Import Substitution and Economic Growth


 Maurice Fisher
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1 Import Substitution and Economic Growth Mauro Rodrigues University de Sao Paulo, Brazil Abstract Despite Latin America s dismal performance between the 1950s and 1980s, the region experienced strong capital deepening. We suggest that these facts can be explained as a consequence of the restrictive trade regime adopted at that time. Our framework is based on a dynamic HeckscherOhlin model, with scale economies in the capitalintensive sector. Initially, the economy is open and produces only the laborintensive good. The trade regime is modeled as a move to a closed economy. The model produces results consistent with the Latin American experience. Speci cally, a su ciently small country experiences no longrun income growth, but an increase in capital. JEL Classi cation: O41, F12, F43, E65 Keywords: Trade Policy, Growth, Latin America Department of Economics, University of Sao Paulo. Av. Prof. Luciano Gualberto 908, Sao Paulo, SP, , Brazil. Phone: Fax: I am specially indebted to Hal Cole, Matthias Doepke and Lee Ohanian for their help and encouragement. I also thank Andy Atkeson, Roger Farmer, Carlos Eduardo Goncalves, Bernardo Guimaraes, Miguel Robles and JeanLaurent Rosenthal for valuable suggestions and comments. Financial support from Capes (Brazilian Ministry of Education) and Fundacao Instituto de Pesquisas Economicas (Fipe) is gratefully acknowledged. All errors are mine. 1
2 1 Introduction Between the 1950s and 1980s, Latin American countries pursued import substitution (IS) as a development strategy. A set of policies was implemented with the objective of developing an internal manufacturing sector. A crucial element of the IS strategy was to grant high levels of protection to domestic producers, largely closing these economies to international trade. Despite these e orts, most countries in the region were unable to gain any signi cant ground relative to the industrial leaders. In 1950, Latin America s GDP per capita was 27 percent of that of the U.S.; in 1980, this number was 29 percent. Figure 1 displays this pattern: relative income remained roughly stable throughout the 1950s, 1960s and 1970s, before collapsing in the 1980s. While other countries or regions also failed to develop during this period, a key distinctive feature of the Latin American case is that low growth went along with strong capital deepening. Table 1, based on Hopenhayn and Neumeyer (2004), illustrates this point. Although Latin America s growth rate in output per capita was similar to that of the U.S. between 1960 and 1985, capitaloutput ratio increased at a rate comparable to the fastgrowing countries of East Asia. Furthermore, productivity measured as total factor productivity (TFP) grew at a slow rate especially relative to the U.S. In other words, Latin America fell behind the world technological frontier represented here by the U.S. during this period. 1 This paper suggests that a single explanation, namely the adoption of import substitution policies, can account for the unique combination of low productivity with strong capital deepening which characterized Latin America in that period. We argue that the sectors targeted by these policies were subject to economies of scale. Given the small size of the average Latin American country, these industries were unable to develop once restrictions to 1 This pattern was also identi ed by Syrquin (1986). Moreover, Cole et al. (2005) show that Latin America s capitaloutput ratio has approached that of the U.S. since the 1950s, even though there has been no catch up in terms of income per capita. 2
3 international trade were imposed. As a result, the region stagnated. The analytical framework presented here is based on a dynamic HeckscherOhlin model with two factors, capital and labor, and two sectors, a laborintensive sector and a capitalintensive sector. Production of the capitalintensive good is subject to economies of scale. A country is assumed to be initially at an openeconomy steady state in which it is fully specialized in the production of the laborintensive good. IS is modeled as an unanticipated move to a situation where there is no trade in goods. The model is qualitatively consistent with important features of the Latin American experience. Speci cally, for a su ciently small country, IS will lead to no longrun growth in output per capita. Capital per capita will however increase and, as a result, measured TFP will fall. This result follows because Factor Price Equalization holds in the model. That is, the return on capital depends on the world capital stock, but not on the distribution of capital across countries. This implies that an open economy may display a relatively low capital stock in steady state. Closing the economy raises temporarily the return on capital, which leads to capital deepening in the long run. Nevertheless, if the economy is su ciently small, output per capita will not take o due to the lack of scale. Quantitatively, the model is able to approximate some key facts of the Latin American development experience. Speci cally, it implies that the average Latin American country exhibits high rates of capital deepening, but growth rates in output per capita that are similar to those of the U.S. Consequently, the model can produce low TFP growth rates as in the data. An important implication of this theory, which emphasizes scale e ects, is that larger countries should do relatively better than smaller countries after adopting IS policies. Such prediction is in line with the experience of Brazil and Mexico, the largest economies in the region. Between 1950 and 1980, Brazil increased from 17 to 28 percent of the U.S. GDP per capita, while Mexico increased from 25 to 34 percent. Figure 2 shows that these countries 3
4 signi cantly outperformed the average Latin American country during the IS years. This implication is also compatible with empirical evidence from Ades and Glaeser (1999) and Alesina, Spolaore and Wacziarg (2000), which have shown that, among countries that are relatively closed to trade, larger economies tend to grow faster and have higher per capita incomes. But when more open economies are considered, this size premium tends to disappear. Several scholars have considered Latin America s trade regime as a possible source for its lack of development (see for instance Balassa, 1989, Lin, 1989, Edwards, 1995, Taylor, 1998, Hopenhayn and Neumeyer, 2004, Manuelli, 2005, Cole et al., 2005). Speci cally, they argue that these economies have been largely closed to international trade, especially when compared with countries that successfully reduced their gap relative to the industrial leaders in a similar period. The present paper provides a dynamic general equilibrium model to explore this relationship. In addition, the study analyzes the implications of Latin America s trade regime for capital accumulation and aggregate productivity. The emphasis on scale is motivated by contributions of economists during the IS years, which identi ed problems such as smallscale and ine cient production plants, especially in consumer durables and capital goods sectors. For instance, in the 1960s Scitovsky (1969) pointed out that the automobile industry required plants with an annual output of 250,000 units in order to minimize costs. Nonetheless, there were eight Latin American countries with established automobile industries, whose combined production of around 600,000 cars and trucks was generated by 90 rms. 2 This study is related to the classical work of Johnson (1967), which was also motivated by the unsatisfactory results of IS policies. In the context of the static HeckscherOhlin model, the author has shown that, if the capitalintensive sector is protected by a tari, an exogenous increase in the capital stock may not lead to growth in national income. This 2 Other references include Balassa (1971), Baer (1972) and Carnoy (1972). 4
5 follows because capital accumulation shifts resources towards the protected sector, amplifying the ine ciency imposed by the tari. 3 The present paper generates similar results, but considers an alternative mechanism in which scale plays a crucial role. In addition, here capital accumulation occurs endogenously. The modeling strategy is closely related to dynamic HeckscherOhlin models, as in Baxter (1992), Ventura (1997), Atkeson and Kehoe (2000), Cunat and Ma ezzoli (2004), Bajona and Kehoe (2006a, 2006b) and Ferreira and Trejos (2006). These papers typically study economies composed of two standard competitive sectors (with di erent factor intensities) and two factors, capital and labor, where capital is reproducible. We add to them by considering a capitalintensive sector characterized by economies of scale and imperfect competition. Speci cally, the production structure is similar to Ethier (1982) and Helpman and Krugman (1985). While the laborintensive good is produced by competitive rms using a standard constant returns to scale technology, the capitalintensive sector is composed of di erentiated variety producers, which behave as monopolistic competitors and operate a production function subject to a xed cost. Economies of scale arise from the expansion of the set of varieties available. Such structure is particularly useful, since it allows for Factor Price Equalization even in the absence of perfect competition. Furthermore, as in Grossman and Helpman (1989, 1990), RiveraBatiz and Romer (1991) and Young (1991), growth takes place here through the introduction of new goods. The paper is organized as follows. Section 2 describes the model and analyzes the steady state of a closed economy. Section 3 introduces international trade and describes the steady state of an open economy. Section 4 assesses qualitatively the longrun e ects of the policy change on capital, income and consumption per capita. Section 5 extends the model to allow for longrun growth. Section 6 presents a quantitative application of the model. Section 7 concludes. 3 This argument was later formalized by Bertrand and Flatters (1971) and Martin (1977). 5
6 2 The Model Time is discrete and indexed by the subscript t, t = 0; 1; 2; ::: There is no uncertainty. There are two basic factors: capital and labor; and two sectors: a laborintensive sector (sector 1) and a capitalintensive sector (sector 2). The laborintensive sector is competitive and subject to constant returns to scale. The capitalintensive sector generates output by combining a set di erentiated varieties in a DixitStiglitz fashion. Each variety is produced using capital and labor, but there is a xed cost. Variety producers behave as monopolistic competitors. This structure gives rise to scale economies in sector 2. Goods 1 and 2 (produced respectively by sectors 1 and 2) are combined to generate the nal good, which can be either consumed or invested. There is a measure N of identical in nitelylived households, which is interpreted as the scale of the economy. Factors are fully mobile across sectors, but immobile across countries. There is no international borrowing or lending. The remainder of this section describes the basic features of the model, along with main analytical results. Details on rstorder and equilibrium conditions can be found in Appendix Production The nal good Y is produced by a competitive rm which combines the laborintensive good (Y 1 ) and the capitalintensive good (Y 2 ) through a CobbDouglas production function Y t = Y $ 1t Y2t 1 $. The price of the nal output is normalized to 1; p 1 and p 2 denote respectively the prices of the labor and the capitalintensive good. The production structure of the laborintensive sector is also standard. Competitive rms operate a CobbDouglas technology, with capital (K 1 ) and labor (L 1 ) as inputs, that is, Y 1t = K 1 1t L 1 1 1t. 4 See Supplemental Materials for the appendices of this paper. 6
7 The capitalintensive sector is nonetheless subject to economies of scale. Production is modeled as a twostage process. In the rst stage, a continuum of measure n monopolistic competitors use capital and labor to produce di erentiated varieties. In the second stage, a competitive rm combines those varieties to assemble good 2. For this last stage, we assume a CES production function with elasticity of substitution 1=(1 ), in which each variety enters symmetrically: 0 Zn t 1 Y 2t x it di A 0 1= ; 0 < < 1 where x i is the quantity of variety i used in the production of Y 2. The secondstage rm chooses the quantity of each available variety, taking as given the prices of these varieties and the price of good 2. The solution of this problem yields the demand for a given variety i: x it = pit p 2t 1 1 Y2t (1) where p i is the price of variety i. In the rst stage, each variety i is produced using capital (K i ) and labor (L i ), which are combined through a CobbDouglas production function. Additionally, each producer has to pay a xed cost f in units of its own output. In other words, x it = K 2 it L1 2 it 1. f, where 2 > 1, i.e., sector 2 is more capital intensive than sector Variety producers behave as monopolistic competitors, that is, variety i s producer chooses p i and x i to maximize pro ts, subject to its own demand function (1). The solution of this problem yields a constant markup over the marginal cost ( ): p it = p t = 1 t = 1 r 2 t w 1 2 t 2 2 (1 2 ) 1 2 (2) 7
8 where r and w are respectively the rental rate of capital and the wage rate. The measure of available varieties n is determined by a free entry condition, which implies that pro ts are always equal to zero in the rst stage, that is, p t x it = t (x it + f). This condition, along with equation (2), imply that production x i is constant across time and varieties: x it = x = 1 f This means that expansion and contraction of sector 2 take place through changes in the number of varieties, but not through changes in output per variety. By symmetry, each variety uses the same quantity of inputs, i.e., K i = K 2 and L i = L 2 for all i. 2.2 Households There is a continuum of measure N in nitelylived households. At any point in time t, each household is endowed with k t units of capital and one unit of time, which is supplied inelastically. Income can be used either for consumption or investment. For a given initial level of capital k 0, the representative household chooses sequences of consumption fc t g 1 t=0 and capital stock fk t+1 g 1 t=0 to maximize a timeseparable lifetime utility, with discount factor and instantaneous utility function u(c), which is twicedi erentiable, strictly increasing and strictly concave. Capital depreciates at the constant rate. Firstorder conditions then yield the usual Euler equation u 0 (c t ) = u 0 (c t+1 )(r t ). 2.3 Market clearing The following equations represent respectively the equilibrium conditions for the nal good, capital and labor markets: 8
9 Y t = N[c t + k t+1 (1 )k t ] Nk t = K 1t + n t K 2t N = L 1t + n t L 2t Focus is initially given to the closedeconomy equilibrium. Therefore, domestic markets for goods 1 and 2 also clear. 2.4 Closedeconomy steady state In what follows, variables with no time subscript denote their respective steadystate values. The choice of functional forms allows us to reach closedform solutions for the main variables in steady state. Appendix 2 describes how to obtain expressions for number of varieties (n), capital per capita (k), output per capita (y) and consumption per capita (c). In particular, the impact of country size on n, k, y and c depends on parameter values. Assumption 1 guarantees that those variables are all increasing in N. Assumption 1 > (1 $) 2 1 $ 1 Consider an increase in N, which leads to a higher demand for each existing variety and, everything else constant, to positive pro ts. Assumption 1 ensures that entry (in the form of higher n) will restore zero pro ts in this situation. Speci cally, an increase in n has two opposite e ects on pro ts per variety. On one hand, it leads to higher prices and revenues per variety, given that the marginal product of each existing variety is an increasing function of n. 5 On the other hand, it also raises costs per variety: the expansion of the capitalintensive 5 From the production function of good 2, the marginal product of variety i is is increasing in n t. 9 nt R x it 0 1= 1 x 1, which it
10 sector (corresponding to the increase in n) is associated with an increase in k and, as a result, with higher wages. Assumption 1 guarantees that the demand for each variety is su ciently elastic, such that costs increase faster than revenues as entry takes place. Consequently, an increase in the number of varieties will eventually drive pro ts back to zero. 6 This result is summarized by the following proposition. Appendix 3 contains proofs for all analytical results of the paper. Proposition 1 Given Assumption 1, steadystate per capita output, capital and consumption are increasing functions of N in a closed economy. In other words, the presence of scale economies enables larger internal markets to support a higher number of varieties in steady state. As a result, they will display higher per capita income, capital and consumption when closed. All remaining variables can also be expressed in terms of N. For the remainder of the paper, z(n) will denote the steadystate value of a variable z in a closed economy. 3 Openeconomy Equilibrium Trade is introduced in the model through a simple extension of the framework in section 2. In particular, there are now two countries, home and foreign, with sizes N and N respectively, where N + N = 1. These economies share all remaining parameters. Variables with an asterisk refer to the foreign country. Economies are allowed to trade good 1 and varieties costlessly. Good 2 and the nal good are then assembled internally by each country. The world market clearing condition for good 1 is therefore Y 1t + Y 1t = K 1 1t L 1 1 1t + K 1 1t L 1 1 1t, where Y 1 and Y 1 now stand for 6 Section 5 shows that Assumption 1 is necessary to guarantee the existence of a balanced growth path when country size grows at a constant rate. 10
11 the amounts of good 1 used by the home and the foreign country respectively, while their total production is denoted by their respective production functions. A measure of n (n ) varieties is produced by the home (foreign) country, such that there are now n + n varieties available to generate good 2 in each economy. Quantities of good 2 are then Y 2t = (n t + n t ) 1= x d t and Y2t = (n t + n t ) 1= x d t. 7 The home (foreign) country utilizes x d (x d ) units of each of the n + n varieties. Market clearing implies that x = x d t + x d t. The description of the open economy equilibrium is completed by the optimality conditions for each of the agents, along with market clearing conditions for factors and goods that are not traded internationally. Such equations are analogous to those of the closedeconomy case, except that there are now two of each (one for each country). Nevertheless, optimality conditions for sector 1 rms and variety producers may not hold as equalities. The presence of international trade allows for the possibility of complete specialization of these economies either in the production of good 1 or in the production of varieties. Since sector 1 is competitive, it follows that: p 1t r 1 t w 1 1 t ; with equality if K 1 1t ; L 1t > 0 (3) 1 (1 1 ) 1 1 where the righthand side is the marginal cost of a rm in sector 1. Similarly for a variety producer: p t 1 r 2 t w 1 2 t ; with equality if n 2 t > 0 (4) 2 (1 2 ) 1 2 Analogous conditions hold for the foreign country. For countries with su ciently low capital per capita, condition (4) does not bind and the economy fully specializes in the production of good 1. Likewise, condition (3) does not bind when capital per capita is su ciently high, so that the country only produces varieties. For intermediate values of 7 These equations were derived using the fact that production x i is constant across time and varieties. 11
12 capital per capita, the economy will produce some of good 1 and some varieties. This set of intermediate values is often referred as the cone of diversi cation by the international trade literature. If both home and foreign country capital stocks lie within the cone of diversi cation, conditions (3) and (4) bind for the two economies. Consequently, they will face the same factor prices r and w. 8 This result is commonly known as the Factor Price Equalization theorem. 3.1 Openeconomy steady state In steady state, the rental rate of capital is determined uniquely by the discount factor and the depreciation rate. Since the countries share these parameters, they will display the same rental rate r = r = 1= (1 ). This implies that sectoral capitallabor ratios, k 1 and k 2, and therefore the wage rate are also equalized across countries. In other words, Factor Price Equalization holds in steady state. Proposition 2 establishes this result. Proposition 2 In an openeconomy steady state, r, w, p 2, k 1, k 2, K 2 and L 2 are equalized across countries. Proposition 2 also implies that conditions (3) and (4) hold as equalities in steady state for both countries. In other words, their steady state capital stocks lie within the cone of diversi cation. Proposition 3 states that openeconomy prices and factor intensities are the same as in a closed economy of size N + N = 1. Proposition 3 Openeconomy steady state values for r, w, p, p 1, p 2, k 1, k 2, K 2 and L 2 coincide with their respective steady state values in a closed economy of size 1. 8 If equations (3) and (4) bind for both countries, then p 1t = r 1 rt wt =[ 1 1 (1 1) 1 1 ] and p t = (1=)rt 2 wt 1 2 These two expressions imply that r t = rt and w t = wt. =[ 2 2 (1 2) 1 2 ] = (1=)r 2 t wt t wt =[ 1 1 (1 1) 1 1 ] = =[ 2 2 (1 2) 1 2 ]. 12
13 The last proposition also establishes that the openeconomy steady state satis es the equations that characterize the closedeconomy steady state for N = 1. This result allows us to pin down world quantities in steady state. For instance, the world capital stock is equivalent to the capital stock of a closed economy of size 1. For this reason, z(1) denotes the world value of a given variable z in steady state. Nonetheless, countrylevel quantities cannot be determined by such a strategy, since it does not guarantee that domestic markets clear. In particular, although the world capital stock is uniquely determined, there are several ways to allocate this capital across countries. To see this, let k and k be respectively the home and foreign capital per capita, such that Nk + N k = k(1). Moreover, assume that these capital stocks lie within the cone of diversi cation, i.e. k; k 2 [k 1 (1); k 2 (1)]. 9 Then market clearing in home capital and labor markets implies that the number of varieties produced by the home country is: 10 n = N k k 1 (1) L 2 (1) k 2 (1) k 1 (1) The equation above shows how the patterns of production and trade are a ected by changes in the distribution of capital across countries. If k = k 1 (1) the lower limit of the cone of diversi cation then n = 0, so that the home country specializes in the production of good 1 and all varieties are generated by the foreign country. Since varieties are subject to a capitalintensive production process, higher values of k are then associated with a larger share of varieties being produced in the home country. When k reaches the upper limit of the cone of diversi cation k 2 (1), it follows that nl 2 (1) = N, i.e. all factors are allocated to the production of varieties. 9 In the lower limit of the cone of diversi cation, all factors are allocated to the production of good 1, i.e., K 1 = Nk and L 1 = N, so that k = K 1 =L 1 = k 1 (1). In the upper limit of the cone of diversi cation, all factors are allocated to the production of varieties, i.e., nk 2 = Nk and nl 2 = N, so that k = K 2 =L 2 = k 2 (1). Values in between these limits correspond to production structures that mix good 1 and varieties. 10 This equation can be obtained from the market clearing conditions in home capital and labor markets, that is, k 1 (1)L 1 + nk 2 (1) = Nk and L 1 + nl 2 (1) = N. 13
14 Furthermore, the distribution of capital across countries also determines the distribution of income and consumption in steady state. Countries with higher capital per capita will display higher consumption and income per capita. This follows from the fact that per capita income and consumption are linear functions of k in steady state, i.e. y = w(1) + rk and c = w(1) + (r )k. 4 Import Substitution This section uses the framework developed previously to analyze the impact of trade restrictions. Analytical results emphasize steadystate comparisons between the closed and the openeconomy equilibrium, especially regarding capital, income and consumption per capita. More precisely, we assume that the home country is initially open and fully specialized in the production of the laborintensive good. In other words, initial capital per capita is given by k open = k 1 (1) the lower limit of the cone of diversi cation and initial income and consumption per capita are respectively y open = w(1)+rk 1 (1) and c open = w(1)+(r )k 1 (1). Import substitution is modeled as an unanticipated move to a closedeconomy situation. The economy remains closed for a su ciently long period of time, so that it can reach its closedeconomy steady state. In the new steady state, capital, income and consumption per capita are given respectively by k closed = k(n), y closed = y(n) and c closed = c(n). It is important to note that, in an openeconomy situation, per capita income, consumption and capital depend on the size of the world economy (N + N = 1), but not on the size of the home market N. This stands in contrast with the closedeconomy steady state, in which those objects are increasing functions of N. Proposition 4 analyzes the relationship between country size and the impact of import substitution on capital, income and consumption per capita. 14
15 Proposition 4 1. There exists a unique N k 2 (0; 1) such that k closed k open if N N k and k closed < k open if N < N k 2. There exists a unique N y 2 (0; 1) such that y closed y open if N N y and y closed < y open if N < N y 3. There exists a unique N c 2 (0; 1) such that c closed c open if N N c and c closed < c open if N < N c 4. N k < N y < N c There are two e ects of IS on capital per capita. On one hand, since the country now needs to produce varieties (which are capital intensive), capital has a tendency to increase in a closed economy. On the other hand, the smaller scale (relative to the open economy) forces capital to shrink. If N is su ciently low, the latter e ect dominates so that k falls. Similar e ects apply to income per capita. However, the reduction on scale implied by the trade restriction also produces a fall in the wage rate. 11 This brings an extra e ect into play, which contributes to decrease y. For this reason, when N is such that k open = k closed, closing the economy leads to a fall in longrun income per capita (part 4 of Proposition 4). Put di erently, if N = N y, the economy experiences capital deepening, but output per capita does not show any longrun growth. These results show how the model can qualitatively account for key features of the Latin American experience during the IS period. In particular, su ciently small countries (with size around N y ) display low growth in output per capita, but high growth in capital per 11 Appendix 2 demonstrates that the steadystate wage is an increasing function of N. In an open economy, the wage rate is that of a closed economy of size 1. In a closed economy, the relevant scale is the size of the home market. Therefore, the imposition of trade restrictions produces a fall in the wage. 15
16 capita. As a result, measured TFP falls. 12 Furthermore, larger countries can be more successful in reducing their gap relative to industrial leaders, which is consistent with the cases of Brazil and Mexico. Proposition 4 also allows us to analyze the e ects of IS on consumption per capita and therefore the longrun welfare implications of the model. Speci cally, N c > N y means that the size requirement to generate longrun growth in consumption is even more strict. This follows because at N = N y the economy reaches the same per capita income as initially, but needs a higher level of investment in steady state. In other words, growth in income per capita is not necessarily associated with longrun welfare gains. Corollary 1 analyzes the impact of the policy change on capitaloutput ratios: Corollary 1 For any N 2 (0; 1), k closed =y closed = k closed =y closed and k open=y open < k closed =y closed. According to Proposition 1, two closed economies will not display convergence in capital and output per capita, unless they are of equal size. Nonetheless, Corollary 1 establishes that convergence will happen in terms of capitaloutput ratios. More importantly, the result also implies that the home country will experience an increase in its capitaloutput ratio independently of its size. This means that the policy change will induce capital deepening, whether or not there are gains in terms of output per capita. 4.1 Implications for TFP Assume that TFP (denoted by A) is measured using a CobbDouglas production function for the aggregate economy, with the nal output Y as a function of aggregate stocks of capital and labor, K and N. More precisely, Y t = A t K t N 1 t, with 2 ( 1 ; 2 ). Measured TFP 12 Although Table 1 reports some TFP growth, the fall in TFP produced by the model is consistent with the data. The reason is that the model has no intrinsic source of longrun growth. In a growing economy, this corresponds to an increase in TFP at a rate lower than trend. Section 5 shows that the model can be easily extended to allow for longrun growth. 16
17 growth is then A b = by b k, where by = (1=T ) ln(y closed =y open ) and b k = (1=T ) ln(k closed =k open ) are respectively the annual growth rates of capital and output per capita over a time interval T. Clearly, TFP falls for countries with size around N y in Proposition 4, since they display increase in k, but relatively no change in y. One can show that the negative e ect on measured productivity occurs even in relatively large economies. Furthermore, the TFP loss is inversely related to country size (see Appendix 2 for derivation). The decrease in TFP is associated with the reduction of the set of varieties available to the country. Speci cally, the number of varieties is an increasing function of market size. Closing the economy diminishes the size of the market from 1 (size of the world economy) to N (size of the internal market). Since this e ect is stronger for smaller economies, they tend to experience sharper drops in TFP. This implication is related to Proposition 4, especially regarding the e ect on output per capita. More precisely, the trade restriction a ects output per capita in two opposite ways: it leads to an increase in the capitaloutput ratio (which contributes to raise y), but to a decrease in TFP (which contributes to lower y). The impact on y will therefore depend on country size. In particular, smaller countries are more likely to experience reductions in longrun output per capita, given that the TFP e ect tends to more than compensate the capital deepening e ect for these economies. 5 Balanced Growth Path This section extends the model to allow for longrun growth. Speci cally, country sizes now increase at the constant rate g(n) which is common to both economies, i.e., N t = N 0 [1+g(N)] t and N t = N 0 [1+g(N)] t. Initial sizes are normalized as N 0 +N 0 = 1. Assuming CRRA preferences, Proposition 5 shows that per capita output, capital and consumption 17
18 exhibit the same growth rate on a balanced growth path. Proposition 5 On a balanced growth path, per capita output, capital and consumption grow at the same rate, which is given by: g(y) = g(k) = g(c) = (1 )(1 $) (1 $ 1 ) (1 $) 2 g(n) (5) Notice that the number of varieties can continuously expand as a result of size growth, allowing per capita quantities to display a longrun trend. In the aggregate, this trend appears as TFP growth: ba = g(y) g(k) = (1 )(1 )(1 $) (1 $ 1 ) (1 $) 2 g(n) (6) Proposition 5 also shows that Assumption 1 is necessary for the existence of a balanced growth path. This assumption constrains the parameters of the model so that k, y and c display positive longrun growth rates. The balanced growth path can be solved as usual. First, detrend all variables by their respective longrun growth rates. Then recast the model in terms of detrended variables and solve for the steady state. This procedure yields a system of equations analog to that of previous case, in which there was no longrun growth. Consequently, Propositions 1 through 4 hold for the balanced growth path as well. However, these results now refer to the relationship between detrended variables and initial country sizes N 0 and N 0. 6 Quantitative Application So far we have analyzed mainly the model s long run implications, emphasizing comparisons of steady states and balanced growth paths. This section addresses the dynamic impact 18
19 of IS policies, from a quantitative standpoint. In particular, transition paths are computed, following the introduction of trade restrictions in the model. Additionally, the model s quantitative implications are evaluated, focusing mainly on the e ects on income per capita, capitaloutput ratio and TFP. Outcomes are compared with actual growth rates for Latin America during the period , as displayed in Table 1. The remainder of this section describes the choice of parameter values, then presents transition paths, and nally discusses numerical results from the quantitative exercise. 6.1 Parameter Values Capital shares ( 1 and 2 ) and the share of the laborintensive good ($) are taken from Cunat and Ma ezolli s (2004) work on the dynamic HeckscherOhlin model, i.e., 1 = :17, 2 = :49 and $ = :61. Following Gollin (2002), = :30. The size of a country is measured by its stock of e ciency units of labor N = EL, where L is population and E is an index of e ciency. 13 Let g(e) be the growth rate of e ciency units and assume no population growth. 14 The aggregate production function can be then written as Y t = A t K t (E t L t ) 1. Although A and E play similar roles in this equation, they are fundamentally distinct in the model: while E follows an exogenous process, A is an outcome of the model. This distinction is explored here to calibrate the parameters g(e) and. More precisely, equations (5) and (6) imply that the longrun growth rates of output per capita (Y=L) and A are given respectively by: 13 Tre er (1993) has shown that, when the labor input is measured in this fashion, Factor Price Equalization is consistent with observed crosscountry wage di erences. 14 Increasing the population growth rate from zero has no signi cant impact on our main quantitative results. 19
20 g(y =L) = g(a) = 1 + (1 )(1 $) (1 $ 1 ) (1 $) 2 (1 )(1 )(1 $) g(e) (1 $ 1 ) (1 $) 2 g(e) (7) Parameters g(e) and are calibrated such that their values replicate growth rates of Y=L and A for the U.S. economy between 1960 and In particular, the growth rate of productivity net of physical and human capital is used to measure g(a). The values g(e) = 1:27% and = :96 yield g(y=l) = 1:30% and g(a) = 0:02%, which are consistent with actual growth rates reported by Klenow and RodriguezClare (1997). 15 Values for the discount factor and the depreciation rate are set respectively at = :96 and = :1. Moreover, u(c) = ln c. 6.2 The impact of IS policies We now consider the impact of IS policies on an average Latin American country. As in previous sections, the initial distribution of capital is set such that the home country is fully specialized in the production of the laborintensive good. At time zero, barriers to international trade are erected. In 1948, the U.S. was responsible for 38.2 percent of Latin America s imports and 52 percent of the region s exports. 16 For this reason, the U.S. is chosen to represent the rest of the world. The size of an average Latin American country is estimated as follows. The e ciency gap E=E is calibrated such that the initial steady state matches Latin America s GDP per capita 15 These values are consistent with those shown in Table 1. Klenow and RodriguezClare s (1997) paper is also the data source used by Hopenhayn and Neumeyer (2004), work in which Table 1 is based. 16 BulmerThomas (2003). 20
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