metadata: authors: 0: author: Li,Zhiyun
1: author: Lin, Justin Yifu
count: World
docna: 0: docna: Endogenous institution formation under a
            catching-up strategy in developing countries
docty: Policy Research Working Paper
subtopic: Economic Theory & Research,Human Rights,Industrial Economics,Food Security,Economic Growth,Armed Conflict
teratopic: Macroeconomics and Economic Growth,Finance and Financial Sector Development,Private Sector Development
abstracts: cdata!: This paper explores endogenous
            institution formation under a catching-up strategy in
            developing countries. Since the catching-up strategy is
            normally against the compartive advantages of the developing
            countries, it can not be implemented through laissez-faire
            market mechanisms, and a government needs to establish
            nonmarket institutions to implement the strategy. In a
            simple two-sector model, the authors show that an
            institutional complex of price distortion, output control,
            and a directive allocation system is sufficient to implement
            the best allocation for the catching-up strategy.
            Furthermore, removing any of the three components will make
            it no longer implementable. The analysis also compares the
            best allocation and prices under the catching-up strategy
            with their counterparts under no distortions. The results of
            this paper provide important implications for understanding
            the institution formation in the developing countries that
            were pursuing a catching-up strategy after World War II.
repnme: repnme: Endogenous institution formation under a
            catching-up strategy in developing countries
display_title: Endogenous institution formation
            under a catching-up strategy in developing countries
listing_relative_url: /research/2008/12/10091417/endogenous-institution-formation-under-catching-up-strategy-developing-countries
topicv3: Education, Skills Development and Labor
            Market m1326135 1484,Agriculture and Food Security m1326205 435,Economic Growth m1326241 471,Political Violence and War m1327310 2462,Discrimination m1505707 3379
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Macroeconomics and Economic Growth,Finance and Financial Sector Development,Private Sector Development
no_of_pages: 44
author_keys: 0: author_key: 616280
model_extractions: WPS4794 Policy ReseaRch WoRking PaPeR 4794 Endogenous Institution Formation under a Catching-up Strategy in Developing Countries _Justin Yifu Lin Zhiyun Li_ The World Bank Development Economics Vice Presidency December 2008
Policy ReseaRch WoRking PaPeR 4794

# **Abstract**

This paper explores endogenous institution formation under a catching-up strategy in developing countries. Since the catching-up strategy is normally against the compartive advantages of the developing countries, it can not be implemented through _laissez-faire_ market mechanisms, and a government needs to establish nonmarket institutions to implement the strategy. In a simple two-sector model, the authors show that an institutional complex of price distortion, output control, and a directive allocation system is sufficient to implement the _best_ allocation for the catching-up strategy. Furthermore, removing any of the three components will make it no longer implementable. The analysis also compares the best allocation and prices under the catching-up strategy with their counterparts under no distortions. The results of this paper provide important implications for understanding the institution formation in the developing countries that were pursuing a catching-up strategy after World War II.

This paper—a product of the Development Economics Vice Presidency—is part of a larger effort in the department to study development strategies and economic growth in developing countries. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at zhiyun.li@univ.ox.ac.uk.

_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
Endogenous Institution Formation under a Catching-up Strategy in Developing Countries!

Justin Yifu LIN Zhiyun LI The World Bank Economics Department University of Oxford Key Words: development strategy: institution; price distortion; output control; directive allocation system JEL Classification: D02, 017, 020, P41 ' Justin Yifu LIN, World Bank, 1818 H Street, NW, Washington, DC 20433,USA, Email: justinlin@worldbank.org; Zhiyun LI (corresponding author), University College, High Street, Oxford, OX1 4BH, Email: zhiyun.li@univ.ox.ac.uk. This is a preliminary version, and comments are welcomed.
# 1 Introduction

After World War II, many former colonial or semi-colonial countries in Asia, Africa and Latin America achieved their political independence. After that, how to realize rapid economic development and also achieve economic independence became new challenges for political leaders in those countries. Compared with industrialized countries, such as the United States and countries in Western Europe, these newly independent and less developed countries had extremely low income levels, living standards and economic growth rates. A common feature of the developing countries was that they heavily specialized in the production and export of primary commodities, and imported most industrial goods from the wealthy industrialized countries. Historically, the lack of modern industrial sectors, especially heavy industries, which were the basis of military strength and economic power, had forced many countries in the developing world to yield to the colonial powers. After achieving independence, the political leaders and elites in those countries naturally experienced an impetus towards the rapid development of large heavy industries, and commonly adopted an ideology of economic nationalism (Lal and Myint, 1996, chapter 7).

In the 1940s and 1950s, with still fresh memories of the Great Depression in capitalist countries, economists and policy makers began to cast doubt on the sound functioning of a laissez-faire market mechanism, even in ‡edging market economies. The rise of Keynesism as a new economic doctrine in the Western countries also re‡ected the belief that the market encompassed insurmountable defects, and government needed to provide supplementary policy measures to sustain a stable and well-functioning economy. In sharp contrast to the deep crisis in the Western countries in the 1930s, the socialist Soviet Union, having adopted a planned economic system and prioritized the development of heavy industries, was experiencing rapid economic growth and successfully transformed itself from a traditional agrarian economy into an industrial economy<sup>1</sup> . That seemingly great success of the Soviet Union, at least at that time, in‡uenced the political leaders of the developing coun-

> 1 After succeeding Lenin and consolidating his power, in 1929, Stalin started to pursue in earnest the prioritized development of heavy industries through a series of ...ve-year plans (Gregory and Harrison, 2005; Gregory and Stuart, 2001). The share of heavy industry in Soviet industrial output rose rapidly (Moravcik, 1965; Allen, 2003) and the Soviet Union quickly became a global military power before World War II.

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tries, whether they were socialist countries or not, and encouraged them to adopt similar strategies to achieve rapid industrialization<sup>2</sup> .

With the desire for rapid industrialization, the governments in the developing countries took various measures to facilitate the growth of the industrial sector. And it was commonly believed that a high proportion of economic surplus should be directed to investment in industrial sectors, just as had been done in the period of "socialistic primary accumulation" in the Soviet Union.

One important ...nding is that, though the developing countries were quite di¤erent from each other in political regime, economic size, geographic features and cultural traditions, very similar institutions were established in those countries after World War II, to implement the catching-up strategy of rapid industrialization. In this paper, we will investigate the rationale behind those institutional arrangements, and use a simple model to show that such institution formation is endogenous to a government’s adoption of catching-up strategies.

Institution here is de...ned as a set of non-technologically determined constraints that govern and shape economic agents’ interactions, in part helping them to form expectations of other agents’actions and the results of their own actions (Lin and Nugent, 1995; Greif, 1998). It is clear from this de...nition that institutions consist of both formal entities, like laws, statemandated rules, and commercial contracts, and informal ones, like social norms, customs and ideologies.

Among the similar institutional arrangements across the developing countries implementing catching-up strategies, the ...rst and most important was price distortion, such as the "price scissor" adopted mainly in socialist countries and the "import substitution" policy adopted in many other developing countries. Price scissor was a kind of price discrimination against non-industrial sectors, such as agriculture. For example, in China and the Soviet Union, agricultural products were procured by the government at

> 2 In Krueger’s (1995) article in the Handbook of Development Economics, she summarized ...ve dominant thoughts in development economics, as below: 1) the desire and drive for "modernization"; 2) the interpretation of "industrialization" as the route to modernization; 3) the belief in "import substitution" as a necessary policy to provide protection for new "infant" industries; 4) the distrust of the private sector and the market and the belief that government should take the leading role in development; and 5) a distrust of the international economy and pessimism that exports from developing countries could grow.

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prices lower than market equilibrium prices, and sold at those low prices to residents in urban areas where the industries were located. "Import substitution" implies that governments export domestic primary goods, while prohibiting the import of industrial products, so as to protect the development of domestic industrial sectors. It was adopted by many Latin American countries from the 1930s to the late 1980s. Under import substitution, the prices of domestic industrial products were normally higher than corresponding international prices<sup>3</sup> . In essence, import substitution is also, at least partially, a kind of price distortion.

The second kind of institutional arrangement is directive allocation systems for output and production factors. In many developing countries, the procurement and sale of commodities at regulated prices were typically operated and controlled by the governments, and the allocation of production factors was commonly through directive allocation, rather than market mechanisms. As a result the public sector played an important role in non-socialist developing countries implementing catching-up strategies. For example, in India, 62.1% of total productive capital and 26.7% of total labor in industry was in the public sector by 1978-1979 (Krueger, 1995), and in Brazil, in 1984, 81 of the 200 largest enterprises were state-owned, which accounted for 74.2% of the total capital and 56.3% of the total net income (Lin, et. al, 1999, Chapter 2).

Third and ...nally, the governments adopting a catching-up strategy heavily intervened in the production decision of enterprises, through such measures as government ownership, direct government operation, investment licensing, etc. It is understandable that, in socialist countries, nearly all the economic activities were directly or indirectly under the control of government. However, in non-socialist developing countries, there was also extensive government intervention in the production activities of enterprises. For example, in post war India, government permission was required for new investment by any of the 20 largest industrial houses, and it was permissible only when that investment could not be carried out by other industrial houses (Krueger, 1995). In fact, in those developing countries, even the private sectors were subject to substantial control by the state political and

> 3 It was documented that, in India, the e¤ective rate of protection (ERP) were well above 100% for 39 industries (of a 76 industry classi...cation) in 1968-69 (Bhagwati and Srinivasan,1975), and in Turkey, the ERPs of the infant industries were normally over 200% even after twenty years of their establishment (Krueger and Tuncer, 1982).

3
economic apparatus, among which the most important is output control.

In this paper, we will argue that the institutional complex of price distortion, output control and directive allocation is indeed endogenous to the government choice of catching-up strategies in the developing countries (Lin, et. al, 1994, 1996, 2007)<sup>4</sup> . The endowment structures of the developing countries commonly featur scarcity in capital and abundance in labor supply, while the development of industries, especially heavy industries, requires huge amounts of capital investment. Given the endowment structures of the developing countries, prioritizing the development of industrial sectors is obviously against the comparative advantages of the economies, and enterprises in heavy industry sectors are not viable in free competitive markets (Lin, 2003). Therefore, that kind of catching-up strategy can not be implemented through laissez-faire market mechanisms. To implement that strategy, the government needs to exclude market functioning and establish certain institutional arrangements that can facilitate the development of the industrial sectors.

First of all, a government pursuing catching-up strategies needs to reduce the costs of industrial production. Capital is expensive in the developing countries and market interest rates are high, which implies that capital-intensive production should be quite costly and non-pro...table in the developing countries. To reduce production costs, the government needs to ...x the interest rates at low levels, and reduce the prices of consumption goods, such as agriculture products, because cheaper consumption goods will reduce the labor costs of the industrial sectors. Through this kind of price distortion, the government can reduce the costs of industrial production. As was mentioned before, "price scissor" in both socialist and non-socialist economies<sup>5</sup> and the policy of "import substitution" adopted by many developing country governments can be grouped into the institutional arrangement of price distortion.

Second, the government needs to set up a directive allocation system. Price distortion implies that the prices of many products are arti...cially set

> 4 The institution in this paper refers to institution arrangement when is a set of behavioral rules that govern agents’behaviors in speci...ed domains, not instituional structure which is totality of institutional arrangements (Lin and Nugent, 1995).

> 5 Sah and Stiglitz (1984) investigate the e¤ects of price scissors on industrial accumulation in socialist countries. Rattsø and Torvik (2003) study the price discrimination against agriculture to promote industrialization in Sub-Saharn Africa.

4
at below market-clearing levels, and as a result, there exists excess demand for those products. To su¢ ciently allocate the under-priced products and factors to target industries, the government needs to establish a directive allocation system, and secure its position as monopolistic purchaser of those goods. Otherwise, either non-industrial sectors will compete with industrial sectors for those under-priced goods, or they can be sold in other markets at higher prices. This also explains the agriculture collectivization movements in China and the Soviet Union, and why public ownership and direct government control were also prevalent in many non-socialist developing countries.

Finally, the government also needs to intervene in the enterprises’production activities. When workers in enterprises can freely decide how much to produce or how high to set their wages, they will take action for their own bene...ts. For example, if wages are ...xed by the government at low levels, the workers will have low incentives to exert e¤ort. In this case, an output requirement set by the government may guarantee the lowest level of e¤ort input by the workers.

There has been a large literature studying the endogenous formation of economic or political institutions and the government’s role in economic development. The early literature commonly assumed that the government acts as a benevolent social guardian of the economy, and its role is to establish certain institutions and take relevant measures just to compensate for the defects of the market mechanism. But later observation of inef...cient government intervention and government corruption has led to new consideration of the role of the government and the formation of economic and political institutions. A new strand of literature began to explore this problem from the perspective of political economy, by clearly introducing the incentives of politicians in the government and interest groups (Grossman and Helpman, 1994; Shleifer and Vishny, 1994, 1998; Acemoglu, 2006, 2007). According to this theory, the government intervenes in the economy and establishes certain institutional arrangements to maximize the payo¤s of special interest groups, or merely for the purpose of rent-seeking. Shleifer and Vishny (1994, 1998) emphasize the grabbing-hand nature of governments and suggest that government controls over enterprises come about when politicians can use public resources to buy o¤ enterprise managers, for their cooperation in redistributing economic or political rents. Acemoglu (2006) shows in a simple model that political elites choose policies to in5
crease their income and to directly or indirectly transfer resources from the rest of society to themselves, which leads to distortions and thus ine¢ cient allocation in the economy.

However, in the developing countries that were pursuing the catching-up strategies, the establishment of various institutional arrangements by the governments was obviously not for the purpose of acquiring rents by the political elites, and neither were there particular bene...ciary groups of those institutional arrangements, at least in the short run (Lin, et al., 2006). In such economic environments where economic activities were highly regulated and the role of the market was relatively limited, the political elites did not have much room for rent-seeking either. On the contrary, during the transition period of many socialist countries in the 1990s, with the collapse of traditional plan systems, there were much more serious corruption problems in the governments than before. In fact, the political leaders of those developing countries adopted the catching-up strategies under the good will that national prosperity can soon be achieved through rapid industrialization.

In this paper, in a simple two-sector model, we will prove that, in the developing countries, the formation of that special institutional complex of price distortion, directive allocation and output control is endogenous to the governments’ adoption of a catching-up strategy. Furthermore, that institution complex is both necessary and su¢ cient for implementing the best allocation for catching-up strategy. In our two-sector model, e¤ort is introduced as an inherent control variable of economic agents, which is not observable and cannot be directly controlled by the government. But the behaviors of the agents can be indirectly regulated by the external economic environments, which is designed purposely by the government. So the problem of the government is how to design optimal institutional arrangements to implement the best allocation for catching-up strategy, given the interest con‡ict and incentive problem of the economic agents.

We prove in our model that the best allocation is implementable by a combination of price distortion, directive allocation system and output control, and none of these three components is dispensable for that implementation. The intuition behind this result is that, without output control, the agents will reduce their e¤ort inputs and less outputs in both sectors will be produced, and as a result, less surplus can be mobilized for capital accumulation. Without price distortion, the equilibrium price of consumption 6
goods will be higher, and therefore raise the labor cost of production. And without directive allocation of capital, the agents can adjust their capital demands to e¤ort inputs, which will ...nally result in more consumption and less capital accumulation.

The remaining parts of this paper are organized as follows: Section 2 presents a basic two-sector model, and characterizes the optimal allocation and shadow prices under no distortion. Section 3 introduces the catchingup strategy into the model. By solving a central planner’s problem, we characterize the best allocation for implementing that catching-up strategy. Section 4 turns to study the implementation of that best allocation by the government, and proves that that best allocation is implementable by an institutional complex of price distortion, output control and directive allocation system. Section 5 is a counter-factural analysis, where we alternatively remove one part of that institutional complex, while keeping the other two parts unchanged, and explore its impact on ...nal allocations. Section 6 is a short conclusion.

# 2 The Model and Optimal Allocation

## 2.1 Model Setup

There are two sectors in the economy: capital goods sector and consumption goods sector. The production of either goods requires both capital and labor inputs. Total capital K = K1 + K2, where K1 is capital input in the capital goods sector and K2 in the consumption goods sector. Similarly, we have total labor L = L1 + L2. It is assumed that labor is not intersectoral transferrable in our economy<sup>6</sup> . For simplicity and without loss of generality, we normalize L = 1 and let L1 = � and L2 = 1 � �, � 2 (0; 1). The endowment structure of the economy is measured by per capita capital, k = K=L, which is normally low in the developing countries.

The production of capital goods (goods 1) is more capital intensive than that of consumption goods 2 (goods 2), and their production functions are

> 6 For example, in China, peasants in rural areas are not allowed to work in manufactories in urban areas, under the regulation of hukou system. Also, the production of di¤erent goods requires di¤erent skills, and it is di¢ cult for workers in one sector to acquire the required skills for production in another sector in short time.

7
where ej is the per capita e¤ort input of a worker in sector j, and ejLj may be interpreted as e¤ective labor input. We assume workers in the same sector are homogenous. The production function Fj(�; �) is homogenous of degree one in Kj and ejLj. Per capita output and per capita capital in sector j are respectively yj = L<sup>Yj</sup> j<sup>andkj=K</sup> Lj<sup><u>j</u>.</sup> Total capital balance constraint implies that �k1 +(1 � �)k2 = k. For per capital output, we have It is obvious that fj(kj; ej) is homogenous of degree one in kj and ej. Consumption goods 2 can be used only for consumption and are not preservable, and capital goods 1 can be used for either consumption or investment.

Though economic agents in both sectors are assumed to have the same preference, they are heterogenous in essence since they are in di¤erent sectors, having di¤erent skills, and labor is not intersectoral transferrable. The utility function of agents in sector j is where xij is the amount of goods i consumed by an agent in sector j, and ej is his e¤ort input. u(�; �) is strictly concave in (x1j; x2j) and satis...es the Inada conditions, and the disutility of e¤ort, C(ej), is strictly convex satisfying the conditions that C<sup>0</sup> (0) = 0 and C<sup>0</sup> (1) = 1.

# 2.2 Optimal Allocation

For later comparison with distorted allocation under catching-up strategy, we ...rst study the optimal allocation in the benchmark case of no distortion. The social welfare function is standard and de...ned as 8
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# 3 Catching-Up Strategy and a Central Planner Problem

In this section, we introduce the catching-up strategy into the model, and by solving a central planner’s problem, we characterize the best allocation for implementing that strategy. In the next section, we will study how to implement that best allocation, given the interest con‡icts between the agents and the government. Similar to Sah and Stiglitz (1984, 1987), we study this problem in a static model, and thus abstract the dynamic e¤ects of industrial accumulation. However, it will be clear that a static model is su¢ cient to capture the main trade-o¤s that determine the endogeneity of institutional formation under a catching-up strategy.

As was stated above, when implementing a catching-up strategy, the government in a developing country tries to mobilize enough economic surplus to invest in industry. In our model, since consumption goods can only be used for consumption, the total surplus that is available for investment in industrial sectors is the net output of capital goods, I, that is, The total amount of industrial accumulation is equal to the di¤erence between total output and consumption of capital goods. We assume the government’s objective function is a weighted average of social welfare and industrial accumulation I in the following form where � is a weight proxy of I in government’s objective function. When � = 0, U<sup>G</sup> returns to the benchmark case of the social welfare function. And the central planner problem for the government is thus 13
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with an objective function (2) di¤erent from that of the government (22). For example, unlike the government, the economic agents may not care much about the development of heavy industries or accumulation of capital goods. To implement the best allocation for the catching-up strategy, the government needs to establish relevant institutions and impose various constraints on agents’economic activities. Since that catching-up strategy cannot be implemented through market mechanisms, restricting the functioning of market mechanism is a natural objective of the government in its design and establishment of relevant institutional arrangements. Those institutional arrangements can be divided into three categories, and each corresponds to special policy variables in our model:

1. Distorted price system, commonly known as "price scissor" in the literature, but the policy of "import substitution" is also a kind of price distortion arrangement in essence. By distorted price system, we mean in our model that product and factor prices are control variables of the government, including the relative price of consumption goods p, interest rate r and wage levels wj.

2. Directive allocation system, which implies that the allocation of products and factors are through government directives rather than through market mechanism. In our model we study only the case in which the allocation of capital is under the control of government, while both consumption and capital goods are still allocated through the market mechanism. This setting weakens the role of government in allocating resources and products, especially for the governments in socialist countries. However, this weakened setting is enough to demonstrate the function of a directive allocation system under catching-up strategies. In our model, it implies that kj is a control variable of the government.

3. Deprivation of autonomy of producers, which means that production activities in the economy are under close control of the government, such as quantity control, investment licensing, export licensing, etc. In our model, deprivation of production autonomy implies that producers in both sectors face the output obligations, qj, imposed by the government.

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Therefore, the control variables of the government are fp; r; wj; qj; kjg, and the choice variables of an agent in sector j are his demand for products xij and his e¤ort input ej. We investigate the interaction between the government and agents in a two-stage game of complete information. First the government determines the economic environment by specifying the choice of policy variables fp; wj; r; qj; kjg. Second, facing the economic constraints, the agents in both sectors make their own utility-maximization decisions, and then the ...nal allocation is realized as an equilibrium outcome. As the ...rst step, we solve the best responses of the economic agents, given the exogenous parameters fp; wj; r; qj; kjg. We normalize the reservation utility for agents in both sectors as 0.

# 4.1 Best Responses of Agents

Facing the exogenously given economic institutions or constraints fp; wj; r; qj; kjg, the problem of an agent in sector j is as follows: The price restrictions fp; r; wjg a¤ect the income level and consumption decision of the agent, the output requirement qj jointly with the capital allocation kj determine the minimal e¤ort input of the agent. The Lagrangian of the problem is The budget constraint is binding at optimality, and the optimal conditions are 19
Our interest is in the case that the quantity constraint is also binding at optimality, otherwise the output obligation imposed by the government does not a¤ect the optimal e¤ort inputs of the agents. It corresponds to the case that �2 > 0 and qj � fj(kj; ej) = 0. And the Lagrangian multipliers satisfy The condition of �2 implies that the marginal cost of e¤ort is higher than the marginal revenue/adjusted-utility of e¤ort input when the output constraint is binding. The value function of problem P<sup>A</sup> is the indirect utility function of agents in sector j, denoted as vj(p; r; wj; qj; kj), and the optimal e¤ort input is ej(qj; kj).

Lemma 8 Given the economic environment fp; r; wj; qj; kjg, the indirect utility function of agents in sector j satis...es and for optimal e¤ort supply ej(qj; kj), we have The results of comparative statics analysis of vj and ej will be extensively used in solving the optimal policy problem of the government in the next section. The Appendix also provides the results of comparative statics analysis on the demand functions x1j and x2j. Using the same example as before, we derive the close-form demand functions, e¤ort inputs and the indirect utility function of the agent as below.

Lemma 9 Given the economic environment fp; r; wj; qj; kjg, in the example 20
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> AL —xX Aq AL — —x Ak —x

A = — — —
It is obvious that the total industrial accumulation is equal to the sum of total surplus of both production sectors. From (39), we get the following results of comparative statics that, given other things equal, the total industrial accumulation I satis...es And the government’s problem is reformulated as: where �> 0 measures the weight of industrial accumulation in the government’s objective function. Here we have normalized the reservation utility of the agents in both sectors to be 0. The restriction of vj � 0 also implies that the government has limited implementation power, and extreme exploitation of a certain sector is not possible<sup>9</sup> . M = fp; r; wj; qj; kjg represents the set of available policy instruments of the government, in which k1 and k2 are interdependent through �k1 + (1 � �)k2 = k. Let vG(M ) be the value function of problem P(M ), and M<sup>0</sup> � M be a subset of M , that is, M 0 represents a smaller set of policy instruments. It is obvious that Proof. The proof is self-evident. For 8M<sup>0</sup> � M , suppose control variables zj 2 M<sup>0</sup> , and yj 2 M �M<sup>0</sup> . Suppose the optimal solution of P(M<sup>0</sup> ) are fzj<sup>�; y</sup> j<sup>�gwherez</sup> j<sup>�’sarechosenbythegovernmentandy</sup> j<sup>�’sareequilibrium</sup> levels of yj. In problem P(M ), the government can simply choose zj = zj<sup>�</sup> and yj = yj<sup>�,thenachievethesamevalueofvG(M0).</sup>

> 9 However, if we relax this constraint or introduce discrimination against certain group of agents, i.e. the peasants, this framework can be used to study inequality under the catching-up strategy, or famine in former socialist economies.

22
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by output regulation and capital allocation, and given this, r, and wj’s jointly determine the agent’s income level. Though total income level and relative price, p, are uniquely determined by the optimal conditions, the composition of interest and labor income is not uniquely determined when both r and wj’s are control variables of the government. We introduce a natural behavioral restriction on government’s selection of the interest rate, that is, the government sets the interest rate at the level of marginal capital output of both sectors Proposition 11 For a government that implements CAD strategy using three groups of policy instruments, the optimal choice of the policy variables fp; r; wj; qj; kjg, j = 1; 2, satis...es where xij and ej are given by the solutions to problem P<sup>A</sup> .

Using the same example as above, we will prove that the best allocation for catching-up strategy is implementable, and will characterize the optimal institutional arrangements for implementing that strategy. In that example, we know the demand functions are and the e¤ort inputs are 25
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of the three components of the institutional complex is removed<sup>10</sup> . Each removal changes one facet of the economic institutional arrangement, and endows the agents with more freedom than before in their economic decisions. For a policy variable that is removed from the pool of the government’s policy instruments, its equilibrium value will be determined through a market mechanism. We will compare the equilibrium values of those variables with their counterparts in best allocation.

# 5.1 Necessity of Output Control

What is the impact of removing output controls, when the other two components of the institutional complex are kept unchanged? In this case, the agents face only the institutional constraints of price distortion and directive allocation of capital, but they can freely decide how much to produce. Under the less restrictive institutional constraints of fp; r; wj; kjg, the problem for the agent in sector j is now We easily get the optimal conditions that We denote the solution to this problem as nx<sup>Q</sup> 1j<sup>; x</sup> 2<sup>Q</sup> j<sup>; eQ</sup> j o, where the superscript Q means that there is no quantity control over the producers. By intuition, without output control, the agents will invest less e¤ort and the result will be less output of the corresponding product, which is proved in the following proposition.

Proposition 15 Given the institutional constraints of price distortion and directive capital allocation, fp;^ ^r; w^j; k<sup>^</sup> jg, the e¤ort input of an agent facing

> 10 Removing all the components implies a situation of no government intervention at all (free market economy).

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no output control is lower than that in the best allocation, that is, Proof. Suppose not, then e^j < e<sup>Q</sup> j<sup>andtheoutputofproductfj(^kj; eQ</sup> j<sup>)></sup> ^ ^ qj, which implies that the quantity constraint is not binding in (P<sup>A</sup> ). So ej cannot be the best e¤ort input level in the best allocation for implementing the catching-up strategy.

Proof. It is self-evident, given ^ej � e<sup>Q</sup> j<sup>and the formula of demand functions.</sup> These results demonstrate that there is an "over" supply of e¤ort under the full constraints of the institutional complex, in the sense that the marginal cost of e¤ort input is higher than its marginal revenue (remember the optimal conditions of problem P<sup>A</sup> ). So when a government implements the catching-up strategy, it will compel the agents to exert more e¤ort than they would do in free market situations. So to guarantee a certain level of e¤ort inputs, the government needs to impose the output requirements on the production of the agents, and output control is indispensable for implementing the best allocation for the catching-up strategy.

# 5.2 Necessity of Price Distortion

When the agents face only quantity control and directive allocation of capital and there is no price regulation, agent j’s problem is to choose optimal consumption and e¤ort inputs under the constraints of fqj; kjg. In this case, the demand for products in both sectors is determined only by consumer demand, not by government demand. The problem for agent j is thus The key di¤erence between this problem and problem P<sup>A</sup> lies in the fact that when price is liberalized, equilibrium price levels are determined only by market equilibrium. It is obvious that the distorted prices in the best 31
allocation, fp;^ ^r; w^jg , are not sustainable as market equilibrium prices, since there is at least excess supply of capital goods 1. So removing the component of price distortion implies that the ...nal allocation is (strictly) inferior to that under the full constraints of the institutional complex.

In the problem above, ej is uniquely determined by qj = fj(kj; ej). In our speci...c example, the demand function is given by The market equilibrium requires that The constraint of output controls also requires that and we get and again, the superscript P means that there is no price regulation by the government.

Proposition 17 Given the same optimal policy controls fk<sup>^</sup> j; ^qjg, the relative price of consumption goods under additional price control is lower than that without price control, that is Proof. Remember that 32
It is intuitive that when removing the price regulation, the equilibrium price of consumption goods becomes higher, but it is even higher than p<sup>�</sup> , the price that supports the optimal allocation in a Walrasian equilibrium. This is because the production of both sectors is still distorted under output control and directive allocation of capital.

# 5.2.1 Necessity of a Directive Allocation System

The government’s objective of establishing the directive allocation system is to allocate those under-priced products and production factors to target sectors, i.e. the capital goods sector. Speci...cally, in our model, removing the directive allocation system implies that the allocation of capital kj is through market allocation schemes, rather than through government directive allocations. In this subsection, we investigate the e¤ects of removing the directive allocation system.

First, it is natural that, in a free market, if the interest rate is lower than the market-clearing level (i.e. r^ < r<sup>�</sup> ), there will exist excess demand for it, and if r^ > r<sup>�</sup> , there then exists excess supply of capital. So it is selfevident that the government needs to establish a directive allocation system to direct the allocation of products and production factors at controlled prices. In this subsection, we study a somewhat di¤erent environment in which the agents still face output controls imposed by the government. And we will see why the best allocation is not achievable when there are only price and output controls fp; r; wj; qjg. In this case, the agents can decide their capital demand or supply so that their marginal rate of transformation between capital and e¤ort is equal to the corresponding level of the marginal rate of substitution. Speci...cally, we are interested in the question: When capital is tradable at the regulated price r^, do the agents have incentives to sell or purchase additional capital at the initial allocation of fx^ij; ^ej; k<sup>^</sup> jg? We de...ne the additional demand/supply of capital by an agent in sector j as where kj is the ...nal per capita capital used for production in sector j. And 33
the agent’s problem is Given the ...xed output requirement qj, an agent can reduce capital demand by increasing e¤ort input, or vice versa. And the optimal combination of capital and e¤ort inputs is determined by relative prices and output requirements fp; r; wj; qjg. The Lagrangian of the problem is and the optimal conditions are By rearrangement, the optimal conditions are now Remember in trinity institutional arrangements, the conditions for marginal rate of transformation is while in this case, it is Using our speci...c example, the condition for the marginal rate of trans34
formation under only price and output controls, fp;^ ^r; w^j; ^qjg, is and the corresponding MRT conditions under trinity institutional arrangements is where �1 = � and �2 = �. We want to compare the value of kj to k<sup>^</sup> j.

As a starting point for analysis, we ...rst assume kj = k<sup>^</sup> j, which implies ^ that �k1 = 0 and ej = ej since the output requirements remain unchanged. For sector j agent, it is obvious that To get the optimal condition to held, we need to reduce the capital input below k<sup>^</sup> j and increase the e¤ort input over e^j, and we get the following result.

Proposition 18 When there are only regulations on prices and outputs, fp;^ ^r; w^j; ^qjg, and capital is tradable, the demand for capital in either sector is strictly lower than that in three-in-one environments, that is, kj < k<sup>^</sup> j, for j = 1; 2.

Given the opportunity of trading capital and if that trade can really happen, we will have that the incomes of agents in both sectors will be ^ ^ ^ higher than before, that is, wjej � r�kj + rk > wjej + rk, which will result in greater demand for both products than under trinity institutional arrangements.

Corollary 19 When there are only regulations on prices and outputs, fp;^ ^r; w^j; ^qjg, and capital trade is feasible, there will be more consumption of capital goods and less industrial accumulation than in the best allocation, speci...cally, It is worth metioning that the above results are based on the condition that capital trade is feasible. Only under this condition could the agents 35
^ purchase or sell capital at the regulated price r. And with that opportunity, the agents are able to adjust their e¤ort inputs and consumption decisions, and therefore a¤ect the ...nal allocation in this economy.

# 6 Conclusion

After the Second World War, many newly independent countries adopted the catching-up strategy of rapid industrialization. However, for those developing countries, prioritizing the development of industrial sectors, especially the heavy industry sectors, was against the comparative advantages of their economies. And the catching-up strategy was not implementable by laissez-faire market mechanisms. To implement that strategy, the governments need to establish a series of institutions that exclude the functioning of markets and are able to mobilize enough economic surplus for industrial accumulation. Under the catching-up strategy, similar institutional arrangements were established in those developing countries, no matter whether they were socialist countries.

In this paper, we develop a simple two-sector model to explain the rationale behind that institution formation in those developing countries. We prove that the best allocation for a catching-up strategy can be implemented by an institutional complex that consists of price distortion, output control and a directive allocation system. We further explore the counterfactual effects of alternatively removing one part of the institutional complex on ...nal economic allocations. We show the following results: (1) removing price regulation will result in higher price of consumption goods, (2) removing output control will induce less e¤ort inputs by the agents, and (3) removing the directive capital allocation system will result in more consumption and less industrial accumulation. In short, none of these three components of this institutional complex is dispensable for a successful implementation of the catching-up strategy. In a simple two-sector model, this paper provides a framework for understanding the endogenous institution formation under the catching-up strategy in developing countries after World War II, and shows that how a government can establish certain institutional arrangements to implement allocations that are not implementable by laissez-faire market mechanisms.

The formation and evolution of economic institutions in developing coun36
tries under various development strategies is a important topic for research. This paper represents a ...rst step in this line of research, and more work certainly needs to be done in the future. First, this paper studies just the formation of special economic institutions under the catching-up strategy, and does not explore the dynamic e¤ects of that institutional arrangements on the long run economic growth, which requires the development of dynamic models. Second, the framework developed in this paper can be extended to investigate various issues in economic development, such as famines in the developing countries and socialist countries, the relationship between inequality and development strategy, and so on. And ...nally, for the testable hypotheses that arise from the theoretical model, we also need to verify those hypotheses through rigorous empirical research.

# A Comparative Statics Analysis of xij’s

For demand functions, we have Proof. The optimal conditions for the problem is 37
~~—~~ ~~<u>-— 1</u>~~ 0 | ~~—~~ ~~<u>1</u>~~ 0| ~~a~~ o ~~~~~ ~~<u>1</u>~~ | ~~—~~
~~~ a~~ S | ~~<u>-~ 1</u>~~ 0 ~~— 1~~ 0- | ~~—~~ ~~<u>0</u>~~ | oe
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