Tariffs and Schumpeterian growth

Journal of International Economics 42 (1997) 425–452

Tariffs and Schumpeterian growth a b, Elias Dinopoulos , Constantinos Syropoulos * a

b

Department of Economics, University of Florida, Gainesville, FL 32611, USA Department of Economics, Florida International University, University Park Campus, Miami, FL 33199, USA

Abstract The paper develops a dynamic multi-country, multi-commodity model of Schumpeterian growth, trade, and tariffs. The presence of a nontraded final good sector generates differences in long-run growth across countries. Furthermore, if the growth intensity of the nontraded good is lower than the growth intensity of traded goods, then the liberalization of trade raises the long-run growth of all trading partners. The paper also analyzes the implications of multilateral, bilateral and unilateral schemes of trade liberalization for long-run growth and welfare. Keywords: Economic growth; R&D; Tariffs; Trade liberalization; Bilateralism; Multilateralism JEL classification: F10; F12; F13; F15; O32; O41

1. Introduction The precise theoretical connection between trade liberalization and long-run economic growth has not been investigated adequately.1 There are at least two good reasons for this important gap in trade theory. First, the neoclassical growth theory, which dominated the thinking of mainstream economists until recently, does not leave any room for policy effects on long-run economic growth. Second, a comparative analysis of trade liberalization schemes (e.g. unilateral, bilateral or *Corresponding author. Tel.: 001 305 348 2592; fax: 001 305 348 1524; e-mail: [email protected]. 1 Bhagwati (Bhagwati, 1988, Chapter 1) provides an excellent discussion of the relationship between growth and trade liberalization in the postwar period. 0022-1996 / 97 / $17.00  1997 Elsevier Science B.V. All rights reserved PII S0022-1996( 96 )01477-8

426

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

multilateral tariff reductions) requires a general equilibrium framework with at least three trading countries. Until recently, this requirement rendered the analysis difficult, if not intractable. A small but growing body of literature has examined the effects of tariffs on growth and welfare. For example, Brock and Turnovsky (1993) analyzed the impact of import tariffs on growth and welfare in a small neoclassical economy. They found that tariffs generate short-run benefits but long-run costs for the intervening country. Galor (1994) also examined the effects of income redistribution, induced by tariffs, on welfare of a small, overlapping generations economy. He identified sufficient conditions under which an infinitesimal tariff raises short-run and long-run welfare.2 Beginning with the work of Romer (1986), developments in endogenous growth theory made possible the construction of simple formal models that place at center stage the relationship between trade policy changes and long-run growth. Segerstrom, Anant and Dinopoulos (Segerstrom et al., 1990) analyzed the impact of prohibitive tariffs in a multi-sectoral, general-equilibrium model of North– South trade and growth. They established that, as the number of protected industries in the North increases, resources shift from research activities to manufacturing of final goods, resulting in a decline in global growth. Grossman and Helpman (1991 Chapter 6) considered the welfare implications of infinitesimal tariffs in a model of a small open economy with endogenous innovations occurring in a sector of nontraded intermediate products. They found that, under certain conditions, a small tariff increases long-run growth and welfare. Rivera–Batiz and Romer (1991a) analyzed the effects of symmetric, across-the-board tariffs on global growth in a two-country model with innovation taking the form of increased varieties in the traded goods sector. They found a U-shaped relationship between tariffs and long-run growth and proposed a useful decomposition of supply-side mechanisms that transmit the effects of protection on growth. Dinopoulos and Segerstrom (1996) utilized a two-country model of growth through endogenous quality improvements to analyze the effects of symmetric tariffs, imposed by two structurally identical countries, on technological progress and long-run growth. They also found a U-shaped relationship between tariffs that protect technologically inferior firms and growth. Osang and Pereira (1996) studied the effects of tariffs on growth and welfare in a small economy with endogenous growth based on human capital accumulation. They showed that tariffs reduce growth even in the short run and that their welfare effects are generally ambiguous. This paper investigates the effects of tariff changes on long-run Schumpeterian growth and welfare. (Schumpeterian growth is a type of endogenous growth based on Schumpeter’s (Schumpeter, 1942) description of technological change through

2

A related strand of the literature also addressed the effects of moving from autarky to free trade on long-run growth and welfare (see, e.g., Rivera–Batiz and Romer, 1991b and Taylor, 1994).

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

427

creative destruction.3 Dinopoulos (1994) provides an overview of Schumpeterian growth theory.) Our model differs from the ones in the studies mentioned above in a number of respects. For example, we consider a three-country setting with a final nontraded good produced in each country and investigate demand-based channels of tariff changes and trade liberalization strategies. Additionally, we abandon the assumption of a continuum of identical industries (sectors) and allow for interindustry asymmetries in technological opportunities, productivity of labor in R&D and expenditure shares. In addition to the nontraded final good, there are three final traded goods in our model.4 Labor is the only primary factor of production; it can be used to produce the final goods and R&D services. R&D services result in random discoveries of better production techniques which enhance the productivity of labor employed in the manufacturing of final goods. In other words, Schumpeterian growth arises because of endogenous process innovations. To have determinate trade patterns, we suppose that each country i has a relative productivity advantage in good i; thus, country i exports good i and imports the other two traded goods. We assume there are no technological spillovers and that firms located in any one country are able to improve the country’s state-of-the-art production techniques in the export and nontraded final good sectors. These assumptions preserve trade patterns and ensure that they are independent from tariff policies, thereby rendering the analysis tractable.5 The model has a unique steady-state equilibrium with no transitional dynamics. As is standard in models of Schumpeterian growth, the expected instantaneous utility of consumers grows over time. The analysis generates several novel insights. For example, a reduction in a country’s tariffs causes the country’s (real) consumption expenditure to fall (owing to tariff revenue effects) and shifts relative expenditures toward the traded and away from the nontraded good sectors, thereby affecting the intersectoral allocation of resources. These expenditure changes raise the profitability of R&D in the country’s export sector and reduce the profitability of R&D in its nontraded sector (Proposition 1). The result is a demand-based mechanism that links tariffs to growth, which is absent in models of endogenous growth mentioned earlier. If the nontraded good is absent, tariff changes will not affect the intersectoral allocation of resources and, therefore, will not impact upon long-run growth. The model generates differences in the long-run growth of national standards of living (measured by the growth of a representative consumer’s expected instanta-

3

Early studies of Schumpeterian growth include Segerstrom et al. (1990); Grossman and Helpman (1991); Aghion and Howitt (1992). 4 The model can be readily generalized to incorporate N(.3) countries and N 11 final goods without changing the qualitative results of the paper. 5 Feenstra (1996) also adopted the assumption of no international spillovers in a model of horizontal product differentiation and unequal growth and provided a detailed discussion of its empirical relevance.

428

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

neous utility). Although trade equalizes the component of growth originating in the traded good sectors, it does not equalize the component of growth with roots in the nontraded sector. Countries with higher growth in the nontraded sector experience higher long-run growth in their living standards relative to other countries. The extent to which long-run growth differs across countries depends on inter-country differences in size, on relative R&D labor productivities across sectors and countries, and on national tariff policies (Proposition 2). This comparative growth result complements the analysis of Feenstra (1996) of unequal growth rates in a model with cross-price effects, where the degree of inequality in growth depends on differences in country size and the elasticity of substitution between final goods. The above findings reveal some of the dangers of drawing policy conclusions on the basis of cross-country growth regressions (see Barro, 1991). Consider a world consisting of symmetrically positioned countries which differ only in their tariff levels. In this world, the countries with the higher tariffs would devote more resources to their nontraded sectors and thus would exhibit relatively higher levels of growth. Accordingly, cross-country growth regressions would identify the existence of a positive correlation between growth and protection. Yet, this finding does not imply that a country that raises its tariffs would experience higher levels of growth. We show that the effect of tariffs on a country’s growth is determined by the relative growth potential of each sector (captured by sectoral growth intensities that depend on technological opportunities, labor productivities and consumer preferences). An increase in a country’s import tariffs causes the country’s long-run growth to fall (rise) if the growth intensity of its export sector is higher (lower) than the growth intensity of its nontraded good sector (Lemma 1). In addition, such tariffs adversely affect growth in the living standards of other countries because tariffs retard growth of the intervening country’s export sector. Consequently, in the empirically relevant case where the nontraded sector is less progressive than the traded sectors, higher tariffs reduce growth of all countries. Cross-country studies that do not separate international growth linkages from the effects of policies on the intersectoral allocation of resources within countries might lead to the erroneous conclusion that trade liberalization retards national long-run growth. If the nontraded good is absent or if sectoral growth intensities do not differ (as is commonly assumed in models of Schumpeterian growth with a continuum of identical industries), then tariff changes do not affect long-run growth of the policy active country. If the nontraded good is present and sectoral growth intensities differ, then, unlike Rivera–Batiz and Romer (1991a) and Dinopoulos and Segerstrom (1996), the relationship between tariffs and long-run growth is monotonic. To shed further light on the relationships among trade liberalization, growth, and welfare, we analyze the effects of three liberalization schemes: unilateral, bilateral and multilateral. We find that these trade liberalization schemes raise

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

429

growth in all countries when the nontraded sector is less progressive than the traded good sectors, which is a sufficient condition (Proposition 3). This substantiates the notion that growth-oriented governments may very well view Europe 1992, the formation of NAFTA, the possible reduction of Japanese trade barriers (perhaps through U.S. pressure), and the efforts to reduce trade obstacles multilaterally under the auspices of the WTO as complements rather than as substitutes.6 Our three-country framework also allows us to compare the relative merits of the trade liberalization schemes with respect to growth and welfare. We find that, under conditions of symmetry, a given degree of global trade liberalization generates a larger long-run growth for every country if it takes the form of multilateral as opposed to bilateral or unilateral tariff cuts. Generally, the impact of tariffs on welfare is ambiguous. This is so because even if trade liberalization promotes growth, its level effect remains ambiguous owing to second-best considerations.7 We provide sufficient conditions, however, under which the welfare ambiguities of trade liberalization disappear. The building blocks of the model, its basic assumptions and an analysis of the steady-state equilibrium are presented in Section 2. Section 3 investigates the effects of tariff changes on long-run Schumpeterian growth. Section 4 explores some of the welfare implications of trade liberalization. Section 5 offers some concluding comments. The proofs to all propositions are relegated to Appendix A. Appendix B contains the formal algebra of several arguments and is available from the authors upon request.

2. A model of Schumpeterian growth and trade This section develops the model by drawing elements from Taylor (1993), Dinopoulos (1994), and Dinopoulos and Kreinin (1996). There are several 6

The growth-enhancing effects of regional economic integration provide a novel explanation of the widespread belief among policy makers that participation in a trading bloc is a ‘‘good thing’’, which is consistent with the facts that no member of the European Union has left the union and, in addition, several countries in Europe and in the Americas have expressed their desire to join the EU and NAFTA, respectively, in the future. Interestingly, our model also captures the notion that even countries that remain outside a regionally integrated area may enjoy positive spillover effects owing to economic growth. This may partly explain why the United States had an economic interest to support the creation and enlargement of the European Community since its inception in the 1950s. Finally, our basic finding is also consistent with the notion that growth-oriented considerations played an instrumental role in the current U.S. administration support of NAFTA and the Uruguay Round of the GATT negotiations. 7 See Bhagwati and Srinivasan (1983), Chapter 27, for a review of the early literature on uniform versus preferential tariff reductions and welfare. Recent studies on preferential trading arrangements include Kennan and Riezman (1990), Krugman (1991), Bagwell and Staiger (1993), and Bond and Syropoulos (1996a), (1996b).

430

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

differences, however, between this model and the ones in the above studies. None of these studies investigated the effects of tariff policies on long-run growth explicitly and none of these studies analyzed the role of nontraded goods. The model consists of three countries and four final goods, one of which is nontraded. Labor is the only factor of production which can be allocated to two broadly defined activities: manufacturing of final goods and production of R&D services. R&D services are needed for the (stochastic) discovery of better production techniques that increase the productivity of labor in manufacturing of final goods. Labor can move freely and costlessly across activities within each country, so at each instant in time workers receive the same reward regardless of where they are employed. Following the practice of earlier studies of endogenous growth, we assume that every country’s labor endowment is fixed over time. The empirical validity and relevance of this assumption has been recently questioned by Jones (1995a) because it results in explosive growth equilibria in the presence of positive population growth, which is contrary to time series evidence. Two approaches have been adopted to remove what are now called intertemporal growth ‘‘scale effects.’’ The first has been proposed by Young (1995) who developed a closed economy model with horizontal and vertical product differentiation. Endogenous quality increments generate endogenous long-run growth, whereas the rate of variety accumulation is proportional to the exogenous rate of population growth. The second approach has been proposed by several recent studies (e.g. Jones, 1995b; Dinopoulos and Segerstrom, 1996; Kortum, 1996). This approach removes growth scale effects by assuming that the effectiveness of R&D diminishes over time. We adopt the assumption of constant labor endowments because the empirical validity of studies without intertemporal growth scale effects has not been unequivocally established yet. However, if the R&D difficulty is assumed to be proportional to the size of the market, captured by the number of individuals consuming a good (as in a specification proposed in Dinopoulos and Segerstrom, 1996), the results of the present paper remain valid. Process innovation is the engine of Schumpeterian growth in the model. It is endogenous, sector specific, and modeled through stochastic and sequential R&D races. The instantaneous probability of discovering a better production technology in each sector during an R&D race is equal to the quantity of R&D resources devoted to the race. Thus, more R&D resources increase the frequency of innovations and accelerate the rate of technological progress. The winner of each R&D race enjoys temporary monopoly profits until it is replaced by the winner of the next R&D race. These temporary monopoly profits fuel the process of innovation and growth through creative destruction. The arrival of innovations for each good is governed by a Poisson process, the intensity of which is equal to sectoral R&D investment. The random intervals between innovations follow an exponential distribution. There is a stock market in each country that channels consumer savings to firms

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

431

engaged in R&D. The instantaneous interest rate clears the stock market at each instant in time. The representative consumer in each country maximizes her expected discounted lifetime utility, each firm maximizes its expected discounted profits, and the labor market in each country clears at each instant in time. There is free entry in each R&D race, which by symmetry drives the expected discounted profits of firms conducting R&D to zero. Consumers and firms take the tariffs imposed by governments as given, and tariff revenues are redistributed to consumers in a lump-sum fashion. By assumption, tariffs are the only policy instruments used by governments. (The analysis can be easily extended to consider other instruments.) In order to simplify the analysis and exposition, we focus on symmetric patterns of trade. Specifically, we specify technology in such a way so that it induces every country to produce two final products, one of which is traded and the other is not. Each country can improve the productivity of labor employed in these sectors through technical change. Technical change can come about through the production of nontraded R&D services.8 Technological opportunities (measured by quality increments), R&D labor productivities, and expenditure shares can differ across industries within a country. Throughout the paper, superscripts will refer to countries and subscripts will identify commodities. Also, where appropriate, subscripts will identify a typical firm participating in an R&D race.

2.1. Consumer behavior The intertemporal utility function of the representative consumer in country i is `

E

U ; e 2rt ln(u i (t)) dt, ; i [ N ; h1, 2, 3j i

(1)

0 i

where r .0 is the (constant) subjective discount rate, and ln(u (t)) is the consumer’s instantaneous utility at time t. The function u i (t) takes the Cobb– Douglas form

P [d (t)] , where a . 0 and O a 5 1. 3

3

u i (t) ;

j 50

i j

aj

j

j

(2)

j 50

i

d j (t) is the quantity of good j demanded by the representative consumer in country i at time t. At time t, the consumer allocates her instantaneous consumption expenditure 8

This assumption can be relaxed but is adopted here because it allows us to bypass problems related to endogenous determination of trade patterns.

432

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

E i (t) across all available goods. Solving the consumer’s static optimization problem, we obtain the instantaneous demand functions d ij (t) 5 aj E i (t) /p ji (t), ; j 5 0, 1, 2, 3 and ;i [ N i

(3) i

where p j (t) denotes the price of good j in country i. Let L represent the number of consumers in country i and assume that each individual is endowed with one unit of labor. The aggregate demand for good j in country i then is D ij (t)5L i d ji (t). The indirect utility of the representative consumer can be obtained by substituting Eq. (3) into Eq. (2) and then into Eq. (1). This consumer maximizes her expected discounted lifetime indirect utility by allocating her income between consumption expenditure and savings. Appendix B solves the intertemporal optimization problem and derives the following differential equation: E~ i (t) ]] 5 r i (t) 2 r, ; i [ N E i (t)

(4)

where r i (t) is the instantaneous interest rate. Let q j (t) and t ij (t) respectively denote the world price and the ad-valorem tariff (tax) that country i levies on its imports of good j at time t, and define T ij (t);11t ij (t). Then the domestic and world prices for country i’s importables will satisfy p ij (t)5T ij (t)q j (t). For simplicity, we will assume that no country intervenes in its export and nontraded goods markets, so T ij (t)51 and p ij (t)5q j (t) if good j is exported or not traded. Let Y ij (t) and Yj (t);o i e N Y ji (t) respectively denote the expenditure on good j by country i and the world as a whole, measured at world prices. Utilizing Eq. (3), we obtain: q j (t)D ij (t) 5 Y ij (t), where Y ij (t) ; aj L i E i (t) /T ij (t), ; j 5 0, 1, 2, 3

FO G

D hj (t) 5 Yj (t).

q j (t)

(5a) (5b)

h[N

Our analysis focuses on steady-state equilibria, so time arguments of functions and variables can be suppressed without loss of generality.

2.2. Product markets and the pattern of trade Let X ij and n (i, j)e h0, 1, 2,...j respectively denote the output of good j and the number of process innovations undertaken in industry j of country i. Also, let mj .1 and L ij respectively denote the increment in labor productivity per innovation in industry j and the amount of labor allocated to manufacturing good j in country i. The following equations describe the production functions of final goods at time t:

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

i j

X 5

H

n (i, j ) i m 11 Lj j

L

i j

if j 5 0, i if j ± 0, i

433

(6)

Eq. (6) states that one unit of labor in country i can produce m 011 n (i,0) units of n (i,i ) the nontraded good 0 or m 11 units of traded good i. It also states that one unit i of labor can produce one unit of any traded good j that is not identified with country i. Together these equations imply that country i has a comparative advantage in good i and therefore exports this good in exchange for imports of good j (±0, i) from its trading partners. This pattern of trade emerges at time zero when n (i, j)50 because mj .1. Endogenous innovations in every country i raise n (i, j) and therefore reinforce the initial trade pattern. Eq. (6) also captures the notion that knowledge of production techniques does not cross national borders and is consistent with the model’s Ricardian production structure. This production structure implies that tariffs can be viewed as rentextracting devices that transfer foreign profits to domestic residents (see Brander and Spencer, 1981 and Romer, 1994 for similar treatments of tariffs). Consider now the firm that wins an arbitrary race, say the race that results in innovation n (i, j). This firm reduces its marginal cost of manufacturing good j(50, i) from w i /m nj (i , j ) to w i /m j11 n (i , j ) where w i is the wage rate in country i. The closest competitor to the winner of the n (i, j) race, also located in country i, has a n (i , j ) marginal cost equal to w i /m nj (i , j ) which is strictly larger than w i /m 11 . The j profits of the winner of the n (i, j) race are maximized at a price set slightly below the marginal cost of its closest competitor (Bertrand competition). Consumers buy the product which uses the state-of-the-art technology, even if the winner of the n (i, j) race charges a price equal to the marginal cost of its closest competitor. The instantaneous profit for the winner of an arbitrary race n (i, j) in country i’s sector j(50, i) is

p i0 5 [ p 0i 2 w i /m 011 n (i,0) ][D 0i ] p ii 5 [qi 2 w i /m i11 n (i,i ) ]

(7a)

FO G

D hi .

(7b)

h[N

The expression in the first bracket of Eq. (7a) ((7b)) denotes the instantaneous, per-unit profit flow of the winner of the n (i, 0)21 race in the nontraded good sector (the n (i, i)21 race in the export sector) of country i. The expression in the last bracket of Eq. (7a) ((7b)) corresponds to the aggregate demand for country i’s nontraded (exported) good. Utilizing Eq. (5a) and Eq. (7a), along with p i0 5w i / m n0 (i,0) and qi 5w i /m in (i , i ) yields

p i0 5 [1 2 1 /m0 ] p 0i D 0i 5 [1 2 1 /m0 ]Y 0i

(8a)

p ii 5 [1 2 1 /mi ]qi [Sh[N D hi ] 5 [1 2 1 /mi ]Yi .

(8b)

434

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

Since the mj s in Eq. (8a) and (8b) are constant, it follows that the profit flow of the winner of the n (i, j)21 R&D race is proportional to the aggregate expenditure on good j(50, i). Notice that Bertrand competition, which results in limit pricing, exerts a downward pressure on product prices. Every time an innovation occurs, the increase in output is met with a corresponding fall in product prices. The Cobb–Douglas structure of preferences abstracts from cross-price effects and results in constant sectoral expenditures over time. Thus, in a steady-state equilibrium, aggregate consumption expenditure must remain constant, which by Eq. (4) implies r i (t) 5 r ;

(9)

that is, the steady-state instantaneous interest rate is equal to the (constant) subjective discount rate.9

2.3. The market for innovations In addition to manufacturing the nontraded good 0 and the traded good i, country i devotes resources to R&D services that improve the productivity of labor employed in manufacturing. Let R ijk denote the quantity of R&D services devoted by firm k to an arbitrary R&D race in sector j(50, i) in country i. R j ki dt is firm k’s instantaneous probability of discovering the state-of-the-art process innovation that raises the number of innovations from n (i, j) to 11 n (i, j), where dt is an infinitesimal time increment; thus, 12R j ki dt is the instantaneous probability that firm k will not discover the new process innovation. R ij dt5o k R j ik dt is the sector-wide instantaneous probability of success in sector j(50, i). This formaliza9

Constancy in consumption expenditure measured in labor units is consistent with a steady-state equilibrium in which quantities consumed grow because, every time an innovation occurs, the upward jump in sectoral output is matched by an instantaneous downward jump in its price. Eq. (3) and limit pricing by firms ensure the emergence of this result. The assumption of logarithmic instantaneous utility function introduces a convenient additive separability between changes in expenditures and changes in prices determining quantities consumed. Because the representative consumer takes prices as given, she chooses aggregate expenditure rather than aggregate consumption when she maximizes her intertemporal utility. Thus, in the long-run equilibrium, the instantaneous interest rate equals the subjective discount rate and the continuous decline in prices generates endogenous growth of per capita real consumption measured by subutility ln (u i ). Taylor (1993) and Feenstra (1996), among others, have obtained the same result in endogenous growth models with process innovations. Endogenous growth models that do not consider a logarithmic instantaneous utility function (i.e. Romer, 1986; Aghion and Howitt, 1992; King and Levine, 1993; Osang and Pereira, 1996) use the final consumption good as the numeraire. In this class of models, consumption coincides with consumption expenditure and, therefore, the long-run growth rate of per capita consumption (i.e. the endogenous growth rate) is equal to the difference between the instantaneous interest rate and the (constant) subjective discount rate.

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

435

tion of R&D technology states that the arrival of innovations follows a Poisson process with intensity R ij . We also assume that one unit of labor generates uj units of R&D services in sector j(50, i), where uj is a positive constant output–input ratio.10 The flow of instantaneous profits induces firms to participate in R&D races, which are assumed to be sequential and sector-specific. Letting S ij denote the expected discounted profits of a successful innovator during an arbitrary R&D race, we will have

p ij p ij ]] S ji 5 ]] 5 , for j 5 0, i. r i 1 R ji r 1 R ji

(10) i

A successful innovator discounts the flow of instantaneous profits p j by the market interest rate r i (which by Eq. (9) is equal to the subjective discount rate r ), plus the industry-wide instantaneous probability R ij that the next innovation will occur (which will terminate her temporary monopoly power.)11 Consider now the maximization problem of an arbitrary firm k participating in a typical R&D race in sector j of country i. The expected discounted profits of this firm are given by S ij R ijk dt 2 w i (R ijk /uj ) dt.

(11)

The first term in Eq. (11) is the expected discounted benefit from participating in the R&D race. At each instant during the race, firm k can obtain S ij with instantaneous probability R j ki dt. The second term in Eq. (11) represents the (labor) cost of participating in the race. Firm k hires R j ik /uj ( j50, i) workers and pays each worker the prevailing wage w i for an infinitesimal period of time dt. Each firm in a race chooses R ijk to maximize the expression in Eq. (11). Free entry into each R&D race drives this expression to zero. Even though the size of 10

This formulation of R&D technology implies instantaneous constant returns. In the absence of a continuum of industries constant instantaneous returns to R&D do not yield unorthodox comparative steady-state results. See Houser (1994) and Segerstrom (1995) who provide more details on the role of instantaneous diminishing returns to R&D in the context of Schumpeterian growth models. 11 Eq. (10) can be derived from the definition of expected discounted profits `

S ij 5

0 i

F

z

E Ep exp(2rx) dx i j

0

G

R ij exp(2R ij z) dz

where R j is the intensity of the Poisson process that governs the arrival of innovations at the steady-state equilibrium. The term in square brackets is the flow of instantaneous profits discounted to time zero when the innovation occurs. Monopoly profits last for a random time interval equal to z.0. The next innovation occurs at time z, variable z is exponentially distributed with parameter R ij , and the expression R ij exp(2R ij z) is the probability that the next innovation occurs at time z. The outer integral is the expectation operator over variable z. Eq. (10) is obtained after performing the integration.

436

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

each firm is indeterminate, the zero profit condition helps determine the sectoral level of R&D investment R ij . From Eq. (11) we have i

i

S j 5 w /uj .

(12)

Combining Eq. (10) with Eq. (12), utilizing Eqs. (8a) and (8b), and rearranging terms in the resulting expressions yields

F G F G

Ri 1 r ]0 5 1 2 ] (Y 0i /w i ) 2 ], u0 m0 u0

(13a)

R ii 1 r ] 5 1 2 ] (Yi /w i ) 2 ]. ui mi ui

(13b)

The expressions in Eqs. (13a) and (13b) reveal that the R&D investment in sector j is larger the larger is aggregate expenditure on good j, measured in labor units of the country producing it.

2.4. Labor markets The labor market in each country is perfectly competitive and ensures that the wage rate adjusts so that the overall quantity of labor demanded is equal to the fixed supply. There are four components to the demand for labor in country i: the demand for labor, R ij /uj , by firms engaged in R&D in sectors j(50, i); and the demand for labor, L ji , by the firm that manufactures a final good using the state-of-the-art technology, which is L i0 5[1 /m0 ](Y i0 /w i ) and L ii 5[1 /mi ](Yi /w i ) for 12 the nontraded and the exported goods, respectively. The full employment of labor condition for a typical country i can thus be written as:

F G

FG

R i0 R ii 1 1 ] 1 ] 1 ] (Y i0 /w i ) 1 ] (Yi /w i ) 5 L i . u0 ui m0 mi

(14)

From Eqs. (13a) and (13b) and the above it follows that the sectoral demands for labor in country i’s nontraded and export sectors are (Y i0 /w i )2 r /u0 and (Yi /w i )2 r /ui , respectively. Consequently, Eq. (14) can be rewritten as i

i

i

i

(Y 0 /w ) 1 (Yi /w ) 5 L 1 r /u0 1 r /ui ,

(15)

which indicates that the sum of aggregate (real) expenditures on country i’s nontraded and exported goods is constant and invariant to changes in tariffs. 12

The expressions for L i0 and L ii can be derived as follows. Equilibrium in country i’s nontraded good and export sectors requires D i0 5X i0 and o h D hi 5X ii , respectively. Utilizing Eqs. (5a) and (5b) and Eq. n (6), these conditions can be rewritten as Y i0 /p i0 5L i0 m 11 and Yi /qi 5L ii m i11 n , respectively. Price 0 competition in product requires p i0 5w i /m 0n and qi 5w i /m ni . Substituting these expressions in the last two equations and solving for L i0 and L ii , respectively, leads to the desired expressions.

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

437

2.5. Steady-state market equilibrium Because both R&D investments and consumption expenditures are choice variables, the model does not have any transitional dynamics, so we can focus on steady-state analysis.13 Appendix B describes the structure and functioning of national stock markets. These markets channel consumer savings to firms engaged in R&D in each country and diversify aggregate risk. By Walras Law, the stock market will be in equilibrium if all other markets are in equilibrium. In this paper we assume that national savings are used to finance only domestic R&D investments and, consequently, we abstract from international capital flows. This implies that every country’s trade account will be balanced at each instant in time, i.e.

O (q D ) 5 O (q D ). i

h i

h±0,i

i j

j

(16)

j ±0,i

The left-hand side (LHS) of Eq. (16) is the value of country i’s exports evaluated at world prices. The right-hand side (RHS) of Eq. (16) is the value of country i’s imports also evaluated at world prices. Adding qi D ii to both sides of Eq. (16) and utilizing Eqs. (5a) and (5b) yields

O (q D ) 5O (q D ) ⇒ Y 5O Y . i

h[N

h i

j

j ±0

i j

i j

i

j ±0

These equations state that the world expenditure on country i’s exported good must be equal to country i’s expenditure on all traded goods. Utilizing the definition for Y ij from Eq. (5a), this relation can be rewritten as

F G

O

wi (Yi /w i ) 5 ] (Y i0 /w i ), where w i ; (aj /T ij ). a0 j ±0

(17)

Eq. (17) indicates that the world expenditure on country i’s exportable is proportional to country i’s expenditure on its nontraded good. The factor of proportionality depends on the expenditure share a0 and on w i , which is an index of country i’s tariff structure. Equivalently, w i can also be thought of as an index of trade liberalization. Given taste parameters, the larger w i is the more liberal is country i’s trade policy.14 The (transformed) trade balance condition in Eq. (17) reveals that if country i were to adopt a more liberal stance in trade policy, then 13 Dinopoulos (1994, Appendix B) analyzes formally this issue and shows that the economy jumps from one steady state to the next if a parameter of the model changes. The absence of transitional dynamics simplifies the analysis substantially. 14 If country i’s tariffs are infinitely large, then w i 5 ai ; if country i is a free trader, then w i 512 a0 . Since ai 1 a0 ,1, we must have ai , w i ,12 a0 for any other tariffs.

438

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

relative expenditures would shift toward the traded good (i.e. Yi /Y i0 would rise). In addition, Eq. (17) indicates that Yi /Y 0i does not depend on any country’s wage rate. Eq. (15) and Eq. (17) can be solved simultaneously to obtain the following expressions for equilibrium real expenditures on country i’s nontraded and exported goods, respectively:

a0 i i i Y 0 /w 5 ]]]i [L 1 r /u0 1 r /ui ], a0 1 w

(18a)

i

w Yi /w i 5 ]]]i [L i 1 r /u0 1 r /ui ]. a0 1 w

(18b)

Substituting Eqs. (18a) and (18b) in Eqs. (13a) and (13b) yields the following solutions for steady-state equilibrium R&D investments:

F GS F GS

1 i R 0 5 u0 1 2 ] m0 1 R ii 5 ui 1 2 ] mi i

D

a0 i ]]] i [L 1 r / u0 1 r / ui ] 2 r, a0 1 w i

D

w ]]]i [L i 1 r /u0 1 r /ui ] 2 r. a0 1 w

(19a)

(19b)

i

For R 0 and R i to be positive, the expressions in the RHS of the relations in Eqs. (19a) and (19b) must be positive. Since we have ai , w i ,12 a0 (see footnote 14), a sufficient (though not necessary) condition for the existence of unique steadystate equilibrium with positive R&D investments is

H

J

r r L i . max ]]]]], ]]]]]] 2 r /u0 2 r /ui . u0 [1 2 1 /m0 ]a0 ui [1 2 1 /mi ](1 2 a0 )

(20)

Clearly, this condition will be satisfied if country i’s labor endowment is sufficiently large. In the steady-state equilibrium, aggregate consumption expenditures, R&D investments, relative wages, and the intersectoral allocation of labor remain constant over time. New and better production techniques are discovered indefinitely through sequential R&D races. These techniques enhance the productivity of labor in manufacturing of final goods and increase their output. These increases in output are matched by offsetting instantaneous reductions in final good prices which lead to a perpetual increase in the instantaneous utility of each consumer. The winner of an R&D race enjoys temporary monopoly profits, which are paid back to consumers / investors as dividends for financing the R&D investments. The random time intervals between innovations are exponentially distributed and serve as patents for the winners of R&D races. Firms are created and destroyed through the introduction of better techniques of production. Thus, the evolution of technology follows Schumpeter’s description of creative destruction and results in

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

439

Schumpeterian growth. There is aggregate uncertainty, but consumers can diversify their portfolios and thus avoid aggregate risk. Proposition 1 summarizes the dependence of the endogenous variables on tariffs. Proposition 1. If a0 ±0, then an increase in country i’ s trade liberalization index w i , caused by a fall in any of country i’ s tariffs, will 1. (a) reduce the steady-state level of R& D investment in country i’ s nontraded good sector, R i0 ; (b) raise the steady-state level of R& D investment in country i’ s export sector, R ii ; (c) not affect the steady-state level of R& D investments in the nontraded and export sectors of any other country j(± i) ; 2. (a) reduce the steady-state real expenditure on country i’ s nontraded good, Y i0 /w i ; (b) raise the steady-state real expenditure on country i’ s exportable, Yi /w i ; (c) not affect the steady-state level of real expenditure on exportables of any other country j, Yj /w j , ( j ± i) ; 3. (a) reduce country i’ s per capita real expenditure, E i /w i , and will not affect the per capita real expenditure of any other country j, E j /w j , ( j ± i). In the model, tariffs are rent-extracting devices that affect only country i’s real expenditures. More specifically, a reduction in country i’s tariffs causes its tariff revenues to diminish and its per-capita consumption expenditure Ei /w i to fall. Because expenditure shares are constant, country i reduces its expenditure on all goods except on the importable whose tariffs fall. At constant wage rates, country i’s trade balance goes into deficit. This forces country i’s factoral terms of trade to decline and spurs export demand. For trade to be balanced, the world expenditure on country i’s exportable must rise relative to the initial situation. The contraction in country i’s expenditure on its nontraded good reduces the demand for manufacturing labor and the profitability of R&D in the nontraded sector. At the same time, however, the increase in world expenditure on country i’s exportable raises the demand for manufacturing labor and the profitability of R&D in this sector. These developments cause labor in country i to be relocated from its nontraded to its export sector, thereby causing R&D investment in the former to decline and R&D investment in the latter sector to rise. It is worth noting that the absence of cross-price effects along with the Ricardian structure of the model and the condition for balanced trade generate a strong separability that removes any international spillover effects of a country’s tariff policies on the intersectoral allocation of labor in its trading partners. This property is reflected in Eqs. (18a) and (18b) and Eqs. (19a) and (19b), which indicate that the allocation of resources in any country i depends only on the country’s own tariff structure. Intuitively, this is so because the response in

440

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

country i’s export supply to a fall in country i’s tariffs is met with a corresponding adjustment in its factoral terms of trade that keeps the real expenditure of any other country h(±i), E h /w h , intact. If the nontraded good is absent, then changes in tariffs do not affect the intersectoral allocation of labor, once again, because expenditure shares are constant and the production structure is Ricardian. Precisely, if a0 50 (⇒o j ±0 aj 51), which implies that the nontraded good is not valued in consumption, then Y i0 and R i0 would equal 0. Furthermore, Yi and R i0 would be invariant to changes in tariffs. This is so because any change in w i would be absorbed by an offsetting change in E i that keeps w i E i constant and, consequently, Yi and R ii . Thus, an important function of the nontraded good is that it breaks the special relationship that exists between w i and E i in its absence, and which renders tariffs equivalent to consumption taxes that do not affect long-run growth (see Osang and Pereira (1996), footnote 6, for a similar result in a different setting.) As we shall see shortly, the nontraded final good can also play another important function: it can help generate long-run differences in the growth of living standards across countries.

3. Trade liberalization and Schumpeterian growth In this section we investigate the relationship between several trade liberalization schemes and long-run growth. Following the standard practice of Schumpeterian growth models, we define country i’s long-run growth as the change of its expected steady-state instantaneous utility ln(u i ). After performing the standard substitutions and algebra, we obtain the following expression

% [ln(u i )] 5 tG i 1 F i 1 C

(21)

for the expected instantaneous utility at the steady-state equilibrium. %[?] is the expectation operator and G i ; a0 ln( m0 )R i0 1

O a ln( m )R , j

j

j j

(22)

j [N

F i ; ln(E i /w i ) 1

O a [ln(w ) 2 ln(w )] 2O a ln(T ),

j ±0,i

O a ln(a ).

i

j

j

j

i j

(23)

j ±0

3

C;

j

j

(24)

j 50

In the steady-state equilibrium, only the first term in the RHS of Eq. (21) depends on time. Differentiating Eq. (21) with respect to time yields country i’s long-run growth as the change in %[ln(u i )], which is G i . There are two broadly

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

441

defined sources for country i’s long-run growth which correspond to the two terms in the RHS of Eq. (22). The first term captures the contribution of country i’s nontraded final good; the second term is the combined effect of all traded sectors. Notice that this latter term appears in every country’s growth and captures the effect of country i’s export sector and a sum of terms reflecting the international spillovers of price reducing innovations in the rest of the world.15 Each of the terms in Eq. (22) has an intuitive interpretation. To see this, consider the nontraded final good. Every time an innovation occurs, the instantaneous utility jumps by a constant factor ln( m0 ). The expected frequency of these jumps is captured by R i0 , which is also the intensity of the Poisson process governing the arrival of innovations. Therefore, ln( m0 )R 0i corresponds to the expected jump in instantaneous utility originating in the nontraded sector. This jump is weighted by the expenditure share of the nontraded good a0 in order to incorporate the good’s relative valuation in the overall consumption bundle. The other terms in Eq. (22) can be interpreted similarly. Now consider the levels of long-run growth, G i and G j , of any two countries i and j. Which country experiences the largest growth? The contribution of the traded sectors to growth appears identically in the growth of both countries living standards, but the contribution of the nontraded good sector does not because R i0 depends on country-specific parameters. Thus, there is no intrinsic reason to expect G i 5G j . Proposition 2. The long-run growth levels in countries i and j can be ranked as follows: j L i 1 r /u0 1 r /ui L 1 r /u0 1 r /uj ]]]]] ]]]]] G _ G iff _ , ; i ± j [ N. a0 1 w i a0 1 w j i

j

International differences in the contribution of the nontraded sectors to long-run growth give rise to long-run differences in national growth levels. Countries with relatively larger factor endowments, lower labor productivity in R&D devoted to the nontraded or export sectors and more protectionist policies (captured by relatively lower f s) are more likely to experience higher long-run growth relative to other countries. Proposition 2 complements the findings of Feenstra (1996) who studied the role of knowledge spillovers and trade between two countries on national (unequal) growth rates in a model of variety accumulation. In Feenstra’s model, the presence of cross-price effects leads to corner solutions where, in the 15

Appendix B derives an alternative expression for the long-run growth of country i which is 3 ˆ i 5≠ln(uˆ i ) / ≠t5(≠uˆ i / ≠t) / uˆ i 5o 3j 50 aj ( mj 21)R ij , where uˆ i 5 j 50 %[d ij ] aj . This expression captures the G long-run growth rate of country i’s (appropriately weighted) consumption index. The two expressions of long run growth differ only in the fixed weights of sectoral R&D investments, but G i is preferable ˆ i because it is a component of country i’s expected discounted welfare (see Eq. (25)). over G

P

442

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

long run, one country’s share in global consumption expenditure approaches unity. Also, differences in labor endowments and in the elasticity of substitution between two final goods in his model provide a supply-based mechanism that generates transitional unequal growth rates under free trade. Three assumptions in our model are necessary conditions for the emergence of long-run differences in growth across countries. First, the assumption of no international knowledge spillovers in the nontraded sector results in independent country-specific R&D races which generate intrasectoral growth differences. If complete international spillovers of knowledge are allowed (i.e. firms in every country can invent the next quality generation), then the R&D race associated with each discovery in the nontraded sector would be global. The winner of each race could sell the state-of-the-art technology to firms manufacturing the nontraded good in each country—these firms could be multinational corporations—which would eliminate any international differences in growth emanating from the nontraded sector. In general, complete international spillovers in growth models of the quality-ladders type render their results on growth convergence similar to those of product-variety models with knowledge diffusion. Second, trade equalizes the contribution of the traded goods to long-run growth in instantaneous utility even when international spillovers in technology are absent. Therefore, if all final goods are traded, then long-run growth in the national standards of living converges. Third, the assumption of constant expenditure shares in consumer preferences precludes the possibility of corner solutions. If, instead, expenditure shares depended on product prices, as in Feenstra (1996) where consumer preferences are CES, specialization in the production of a single product (possibly the nontraded good) could arise in the long run.16 ,17 Recall from Proposition 1 that tariff changes alter the sectoral composition of R&D investments and thus have an ambiguous effect on long-run growth, which depends positively on R&D investments in all sectors. To examine the effects of tariffs and of different trade liberalization schemes on long-run growth it is useful to define the growth intensity Gj of sector j as (D1)

Gj ; ajuj [1 2 1 /mj ] ln( mj ), ; j 5 0, 1, 2, 3.

16 Following the reasoning of Feenstra (1996), suppose that the elasticity of substitution in consumption between any two final goods is the same and exceeds unity. Then, it can be shown that the sector with the highest initial growth rate will eventually account for all consumption in the world; R&D investment in all other sectors (which depends positively on sectoral expenditure shares) would cease. 17 Proposition 2 identifies one possible source of differences in long-run growth across countries that has its roots in R&D investments in nontraded sectors. Testing the empirical relevance of the proposition requires generalizing the model so as to incorporate differences in expenditure shares and technological opportunities across the nontraded sectors of trading partners and then measuring relative differences in R&D investments in these sectors. Additionally, one would have to overcome the difficulties due to the presence of aggregate uncertainty that amplifies the measured differences in growth rates across countries, especially when these rates are based on small time series samples.

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

443

This intensity captures the contribution to national long-run growth of a dollar spent on the final good j. The Ricardian structure of production enables us to define sectoral growth intensities in terms of sector-specific technological parameters. Sectors with large innovations, high R&D labor productivity, and big expenditure shares are characterized by high sectoral growth intensities. Lemma 1. If a0 ±0, then trade liberalization affects country i’ s expected long-run growth as follows: (a)

≠G i / ≠w i v 0 and ≠ 2 G i / ≠(w i )2 v 0 as Gi v G0 ; i [ N

(b)

≠G i / ≠w j . 0 and ≠ 2 G i / ≠(w j )2 , 0 ; j ± i [ N.

Lemma 1 reveals how long-run national growth levels depend on the indices of trade liberalization in the presence of a nontraded final good. Part (a) indicates that trade liberalization by country i will raise, reduce or not affect its own long-run growth depending on whether the country’s export sector growth intensity exceeds, falls below or equals the growth intensity of its nontraded sector, respectively. This is so because trade liberalization spurs R&D investment (and, consequently, growth) in the export sector, but also reduces R&D investment (and, therefore, growth) in the nontraded sector. Part (b) states that country i’s growth is an increasing (and concave) function of any other country j’s trade liberalization index, w j . This is so because any reduction in country j’s tariffs raises R&D investment in country j’s export sector (see Proposition 1), which in turn reduces the world price of its exportable thereby raising the long-run growth levels of its trading partners. The concavity of G i in w i when Gi . G0 and in w j ( j ±i) captures the notion of diminishing returns to trade liberalization. The larger the initial levels of protection (low w s) the larger the growth-promoting effects of trade liberalization. For further insight, consider a world in which all countries are similar but, say, country 1’s initial tariffs are largest, i.e. L i 5L, uj 5u, mj 5 m, aj 5 a (i, j [N) and w 1 , w 2 5 w 3 . By Proposition 1, country 1’s standard of living will grow faster than the living standards of its trading partners. If country 1 marginally reduces its tariff(s), then by Lemma 1 the dispersion of growth across countries will diminish; growth in countries 2 and 3 will accelerate, and if G1 . G0 , even growth in country 1 will accelerate, but the change in G 1 will be less pronounced relative to the changes in G 2 and G 3 . If one of the less protectionist countries reduces its tariff(s) instead, then divergence rather than convergence of growth across countries will be observed. Trade liberalization can take several forms. It can be unilateral, bilateral or multilateral. It can also be regional, as in the case of customs unions and free trade areas. Proposition 3 studies the implications of these forms of trade liberalization for long-run growth by focusing on what appears empirically to be the most

444

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

relevant case: the growth intensity of the nontraded sector is the lowest in each country.18 Proposition 3. If a0 (Gi 2G0 ).0 for all i [N, then the long-run growth of all countries rises as a result of 1. unilateral trade liberalization; 2. bilateral trade liberalization; 3. multilateral trade liberalization; 4. the formation of a free trade area or a customs union by any two countries that abide by Article XXIV of the GATT.19 Unilateral, bilateral, multilateral and regional types of trade liberalization promote long-run growth, if the nontraded sector is less progressive than the traded good sectors.20 Interestingly, the second-best features of the model—including dynamic imperfect competition, the existence of arbitrary tariffs by any country, and terms of trade effects—do not overturn the growth-related impact of tariff changes. But which trade liberalization scheme is more conducive to economic growth? For example, will the multilateral approach give rise to higher or lower growth rates for trade liberalizing partners than, say, the bilateral approach? To tackle this issue we must have an index of world trade liberalization. One such index is the following combination of the indices f i of the three individual countries: (D2)

F ; k1 w 1 1 k2 w 2 1 k3 w 3 , where

O k 5 1. j

j [N

Given the kj s, any reduction in tariffs raises F in (D2). We will say that two trade liberalization schemes are equivalent if they raise F by the same amount. The presence of asymmetries in technology, factor endowments and the initial 18

Baumol et al. (1985) calculated sectoral annual growth rates of productivity growth for the US over the period 1947–76. They classified sectors into two categories, stagnant and progressive, using four different measures of productivity growth, including total factor productivity. The stagnant category included hotels, personal and repair services, business and professional services, movies and amusement services, medical services, government enterprises, etc., most of which involve nontraded goods and services. The annual total factor productivity growth for the stagnant category was about 20.84 compared to 1.09 for the progressive category. In addition, Scherer (1984) reported that approximately 98% of the US private R&D is undertaken by corporations operating in manufacturing and mining, which are sectors associated principally with the production of traded commodities. These figures suggest that the traded sector is relatively more progressive in the US. For the purposes of this paper, it is sufficient to assume that the nontraded final good sector has the lowest growth intensity. 19 Article XXIV of the GATT sanctions the formation of free trade areas and customs unions but constrains member countries not to raise their external tariffs beyond pre-union levels. By definition, members of such arrangements must dismantle all tariffs on internal trade. 20 As can be easily verified from Eq. (22), this condition can be relaxed for bilateral and multilateral trade liberalization schemes.

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

445

tariffs of countries condition the impact of different regimes on national growth levels, and raise questions about the relevance of F as a measure of global trade liberalization. We bypass these difficulties by considering symmetric environments. Though restrictive, our approach is nonetheless valuable because it helps pinpoint several intrinsic differences that exist between unilateral, bilateral and multilateral tariff cuts. Proposition 4. Suppose L i 5 L, uj 5u, mj 5m, aj 5a, kj 5k for all i, j [N. In addition, suppose that all countries initially levy identical tariffs. Then, the long-run growth of a trade liberalizing country’ s standard of living can be ranked as follows across equivalent trade liberalization schemes: i i G iunilateral , G bilateral , G multilateral .

Proposition 4 shows that countries that liberalize trade experience larger long-run growth when a predefined measure of global trade liberalization is spread over more countries. This is so for two reasons: the first involves the contribution of a country’s nontraded sector to growth; the second has to do with the impact of the traded sectors. Under the stated conditions, any country contemplating trade liberalization must reduce its own tariffs less under a multilateral arrangement than under a bilateral accord than under a unilateral move, respectively, for the global rate of protection F to remain constant. In other words, we will have w iunilateral . w ibilateral . w imultilateral for all i [N. Because R i0 is decreasing and convex in w i (see Eq. (19a)), the impact of a country’s nontraded sector on growth (at the margin and absolutely) successively becomes more intense as one considers equivalent unilateral, bilateral and then multilateral tariff reductions. At the same time, as trade liberalization is spread across more countries, the contribution of the traded sectors to growth also increases because R jj is increasing and concave in w j ( j [N) (see Eq. (19b)). Notice that sectoral growth intensities play no role in Proposition 4 because long-run growth levels are compared across liberalization regimes and not relative to the original situation. Proposition 4 generalizes in higher dimensions.

4. Welfare implications of trade liberalization This section investigates the welfare implications of different trade liberalization strategies in the presence of Schumpeterian growth. Its main goal is to highlight insights that are missing in static analyses. From Eq. (1) and Eq. (21), and after carrying the requisite integration, country i’s expected discounted welfare takes the form

446

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452 `

E

V ; % [U ] 5 e 2rt % [ln(u i (t))]dt 5 (1 /r 2 )[G i 1 r F i 1 r C] i

i

(25)

0 i

i

where G , F and C are defined in Eq. (22), Eq. (23) and Eq. (24), respectively. The G i term in Eq. (25) captures the growth-related component of country i’s expected discounted welfare. Because technical change in the export sectors of all countries affects G i and such change depends on the tariffs of individual countries, trade liberalization in one country generates growth-related externalities that raise welfare of all other countries. The F i term in Eq. (25) contains the familiar terms which include country i’s income, factoral terms of trade and direct tariff effects (see Eq. (23)) discounted appropriately. Appendix B contains expressions for the equilibrium values of the components of F i . By Eq. (24), the C term in Eq. (25) does not depend on tariffs. Consider the effect of a change in country i’s tariff on imports of good j on welfare of a representative individual in country h. Differentiating Eq. (25) with respect to T ij and transferring terms appropriately yields

r 2 [≠V h / ≠T ji ] 5 ≠G h / ≠T ji 1 r (≠F h / ≠T ji ), for i, h [ N.

(26)

The first term in the RHS of Eq. (26) captures the welfare effect of a tariff change via its impact on growth. The second term in the RHS of Eq. (26) captures the level effect on welfare. In general, tariff changes affect expected discounted welfare ambiguously. Proposition 3 has clarified the nature and the intuition behind the growth term ≠G h / ≠T ij , so there is no need to discuss this effect here. The sign of the level effect ≠F h / ≠T ij is generally ambiguous because of secondbest considerations. In the spirit of Proposition 4, however, it is possible to consider symmetric economic environments where the welfare level effect of tariff cuts are determinate. Hereafter, we discuss the differential impact of the three trade liberalization schemes considered earlier, relegating all algebraic details to Appendix B. A unilateral and nondiscriminatory tariff cut by country i (assuming all other countries impose identical tariffs) generates a negative welfare level effect for country i. This is so because the presence of constant expenditure shares and complete specialization in production imply that an intervening country’s terms of trade improve with increases in its tariffs while the country’s volume of imports does not change. Everything else being the same, a symmetric bilateral reduction of tariffs on trade between two trading partners results in positive level effects for both countries because it causes their volume of internal trade to rise and their factoral terms of trade to improve. Lastly, symmetric across-the-board multilateral tariff cuts generate a welfare enhancing level effect for all trading partners because their terms of trade do not change but their volume of trade expands.

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

447

Will countries always prefer, on welfare grounds, multilateral over bilateral tariff cuts? The answer is: It depends. Even though the growth component of a country’s discounted welfare is largest under the multilateral approach, countries that consider liberalizing their trade may, nonetheless, opt for the bilateral solution if it gives rise to a sufficiently larger level effect than a corresponding multilateral agreement. The level effect of bilateral accords is negative for outside countries, as is well understood from static analyses of preferential trading arrangements (e.g. Bond and Syropoulos, 1996a). The novel point here is that bilateralism could benefit outside countries if the positive growth spillover effect is sufficiently strong.

5. Concluding remarks We developed a dynamic, multi-country, multi-commodity, general equilibrium model of Schumpeterian growth, tariffs and trade. The presence of a nontraded sector experiencing endogenous growth generates cross-country long-run growth differences in national standards of living; it also creates a demand-based mechanism that transmits the effects of tariff changes on long-run growth and welfare. Higher tariffs shift resources from traded to nontraded sectors and create negative growth spillovers for the rest of the world. Although the effect of tariff changes on a country’s long-run growth is ambiguous, higher tariffs reduce growth if the country’s nontraded sector is less progressive (i.e. has a lower growth intensity) than the country’s export sector. Interestingly, under conditions of symmetry, the long-run growth of every trade-liberalizing country is larger when tariffs cuts are spread over more countries. For this reason, unilateral tariff cuts are dominated by bilateral tariff reductions which are, in turn, dominated by multilateral trade agreements. The analysis also reveals that there exist circumstances under which trade liberalization exhibits diminishing returns with respect to growth, i.e. the marginal effect of tariff changes on growth falls as countries move closer to free trade. Although welfare considerations in the model generally raise second-best ambiguities, valuable insight on the welfare effects of unilateral, bilateral and multilateral trade arrangements is possible to obtain in the context of symmetric environments. The model represents a contribution to the literature of trade liberalization (preferential or otherwise) which emphasizes endogenous, long-run growth effects. Under the empirically plausible assumption that nontraded goods are on average less progressive than traded goods, the analysis provides support to the view that regional trade arrangements can raise the long-run growth and welfare of all countries in the world. Forward-looking governments interested in technological progress and growth in national standards of living (and not constrained by the influence of special interests) would probably be inclined to support any strategy of trade liberalization. Europe 1992, NAFTA and the WTO may all be growth-

448

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

creating trade liberalization schemes carrying profound dynamic welfare implications. Diminishing returns to trade liberalization have the interesting implication that countries under the umbrella of highly protective trade regimes (e.g. countries switching from import-substituting to export-oriented trade regimes) are likely to experience larger growth than countries with initially low trade barriers (e.g. advanced industrial countries). Moreover, a marginal reduction in tariffs by the most (least) protectionist country reduces (increases) the dispersion of growth across countries. The analysis raises several concerns regarding the interpretation of findings based on cross-country growth regressions. Typically, such studies (e.g. Barro, 1991) regress variables measuring country-specific structural and policy characteristics on growth rates of per capita GNP across countries. Since this methodology does not capture cross-country growth spillovers of trade policies, the danger exists of drawing erroneous inferences on the linkage between tariffs and long-run growth. For example, consider a Schumpeterian global economy that consists of many structurally identical countries. A cross-country growth regression would reveal the existence of a positive partial correlation between growth and tariffs. Countries with higher tariffs would devote more resources to their nontraded sectors and thus exhibit larger long-run growth than their less protectionist trading partners. As we have seen earlier, however, this finding does not imply that larger tariffs necessarily promote the intervening country’s long-run growth! On the contrary, larger tariffs may, and in the empirically plausible cases will, retard the growth prospects of the intervening country, as well as the growth prospects of its trading partners. Econometric estimation of structural models based on time-series data are, therefore, more appropriate for the study of the causal relationship between trade policies and growth. Of course, our conclusions depend on and are limited by the assumptions of our model. Population growth and the removal of scale effects, for example, can make the model conform better to the real world. The introduction of physical or human capital accumulation would generate transitional dynamics which are standard in growth models. As it is constructed now, the model lacks transitional dynamics. Nonetheless, the presence of aggregate uncertainty generates complex time series patterns. For example, the discrete sequence of observations on each sectoral output and price follows a random walk with constant positive drift (see Aghion and Howitt (1992) for details). In a three-country model with four final goods, the discrete sequence of real per capita GNP growth is a linear combination of four nonstationary stochastic Poisson processes, so it would be difficult to determine, on the basis of time-series observations, whether the model has transitional dynamics or not. The assumption of no international spillovers is also restrictive. Its relaxation would change some of the results but it would also complicate the analysis. Lastly, future research should enrich the endowment and ownership structures to shed

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

449

light on the relationship between trade policies and income distribution in growththeoretic environments.

Acknowledgments We would like to thank Kenneth Carlaw, Gordon Hanson, Beverly Jonnes, Douglas Marcouiller, the editor Robert Feenstra, the referees, and participants at the Canadian Economic Association Meetings in Calgary, at the 13th Annual Conference on International Trade at the University of Western Ontario, and at the AEA Meetings in Washington D.C. for valuable comments and suggestions on earlier versions of this paper.

Appendix A Proof of Proposition 1 Parts (a) and (b) readily follow from differentiation of Eqs. (18a) and (18b) and Eqs. (19a) and (19b). Part (c) follows from Eq. (5a), which implies that E i /w i 5 (a0 L i )21 (Y 0i /w i ), and part (19b). i Proof of Proposition 2 It follows from Eq. (22) upon observation of the property G i _G j iff R i0 _R j0 and Eq. (19a). i Proof of Lemma 1 For future use, differentiate Eqs. (19a) and (19b) twice with respect to w i to obtain ≠ 2 R i0 / ≠(w i )2 5 2R i0 (a0 1 w i )22 . 0, ; i [ N 2

i

i 2

i

i

i 2 21

≠ R i / ≠(w ) 5 2 2a0 R i [w (a0 1 w ) ]

(A1)

, 0, ; i [ N.

i

(A2) i

Part (a): Differentiation of G in Eq. (22) with respect to w yields ≠G i / ≠w i 5 ai ln( mi )[≠R ii / ≠w i ] 2 a0 ln( m0 )[≠R i0 / ≠w i ] L i 1 r /u0 1 r /ui 5 a0 (Gi 2 G0 )]]]]] ; (a0 1 w i )2 L i 1 r /u0 1 r /ui 2 i i 2 ≠ G / ≠(w ) 5 2 2a0 (Gi 2 G0 )]]]]] . (a0 1 w i )3 Eqs. (A3) and (A4) readily imply part (a) of the Proposition.

(A3)

(A4)

450

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

Part (b): Differentiation of G i in Eq. (22) with respect to w j ( j ±i) yields ≠G i / ≠w j 5 aj ln( mj )[≠R jj / ≠w j ] . 0 ; j ± i [ N;

(A5)

≠ 2 G i / ≠(w j )2 5 aj ln( mj )[≠ 2 R jj / ≠(w j )2 ] , 0 ; j ± i [ N.

(A6)

The signs of the expressions in Eqs. (A5) and (A6) follow from Proposition 1(a) and Eq. (A2), respectively, under the assumption that a0 ±0. i Proof of Proposition 3 Part (a) follows upon observation of the fact that unilateral trade liberalization raises w i , which by Lemma 1(a) raises G i . The remaining parts also follow from the fact that the other types of trade liberalization raise both w i and w j (i ±j), and from Lemma 1. i Proof of Proposition 4 Define G i0 ≡a0 ln( m0 )R i0 and G≡o j ±0 aj ln( mj )R jj so that G i 5G i0 1G, as in Eq. (22). Also, let subscripts ‘O’, ‘U’, ‘B’ and ‘M’ respectively denote the ‘original’ state of the world, ‘unilateral’ trade liberalization by country i, ‘bilateral’ trade liberalization by countries i and j, and ‘multilateral’ trade liberalization. To prove the proposition it is sufficient to prove the following: (a) G0 iU ,G0 iB ,G i0M for every country i that participates in trade liberalization; (b) GU ,GB ,GM . Part (a): Suppose that country 1 liberalizes its trade unilaterally. This raises w 1 from w 1O to w 1U and the global liberalization index F from FO to FU . If, additionally, either country 2 or country 3 also reduced its tariffs on imports from country 1 so that FB 5 FU , then by the definition of F we would have w 1U . w 1B . 1 1 Similarly, if all countries liberalized their trade so that FM 5 FB , then w B . w M . 1 1 1 1 1 Thus, w U . w B . w M . Since by Proposition 1 G 0 is decreasing in w we must have 1 1 1 G 0U ,G 0B ,G 0M . The argument for countries 2 and 3 is similar, so this completes the proof to part (a). Part (b): Our symmetry assumptions imply F 5(w 1 1 w 2 1 w 3 ) / 3, Gj 5 G 5 au [121 /m ] ln( m ) and L i 5 L 5L 1 r /u0 1 r /u for all i, j [N. Consequently, for 1 2 3 1 any given F, we can write w 53F 2 w 2 w . Substituting w in the definition of 2 3 G allows us to write G;G(w , w ). It is now easy to verify that

F

G

≠ 2 R jj ≠ 2 R 11 ≠ 2G ]] ]] ]] 5 a ln( m ) 1 , 0, ; j 5 2, 3 ≠(w j )2 ≠(w 1 )2 ≠(w j )2

F G

2 ≠ 2 R 11 ≠ G ]]] ]] 5 a ln( m ) , 0, ; j ± h 5 1, 2 ≠w j ≠w h ≠(w 1 )2

(A7)

(A8)

which, taken together, imply that G(w 2 , w 3 ) is concave in its arguments. The negative sign in the RHS of Eq. (A7) and Eq. (A8) is obtained from Eq. (A2). Differentiating G(w 2 , w 3 ) totally yields

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

SF

dG 5 a ln( m )

G F

G D

≠R 2 ≠R 1 ≠R 3 ≠R 1 ]]22 2 ]]11 dw 2 1 ]]33 2 ]]11 dw 3 . ≠w ≠w ≠w ≠w

451

(A9)

Utilizing Eq. (19a) and Definition (D1), Eq. (A9) can be rewritten as

S

F

G G D

(2a0 1 w 1 1 w 2 ) 1 2 2 dG 5 a0 GL (w 2 w ) ]]]]]] dw (a0 1 w 1 )2 (a0 1 w 2 )2

F

1

3

(2a0 1 w 1 w ) 3 1 (w 2 w ) ]]]]]] dw 1 2 3 2 (a0 1 w ) (a0 1 w ) 1

3

(A10)

after performing the requisite differentiation. The RHS of Eq. (A10) reveals that the condition for G to attain a global maximum is w 1 5 w 2 5 w 3 . Additionally, Eq. (A10) indicates that for any given w 3 (resp., w 2 ) G attains a local maximum when w 1 5 w 2 (resp., when w 1 5 w 3 ). Now assume that country 1 has liberalized its trade unilaterally, so w 1 5 w U1 and F 5 FU . Next, suppose that countries 1 and 2 sign an agreement to reduce their tariffs bilaterally so that FB 5 FU . From Eq. (A10) and the discussion preceding it, 2 3 1 2 G will rise if dw .0, dw 50 and w U . w 0 initially. In fact, G will attain a local 1 2 maximum if w and w move in the direction of their equalization so that eventually w 1B 5 w 2B . (The argument is similar if countries 1 and 3 were to sign a bilateral agreement instead, and is therefore omitted.) After the completion of the bilateral agreement, the three countries proceed to negotiate a multilateral reduction in tariffs so that FM 5 FB 5 FU . If initially w 1B 5 w 2B and w 1B . w 30 , then dw 3 .0 would imply dG.0. The situation is especially simple when w 1h 5 wh 2 5 wh 3 for all h[hO, U, B, Mj. In this case we will have w jU . w jB . w jM . wO j for all h[N, which readily implies GU ,GB ,GM and thus completes part (b). i

References Aghion, P. and P. Howitt, 1992, A model of growth through creative destruction, Econometrica 60, 323–352. Bagwell, K. and R.W. Staiger, 1993, Multilateral tariff cooperation during the formation of regional free trade areas, NBER Working Paper No. 4364. Barro, R. 1991, Economic growth in a cross section of countries, Quarterly Journal of Economics 106, 407–443. Baumol, W., S. Blackman, and E. Wolff, 1985, Unbalanced growth revisited: asymptotic stagnancy and new evidence, American Economic Review 75, 806–817. Bhagwati, J., 1988, Protectionism (MIT Press, Cambridge, MA). Bhagwati, J. and T.N. Srinivasan, 1983, Lectures on International Trade (MIT Press, Cambridge, MA). Bond, E.W. and C. Syropoulos, 1996a, The size of trading blocs: market power and world welfare effects, Journal of International Economics, 40, 411–438.

452

E. Dinopoulos, C. Syropoulos / Journal of International Economics 42 (1997) 425 – 452

Bond, E.W. and C. Syropoulos, 1996b, Trading blocs and the sustainability of inter-regional cooperation, in: M. Canzoneri, W. Ethier and V. Grilli, eds., The new transatlantic economy (Cambridge University Press, New York). Brander, J. and B. Spencer, 1981, Tariffs and the extraction of foreign monopoly rents under potential entry, Canadian Journal of Economics 14, 371–389. Brock, P.L. and S. Turnovsky, 1993, The growth and welfare consequences of differential tariffs, International Economic Review 34, 765–794. Dinopoulos, E., 1994, Schumpeterian growth theory: an overview, Osaka City University Economic Review 29, 1–21. Dinopoulos, E. and M. Kreinin, 1996, Schumpeterian growth and international transmission of technology, University of Florida, mimeo. Dinopoulos, E. and P. Segerstrom, 1996, The dynamic effects of contingent tariff protection, Michigan State University, mimeo. Feenstra, R., 1996, Trade and uneven growth, Journal of Development Economics 49, 229–256. Galor, O., 1994, Tariffs, income distribution and welfare in a small overlapping-generations economy, International Economic Review 35, 173–192. Grossman, G. and E. Helpman, 1991, Innovation and growth in the global economy (MIT Press, Cambridge, MA). Houser, C., 1994, Stability in neo-Schumpeterian models of growth, University of Florida, mimeo. Jones, C., 1995a, Time series tests of endogenous growth models, Quarterly Journal of Economics 110, 495–525. Jones, C., 1995b, R&D based models of economic growth, Journal of Political Economy 103, 759–784. Kennan, J. and R. Riezman, 1990, Optimal tariff equilibria with customs unions, Canadian Journal of Economics 23, 70–83. King, R. and R. Levine, 1993, Finance entrepreneurship and growth: theory and evidence, Journal of Monetary Economics 32, 513–542. Kortum, S., 1996, Research and productivity growth: theory and evidence from patent data, Boston University, mimeo. Krugman, P.R., 1991, Is bilateralism bad? in: E. Helpman and A. Razin, eds., International Trade and Trade Policy (MIT Press, Cambridge, MA). Osang, T. and A. Pereira, 1996, Import tariffs and growth in small open economy, Journal of Public Economics 60, 45–71. Rivera–Batiz, L. and P. Romer, 1991a, International trade with endogenous technological change, European Economic Review 35, 971–1004. Rivera–Batiz, L. and P. Romer, 1991b, Economic integration and endogenous growth, Quarterly Journal of Economics 106, 531–555. Romer, P., 1986, Increasing returns and long-run growth, Journal of Political Economy 94, 1002–1037. Romer, P., 1994, New goods, old theory, and the welfare costs of trade restrictions, Journal of Development Economics 43, 5–38. Scherer, F.M., 1984, Technological change and the modern corporation, in: Bock, Goldschmid, Millstair, Scherer, eds., The impact of the modern corporation (Columbia University Press, New York). Schumpeter, J., 1942, Capitalism, socialism and democracy (Harper and Row, New York). Segerstrom, P., 1995, A quality ladders growth model with decreasing returns to R&D, Michigan State University, mimeo. Segerstrom, P., T.C.A. Anant and E. Dinopoulos, 1990, A Schumpeterian model of the product life cycle, American Economic Review 80, 1077–1091. Taylor, S., 1993, Quality ladders and Ricardian trade, Journal of International Economics 34, 225–243. Taylor, S., 1994, Once-off and continuing gains from trade, Review of Economic Studies 61, 589–601. Young, A., 1995, Growth without scale effects, NBER Working Paper No. 5211.