Trade, product cycles, and inequality within and between countries

Trade, product cycles, and inequality within and between countries Susan Chun Zhu Department of Economics, Michigan State University Abstract. This paper incorporates Northern product innovation and product-cycledriven 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 are the most skill intensive by Southern standards. Hence, 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. JEL classification: F1 Commerce international, cycles de produit, et ine galite a` l inte rieur des pays et entre eux. Ce mémoire incorpore le processus d innovation et de transfert de technologie engendre par le cycle du produit dans le Nord dans le continuum de produits d un modèle Hecksher-Ohlin. La cre ation de biens a` forte intensite en habilete s ame` ne le Nord à transférer la production de biens a` moins forte intensite en habilete s vers le Sud. Ces biens relocalise s sont ceux qui sont les plus intensifs en habilete s dans le Sud. En conséquence, les cycles de produit augmentent la demande de main d œuvre qualifie e et donc l ine galite entre les régions. Voila` qui ne va pas dans le sens de ce que le the ore` me de Stolper-Samuelson sugge` re, mais s accorde bien avec le fait que les ine galite s de salaires augmentent dans le Nord et le Sud. De plus les cycles de produit augmentent l ine galite entre pays. Meˆ me si le transfert de technologie diminue l e cart de revenu entre le Nord et le Sud, cet effet est plus que compensé par l effet de l innovation de produit. Ce mémoire examine aussi les effets de bien-eˆ tre des cycles de produit. Les cycles de I am indebted to Dan Trefler for his encouragement and many helpful comments. I also thank Tony Creane, Nancy Gallini, Wolfgang Keller, Angelo Melino, Diego Puga, Martin Richardson, Aloysius Siow, Nadia Soboleva, and especially two anonymous referees for helpful comments and suggestions. Financial support from the Social Sciences and Humanities Research Council of Canada is gratefully acknowledged. Email: huc@msu.edu Canadian Journal of Economics / Revue canadienne d Economique, Vol. 37, No. 4 November / novembre 2004. Printed in Canada / Imprimé au Canada 0008-4085 / 04 / 1042 1060 / # Canadian Economics Association

Trade, product cycles, and inequality 1043 produit engendrent des avantages pour le Nord et le Sud, et ame liorent le sort des travailleurs hautement qualifiés dans les deux re gions. 1. Introduction There is increasing evidence that in recent decades wage inequality between skilled and unskilled workers has grown not only in many Northern countries, but also in some Southern countries (Feenstra and Hanson 1996, 1997; Robbins 1995; Cragg and Epelbaum 1996; Hanson and Harrison 1999; Berman, Bound, and Machin 1998). The pervasiveness of rising wage 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 wage 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 wage inequality in both regions can be explained within a Heckscher-Ohlin framework. To this end, I incorporate technical change into the continuum-of-goods Heckscher-Ohlin model (Dornbusch, Fischer, and Samuelson 1980). I consider a world economy driven by Northern product innovation. I further assume that new goods use relatively more skilled labour than old goods. This assumption is consistent with the experience of the past several decades, which have seen the rapid spread of computers and other new technologies in workplaces. Since these new technologies favour skilled workers, technical change is considered by many economists as a dominant factor contributing to rising inequality in developed countries (e.g., Krueger 1993; Goldin and Kat 1998; Berman, Bound, and Griliches 1994; Autor, Kat, and Krueger 1998). While R&D-induced or computer investmentinduced technical change is likely to be a major force raising the demand for skills in developed countries, such factors would seem to be less relevant in developing countries where innovative capacity is limited. If technical change matters for these countries, the mechanism must be via trade or foreign direct investment. In this paper I show that international trade serves as a channel through which technical change originated in the North spreads to the South. Specifically, the creation of new, skill-intensive goods can endogenously induce developed countries to move less skill-intensive goods to developing countries. In this paper I present a new theory of product cycles. Unlike Vernon s (1966) original product-cycle model, this new theory has nothing to do with the ongoing process of standardiing new goods. Instead, in my model product cycles are generated by rich general equilibrium interactions between international trade and labour markets. What is particularly interesting about this new theory of product cycles is that it has important implications for the domestic distribution of income. With the partial exception of Dinopoulos

1044 S. Chun Zhu and Segerstrom (1999), 1 domestic income distribution issues have not been addressed by previous product-cycle models (e.g., Vernon 1966; Krugman 1979; Dollar 1986; Flam and Helpman 1987; Jensen and Thursby 1987; Grossman and Helpman 1991). The core result is that product innovation and technology transfer increase inequality within both regions. In this model rising wage inequality is driven by increased demand for skilled labour due to changes in the product mix. When new, skill-intensive goods are introduced, the relative demand for Northern skilled labour increases, thus raising Northern inequality. If the aggregate elasticity of substitution between Northern skilled labour and unskilled labour 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 labour 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 labour increases. Thus inequality also rises in the South. 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, dominates. This result differs sharply from Krugman (1979). The difference arises from the way technology transfer is modelled: in Krugman, technology transfer is exogenous. Krugman considers the case where there is an increase in the rate of technology transfer while the rate of product innovation is kept constant, and he 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. The simplicity of the model allows me to derive a rich set of welfare implications of product cycles. The terms of trade move in favour 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. It is worth pointing out that Feenstra and Hanson (1996) and Xu (2003) also extend the continuum-of-goods Heckscher-Ohlin model in order to explain rising inequality within both the North and the South. Like mine, their explanation relies on changes in the product mix. However, there are two major differences between my work and theirs. First, the source of 1 Dinopoulos and Sergerstrom (1999) present a dynamic general equilibrium model of North- North trade that has implications for wage inequality in Northern countries. However, it does not deal with Southern countries.

Trade, product cycles, and inequality 1045 product-mix changes is very different. In Feenstra and Hanson (1996), a higher rate of return to capital investment in the South causes production relocation from the North to the South. In Xu (2003), changes of the product mix are attributed to tariff reductions in the South and the resulting change in the boundary between traded and non-traded goods. In contrast, in my model Northern product innovation drives all the changes in production patterns. Second, in Feenstra and Hanson (1996) and Xu (2003), widening inequality in the North is entirely caused by production relocation from the North to the South. In contrast, in my model the creation of new, skill-intensive goods is the dominant factor contributing to inequality in the North. In particular, rising inequality can occur in the North without the relocation of older, less skill-intensive goods to the South. This result accords well with the empirical finding that the use of computers and other new technologies is a dominant factor explaining rising wage gap in developed countries (Krueger 1993; Goldin and Kat 1998; Berman, Bound, and Griliches 1994, Autor, Kat, and Krueger 1998). 2 Beaulieu, Benarroch, and Gaisford (forthcoming) and Long, Rieman, and Soubeyran (forthcoming) also examine the issue of rising inequality within both the North and the South. However, the mechanism of inequality in these two papers differs from that in my model. In Beaulieu, Benarroch, and Gaisford (forthcoming), the growing wage gap is due to the Stolper-Samuelson effects rather than product-mix changes. Specifically, a reduction in trade barriers in the skill-intensive high-tech sector typically raises the relative prices of skill-intensive goods, leading to rising wage gap in both regions. In Long, Rieman, and Soubeyran (forthcoming), trade liberaliation not only directly affects product prices, but also indirectly influences human capital accumulation. Hence, in addition to the Stolper-Samuelson mechanism, their model suggests a new channel through which trade liberaliation affects the wage gap between skilled and unskilled workers. The paper is organied as follows. In section 2 I describe the basic model. In section 3 I illustrate the effects of product cycles on labour markets and conclude that inequality can rise within and between countries. In section 4 the welfare implications of product cycles are examined. Conclusions are drawn in section 5. 2. The basic model The set-up is based on Dornbusch, Fischer, and Samuelson (1980). There are two regions (the North and the South), two factors (skilled and unskilled 2 Using a monopolistic competition model with non-homothetic production, Dinopoulos, Syropoulos, and Xu (1999) show that a move from autarky to free intra-industry trade increases wage inequality in Northern countries. The mechanism of inequality operates in product markets characteried by monopolistic competition and relates the sie of the firm to the mix of factor inputs and factor prices. Sener (2001) develops a dynamic model of North- North trade that has implications for rising inequality in Northern countries. In his model inequality results from a Schumpeterian version of the Stolper-Samuelson effects.

1046 S. Chun Zhu labour), and a continuum of goods indexed by 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 labour markets are perfectly competitive. Furthermore, there are no trade barriers in the model. Trade is always balanced. I focus on the complete specialiation equilibrium where the North produces more skill-intensive 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 labour and the South is relatively abundant in unskilled labour. Further, the difference in labour endowment is so large that the relative wage for skilled labour 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 to index a more skill-intensive good. Then, it can be shown that the North has a comparative advantage in skill-intensive goods (,n] while the South has a comparative advantage in unskilled-intensive goods [0,). Good 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 is determined by p N () ¼ p S (), (1) where p i () is the price of good in region i (¼N,S). On the demand side, I assume that all individuals have identical preferences, which are represented by the CES utility function U ¼ Z n 0 x() 1 d 1 ( >1), (2) where x() is the consumption of good and is the elasticity of substitution between goods. Equilibrium is characteried by conditions of balanced trade and labour market clearing. Let Y i be national income in region i. Let p i () be h i p N() 1 1 1 d the price of good. Let P R 0 p S() 1 d þ R n be the aggregate price index. With identical CES preferences, the balance-of-trade condition is Z p S () 1 Z n p N () 1 Y N d ¼ Y S d: (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

( Z Y ) ( N p S () 1 Z Y n ) S p N () 1 B() ln d ln d ¼ 0: (4) p N () p S () p S () p N () 0 Trade, product cycles, and inequality 1047 Using good as numeraire simplifies the following analysis. Let H i and L i be the supply of skilled and unskilled labour, respectively. Let w Hi and w Li be the wages of skilled and unskilled workers, respectively. Define h i H i /L i and w i w Hi /w Li. I assume that dh i /dw i 0anddL i /dw i 0, thereby allowing for the possibility that unskilled labour may obtain skills when the relative wage rises. 3 Let Hi d and L d i be the aggregate demand for skilled and unskilled labour, respectively. Let H i (w i, ) andl i (w i,) be the amount of skilled and unskilled labour, respectively, required to produce one unit of good. Finally, define h i (w i, ) H i (w i,)/l i (w i, ). To simplify notation, in the following I will drop w N and w S as arguments. However, this should not be misconstrued as an assumption that substitution between the two types of labour is restricted. The aggregate demand for Northern skilled labour is HN d ¼ R n x()h N()d. With CES preferences, world demand for Northern good is x() ¼ [p N ()/P] 1 (Y N þ Y S )/p N (). With ero profits, p N () ¼ w HN H N () þ w LN L N (). Plugging x()intohn d, the condition of Northern skilled labour market clearing can be expressed as Z n H N ¼ HN d ¼ p N () 1 (Y N þ Y S )H N () d: (5) P w HN H N () þ w LN L N () Similarly, the condition of Northern unskilled labour market clearing is Z n L N ¼ L d N ¼ p N () 1 (Y N þ Y S )L N () d: (6) P w HN H N () þ w LN L N () Since I am interested in the wage gap between skilled and unskilled labour, I combine equations (5) and (6) and express the labour market clearing conditions in terms of w N. To this end, define N() H d N =H N L d N =L N. N() is the excess demand for skilled labour relative to unskilled labour in the North. With some manipulation, N () ¼ 0 can be written as 4 3 Note that this assumption is made for simplicity. The model can be generalied easily to allow an endogenous skill decision (see Dinopoulos and Segerstrom 1999; Sener 2001; Beaulieu, Benarroch, and Gaisford, forthcoming). 4 The skilled labour market equilibrium condition (5) can be rewritten as Z n HN d ¼ Y N þ Y S H N w LN H N P 1 p N () 1 h N () d ¼ 1: (7) 1 þ w N h N () Similarly, the unskilled labour market equilibrium condition (6) yields Z n L d N ¼ Y N þ Y S L N w LN H N P 1 p N () 1 h N d ¼ 1: (8) 1 þ w N h N () Equation (7) minus equation (8) results in the labour market equilibrium condition (9).

1048 S. Chun Zhu Z n p N () 1 ½h N () h N Š N() d ¼ 0: (9) p N () 1 þ w N h N () Similarly, the corresponding Southern labour market clearing condition SðÞ¼H S d=h S L d S =L S can be written as Z p S () 1 ½h S () h S Š S() d ¼ 0: (10) 0 p S () 1 þ w S h S () The competitive margin and relative wages (w N,w S ) are determined simultaneously by equations (4), (9), and (10). 5 In particular, the competitive margin serves as a link between the two labour markets. In this model prices of goods and national income are also endogenied. The proof of existence and uniqueness of the equilibrium in Dornbusch, Fischer, and Samuelson (1980) can be applied with only minor modifications. 3. Product cycles and inequality While Dornbusch, Fischer, and Samuelson (1980) examine endowment changes, I focus on the impact of technical change on labour markets and trade patterns. In this paper technical change takes the form of product innovation in the North. 6 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 my goal is to examine the impacts of innovation rather than its determinants, I assume that product innovation is exogenous. Second, in the light of recent work on technology-skill complementarities, 7 I assume that new goods use relatively more skilled labour than old goods. Note that this assumption is made for analytical convenience. It can be shown that all results hold under a weaker assumption that on average new goods are more skill intensive than existing Northern goods. 5 Both Y i /p i () and p i ()/p i () (i ¼ S,N) can be expressed in terms of w i : Y i /p i () ¼ [(w i h i þ 1) L i ]/ [(w i h i () þ 1) L i ()], and p i ()/p i () ¼ [(w i h i () þ 1) L i ()]/[(w i h i () þ 1) L i ()]. 6 Process innovation is taken up in Zhu and Trefler (forthcoming). 7 Goldin and Kat (1998) document that technology-skill complementarities existed in manufacturing early in this century. Krueger (1993) and Berman, Bound, and Griliches (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 organiation also increase the demand for skilled labour. The theoretical work on technology-skill complementarities includes Galor and Tsiddon (1997).

Trade, product cycles, and inequality 1049 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. 3.1. 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)). The creation of new goods also directly affects the Northern labour market. Since new goods are more skill intensive than all existing Northern goods, the creation of new goods raises the relative demand for skilled labour. Thus, the relative wage of skilled labour rises. This, together with the increase in national income just discussed, implies that the wage of Northern skilled labour 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 labour rises or falls in equilibrium hinges on the degree of substitutability between Northern skilled and unskilled labour. Unskilled labour can be substituted for skilled labour in three ways. First, cheaper unskilled labour replaces skilled labour within production of each good, that is, within-good substitution. Second, by the Rybcynski effect, production of less skill-intensive goods expands, that is, between-good reallocation. Third, in response to rising wage inequality some unskilled labour upgrades and becomes skilled labour. When Northern skilled and unskilled workers are sufficiently substitutable, the oversupplied unskilled labour 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 formalie this idea. 3.2. 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 þ dt, new goods are introduced over the range (n,n þ dn). I consider the impact of changes in t and hence n on w S, w N, and. As discussed above, the conclusion that Northern innovation leads to product cycles (i.e., raises ) hinges on the degree of substitutability between skilled and unskilled labour in the Northern production. Let " a N d ln (Hd N =Ld N )=d ln w N be the aggregate elasticity of substitution

1050 S. Chun Zhu between Northern skilled and unskilled labour. Theorem 1 formalies this observation. 8 THEOREM 1. There exists a constant " 2 (0,) such that " a N > ", d =dt > 0. That is, if and only if skilled and unskilled labour 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. The critical degree of substitutability between Northern skilled and unskilled labour (") 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 labour market. In order to absorb the oversupplied unskilled labour, a larger value of " is required. Theorem 1 also implies that " a N > is a sufficient condition for product cycles to occur. In particular, when approaches 1 (i.e., preferences are represented by the Cobb-Douglas utility function), the sufficient condition becomes " 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; Kat and Murphy 1992; Heckman, Lochner, and Taber 1998, and Krusell et al. 2000). 3.3. The role of the elasticity of substitution I have discussed how product cycles rest on the substitutability between skilled and unskilled workers. In this section I further develop this point and show that care is needed in 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 Rybcynski effect). The elasticity of substitution between skilled and unskilled labour in the production of good is defined as " N () d ln h N ()/d ln w N. (Recall that w N w HN /w LN is the relative wage of Northern skilled labour and h N () h HN ()/h LN () is the relative employment of skilled labour in good.) Using the labour demand equations in (5) and (6), " a N can be expressed as a weighted average of within-good elasticities of substitution between factors (" N ()) and the elasticity of substitution between goods (): R n " a N ¼ ½ p N() Š 1 LN () HN ()" N ()d R n Y LN Y HN ½ p N() Š 1 d " R n ½ þ 1 p # N() Š 1 LN () HN ()d R n Y LN Y HN ½ p N() Š 1, (11) d 8 Proofs are available upon request.

Trade, product cycles, and inequality 1051 where LN () w LN L N ()/p N () is the cost share of Northern unskilled labour in good, HN () w HN H N ()/p N () is the cost share of Northern skilled labour, Y LN w LN L N /Y N is the national income share of unskilled labour, and Y HN w HN H N /Y N is the national income share of skilled labour. Note that the second term in equation (11) is always positive. 9 Equation (11) is a continuum-of-goods version of the aggregate elasticity of substitution discussed in Jones (1965). As " N () increase, " a N becomes larger. When " N () ¼ 0 (i.e., no within-good substitution), labour market adjustment depends on a Rybcynski-style reallocation of output between skill-intensive and unskilled-intensive goods. This is captured by the second term in equation (11). A bigger value of implies a stronger substitution effect via output reallocation. This is because, with a bigger, 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, 10 alargervalueof 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 Kat and Murphy (1992). It also helps one to understand how the Feenstra- Hanson model equilibrates: even though they assume that there is no substitution between skilled and unskilled labour within goods production (" N () ¼ " S () ¼ 0), equilibration occurs via a Rybcynski-style reallocation. Both " N () and affect not only the sign of d =dt, but also its magnitude. The more substitutable unskilled labour is for skilled labour, the bigger is the rate of technology transfer. With small values of " N () and, oversupplied unskilled Northern labour can be only partially 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, that is, by reducing. The higher " N () and are, the weaker is the pressure to lower and, hence, the more effective is the product-cycle pressure to raise. The elasticities of substitution in the South (" S () d ln h S ()/d ln w S ) affect d =dt in a similar way. To formalie these observations, write " i as a function of a shift variable i (i ¼ S,N). i shifts the entire " i (, i ) 9 Using h N () h N w N h N () þ 1 ¼ HN() Y HN ¼ Y LN LN (), w N Y LN w N Y LN equation (9) can be rewritten as R n ½ p N() Š 1 ½ LN () Y LN Šd ¼ 0. Combining this with LN () 2 ¼ ½ LN () Y LN Š 2 þ2½ LN () Y LN ŠY LN þ YLN 2 yields R n ½ p N() Š 1 LN () 2 R d > YLN 2 n ½ p N() Š 1 d. It follows that R n ½ p N() Š 1 LN () HN ()d ¼ R n ½ p N() Š 1 LN ()d R n ½ p N() Š 1 LN () 2 d < R n Y HN Y LN ½ p N() Š 1 d. 10 Consider two Northern goods 1 and 2. The change in the relative good price is d ln [p N ( 2 )/ p N ( 1 )]/dt ¼ [ HN ( 2 ) HN ( 1 )]d ln w N /dt. This is positive when 2 > 1, i.e., 2 is more skill intensive than 1.

1052 S. Chun Zhu schedule up. That is, a large i makes the " i more elastic. The results are summaried in theorem 2. THEOREM 2. d =dt is increasing in S, N, and. 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. 3.4. 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 pule can be resolved by embedding technical change into the continuum-of-goods Heckscher-Ohlin model. Recall that w i ¼ w Hi /w Li (i ¼ 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 /dt > 0. (ii) Assume " a N > ". Then dw S /dt > 0. That is, product cycles raise inequality in the North. If Northern skilled and unskilled labour are sufficiently substitutable, then product cycles also raise inequality in the South. The creation of new, skill-intensive goods raises the relative demand for Northern skilled labour. Thus, the relative wage in the North rises. It is worth noting that this result holds whether rises or falls. Even if falls, thereby increasing the relative demand for Northern unskilled labour, 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, Bound, and Griliches 1994; Autor, Kat, and Krueger 1998; Berman, Bound, and Machin 1998). In contrast, technology transfer (rising ) is the only factor affecting the relative labour 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 labour in the South, leading to wage inequality there. 11 The condition " a N > " in theorem 3 ensures that will rise. 11 Zhu (2003) examines empirically the extent to which increasing demand for skilled workers can be explained by product cycles, that is, 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 with rising demand for skilled workers in a large panel of industries and countries.

Trade, product cycles, and inequality 1053 This basic insight of theorem 1 appears in Feenstra and Hanson s (1996) study on outsourcing and inequality in the United States and Mexico. However, my work also differs from theirs in several major aspects. First, the driving force is different. In my two-factor model (skilled labour and unskilled labour), all the changes in labour markets and trade patterns are driven by Northern product innovation. In contrast, in Feenstra and Hanson s threefactor model (capital, skilled labour and unskilled labour), a higher rate of return to capital investment in the South causes production relocation from the North to the South. Second, Feenstra and Hanson consider a partial equilibrium model. This is because they mainly examine the impact of foreign direct investment on labour demand within a single industry. In contrast, since I am interested in the general equilibrium interactions between international trade and labour markets, I use a general equilibrium model of trade in final goods. In particular, my model has richer general equilibrium feedbacks through the trade balance. Third, in Feenstra and Hanson there is no substitutability between skilled and unskilled labour. This is incompatible with the focus on such elasticities that dominates the literature on wage inequality (e.g., Kat and Murphy 1992). In contrast, in my model the substitutability between skilled and unskilled workers plays a central role in generating product cycles. Finally, in Feenstra and Hanson Northern inequality is entirely driven by production relocation. In contrast, in my model Northern product innovation is the dominant factor behind rising inequality in the North. It is also worth noting that the wage gap between skilled and unskilled workers is rising in some but not all less developed countries. One explanation for falling inequality in some Southern countries is that these countries may experience a rapid growth in the relative supply of skilled workers, which largely results from expansion of public education. This explanation is supported by Lam and Levison (1992) on Brail, and Kim and Topel (1995) on South Korea. In both empirical studies strong evidence is found that declining education differentials are closely associated with relative labour supply shifts. To formalie this idea, I can extend the model by incorporating a shift in the skill composition of Southern labour force. 12 It can be shown that when the shift in the relative supply of skilled labour is greater than the shift in the relative demand for skilled labour (due to production relocation), the wage gap between skilled and unskilled labour can fall. 3.5. Rising inequality between countries Product cycles increase inequality not only within countries, but also between countries. Northern product innovation and endogenous technology transfer 12 Here, the change in the relative labour supply means a shift of the labour supply curve rather than a movement along an upward-sloping labour supply curve. This is because an expansion of public education reduces the cost of education and thus induces more workers to get education for any given wage rate.

1054 S. Chun Zhu 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 transfer on Northern income. Thus, product cycles widen the North-South income gap. 13 THEOREM 4. d(y N /Y S )/dt > 0. That is, product cycles widen the North-South income gap. Theorem 4 further implies that when the elasticity of substitution between goods () is close to unity, the rate of technology transfer (d ln =dt) can never exceed the rate of product innovation (d ln n/dt). 14 Theorem 4 stands in sharp contrast to Krugman (1979). The difference mainly arises from the way technology transfer is modelled. In Krugman, technology transfer is exogenous. Krugman considers the case where there is an increase in the rate of technology transfer while the rate of Northern innovation is kept constant, and he 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 with 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. 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 a change in the terms of trade. This is the basis for further analysis of national welfare and labour welfare. 4.1. 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 13 An extension of the model by including the increasing supply of Southern skilled labour can help one explain the income catch-up by some newly industrialied countries in recent decades. 14 When approaches 1, the balance-of-trade condition in equation (3) implies d ln (Y N =Y S ) ¼ dt d ln (n ) d ln dt dt : By theorem 4, d ln (Y N /Y S )/dt > 0. Thus, d ln n=dt > d ln =dt.

Trade, product cycles, and inequality 1055 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, 132.) Using the above definition, the change in Northern terms of trade may be R n written as dp N =dt ¼ Y S ½ p N()=PŠ 1 R ½d ln p N ()=dtšd Y N ½ Š 1 ½d ln p S ()=dt 0 p S()=P h Šd. (Recall that P R 0 p S() 1 d þ R i n p N() 1 1 1 d is the aggregate price index.) The change in Southern terms of trade is dp S /dt ¼ dp N /dt. 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 " a N > ".Then dp N /dt > 0 and dp S /dt < 0. That is, the terms of trade rise in the North and fall in the South. 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 worsens the terms of trade. When product cycles raise the relative wages of skilled labour in both regions, the goods that use relatively more skilled labour become more expensive within each region (see fn. 10.) 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. 4.2. National welfare Since each region has two types of labour, 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 labour in the region can be made better off (see Dixit and Norman 1980, 20). When all types of labour have the same CES preferences, it is straightforward to derive the Northern indirect utility as U N ¼ Y N /P. Then the change in Northern welfare can be further derived as d ln U N dt ¼ 1 1 p N (n) 1 dn P dt þ 1 Y N dp N dt : (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.

1056 S. Chun Zhu This differs markedly from Krugman (1979), who finds that technology transfer must make 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. 15 In contrast, in my model, although technology transfer shifts income from the North to the South, it is a second-order effect compared with the effect of product innovation. It can be shown that product cycles improve the terms of trade in the North. 16 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 dt ¼ 1 1 p N (n) 1 dn P dt þ 1 Y S dp S dt : (13) Equation (13) suggests that new goods benefit the South to the same extent as the North. It can be shown that 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 summaries these results. THEOREM 6. Assume " a N > ". Then du N /dt > 0 and du S /dt > 0. That is, product cycles improve welfare in both the North and the South. 4.3. Labour welfare It is worth pointing out that previous product-cycle models largely consider one type of labour and thus cannot have any welfare implications for different types of labour. In this paper labour welfare is measured by the indirect utility of each type of labour. Let U HN and U HS denote the indirect utility of skilled labour in the North and the South, respectively. Note that U Hi ¼ w Hi /P(i ¼ S,N). Then the change in welfare of skilled labour may be written as d ln U Hi dt ¼ 1 1 p N (n) 1 dn P dt þ 1 Y i dp i dt þ Y Li d ln w i, i ¼ S,N: (14) dt The first term indicates that new goods benefit skilled labour in both regions to the same extent. The second term reflects the welfare effects of terms of trade. Specifically, improved terms of trade in the North (dp N /dt > 0) make Northern 15 Similar to Krugman (1979), Dollar (1986) considers the case where there is an increase in the rate of technology transfer while the rate of product innovation is kept constant. In Dollar s model technology transfer also worsens the terms of trade in the North. 16 Jensen and Thursby (1987) develop a product-cycle model with endogenous innovation but exogenous technology transfer. Since an increase in the rate of technology transfer raises the rate of innovation, the Northern terms of trade may not deteriorate with an increased transfer rate.

Trade, product cycles, and inequality 1057 skilled labour better off, while worsened terms of trade in the South (dp S / dt < 0) make Southern skilled labour worse off. However, for Southern skilled labour, the loss from worsened terms of trade is fully offset by the gain from new goods (see equation (13) and theorem 6). Further, as suggested by the third term in equation (14), when product cycles shift domestic income from unskilled to skilled labour, welfare of skilled labour is further improved in both regions. Therefore, skilled labour in both regions must be better off. Let U LN and U LS denote the indirect utility of unskilled labour in the North and the South, respectively. The change in welfare of unskilled labour can be derived as d ln U Li dt ¼ 1 1 p N (n) 1 dn P dt þ 1 Y i dp i dt Y Hi d ln w i, i ¼ S,N: (15) dt A comparison of equations (14) and (15) reveals that the divergence in welfare between skilled and unskilled labour within each region is entirely caused by domestic income redistribution. In particular, as implied by the third term in equation (15), rising domestic inequality lowers welfare of unskilled labour in both regions. This negative welfare effect offsets the gains from product cycles (e.g., the creation of new goods). Thus, it is less certain whether unskilled labour would be better or worse off. If the negative effect of increasing wage gap dominates, unskilled labour in both regions can be worse off. These results are summaried in theorem 7. THEOREM 7. Assume " a N > ". Then (i) du HN /dt > 0 and du HS /dt > 0. That is, product cycles improve welfare of skilled labour in both the North and the South. (ii) du HN /dt 0 0 and du HS /dt 0 0. That is, unskilled labour in both regions may gain or lose from product cycles. 5. 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 continuum-of-goods Heckscher-Ohlin model. It shows that inequality can rise in both regions. The intuition is simple. The creation of new, highly skillintensive goods in the North raises the relative demand for Northern skilled labour and hence raises inequality. When the aggregate elasticity of substitution between skilled and unskilled labour is sufficiently large in the North, 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

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