North-South Technological Diffusion: A New Case for Dynamic Gains from Trade∗ Michelle Connolly†

Diego Valderrama‡

Duke University

Federal Reserve Bank of San Francisco September 28, 2007

Abstract This paper studies the transitional dynamics in a quality ladder model of endogenous growth in which North-South trade leads to technological diffusion through reverse engineering of intermediate goods. The concept of learning-to-learn is incorporated into both imitative and innovative processes, which in turn drive domestic technological progress. International trade with imitation leads to feedback effects between Southern imitators and Northern innovators who compete for the world market. Consequently, both regions face transition paths dependent on their relative technologies. We solve the model numerically and obtain the transition paths and welfare effects of Southern trade liberalization. We find that Southern trade liberalization leads to welfare gains for the South and welfare losses for the North. However, we also show that Southern trade liberalization implemented together with a system of intellectual property rights can be welfare enhancing for both countries. We demonstrate that focusing solely on steady-state results leads to incorrect welfare interpretations. JEL Codes: F1, F43, O31, O40 Key Words: Technological Diffusion, Learning to Learn, Imitation, Innovation, Dynamic Welfare Effects, Feedback Effects ∗ The

views expressed herein are those of the authors and do not necessarily reflect those of the Federal Reserve Bank of San Francisco or the Federal Reserve System. We would like to thank Robert Evenson, Enrique Mendoza, Xavier Sala-i-Martin, and T.N. Srinivasan for their guidance. We also appreciate helpful comments from Amy Glass, James Harrigan, Louise Keely, Kent Kimbrough, Philip Levy, Robert Mundell, Pietro Peretto, David Prentice, Nelson Sa, and Kei-Mu Yi. We thank Gregory Snyders for valuable research assistance. † Department of Economics, 305 Social Sciences, Box 90097, Durham, NC 27708-0087, USA. Telephone: +1 (919) 660-1819. Facsimile: +1 (919) 684-9874. Email: [email protected]. ‡ Corresponding author: Economic Research, 101 Market Street, MS 1130, San Francisco, CA 94105, USA. Telephone: +1 (415) 974-3225. Facsimile: +1 (415) 974-2168. Email: [email protected].

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1

Introduction

This paper considers the dynamic implications of North-South trade for both developed and developing nations. In particular, the paper derives the transitional dynamics for both countries resulting from technological diffusion through reverse engineering of traded intermediate goods. Since trade forces competition across countries for markets, the dynamic implications of technological diffusion are critical to understanding not only the evolution of technology in less-developed countries (LDCs or the “South”) but also the rate of innovation in developed countries (DCs or the “North”). Most of the current endogenous growth literature emphasizes technology as the engine of growth. Hence, the location of technological innovation, its diffusion, and whether or not this diffusion feeds back and affects the original source of the technology, are crucial to understanding time paths for both DCs and LDCs. This paper aims to make three contributions to the existing literature on North-South technological diffusion. First, this paper is, to our knowledge, one of the few papers that derives the transitional dynamics of a quality ladder model under free trade.1 Of particular interest are the transitional dynamics experienced by the South when its firms successfully imitate Northern technology, with the possibility of using imitation to leapfrog Northern firms. One classic example is that of the Japanese car manufacturers Honda, Toyota, and Nissan that initially reverse engineered European luxury cars to improve the designs their own luxury automobiles (Acura, Lexus, and Infinity) and increased their share of the luxury automobile market from 4.4% in 1986 to 26.6% in 1991.2 Second, the paper introduces the notion that both imitation and innovation depend positively on past learning-to-learn in research, whether imitative or innovative. Thus, a positive externality both from past imitation and past innovation exists, although the positive externality from innovation is assumed to be greater. Learning-to-learn differs from the more common notion of learning-by-doing in that the skills gained are applicable to different types of research, as opposed to being limited to the exact task in which the learning occurs. Third, the paper explicitly considers imports of Northern capital goods in modeling the cost of imitation for the South. Technological diffusion to the South is faster the greater the imports of Northern capital goods (embodied technology). This is consistent with empirical evidence in Connolly (2003) who finds that high technology imports positively impact production in developing countries through their direct effect on production and through their indirect effect on domestic innovation and imitation.3 1 See

also Connolly and Valderrama (2005). (1993, p. 36). 3 High technology imports also impact positively developed country production. 2 Bolton

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We use numerical simulations to demonstrate the importance of considering feedback effects between the North and the South both in transition and in steady state. In particular, we show that Southern trade liberalization can be welfare reducing for the North, even though trade liberalization is welfare enhancing in steady-state. Southern trade liberalization expands the long run size of the potential market that each Northern innovator hopes to sell to, thus increases profits earned by Northern firms, and increases Northern consumption growth. However, two effects lower Northern consumption growth. First, Northern firms must increase the resources dedicated to research and development to take advantage of the larger market. Second, Southern trade liberalization also increases competition from Southern imitators and increases the probability that a Southern firm may imitate a Northern technology and replace the Northern product due to the South’s lower production costs. This reduces the North’s expected monopoly profits reduce Northern consumption growth. During transition, the rate of Northern consumption growth is slower. After transition, the rate of growth is faster. We find that the transition costs can exceed the long run gains and that in those cases the North is worse off. As usual, Southern trade liberalization enhances welfare for the South. In the long run, the Southern consumption growth is the same as Northern consumption growth, thus it also is higher. The South also from the transition effects. Thus, the South is unambiguously better off. The welfare effects are robust to changes in the parameters that govern the research and development. We show that Southern trade liberalization implemented together with a system of intellectual property rights (IPRs) can be potentially welfare enhancing for both countries. That is, if Southern imitators pay Northern innovators for “using” their technology in imitation, then the fraction of intermediate goods produced by Northern firms will increase as Northern profitability increases, increasing long run growth and reducing the Northern transition costs. Meanwhile, both countries also benefit from the increased competition brought about by the lower Southern tariffs. This occurs even as the South ends up having a lower share of “high tech ” intermediate product markets. We find that factors that increase the speed of transition reduce the costs for the North, increase the benefit for the South, while leaving the new steady state growth rate of consumption unchanged. We also find that a reduction in trade costs increases competition and frees up resources, benefiting the North and the South. The paper is organized as follows. The rest of this section reviews related papers in the growth literature that consider the interaction of international trade and technological diffusion. Section 2 provides empirical motivation for the modeling of imitation. Section 3 develops the model. Section 4 presents results and Section 5 concludes.

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Related Literature There are two strands in the growth literature that consider different aspects of trade and technology. The first strand focuses on the effect of North-South trade when it leads to Northern specialization in industries exhibiting positive externalities and Southern specialization in industries lacking such positive externalities (Young (1991); Stokey (1988)4 ). Within that type of model, the LDC experiences negative dynamic effects which could potentially outweigh the static gains from trading with a DC. For example, in Young’s (1991) model, learning-by-doing in production drives growth . This learning-by-doing is bounded within the production of any given good, but exhibits positive externalities across goods. Once learningby-doing for a given good is exhausted in one country, then a second country that begins production of the same good does not benefit from any learning-by-doing. Combined with the assumption of no international technological diffusion, this implies that, if trade leads an LDC to specialize in the production of goods previously produced in the DC, it will experience technological progress at a rate less than or equal to its autarky rate. Hence, the LDC will face dynamic losses from trade that could possibly outweigh the static gains from trade with a DC. The second strand of literature considers the effect of North-South trade on technological progress and diffusion (Krugman, 1979; Dollar, 1986; Grossman and Helpman, 1991a,b; Rivera-Batiz and Romer, 1991; Barro and Sala-i-Martin, 1997; Glass, 1997).5 In this category of papers, some consider feedback effects between the North and the South in steady state, but do not analyze transitional dynamics for either region (in particular Grossman and Helpman (1991a,b)). Barro and Sala-i-Martin (1997) derive transitional dynamics for the South but cannot consider the possibility of a feedback effect for the North since they assume no trade in intermediate goods. Hence, no transition path exists for the North. This paper combines aspects of both strands of the literature. Relative to the first strand, this paper considers what happens if the South specializes in imitation, an activity assumed to have smaller positive externalities than innovation. Relative to the second strand, this paper also considers the effects of NorthSouth trade on technological progress in both regions. Since trade causes a feedback effect between Northern and Southern research, the feedback effect in turn affects not only the steady state, but also the transition to steady state in both the North and the South. Hence, the issue of North-South trade is considered not only in terms of whether trade leads to Southern specialization in imitation, but also in terms of how such 4 Stokey’s model considers specialization in a traditional sector with no learning-by-doing versus specialization in industries with learning-by-doing, but does not consider North-South trade. 5 Rivera-Batiz and Romer (1991) consider the effect of increased economic integration through trade between two similar developed countries.

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trade affects the diffusion of technology to the South and, in turn, worldwide growth. Rutherford and Tarr (2002) incorporate expanding intermediate goods varieties as an engine of growth into a computable general equilibrium model. They estimate gains from trade to range from a minimum of 3% up to a 25% gain in Hicksian equivalent variation. Our paper incorporates Rutherford and Tarr’s notion that access to intermediate goods is important, but it further develops the theoretical model for demonstrating the importance of feedback effects caused by technological diffusion.

2

Imitation and Learning-to-Learn

Among the different possible channels of technological diffusion, we are interested in analyzing the role of trade in the diffusion of technology. In particular, we are interested in the reverse engineering of technology embodied in traded goods. Several empirical studies consider the possible link between general imports and technological diffusion (Eaton and Kortum, 1996a,b; Coe and Helpman, 1997; Coe et al., 1997; Keller, 1998; Coe and Hoffmaister, 1999).6 Trade based convergence clubs also provide evidence that trade is likely an important channel for technological diffusion (Ben-David, 1993, 1996; Ben-David and Rahman, 1996). Moreover, in a survey of 26 U.S. firms whose technology had diffused to non-U.S. competitors, Mansfield and Romeo (1980) found that U.S. firms felt that reverse engineering was the most frequent channel through which technology “leaked out.” Beyond the static benefits of imitation, reverse engineering leads to learning. Successful imitation by a firm increases that firm’s insight into how goods are engineered and improved upon. Imitation not only makes a firm better at future imitation but also improves its chances of successfully inventing the next quality level on its own. For example, Advanced Micro Devices, Inc. and Samsung both initially specialized in reverse engineering and cloning leading edge technology, but have since switched to innovative research. This learning differs from learning-by-doing in that the skills gained are general and thus applicable to different types of research within an industry. We therefore refer to this as learning-to-learn. This is much like graduate studies, where the first years in graduate school are spent reverse engineering the pre-existing stock of academic knowledge. During that time, students attain the skills and detailed understanding of the subject matter necessary to hopefully “innovate” on their own. Using panel data for DCs and LDCs, Connolly (2003) finds a significant positive relationship between high technology imports from DCs as a share of GDP and domestic innovation and imitation.7 Additionally, 6 Coe

et al. (1997) consider machine and equipment imports rather than general imports. further finds that the importance of high technology imports to domestic research is greater in LDCs countries

7 Connolly

5

there is evidence that importing advanced Northern capital goods lowers the Southern cost of imitation because of general exposure to imports, and servicing and distribution by local importing firms.8,9 Finally, trade increases the incentives to imitate by providing access to larger international markets.10

3

Two-Country Quality-Ladder Model

We extend the basic setup of Barro and Sala-i-Martin (2004, Ch. 7) to an open economy situation. We model technological diffusion through reverse engineering of technology embodied in intermediate goods. We assume no domestic or international enforcement of intellectual property rights. The South experiences learning-to-learn effects even if trade with the North leads to Southern specialization in imitative research. As long as the South imitates goods that it did not previously produce, it benefits from learning-to-learn in research.11,12 We consider the quantitative effects of international trade with imitation, assuming that the two countries are starting from steady-state positions with partial Southern trade barriers and the North is the lead innovating country. Trade is balanced at all times so there are no international capital flows. The domestic interest rate is determined by domestic technology. With trade, firms can use imports of intermediate goods in final goods production. Southern firms import any intermediate goods that have not yet been copied, and export the Southern final good, as well as any lead intermediate goods that they have reverse engineered.13 Since the South can immediately import higher quality Northern intermediate goods for use in final goods production, it is not limited by its own ability to produce intermediate goods. With sufficiently low trade barriers, both Northern and Southern output growth will be determined by Northern technological progress. than in DCs countries. This may reflect the fact that, since LDCs are often not highly integrated with DCs, the role of trade in physical goods is all the more important for the diffusion of technology to the LDC. Thus trade appears to play an important role in technological diffusion and, in turn, conditional convergence, particularly for LDCs nations. 8 For example, if each individual exposed to a good has a certain probability of imitating it, then the number of people exposed to the good should positively affect the overall probability that the good is imitated. 9 Lesley (1924) provides anecdotal evidence of three independent U.S. imitations of previously imported European Portland cement during the late 1800s: by an individual who used Portland cement in construction, by a company that made concrete products, and by a large importing firm that distributed Portland cement within the U.S. The importance of exposure to a good is also demonstrated in Thomson’s (1987) study of 3,500 U.S. sewing machine patents, in which he finds that patenting activity followed sewing machine sales both geographically and temporally. 10 Sokoloff (1988) finds that U.S. counties from 1790 to 1846 with access to navigable waterways had higher patenting rates than counties without such access. Moreover, he finds an increase in county patenting rates after the introduction of new waterways in or adjacent to these counties. Thus, both exposure to goods and access to larger markets appear to play important roles in research activity. 11 This contrasts with Young’s (1991) model, which assumes that if learning-by-doing for a given good is exhausted in one country, then a second country which begins production of the same good will not benefit from any learning-by-doing. 12 van Elkan (1996) considers the issue of human capital accumulation and technological diffusion. For tractability, we consider research experience without specifically modeling it as human capital. 13 With lower equilibrium Southern marginal costs of production, Southern firms can underprice lead Northern firms. Hence, both countries will switch to using copied intermediate goods in their final goods production whenever available.

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Furthermore, since importing firms are responsible for distributing and servicing these intermediate goods, they learn a great deal about the goods they are selling. They learn which products are in greatest demand, what are the most recent developments within the industry, how to adapt the goods to local conditions if necessary, and how to fix or replace the goods they sell. Hence, importing intermediate goods lowers the cost of imitation. Thus, for a given infrastructure level and past learning-to-learn, countries with greater openness to imports face lower costs of imitation. As trade barriers decrease, Northern firms can sell to a larger market but are concerned with the joint probability of losing their market either to the next innovation or to a lower-priced imitation. Relative to being closed to intermediate goods imports, where Southern firms only needed to imitate Northern goods one quality rung above the current Southern quality level, trade forces Southern firms to imitate lead Northern goods, possibly several quality rungs above their own experience level. Still, since trade in physical goods allows for reverse engineering, it is possible for Southern firms to imitate Northern goods several quality levels ahead of the technology currently produced in the South. The cost and speed of imitation in each sector depends on how large a technology gap needs to be bridged by Southern imitators.

3.1

Consumer’s Problem

The Northern consumer makes consumption and savings decisions to maximize the present value lifetime utility Z

∞

u(C¯N )e−ρt dt 0 ! ¯ 1−θ − 1 C N u(C¯N ) = 1−θ max ∗

{CN ,CS ,v}t→∞

(3.1) (3.2)

κ ∗ 1−κ C¯N = CN CS

(3.3)

v˙ = w + rN v − EN

(3.4)

EN = PN CN + PS∗ CS∗ .

(3.5)

The constant relative risk aversion instantaneous utility function is given by (3.2). The inter-temporal elasticity of substitution is equal to

1 θ.

Equation (3.3) is a Cobb Douglas aggregator that defines the

Northern composite good, C¯N , in terms of Northern and Southern final goods consumed in the North, CN and CS∗ , respectively, with domestic expenditure-share parameter κ. In the model, exports are denoted by an asterisk ∗. Thus, CS∗ represents Southern final goods exports. The return to assets, v, in the North is 7

rN , and the wage rate is w. Households supply one unit of labor inelastically every period. Equation (3.4) gives the evolution of the value of assets, v, ˙ as the difference of labor and interest income minus Northern consumption expenditures, EN . Equation (3.5) gives total expenditures by the North, EN , for a given set of prices PN and PS∗ for final goods CN and CS∗ , respectively. The consumption-based price index, P¯N , is defined as the minimum expenditure, EN , such that the composite good index, C¯N = 1, for a given set of prices (Obstfeld and Rogoff, 1996, Ch. 4): P¯N =



PN κ

κ 

PS∗ 1−κ

1−κ .

(3.6)

Given standard calculations, we obtain two expressions for the Northern consumer demand for domestic goods and imported Southern goods: P¯N ¯ CN PN P¯N CS∗ = (1 − κ) ∗ C¯N . PS CN = κ

(3.7) (3.8)

Substituting the demand expressions into the household’s utility maximization problem yields the usual expression for consumption growth: C¯˙ N 1 = θ C¯N

! P¯˙N rN − ¯ − ρ . PN

(3.9)

The problem of the Southern household is entirely symmetric: Z

∞

u(C¯S )e−ρt dt 0 ! ¯ 1−θ − 1 C S u(C¯S ) = 1−θ max

∗ ,C ,v} {CN t→∞ S

(3.10) (3.11)

∗ 1−β β C¯S = CN CS

(3.12)

v˙ = w + rS v − ES

(3.13)

∗ ES = PS CS + PN∗ CN .

(3.14)

We assume that both countries spend the same proportion on the goods produced in the North, (i.e.,

8

β = 1 − κ). The resulting expression for the Southern households’ demand functions are

P¯S =



PN∗ κ

(κ) 

PS 1−κ

(1−κ) (3.15)

P¯S ¯ CS PN∗ P¯S CS = (1 − κ) C¯S . PS ∗ CN =κ

3.2

(3.16) (3.17)

Final Goods Production

We now consider the production sector of the economy, beginning with final goods production. We begin from a conventional quality ladder model (Grossman and Helpman, 1991a,b; Aghion and Howitt, 1992; Barro and Sala-i-Martin, 1997, 2004). Technology is embodied in intermediate goods. Thus, final goods output in each country is driven by technological advances in the quality of domestically available inputs, regardless of country of origin. The aggregate final goods production function, undertaken by many perfectly competitive firms, in the North (country N) and the South (country S) is:

Yi = Ai Lα i

J  X

q kNj x ˆikj

1−α

, i ∈ {N, S}

(3.18)

j=1

A is a productivity parameter dependent upon the country’s institutions, such as tax laws, property rights, and government services, and L is the labor input used by the representative firm for final goods production. ˆikj is the quality-adjusted level of intermediate good j used in final goods production (there are a fixed q kNj x number, J, of intermediate sectors.) The intermediate goods can be either domestic or foreign-produced. From equation (3.18) we see that as the quality level of intermediate goods used rises so does the final goods output. We assume that each country produces a different final good. Final goods in each country can be transformed one-to-one into consumption goods, research resources, innovated and imitated intermediate goods, and can be used for payment for imports from the other country at the appropriate relative prices. The Southern country imposes tariffs on intermediate goods and final goods manufactured in the North.14 The tariff rates are τXS for intermediate goods and τYS for final goods. In addition, each country faces transportation costs, t, which are based on free-on board prices. Given the tariffs and transportation costs, we assume that final goods production in each country is competitive. Let the final good in the North sold 14 The

tariff revenues are returned in a lump-sum to Southern residents.

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in the north, YN , be the numeraire, so PN = M CN = 1, where M CN is the marginal cost of final goods production in the North. Northern final goods sold in the South facing tariffs and transportation costs have price PN∗ = (1 + τYS + t). Southern final goods sold in the South have prices equal to their marginal cost of production PS = M CS , which is determined in equilibrium. Southern final goods sold in the North face prices PS∗ = PS (1 + t). Since final goods can be transformed one-to-one into consumer goods in each country, consumer goods and final goods have the same prices.

3.3

Intermediate Goods Production and Industrial Structure

We assume that intermediate good producers engage in Bertrand price competition, resulting in limit pricing, following Barro and Sala-i-Martin (2004, Ch. 7). With limit pricing, only the highest-quality good is sold in each sector. The quality of each good increases with successful innovations. Each quality improvement can be thought of as stepping one rung further up a ladder. The size of each step reflects the size of quality improvements. As often assumed, we set the size of this step to be a constant, q, greater than 1. The rung at which the good is located on a quality ladder is denoted by k. Normalizing so all goods begin at quality level 1, the quality level of an intermediate good in sector j rises from 1 to q with the first innovation, to q 2 with the second innovation, and to q kj with the kj -th innovation. Which country actually produces the intermediate goods used in final goods production depends on each country’s technological level, as well as trade barriers. By assumption, the North is the more technologically advanced country. Therefore it must innovate to push forward its (and the world’s) technology frontier. The South can increase its domestic technology by imitating Northern technology, at least until the gap in their technology levels is eliminated. Once knowledge of how to produce an intermediate good exists domestically, it can be produced using the final goods production function. Therefore, the marginal cost of producing an intermediate good equals the marginal cost, M Ci , of producing the final good. So, the marginal cost of producing an intermediate good is independent of its quality level and is identical across all domestic sectors. Recall that we assumed that the Northern final good is numeraire (M CN = PN = 1). We further assume that structural parameters are such that in equilibrium marginal costs are greater in the North than in the South (M CN > M CS ). This enables a successfully-imitating intermediate goods Southern firm to capture the world market. We assume that knowledge of how to make a good is public knowledge within a country.15 The lead innovating firm in each sector uses limit pricing to wipe out sales of lower-quality intermediate goods in its 15 One

could think of countries as having domestically enforced patents that protect the lead firm’s domestic monopoly of that quality good, while at the same time disseminating without any cost acquired knowledge to other domestic firms.

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sector.16 Further, we assume that innovations are drastic. That is, the size of quality improvements is large enough that a Northern firm can hold the world market with a single quality level improvement over a Southern copy. A Southern firm can capture the world market by imitating (and underpricing) the lead Northern good. Hence, there is a Vernon-type product cycle where production shifts from the North to the South with successful Southern imitation and back with subsequent Northern innovation. Intermediate goods firms decide how many resources to devote to research based on the expected present value of profits for successful research, which depends on the probabilities of innovation and imitation. Within an intermediate goods sector j, presently at quality level kN j , pIkN j is the probability per unit of time that the (kN j + 1)th innovation occurs and it is given by:

pIkN j = zIkN j ϑkN j ϕIkN j ,

(3.19)

where ϑkN j = βI q kN j , ϕIkN j =

1 q ζI

−kN j α

and .

The probability of innovation pIkN j follows a Poisson process, which depends positively on resources devoted to research, zIkN j , and past industry-specific domestic learning-to-learn, ϑkN j , and negatively on the complexity, ϕIkN j , of the good upon which firms are attempting to improve.17 βI reflects a positive externality from past experience, while ζI is a fixed cost of innovative research. The probability, pCkN j , of imitating the current lead technology, kN j , follows a similar form:

pCkN j = zCkN j ϑkSj ϕCkN j ,

(3.20)

16 Even without domestic IPR protection, the existence of any fixed cost to imitation will effectively preclude domestic imitation of a domestic good. 17 The forms assumed for ϑ and ϕ guarantee constant returns to innovative research with respect to current technology levels (kij ). This is needed to consider a balanced growth path in steady state. Furthermore, this setup is reasonable if there are an infinite number of potential innovations, implying no diminishing returns to innovative research and development (Romer, 1990).

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where ϑkSj = max(βC q kSj , βI q kN j ), ϕCkN j =

eω −kN j q α ζC qˆjσ

for

σ > 1,

q kSj , and q kN j  ηM M ω= F ηF . QN

qˆj =

Learning depends on the highest past experience within that sector whether gained through imitation or through innovation.18 Relative to the cost of innovation, two new factors affect the cost of imitation,

ζC qˆjσ eω .

First, the cost of

imitation depends positively on the sector j South/North technology ratio, qˆj , and reflects the increasing cost of imitation as Southern technology approaches that of the North. Hence, there are decreasing returns to imitation as the pool of goods that can be targeted for imitation decreases. The parameter σ affects how quickly the cost of imitation rises as the technology gap falls.19 Since the cost of imitation is increasing as the North-South technology gap decreases, the probability of imitation and, consequently, the probability of innovation both change in transition to steady state. Second, the cost depends negatively on the interaction,   ηM ω = QMN F ηF , between the two countries. This is measured by the interaction of Southern imports kN j (1−α) PJ of intermediate goods, M , scaled by the aggregate Northern technology level, QN = j=1 q α , and the scale of Southern infrastructure, F , with elasticities ηM and ηF respectively.20 We assume that the externality from past innovative experience, βI , is greater than those from imitation, βC . Similarly, the fixed cost of imitation, ζC , is assumed to be less than the cost of innovation, ζI .

21

With monopolistic competition in the intermediate good sectors, expected profits depend on the type of competition faced by the firm. There are three different types of firms: Northern firms facing Northern competition, nN N , Northern firms facing Southern competition, nN S , and Southern imitating firms facing Northern competition, nSN . Since there are J sectors, J = nSN + nN S + nN N .22 Pricing of intermediate goods will be determined by the competition that each producer faces. Northern firms facing Northern competition (there are nN N of these) choose a limit price slightly below q times the the sector has no imitative experience, then q kSj = 0, and if it has no innovative experience, then q kN j = 0. the experienced gained from imitation increases one-to-one with qˆ, σ must be greater than 1 for the probability of imitation to fall as qˆ increases. This guarantees a smooth transition. 20 In the model, we specify F as a parameter. 21 This is consistent with the empirical findings of Mansfield et al. (1981). 22 In the numerical experiments, we set the mass equal to one (J = 1), substituting summation signs by integrals where appropriate, so that so that the ns represent the fraction of the world market of intermediate goods held by type of firm. 18 If

19 Since

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lowest price at which the previous innovator could sell, since their product is q times more productive than its predecessor. Since the northern final good is the numeraire, M CN = 1, PN N = qM CN = q is the lowest price at which the previous innovator could sell in the North, and PN∗ N = q(1 + τXS + t) is the lowest price at which it could sell in the South without earning negative profits as they face Southern tariffs on intermediates of τXS and ad-valorem transportation costs, t.23 At these limit prices, world sales of all older technologies are wiped out. Similarly, Northern firms facing Southern competition, nN S , set limit prices PN S = qM CS (1 + t) = qPS (1 + t) domestically and PN∗ S = qM CS = qPS abroad. Southern firms, ∗ nSN , always face Northern competition and choose limit prices PSN = 1 for exports to the North and

PSN = 1 + τXS + t for domestic sales.24

3.4

Resource Constraints and Trade Balance

In either country i, for a given limit price, Px , and final goods price, Pi , implied demand for intermediate goods in sector j is

 1 Pi α xij = Li Ai (1 − α)q kij (1−α) . Px

(3.21)

Substituting the implied demands (3.21) into (3.18) and for the appropriate limit prices and aggregating across intermediate goods sectors obtains reduced form expressions for aggregate output in each country: h i α−1 1−α α−1 YN = QN ΛN nN N + nN S (1 + t) α PS α + nSN q α , # "    1−α  1−α α α 1−α PS PS + nN S + nSN q α , YS = QN ΛS nN N 1 + τXS + t 1 + τXS + t   1−α J X kN j (1−α) 1−α α 1/α α where QN = q i ∈ {N, S}. and Λi = Li Ai q j=1

(3.22) (3.23)

QN represents the Northern aggregate quality index. Note that aggregate production in both countries depends on QN , since limit pricing with free trade insures that only the highest quality technology will be used. Hence, even when an intermediate good is produced in the South, its quality level is the same as the lead Northern quality level. In steady state, sector shares, nN N , nN S , and nSN , are constant. Both countries’ steady-state growth rates depend solely on Northern technological progress, at least so long as the North remains the lead innovating country. Still, international trade and the subsequent risk of losing the market for a given intermediate good to Southern imitation causes the Northern rate of innovation to 23 This 24 The

holds if q(1 − α) ≤ 1. If instead q(1 − α) > 1, then Northern firms will use monopoly pricing. assumption of drastic innovations implies that q >

(1+τX +t) S . M CS

13

depend on the Southern rate of imitation. There are two world resource constraints reflecting that final goods produced by each country, YN and YS can be consumed, used for research, or transformed into intermediate goods: ∗ ∗ YN = CN + XN + ZN + CN + XN + TRANSN ,

(3.24)

YS = CS + XS + ZS + CS∗ + XS∗ + TRANSS , where   PN∗ S PN∗ N ∗ ∗ ∗ TRANSN = t nN S XN + n X + C NN NN S N , 1 + τXS + t 1 + τXS + t  ∗  PSN ∗ TRANSS = t nSN XSN + PS CS∗ , 1+t ∗ ∗ ∗ XN = nN S XN S + nN N XN N , XN = nN S XN S + nN N XN N ,

(3.25)

and

∗ XS = nSN XSN , and XS∗ = nSN XSN .

TRANSN and TRANSS reflect ad-valorem transportation costs (based on free on board prices) and asterisks, ∗, denote exports. The resources used in Northern intermediate good production is given by sum ∗ . of those resources used to produce intermediate inputs used domestically, XN , and those exported XN

Similarly, resources used in Southern intermediate good production is given by the sum of resources used to produce intermediate inputs used domestically, XS , and those exported, XS∗ . The intermediate input terms ∗ with two subscripts (e.g., XN N ) refer to resources used in the production of each type of intermediate good

per firm. We derive an expression for the Northern trade balance, TBN (a similar expression can be derived for its ∗ , Southern counterpart). The Northern trade balance is given by the difference of exports of final goods, CN ∗ ∗ ∗ and intermediate goods XN S and XN N minus imports of Southern final goods CS and imports of Southern

intermediate goods, XS∗ : ∗ ∗ ∗ ∗ ∗ ∗ ∗ TBN = PN (1 + τYS + t)CN + PN∗ S nN S XN S + PN N nN N XN N − PSN nSN XSN − CS (1 + t)PS ,

(3.26)

where τYS are Southern tariffs on final goods. We wish to focus the impetuous for trade as resulting from differences in the ability to produce intermediate goods and final goods, and to abstract from consumption smoothing motivated goods flows. Thus we assume that the relative price of imports, PS , will adjust to balance trade each period.

14

3.5

Transitional Dynamics

The model dynamics depend on the rate of innovation and imitation, the relative level of the two technologies, the rate of growth of consumption in each country, and the relative price level. Since the probabilities of innovation and imitation of a particular industry depend on the South/North technology ratio within that industry, these equilibrium probabilities are industry-specific. However, to characterize the transition path for the aggregate economies, it is sufficient to consider the average domestic industry (denoted by the sector subscript a). Given the definitions of the average quality levels in each country (under the assumption that the North specializes in innovation and the South specializes in imitation) we derive an expression for the evolution of ˆ the South/North technology ratio, Q: ·

 1−α  ˆ Q Q˙ S Q˙ N = − = q α − 1 (pCkN a − pIkN a ) . ˆ QS QN Q

(3.27)

We derive expressions for the evolution of the industrial structure. That is, we need to determine the composition of Northern intermediate goods-producing firms that face only Northern competition, those that face Southern competition, and Southern intermediate goods producing firms. Entry and exit into these three categories depends on the probabilities of successful innovation and imitation, pI and pC :

n˙ N N = pI (1 − pC )nN S − [pI pC + (1 − pI )pC ]nN N

(3.28)

n˙ N S = pI (pC nN N + nSN ) − [(1 − pI )pC + pI (1 − pC )]nN S

(3.29)

n˙ S = (1 − pI )pC (nN N + nN S ) − pI nSN .

(3.30)

The first equation (3.29) states that the change in the number of Northern intermediate good-producing firms that face only Northern competition, n˙ N N , is equal to the number of Northern firms facing Southern competition, nN S times the joint probability that there is innovate but no imitation imitation, pI (1 − pC ), minus the number of Northern intermediate good-producing firms that face Northern competition that loose the market upon imitation [pI pC + (1 − pI )pC ] = pC . The other two equations are derived in similar fashion. From these entry-exit conditions, and given that the probability of innovation and imitation are equalized in steady state (we will show this later), we derive expressions for the steady-state decomposition of

15

intermediate goods sectors into these three categories: (1 − pI ) J 2 − pI nSN = 1 − pI nN N = . 1 − pI

nSN = nN N nN S

(3.31)

In steady state, faster rates of innovation, pI , reduce the fraction of intermediate goods produced in the South, nSN , and increase the fraction of intermediate goods produced by firms that face Southern competition, nN S . We then derive expressions for the average resources spent on innovation and imitation (i.e., R&D). Substituting into the two resource constraints, (3.24) and (3.25), for the Yi from the production functions, (3.22) and (3.23), and for the Xi from the implied demand functions, (3.21), yields an expression for total resources, Zi , devoted to research in each country: (

ZN

  α−1 −1 α−1 −1 1−α 1−α  α α α α α =QN ΛN nN S (1 + t) PS + nN N + nSN q − nN S (1 + t) PS + nN N q " #    α1  tqPS 1−α PS nN S 1 + (1 + tq) − ΛS + nN N q 1 + τXS + t 1 + τXS + t )

(3.32)

− χN − (1 + t)χ∗N * ZS =QN

− χS − (1 + tPS )χ∗S

"  1−α  1−α   α1 #) α α 1−α PS PS PS + Λ S nN S + nN N + nSN q α − (1 − α) 1 + τXS + t 1 + τXS + t 1 + τXS + t  + 1−α t (3.33) − ΛN nSN (1 − α)q α 1+ , 1+t (



, and χ∗S ≡

∗ CS QN

Average resources devoted to research, Zia =

Zi J ,

where χN ≡

CN QN

, χ∗N ≡

∗ CN QN

, χS ≡

CS QN

. can be substituted into the functional forms for inno-

vation and imitation (3.19) and (3.20) to yield reduced form expressions for the probabilities of the average

16

rate of innovation, pIkN a , and imitation, pCkN a :

pIkN a

(



 −1 −1 1−α  PS + nN N + nSN q − nN S (1 + t) α PSα + nN N ΛN nN S (1 + t) q # "     α1 1−α tqPS PS − ΛS nN S 1 + (1 + tq) + nN N q 1 + τXS + t 1 + τXS + t )

βI = ζI

α−1 α

α−1 α

1−α α



(3.34)

− χN − (1 + t)χ∗N pCkN a

βC eω ˆ 1−σ = Q ζC ( + ΛS

* − ΛN nSN (1 − α)q 

nN S + nN N

PS 1 + τXS + t +

1−α α

 1+

t 1+t



"  1−α α 1−α + nSN q α

PS 1 + τXS + t

  1−α α − (1 − α)

PS 1 + τXS + t

− χS − (1 + tPS )χ∗S .

 α1 #)

(3.35)

The cost of imitation, and hence the probability of imitation for the average sector, depends on the average ˆ= South/North technology ratio, which equals the aggregate South/North technology ratio, Q

QS QN

. Since the

ˆ interest rates and growth probabilities of innovation and imitation in the average industry change with Q, rates will also change during the transition to steady state. We now derive the growth rate of consumption in each country. The rates of growth of consumption depend on the country-specific interest rates, (3.9), and on the evolution of relative prices. In turn, the interest rates (rN and rS ) are determined by two free-entry conditions which state that, with free entry, firms devote resources to research until they exactly equal the expected present value of profits:

pIkN a E(vIkN a +1 ) = ZIkN a

(3.36)

pCkN a E(vCkN a ) = ZCkN a ,

where Z

E(vIkN a +1 ) = πIkN a +1 Z E(vCkN a ) = πCkN a

∞

t ∞

(3.37)

Rs

e− t [rN (v)+pCkN a +1 (v)+pIkN a +1 (v)−pCkN a +1 (v)pIkN a +1 (v)]dv ds,

and

s e− t [rS (v)+pIkN a (v)]dv ds.

R

t

The E(v) in equations (3.36) and (3.37) represent the expected present value of profits from successful research. In the case of innovation, it is discounted by the Northern interest rate and by the probability of losing sales to either imitation or to the (kN a + 2)th innovation. In the case of imitation, it is discounted by the Southern interest rate and the probability of losing sales to the (kN a + 1)th innovation.

17

Differentiating both sides of the free-entry conditions (3.36) and (3.37), using Leibniz’s rule for the left-hand side of the equations, yields expressions for the interest rates in both countries:

rN =

pIkN a πIkN a +1 Z˙ IkN a p˙IkN a π˙ IkN a +1 + − − ZIkN a ZIkN a pIkN a πIkN a +1 (3.38)

− pCkN a +1 − pIkN a +1 + pCkN a +1 pIkN a +1 rS =

Z˙ CkN a p˙CkN a π˙ CkN a pCkN a πCkN a + − − − pIkN a . ZCkN a ZCkN a pCkN a πCkN a

The interest rate in each country determines, in the long run, the growth rate of output, consumption, and research expenditures in each country. We can derive two consumption growth conditions by taking natural logs and derivatives of (3.7) and (3.17) and substituting in for the growth rates of aggregate consumption (3.9) and for the price indexes (by taking logs and derivatives of (3.6) and (3.15)): C˙ N 1 P˙ ∗ = (1 − κ) S∗ + CN PS θ C˙ S P˙S 1 = −κ + CS PS θ

P˙ ∗ rN − ρ − (1 − κ) S∗ PS ! P˙S rS − ρ − (1 − κ) . PS

! (3.39)

∗ for the South, can The rate of growth of consumption imports in each country, CS∗ for the North and CN

be equally derived. Since PS∗ = PS (1 + t), then the growth rate of each component of the composite good in each country only depends on the interest rate in that country and the change in the relative prices, PS . Since χN ≡

CN QN

, χS ≡

CS QN

, we can derive expressions for rate of consumption, relative to the Northern

technology level (i.e. the world technology frontier), in each country: !  1−α  P˙S rN − ρ − (1 − κ) − q α − 1 pIkN a PS !  1−α  P˙S rS − ρ − (1 − κ) − q α − 1 pIkN a . PS

C˙ N Q˙ N P˙S 1 χ˙ N = − = (1 − κ) + χN CN QN PS θ C˙ S Q˙ N P˙S 1 χ˙ S = − = −κ + χS CS QN PS θ

(3.40)

From the expressions if follows that in steady state there will be interest rate equalization between the two countries. So, even though there are no international capital flows, the diffusion of technology is sufficient to yield interest rate equalization between countries in the long run. Using these two equations that describe the relative level of consumption in each country, (3.40), two of our firm category net entry conditions, (3.29) and (3.30), and the expression for growth of the South/North ˆ χN , χS , nN S , and technology ratio (3.27) gives us a system of five differential equations in the variables Q,

18

ˆ nN S , and nSN , these characterize the transition paths for nSN . Together with three initial conditions for Q, the North and the South.

4

Trade Experiments

We solve the model numerically for reasonable parameter values that yield saddle path stability and realistic growth rates. The solution method works by linearizing the five differential equations that characterize the model dynamics around the balanced growth path. Benchmark parameter values are based on theoretical and empirical priors. Table 1 describes parameter values used. Further, a wide range of parameter values yield similar stable saddle paths to steady state, differing principally in terms of the steady-state levels of ˆ nN S , nSN , χN , and χS to which they approach.25 Q, Table 1: Benchmark Parameters ρ=.02 θ=3 α=0.7 q=1.5 σ=3.5 βI =0.9 βC =0.6 ζI =6 ζC =2 AN =3.5 AS =3 LN =5 LS =6.25 ηM =2 ηF =1.5 t=0.01 F =0.0037 τXS =0.05 τYS =0.05

subjective discount rate 1 θ =constant inter-temporal elasticity of substitution labor share in production size of quality improvements ˆ elasticity of cost of imitation w.r.t. Q externality from innovation externality from imitation fixed cost of innovation fixed cost of imitation N. productivity parameter S. productivity parameter N. work force S. work force elasticity of ω w.r.t. QMN elasticity of ω w.r.t. F ad-valorem transport cost transportation and communication infrastructure S. intermediate goods tariff S. final goods tariff

25 Still, the parameter space contains combinations that yield non-existent steady states, globally convergent and globally divergent paths, as well as paths with endogenous cycles. We focus on saddle paths with all real eigenvectors and only three negative eigenvalues in the linearized transition matrix, leading to saddle path stability given the three non-jumping state variables.

19

4.1

Benchmark Experiment: Generalized Southern Trade Liberalization

The first experiment we consider, the benchmark experiment, is a generalized Southern trade liberalization: the Southern country drops tariffs for intermediate goods and final goods from 5% to 1% in period 0. Column (1) of Table 2 shows the value of parameters, steady state values, and compensating variations of consumption arising from the generalized Southern trade liberalization. The first column, labeled pre, shows the parameters and the steady state values of key variables before the trade liberalization. The second column, labeled post show the values of the new parameters and the new steady state. Following a generalized trade liberalization, in the new steady state, both the North and the South face increased international competition: the share of Northern firms facing only Northern competition, nN N , drops and so does the fraction of intermediate goods produced in the South, nSN . In the new steady state, the increase in international competition raises up the rate of innovation and growth. Even though the fraction of intermediate goods produced in the South drops in steady state, the relative level of Southern ˆ technology increases (higher Q). Figure 1 shows the transition path for key variables for the South as it moves from having tariffs of 5% to 1% on intermediate imports, τYS , and final goods, τXS : the evolution of the South/North technology ratio, ˆ the average probabilities of innovation and imitation, pC and pI , the interest rate in each country, rN and Q, rS , and the level of the composite good in each country, C¯N and C¯S . In all the figures, the policy change occurs in period 5. After an initial drop, the probability of imitation jumps above its initial level and gradually declines to a new higher steady state.26 Innovation drops and gradually rises until it hits its new higher steady state equalling imitation. Since the rate of imitation is generally above that of innovation during the transition, ˆ During the Southern technology is catching up to that of the North. This is reflected by an increase in Q. the transition, Southern intermediate producing firms benefit because there is cheaper access to imported intermediate goods, which lowers their innovating costs. Thus, the rate of return of intermediate producing firms in the South is higher. The South also demands more imports as well, as their relative cost is lower. During the initial periods of transition, Northern firms are made worse off due to the increased Southern competition and faster imitation. Moreover, with the lower tariffs in the South, Northern intermediate firms that face Northern competition and export to the South cannot charge as much for their products (with 26 It

should be noted that, given our system of five differential equations and three state variables, we have three negative eigenvalues determining the evolution of the system. As noted in Eicher and Turnovsky (2001), the presence of multiple eigenvalues leads to non-monotonicities in the evolution of the variables. In our case, this leads to some jumpiness during the first periods after a policy change.

20

21 0.2148 0.1423 0.0408 0.3224 0.4398 0.3138 0.2464 0.9957

0.2125 0.1410 0.0403 0.1920 0.4406 0.3130 0.2465 1.0179 -0.31 2.24 0.40

3.5 0.9 0.6 6 2 2 1.5 0.0037 0.01 0.01 0.01

3.5 0.9 0.6 6 2 2 1.5 0.0037 0.01 0.05 0.05 0.2142 0.1420 0.0407 0.2477 0.4400 0.3136 0.2464 1.0023

3.5 0.9 0.6 6 2 2 1.5 0.0037 0.01 0.02 0.02

1.15 1.16 0.24

0.2156 0.1428 0.0409 0.2032 0.4396 0.3141 0.2464 0.9978

3.5 0.9 0.6 6 2 2 1.5 0.0037 0.01 0.01 0.02

Intermediate good tariff cut pre post

Benchmark general trade lib pre post

0.2134 0.1415 0.0405 0.2999 0.4403 0.3133 0.2464 0.9992

3.5 0.9 0.6 6 2 2 1.5 0.0037 0.01 0.02 0.01

-0.46 0.18 -0.14

0.2142 0.1420 0.0407 0.2477 0.4400 0.3136 0.2464 1.0023

3.5 0.9 0.6 6 2 2 1.5 0.0037 0.01 0.02 0.02

Final good tariff cut pre post

(3)

0.2148 0.1423 0.0408 0.3224 0.4398 0.3138 0.2464 0.9957

3.5 0.9 0.6 6 2 10 1.5 0.0037 0.01 0.01 0.01

-0.27 2.28 0.40

0.2125 0.1410 0.0403 0.1920 0.4406 0.3130 0.2465 1.0179

3.5 0.9 0.6 6 2 10 1.5 0.0037 0.01 0.05 0.05 0.2205 0.1455 0.0418 0.2910 0.4381 0.3158 0.2462 0.9942

3.5 0.9 0.6 5.85 2.15 2 1.5 0.0037 0.01 0.01 0.01

0.94 3.20 1.39

0.2125 0.1410 0.0403 0.1920 0.4406 0.3130 0.2465 1.0179

3.5 0.9 0.6 6 2 2 1.5 0.0037 0.01 0.05 0.05

post

pre

pre

post

IPR payments

(5)

Fast diffusion

(4)

0.2136 0.1416 0.0405 0.2302 0.4402 0.3133 0.2464 1.0165

3.5 0.9 0.6 6 2 2 1.5 0.0037 0.0001 0.05 0.05

1.45 1.35 0.19

0.2125 0.1410 0.0403 0.1920 0.4406 0.3130 0.2465 1.0179

3.5 0.9 0.6 6 2 2 1.5 0.0037 0.01 0.05 0.05

Trade cost drop pre post

(6)

CV refers to the compensated variation of consumption following the policy change and are presented as percentages. See main text for explanation.

nN S nN S nN N PS CV North South Steady State

Parameters σ βI βC ζI ζC ηM ηF F t τXS τYS Steady State pI = pC rN = rS ˙ C/C ˆ Q

(2)

(1)

Table 2: Numerical Examples Effects of Trade Liberalization

Figure 1: Generalized Southern Trade Liberalization Intermediate goods tariff τXS and final goods tariff τY S reduced from 5% to 1% 22

price PN∗ N = q(1 + τXS + t)) and thus loose monopoly profits per good sold. Both of these forces reduce the profitability of Norther firms, and reduce the interest rate in the North. Other forces raise demand for Northern produced intermediate inputs and increase the profitability in the North. Initially, Southern demand for imports increases because of their lower cost. However, this is not enough to offset the increased Southern competition and so, overall, the Northern interest rate is lower than the pre-policy interest rate for several periods. Eventually, as the Southern country grows, the Southern demand for intermediate inputs rises even further. This faster growth enlarges the total size of the market for intermediate goods, which raises the profitability of both Northern and Southern firms. The Northern interest rate eventually surpasses the prepolicy change rate. In the new steady state, the Northern profitability and interest rate will be permanently higher. This happen even as the monopoly profits per firm are reduced due to the relative price drop. With higher steady-state rates of technological progress, output and consumption growth increases in the North and the South. This reflects the dynamic benefits for the South of increased trade with a more developed region, even when it specializes in imitative activities. The path of the interest rate and prices are important determinants of the path of consumption during the transition.27 The middle left hand panel in Figure 1 shows Northern consumption grows at a slower rate than Southern consumption throughout the transition, this mainly reflects the lower interest rate in the North than in the South. Moreover, the Northern interest rate is lower than the pre-policy change interest rate for quite some time which results in welfare losses for the North. This reflects the lower level of profitability of Northern firms. After several periods, as the South grows enough, Northern firms surpass pre-policy change profitability and Northern consumption grows faster. In the new steady state, the growth rate of consumption in both countries is faster. The last three rows of Table 2 present the compensating variations for the South and for the North from the generalized Southern trade liberalization including the transition, and the compensating variation comparing the steady state growth rates and ignoring the transition.28 The compensating variations represent the percentage change in the equilibrium path of consumption under initial conditions necessary to make the household indifferent between the South maintaining tariffs on all imports at 5% versus lowering them to 1%. The transition period to a new steady state is important to consider, both for the positive behavior of the economy and for normative considerations. Taking into account the transition, we find that the South 27 There 28 We

are also impact effects of the policy change on consumption, which are taken into account in the welfare calculation. compute the compensating variations along the lines suggested by Lucas (1987).

23

unambiguously benefits from the increased openness to Northern imports. The South would require a 2.2% increase in the equilibrium path of consumption under initial conditions to be willing to maintain its tariffs. However, for the North the costs of transition dominate the steady-state welfare gains. When these costs of transition are included, Northern welfare falls despite a higher future steady-state growth rate. The North would be willing to give up about 0.3% of their initial equilibrium consumption path to avoid this increased competition from Southern imitators. The transition cost is sufficiently large that the welfare loss during transition outweighs the steady-state welfare gain for the North. Notice that, if we consider only the steadystate effects, shown in the last row of the table, both the North and the South gain from Southern trade liberalization; each would require a 0.4% increase in their initial consumption path to be indifferent to not liberalizing Southern trade.

4.2

Reduction in Southern Tariffs on Intermediate Goods

To better understand the effects of the generalized Southern trade liberalization, we consider a drop of each tariff rate in turn: first the intermediate goods tariff and then the final goods tariff. The numerical model dynamics is rather sensitive to changes in the tax rates, leading to explosive dynamics in some instances. We only consider a drop in each tariff rate from 2% to 1% instead of the drop from 5% to 1% that we considered in the generalized trade experiment. Thus, we will focus on the direction of the effects of each tariff change and not on the magnitudes. Column (2) in Table 2 shows the parameters, steady states, and compensating variation due to a reduction in the Southern intermediate goods tariff from 2% to 1%. A decrease in intermediate good tariffs decreases the Southern price of intermediate good imports from the North manufactured by firms that face Northern competition (with price PN∗ N = q(1 + τXS + t)). The Southern price of Southern produced intermediate inputs (PSN = 1 + τXS + t) also drops. The price of intermediate imports manufactured by Northern firms that face Southern competition (PN∗ S = qM CS = qPS ) is unaffected by the direct effect of the tariff drop given the assumption of limit pricing. Thus, the South’s relative demand for intermediate goods imports produced by firms facing Northern competition increases and the demand for Southern intermediate goods also increases. Through the balanced trade equation, the relative price of Southern consumption goods, PS , drops. The drop of relative prices decreases the South’s relative demand for intermediate goods imports from firms facing Northern competition as well as the demand for Southern intermediate goods. Thus, we have opposing forces on the relative demand for intermediate goods. Recall the reduced from expression for Southern output,

24

equation (3.23): " YS = QN ΛS nN N



PS 1 + τXS + t

 1−α α + nN S + nSN q

1−α α



PS 1 + τXS + t

#  1−α α

Notice the PS and τXS have opposing effects on Southern output. Thus, the impact on Southern output is ambiguous. In the numerical experiment, the positive effect on demand dominates. Both Northern and Southern firms are more profitable in the new steady state. The South benefits throughout the transition from cheaper imports of intermediate goods, which reduces the cost of imitation. The increased demand for Northern intermediate good exports increases the profitability of Northern firms and thus increases the rate of innovation. Since the relative Southern technology level is lower in the post-policy steady state, it must be the case that the rate of innovation grows higher than the rate of imitation during the transition. A cut in intermediate goods taxes improves welfare both for the North and the South. This is true despite the South having a lower share of intermediate good production. Also, the North faces a reduction slight reduction in its share of the highly-profitable nN N sector. In the new steady state, the increased demand for Southern imports, with its positive effect on Southern consumption and expanded world market for intermediate goods, is enough to drive up the rate of world growth.

4.3

Reduction in Southern Tariffs on Final Goods

Column (3) in Table 2 shows the parameters, steady states, and compensating variation due to a reduction in the Southern final goods tariff. A decrease in Southern final goods tariffs affects the relative demand for consumption goods, increasing the Southern demand for Northern final goods imports and decreasing the demand for Southern consumption goods.29 . A cut in the Southern final goods tariff, through the balanced trade equation, reduces PS . The drop in the Southern relative price level reduces the relative price of Northern intermediate goods that face Southern competition (with price PN∗ S = qM CS = qPS ) relative to the price of Northern goods that face Northern competition (PN∗ N = q(1 + τXS + t)) and Southern goods (PSN = 1 + τXS + t). The relative markup of Northern goods facing Southern competition is lower. Thus, a cut in final goods tariffs, through its effects on prices, increases the competition. The price change reduces the Southern demand for intermediate goods produced by Northern firms facing Northern competition and produce by Southern firms . While the North 29 Recall

∗ = (1 + τ that Northern consumption goods sold in the South face have prices PN YS + t)

25

gains exports to the South of nN S goods, they loose exports of nN N . Northern intermediate goods exports that face Northern competition have larger markups than those that face Southern competition. Moreover, markups on Northern intermediate goods exports that face Southern competition are reduced. As a result, the profitability of Northern firms is reduced. This is reflected in the reduction in the Northern interest rate and the world growth rate in the new steady state. It is also reflected in the increase in the share of Southern firms which capture Northern markets (nSN increases). Northern welfare is reduced because of transition costs and a lower steady state rate of growth. A reduction in the Southern relative price level leads to a reduction in Southern final output as the demand for intermediate good inputs drops. However, while Southern consumers loose income from intermediate good production, they benefit because consumer goods imports are cheaper. Also, there is greater competition as the markup for Northern intermediate goods imports is lower. In the end, the transition welfare gains for the South are large enough to offset the new steady state looses from the lower world growth rate.

4.4

High Rate of Technological Diffusion

We consider an experiment with generalized Southern trade liberalization when the rate of technological diffusion is high (column (4) in Table 2). This experiment allows us to highlight the importance of the transition in the generalized trade liberalization experiment. In this experiment, the elasticity of the relative cost term to imports of intermediate goods is high, ηM = 10, before and after the generalized Southern trade liberalization. Compared to the benchmark experiment, the rate of technological diffusion does not impact either the pre- or post-trade reform steady states, it only affects the transition by speeding it up. We consider the transition effects for each country. For the North, a rapid technological diffusion has effects that have opposing impact on its welfare during transition. On the one hand, faster technological diffusion increases the rate at which Northern technologies loose market share and reduces Northern welfare because the higher probability that the South will successfully imitate and take over a market. On the other hand, faster technology diffusion increases the relative size of the Southern market during transition, and increases competition from Southern firms that lowers the monopoly distortions to the North, increasing North welfare. Overall, the faster the diffusion, the more the positive Northern welfare effect dominates the negative and Northern welfare improves relative to the benchmark experiments. The effects of faster diffusion are unambiguously positive for the South. Recall that we obtained from the trade liberalization experiment that the negative welfare effect on the North was driven by welfare effects during transition. When we increase the rate of technological diffusion, the transition is faster, and thus the welfare costs for

26

the North are reduced. Moreover, the welfare gains for the South are magnified.

4.5

Southern IPR Payments to the North

We now consider a generalized Southern trade liberalization concurrent with imposition of IPRs. Specifically, we force Southern imitators to pay a licensing fee to Northern firms. We model this as raising the fixed cost of imitation, ζC , from 2 to 2.15, while lowering the fixed cost of innovation, ζI , from 6 to 5.85. Column (5) in Table 2 shows the parameters and the steady states for the IPR experiment. The imposition of low-level IPRs leads to a higher steady-state growth rate for each country than Southern trade liberalization alone. The growth of the world technology frontier is determined by the rate of innovation. In this experiment, the South subsidizes Northern innovation, which drives up the growth rate for both countries in the new steady state. In the new steady state there is a larger fraction of production done by Northern firms that face Southern competition (nN S = 0.3158) than in either the pre-policy change steady state or in the benchmark generalized Southern trade liberalization experiment. So, even as the North benefits from lower innovation costs, the sector that benefits the most is the more competitive nN S sector. In this sense, there is more competition with trade liberalization and IPR payments than in the case of trade liberalization alone. In principle, the transfer of resources from the South to the North due to the IPR payments could have hurt the South in terms of welfare. However, the South gains both from the transition and the faster steady state growth. In fact, the South is better off with the trade liberalization and IPR payments than with the trade liberalization alone.30 Despite the higher IPRs, the South has an even greater welfare gain. Now the South would require a 3.2% (vs. 2.2%) increase in its initial equilibrium consumption path to be willing to remain closed to intermediate goods imports and avoid any IPRs. The North also gains from a trade liberalization together with the imposition of IPR rights. The faster transition to the new steady state and the faster growth rate arising from the IPR payments are enough to offset the losses that the North suffers from the Southern trade liberalization. The North would now require a .9% increase in the equilibrium path of consumption under initial conditions to be equally happy without Southern trade liberalization and increased IPR enforcement. Figure 2 shows the evolution of the key variables during the transition to steady state. The paths are quite similar to those in Figure 1. The Southern interest rate both rises more and faster towards the new higher steady state. Noticeably, the Northern interest rate rises more and faster as well. The higher path of interest rates imply that consumption grows faster in both countries than in the benchmark generalized trade 30 Although

not in the table, the policy change for this IPR experiment is higher than that would result from one where IPR payments are made but where no trade liberalization occurs.

27

Figure 2: Southern Generalized Trade Liberalization with IPRs Intermediate goods tariff τXS and final goods tariff τY S lowered from 5% to 1%, fixed cost of imitation ζC raised from 2 to 2.15, and fixed cost of innovation ζI lowered from 6 to 5.85 28

liberalization experiment. The IPR payments subsidize Northern innovation as they lower its cost, raising its probability of success (see the higher path of the probability of innovation, pI ). Southern intermediate goods producing firms face increased costs of imitation internalizing the negative effects they have on innovation. However, the greater flow of innovation outweigh these costs (leading to a higher path of the probability imitation, pC ). Again, the Southern technology level increases relative to that in the North, but is lower in steady state than that obtained with the benchmark experiment. In the new steady state, the South looses in terms of its share of intermediate products produced in the South (nSN ), even relative the the benchmark experiment. Even as it looses market share in intermediate good production, the South is better off than pre-trade liberalization and better off than liberalizing trade alone. The IPR experiment demonstrates that the welfare loss to the North in the pure trade liberalization experiment is not due to trade per se, but rather to the lack of IPRs. There is a positive externality from Northern innovation to Southern imitation since each new innovation by Northern firms lowers the cost of Southern imitation. This is because, holding constant research experience, the cost of imitation depends negatively on the pool of goods left to be imitated, that is, it depends negatively on the technology gap between the two countries. The licensing fee, imposed in the IPR experiment, helps internalize this externality.

4.6

Trade Cost Reduction

We consider the effect of a reduction of trade costs instead of a Southern trade liberalization. Specifically, we lower trade costs, t, from 1% to 0.01%, virtually eliminating trade costs. The trade costs reduction is different than a worldwide trade liberalization: a tariff reduction changes relative prices but does not have net resource costs (as tariff revenues are returned to residents in a lump-sum), while a reduction in trade costs releases resources (see equations (3.24) and (3.25)) to the rest of the economy in addition to changing relative prices. Columns labeled (6) in Table 2 shows the parameters and the steady states for this trade cost reduction experiment. A reduction in trade costs raises the steady state innovation and imitation rates, and the steady state growth rate. The qualitative effects of trade cost reduction on the steady state variables is very similar to the effects of the benchmark generalized trade liberalization. This is not surprising given that the impact of prices is largely the same. A drop in trade costs works in a similar way to a reduction in tariffs: reducing the price of Northern consumption goods sold in the South (PN∗ = (1 + τYS + t)), the price of the Southern price of intermediate good imports from the North manufactured by firms that face Northern competition

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(PN∗ N = q(1 + τXS + t)), and the price of Southern produced intermediate inputs (PSN = 1 + τXS + t). These firms are forced to reduce the markup to stave off Southern competition, loosing monopoly rents, while the demand for these inputs rises. The price of intermediate imports manufactured by firms that face Southern competition (PN∗ S = qM CS = qPS ) is unaffected. The differences between the trade cost reduction and the generalized trade liberalization occur mainly during the transition. While the impact price effects and the pattern of interest rates are also similar, the generalized trade liberalization does not release resources while the trade cost reduction does. Figure 3 shows the evolution of the key variables. The behavior of interest rates, innovation and imitation rates, and the relative price level is similar to the generalized trade liberalization shown in Figure 1. However, in the trade cost reduction experiment, the consumption level in the North does not drop on impact. Also, as there are larger overall resources, the demand for all products grows at a faster rate. This increases the returns to imitative and innovative activity and the growth rate of consumption on both countries. The welfare results in the trade cost reduction are therefore different from the results of the benchmark generalized Southern trade liberalization experiment. Since Northern consumption does not drop on impact because the reduction in trade costs frees up resources, the transition loses are mitigated. The trade cost reduction results in welfare gains to the North and to the South, even taking into account transition.

4.7

Sensitivity Analysis

We now explore the sensitivity of the generalized Southern trade liberalization experiment to changes in the model’s parameters. Table 3 shows the value of parameters, steady state values, and compensating variations of consumption from the sensitivity analysis. Column (1) repeats the results from the benchmark generalized Southern trade liberalization. For each set of columns, the trade liberalization experiment is repeated, in turn, with a low trade cost, t; a high innovation externality, βI ; a high imitation externality, βC ; and a high fixed cost of innovation, ζI . Each of these parameters remains constant before and after the generalized Southern trade liberalization. The steady state of the model is sensitive to the size of trade costs, the innovation externality, and the fixed cost of innovation. Relative to the benchmark case, low trade costs (t = 0.01%, column (7)) leads to a higher growth rate, a higher relative Southern technology level, and a smaller market share for less-competitive Northern firms that only face Northern competition and for Southern firms. Through the balanced trade equation, lower trade costs also lead to lower Southern relative price levels, PS . Lower trade costs reduce the rents earned by Northern firms that face Northern competition as the markup for their

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Figure 3: Trade Cost Reduction Trade costs t lowered from 1% to 0.01% 31

Table 3: Effects of Generalized Southern Trade Liberalization Sensitivity Analysis

Parameters βI βC ζI ζC ηM t τXS τYS Steady State pI = pC rN = rS ˙ C/C ˆ Q nSN nN S nN N PS CV North South Steady State

(1)

(7)

(8)

(9)

(10)

Benchmark

Low trade cost

High imitation extern βC pre post

High innovtion cost ζI pre post

pre

post

pre

post

High innovation extern βI pre post

0.9 0.6 6 2 2 0.01 0.05 0.05

0.9 0.6 6 2 2 0.01 0.01 0.01

0.9 0.6 6 2 2 0.0001 0.05 0.05

0.9 0.6 6 2 2 0.0001 0.01 0.01

1.0 0.6 6 2 2 0.01 0.05 0.05

1.0 0.6 6 2 2 0.01 0.01 0.01

0.9 0.8 6 2 2 0.01 0.05 0.05

0.9 0.8 6 2 2 0.01 0.01 0.01

0.9 0.6 6.1 2 2 0.01 0.05 0.05

0.9 0.6 6.1 2 2 0.01 0.01 0.01

0.2125 0.1410 0.0403 0.1920 0.4406 0.3130 0.2465 1.0179

0.2148 0.1423 0.0408 0.3224 0.4398 0.3138 0.2464 0.9957

0.2136 0.1416 0.0405 0.2301 0.4402 0.3133 0.2464 1.0165

0.2159 0.1429 0.0410 0.3034 0.4395 0.3142 0.2463 0.9943

0.2369 0.1549 0.0450 0.3280 0.4328 0.3217 0.2455 1.0111

0.2395 0.1563 0.0454 0.3727 0.4320 0.3226 0.2454 0.9891

0.2125 0.1410 0.0403 0.1845 0.4406 0.3130 0.2465 1.0179

0.2148 0.1423 0.0408 0.3009 0.4398 0.3138 0.2464 0.9957

0.2088 0.1389 0.0396 0.0916 0.4417 0.3117 0.2466 1.0188

0.2111 0.1402 0.0401 0.2437 0.4410 0.3125 0.2465 0.9966

-0.31 2.24 0.40

-0.59 1.97 0.41

-0.97 1.52 0.40

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-0.30 2.25 0.40

-0.06 2.50 0.40

products is lower in the South. Similarly, the price of Southern produced intermediates sold in the South is lower. Thus, monopoly distortions are diminished relative to the benchmark case. At the same time, lower trade costs enlarge markets for all intermediate producers, leading to higher innovation rates and thus a higher growth rate both before and after the generalized Southern trade liberalization. Interestingly, lower trade costs, while increasing the growth rates in steady state, also increase the relative cost of transition relative to the steady state gain. Thus, if the trade cost is high enough, then the North is made better off after a generalized Southern trade liberalization. This happens because the North does not suffer as much from the negative effects of Southern competition on its intermediate goods firms as the North and the South are relatively more “segmented.” A high innovation externality, (βI = 1, column (8)) has similar qualitative effects on steady state values as a lower trade costs: higher growth rate, higher relative Southern technology level, and smaller market shares for Northern firms that only face Northern competition and for Southern firms. A high innovation externality increases rents to the North, as it reduces the cost of innovation. This has a direct effect on the rate of innovation and growth in the North, and thus in the South as well. The innovation externality does not have the same impact effect on prices as the trade costs. However, given the faster growth rate, demand for final goods increases. Through the balanced trade equation, in steady state the Southern relative price level is lower which reduces rents for Northern firms that face Northern competition and for Southern firms. In terms of transition, a high innovation externality worsens the transition costs for the North relative to the steady state gains and reduces the transition benefits to the South. This happens as a higher innovation externality encourages more resources to be devoted to innovation in the North during transition, increasing the transition costs due to a lower initial path of consumption. In fact, if the innovation externality is below 0.89 then the transition costs no longer dominate the welfare gains and a generalized trade liberalization is welfare improving for both countries.31 A high fixed cost of innovation, shown in column (10), has the opposite effect on steady state values than the high innovation externality relative to the benchmark experiment. Similarly, as the fixed cost of innovation increases, the transition cost decrease relative to the steady state welfare gain. If the fixed costs of innovation is high enough, then both North and South benefit from a generalized Southern trade liberalization. Unlike the case for the innovation externality, only the relative South-North technology steady state ˆ is sensitive to the size of the imitation externality (βC = 6.1, column (9)). Importantly, the steady value, Q, state growth rate of consumption is not affected by the imitation externality. Thus, the size of imitation 31 The

numerical results are not shown but they are available from the authors upon request.

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externality only has welfare effects through its impact on transition compared to the benchmark case: a higher imitation externality increases competition from Southern firms during the transition and speeds up this transition. The greater competition tends to lower the Northern transition costs and increases the Southern transition gains.32 While not shown in the table, the welfare results are robust to changes in the imitation externality. The welfare results of the generalized trade liberalization experiment are robust to changes in parameters. That is, when the South reduces its tariffs, the transition effects can be large enough to dominate the steady state growth gain. For the South, the transition effects are positive; for the North, the transition cost is larger than the steady state gain and thus it suffers an overall welfare loss. The transition costs can be lessened and Northern welfare can improve post a generalized Southern trade liberalization if the feedback effects are reduced when the two markets are more segmented (e.g. high trade costs) or when there are weaker incentives to innovate and less resources are devoted to those activities (low innovation externality or high innovation costs). However, in those instances, long run growth is lower both before and after transition, and the South is made worse off. Only in the case of IPR payments did we obtain that a generalized Southern trade liberalization is beneficial to the North, to the South, leads to higher growth rates.

5

Conclusion

This paper presents an endogenous model of growth through technological progress, demonstrating both static and dynamic benefits for less-developed countries when trading with developed countries. The concept of learning-to-learn in both imitative and innovative research is introduced, and a potential mechanism through which trade affects the diffusion of technology is modeled. International trade with imitation leads to feedback effects between Southern imitators and Northern innovators who compete for the world market. Both countries face transition paths dependent on the relative technologies in the two countries. In our numerical analysis, a generalized Southern trade liberalization leads to higher world growth, demonstrating dynamic benefits to the South of increased trade with a more-developed country. Northern welfare is lowered as a consequence of greater interaction with the South, despite increased world growth in the long run, because the transition to steady state entails large transition costs borne principally by the North. However, these losses are attributable to the lack of internationally enforced IPRs rather than trade liberalization per se. If the South increases IPRs at the same time that it opens to imports of 32 While not shown in the table, a high imitation cost elasticity with respect to the relative Southern technology level, σ, and a lower imitation fixed cost, ζC , also speed up transition while leaving steady state values, other than the relative technology ˆ unchanged. level Q,

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intermediate goods, then both regions will increase their welfare. For the South, this welfare gain is greater than when opening to imports without imposing IPRs. Moreover, while particular welfare results depend on parameter choices, we demonstrate that focusing solely on steady-state results can lead to incorrect welfare interpretations. This paper provides a dynamic argument, especially from the point of view of developing nations, in favor of free trade. This is particularly relevant for sectors with high technology components. Unfortunately, these are often the very sectors that developing countries choose to protect using trade barriers in an attempt to foster industrialization in infant domestic industries. Moreover, in a world where technology drives growth and research in the South affects that in the North, our findings suggest that the South may benefit by providing some degree of intellectual property rights to foreign firms. In terms of future research, the process of learning-to-learn suggests that a country that is handed technology may not be able to move beyond that technology as easily as if the country had created or imitated that technology on its own. Thus, there is an issue of hysteresis to be considered, which has important implications for LDCs and their technological development.

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6

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