Trade, Product Cycles and Inequality Within and Between Countries

Transcription

1 Trade, Product Cycles and Inequality Within and Between Countries Susan Chun Zhu October 12, 2003 Abstract This paper incorporates Northern product innovation and product-cycle-driven technology transfer into the continuum-of-goods Heckscher-Ohlin model. The creation of very skill-intensive goods induces the North to transfer production of older, less skill-intensive goods to the South. These relocated goods must be the most skill intensive by Southern standards. Thus, product cycles raise the relative demand for skilled workers and thus wage inequality within both regions. This runs contrary to the Stolper-Samuelson theorem, but accords well with the fact that wage inequality has risen in both Northern and Southern countries. Moreover, product cycles increase income inequality between countries. Although technology transfer narrows the North- South income gap, this effect is more than offset by the effect of product innovation. This paper also examines welfare implications of product cycles. Product cycles benefit both the North and the South and make skilled workers in both regions better off. Further, an increase in the supply of Southern skilled labor can raise the rate of technology transfer and narrow the North-South income gap. (JEL classification: F1, Keywords: international trade, product cycles, inequality) Department of Economics, Michigan State University, Marshall Hall, East Lansing, MI, 48824, USA. I am indebted to Dan Trefler for his encouragement and many helpful comments. I also thank Nancy Gallini, Wolfgang Keller, Angelo Melino, Diego Puga, Martin Richardson, Aloysius Siow, and Nadia Soboleva. Financial support from the Social Sciences and Humanities Research Council of Canada is gratefully acknowledged.

2 1. Introduction The product cycle is not a new concept. It was minted by Vernon (1966) nearly forty years ago. Since Krugman (1979) first formalized it by using a one-factor model featuring exogenous technical change, many other authors have extended various aspects of his model. Jensen and Thursby (1987) endogenized the innovation process. Dollar (1986) incorporated capital movement in a three-factor model. Flam and Helpman (1987) focused on quality upgrading rather than expansion of goods varieties. Grossman and Helpman (1991) endogenized both innovation and technology transfer. Although these authors examined many implications of the product cycle, they neglected its impacts on the domestic distribution of income. 1 There is increasing evidence that in recent decades, inequality has grown not only in many Northern countries, but also in some Southern countries ( e.g., Feenstra and Hanson 1996, 1997, Robbins 1995, Cragg and Epelbaum 1996, Hanson and Harrison 1999, Berman et al. 1998). The pervasiveness of rising inequality leads people to think international trade might be an important factor (e.g., Wood 1994, Leamer 1996). However, the traditional Stolper-Samuelson theorem predicts that when inequality increases in the North, it should decline in the South. Thus, some authors claim that the traditional Heckscher-Ohlin model, the backbone of the Stolper-Samuelson theorem, fails (e.g., Robbins 1995). One purpose of this paper is to show that widening inequality in both regions can be explained within a Heckscher-Ohlin framework. To this end, I incorporate technical change 1 Dinopoulos and Segerstrom (1999) present a dynamic model of North-North trade that has implications for wage inequality in Northern countries. However, it does not deal with Southern countries. 1

3 into the continuum-of-goods Heckscher-Ohlin model (Dornbusch et al. 1980). There are two countries (the North and the South), two factors (skilled and unskilled labor), and a continuum of goods which can be uniquely ranked in order of increasing skill intensity. I focus on the complete specialization equilibrium in which the South specializes in less skillintensive goods and the North specializes in more skill-intensive goods. In contrast to the main concern of Dornbusch et al. about endowment changes, I consider a world economy driven by Northern product innovation. Since my goal is to examine the impact of technical change rather than its determinants, I assume that product innovation is exogenous. In light of recent work on technology-skill complementarities (e.g., Goldin and Katz 1998, Autor et al. 1998), I further assume that new goods use relatively more skilled labor than old goods. However, technology transfer is endogenized and driven by product innovation. The core result is that product innovation and technology transfer increase inequality within both regions. When new goods are introduced, the relative demand for Northern skilled labor increases, thus raising Northern inequality. If the aggregate elasticity of substitution between Northern skilled labor and unskilled labor is sufficiently large, the introduction of new goods makes the North less competitive in low-end goods. The result is technology transfer the North moves production of its older, less skill-intensive goods to the South. Such technology transfer reduces the relative demand for Northern unskilled labor and aggravates the wage gap in the North. At the same time, since the transferred Northern goods are more skill intensive than the previously produced Southern goods, the relative demand for Southern skilled labor increases. Thus inequality also rises in the South. The basic insight of this core result was initially suggested by Feenstra and Hanson s 2

4 (1996) observations on outsourcing and inequality in the United States and Mexico. However, there are several major differences between my work and theirs. First, the driving force is different. In Feenstra and Hanson s three-factor model (capital, skilled labor and unskilled labor), a higher rate of return on capital investment in the South causes production relocation. In my two-factor model, Northern product innovation drives all the changes in labor markets and trade patterns. I am describing product cycles. Second, Feenstra and Hanson close their model with an exogenous, upward sloping supply of labor to their single industry. I close my model with a general equilibrium trade balance equation. Third, in Feenstra and Hanson there is no substitutability between skilled and unskilled labor. This is incompatible with the focus on such elasticities that dominates the literature on wage inequality (e.g., Katz and Murphy 1992). In my model, the substitutability between skilled and unskilled workers plays a central role in generating product cycles. Product cycles increase inequality not only within countries, but also between countries. Product innovation and endogenous technology transfer have opposing effects on the North-South income gap. Unlike product innovation, technology transfer narrows the gap. However, the product innovation effect, being more direct, must dominate. This result differs sharply from Krugman (1979). The difference arises from the way technology transfer is handled: in Krugman, technology transfer is exogenous. Krugman considers the case where there is an increase in the rate of technology transfer while keeping the rate of product innovation constant, and concludes that the income gap can be narrowed. In my model, however, technology transfer is induced by product innovation and, in equilibrium, may not catch up with it. 3

5 The simplicity of the model allows me to derive a rich set of welfare implications of product cycles. The terms of trade move in favor of the North and against the South. The North further benefits from a wider range of new products. Strikingly, the South also benefits from product cycles. This is because the loss to the South from worsened terms of trade is entirely offset by the gain from new goods. At the same time, since income is redistributed from unskilled to skilled workers, skilled workers in both regions are better off. The above model can be extended by including an increase in the supply of Southern skilled labor. This extension helps to explain the income catch-up by some newly industrialized countries. An increase in the supply of Southern skilled labor raises the rate of technology transfer and narrows the North-South income gap. The paper is organized as follows. Section 2 describes the basic model. Section 3 illustrates the effects of product innovation and technology transfer on labor markets and concludes that inequality can rise within and between countries. Section 4 examines the welfare implications of product cycles. Section 5 extends the model by allowing for an increase in the supply of Southern labor. Section 6 draws conclusions. 2. The Basic Model The set-up is based on Dornbusch et al. (1980). There are two regions (the North and the South), two factors (skilled and unskilled labor), and a continuum of goods indexed by z in the interval 0, n]. I make the standard Heckscher-Ohlin assumptions. Production functions are quasi-concave and exhibit constant return to scale. Goods markets and labor markets are perfectly competitive. Furthermore, there are no trade barriers in the model. Trade is 4

6 always balanced. I focus on the complete specialization equilibrium where the North produces more skillintensive goods and the South produces less skill-intensive goods. To this end, I make two additional assumptions. First, the North is relatively abundant in skilled labor and the South is relatively abundant in unskilled labor. Further, the difference in labor endowment is so large that the relative wage for skilled labor is lower in the North than in the South. Second, there are no factor intensity reversals. This implies that goods can be ranked uniquely by skill intensity independently of factor prices. I use a higher z to index a more skill-intensive good. Then, as shown in lemma 1 in appendix A.1, the North has a comparative advantage in skill-intensive goods (z, n] while the South has a comparative advantage in unskilled-intensive goods 0, z). Good z is the competitive margin. It is the only good that is produced in both regions. Under the assumption that there are no trade barriers, the value of z is determined by p N (z) = p S (z) (1) where p i (z) is the price of good in region i (= N, S). On the demand side, I assume that all individuals have identical preferences which are represented by the CES utility function U = 0 ] σ x(z) σ 1 σ 1 σ dz (σ > 1) (2) where x(z) is the consumption of good z and σ is the elasticity of substitution between goods. 5

7 Equilibrium is characterized by conditions of balanced trade and labor market clearing. Let Y i be national income in region i. Let p i (z) be the price of good z. Let P p 0 S(z) 1 σ dz + ] 1 n p N(z) 1 σ 1 σ dz be the aggregate price index. With identical CES preferences, the balance-of-trade condition is ] 1 σ ps (z) n ] 1 σ pn (z) Y N dz = Y S dz. (3) P P 0 The left-hand side is the value of Northern imports and the right-hand side is the value of Northern exports. Combining the balance-of-trade condition with equation (1) yields { Y N B(z) ln p N () 0 ] { 1 σ ps (z) Y S dz} ln p S () p S () ] 1 σ pn (z) dz} = 0. (4) p N () Using good as numeraire simplifies the following analysis. Let H i and L i be the supply of skilled and unskilled labor, respectively. Let w Hi and w Li be the wages of skilled and unskilled workers, respectively. Define w i w Hi /w Li. Let H i (w i, z) and L i (w i, z) be the amount of skilled and unskilled labor, respectively, required to produce one unit of good z. Finally, define h i H i /L i and h i (w i, z) H i (w i, z)/l i (w i, z). To simplify notation, in the following I will drop w N and w S as arguments. However, I am not assuming that substitution between the two types of labor is restricted. The aggregate demand for Northern skilled labor is HN d = x(z)h N(z)dz. With CES preferences, world demand for Northern good z is x(z) = p N (z)/p ] 1 σ (Y N + Y S )/p N (z). With zero profits, p N (z) = w HN H N (z) + w LN L N (z). Plugging x(z) into HN d, the condition of Northern skilled 6

8 labor market clearing can be expressed as H N = H d N = pn (z) P ] 1 σ (Y N + Y S )H N (z) dz. (5) w HN H N (z) + w LN L N (z) Similarly, the condition of Northern unskilled labor market clearing is L N = L d N = pn (z) P ] 1 σ (Y N + Y S )L N (z) dz. (6) w HN H N (z) + w LN L N (z) Since I am interested in the wage gap between skilled and unskilled labor, I combine equations (5) and (6) and express the labor market clearing conditions in terms of w N. To this end, define N () HN d /H N L d N /L N. N () is the excess demand for skilled labor relative to unskilled labor in the North. With some manipulation, N () = 0 can be written as 2 N(z) z ] 1 σ pn (z) h N (z) h N ] dz = 0. (9) p N () 1 + w N h N (z) Similarly, the corresponding Southern labor market clearing condition S () = H d S /H S 2 The skilled labor market equilibrium condition (5) can be rewritten as HN d = Y N + Y S H N w LN H N P 1 σ Similarly, the unskilled labor market equilibrium condition (6) yields L d N = Y N + Y S L N w LN H N P 1 σ p N (z) 1 σ h N (z) dz = 1. (7) 1 + w N h N (z) h N p N (z) 1 σ dz = 1. (8) 1 + w N h N (z) Equation (7) minus equation (8) results in the labor market equilibrium condition (9). 7

9 L d S /L S can be written as S(z) z 0 ] 1 σ ps (z) h S (z) h S ] dz = 0. (10) p S () 1 + w S h S (z) The competitive margin z and relative wages (w N, w S ) are determined simultaneously by equations (4), (9) and (10). 3 serves as a link between the two labor markets. In this model prices of goods and national income are also endogenized. The proof of existence and uniqueness of the equilibrium in Dornbusch et al. (1980) can be applied with only minor modifications. 3. Product Cycles and Inequality In contrast to the concern of Dornbusch et al. with endowment changes, I focus on the impact of technical change on labor markets and trade patterns. In this paper technical change takes the form of product innovation in the North. This is consistent with the fact that new goods are mainly invented and first produced in a few industrial countries. In the 1980s the United States, Japan, Germany, Great Britain and France accounted for 91% of total R&D expenditures in the OECD area, and the United States alone accounted for more than half of total R&D expenditures (calculated using the OECD ANBERD Database 2000). Krugman (1979) and Grossman and Helpman (1991) also make a similar assumption. I make two additional assumptions about Northern product innovation. First, since 3 Both Y i /p i () and p i (z)/p i () (i = S, N) can be expressed in terms of w i : Y i /p i () = (w i h i + 1) L i ] / (w i h i () + 1) L i ()], and p i (z)/p i () = (w i h i (z) + 1) L i (z)] / (w i h i () + 1) L i ()]. 8

10 my goal is to examine the impacts of innovation rather than its determinants, I assume that product innovation is exogenous. Second, in light of recent work on technology-skill complementarities, 4 I assume that new goods use relatively more skilled labor than old goods. Note that this assumption is made for analytical convenience. It is shown in appendix A.3 that all results hold under a weaker assumption that on average new goods are more skill intensive than existing Northern goods. In this section I will provide a weak condition guaranteeing that as the North produces more new goods, it loses competitiveness in less skill-intensive goods. As a result, older less skill-intensive Northern goods migrate South. Following Krugman (1979) I will use the term technology transfer to refer to this process of production relocation. I will also examine the implication of product cycles for inequality within and between countries Outline The creation of new goods has a direct impact on the trade balance. The utility function in equation (2) implies that for given income and prices, consumers would be better off if they have a wider range of goods. Thus, as new goods become available, consumers allocate some of their budget to new goods and spend less on all old goods. This leads to a shift in demand from Southern goods to Northern goods. Ceteris paribus, the North develops a trade surplus. To restore the trade balance, Northern national income must rise (see equation 3). 4 Goldin and Katz (1998) document that technology-skill complementarities existed in manufacturing early in this century. Krueger (1993) and Berman et al. (1994) report that use of computers raises the demand for skills. Bresnahan, Brynjolfsson and Hitt (2002) find that information technology and the corresponding change in firm organization also increase the demand for skilled labor. The theoretical work on technologyskill complementarities includes Galor and Tsiddon (1997). 9

11 The creation of new goods also directly affects the Northern labor market. Since new goods are more skill intensive than all existing Northern goods, the creation of new goods raises the relative demand for skilled labor. Thus, the relative wage of skilled labor rises. This, together with the increase in national income just discussed, implies that the wage of Northern skilled labor must rise. At the same time, the creation of new goods leads to an excess supply of Northern unskilled workers. Whether the wage of unskilled labor rises or falls in equilibrium hinges on the degree of substitutability between Northern skilled and unskilled labor. Unskilled labor can be substituted for skilled labor in two ways. First, cheaper unskilled labor replaces skilled labor within production of each good, i.e., withingood substitution. Second, by the Rybczynski effect, production of less skill-intensive goods expands, i.e., between-good reallocation. When Northern skilled and unskilled workers are sufficiently substitutable, the oversupplied unskilled labor can be absorbed without lowering their wage. In this case, the North loses its competitiveness in less skill-intensive Northern goods so that these goods move South. In the above I have sketched out a simple story about product cycles. In the following section I will formalize this idea Product Cycles I introduce new goods as follows. Let t index the state of technology and let n be the highest goods index given t. As technology evolves from t to t +, new goods are introduced over the range (n, n + dn). I consider the impact of changes in t and hence n on w S, w N, and z. As discussed above, the conclusion that Northern innovation leads to product cycles (i.e., raises z) hinges on the degree of substitutability between skilled and unskilled labor 10

12 in the Northern production. Let ε a N d ln(hd N /Ld N )/d ln w N be the aggregate elasticity of substitution between Northern skilled and unskilled labor. Theorem 1 formalizes this observation. Theorem 1. There exists a constant ε (0, σ) such that ε a N > ε dz/ > 0. That is, if and only if skilled and unskilled labor are sufficiently substitutable in the production of Northern goods, Northern innovation sets up product cycles in which new goods are initially produced in the North and then relocated to the South. Proof. See appendix A.4. The critical degree of substitutability between Northern skilled and unskilled labor (ε) depends on factor intensity differences across goods. If the differences are large, the creation of very skill-intensive goods imposes more pressure on the unskilled labor market. In order to absorb the oversupplied unskilled labor, a larger value of ε is required. Theorem 1 also implies that ε a N > σ is a sufficient condition for product cycles to occur. In particular, when σ approaches 1 (i.e., preferences are represented by the Cobb-Douglas utility function), the sufficient condition becomes ε a N > 1. Empirically, this sufficient condition is likely to be satisfied. Most estimates of the aggregate elasticity of substitution are between 1 and 2 (Johnson 1970, Freeman 1986, Katz and Murphy 1992, Heckman et al. 1998, and Krusell et al. 2000) The Role of the Elasticity of Substitution I have discussed how product cycles rest on the substitutability between skilled and unskilled workers. This section further develops this point and shows that care is needed in 11

13 thinking about the aggregate elasticity of substitution. The aggregate elasticity of substitution incorporates direct factor substitution within goods as well as indirect factor substitution via changes of output mix (i.e., the Rybczynski effect). The elasticity of substitution between skilled and unskilled labor in the production of good z is defined as ε N (z) d ln h N (z)/d ln w N. (Recall that w N w HN /w LN is the relative wage of Northern skilled labor and h N (z) h HN (z)/h LN (z) is the relative employment of skilled labor in good z.) Using the labor demand equations in (5) and (6), ε a N can be expressed as a weighted average of within-good elasticities of substitution between factors (ε N ( )) and the elasticity of substitution between goods (σ): ε a N = p z N(z)] 1 σ θ LN (z)θ HN (z)ε N (z)dz Y LN Y HN p z N(z)] 1 σ dz + σ 1 z p ] N(z)] 1 σ θ LN (z)θ HN (z)dz Y LN Y HN p z N(z)] 1 σ dz (11) where θ LN (z) w LN L N (z)/p N (z) is the cost share of Northern unskilled labor in good z, θ HN (z) w HN H N (z)/p N (z) is the cost share of Northern skilled labor, Y LN w LN L N /Y N is the national income share of unskilled labor, and Y HN w HN H N /Y N is the national income share of skilled labor. Note that the second term in equation (11) is always positive. 5 Equation (11) is a continuum-of-goods version of the aggregate elasticity of substitution discussed in Jones (1965). As ε N ( ) increase, ε a N becomes larger. When ε N( ) = 0 (i.e., no within-good substitution), labor market adjustment depends on a Rybczynski-style realloca- 5 h Using N (z) h N θ w N h N (z)+1 = HN (z) Y HN Y w N Y LN = LN θ LN (z) w N Y LN, equation (9) can be rewritten as p N(z)] 1 σ θ LN (z) Y LN ] dz = 0. Combining this with θ LN (z) 2 = θ LN (z) Y LN ] θ LN (z) Y LN ] Y LN + YLN 2 yields z p N(z)] 1 σ θ LN (z) 2 dz > YLN 2 n z p N(z)] 1 σ dz. It follows that z p N(z)] 1 σ θ LN (z)θ HN (z)dz = z p N (z)] 1 σ θ LN (z)dz z p N (z)] 1 σ θ LN (z) 2 dz < Y HN Y LN z p N (z)] 1 σ dz. 12

14 tion of output between skill-intensive and unskilled-intensive goods. This is captured by the second term in equation (11). A bigger value of σ implies a stronger substitution effect via output reallocation. This is because with a bigger σ, consumers are more willing to substitute cheaper goods for more expensive ones. Therefore, as the creation of new goods raises the relative wage of Northern skilled workers and with it the relative prices of skill-intensive goods, 6 a larger value of σ facilitates output reallocation from skill-intensive goods to less skill-intensive ones. This increases the capacity to absorb oversupplied unskilled Northern workers. Equation (11) thus helps one to understand what has been estimated by researchers such as Katz and Murphy (1992). It also helps one understand how the Feenstra-Hanson model equilibrates: even though they assume that there is no substitution between skilled and unskilled labor within goods production (ε N ( ) = ε S ( ) = 0), equilibration occurs via a Rybczynski-style reallocation. Both ε N ( ) and σ affect not only the sign of dz/, but also its magnitude. The more substitutable unskilled labor is for skilled labor, the bigger is the rate of technology transfer. With small values of ε N ( ) and σ, oversupplied unskilled Northern labor can only partially be absorbed by factor substitution within goods and output reallocation between existing goods. Most of the absorption must come from expanding the production of the least skillintensive goods, i.e., by reducing z. The higher ε N ( ) and σ are, the weaker the pressure to lower z and, hence, the more effective the product-cycle pressure to raise z. The elasticities of substitution in the South (ε S ( ) d ln h S ( )/d ln w S ) affect dz/ in a similar way. To formalize these observations, write ε i as a function of a shift variable β i (i = S, N). β i shifts 6 Consider two Northern goods z 1 and z 2. The change in the relative good price is d lnp N (z 2 )/p N (z 1 )]/ = θ HN (z 2 ) θ HN (z 1 )]d ln w N /. This is positive when z 2 > z 1, i.e., z 2 is more skill intensive than z 1. 13

15 the entire ε i (, β i ) schedule up. That is, a large β i makes the ε i more elastic. The results are summarized in theorem 2. Theorem 2. dz/ is increasing in β S, β N and σ. That is, an increase in either region s within-good elasticities of substitution between factors or the elasticity of substitution between goods raises the rate of technology transfer. Proof. See appendix A Rising Wage Inequality Within Countries In recent decades many developed countries and some developing countries have experienced rising wage inequality. This poses a challenge to traditional trade theory. The Stolper- Samuelson theorem appeals to shifting terms of trade to predict that rising inequality in developed countries will go hand in hand with falling inequality in developing countries. This contradiction has led some authors to doubt the relevance of the Heckscher-Ohlin framework (e.g., Robbins 1995). Interestingly, the next theorem shows that this puzzle can be resolved by embedding technical change into the continuum-of-goods Heckscher-Ohlin model. Recall that w i = w Hi /w Li (i = N, S) is the wage of skilled relative to unskilled workers. It is the measure of within-country inequality in my model. Theorem 3. (i) dw N / > 0. (ii) Assume ε a N > ε. Then dw S/ > 0. That is, product cycles raise inequality in the North. If Northern skilled and unskilled labor are sufficiently substitutable, then product cycles also raise inequality in the South. Proof. See appendix A.4. 14

16 The creation of new, skill-intensive goods raises the relative demand for Northern skilled labor. Thus, the relative wage in the North rises. It is worth noting that this result holds whether z rises or falls. Even if z falls, thereby increasing the relative demand for Northern unskilled labor, this effect is entirely offset by the effect of newly created goods. This is consistent with the empirical finding that domestic skill-biased technical change is likely the main factor behind rising inequality in developed countries (e.g., Berman et al. 1994, Autor et al. 1998, Berman et al. 1998). In contrast, technology transfer (rising z) is the only factor affecting the relative labor demand in the South. The goods that migrate South may be the least skill intensive from a Northern perspective, but they are the most skill intensive from a Southern perspective. Technology transfer therefore raises the relative demand for skilled labor in the South, leading to wage inequality there. 7 The condition ε a N > ε in theorem 3 ensures z to rise Rising Inequality Between Countries Product cycles increase inequality not only within countries, but also between countries. Northern product innovation and endogenous technology transfer have opposing effects on the North-South income gap. Unlike product innovation, technology transfer narrows the North-South gap. This raises the concern about whether technology transfer will help the South to catch up with the North. The next theorem shows that this concern is unwarranted. Since the effect of product innovation is more direct, it offsets the negative effect of technology 7 Zhu (2003) examines empirically the extent to which increasing demands for skilled workers can be explained by product cycles, i.e., by U.S. innovation and the subsequent relocation of production to U.S. trading partners. She finds strong evidence that product cycles are significantly and positively correlated to rising demand for skilled workers in a large panel of industries and countries. 15

17 transfer on Northern income. Thus, product cycles widen the North-South income gap. 8 Theorem 4. d(y N /Y S )/ > 0. That is, product cycles widen the North-South income gap. Proof. See appendix A.4. Theorem 4 further implies that when the elasticity of substitution between goods (σ) is close to unity, the rate of technology transfer (d ln z/) can never exceed the rate of product innovation (d ln n/). 9 Theorem 4 stands in sharp contrast to Krugman (1979). The difference mainly arises from the way technology transfer is handled. In Krugman, technology transfer is exogenous. Krugman considers the case where there is an increase in the rate of technology transfer while keeping the rate of Northern innovation constant, and concludes that the North-South gap can be narrowed. In my model, however, technology transfer is endogenous. Since the rate of technology transfer lags behind the rate of innovation, the effect of technology transfer on the income gap is of a second order compared to the effect of product innovation. This completes the discussion of the implications of product cycles for inequality within and between countries. I now turn to welfare analysis. 8 An extension of the model by including the increasing supply of Southern skilled labor can help one explain the income catch-up by some newly industrialized countries in recent decades. See section 5 for more detail. 9 When σ approaches 1, the balance-of-trade condition in equation (3) implies d ln(y N /Y S ) = d ln(n z) By theorem 4, d ln(y N /Y S )/ > 0. Thus, d ln n/ > d ln z/. d ln z. 16

18 4. Welfare Analysis The simplicity of this model allows me to derive a rich set of welfare implications of product cycles. In this section I will first examine change in the terms of trade. This is the basis for further analysis of national welfare and labor welfare Terms of Trade In a model with a continuum of goods, it is natural to define terms of trade as a price index using initial net exports as the weights. By this definition, an increase in the terms of trade implies that the initial consumption bundle is cheaper at the new prices than at the old ones. This further implies that improved terms of trade always benefit consumers. (See Dixit and Norman 1980, p.132.) Using the above definition, the change in Northern terms of trade may be written as dp N / = Y S n p N(z)/P ] 1 σ d ln p N (z)/] dz Y N p 0 S(z)/P ] 1 σ d ln p S (z)/] dz. (Recall that P p 0 S(z) 1 σ dz + ] 1 n p N(z) 1 σ 1 σ dz is the aggregate price index.) The change in Southern terms of trade is dp S / = dp N /. Theorem 5 states that product cycles improve the terms of trade in the North while worsening the terms of trade in the South. Theorem 5. Assume ε a N > ε. Then dp N/ > 0 and dp S / < 0. i.e., the terms of trade rise in the North and fall in the South. Proof. See appendix A.4. It is worth noting that product innovation improves the terms of trade in the North. This is in contrast to the conventional result that technical progress in the export sector generally 17

19 worsens the terms of trade. When product cycles raise the relative wages of skilled labor in both regions, the goods that use relatively more skilled labor become more expensive within each region (see footnote 6.) Note that good is the least skill intensive from a Northern perspective while it is the most skill intensive from a Southern perspective. Thus, in terms of good, the relative price of any Northern good increases and the relative price of any Southern good decreases, implying that the terms of trade must rise in the North and fall in the South National Welfare Since each region has two types of labor, care is needed in measuring national welfare. If the government can do a lump-sum transfer within a region, or can redistribute domestic income optimally through a complete set of indirect taxes, then a higher indirect utility, which is derived using national income, will imply that all types of labor in the region can be made better off (see Dixit and Norman 1980, p.20). When all types of labor have the same CES preferences, it is straightforward to derive the Northern indirect utility as U N = Y N /P. Then the change in Northern welfare can be further derived as d ln U N = 1 σ 1 pn (n) P ] 1 σ dn + 1 Y N dp N. (12) The first term reflects the gain from consuming new goods. The second term captures the effect of terms of trade. Since the terms of trade improve in the North (see theorem 5), equation (12) suggests that the North will always benefit from product cycles. This differs markedly from Krugman (1979) who finds that technology transfer must make 18

20 the North worse off. The difference arises from the different impact of technical change on the terms of trade. In Krugman, when the rate of technology transfer catches up with the rate of product innovation, the terms of trade in the North will fall. In contrast, in my model, although technology transfer shifts income from the North to the South, it is a second-order effect compared to the effect of product innovation. As shown in theorem 5, product cycles improve the terms of trade in the North. Thus, even when technology transfer reduces Northern income, the North is still better off. Likewise, the change in Southern welfare (U S ) can be written as d ln U S = 1 σ 1 pn (n) P ] 1 σ dn + 1 Y S dp S. (13) Equation (13) suggests that new goods benefit the South to the same extent as the North. As shown in appendix A.4, the gain from new goods always outweighs the loss to the South from worsened terms of trade. Therefore, the South is also better off from product cycles. Theorem 6 summarizes these results. Theorem 6. Assume ε a N > ε. Then du N/ > 0 and du S / > 0. That is, product cycles improve welfare in both the North and the South. Proof. See appendix A Labor Welfare Labor welfare is measured by the indirect utility of each type of labor. When national welfare improves and wage inequality rises, skilled labor in both the North and the South must be 19

21 better off. 10 For unskilled workers, it is less certain whether they would be better or worse off. The creation of new goods benefits all types of workers. However, technology transfer has very different effects on skilled and unskilled workers. As discussed, technology transfer shifts income from the North to the South and raises wage inequality in both regions. The former effect benefits all types of Southern labor and hurts all types of Northern labor. The latter effect benefits skilled labor in both regions and hurts unskilled labor in both regions. Therefore, technology transfer makes Southern skilled labor better off and makes Northern unskilled labor worse off. 5. Increasing Labor Supply The above model can be extended by including an increase in the supply of Southern skilled labor. This extension helps to explain the income catch-up by some newly industrialized countries in recent decades. This is also similar in spirit to the new growth literature in which human capital accumulation plays a central role in promoting economic growth (e.g., Romer 1990). In the following I assume that the supply of Southern skilled labor is increased exogenously. Specifically, let γ HS d ln H S / be the rate of increase in the supply of Southern skilled labor. I further assume that the increasing supply of Southern skilled workers does not violate the assumption that the relative supply of skilled labor is much 10 Note that du i d(w Hi /P ) d(w Li /P ) du Hi dl i = H i + L i = H i + L i (i = S, N) where U Hi and U Li are the indirect utility of skilled and unskilled labor, respectively. When wage inequality rises, du Hi / must be larger than du Li /. Therefore, if du i / > 0, then du Hi / > 0. 20

22 lower in the South than in the North, so that w S > w N still holds. An increase in the supply of Southern skilled workers raises the rate of technology transfer. The reasons are simple. First, an increasing supply of skills causes the wage of skilled workers to fall, thus making the South more competitive in skill-intensive goods. Second, by the Rybczynski effect, the South expands production of more skill-intensive goods. An increase in the supply of Southern skilled labor further affects wage inequality in both regions. When the rate of technology transfer is larger (due to γ HS ), the demand for Northern unskilled labor is less. Thus, the negative effect of product cycles on Northern inequality is augmented. In the South, however, although the demand for Southern skills increases, its effect on the relative wage is offset by the more direct effect of an increasing supply of skilled labor. Thus, the negative effect of product cycles on Southern inequality is mitigated. Theorem 7. (i) dz/ is increasing in γ HS. (ii) dw N / is increasing in γ HS and dw S / is decreasing in γ HS. That is, an increase in the supply of Southern skilled labor raises the rate of technology transfer. Further, it augments the negative effect of product cycles on Northern inequality and mitigates the negative effect of product cycles on Southern inequality. Proof. See appendix A.4. More importantly, the increased supply of Southern skills enables the South to catch up with the North. The next theorem formalizes this point. Theorem 8. There exists a positive constant γ such that γ HS > γ d(y N /Y S )/ < 0. That is, if the increase in the supply of Southern skilled labor is large enough, the North- South income gap is narrowed. 21

23 Proof. See appendix A.4. Theorem 8 establishes that when the increase in the supply of Southern skilled labor is big enough, the North-South gap can be narrowed. 11 This result follows the observation that an increasing supply of Southern skilled workers can raise the rate of technology transfer. 6. Conclusions Previous work on the product cycle neglects its implications for domestic income distribution. However, in recent decades, inequality has risen in both developed countries and some developing countries. Since this contradicts the Stolper-Samuelson theorem, it poses a challenge to traditional trade theory. This paper incorporates product innovation and technology transfer into the continuumof-goods Heckscher-Ohlin model. It shows that inequality can rise in both regions. The intuition is simple. The creation of new, highly skill-intensive goods in the North raises the relative demand for Northern skilled labor and hence raises inequality. When the aggregate elasticity of substitution between skilled and unskilled labor in the North is sufficiently enough, the creation of new goods causes the North to lose competitiveness in older goods. These older Northern goods thus migrate South. Since these older goods are the least skill intensive of the goods produced in the North and the most skill intensive of the goods produced in the South, technology transfer reduces the relative demand for Northern unskilled labor and increases the relative demand for Southern skilled labor. This aggravates inequality in 11 Note that the effect of increasing labor supply on the North-South gap can arise in the absence of Northern product innovation (i.e., dn/ = 0). In this case, the cutoff γ becomes zero. 22

24 the North and also creates inequality in the South. Product cycles increase inequality not only within countries, but also between countries. Product innovation widens the North-South income gap while technology transfer narrows the gap. Since the effect of technology transfer is entirely offset by the effect of product innovation, product cycles increase the North-South gap. This simple model also has rich welfare implications of product cycles. Product cycles benefit both the North and the South. At the same time, since income is redistributed from unskilled to skilled workers, skilled workers in both regions are better off from product cycles. Finally, an increase in the supply of Southern skilled labor raises the rate of technology transfer. This narrows the North-South income gap and can explain some of the trends in cross-country convergence. 23

25 A. Appendix Let H i and L i be the supply of skilled and unskilled labor, respectively, in region i (= S, N). Let w Hi and w Li be the wages of skilled and unskilled workers, respectively. Define w i w Hi /w Li. Let H i (w i, z) and L i (w i, z) be the amount of skilled and unskilled labor, respectively, required to produce one unit of good z. Define h i H i /L i and h i (w i, z) H i (w i, z)/l i (w i, z). Let p i (z) be the price of good z. Let θ Hi (w i, z) w Hi H i (w i, z)/p i (z) be the cost share of skilled labor. Let θ Li (w i, z) w Li L i (w i, z)/p i (z) be the cost share of unskilled labor. Let Y Hi w Hi H i /Y i be the national income share of skilled labor. Let Y Li w Li L i /Y be the national income share of unskilled labor. Finally, let ε i (z) ln h i (z)/ ln w i be the elasticity of substitution between skilled and unskilled labor in good z. To simplify notation, I drop w N, w S and t as arguments. A.1. Comparative Advantage Lemma 1. Let C(w Hi, w Li, z) be the unit cost of producing good z in region i. Assume that C( ) is twice differentiable. If w S > w N, then C(w HN, w LN, z)/c(w HS, w LS, z)] / z < 0. Proof. Since C(w Hi, w Li, z) is homogenous degree of one in w Hi and w Li, C(w Hi, w Li, z) = w Li C(w i, 1, z). Differentiating this with respect to w Li yields C(w Hi, w Li, z)/ w Li = C(w i, 1, z) w i C(w i, 1, z)/ w i. By Shepard s Lemma, I have L i (z) = C(w Hi, w Li, z)/ w Li. Combining the above two equations yields C(w i, 1, z)/ w i = H i (z). It follows that ] ln C(wHi, w Li, z) = ] lnwli C(w i, 1, z)] = ] ln C(wi, 1, z) w i z w i z w i z = ] ln C(wi, 1, z) = ] H i (z) z w i z L i (z) + w i H i (z) = z h i (z) 1 + w i h i (z) ] = h i(z)/ z 1 + w i h i (z)] 2 > 0. Hence, if w N < w S, then ln C(w HN, w LN, z)/ z < ln C(w HS, w LS, z)/ z, which implies C(w HN, w LN, z)/c(w HS, w LS, z)] / z < 0. Therefore, C(w HN, w LN, z) and C(w HS, w LS, z) will intersect only once. I claim that the intersection z must be in the interval 0, n]. Suppose that z were not in the interval 0, n]. Then schedule C(w HN, w LN, z) would be either below or above C(w HS, w LS, z) in the interval 0, n], which implies that either the North or the South would produce all the goods. This further implies that wages would be zero for the region which did not produce any goods. In this case it would be optimal to allocate some goods production to this region. This contradicts the assumption that z was not in the interval 0, n]. Therefore, there is a unique z 0, n] satisfying C(w HN, w LN, z) = C(w HS, w LS, z). Further, for z < z, C(w HN, w LN, z) > C(w HS, w LS, z); for z > z, C(w HN, w LN, z) < C(w HS, w LS, z). 24

26 A.2. Downward Sloping Aggregate Labor Demand Curve Lemma 2. Given z, N(z)/ w N < 0 and S(z)/ w S < 0. Proof. I only consider the Northern labor market. Let me start with the case where the technology is Leontief, i.e., ε N ( ) = 0. Differentiating N(z) in equation (9) with respect to w N yields dn(z) dw N = σ ] 1 σ pn (z) θ HN(z) Y HN]θ LN(z)dz. (14) p N () wn 2 Y LN z Since 1 σ n pn (z) z p N ()] θhn (z) Y HN ]dz = 0, 12 and θ HN (z) Y HN increases in z, there exists z 0 (z, n) such that (i) when z = z 0, θ HN (z) Y HN = 0;(ii) when z < z 0, θ HN (z) Y HN < 0; and (iii) when z > z 0, θ HN (z) Y HN > 0. Further, since θ LN (z) decreases in z, I have (i) when z z 0, θ LN (z) θ LN (z 0 ); and (ii) when z > z 0, θ LN (z) < θ LN (z 0 ). Therefore, equation (14) implies dn(z) dw N < σ w 2 N Y LN + σ w 2 N Y LN = σθ LN(z 0 ) w 2 N Y LN z 0 z ] 1 σ pn (z) θ HN(z) Y HN]θ LN(z 0 )dz p N () ] 1 σ pn (z) θ HN(z) Y HN]θ LN(z 0 )dz p N () ] 1 σ pn (z) θ HN(z) Y HN]dz = 0. p N () z 0 n z It is easy to see that for other types of technology allowing for substitution between skilled and unskilled labor i.e., ε N ( ) > 0, dn(z)/dw N < 0 still holds. A.3. Total Differential Equation System Totally differentiating equilibrium conditions (4), (9) and (10) yields the differential equation system c jk ] dz dw S dw N = b j ], where c jk ] = B z B ws B wn S z S ws 0 N z 0 N wn and b j ] = B t S t N t. (15) The elements and signs of c jk ] and b j ] are as follows. Since the North has a comparative advantage in more skill-intensive goods, c 11 is positive (see lemma 1.) Because the excess 12 Using h N (z) h N w N h N (z)+1 = θ HN (z) Y HN w N Y LN, equation (9) can be rewritten as n 1 σ pn (z) p N ()] θhn (z) Y HN ] dz = 0. 25

27 relative demand for skilled labor decreases in the relative wage of skilled labor (see lemma 2), c 22 and c 33 are negative. The signs of other elements in c jk ] are implied by the convention of goods ranking that a higher indexed good uses relatively more skilled labor. 0 c 11 = p S(z) 1 σ dz + p N(z) 1 σ dz p 0 S(z) 1 σ dz p N(z) 1 σ dz σ z ln C N(w HN, w LN, z) C S (w HS, w LS, z) > 0 c 12 = σ θ HS (z) Y HS ] > 0 c 13 = σ Y HN θ HN (z)] > 0 w S w N c 21 = θ HS(z) Y HS > 0 w S Y LS 1 z ] 1 σ ps (z) c 22 = ws 2 Y {θ LS(z)θ HS(z) σ ε S (z)] σθ LS(z)Y HS} dz < 0 c 23 = 0 LS 0 p S () c 31 = Y HN θ HN (z) > 0 c 32 = 0 w N Y LN 1 n ] 1 σ pn (z) c 33 = wn 2 Y {θ LN(z)θ HN(z) σ ε N (z)] σθ LN(z)Y HN} dz < 0 LN z p N () p N (n) 1 σ dn b 1 = p z N(z) 1 σ dz > 0 b 2 = 0 ] 1 σ pn (n) θ HN (n) Y HN ] dn b 3 = p N () w N Y LN < 0 Since c jk > 0, c jk ] 1 exists. Thus, differential equations system (15) implies dz dw S dw N = c jk 1 (c 22 c 33 b 1 c 12 c 33 b 2 c 22 c 13 b 3 ) (16) = c jk 1 c 21 c 33 b 1 + (c 11 c 33 c 13 c 31 )b 2 + c 21 c 13 b 3 ] (17) = c jk 1 c 31 c 22 b 1 + c 12 c 31 b 2 + (c 11 c 22 c 21 c 12 )b 3 ] (18) Note that all my results hold under the weaker assumption that on average new goods are more skill-intensive than all old Northern goods, i.e., θ HN (n) > Y HN. This implies that b 3 is always negative. Since the following results depend on the sign of b 3 rather than the magnitude of b 3, the weaker assumption will not change my results qualitatively. A.4. Proofs of Theorems Proof of theorem 1: 26

28 Proof. The aggregate elasticity of substitution between skilled and unskilled labor in the North can be derived as follows. Combining equations (5) and (6) yields H d N L d N = 1 w N z z ] 1 σ pn (z) wn h N (z) dz p N () 1+w N h N (z) ] 1 σ pn (z) 1 p N () 1+w N h N (z) dz. Thus, Using ε a N ln(hd N /Ld N ) = 1 + ln ln w N ln w N n ln w N z (1 σ)θ HN ()Y LN ε a N = ln ln w N ] 1 σ pn (z) 1 p N () pn (z) p N () z pn (z) p N () pn (z) z p N () ] 1 σ w N h N (z) 1 + w N h N (z) dz. pn (z) dz = 1+w N h N (z) ] 1 σ dz and n ln w N z σ ε N (z)] θ LN (z)θ HN (z)dz + (1 σ)θ LN ()Y HN n as p z N(z)] 1 σ θ LN (z)θ HN (z)ε N (z)dz Y LN Y HN p z N(z)] 1 σ dz + σ ] 1 σ w N h N (z) dz p N ()] 1 σ εn (z) σ] θ LN (z)θ HN (z)dz ] 1 σ pn (z) wn h N (z) p N () ] 1 σ pn (z) p N () dz, ε a N 1 z 1+w N h N (z) dz = ] 1 σ pn (z) p N () can be further derived p ] N(z)] 1 σ θ LN (z)θ HN (z)dz Y LN Y HN p z N(z)] 1 σ. (19) dz The first term in equation (19) represents within-good substitution, and the second term measures between-good reallocation. Equation (16) implies that with b 2 = 0, dz/ > 0 if and only if c 13 b 3 > c 33 b 1. Plugging c 13, c 33, b 1 and b 3 into c 13 b 3 c 33 b 1, I obtain that c 13 b 3 > c 33 b 1 if and only if ε a N > ε σ Y HN θ HN (z)] Y LN θ LN (n)] Y HN Y LN. Since 0 < Y HN θ HN (z) < Y HN, and 0 < Y LN θ LN (n) < Y LN, I have ε (0, σ). In order to highlight the impact of industry skill intensities on ε, I consider two extreme cases. In the first case, production of all the goods uses very similar technology such that Y HN θ HN (z) and Y LN θ LN (n) approach 0, implying that ε also approaches 0. Thus, ε a N > ε can be easily satisfied. In the second case, production of each good uses very different technology such that both θ HN (z) and θ LN (n) approach 0, implying that ε approaches σ. If there is no within-industry substitution, then ε a N > ε does not hold. Proof of theorem 2: 27

29 Proof. dz/ can be rewritten as dz = b 1 c 13 b 3 /c 33 c 11 c 12 c 21 /c 22 c 13 c 31 /c 33. (20) Since c 22 decreases in β S, from equation (20) it is easy to see that dz/ increases in β S. Equation (20) also implies d 2 z dβ N = c 13c 22 (c 11 c 22 c 12 c 21 )b 3 c 13 c 31 c 2 22b 1 c jk 2 dc 33 dβ N > 0 Similarly, since both c 22 and c 33 decrease in σ, d 2/dσ > 0. Proof of theorem 3: Proof. Equation (18) implies that with b 2 = 0, dw N / > 0 always holds. Combining b 2 = 0 with equations (16) and (17) yields dw S = c 21 c ij c 33b 1 + c 13 b 3 ] = c 21 c 22 dz. Thus, dw S / and dz/ have the same sign. By theorem 1, if ε a N follows that dw S / > 0. Proof of theorem 4: Proof. The balanced trade condition (3) implies > ε, then dz/ > 0. It d ln(y N /Y S ) = Using n p N(z) 1 σ d p 0 S(z) 1 σ d ln p S(z) p S () p N (z) 1 σ dn n p N(z) 1 σ dz p 0 S(z) 1 σ dz + p N(z) 1 σ dz p 0 S(z) 1 σ dz d n p N(z) 1 σ dz ] n p N(z) 1 σ d ln p N (z) p N dz p () 0 S(z) 1 σ d +(1 σ) p N(z) 1 σ dz ln p N (z) p N () ] dz = ] dz = 0 p S(z) 1 σ dz p N(z) 1 σ dz { θ LN () Y LN ] d ln w N { θ LS () Y LS ] d ln w S ln p S(z) p S () 0 p S(z) 1 σ dz ln p S() ln p N () d ] dz. } d and }, the change 28

30 in the North-South gap can be rewritten as d ln(y N /Y S ) = + (1 σ) p N (z) 1 σ p N(z) 1 σ dz { dn θ LN () Y LN ] d ln w N p 0 S(z) 1 σ dz + p N(z) 1 σ dz p 0 S(z) 1 σ dz d n p N(z) 1 σ dz + Y LS θ LS ()] d ln w S + ln p S() p N () } d (21) Plugging equations (16), (17) and (18) into equation (21) yields d ln(y N /Y S ) = 1 b 1 c ] 11c 22 (c 33 b 1 c 13 b 3 ) + ln p S()/p N ()] d σ c jk > 0. Proof of theorem 5: Proof. Using the balance-of-trade condition (3), the change in the terms of trade in the North can be derived as dp N ] 1 σ pn (z) d = Y S z P ln p ] ] 1 σ N(z) ps (z) d dz Y N p N () 0 P ln p ] S(z) dz p S () ] 1 σ pn (z) +Y S dz d P ln p N() p S (). (22) Since p N () = p S () always holds, d ln p N ()/p S ()] / = 0. Thus, the last term in equation (22) vanishes. Note that d ln p i(z) = θ p i () Li() θ Li (z)] d ln w i ln p i() d. Plugging these results together with the balance-of-trade condition into equation (22) yields dp N ] { 1 σ ps (z) = Y N dz θ LN () Y LN ] d ln w N P 0 + Y LS θ LS ()] d ln w S + ln p S() p N () } d. By theorem 3, when ε a N > ε, both dw S/ and d/ are positive. By lemma 1, ln p S ()/p N ()] / > 0. At the same time, dw N / > 0, θ LN () > Y LN and Y LS > θ LS (). Therefore, dp N / > 0. It follows that dp S / = dp N / < 0. Proof of theorem 6: Proof. With CES preferences, the Northern indirect utility is U N = Y N /P, where P p 0 S(z) 1 σ dz + p N(z) 1 σ dz ] 1 1 σ is the aggregate price index. The change in Northern (23) 29