Trade and Economic Growth

Transcription

1 Trade and Economic Growth Paul S. Segerstrom Stockholm School of Economics For the Palgrave Handbook of International Trade Current version: April 15, 211 Acknowledgments: This research was financially supported by the Wallander Foundation. Author: Paul S. Segerstrom, Stockholm School of Economics, Department of Economics, Box 651, Stockholm, Sweden ( Tel: , Fax: ).

2 1 Introduction In the widely used textbook International Economics: Theory and Policy by Paul Krugman and Maurice Obstfeld (29), a case is made for why free trade is better than protectionism. It is argued that the conventionally measured costs of deviating from free trade are large, that there are additional benefits from free trade that add to the costs of protectionist policies when there are economies of scale in production, and any attempt to pursue sophisticated deviations from free trade is likely to be subverted by the political process. While all of these arguments are important, one of the potentially most important reasons for favoring free trade is not presented in standard textbooks like Krugman and Obstfeld: namely, that trade liberalization promotes technological change. The argument is fairly easy to state. When trade barriers between countries are lowered, firms earn higher profits from exporting their products and consequently higher overall profits. Because these profits represent a reward for innovating and developing new products or lower cost ways of producing existing products, firms have a stronger incentive to innovate when there are lower trade barriers between countries. They devote more resources to research and development (R&D) and innovate more often. People living in these liberalizing countries benefit from faster technological change. More than any other development, what has led economists to take this argument seriously is the experience of the East Asian tigers : Hong Kong, Taiwan, South Korea and Singapore. While other developing economies pursued the strategy of import-substituting industrialization and experienced relatively low rates of economic growth, the East Asian tigers adopted much more open trade policies and experienced miracle rates of economic growth. Real Gross Domestic Product (GDP) in the tiger economies grew at an average annual rate of 8-9 percent from the mid-196s until the 1997 Asian financial crisis. This compares with 2-3 percent growth rates in the United States and Western Europe during the same time period. Since the East Asian tigers were much more export-oriented than other developing economies and they experienced much higher rates of economic growth, the connection between trade policy and technological change could be very important, indeed, it could be more important for welfare than the static welfare gains from trade liberalization that are emphasized in standard economics textbooks. Thinking about the East Asian growth miracle lead Robert Lucas (1988, 5) to write: I do not see how one can look at figures like these without seeing them as representing 1

3 possibilities. Is there some action a government of India could take that would lead the Indian economy to grow like [South Korea s]? If so, what, exactly?...the consequences for human welfare involved in questions like these are simply staggering: Once one starts to think about them, it is hard to think about anything else. The rest of this chapter is organized as follows: In section 2, I provide an overview of the literature on trade and growth. I discuss the different types of models that have been developed, the results that have been obtained and also the evidence that there is a connection between trade policy and economic growth. The literature on trade and growth is challenging to read because even the simplest models take many steps to solve. To help the reader get into this literature, I present in section 3 a relatively simple model of trade and growth. I spell out how this model is solved in considerable detail so it can serve as a useful entry point for readers into the rest of the literature. I also discuss what happens when some of the strong assumptions in the model are relaxed. Finally, I offer some concluding comments in section 4. 2 An Overview of the Literature In discussing the literature on trade and growth, it is natural to begin with the earliest models of endogenous growth. Before endogenous growth models were introduced in the late 198s, there were only growth models where the rate of technological change was assumed to be exogenously given (i.e., Solow 1956). These exogenous growth models could not explain how public policies like trade liberalization could have any effect on technological change. But with the development of endogenous growth models, economists finally had a theoretical framework where public policies could influence the rate of technological change and consequently, the rate of economic growth. 2.1 First-Generation Endogenous Growth Models The earliest endogenous growth models were developed in papers by Romer (199), Segerstrom, Anant and Dinopoulos (199), Grossman and Helpman (1991) and Aghion and Howitt (1992). These models explored the incentives firms have to engage in R&D activities aimed at discovering new products or processes (that is to say, developing new ideas). A key feature which distinguishes these models from earlier exogenous growth models is that the assumption of perfectly competitive product markets is relaxed. In all four papers, firms that innovate earn monopoly profits, at least temporarily, as a reward for their past R&D efforts. The incentives that profit-maximizing firms 2

4 have to engage in R&D help to determine the equilibrium rate of technological change and because public policy choices can affect these incentives, they can influence the long-run (or steady-state) rate of economic growth. The papers by Romer (199), Grossman and Helpman (1991) and Aghion and Howitt (1992) do not directly address trade policy issues and instead study closed-economy models where there is no international trade. In Romer (199), firms do R&D to develop new varieties of intermediate inputs used in production of a final good. When Romer solves his model, he finds that the steady-state equilibrium rate of economic growth without government intervention is unambiguously lower than the welfare-maximizing (or optimal) economic growth rate and that by appropriately subsidizing R&D investment, the optimal outcome can be achieved as a steady-state equilibrium outcome. In Grossman and Helpman (1991) and Aghion and Howitt (1992), firms do R&D to develop new ideas that are not just different (like new varieties of intermediate inputs in Romer) but are better in some sense (higher quality products in Grossman and Helpman, lower cost technologies for producing existing products in Aghion and Howitt). As a result, there is an additional business-stealing externality associated with R&D investment in these models, since innovating firms are able to drive other firms out of business and the equilibrium economic growth rate without government intervention can be either greater than or less than the optimal economic growth rate. These papers make a case for either subsidizing or taxing R&D expenditures depending on the size of innovations and other parameter values. Even though Romer (199), Grossman and Helpman (1991) and Aghion and Howitt (1992) do not directly address trade policy issues, these papers do have interesting implications for international trade. All three models imply that the long-run rate of economic growth is an increasing function of factor endowments, which has subsequently become known as the scale effect property. In Romer (199), the economic growth rate is higher when the economy has more human capital and in the other two papers, the economic growth rate is higher when the economy has more labour. What this means is that if two such identical closed economies suddenly become fully integrated through free trade in goods, it is as if one of the economies suddenly became twice as large. Going from autarky to free trade in these types of models increases the long-run rate of economic growth by stimulating firms to devote more resources to R&D. The first paper on endogenous growth to directly address trade policy issues is Segerstrom, Anant and Dinopoulos (199). This paper presents a North-South trade model where firms do R&D to develop higher quality products. These products are initially discovered and produced by firms 3

5 in the North (developed countries) and are exported to the South (developing countries). Northern firms that innovate receive patent protection for their products and earn monopoly profits until their patents expire. Then production shifts to the South where wages are lower and the products are exported back to the North. The paper studies the steady-state equilibrium effects of tariffs designed to protect dying industries in the North from southern competition. It is shown that when more northern industries are protected from southern competition using prohibitive tariffs, this leads to higher relative wages for northern workers and a lower rate of innovation in the North. Because a lower rate of innovation results in a lower rate of economic growth, this paper links protectionist trade policies with lower economic growth. Instead of studying trade policy in a North-South trade context, Rivera-Batiz and Romer (1991a) study trade policy in a model with two perfectly symmetric countries that impose the same tariff on all imported goods. They build directly on the earlier paper by Romer (199) when it comes to the preferences and technology of each country. Focusing on the steady-state equilibrium effects of trade policy choices, Rivera-Batiz and Romer find a U-shaped relationship between the common tariff and economic growth. Starting from the point where the tariff rate equals zero, the economic growth rate decreases as the tariff rate increases. As the tariff rate continues to increase, the economic growth rate eventually reaches a minimum, and then increases from then on. However, the economic growth rate does not return all the way back to the free trade economic growth rate. Thus, Rivera-Batiz and Romer can conclude that, compared with free trade, trade restrictions reduce the global rate of economic growth. In Rivera-Batiz and Romer (1991a), integration in the sense of full communication of ideas is assumed throughout. Thus the entire stock of ideas in the world is available for researchers in each country to use in the development of new ideas. This assumption is relaxed in the companion paper Rivera-Batiz and Romer (1991b). Using a knowledge-driven specification for R&D where human capital and knowledge are used as inputs to produce new ideas, they find that integration that involves free trade in goods alone (without flows of ideas) has no effect on the long-run rate of economic growth. But if integration involves both free trade in goods and free flow of ideas, such integration results in permanently faster economic growth. Rivera-Batiz and Romer also study a lab-equipment specification for R&D where ideas are produced using the same technology as goods. In this case, free flow of ideas is not important and integration that involves free trade in goods alone results in a permanently higher economic growth rate. 4

6 2.2 Second-Generation Endogenous Growth Models All of the above-mentioned endogenous growth models have a scale effect property, namely, that the steady-state rate of economic growth is an increasing function of population size. Indeed, the scale effect property is highlighted by Rivera-Batiz and Romer (1991b) as being the key to why economic integration is growth-promoting in endogenous growth models. However, this very property was called into question in an important paper by Jones (1995a). To see that the scale effect property represents a problem for endogenous growth theory, it suffices to consider the U.S. evidence using the endogenous growth model developed by Grossman and Helpman (1991). During the time period , the number of scientists and engineers engaged in R&D in the US grew from less that 2, to almost one million, a more than five-fold increase. The steady-state economic growth rate is proportional to the R&D employment level in Grossman and Helpman (1991), so an increase in population size that leads to a five-fold increase in R&D employment should also lead to a five-fold increase in economic growth. But, as Jones (1995a) points out, there has been no upward trends in the economic growth rates of the US, France, Germany or Japan since 195 in spite of substantial increases in population size and R&D employment. The scale effect property is clearly in conflict with empirical evidence. In response to the Jones critique of first-generation endogenous growth models, a variety of second-generation endogenous growth models have been developed that do not have the scale effect property, including Jones (1995b), Kortum (1997), Segerstrom (1998), Young (1998) and Howitt (1999). All of these papers get rid of the scale effect property by making different assumptions about R&D. Jones (1995b) modifies the R&D technology in Romer (199) by assuming that existing knowledge does not contribute as much to the creation of new knowledge, that is, by assuming weaker knowledge spillovers in R&D activities. Kortum (1997) and Segerstrom (1998) modify the R&D technology in Grossman and Helpman (1991) so that innovating becomes progressively more difficult over time. Young (1998) and Howitt (1999) study models where there are two types of R&D: horizontal R&D aimed at developing new product varieties and vertical R&D aimed at developing improved versions of existing products. With just vertical R&D, these models would have the scale effect property but with both types of R&D taking place, the product proliferation resulting from horizontal R&D serves to nullify the scale effect. All of the above-mentioned second-generation models are closed-economy models that look at a single economy in isolation. Significant progress has been made at extending these models to 5

7 allow for international trade. I present two examples of papers that yield important insights using second-generation models of trade and growth. The first example is Dinopoulos and Segerstrom (1999) and is particularly worth discussing for its trade policy implications. They present a model with two perfectly symmetric countries that impose the same tariff on all imported goods, as in Rivera-Batiz and Romer (1991a). But unlike in this earlier work, there are two factors (unskilled and skilled labor) that are used in both production and R&D activities. Furthermore, there is endogenous skill acquisition: workers are born with different ability levels and they choose whether or not to spend time training to become skilled. Dinopoulos and Segerstrom focus on the effects of trade liberalization, that is, a reduction in the common tariff rate. Assuming that R&D is the skill-intensive activity (compared to production), they find that trade liberalization increases the relative wage of skilled workers, induces more workers to choose to acquire skills, and increases the rate of technological change (either temporarily or permanently depending on the R&D specification). This paper is interesting because it helps to explain the large increase in wage inequality that was observed in the 198s. This was a time period when many countries were reducing their import tariffs and opening up to international trade. In the model, trade liberalization not only promotes technological change, it also increases wage inequality within countries (and wage dispersion within industries). The second example is Dinopoulos and Segerstrom (21) and illustrates the usefulness of trade and growth models for thinking about intellectual property rights (IPR) issues. They present a model of North-South trade where firms do innovative R&D to develop higher-quality products in the North and then do adaptive R&D to learn how to transfer their production to the South. The profit flows earned by firms jump up when they are successful in transferring their production to the South and each production transfer is associated with a royalty payment from the foreign affiliate to its parent for the use of the parent firm s technology. When firms are successful in transferring their production to the South, they also become exposed to a positive rate of imitation by southern firms. Dinopoulos and Segerstrom show that stronger IPR protection in the South leads to an increase in the rate of technology transfer to the South within multinational firms and an increase in R&D employment by southern affiliates of northern multinationals. Empirical support for these properties has been found in Branstetter, Fisman and Foley (26), who conclude that improvements in IPR protection resulted in significant increases in technology transfer from US-based multinationals to their affiliates in developing countries. 6

8 2.3 Trade and Growth with Firm-Level Productivity Differences All of the previously-mentioned models of trade and growth have representative firms and assume away any firm-level differences. This modeling approach has been called into question by empirical research showing that there are large and persistent productivity differences among firms in narrowly defined industries and that these productivity differences are important for understanding both trade and growth. In Clerides, Lach and Tybout (1998) and later papers, researchers have found that many firms do not export their products and it is the most productive firms that tend to export. Trade liberalization induces the least productive firms to exit and induces more productive non-exporting firms to become exporters, market share reallocations that contribute in a significant way to productivity growth. In a seminal contribution to trade theory, Melitz (23) developed the first model of international trade with firm-level productivity differences that can account for this empirical evidence. Melitz s model is particularly interesting because it highlights a new mechanism linking trade liberalization with productivity growth. In the model, each firm incurs a fixed cost to develop a new product variety. Then the firm draws from a productivity distribution and learn how productive it is at producing the new variety. With this knowledge, the firm decides whether to exit, just produce for the local market, or incur an additional fixed cost to enter each export market. Melitz solves this symmetric country model for a steady-state equilibrium and he finds that only the more productive firms export, less productive firms choosing to only produce for the domestic market. Solving for the steady-state equilibrium effects of lowering trade costs between countries, he finds that such trade liberalization permanently increases overall productivity in the world economy by inducing the least productive firms to exit and more productive non-exporting firms to become exporters. The model by Melitz (23) has a stationary steady-state equilibrium with zero productivity growth and thus is not really an endogenous growth model. Trade liberalization leads to a one-time increase in productivity. But endogenous growth models with Melitz-type properties have recently been developed. One such model is Gustafsson and Segerstrom (21) where firms develop new product varieties and another such model is Haruyama and Zhao (28) where firms develop higher quality products. In both models, trade liberalization induces the least productive firms to exit and more productive non-exporting firms to become exporters, resulting in faster productivity growth. 7

9 2.4 Empirical Evidence While all of the previously-discussed models of trade and growth have the property that trade liberalization promotes growth (at least temporarily), this is not a general conclusion in the theoretical literature. For example, in a model with asymmetric countries that builds on Romer (199), Grossman and Helpman (199) find when a country reduces its tariff on imports of final goods, this decreases the long-run rate of economic growth in the world economy if the country has a comparative disadvantage in R&D. And even in the symmetric country case, trade liberalization does not have to promote growth. Baldwin and Forslid (2) present a symmetric two-country model where lower trade costs increase the profits that firms earn from exporting but this is exactly offset by the lower profits that firms earn from selling domestically, given the assumption of CES preferences. Lower trade costs have no effect on overall firm profits and consequently no effect on the long run rate of economic growth. Also Baldwin and Robert-Nicoud (28) present a symmetric 2-country model with firm-level productivity differences where, in two out of five R&D specifications, trade liberalization permanently lowers the economic growth rate. I turn now to discussing what empirical researcher have found about this issue. Is there empirical support for the property that trade liberalization promotes growth? Do countries that open up to international trade grow more rapidly? In the empirical literature on trade and growth, perhaps the most influential early paper is Sachs and Warner (1995). They study 79 countries during the time period and categorize each country as open or closed. A country is categorized as being open if: for the duration of the 197s and 198s, the country s average tariff rate was less than 4 percent; non-tariff barriers covered less than 4 percent of trade; its black market exchange rate premium was less than 2 percent; there was no state monopoly on major exports; and there was no socialist economic system. If any of these five conditions is not satisfied, a country is categorized as closed. Using this categorization, Sachs and Warner examine whether the real annual per capita growth in GDP over the time period was higher for open countries than for closed countries. They find a surprisingly large and statistically significant effect: the average rate of economic growth for the open countries was 2.2 percent higher than for the closed countries (regression 7 in table 11). Sachs and Warner conclude that there is strong evidence that protectionist trade policies reduce overall growth when controlling for other variables. Sachs and Warners conclusions have been called into question in a paper by Rodriguez and 8

10 Rodrik (2). They argue that the Sachs-Warner findings are less robust than claimed, because of difficulties in measuring openness, the statistical sensitivity of the specifications, the collinearity of protectionist policies with other bad policies, and other econometric difficulties. For example, Rodriguez and Rodrik point out that the Sachs-Warner dummy variable for openness derives its strength mainly from the combination of the black market premium (BMP) and the state monopoly of exports (XMB) variables. Very little of the dummy s statistical power would be lost if it were constructed using only these two indicators. In particular, there is little action in the two variables that are the most direct measures of trade policy: tariff and non-tariff barriers. The Rodriguez- Rodrik paper has led many economists to be skeptical that open trade policies are significantly associated with economic growth. The latest word on this issue is an important paper by Wacziarg and Welch (28). They study a larger sample of 136 countries during the longer time period from 195 to 2. Wacziarg and Welch use the same five-part criterion for openness as in Sachs and Warner (1995) but instead of categorizing a country as being open if it satisfies the openness criterion during the entire time period, they use the data to identify dates of trade liberalization. During the time period from 195 to 2, there are unique dates of trade liberalization for many countries, years when specific countries switched from being closed to being open. For example, the United Kingdom and the United States were already open in 195, Sweden became open in 196, Japan became open in 1964, Chile became open in 1976, Mexico became open in 1986, and both China and India were still closed in 2. Responding to the Rodriguez-Rodrik critique, Wacziarg and Welch check that the dates of trade liberalization do not just capture changes in the black market premium or state monopoly of exports variables, but also reflect broader liberalization. Since dates of trade liberalization can be identified for many countries in the world, it is conceptually straightforward to ask the question, do countries tend to experience faster or slower economic growth rates after trade liberalization? Using standard statistical techniques for analyzing panel data, Wacziarg andwelch provide an answer to this question. They find that trade-centered reform has, on average, robust positive effects on economic growth rates within countries. For the typical country that switches from being closed to being open, the growth rate of real per capita GDP (income per person) increases by 1.4 percent (see table 5). This estimate of 1.4 percent is both highly statistically significant and economically significant. It means that for a typical country growing at an average annual rate of 1.1 percent before trade liberalization, its average annual growth rate jumps up to 1.1 percent percent = 2.5 percent after trade liberalization. 9

11 3 A Simple Model of Trade and Growth In this section, I present a relatively simple two-country model of trade and growth. The two countries are structurally identical, so everything that happens is one country happens in the other country as well. Trade between the two countries is not free and is subject to positive trade costs. The model is a modified and simplified version of Dinopoulos and Segerstrom (1999). 3.1 Household Behavior There is a continuum of households in each country indexed by ability θ [, 1]. All members of household θ have the same ability level equal to θ, and all households have the same number of members at each point in time. Each household is modeled as a dynastic family whose size grows over time at an exogenously given rate n >. Each individual member of a household lives forever. Letting N denote the number of members of each household at time t =, the population size in each country at time t is N(t) = N e nt. Family-optimization considerations determine the allocation of income across final goods, the evolution of consumption expenditure over time, and the decision whether to become skilled or enter the labour force as unskilled workers. In making these decisions, each family takes prices of final products, wages, and the interest rate as given. Each individual knows her own ability level θ, as do all the firms that might potentially hire her. An individual can enter the labour force as unskilled and earn the wage w L from then on. Alternatively, an individual with ability θ can enter the labour force after spending an exogenously given period of time T in training to become skilled. A skilled worker with ability θ earns a wage θw H from then on and does not earn any income during her period of training or apprenticeship. Thus skilled workers with higher ability levels earn higher wages. I assume for simplicity that the training process does not require any real resources (other than the time of the trainee), and therefore the opportunity cost of becoming a skilled worker equals the discounted value of forgone unskilled wage income. I also assume that income is evenly shared within each family (between employed and trainees) so that, at each point in time, consumption expenditure is the same for each member of a family. The optimization problem of a family with ability θ is max U θ q θ N e (ρ n)t ln u θ (t) dt (1) 1

12 subject to the following constraints: ln u θ (t) 1 ln j λ j q θ (j, ω, t) dω, (2) c θ (t) 1 j p(j, ω, t)q θ (j, ω, t) dω, (3) W θ + Z θ = N c θ (t)e nt e R(t) dt. (4) Equation (1) is the discounted utility of a household with ability θ, where ρ > is the constant subjective discount rate, n > is the exogenous population growth rate, and ρ n > will be assumed to guarantee that the integral in (1) converges. Equation (2) defines the static utility function of each household member, where q θ (j, ω, t) denotes the quantity consumed by an individual with ability θ of a good with j improvements (innovations) in its quality in industry ω [, 1] at time t. The parameter λ > 1 captures the size of each quality improvement and λ j denotes the total quality of a good after j innovations. Since λ j is increasing in j, (2) captures in a simple way the idea that consumers prefer higher quality products. This static utility function with a finite number of industries was introduced in Segerstrom, Anant and Dinopoulos (199). Equation (3) states that per capita consumption expenditure c θ (t) at time t must equal the value of all final goods consumed, where p(j, ω, t) and q θ (j, ω, t) denote the price and quantity of a final product with j improvements in its quality in industry ω at time t. Finally, equation (4) is the standard intertemporal budget constraint. From the perspective of time t =, W θ is the family s discounted wage income and Z θ is the value of the family s financial assets. The right-hand side (RHS) of (4) equals the discounted value of the family s consumption and R(t) t r(s) ds is the market discount factor with Ṙ(t) = r(t) denoting the market interest rate at time t. The formal derivation of the solution to the family s dynamic optimization problem is presented in the Appendix. This problem can be solved in four steps. First, solving for the utility-maximizing allocation of consumer expenditure across products within an industry ω at time t yields that consumers only buy the product(s) in each industry with the lowest quality-adjusted price p(j,ω,t) λ j. Second, maximizing static utility (2) subject to the expenditure constraint (3) yields a unit elastic demand function q θ (j, ω, t) = c θ (t)/p(j, ω, t) for the product(s) in each industry with the lowest quality-adjusted price. A unit elastic demand function is the simplest type of demand function. 11

13 Third, maximizing discounted utility (1) subject to the intertemporal budget constraint (4) yields the usual intertemporal optimization condition ċ θ (t) = r(t) ρ. (5) c θ (t) The differential equation (5) states that per capita consumption expenditure grows over time if and only if the market interest rate exceeds the subjective discount rate. When the market interest rate is relatively high, consumers want to save more now and spend more later, resulting on positive growth in per capita consumption expenditure over time. Fourth, training/employment decisions are made to maximize each family s discounted wage income, which is equivalent to maximizing each member s discounted wage income. The latter depends on whether the individual member earns the unskilled wage or becomes a skilled worker and then earns the skilled wage. It is optimal for an individual with ability θ born at time t to train and become a skilled worker if and only if t e [R(s) R(t)] w L (s) ds < t+t e [R(s) R(t)] θw H (s) ds. (6) The left-hand side (LHS) of inequality (6) equals the discounted wage income of an individual from being employed as an unskilled worker and earning the wage w L from time t on. The RHS of (6) is the lifetime income of a skilled worker, who earns zero income during her training period and θw H from time t + T on. I focus on the model s steady-state equilibrium properties where w L, w H and c θ are all constants over time. Then (5) implies that r(t) = ρ for all t. Condition (6) can be used to determine endogenously the steady-state supply of unskilled labor. Because the RHS of (6) is increasing in θ, whereas the LHS is independent of θ, there exists a level of ability denoted by θ such that (6) holds as an equality. All individuals with ability lower than θ choose to remain unskilled, and all individuals with ability greater than θ undergo training and then enter the labour force as skilled workers. Setting (6) to hold as an equality yields t e ρ(s t) w L ds = t+t e ρ(s t) θ w H ds, which simplifies to w L ρ = e ρt θ w H ρ. Solving for the steady-state value of θ then yields θ = w L w H e ρt. (7) Equation (7) implies that the wage of a skilled worker θw H must always be higher than the wage of any unskilled worker w L. An increase in the duration of training T or in the relative wage of 12

14 unskilled labour w L /w H increases the fraction of the population that chooses to remain unskilled θ. The supply of unskilled labour in each country at time t, L(t), equals the number of individuals in the population that choose to remain unskilled: L(t) = θ N(t). (8) The derivation of the steady-state supply of skilled labour at time t is slightly more complicated. A fraction (1 θ ) of each country s population train and become skilled workers, and therefore (1 θ )N(t) individuals either work as skilled workers or are training to become skilled workers in each country at time t. In this sub-population, the skilled workers are the older individuals, namely, those individuals that were born before t T : t T t T n(1 θ )N(s) ds = n(1 θ ) N e ns ds = (1 θ )e nt N(t). (9) The average skill level of workers θ [θ, 1] that have finished training equals θ +1 2 and therefore the supply of skilled labour at time t, measured in efficiency units of human capital, is given by H(t) = (θ +1)(1 θ ) 2 e nt N(t) or more simply H(t) = [1 (θ ) 2 ] e nt N(t). (1) 2 It is obvious from equations (7), (8) and (1) that a decline in the relative wage of unskilled workers decreases θ and L(t), and increases H(t), resulting in a rise of skilled labour abundance H(t) L(t) in each country. In the steady-state equilibrium, each country s factor supplies grow at the same rate as the population because θ is constant over time: Ḣ(t) H(t) = L(t) L(t) = Ṅ(t) N(t) = n. 3.2 Product Markets There is a continuum of industries in each country indexed by ω [, 1]. In each industry, firms produce final consumption goods using unskilled labour. Firms compete in prices and maximize their expected discounted profits. For every firm that knows how to produce a good, one unit of unskilled labour produces one unit of output and production is characterized by constant returns to scale. Thus, each firm has a constant marginal cost of production equal to w L. There are also trade costs separating the two countries that take the iceberg form: τ > 1 units of a good must be produced and exported in order to have one unit arriving at its destination. Thus, the marginal 13

15 cost of a firm serving the domestic market is w L and the marginal cost of a firm serving the foreign market is τw L. I treat the unskilled wage as the numeraire price (w L = 1), that is, I measure all prices relative to the price of unskilled labour. In each industry, I will refer to the firms that produce the state-of-the-art quality product as quality leaders and I will use the term quality followers to refer to firms producing a product one quality step below the highest-quality product. When a firm wins a R&D race and becomes a quality leader, it receives a patent to exclusively produce the new product and sell it to all consumers in the world. This patent expires (or ceases to be enforced) when further innovation occurs in the industry. All products that are not protected by patents can be produced competitively in both countries. I will refer to the two countries as Home and Foreign. Consider a Home quality leader that exports its product to the Foreign market (the analysis of the exporting behavior of a Foreign quality leader is identical because of structural symmetry between the two countries). Because unit costs of all Foreign quality followers are identical (w L = 1) and Home quality followers have higher unit costs when serving the Foreign market (τw L > w L ), Home leaders compete against a competitive fringe of Foreign followers in the Foreign market (and against a competitive fringe of Home followers in the Home market). Let Q l denote the output that the Home leader sells to Foreign consumers, let P l price that Foreign consumers pay for the state-of-the-art quality product, let Q f of Foreign followers, and let P f denote the denote the output denote the price that Foreign followers charge Foreign consumers. With the competitive fringe of Foreign followers charging the competitive price P f flow earned by the Home leader from selling to Foreign consumers is πl = Pl Q l τq l if Pl λ if Pl > λ. If the price charged by the Home leader is too high (P l = 1, the profit > λ), then all Foreign consumers buy from Foreign followers. The Home leader has to charge a sufficiently low price to attract Foreign consumers (P l λ) and I assume that in the borderline case (P l = λ) where consumers are indifferent, they only buy from the firm selling the higher quality product (the Home leader). Taking into account that consumer demand is unit elastic, the profit flow earned by the Home 14

16 leader becomes πl = P c N (t) l P τ c N (t) l P if Pl λ l if Pl > λ, where c is the per capita consumption expenditure in the Foreign country and N (t) is the number of consumers in the Foreign country. Assuming that τ (1, λ), this profit flow is maximized by charging the limit price P l = λ > 1. In equilibrium the Home leader sells Q l = c N (t)/λ, Foreign followers sell Q f = and the Home leader earns the profit flow [ πl = c N (t) 1 τ ]. λ Note that trade liberalization (τ ) contributes to increasing the profits earned from exporting. Because a Home quality leader faces segmented markets and does not incur the trade cost τ when selling to Home consumers, the analysis of price competition in the Home market is identical to the analysis in the Foreign market when τ = 1. The Home quality leader charges the limit price P l = λ > 1 to Home consumers, the Home leader sells Q l = cn(t)/λ to Home consumers, Home followers sell Q f = to Home consumers and the Home leader earns the profit flow [ π l = cn(t) 1 1 ], λ where c and N(t) are per capita consumption expenditure and population in the Home country. Structural symmetry across the two countries implies that c = c and N(t) = N (t). Therefore, each quality leader (Home or Foreign) exports the state-of-the-art quality product as well as sells to domestic consumers and earns the global profit flow [ π π l + πl = cn(t) τ ]. (11) λ The product market equilibrium has three interesting features. First, only the state-of-the-art quality products are produced and traded. Second, all followers charge the same price P f = P f = 1 which is used as the numeraire, and all quality leaders charge the same price P l = P l = λ > 1 since they are price-constrained by domestic follower firms selling inferior quality goods. Third, trade liberalization (τ ) does not have any effect on relative prices (of domestically produced goods versus imported ones) but increases the global profit flows of quality leaders [τ = π ]. Because trade liberalization has no effect on domestic relative prices in either country, any 15

17 effect that trade liberalization has on relative wages (w H /w L ) must operate through some channel other than the traditional Stolper-Samuelson mechanism. The previously established property that a reduction in τ directly increases the global profit flows of quality leaders will turn out to be significant. 3.3 R&D There are sequential and stochastic R&D races in each industry ω [, 1]. These races result in the discovery of higher-quality products. Only skilled workers can engage in R&D activities, unskilled workers being employed in production activities. All firms participating in a R&D race use the same R&D technology and there is free entry into each race. A firm i that hires h i (ω, t) skilled workers to engage in R&D in industry ω at time t is successful in discovering the next higher quality product with instantaneous probability I i (ω, t) = h i(ω, t) X(ω, t), (12) where X(ω, t) is a function that captures the difficulty of conducting R&D. By instantaneous probability (or Poisson arrival rate), I mean that I i (ω, t) dt is the probability that the firm will innovate by time t + dt conditional on not having innovated by time t, where dt is an infinitesimal increment of time. This R&D technology was introduced in Segerstrom (1998). The returns to R&D investment are independently distributed across firms, across industries, and over time. Thus the industry-wide instantaneous probability of success in industry ω at time t is I(ω, t) = i I i(ω, t) in the Home country and I (ω, t) = i I i (ω, t) in the Foreign country. The global arrival of innovations in each industry is governed by a Poisson process whose intensity equals I(ω, t) + I (ω, t). Higher levels of R&D investment increase the expected frequency of innovations and result in a higher rate of technological change. Concerning the function X(ω, t), I assume that R&D starts off being equally difficult in all industries [X(ω, ) = X for all ω where X > is a constant] and the level of R&D difficulty grows over time according to Ẋ(ω, t) X(ω, t) = µ[i(ω, t) + I (ω, t)], (13) where µ > is a constant. This differential equation captures the notion that ideas that are easier to discover tend to be discovered earlier in time. The assumption µ > is the reason why the model does not have the scale effect property. In the first-generation endogenous growth model by 16

18 Grossman and Helpman (1991), µ = is assumed and consequently the long-run economic growth rate is an increasing function of population size in their model. I solve the model for a symmetric steady-state equilibrium where both Home and Foreign innovation rates are constant over time and do not vary across industries, that is, I(ω, t) = I = I (ω, t) = I for all ω and t. It immediately follows from (13) that X does not vary across industries, that is, X(ω, t) = X(t) for all ω and t. Furthermore, I solve for a steady-state equilibrium where relative R&D difficulty x(t) X(t)/N(t) is constant over time. Thus X(t) grows over time at the constant population growth rate n and it follows that Ẋ(t)/X(t) = µ[i + I ] = µ2i = n fully determines the steady-state innovation rate I = I = n 2µ. (14) Given the steady-state innovation rate, I can solve for the corresponding steady-state growth rate of consumer utility. By substituting for consumer demand q θ = c θ /λ into the representative consumer s static utility function (2), I obtain ln u θ (t) = 1 [ ln λ j(ω,t) c ] θ dω λ = ln c θ ln λ + 1 ln λ j(ω,t) dω, where j(ω, t) is the number of quality improvements in industry ω from time to time t. The last integral in this expression grows over time in the steady-state equilibrium as new higher-quality products are continuously being introduced. The value of this integral equals (I + I )t ln λ or 2It ln λ. Thus, in the steady-state equilibrium, each consumer s utility grows at the deterministic rate g u u θ(t) u θ (t) = 2I ln λ = n ln λ. (15) µ The utility growth rate g u is completely determined by the exogenous rate of population growth n, the R&D difficulty growth parameter µ and the innovation size parameter λ. Utility growth is higher when the population of consumers grows more rapidly, when R&D difficulty increases more slowly over time and when innovations are of larger size. Since this utility growth rate is also the real wage growth rate, it is the proper measure of economic growth in the model. 17

19 Equations (14) and (15) has two important implications. First, they imply that public policy changes like trade liberalization (a decrease in τ) have no effect on the steady-state rate of innovation I and hence the steady-state rate of economic growth g u. In this model, growth is semi-endogenous. I view this as a virtue of the model because both total factor productivity and per capita GDP growth rates have been remarkably stable over time in spite of many public policy changes that one might think would be growth-promoting. For example, plotting data on per capita GDP (in logs) for the US from 188 to 1987, Jones (1995a) shows that a simple linear trend fits the data extremely well. This data leads me to be skeptical about models where public policy changes have large longrun growth effects. Second, they imply that the level of per capita income in the long run is an increasing function of the size of the economy (because positive population growth is associated with positive economic growth). Jones (25) has a lengthy discussion of this weak scale effect property and cites Alcala and Ciccone (24) as providing the best empirical support. Controlling for both trade and institutional quality, Alcala and Ciccone (24) find that a 1 percent increase in the size of the workforce in the long run is associated with 2.5 percent higher GDP per worker R&D Incentives There is a global stock market that channels consumer savings to firms that engage in R&D. Because there is a continuum of industries with simultaneous R&D races, consumers can diversify completely the industry-specific risk and earn the risk-free interest rate r = ρ. Each firm engaged in R&D issues a security that pays the flow of monopoly profits if the firm wins the R&D race and zero if it does not win the race. Let v(t) denote the expected discounted profits of a successful firm (i.e., quality leader) in each industry at time t. Because each quality leader is targeted by R&D firms in both countries that try to discover the next higher quality product, the shareholder suffers a loss v(t) if further innovation occurs. 2 This event occurs with probability [I + I ]dt during the time interval dt, whereas the event of no innovation occurs with probability 1 [I + I ]dt. Over 1 In spite of the arguments in Jones (25), the issue of whether economic growth is semi-endogenous (public policies have no long-run growth effects) or fully-endogenous (public policies have long-run growth effects) remains controversial. For example, Ha and Howitt (27) present evidence that fully-endogenous growth models have better empirical support than semi-endogenous growth models. I think that their analysis has an important limitation. Ha and Howitt implicitly assume that convergence to steady-state is fast, so that with 5 years of data, they can just focus on the steady-state implications of growth models. This assumption is called into question in Steger (23), who calibrates a semi-endogenous growth model using US data and finds that convergence to steady-state is slow: it takes almost 4 years to go half the distance to the steady-state. With such slow convergence, I think that future tests of semi-endogenous growth theory should take into account the transition path implications of the models. 2 Because industry leaders have less to gain from innovating than follower firms, all R&D is done by follower firms in equilibrium. For a model where industry leaders have cost advantages and thus engage in R&D, see Segerstrom (27). 18

20 the time interval dt, the shareholder of a stock issued by a successful R&D firm receives a dividend π(t)dt and the value of the firm appreciates by v(t)dt. The stock market values the firm so that its expected rate of return just equals the riskless rate of return r: v(t) v(t) [1 (I + I )dt]dt v(t) [I + I ]dt + π(t) dt = r dt. v(t) v(t) Dividing both sides by dt and then taking the limit as dt yields v(t) v(t) [I + I ] + π(t) v(t) = r, which can be rewritten as v(t) = π(t) r + I + I v(t)/v(t). (16) The global profit flow π earned by a quality leader is appropriately discounted using the instantaneous market interest rate r and the instantaneous probability I + I of being driven out of business by further innovation (the creative-destruction effect). Also taken into account in (16) are the capital gains v/v that accrue to the firm as the world economy grows. Consider a firm i that is located in the Home country and engages in R&D. This firm chooses its R&D intensity I i to maximize its expected discounted profits, that is, it solves the problem max I i v(t)i i dt w H X(t)I i dt. Free entry into each R&D race drives these expected discounted profits down to zero and implies that v(t) = w H X(t), which can be rewritten as v(t) X(t) = w H w L. (17) In steady-state equilibrium, the reward for innovating v(t) increases over time as the economy grows but X(t) also increases over time as innovating becomes progressively more difficult. The ratio v(t)/x(t) measures the reward for innovating relative to its cost and can be thought of as the relative price of innovation. Equation (17) implies that there is a direct relationship between the relative price of innovation v(t)/x(t) and the relative wage of skilled workers w H /w L. This is a Schumpeterian version of the Stolper-Samuelson mechanism. I will show that trade liberalization increases the relative price of innovation and consequently the relative wage of skilled workers. Since X(t) grows at the constant rate n, the free entry condition v(t) = w H X(t) implies that v(t) also grows at the constant rate n. Using (11) and (14), it follows that the free entry condition 19

21 becomes v(t) = cn(t) [ 2 1+τ ] λ ρ + I + I v/v = w HX(t). Dividing both sides by N(t), I obtain the steady-state R&D condition: c [ 2 1+τ ] λ ρ + 2I n = w Hx. (18) The LHS is the market size-adjusted benefit from innovating and the RHS is the market sizeadjusted cost of innovating. In steady-state calculations, I need to adjust for market size because market size changes over time. The market size-adjusted benefit from innovating is higher when the average consumer buys more (c ), there are lower trade costs associated with exporting (τ ), future profits are less heavily discounted (ρ ), quality leaders are less threatened by further innovation (I ) and quality leaders experience larger capital gains over time (n ). The market size-adjusted cost of innovating is higher when skilled workers earn a higher wage (w H ), and innovating is relatively more difficult (x ). 3.5 Labour Markets Labour markets are perfectly competitive, workers are perfectly mobile across industries and wages adjust instantaneously to equate labour demand and labour supply. Because both countries are structurally identical, I concentrate on the derivation of equilibrium for the Home country. The demand for unskilled labour comes from production by quality leaders since only quality leaders produce in equilibrium and only skilled labour is employed in R&D activities. The assumption of structurally identical countries implies that 5 percent of the world s quality leaders are Home firms and 5 percent are Foreign firms. In industries with a Home quality leader (exporting industries), total output produced equals Q l + τq l. The Home quality leader produces output Q l for the Home market and taking into account trade costs, the Home quality leader needs to produce output τq l at Home in order to sell output Q l in the Foreign market. In industries with a Foreign quality leader, total Home output is zero. Therefore, the total output produced in the Home country is q Q l + τq l 2 = cn(t)(1 + τ), 2λ where q is the average quantity of final output produced in each industry. The Home demand for unskilled labour is given by q and the supply of unskilled labour is given by equation (8). Full 2