamic market equilibria with diverse patterns of
            industrial development. To achieve Pareto efficiency, it
            would require the government to identify the industry target
            consistent with the comparative advantage and to coordinate
            in a timely manner, possibly for multiple times. However,
            industrial policies may make people worse off than in the
            market equilibrium if the government picks an industry that
            deviates from the comparative advantage of the economy.
repnme: repnme: Marshallian externality, industrial
            upgrading, and industrial policies
display_title: Marshallian externality, industrial
            upgrading, and industrial policies
listing_relative_url: /research/2011/09/15036483/marshallian-externality-industrial-upgrading-industrial-policies
topicv3: Industrial Policies m1504172 2847
publishtoextweb_dt: 2011-09-01T00:00:00Z
historic_topic: Macroeconomics and Economic Growth,Industry,Water Resources,Rural Development
no_of_pages: 38
model_extractions: WPS5796 Policy Research Working Paper 5796 Marshallian Externality, Industrial Upgrading, and Industrial Policies _Jiandong Ju Justin Yifu Lin Yong Wang_ The World Bank Development Economics Vice Presidency September 2011
Policy Research Working Paper 5796

# **Abstract**

A growth model with multiple industries is developed to study how industries evolve as capital accumulates endogenously when each industry exhibits Marshallian externality (increasing returns to scale) and to explain why industrial policies sometimes succeed but sometimes fail. The authors show that, in the long run, the _laissezfaire_ market equilibrium is Pareto optimal when the time discount rate is sufficiently small or sufficiently large. When the time discount rate is moderate, there exist multiple dynamic market equilibria with diverse patterns of industrial development. To achieve Pareto efficiency, it would require the government to identify the industry target consistent with the comparative advantage and to coordinate in a timely manner, possibly for multiple times. However, industrial policies may make people worse off than in the market equilibrium if the government picks an industry that deviates from the comparative advantage of the economy.

This paper is a product of the Development Economics Vice Presidency. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at jdju@ ou.edu, justinlin@worldbank.org, and yongwang@ust.hk.

_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
# Marshallian Externality, Industrial Upgrading, and Industrial Policies<sup>�</sup>

Jiandong Ju<sup>y</sup> , Justin Yifu Lin<sup>z</sup> , Yong Wang<sup>x</sup> July 21, 2011 Abstract A growth model with multiple industries is developed to study how industries evolve as capital accumulates endogenously when each industry exhibits Marshallian externality (increasing returns to scale) and to explain why industrial policies sometimes succeed but sometimes fail. The authors show that, in the long run, the laissez-faire market equilibrium is Pareto optimal when the time discount rate is su¢ ciently small or suf...ciently large. When the time discount rate is moderate, there exist multiple dynamic market equilibria with diverse patterns of industrial development. To achieve Pareto e¢ ciency, it would require the government to identify the industry target consistent with the comparative advantage and to coordinate in a timely manner, possibly for multiple times. However, industrial policies may make people worse o¤ than in the market equilibrium if the government picks an industry that deviates from the comparative advantage of the economy.

Key Words: Marshallian Externality, Industrial Policies, Structural Transformation, Industrial Upgrading, Economic Growth JEL Codes: L50, O14, O25, O41

> �This paper bene...ts from the discussions with Gene Grossman, Norman Loayza, and Aart Kraay. Roula Yazigi provides excellent editorial support. Wang gratefully acknowledges the hospitality and ...nancial support from the World Bank during his stay in the 2010-2011 academic year.

> yUniversity of Oklahoma and Tsinghua University. Email Address: jdju@ou.edu

> zWorld Bank. Email address: justinlin@worldbank.org

> xHong Kong University of Science and Technology. Email address: yongwang@ust.hk

1
# 1 Introduction

This paper studies the role of industrial policies in a growth model with multiple industries. In the real world, for better or worse, almost all the economies have adopted and are still adopting various industrial policies.<sup>1</sup> Yet the e¤ect of industrial policies is always highly controversial. On the one hand, many empirical and case studies suggest that industrial policies have mostly failed and the overall performance of industrial policies is very mixed and insigni...cant;<sup>2</sup> but on the other hand, ample research, especially case studies, contends that industrial policies and government facilitation are crucially important for most, if not all, of the cases of successful industrial development.<sup>3</sup> The main purpose of this paper is to help reconcile these two di¤erent empirical facts and views, which tend to convey opposite implications for the desirability of industrial policies. More speci...cally, we try to shed some new light on why "similar" industrial policies work in some cases but fail in others. Any useful discussion on industrial policies must involve the existence of certain market imperfections. In this paper we will revisit and focus on the issue of Marshallian externality, the importance of which is widely recognized in the existing literature. For example, one in‡uential study on coordination failure with the presence of externality is the big-push theory proposed by Rosenstein-Roden and beautifully formalized by Murphy, Shleifer and Vishny (1989). The key policy implication derived from this literature is that government intervention (support) is justi...ed if an industry exhibits Marshallian externality.

However, if the existence of Marshallian externality is a su¢ cient condition for government intervention, how to explain why many "big-push" industrial policies failed? For example, from the 1960s to the 1980s, the former Soviet Union set the capital-intensive and technology-intensive aerospace industry as its target industry, in which Marshallian externality indeed existed. The government tried hard to coordinate and push the industry to be established. But the social welfare loss actually exceeded the gain from such intervention because the resources for consumption goods production were tremendously reduced and resource allocation created huge distortions when developing such an excessively capital-intensive industry. Similar stories of industrial policies could also be told about China, India and many other developing countries after World War II. The dominant social thought at that time was interventionism based on the rationale of "big push". These countries tried to emulate the rich countries by establishing as soon as possible the same industries that prevailed in the most developed countries. Those target industries were typically capital-intensive and also had signi...cant Marshallian externality. Coordination was indeed implemented but

> 1 See, for example, Wade (1990) and Chang (2003), Lin (2009) and Lin and Monge (2010).

> 2 For example, Harrison and Rodriguez-Clare (2009) provide a nice literature review. Also see Pack and Saggi (2006) and the papers cited there.

> 3 For example, Canda (2006) provides fourteen detailed cases studies for successful industrial upgrading; Rodrik (1996, 2006) discussed, among others, the positive role of industrial policies in several East Asia economies; Ohashi (2005) studies the steel industry in Japan. Also see Lin and Monge (2010) and the papers cited in all the aforementioned research.

2
the industrial development largely failed because the target industries simply went against the comparative advantage of those capital-scarce economies (see Lin, 2009). Meanwhile, by contrast, industrial policies are widely believed successful in Japan, South Korea, Singapore, and Taiwan for the same period. These economies followed comparative advantage and upgraded their industries step by step toward more capital-intensive ones as they accumulated capital on the growth path.

These observations suggest that we should bear in mind the factor endowment when examining industrial policies. Unfortunately, almost the whole existing literature of Marshallain externality and industrial policies assumes, presumably for analytical simplicity, that labor is the only input in the production function. As a result, there is no explicit role for capital and the structure of the factor endowments in the discussion of industrialization and policies. A novel feature of this paper is, therefore, to reexamine the industrial policies by explicitly introducing capital (and its accumulation) into our theoretical analysis. Adding this extra layer of complexity not only makes the model more realistic, but more importantly, there are at least three potential gains that warrant such an investigation.

First, it points to the importance of identifying the right industry target that needs government intervention. The existing literature on coordination failure largely ignores this important issue by typically assuming that there exist two industries with only one industry exhibiting Marshallian externality, thus it is common knowledge which industry needs government support. However, as we argued, the existence of Marshallian externality (or pecuniary externality) alone is not su¢ cient to warrant government intervention. Factor endowment also matters. We have to take the capital intensity of each di¤erent industry and the capital abundance into account when identifying the right industry targets. Moreover, the target industry that needs coordination is also changing endogenously as the structure of factor endowment changes over time. Consequently, in our model we assume that there are three industries with di¤erent capital intensities and more than two industries exhibit Marshallian externality. It is necessary to have at least three industries to discuss the e¤ect of industrial policies that aim to facilitate "leap forward" in the industrial upgrading, as occurred in the former Soviet Union and many developing countries.

Second, an important technical question in the literature of industrial policies is how to select an equilibrium because there typically exist multiple equilibria in a coordination game. Discussions have focused on what determines the relative importance of history versus expectation (see, Krugman (1991), Matsuyama (1991), for example). Once capital is introduced into the model, however, agglomeration is no longer the only economic force that determines the production cost (hence the competitiveness) of an industry. The relative price of capital and labor also matters in a general equilibrium fashion. As our model will show, sometimes the factor price e¤ect dominates the agglomeration e¤ect so that the equilibrium may restore uniqueness, making equilibrium selection less controversial.

Third, in the existing literature of coordination failures and industrial poli3
cies, dynamic analyses mainly focus on the stability of an equilibrium by assuming some costly adjustment process in a heuristic and ad hoc way (see Mussa(1978), Panagarya(1986), Krugman(1991), etc.) or when there exists demographic change (see Matuyama, 1991). Besides, none of these papers studies the industrial upgrading in the economic growth framework. However, once capital is introduced, it becomes very natural to examine the industrial policy and industrial upgrading issues in the standard Ramsey growth framework with endogenous saving, which allows us to analyze industrial policies along with GDP growth and industrialization.

In light of these arguments, we build a simple growth model with three industries, each of which exhibits increasing returns to scale (Marshallian externality) and di¤ers in capital intensity. The key result is that industrial policies may succeed or fail, depending on whether the target industry for coordination is correctly identi...ed in a timely manner. We show that in some cases industries may eventually upgrade successfully in an intervention-free market economy despite the existence of Marshallian externality and coordination problems. However, industrial upgrading under laissez-faire policies may be seriously delayed and thus can be Pareto improved if the right industry target is identi...ed in time and "pushed" by the government appropriately. But if the government identi...es the wrong industry and "pushes" it, the economy would end up in an equilibrium Pareto inferior to the laissez-faire market equilibrium. The "right" industry target in our model endogenously changes over time, depending on the capital endowment of the economy. We hope that our model will help deepen our understanding on the important question why industrial policies have succeeded in some circumstances but failed in others, although Marshallian externality always exists in all these cases.

The rest of the paper is organized as follows. Section 2 studies a static economy with only two industries and the basic economic forces are explained. It is extended to a static economy with three industries in Section 3, which allows for the discussion on "leap-forward" industrial upgrading and policies. In the subsequent sections, the industrial upgrading and policies are analyzed in a Ramsey growth framework. In particular, Section 4 studies the dynamic model in which endowment structure changes endogenously. Section 5 examines the robustness of our theoretical results to the variations of the equilibrium concepts and relevant functional forms. The last section concludes.

# 2 Two Industries

Consider a static and small open economy populated by L identical agents, each of whom is endowed with one unit of labor and E units of capital. There are two di¤erent industries, each producing a distinct consumption good. Call them industry 1 and industry 2. The utility function is 4
where the ...nal aggregate consumption C is a composite of both consumption of good 1 (denoted by c1) and consumption of good 2 (denoted by c2). Function C(c1; c2) can take any form as long as C1(c1; c2) > 0 and C2(c1; c2) > 0. Let pi denote the world price of consumption good i. Normalize p1 = 1 and assume p2 = �, where �> 1. Consumption goods can be traded freely at the world market but the production factors (labor and capital) cannot move across borders.

To operate, each ...rm requires one unit of labor. Therefore, the total number of ...rms is L in the economy. The technology to produce good i 2 f1; 2g in each ...rm is: where ni is the total number of ...rms in industry i and ki is capital input in each representative ...rm in industry i. There exists Marshallian externality so A(ni) is a strictly increasing function of ni. To sharpen the analytical results, let us assume A(ni) � A0e<sup>�ni</sup> , where � and A0 are both positive parameters. Without loss of generality assume �2 > �1 so good 2 is more capital-intensive. L is an integer, so is ni.

Both labor and capital can freely move across the two industries. All the markets are perfectly competitive and each ...rm earns zero pro...t in the equilibrium after paying the capital and labor cost. Let w and r denote the equilibrium wage and rental price of capital.

Lemma 1 If both industries operate, then the capital of each ...rm in an industry will strictly increase with the number of ...rms in the same industry.

Proof. The equalization of capital return across the two industries implies which immediately implies that k2(n1) is a strictly decreasing function of n1 and hence a strictly increasing function of n2. (2) can be also rewritten as which implies that k1(n1) must be a strictly increasing function.

The economic intuition is straightforward. When an agent moves, say, from industry 1 to industry 2, the marginal productivity of capital of each ...rm in industry 2 strictly increases and thus becomes larger than that in industry 1, so capital is attracted to industry 2.

Proposition 2 In any equilibrium, at most one industry exists.

5
Proof. By contradiction, suppose in some equilibrium both industries coexist, that is, ni � 1 for both i = 1; 2. The free mobility of capital implies: Zero pro...t condition, equalization of wage across the two industries and (3) jointly imply Labor market clearing condition is Capital market clearing condition is So we have four unknowns: n1,n2, k1, k2 and four equations (3) to (6). Then r and w can be pinned down by (3) and (4) respectively. Consider an individual agent (...rm) in industry 1. If it unilaterally moves to industry 2, then this deviating agent rationally expects that the market-clearing rental price of capital would change from r to r<sup>0</sup> , correspondingly, k1 and k2 also change to k1<sup>0andk</sup> 2<sup>0,whichmuststillsatisfy(3)and(6),itremainstocheckwhetherthe</sup> (entrepreneurial) wage becomes better.

which, according to (4), is equivalent to or which must hold because the previous Lemma implies k2 < k2<sup>0.Itcontradicts</sup> that the economy was in an equilibrium.

This proposition states that the two industries cannot coexist in any equilibrium. Next we explore the necessary and su¢ cient conditions under which only one industry exists. First suppose it is an equilibrium that all the ...rms choose to stay in industry 1, then 6
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K0, and all the ...rms stay in industry 1, so the economy will move northeast along the curve BB until capital reaches �1, at which point all the ...rms move to industry 2, so the economy continues to move northeast until the capital reaches �2, at which point all the ...rms simultaneously shift to industry 3 and stay there afterwards. Therefore, the economy will follow the saddle path and eventually converge to the steady state SS3. In other words, it requires sequential multiple coordination to achieve the Pareto optimality.

# [Figure 1]

Suppose K1<sup>ss</sup> > �1 but K2<sup>ss</sup> < �2. There are still several di¤erent possibilities. When �2 is su¢ ciently close to K2<sup>ss,theParetooptimalallocation</sup> may follow a non-monotonic path as illustrated by curve BHB in Figure 2. The economy starts from industry 1 and then shifts to industry 2 when capital reaches �1, after which the economy stays in industry 2 until capital reaches �2 at point H. The economy stays in industry 3 afterwards and eventually converges to steady state SS3.

# [Figure 2]

However, if �2 is su¢ ciently larger than K2<sup>ss</sup> but not too large (close to K3<sup>ss),theninordertoapproachsteadystate3byfollowingtherule(19),the</sup> economy would have to follow a discontinuous path as illustrated in Figure 3. The economy initially follows the lotus BH and consumption jumps from H to D precisely when capital reaches �2, the economy shifts to industry 3 afterwards and eventually converges to steady state SS3.

# [Figure 3]

Discontinuous consumption is certainly not desirable for consumers and hence cannot be Pareto optimal. When �2 is su¢ ciently larger than K2<sup>ss,it</sup> may be strictly better o¤ to give up industry 3 and instead converge to steady state SS2 with industry 2 although it is feasible to upgrade to industry 3. See Figure 4.

# [Figure 4]

Similar reasoning also applies when K1<sup>ss</sup> < �1, in which case the Pareto optimal dynamic allocation may eventually converge to steady state SS1 with industry 1 when �1 exceeds K1<sup>ss</sup> signi...cantly.

To summarize, Proposition 11 Suppose K(0) is su¢ ciently small. When the time discount rate � is su¢ ciently small ( Ki<sup>ss</sup> > �i for both i = 1; 2), the Pareto optimal allocation is such that industries will upgrade step by step from industry 1 to industry 2 and then to industry 3. When � is su¢ ciently large ( K1<sup>ss</sup> � �1), the Pareto optimal allocation is that the industries will remain in industry 1. When � is in some middle range, the Pareto optimal allocation is such that the industries will ...rst stay in industry 1 and then upgrade to industry 2 and stay there forever.

14
# 4.2 Laissez-faire Market Equilibrium

Next let us examine the market equilibrium (or equilibria). At each time point, given the inherited capital stock, the equilibrium industrial choices are the same as in the static model shown in Section 3. That is, all the ...rms simultaneously and non-cooperatively make their industrial choices (production decision) at each time point. The consumption and saving decisions are made after output is produced. For simplicity, we will focus on the symmetric equilibria in which all the ...rms behave identically. To simplify the analysis, we assume �3 is su¢ ciently small (so that Corollary 8 applies) and �1 < �3 < �2 (so that Lemma 9 applies).

Suppose the initial capital stock is su¢ ciently small (K(0) < E3), so the market equilibrium must start with industry 1. By revoking Corollary 8, we have the following lemma: Lemma 12 Industry 1 can be the industry in the long-run steady state only if K1<sup>ss</sup> 2 (0; E2], industry 2 can be in the steady state only if K2<sup>ss</sup> 2 [E3; E4], industry 3 can be in the steady state only if K3<sup>ss2 [E6,1).</sup> This lemma is useful in determining the steady state of the economy. For example, industry 1 cannot be the steady state industry if � is su¢ ciently small such that K1<sup>ss> E2.Usingthislogic,wecaneasilyobtainthefollowing</sup> proposition after studying the associated Hamiltonian system.

Proposition 13 When � is su¢ ciently large such that K3<sup>ss</sup> < E3, then the only dynamic equilibrium is that industry 1 will persist forever, which is also Pareto optimal. By contrast, when � is su¢ ciently small such that K1<sup>ss</sup> > E4, the economy will eventually approach steady state 3, although there may exist multiple equilibrium transitional dynamic paths, some of which are strictly Pareto dominated.

Proof. According to Corollary 8, the market equilibrium industry must be industry 3 whenever K(t) > E4 and must be industry 1 whenever K(t) � E3.

This proposition implies that the market equilibrium itself is Pareto optimal when people are su¢ ciently impatient, even though each industry exhibits Marshallian externality. When people are su¢ ciently patient, the market itself will successfully upgrade the industry and end up with the Pareto optimal industry in the long run. The most complicated case is when � falls in the middle range, to which we now turn.

Now we have E3 � K3<sup>ss</sup> and K1<sup>ss�E4.Ingeneral,therecouldbeacontin-</sup> uum of di¤erent dynamic market equilibria. For example, consider the following case: K1<sup>ss< E3.Onepossiblemarketequilibriumisthattheeconomyfollows</sup> from the beginning the unique saddle path that converges to steady state 1 (denoted by point SS1). Another possible equilibrium is that the economy stays in industry 1 and capital exceeds E3 at some time point, then the economy may immediately shift to industry 2 or shift to industry 2 after a while so long 15
as capital exceeds E3, and the economy eventually converges to steady state 2 (denoted by point SS2). One possible equilibrium path is depicted by curve BHSS2 in Figure 5. Notice that the economy shifts to industry 2 at point H, which is indeterminate depending on the initial consumption (that is, the y-axis of point B). In other words, there could be in...nite such type of equilibria as long as K2<sup>ss2 [E3; E4].</sup>

# [FIGURE 5]

A third possible equilibrium is illustrated in Figure 6. The economy starts with industry 1 at point B and then switches to industry 2 at point H and stays in industry 2 until point A, at which the economy shifts to industry 3 and stays there forever by following the unique saddle path leading to steady state 3 (denoted by SS3). Again, there can be an in...nite number of such equilibrium as long as K3<sup>ss2 [E6,1):</sup>

# [FIGURE 6]

There may exist other types of equilibria as well. To illustrate the multiplicity of the market equilibria even further, consider the di¤erent case, in which E3 � K1<sup>ss.</sup> It is a possible equilibrium that the economy stays in industry 1 until after the capital exceeds K1<sup>ssat some time t.What happens after time t is</sup> as if we have an economy with initial capital K0 = K(t). What happens when K0 � E3? Suppose E3 � K1<sup>ss�K0�K</sup> 2<sup>ss�E6.</sup> At time 0, the economy could embark on either industry 1 or industry 2. This can be illustrated in the following phase diagram (Figure 7).

# [FIGURE 7]

If the economy chooses industry 1 at time 0 and stays in that industry afterwards, the consumption will be denoted by point C0<sup>AA</sup> , and the equilibrium capital stock and consumption will follow the unique saddle path AA and gradually decrease and eventually the economy approaches steady state 1. Call this equilibrium 1. If industry 2 is chosen at time 0 and the economy stays in that industry, the initial consumption will be point C0<sup>BB</sup> and the equilibrium capital stock and consumption will gradually increase and eventually the economy approaches steady state 2 . Call this equilibrium 2.

It is not obvious which equilibrium path is Pareto superior: although the consumption at steady state 2 is strictly higher than in steady state 1, the consumption on the transitional path is strictly larger at the ...rst equilibrium path and this gap exists at least for a while. We know, however, when �1 � K2<sup>ss,</sup> the ...rst equilibrium path must Pareto dominate the second equilibrium path. Likewise, when �1 � K1<sup>ss,thesecondequilibriumpathParetodominatesthe</sup> ...rst one.

The following phase diagram (Figure 8) demonstrates two other possible types of equilibria, called equilibrium 3 and equilibrium 4, respectively.

16
# [Figure 8]

In equilibrium 3, the economy starts with consumption at point C0<sup>AB</sup> and the economy stays in industry 1, therefore the equilibrium consumption and capital stock will move southeast until it hits the saddle path AA at point H. From that point on, all the ...rms shift to industry 2, so the equilibrium path will move northeast along the saddle path BB, and the economy eventually approaches steady state 2. Since it is a perfect foresight equilibrium in which all the ...rms know when the industry shift will occur, C0<sup>AB</sup> is optimally chosen such that the economy hits the saddle path BB precisely at the time of industry switch. Likewise, if people commonly expect that the industry switch will occur at some capital level di¤erent from H, then the initial consumption will also be adjusted accordingly. On this type of equilibrium path, the consumption ‡ow is smooth but non-monotonic. The initial relatively low consumption is to ensure that capital increases enough to reach the saddle path BB. Conceptually we can Pareto rank these equilibria because we can compute the welfare for each equilibrium numerically or analytically. Notice that equilibrium 3 can never be the Pareto optimal equilibrium unless the capital stock at point H is exactly equal to �1, in which case equilibrium 3 must be Pareto superior to equilibrium 1 (shown in Figure 7).

In equilibrium 4, all the ...rms ...rst stay in industry 2 with initial consumption denoted by point C0<sup>BA</sup> in Figure 8, the equilibrium path moves northwest until it arrives at the saddle path AA at point G, after which all the ...rms switch to industry 1, so the economy moves southwest along AA and eventually approaches steady state SS1.

There may also exist other equilibria which involve an in...nite number of switches across industries. For example, in an equilibrium perfectly coordinated ...rms could be continuously jumping (almost vertically) between the AA path and BB path back and forth, although it is obviously not Pareto optimal because consumption changes discontinuously. The consumption stream could also be smooth in an equilibrium with an in...nite number of switches across industries. In particular, there may exist a limit cycle, as illustrated in the next graph (Figure 9). The equilibrium allocation moves along the closed orbit counterclockwise. At point G, all the ...rms are in industry 1, consumption decreases while capital stock remains unchanged. All the ...rms stay in industry 1 until point M is reached, at which all the ...rms simultaneously shift to industry 2 and stay there so the equilibrium path starts moving northeast. When point B is reached, all the ...rms switch back to industry 1 so the economy moves southwest and meets point G again. Such a limit cycle, if existing, cannot be Pareto optimal unless the capital stock associated with the two switching points B and M are both equal to �1.

# [Figure 9]

The diversity and multiplicity of the market equilibria may help explain why the patterns of industrial development are so di¤erent across di¤erent countries or regions in the real world.

17
# 4.3 Industrial Policies

Since there may exist multiple market equilibria of industrial development and some of them are not Pareto optimal, it creates potential room for welfareenhancing government intervention through various forms of policies, which we generally refer to as industrial policies.

For example, consider the case in Figure 1. If the government is fully benevolent and capable enough, it would coordinate the industries to follow the Pareto optimal equilibrium path as described in Section 4.1. That is, it requires the government to identify the right target industry and coordinate the industrial upgrading for multiple times because the Pareto optimal industry shifts over time as the capital accumulates. Imagine that the government intervention is restricted to selecting a market equilibrium when multiple equilibria exist. As discussed earlier, there can be multiple dynamic market equilibria including those similar to Figures 1, 2, 4, 5, 6, etc., but nothing ensures that the Pareto optimal equilibrium be realized.

If the government ignores the role of the endowment structure and prematurely sets industry 3 as its target industry, which is indeed the case observed in many developing countries that pursued "comparative-advantage-defying" development strategies, then it may want to upgrade the industry as soon as possible. More speci...cally, it would choose industry 2 immediately when the capital exceeds E3 and choose industry 3 immediately when the capital exceeds E6. By doing so, the economy could eventually approach industry 3, but the cost is that the consumption is suppressed too much on the transitional path and the welfare may be even lower than some laissez-faire market equilibrium.

If the government identi...es the right industry target but lacks the capacity to coordinate in time, the outcome is also ine¢ cient. For example, if there exists coordination failure, the economy may not be able to escape the initial equilibrium industry soon enough or even fail to upgrade its industry at all. Or perhaps the government may manage to coordinate to industry 2 after the capital exceeds E3 but for some reason fail to coordinate to industry 3 before the capital closely approaches K2<sup>ss,thentheeconomyeventuallywillconverge</sup> to steady state 2. In other words, the economy only achieves partial upgrading of its industry.

All the above analysis on industrial policies is essentially the selection of a certain market equilibrium out of the multiple market equilibria. Actually the government typically needs to monitor the whole development process to ensure that ...rms are not deviating from the desired path at any point. In other words, the role of government is not only to coordinate the ...rms to change to the right industries at the right time, but also to maintain the status quo for the rest of the time.

If the set of industrial policies is expanded such that the government can implement any resource allocation only subject to the resource feasibility constraint, then a government which pursues "comparative-advantage-defying" development strategies would choose to establish industry 3 from the beginning 18
and it can also eventually achieve industry 3, which can never be achieved by the market itself. Of course, it is not Pareto optimal because the total consumption is depressed too much.

In the pertinent literature, to tackle the multiplicity of market equilibria, it is often assumed that there exists an ad hoc frictional adjustment process, so that whether the industrial upgrading occurs depends on whether "expectation" can dominate "history", which in turns depends on the magnitude of the discount rate and the parameters of the adjustment process (see, for example, Krugman, 1991). If the discount rate is su¢ ciently large and/or the adjustment process is su¢ ciently di¢ cult, then "history" dominates and therefore there is a unique equilibrium, in which industrial upgrading (or industrialization) cannot occur, otherwise "expectation" dominates and there are multiple equilibria, some of which have industrial upgrading. Our previous proposition already partly characterizes how the market equilibrium is a¤ected by the time discount rate. Now, to simplify the analysis, suppose that economy starts with initial capital smaller than E3 and has the strongest path dependence (by revoking Corollary 8) in the sense that the equilibrium remains to be that "all the industries are in industry 1" whenever K(t) 2 (0; E2]. When K(t) exceeds E2, all the ...rms could either suddenly shift to industry 2 or all move to industry 3, depending on people’s expectation; and the industries will stay in industry 3 when K(t) > E4.

In particular, if we resort to the argument that the ...rst mover would unilaterally deviate from industry 1 to industry 3 when K(t) just crosses E2, which can be veri...ed, then it implies If, however, we assume that there exists some su¢ ciently small cost of industrial upgrading and the cost is larger when directly shifting from 1 to 3 than that when shifting from 1 to 2, holding other things unchanged, then the market equilibrium industry is To make the analysis concrete, consider the following parametric example: �1 = 0:1; �2 = 0:2; �3 = 0:4; �2 = 1:2; �3 = 1:44; � = 0:03; L = 100; � = 0:05; � = 0:05; then we have then under rule (21) or rule (22), there exists a unique market equilibrium, in which the ...rms always stay in industry 1 and the economy eventually converges 19
to steady state 1.<sup>5</sup> By contrast, the Pareto optimal equilibrium for this numerical example is exactly given by Figure 1 and the economy will eventually converge to steady state 3. This comparison implies that this "constrained" market equilibrium is not Pareto optimal, therefore, the government may improve the welfare by appropriately "relaxing" the "path dependence" constraint, and alleviating all the constraints once and for all is not su¢ cient to ensure that the Pareto optimal equilibrium be realized because there are many possible market equilibria.

So far we have not been explicit about the concrete policy tools that government can employ to implement its industrial policy. Traditional policy variables include the provision of various forms of subsidies, such as tax rebate/holidays, investment credit, export subsidy, etc., for those investors/...rms that follow the recommendation of the government. Policy variables also include imposing punishment, through tax for example, on those investors/...rms that do not follow the recommendation of the government. All these policy tools are applicable here. It is worth mentioning that, in our model economy, it is often the case that the Pareto optimal allocation can be achieved by the market itself, although not ensured because there are multiple equilibria. Under that circumstance, the best the government can do is just to help reduce the coordination cost among the ...rms because each ...rm/investor has su¢ ciently strong incentive to achieve the Pareto optimal equilibrium and there is no con‡ict of interest among those identical investors/...rms. When the Pareto optimal allocation can never be implemented by the market itself because, for example, there exists coordination failure or su¢ ciently large cost associated with the e¢ ciency-enhancing collective action as we have just discussed, then the government should rectify the relevant market failure with carrot and stick.

Most importantly, we want to emphasize that the crucial prerequisite for successful industrial policy is that the government identi...es the "right" industry target in time, that is, the industry which is most consistent with the capital endowment of the economy. The existence of Marshallian externality itself is insu¢ cient to justify government support for that industry. Moreover, the "right" industry target may endogenously shift over time as the economy develops, therefore successful industrial policy may require sequential and timely "push" instead of "once-and-for-all" intervention, as typically examined in the existing literature. To illustrate the importance of "right identi...cation", we show that when the government identi...es the wrong industrial target and "push" it accordingly, the economy may be even worse o¤ than the laissez-faire market <u>1</u> 5 This is the unique equilibrium under rule (21) because E2 � h �1A�(L) i 1��1 L, since <u>1</u> h �1A�(L) i 1��1 L is the largest possible value for capital when the initial capital is su¢ ciently <u>1</u> small. If E2 < h �1A�(L) i 1��1 L, there may exist a second equilibrium, in which the economy stays in industry 1 until the capital reaches E2, after which the economy swtiches to industry 3 and moves along the saddle path leading to steady state 3. If rule (22) is adopted, no matter <u>1</u> whether E2 � h �1A�(L) i 1��1 L holds or not, there will be a unique equlibrium, in which the ...rms always stay in industry 1 and the economy eventually converges to steady state 1.

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from which we conclude: [1]<sup>@E��(�;</sup> @�<sup>L;�1;�2;�)</sup> > 0 and�lim!1<sup>E�(�; L; �1; �2; �)=</sup> 1, when �1 �<sup><u>1</u></sup> 2<sup>; [2] suppose ���2, then@E��(�;</sup> @L<sup>L;�1;�2;�)</sup> < 0 and Llim!1<sup>E�(�; L; �1; �2; �) =</sup> 0; [3]<sup>@E��(�;L</sup> @�<sup><u>;�1;�2;�)</u></sup> < 0. We can see that the main properties of functions E<sup>�</sup> (�; L; �1; �2; �) and E<sup>��</sup> (�; L; �1; �2; �) are almost the same as in the previous analysis. This implies that all the qualitative features in the previous analysis will remain intact.

# 6 Conclusion

In this paper we develop a growth model with multiple industries to study how industries evolve as capital accumulates endogenously when each industry exhibits Marshallian externality (increasing returns to scale). We show that, in the long run, the laissez-faire market equilibrium is Pareto optimal when the time discount rate is su¢ ciently small or su¢ ciently large. When the time discount rate is moderate, there exists a very rich set of multiple dynamic market equilibria, some of which are Pareto dominated. This may help explain why diverse patterns of industrial development are observed in the real world. To ensure the economy achieve Pareto e¢ ciency, it would require the government to ...rst identify the industry target consistent with the endowment structure and then to coordinate in a timely manner, possibly for multiple times. However, industrial policies may make people worse o¤ than in the market equilibrium if the government picks an industry which deviates too far away from the comparative advantage of the economy even if the industry exhibits Marshallian externality. This may help explain why industrial policies succeeded in some countries but failed in others and why sometimes industrial upgrading may take place even without government support.

Di¤erent from the literature, we highlight that the mere existence of Marshallian externality in an industry is insu¢ cient to justify government support for that industry. Instead, a crucial prerequisite for successful industrial policies is to ...rst identify the "right" industry target in time, that is, the industry which is most consistent with the capital endowment of the economy. Moreover, we show that the "right" industry target may endogenously shift over time as the economy develops, therefore successful industrial policy may require sequential and timely "pushes" instead of "once-and-for-all" intervention, as typically argued in the existing literature. To illustrate the importance of "right identi...cation", we show that when the government identi...es the wrong industrial target and "pushes" it accordingly, the economy may be even worse o¤ than the laissez-faire market equilibrium even though the target industry does exhibit Marshallian externality.

For the sake of analytical simplicity, just like the standard models in the literature, our model also assumes away uncertainty associated with the identi...cation of the right "industrial target". We also ignore the case where there are multiple industries with similar capital intensities but insu¢ cient number of investors (either because of the credit constraint or the scarcity of quali...ed 23
entrepreneurs). Thirdly, industry-speci...c productivity growth is not incorporated into our analyses. It would be interesting to explore those and many other issues in the future.

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