Innovation and imitation in a model of North–South trade

Journal of International Economics 87 (2012) 365–376

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Innovation and imitation in a model of North–South trade Teodora Borota Uppsala University, Economics Department, Box 513, SE-751 20 Uppsala, Sweden

a r t i c l e

i n f o

Article history: Received 1 June 2010 Received in revised form 9 January 2012 Accepted 9 January 2012 Available online 17 January 2012 JEL classification: F12 F43 O31 O33 O34

a b s t r a c t This paper analyzes the growth and welfare effects of trade openness within a North–South framework that predicts the observed intra-industry trade and the North–South specialization over different quality vintages within product lines. The model is used to re-examine the relationship between the innovation in the North and the imitation lag of the South and to address the implications of the (weak) international Intellectual Property Rights (IPR) protection. When the imitation technology is modeled as a function of increasing complexity of targeted products, opening to trade increases the growth rate and welfare of both regions, but results in a larger North–South quality gap. While a full catch-up is possible with no protection of ideas flow, but also with no trade, the quality gap is always positive under full economic integration including trade in goods. Stronger IPR protection increases the gap and has a negative effect on the world growth rate and welfare. © 2012 Elsevier B.V. All rights reserved.

Keywords: North–South trade Quality heterogeneity Endogenous growth Innovation and imitation Intellectual Property Rights

1. Introduction With the large developing regions integrating into the world trade system and the subsequent rapid increase in trade activity between the developed North and the less developed South, concerns have been raised over the common practice of the South to copy Northern innovations and win the market shares due to substantially lower production costs. The developed world has been calling for stronger international IPR protection to prevent the predicted Southern takeover of industries through imitation, instigated by increased export opportunities. A large body of literature has dealt with these issues, especially after the IPR topic was included in the official WTO discussion agenda. 1 However, the conclusions related to the effects of the IPR protection vary. 2 To readdress these concerns, this paper considers a model of the two regions with quality innovation driven growth, incorporating the idea of quality vintages and a link between the R&D productivity and the intensity of innovation. The model is used to revisit the implications of the South opening to trade in goods and the IPR protection policy.

E-mail address: [email protected]. The WTO's Agreement on Trade-Related Aspects of Intellectual Property Rights (TRIPS), was negotiated in the 1986–94 Uruguay Round and it imposed the intellectual property rules into the multilateral trading system. 2 See, e.g. Scotchmer (2004), Saint-Paul (2008), Lai and Qiu (2003), McCalman (2001). 1

0022-1996/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jinteco.2012.01.002

Product cycle models of Grossman and Helpman (1991a,b) are the most commonly used frameworks to address the issues of the North– South trade and the IPR policy in an endogenous growth set-up. Although the articles do not focus on the effect of opening to trade specifically, the models would arguably predict an increase in innovation and imitation rates with this change. The key assumption lies in the R&D technologies specification. Namely, the productivity of the imitation technology in the South is not affected by any conditions of the North, nor by the complexity of the targeted products (or the intensity at which it attempts to imitate). There is a constant labor requirement for copying any product initially invented and produced in the North. An increase in the innovation in the North that would occur with opening to trade and reallocation of Northern labor from manufacturing to R&D reduces the share of products already imitated by the South and raises the value of any Southern copy in the market. With a constant imitation cost, this implies an increase in the imitation rate. In both set-ups above, increased imitation effort reduces the average length of the product cycle and the product life in the North is shorter. Therefore, opening to trade with the South necessarily seems to be bad news for an individual producer. However, to address the debate on industry dominance and the need of the IPR protection to fight imitation, it is necessary to analyze the effect of opening to trade on the share of products retained in the North. Although the result may be ambiguous, it is possible that the increase in the imitation rate will be larger than the increase in the innovation rate. This

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T. Borota / Journal of International Economics 87 (2012) 365–376

implies that trade liberalization may bring incentives for the South to reduce the technological gap and to converge to a steady-state with an increased share of imitated varieties. This paper builds on the product-cycle framework, but there are several diverging points. Firstly, there is a quality ladder for each product line, but different qualities are not perfect substitutes. A whole range of quality vintages, not only state-of-the-art goods, is produced. In other words, there is no immediate replacement of the old products, they are only gradually displaced by goods of higher quality. Empirical estimates of the creative destruction pace range from 4% to 25% per year (see e.g. Caballero and Jaffe (1993)), which supports this modeling assumption. Secondly, in vertical innovation models the product quality is typically assumed to increase by exogenously given steps, while the R&D effort determines the timing (frequency) of innovations. Baumol (2002), among others, documents that the real-world firms face a trade-off between the size of the quality improvement and the frequency of their innovation. 3 This paper allows for the endogeneity only in one channel, but differently from the previous product cycle literature, the focus is on the quality steps instead of on the timing of new product arrival. As in Aghion and Howitt (1992), the R&D productivity is a decreasing function of the quality innovation step; a higher quality improvement implies a higher complexity (difficulty) of R&D, and thus a higher cost in both regions. Incorporating the two features above, the focus is shifted from the analysis of innovation and imitation frequencies to the differences in the quality attainment of the two regions. With opening to trade, the innovation effort in the North increases, which results in the higher innovation steps achieved. This provides higher growth rates of both regions, but does not imply faster catch-up of the South. As the imitation productivity falls due to a higher quality step size, the imitation cost rises disproportionately and the imitation cannot be sustained at the initial quality gap behind the North. This leads the South to target the lower quality varieties for imitation within fewer product lines in equilibrium, instead of attempting to catch up with the North. Therefore, implementing strong international IPR protection to prevent the overtake of Northern industries by the South cannot be justified. Further trade liberalization in the form of a trade cost reduction does not affect the R&D mechanisms and the quality gap, and, therefore, in no sense alters the conclusion regarding the IPR protection. Stronger IPR enforcement only protects monopolistic rents in the North and reduces both the growth incentives and the welfare levels in the two regions. A more recent work in this field is presented in Segerstrom and Dinopoulos (2006), Parello (2008), Sener (2006), Stryszowski (2006). Attempting to correct previous models for the counterfactual positive effect of the labor size on economic growth (the scale effect), these papers remove the increasing returns in the R&D technology. Depending on a specific formulation, this also alters the equilibrium relation between the innovation and imitation efforts found in Grossman and Helpman papers. In Segerstrom and Dinopoulos (2006), the equilibrium imitation in the South is decreasing in the innovation intensity of the North. However, this study analyzes the effect of globalization seen as an increase in the size of the South. The intention here is to regard globalization as a change in the economic environment (opening to trade), not as a change in the resource base (the labor size of an integrated region). Furthermore, in Segerstrom and Dinopoulos (2006) growth is semi-endogenous (a function of the population growth rate), which is supported by the evidence presented in Jones (1995). However, a recent study by Ha and Howitt (2007) argues that the long-run trends in R&D and total factor productivity growth in the US provide more

support for the fully endogenous growth theory with a role for economic policy. Following Ha and Howitt (2007), in the current paper, the equilibrium growth rate is a result of the innovation and imitation mechanisms' interaction, and it is also affected by policy. Finally, the literature on the North–South product-cycle trade and growth implies that the location of all production in an industry shifts between regions when a new product is discovered and then imitated. However, a large body of empirical studies suggests that there exists North–South vertical specialization within industries. 4 When traded goods are distinguished according to the unit quality level, the studies reveal the North–South specialization in different quality ranges within product. 5 Following the aforementioned empirical findings, the present paper develops a dynamic model of trade and growth which is able to replicate the observed intra-industry specialization between the North and the South. To summarize, the effects of the international integration of countries and the related issue of the international IPR protection have been studied extensively, and these studies have been used to recommend stronger or weaker IPR protection. Besides the lack of clear consensus on how beneficial this protectionism is for the South in particular, the existing models also suffer from major shortcomings of failing to predict intra-industry trade and generating scale-effects (due to the increasing returns in R&D technology). In the light of this, the current study corrects for the undesirable scale effect property and contributes by introducing the specialization across quality vintages within industries, which in turn allows for a different modeling of R&D and different predictions for equilibrium R&D efforts and policy implications. The rest of the paper is organized as follows: Section 2 presents the benchmark scenario with the flow of ideas and Southern imitation but no trade in goods, while Section 3 analyzes the effects of opening to trade in goods, as well as the impact of stronger IPR protection. Section 4 concludes the analysis. 2. No trade, flow of ideas 2.1. The model The model considers two regions (the North and the South) which differ in their abilities to conduct R&D, and also in wages (w) their workers earn, with Northern wage higher than that in the South (wN(t) > wS(t)). There is a continuum of goods indexed by j ∈ [0, m(t)]. Each good is represented by a range of varieties (quality vintages) indexed by z(j, t) ∈ [no(j), nN(j, t)], see Fig. 1. Each variety is characterized by a higher quality than the preceding one. The North conducts innovative R&D resulting in a new variety of increased quality compared to the one previously invented. The North produces the whole range of existing varieties, [no(j), nN(j, t)], where nN(j, t) grows through innovation. There is no trade with the South, but the flow of ideas does exist, as the workers in the South conduct imitative R&D. The highest quality variety copied by the South is nS(j, t). The technology gap between the highest quality varieties produced in the North and the South is determined in the equilibrium and is denoted by d, i.e. d(j, t) = nN(j, t) − nS(j, t). In an equilibrium with a positive technology gap (Fig. 1), the two regions' production within each product line overlaps up to the variety nN(j, t) − d(j, t), while varieties [nN(j, t) − d(j, t), nN(t)] have not been copied and are produced only by the North. As there is no trade, the consumption bundles of the two regions are different and consist only of the varieties produced domestically. Although the 4

See e.g. Schott (2004), Fontagne et al. (2008), and Fieler (2010). Concerns have been raised over the use of unit values in the trade data as the proxies for product quality, e.g. in Hallak and Schott (2008) it is found that for several countries export prices and quality have different trends. However, on average, there is still a high correlation between the unit prices and quality. 5

3

Aghion and Howitt (1992) allows for the endogeneity of both innovation step and the frequency in a closed economy set-up. See also Sorger (2011) for an extensive study of this issue.

T. Borota / Journal of International Economics 87 (2012) 365–376

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firms). With r(t) as the market interest rate at time t, the optimization results in the Euler condition C_ ðt Þ ¼ r ðt Þ−ρ: C ðt Þ Fig. 1. No trade, flow of ideas.

technology gap cannot be negative by construction, a steady state equilibrium with a zero gap is possible. The steady-state equilibrium and the particular conditions will be discussed in Section 2.2. 2.1.1. Consumers There is a fixed number of households in both regions whose members each supply one unit of labor inelastically and earn the wage w(t). The number of household members, LN(t) in the North and LS(t) in the South, grows exponentially at the rate gl. The wages in the manufacturing and R&D sectors are the same, and denoted with wN(t) in the North and wS(t) in the South. Labor is not mobile between the regions. Consumers in both regions have the same preferences and the households maximize their lifetime utility ∞ −ðρ−g l Þt

U¼∫ e 0

lnuðt Þdt;

2.1.2. Production Entering firms in the Northern market conduct costly innovative R&D which results in the design of a new variety, and the firm becomes its monopolistic producer. With costly R&D and assumed Bertrand competition of the original and the potential copies in the same market, there is no incentive for any other firm in the North to copy the existing varieties. An imitator's entry into the market and the competition with the first successful innovator would drive the profits down to zero, and would not allow for covering the R&D costs of imitation. For that reason, there is no need for any instrument of the IPR protection domestically. Each firm hires labor l(z, t) and the production technology for any variety is given by

ð1Þ

−ϕ

xN ðz; t Þ ¼ lðz; t ÞqðzÞ

with ρ > gl being the discount factor and u(t) the instantaneous utility per person at time t given by uðt Þ ¼

This paper will analyze a steady-state equilibrium in which wages (wN and wS) and expenditures (CN and CS) do not change over time, keeping the market interest rate constant and equal to the subjective discount factor ρ.


σ σ1 α nð j;t Þ mðt Þ α ∫ ½qð j; zÞxð j; z; t Þ dz dj : ∫ n0 ð jÞ

0

ð2Þ

mðt Þ

0

∫

nðj;t Þ

n0 ð jÞ

ϕ

pð j; z; t Þxð j; z; t Þdzdj

 mðt Þ

pðj; z; t Þ=qðj; zÞα



1 α−1

nðj;t Þ

α

∫0 ∫n ðjÞ ðpðj; z; t Þ=qðj; zÞÞα−1 dzdj 0  α 1 pðj; z; t Þ=qðj; zÞ α−1 ¼ C ðt Þ: α P ðt Þα−1

C ðt Þ ð3Þ

The demand function takes the familiar form, where the share of each variety in the total consumption is given by the share of its quality–price ratio in the index of quality–price ratios of all varieties consumed (P). Dynamic optimization of the lifetime utility maximizes Eq. (1) given Eqs. (2), (4) and the intertemporal budget constraint A_ ðt Þ ¼ wðt Þ−C ðt Þ þ r ðt ÞAðt Þ−g l Aðt Þ;

yielding the optimal monopoly price pN ðj; z; t Þ ¼

ð4Þ

where A(t) represents individual assets as a share in the ownership of domestic firms (a share in the total present value of future profits of

1 ϕ w ðt Þqðj; zÞ : α N

Substituting the expression above for price in the demand function, it follows that the consumers' demand across varieties increases with the quality level if α > ϕ, but the demand for each variety decreases over time as the higher quality varieties are being invented. The South is involved in costly imitative R&D and when a variety is copied successfully, the imitator becomes a monopolistic producer using the same technology as the North. The marginal cost equals wSq(z) ϕ, and the firm charges the monopoly price pS ðj; z; t Þ ¼

which further gives the optimal demand for each variety

xðj; z; t Þ ¼

so the firm faces a marginal cost equal to wNq(z) ϕ, with 0 b ϕ b 1. 6 The monopolist determines the product price by maximizing profits subject to the consumers demand max pðj; z; t Þxðj; z; t Þ−wðt Þqðj; zÞ xðj; z; t Þ subject toð3Þ;

The utility at time t is a quality-augmented CES consumption index with x(z, t) being the consumption of variety z with the quality index q(z). The parameters σ and α measure the substitution between varieties across and within goods. For simplicity, it is assumed that 1 σ = α, and 1−α represents the elasticity of substitution between varieties. With 0 b α b 1, consumers prefer varieties of higher quality (higher z). Given the prices, consumers maximize the instantaneous utility subject to their individual expenditure on all goods (C(t)). This is a problem of static optimization across varieties where consumers maximize utility in Eq. (2) subject to their expenditure C ðt Þ ¼ ∫

;

1 ϕ w ðt Þqðj; zÞ : α S

As in the North, under price competition, no Southern firm will have an incentive to copy an already copied product since its entry drives the profits down to zero and does not allow for covering the R&D costs of the second imitation. Firms from both regions earn profits only at the local markets, and the profits are given by α

Π N ðj; z; t Þ ¼ ð1−α Þqðj; zÞ1−α α

Π S ðj; z; t Þ ¼ ð1−α Þqðj; zÞ1−α


α pN ðj; z; t Þ α−1 C N ðt ÞLN ðt Þ P N ðt Þ


α pS ðj; z; t Þ α−1 C S ðt ÞLS ðt Þ: P S ðt Þ

6 Baldwin and Harrigan (2007) have a similar specification of the production technology. They introduce a positive relation between the marginal cost and the quality produced through the firm's productivity measure, where total profitability is increasing in marginal cost and the quality produced.

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T. Borota / Journal of International Economics 87 (2012) 365–376

At any time t, the innovator's and the imitator's profits increase in total expenditure (CNLN, CSLS) and quality of the variety (q), but will decrease over time as the quality level of the particular variety decreases relative to the highest quality produced (the price–quality index decreases). 2.1.3. R&D processes 2.1.3.1. Horizontal innovation. As in Howitt (2000), the number of products evolves as a result of serendipitous (not deliberate) innovation, and the aggregate flow of products is

The analysis will focus on the balanced growth path (BGP) with a constant size of endogenous quality jumps over time and, therefore, across varieties (γ(j, z, t) = γ(j)). In turn, the growth rate of the quality index (6) collapses to γ(j)(1 − α), and the quality index simplifies to q(j, z) = e (1 − α)γ(j)z. Imitation is conducted by the Southern entrants who hire R&D labor of measure RS(j, t) within a product line, with hS being the human capital parameter and θ(d) > 0 the difficulty parameter. The evolution of the quality index in the South is given by q_ ðnS ðj; t ÞÞ ¼

mN_ ðt Þ ¼ δLN ðt Þ; where δ represents the innovative ability of the population in the region, i.e. the propensity to innovate, equal across all individuals in the North. The growth rate of the number of products (gm) is then given by δ mLN . New product ideas, which result from this form of innovation, N receive their final design and the quality index in the process of quality R&D. 2.1.3.2. Quality innovation. The entering firms in the North hire labor of measure RN(j, t) to conduct quality research within a given product line, thus designing a new variety of higher quality. The quality R&D technology is modeled as q_ ðnN ðj; t ÞÞ ¼

hN RN ðj; t Þ qðnN ðj; t ÞÞ: β

The productivity of labor in R&D is a function of the human capital parameter hN and the difficulty parameter β > 0, with former relating to the characteristics of labor force, and the latter concerning the technological complexity of quality innovation. The change in the quality index is positively related to the quality index of the latest variety invented, which represents the knowledge spillover within the product line, as in Romer (1990) among others. It is assumed that the new product lines benefit from the knowledge spillovers from other products, and thus, the first variety created within a new line improves upon the latest quality level in the economy. The quality index q(j, z) is defined as ( qðj; zÞ ¼

z

eð1−αÞ∫0 γðj;sÞds −ð1−α Þ∫0z γ ðj;sÞds e

if z≥0 if zb0:

ð5Þ

Variable γ(j, z) measures the quality improvement of each successive variety. The quality index of each variety z is thus a product of the quality index of the preceding vintage and the size of the quality improvement, e (1 − α)γ(j, z). Given the expression above (Eq. (5)), it follows that the growth rate of the quality index in product line (j) in the North is given by
 nN ðj;t Þ q_ ðnN ðj; t ÞÞ d ð1−α Þ∫ ¼ γðj; z; t Þdz 0 qðnN ðj; t ÞÞ dt
 nN dγ ðj; z; t Þ dnN ðj; t Þ γðnN ðj; t ÞÞ þ ∫ dz : ¼ ð1−α Þ 0 dt dt

ð6Þ

Diverging from the common practice found in the growth literature, where the size of each quality jump is taken as exogenous when analyzing the endogenous arrival rate of new varieties, the assumption here is exactly the opposite. The invention frequency is exogenous and new varieties arrive with time, i.e. dnNdtðj;tÞ ¼ 1. However, the size of the quality improvement with each new product is left to be determined endogenously. In this way, the range of varieties can also be regarded as the measure of time, so that d(j, t) in fact represents the North–South technology gap in time, and will also be referred to as the technology lag.

hS RS ðj; t Þ qðnS ðj; t ÞÞ: θðdðj; t ÞÞ

When copying varieties of good j, Southern firms are required to make the same quality jump determined by γ(j), which occurred in the North at the time of the variety's invention. 7 Therefore, γ_ ðjÞ ¼ 0 in the South as well, and the BGP growth of the quality index in product line j in the South becomes γ ðjÞð1−α Þn_ S ðjÞ. The main trade-off in this paper is expressed in the relation between the intensity of the quality innovation given by γ, and the technology lag coming from the South given by d(j, t) in a steady-state equilibrium. To analyze this relation, the focus is placed on the steady-state equilibrium in which d = nN − nS is constant. For each new variety invented, one more variety is copied, and the quality growth in the South is given by γ(j)(1 − α). In other words, n_ is the same in both regions and equal to 1, while γ(j) and d(j) are constant, but determined endogenously. The R&D difficulty parameter in the South is proportional to β, but depends on the North–South technology lag. Namely, it can be argued that as the South attempts to imitate more intensively and decrease the lag behind the North, the copying process increases in difficulty, and thus θ = θ(d) is assumed to be a decreasing function of d. This assumption has been supported by the empirical evidence presented in Acemoglu et al. (2006). In those terms, following the idea of Barro and Sala-i-Martin (1997), this factor of proportionality to β is given by the inverse of the quality gap, i.e. the ratio of the highest quality in the South and the one in the North. 8 An additional parameter, η ≥ 1, represents the degree of the IPR protection by the North and directly affects the difficulty (productivity) of copying. 9 Therefore, the productivity of copying ( 1θ ) is decreasing in η and increasing in d. With the free flow of information (η = 1) and no lag in technology (d = 0), θ becomes equal to β. θðdÞ ¼ ηβ

γðnN −dÞð1−α Þ

e

eγnN ð1−αÞ

−γdð1−α Þ

¼ ηβe

2.1.4. R&D optimization The expected benefit of a successful R&D effort (the value of a new variety in sector j) is represented by the expected discounted profits from innovating or copying in the North and the South, respectively. Having assumed that n_ ¼ 1, it is convenient in computational sense to discount the profit flows over the index z, since, under given assumptions, it is equivalent to discounting over time. With wages and expenditures constant over time, the profits change due to the change in the quality–price index. Given the profit 7 Different γ in the South would imply imperfect copying which would result in a similar variety but of different quality. It would, therefore, not be a perfect substitute for the original previously invented and produced in the North. 8 See also Gancia and Zilibotti (2005), Stryszowski (2006) for similar modeling of imitational R&D productivity. 9 Mansfield et al. (1981) find that patents rarely hinder imitation but make it more expensive. This closely corresponds to the idea of making imitation more difficult, and thus more labor demanding and more costly, which would be the interpretation of η. Moreover, η stands for any institutional impediment that may increase the cost of imitation.

T. Borota / Journal of International Economics 87 (2012) 365–376

functions, the values of a new variety (VN(j)) and a copy (VS(j)) in a steady-state are given by

1 βγ ðjÞð1−α Þ: hN

ð8Þ

With equal substitution between varieties within and across different product lines, and with the same production and R&D technologies and free movement of labor (common wage across products), both the benefits and the costs of R&D are independent of the product line variables and its history (number of vintages previously introduced). They are functions of aggregate expenditure, price index, and the quality level attached to the new variety. Therefore, the incentives for innovation in the North and imitation in the South are equal across products, and this results in the same quality jump determined by γ(j) = γ. The quality index of a certain variety vintage (z), regardless of the product line, is given by e (1 − α)γz, with the number of varieties of a certain quality being equal to the number of product lines at the time of their invention. Given that d z = d t, the price– quality index can be written as
α−1 n N ðt Þ α α P N ðt Þ ¼ ∫ mN ðzÞðpN ðzÞ=qðzÞÞα−1 dz ; and using Eq. (7) the value of a new variety invented is given by g m þ γα ð1−ϕÞ C N LN : r−g l þ g m þ γα ð1−ϕÞ mN

Since the cost of innovation (8) is constant over time, the value of innovation at the BGP will be constant with g m ¼ δ mLNN ¼ const, and thus the growth rate of product lines will be equal to the population growth rate (gm = gl) and mLNN ¼ 1δ g l . The arbitrage condition which equalizes the benefits and costs of R&D can then be expressed as ð9Þ

Similar derivation also applies to the South, where the cost of a new copy is given by wS RS ¼ wS

1 θðdÞγð1−α Þ: hS

ð10Þ

The quality–price index and the resulting value of a new copy in the South are given by
α−1 α nS ðt Þ α P S ðt Þ ¼ ∫ mS ðzÞðpS ðzÞ=qðzÞÞα−1 dz −∞

V S ¼ ð1−α Þ

g m þ γα ð1−ϕÞ C S LS ; r−g l þ g m þ γα ð1−ϕÞ mS

As the South copies the varieties of all product lines at the rate d nS = d t, the growth rate of the number of product lines is also given by gm = gl. The ratio mLSS ¼ m LeS−dgl ¼ LLNS gδl edgl is constant over N time and a function of the endogenous technology lag, d. 2.1.5. Labor markets Full employment of labor requires that in both regions at any time t all workers are employed in either R&D sector or manufacturing. Under the assumption of d z = d t, at each point in time, the total R&D labor in either region is equal to the labor requirement for the development of one new variety or a copy in all sectors. Therefore, the full employment labor market conditions for the two regions are given by nN

LN ¼ mN RN þ ∫

−∞

LS ¼ mS RS þ ∫

nN −d

−∞

ϕ

ð12Þ

ϕ

ð13Þ

mN ðzÞq ðzÞxðzÞLN dz

mS ðzÞq ðzÞxðzÞLS dz:

2.2. Steady-state equilibrium analysis Combining the full labor employment conditions, Eqs. (12) and (13), with the R&D optimization conditions (9) and (11) for the North and the South, respectively, two steady-state equilibrium conditions are obtained. The Northern condition pins down the steadystate value of the quality jump (γ) and is given by hN

−∞

g l þ γα ð1−ϕÞ 1 1 g C ¼ wN βγ: r þ γα ð1−ϕÞ δ l N hN

ð11Þ

ð7Þ

The value of introducing a new variety is increasing in its quality– price ratio and the total consumer expenditure in the region. The entry into the R&D race is free, and all participants have access to the same R&D technology, so the benefits of innovation will equal the costs of R&D in a steady-state equilibrium. Given the specification of the R&D technology, the research cost required for each variety innovation in the North is given by

V N ¼ ð1−α Þ

which yields the arbitrage condition in the South g l þ γα ð1−ϕÞ C S LS 1 ¼ wS γθðdÞ: r þ γα ð1−ϕÞ mS hS


α ∞ α qðj; nN Þ 1−α V N ðjÞ ¼ ð1−α Þ C N ∫ P N ðzÞ1−α LN ðzÞe−rðz−nN Þ dz nN pðj; nN Þ
α α ∞ qðj; nS Þ 1−α V S ðjÞ ¼ ð1−α Þ C S ∫ P S ðzÞ1−α LS ðzÞe−rðz−nN Þ dz: nS pðj; nS Þ

wN RN ðjÞ ¼ wN

369


 gL ρ þ γα ð1−ϕÞ ¼ βγ ð1−α Þ þ α : g l þ γα ð1−ϕÞ δ

ð14Þ

The quality jump depends positively on the productivity of the R&D labor (β1) and the human capital level (hN), while a higher interest rate and a larger α (higher elasticity of substitution) decrease γ due to their negative impact on the value of innovation. The innovativeness parameter (δ) has a negative effect on the size of the quality jump in the equilibrium, as a higher horizontal innovation implies a larger number of product lines over which the quality R&D labor is allocated. Without trade in goods, the technology lag of the South has no impact on the quality jump, which is solely determined by the conditions of the North. This results in the vertical Northern condition in (γ, d) space in the steady state equilibrium diagram (Fig. 3). The Southern equilibrium condition is given by hS


 LS g l dgl ρ þ γα ð1−ϕÞ e ¼ θðdÞγ ð1−α Þ þ α : g l þ γα ð1−ϕÞ LN δ

ð15Þ

It is shown in Appendix B that the Southern equilibrium condition is upward sloping in (γ, d) space. With no trade in goods, γ is taken as exogenous by the South, and a higher γ implies a higher value of copying in the South and an increase in the demand for R&D labor. However, the cost of imitation is also a function of γ and is disproportionately higher for a given lag d behind the North. The equilibrium is restored at a larger technology lag d and the implied lower number of product lines where the imitation occurs. The North–South quality gap, qqððnnNS ÞÞ is, thus, increased. Combining the expression above with the Northern steady-state condition, the equilibrium relationship between the quality lag (d)

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T. Borota / Journal of International Economics 87 (2012) 365–376

and quality innovation jump (γ) becomes d¼


 1 h L ln N N η : gl þ γ ð1−α Þ hS LS

ð16Þ

The elasticity of substitution and the degree of information protection both increase the lag of the South as they reduce the value of copying and the productivity of imitative R&D labor. The relative size of the South ( LLNS ) has a negative effect on the lag as it increases the amount of available labor per product line, thus increasing both R&D and productive capacity, with the total number of product lines being a function of LN. By construction, the technology lag of the South cannot be negative, so the assumption hNLN ≥ hSLS is imposed. This assumption implies that the total effective labor in the North is at least as large as the total effective labor in the South. So far, it has been assumed that the human capital level is given by the parameters hN and hS in the North and the South, respectively. However, an alternative formulation, where human capital level is a function of the number of product lines per worker, has been introduced previously in literature. 10 Incorporating this idea through hN ¼ mLNN and hS ¼ mLSS , the equilibrium technology lag d becomes independent of the scale of the (relative) effective labor in the two regions. Consumers in both regions maximize their lifetime utility subject to their budget constraint given by the expression for the change in assets they possess, A, i.e. A_ ¼ w−C þ rA−g l A. Under the assumption of financial autarky, the growth rate of assets, given by A_ w−C A ¼ A þ r−g l , is constant in a steady-state equilibrium with constant w, C, r and gl. It follows that A is constant, which implies C − w = (ρ − gl)A, or in aggregate form  C N LN ¼ wN LN þ ðρ−gl ÞA N

and the R&D arbitrage condition in the South is satisfied at a larger technology lag (and also less product lines and larger quality gap). R&D labor per product line increases, and so does the demand for the manufacturing labor per product line (larger market share due to less competition), but there is no aggregate reallocation of labor across sectors. However, the aggregate quality index in the region is reduced. On the other hand, in a special case with equal effective labor of the regions (hNLN = hSLS), a perfectly free flow of information (η = 1) implies that the North–South quality gap is closed in the longrun as the South completely converges to the Northern technological frontier through copying (d = 0). The steady-state aggregate welfare in the North and the South, respectively, is given by

nN ðgl þγα ð1−ϕÞ 1−α 1−α α 1 e A U N ¼ moα LN −mN ð1−α Þ βγ hN g l þ γα ð1−ϕÞ

ðnN −dÞðgl þγαð1−ϕÞ 1−α 1−α α 1 e U AS ¼ moα LS −mS ð1−α Þ θðdÞγ : hS gl þ γα ð1−ϕÞ

The aggregate welfare is a function of three terms: the initial number of product lines, the total manufacturing labor which is the measure of quantities produced, and the aggregate quality index in the economy. The effect of a higher IPR protection on the steady-state welfare in the North and the South in the no-trade scenario equilibrium is different. While there is no change in the Northern welfare with an increase in η, the welfare in the South decreases due to the increase in the technology lag and the drop in the aggregate quality index of the goods consumed in the South. 3. Trade in goods

in the North, and  C S LS ¼ wS LS þ ðρ−g l ÞA S in the South.  N represents the total Northern assets which are equal to the sum A S of the values of all existing firms in the North at time t, while A stands for the total assets in the South, equal to the sum of the values  ¼ ∫∞ V ðaÞda, where V(a) of all copies at a given time t. Therefore, A 0 stands for the value of the a-period-old firm at time t. Using the expression for the value of R&D (7) and the expression above, one may solve for the consumer expenditures in the North and the South. Utility in both regions is equal to CP , and with constant consumer expenditure, the utility growth is given by the negative of the growth of the quality–price index. It follows that consumer welfare in each region grows due to the increase in the number of product lines (function of population growth) and the increase in quality as a result of R&D efforts. 1−α denðt Þðgl þγα ð1−ϕÞÞ 1 1−α u_ ¼ ¼ ðg l þ γα ð1−ϕÞÞ: α enðt Þðgl þγα ð1−ϕÞÞ dt α u

2.2.1. IPR protection The IPR protection policy parameter is represented by η, with η = 1 implying free information flow, while η > 1 implies stronger protection and has a negative effect on the productivity of imitation. Higher protection of information by the North, and the resulting increase in the difficulty of copying in the South, have no effect on the quality jump, and thus, no effect on the common growth rate. On the other hand, higher protection increases the difficulty of copying 10

See e.g. Dinopoulos and Unel (2011).

3.1. The model This section considers two regions, the North and the South, which are open to trade in goods. There is an iceberg trade cost τ ≥ 1, which implies that τ units of a given good need to be produced in order to place one unit in the export market. The ideas still flow to the South, which imitates and produces varieties at a d technology lag from the highest quality variety in the North. With lower wage cost in the South, as long as τwN > α1 wS , it is profitable to imitate and serve the domestic market in the South.11 With wN > α1 τwS the South will also export copied varieties to the North. The model will be solved for the equilibrium in which this condition holds, i.e. the relative 1 N wage ( ω ¼ w wS ) satisfies ω > α τ, and it is no longer optimal for the North to continue the production of copied varieties.12 However, the range of varieties that have not been copied by the South, [nN(t) − d, nN(t)], are produced and traded exclusively by the North. As presented in the figure below, there is a continuum of goods in the world market indexed by z(t) ∈ [− ∞, nN(t)], but there is no overlapping in the production as in the no trade scenario; the South specializes in the production and trade of low quality varieties, while the North specializes in the high quality ones. The IPR protection policy is still represented by 11 This condition excludes the possibility of limit pricing by the Northern exporters in the Southern market. With a lower relative North–South wage, it would still be profitable to serve the Southern market with a price below the monopolistic price once the R&D costs of innovation have been sunk. The lowest limit price charged by the North is equal to the marginal cost of production, τwN. 12 1 An equilibrium with ατ bωb α1 τ implies an overlap in production of some varieties in the North and the South. Although the equilibrium innovation and imitation efforts are different in this case due to the market size effect on R&D within a product line, the mechanisms at work are the same. Thus, the focus will be on an equilibrium with a complete shift of varieties production to the South once they have been copied. It is shown in the numerical exercise that this is a unique equilibrium under a wide range of the model's parameters.

T. Borota / Journal of International Economics 87 (2012) 365–376

the degree of information protection (η), which affects the difficulty of copying. The composition of the consumption bundles is the same in both regions, as Southern consumers have access to the whole range of varieties due to trade (Fig. 2). However, due to the presence of iceberg trade cost, the quality–price index is different across the regions PN ¼

f

! "  α enN ðgl þγα ð1−ϕÞÞ N wN α−1 −dðgl þγα ð1−ϕÞ 1−e mo g l þ γα ð1−ϕÞ α S

þmo

PS ¼

f

τw α S α−1 −dðgl þγα ð1−ϕÞ e α

#

g

α−1 α

S

þmo

w α S α−1 −dðgl þγα ð1−ϕÞ e α

#

g

α−1 α

α

N

gl þγα ð1−ϕÞ , enN ðgl þγαð1−ϕÞ

S

N

S

i = N, S. Both values are functions of the total world de-

mand. However, they are also functions of a different life length of the new variety, the term not present in the no-trade scenario. In the North, this comes as the explicit cut of the variety life from below, represented by the (1 − e − d(r + γα(1 − ϕ))) term, as the North loses the production of low quality varieties. In the South, this life span change does not come in the form of the finite life of a variety, but rather as an implicit cut of its life from above, as the highest quality in the South is no longer the highest one consumers allocate their expenditure to. In that sense, e − d(gl + γα(1 − ϕ)) term represents the loss

Fig. 2. Trade in goods.

ð17Þ

1 θðdÞγð1−α Þ: hS

ð18Þ

3.2. Steady-state equilibrium analysis The full employment labor market conditions for the two regions are given by N

 w α g þ γα ð1−ϕÞ α−1 −n g −dðrþγα ð1−ϕÞÞ l V N ¼ ð1−α Þ N k e N l 1−e r þ γα ð1−ϕÞ N α w α g þ γα ð1−ϕÞ α−1 −ðn −dÞgl −dðg l þγα ð1−ϕÞÞ l k e N e ; V S ¼ ð1−α Þ S r þ γα ð1−ϕÞ S α

α  α α α−1 α−1 α−1 where kN ¼ CP~N LN þ τ P~ C S LS and kS ¼ τ P~C N LN þ τ P~ C S LS ,with P~ i ¼

1 βγð1−α Þ hN

V N ¼ wN

LN ¼ m

As in the closed economy scenario, the North (the South) conducts innovative (imitative) R&D within the existing and new product lines. The monopolist, innovator or imitator, determines the product price by maximizing profits subject to the consumers demand. This, again, yields the optimal monopoly price pi ðz; t Þ ¼ pi ðzÞ ¼ α1 wi qðzÞϕ with i = N, S. However, the revenue now comes from both domestic and foreign markets, and for the North it comes from the sales of the [nN(t) − d, nN(t)] range of varieties, while the South sells varieties in the range [− ∞, nN(t) − d]. The value of a new variety or a new copy is determined as the discounted stream of profits from the domestic and the foreign markets over the period of firm's operation. However, the life of a variety in the North is now not infinite, but terminates once it has been successfully copied by the South, i.e. d periods after the invention. Therefore, the time span over which the profits are discounted is different in the North and the South, and the values of innovation and imitation are given by

P iα−1

in quality position relative to the highest one in the market, and hence, the loss in the variety's demand share relative to the total consumers demand. The R&D technology is defined in the same way as in the benchmark scenario, and the arbitrage conditions for the North and the South are obtained by equalizing the benefits and costs of R&D

V S ¼ wS

! " ð ð ÞÞ  α enN gl þγα 1−ϕ N τwN α−1 −dðgl þγα ð1−ϕÞ mo : 1−e g l þ γα ð1−ϕÞ α

371

S

LS ¼ m

  α 1 N wN α−1 −dðrþγα ð1−ϕÞÞ βγ ð1−α Þ þ mo kN 1−e hN α

 α 1 S w α−1 −dðgl þγα ð1−ϕÞÞ θðdÞγð1−α Þ þ mo S kS e hS α

ð19Þ

ð20Þ

which, when combined with the arbitrage conditions in the North and the South, Eqs. (17) and (18), yield the first two steady-state equilibrium conditions, which are endogenous in γ and d " #

 −dðgl þγα ð1−ϕÞÞ hN LN ρ þ γα ð1−ϕÞ 1−e ¼ βγ ð1−α Þ þ α g l þ γα ð1−ϕÞ 1−e−dðρþγαð1−ϕÞÞ mN

ð21Þ


 hS LS ρ þ γα ð1−ϕÞ : ¼ θðdÞγ ð1−α Þ þ α g l þ γα ð1−ϕÞ mS

ð22Þ

With the two regions open to trade in goods, the size of the quality jump is not determined exclusively by the North, but also depends on the conditions of the South, so that γ and d are jointly determined by the two equations above. 13 Proposition 1. The size of the quality jump (γ) increases with opening to trade. −dðg þγα ð1−ϕÞÞ

l is necessarily smaller than Proof. With ρ > gl, the term 1−e 1−e−dðρþγαð1−ϕÞÞ 1. Therefore, for the equilibrium condition (21) to be satisfied, the free trade scenario γ has to be larger than γ in the no-trade scenario (condition (14)), thus completing the proof. □ The mechanism behind this effect comes from the fact that the varieties now live only d periods in the North. This translates into the loss of the value of innovation represented by (1 − e − d(ρ + γα(1 − ϕ))), which further implies that the innovators need a larger quality jump to ensure a higher demand and their survival in the market. At the same time, the cut in the life of varieties corresponds to the loss in the production of the whole range of low quality varieties in the aggregate, i.e. those that are now produced exclusively by the South. Therefore, the total demand for Northern production and, hence, the manufacturing labor depends only on (1 − e − d(gl + γα(1 − ϕ))) share of expenditures. The excess manufacturing labor is being reallocated to the R&D sector, which in turn raises γ and the demand for new varieties and for production labor. The process continues until the full employment is restored, but as a result of more resources devoted to R&D, γ will necessarily be higher, when compared to the no-trade scenario.

13 By assuming that learning how to produce within a new product line also contributes to the accumulated knowledge, i.e. hN ¼ mLNN and hS ¼ mLSS , the equilibrium technology lag d and the quality jump γ become independent of the relative effective labor in the two regions.

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T. Borota / Journal of International Economics 87 (2012) 365–376

productivity of copying, and thus, the technology lag of the South, η has an effect on γ in the trade scenario, and consequently on the common growth rate in both regions, still given by u_ 1−α ¼ ðg l þ γα ð1−ϕÞÞ: u α The trade is balanced, and an increase in the market size caused by the opening to trade has no direct effect on the endogenous variables of the model. What plays the central role is the competition effect which introduces the specialization in different ranges of varieties, and thus the static and dynamic benefits of trade. The third endogenous variable in the model is the relative wage N ω¼w wS . Dividing the Northern arbitrage condition by that of the South yields the following condition Fig. 3. Steady state equilibrium.

As proven in the Appendix C, the Northern condition is downward sloping in (γ, d) space (Fig. 3). Namely, with a larger lag of the South, on one hand, the North faces a lower competitive pressure from the South due to increased life of varieties (and thus a lower incentive for R&D), while on the other hand, it is producing a larger range of varieties. Both effects work in favor of reallocating labor to manufacturing, resulting in the lower quality jump. The life of any variety introduced and produced in the South is still infinite, so the Southern equilibrium condition remains unchanged and is given by the upward sloping condition in Fig. 3. However, γ and d in equilibrium will be different. The technology lag d in the trade equilibrium is given by d¼




 1 ρ þ γα ð1−ϕÞ δ LN ln βγ ð1−α Þ þ α η : ð23Þ gl þ γ ð1−α Þ g l þ γα ð1−ϕÞ g l hS LS

Proposition 2. Technology lag of the South (d) increases with opening to trade. Proof. In the special case with no IPR protection (η = 1) and an equal size of the effective population (hNLN = hSLS), the proof is straightforward. In this case, the lag of the South in the no trade scenario given by Eq. (16) is equal to zero.   In the trade scenario, with an increase in ð1−ϕÞ γ, the term βγ ð1−α Þ þ α gρþγα becomes larger than hmN LNN ¼ gδl , l þγα ð1−ϕÞ and thus, the logarithm term is larger than zero. Therefore, d > 0 in the trade equilibrium. For a general case, Appendix B shows that the Southern equilibrium condition is upward sloping in (γ, d) space. Therefore, the increase in γ with opening to trade in goods results in a higher d in the trade equilibrium. □ Higher innovation effort of the North raises the incremental quality addition, and thus, the complexity of new varieties, which ultimately become targets of the Southern imitative activity. With the R&D technology in the South being a function of this complexity, the rise in imitation costs outruns the increase in the value of a new (higher quality) copy at a given lag behind the North. The costs and benefits for a potential imitator are equalized for older quality vintages and fewer product lines in equilibrium, when compared to what the result in the world with no trade would be. As shown in Fig. 3, an outward shift in the Northern condition which occurs with trade leads to the intersection with the upward sloping Southern condition at a higher value of both γ and d, which also implies a lager quality gap ( qqððnnNS ÞÞ). This was not the case in the previous literature, where the equilibrium condition of the South was either flat or downward sloping due to the increasing returns in the imitation technology with respect to innovative effort of the North. The role of η as a measure of the IPR protection will be analyzed in the following subsection. It should be noted that by affecting the

ω

1 1−α

¼

 −dðρþγα ð1−ϕÞÞ 1−e hN kN : 1 1 −dðgl þγα ð1−ϕÞÞ hS kS e θðdÞ m

1 1 β mN

S

The relative wage is proportional to the ratio of R&D productivities, corrected by the terms referring to the varieties lifetime and the relative size of the market served by the North and the South ( kkNS ). Therefore, the relative wage does in fact come from the ratio of factual productivities in creating the value of new businesses in the two regions. Trade balance condition can be used to determine kkNS as  α α dðg þγα ð1−ϕÞÞ τα−1 þ ωα−1 e l −1 kN ¼  α : α  kS 1 þ ωα−1 edðgl þγαð1−ϕÞÞ −1 τ α−1 It is shown in the numerical exercise that an increase in the trade cost pushes up the relative wage and has a negative effect on the welfare in both regions. For the sake of analytical analysis, assuming costless trade (i.e. τ = 1) simplifies the relative wage condition to ω¼


 1−α −dðρþγα ð1−ϕÞÞ dγα ð1−ϕÞ hN e 1−e η : hS

ð24Þ

Both γ and d have a positive impact on the relative wage, and so does the degree of information protection, which decreases the productivity of copying. For the model to be one of North–South trade, it is necessary for monopolistic prices in the South to be lower than the competitive prices in the North. Therefore, the equilibrium ω has to be at least α1 . 14 From the condition above, it follows that the equilibrium North–South technology lag in the trading world has to be positive. Moreover, the size of the quality jump needs to be strictly positive in order to satisfy the wage condition for any value of η and the equilibrium condition (21). The welfare in the trade equilibrium is still a function of the aggregate quality index and the amount of goods consumed (manufacturing labor), but is also a function of the relative wage term which determines the terms of trade. The welfare in the North (South) is an increasing (decreasing) function of the relative wage. The aggregate quality index in the North increases with opening to trade due to an increase in γ, provided that the number of varieties (n) is large enough. Furthermore, a range of low quality varieties are now being imported from the South for a lower price which reduces the price index. On the other hand, the manufacturing labor decreases with opening to trade. Therefore, the direction of change in welfare is determined by the prevailing effect: an increase in aggregate quality 14 With a wide range of parameters used in the numerical exercise, ω appears to be larger than α1 . When this is not the case, the relative wage never falls below one, but may call for the limit pricing with the maximum price in the South being equal to the marginal cost in the North, without any loss in generality of the results.

T. Borota / Journal of International Economics 87 (2012) 365–376

373

and access to cheap varieties from the South, relative to a decrease in production. The aggregate quality index of varieties consumed in the South increases as consumers now have access to high quality goods, but also due to the increase in γ. However, the welfare is also a function of quantities consumed. With opening to trade and an increase in d, the range of varieties produced in the South may decrease and this will have a negative impact on the price index in the South. The change in welfare thus depends on whether the production for export allows for enough high quality import to compensate for the increase in the price index. The welfare in the South increases if the consumption of higher quality varieties and a larger production in the South more than compensate for the unfavorable terms of trade. Appendix D discusses the analytics behind these changes in welfare. In a numerical solution, it is shown that the positive effect on the quality index (the quality consumed) is larger than the negative effect on the manufacturing labor in the North (the quantity produced), and also the negative effect on the price index in the South (import of high price varieties from the North). Hence, the welfare is raised in both regions. This result appears to be robust to large changes in all R&D parameters (β, hN, hS, δ, η), the interest rate r, and the population size and growth (L and gL). A high value of α lowers the welfare gains of opening to trade in both regions, as it reduces the incentives for R&D and the effect of trade on the size of the quality jump. With α > 0.98, i.e. mark-up below 2%, the welfare gains are eliminated. Furthermore, the positive welfare result turns out to be sensitive to the variations in the trade cost, which will be discusses in Section 3.2.2. and in Appendix D.

the move from the equilibrium point A to the equilibrium point B with a higher lag and a lower quality jump. Fig. 5 shows these results numerically. In the trade scenario, the positive effect of η on the lag translates into the change in the size of the quality jump. With a higher information protection, γ and welfare in both regions decrease, while the relative wage increases. The effect of η on the technology lag is positive as in the no trade scenario, though the lag is not zero even in the special case of free information sharing and equal effective sizes of the regions. It might be concluded that trade necessarily brings incentives for the specialization of both regions, no matter how weak the IPR protection policy is. In most R&D driven growth models, higher protection of monopoly rights would bring about an incentive to increase R&D effort, which is not the case here. Raising η raises the value of innovation in the North. However, due to the increase in the relative wage it also raises the cost of R&D more than proportionally and puts a downward pressure on the R&D labor demand. Together with the growing lag of the South and thus higher demand for the manufacturing labor in the North, there is a lower R&D effort and a decrease in γ, until the arbitrage condition is satisfied. Intuitively, stronger IPR protection is not enhancing growth but relieving the monopolists from the competitive pressure. In the South, an increase in η lowers the productivity of copying, and the lower quality jump also results in a lower value of imitation, which cannot be compensated for by the decrease in the R&D cost. This brings about a decrease in the Southern research labor and a higher d. Besides the dynamic loss in growth, the static loss in both Northern and Southern welfare comes as a result of the lower quality index, the loss being larger in the South due to the negative effect of the higher relative wage.

3.2.1. IPR protection This section investigates the impact of a higher information protection (η) on the size of the quality jump (γ) (and thus, the growth rate of the economy), on the North–South technology lag (d), the relative wage (ω), and the steady-state utility (welfare). The model is solved numerically, and the effect of an increase in η on the variables of interest is presented below, together with the graphical illustration for the γ − d effect, and the intuition behind the mechanisms driving the results. Details of the parametrization and the calibration of the model are given in Appendix A. In all exercises, the degree of information protection (IPR protection) varies from 1 (which stands for a perfectly free flow of information regarding the blue-prints), to 1.4, a 40% tighter information flow. For a given quality jump (γ), an increase in the degree of the IPR protection causes an increase in the difficulty of imitation, and, thus, an increase in the equilibrium technology lag of the South (d). This shifts the Southern equilibrium condition up (Fig. 4), resulting in

3.2.2. Trade cost The effects of varying the trade cost from 0 to 40% (τ∈ [1, 1.4]) are presented in Fig. 6. As the equilibrium conditions (21) and (22) do not depend on τ, the level of trade cost has no effect on the value of the quality jump and the lag of the South. Intuitively, lower trade cost increases the profitability of exporting, but at the same time reduces the profitability in the domestic market as there is an increased competition from the other region's varieties. These two effects exactly offset each other, and there is no reallocation of labor across sectors, only a change in the foreign vs domestic market profit share for individual firms. However, the trade costs do have an effect on the welfare of the two regions through their impact on the relative wage and direct influence on the price index. The relative wage decreases with trade liberalization (lower τ), which benefits the Southern consumers due to the reduction in the prices of Northern goods, besides the direct positive effect of the reduction in τ on import prices. However, lower relative wage may hurt the Northern consumers. Nevertheless, the negative effect on the relative wage (income) is more than offset by the benefits of the direct reduction in import prices and indirect reduction in the domestic ones (through lower ω). Regarding the welfare effects of opening to trade, the positive result is sensitive to the level of trade cost. While the welfare effect is positive in both regions with the benchmark value of parameters, the gains diminish with a higher τ. As a result, the numerical exercise in Appendix D shows that there exist a certain cutoff level of τ (1.16 for the South and 1.26 for the North) above which the large trade cost eliminates the welfare gains of transition from autarky. The simulation results are certainly more suggestive than conclusive, but it should be noted that the cutoff values fall within the boundaries of the plausible trade cost values. 4. Conclusion

Fig. 4. Trade: increase in IPR protection diagram.

This paper analyzes the impact of trade and IPR protection on the innovation in the North (the size of the quality jumps) and the

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T. Borota / Journal of International Economics 87 (2012) 365–376

Growth in %

Distance

2.47

36 34

d

g

2.46 32

2.45 30 2.44

28 1

1.1

1.2

1.3

1.4

1

1.1

eta

1.2

1.3

1.4

eta

Relative wage

Welfare (South − −)

2.2

4

U

5

w

2.4

2

3

1.8

2 1

1.1

1.2

1.3

1.4

1

1.1

eta

1.2

1.3

1.4

eta

Fig. 5. Trade: the effect of increase in IPR protection.

imitation in the South (the technology lag of the South) in a model with horizontal expansion of products and quality ladders within product lines. The notion of quality vintages is used to reflect the gradual creative destruction within a product line. By considering a model of endogenous R&D driven growth, the paper discusses the growth and welfare effects of opening to trade in goods, as well as changes in the IPR policy, in order to provide answers to some questions brought up by globalization.

Based on the analytical and numerical analyses, it is found that opening to trade increases the growth rate and welfare of both regions. It also results in a larger technology lag in the South, implying an increase in the North–South quality gap and the appearance of more narrow specialization in the South. This is a consequence of a more detailed modeling of the R&D technology, particularly the imitation processes, with the complexity of targeted products directly affecting the productivity of R&D. Furthermore, the technology lag of the South is always positive in

Growth in %

Distance

3

34

d

35

g

4

2

33

1

32 1

1.1

1.2

1.3

1.4

1

1.1

tau

1.2

1.3

1.4

tau

Relative wage

Welfare (South − −)

2.1

5 4

U

w

2.05 3

2 2 1.95

1 1

1.1

1.2

1.3

1.4

1

1.1

tau Fig. 6. Trade: the effect of increase in trade cost.

1.2

tau

1.3

1.4

T. Borota / Journal of International Economics 87 (2012) 365–376

the trading world, contradicting the predicted possibility of the Southern catch-up due to intellectual theft. Stronger IPR protection is not enhancing growth, but relieving the monopolists from the competitive pressure. Besides the dynamic loss in growth, the static loss in both Northern and Southern welfare comes as a result of the lower quality jump and the increase in the price index (higher relative wage and higher technology lag). While a reduction in trade cost has no effect on the equilibrium R&D, it lowers the relative wage and unambiguously makes the consumers of both regions better-off.

Acknowledgments

375

Appendix B. Upward sloping equilibrium condition in the South The technology lag in the no-trade and the trade scenarios are given by the condition d¼




 1 ρ þ γα ð1−ϕÞ δ LN ln βγ ð1−α Þ þ α η g l þ γ ð1−α Þ g l þ γα ð1−ϕÞ g l LS

and its slope is given by

 dd 1 v ¼ ; dðα−1Þ þ dγ g l þ γð1−α Þ γ α ðρg l þ2γg l α ð1−ϕÞþγ2 α 2 ð1−ϕÞ2 Þ ð1−α Þþ ðgl þγαð1−ϕÞÞ2 where v ¼ . For the initial d not being too αðρþγα ð1−ϕÞÞ ð1−α Þþ

g l þγα ð1−ϕÞ

I am grateful to Omar Licandro, Timothy J. Kehoe, Giancarlo Corsetti, Michael Wycherley, Stephan Fahr, Giammario Impullitti, two anonymous referees and numerous seminar participants for invaluable comments and suggestions.

v large (such that it satisfies db ð1−α Þγ ), the technology lag of the South increases with γ. The condition becomes the most binding with gl → 0, but it appears to be satisfied under a wide range of remaining parameters. Therefore, the Southern equilibrium condition is upward sloping in (γ, d) space.

Appendix A. Numerical exercise

Appendix C. Downward sloping trade equilibrium condition in the North

Three parameters in this model (r, α, gl) can be set based on empirical evidence, while the rest of the parameters, (β, LN, S, hN, S, δ, ϕ, τ, η) are to be determined through calibration. The interest rate, equal to the subjective discount factor, is taken to be 0.05, while the population growth rate, gl, is set at 1.18% as the annual world population growth rate. Most empirical studies show evidence of monopolistic mark-ups in the range of 10–40%, with lower mark-ups occurring in the manufacturing industry. Since the model of interest in this paper mostly refers to such industries (i.e. industries with stronger monopolistic competition, less regulation, and a larger number of producers), α is set at 0.85, which implies a moderate mark-up of 17% and the elasticity of substitution between varieties of 6.7. Equal size of the North and the South is assumed in the benchmark case, in order to abstract from the relative size effects. Moreover, it is not clear which measure of the population should be considered for each region (the total population or the workforce in the tradable sector), nor what the right distinction between the North and the South is in the data. Nevertheless, the most important findings of the model appear to be robust to the changes in the relative size of the two regions. R&D productivity in the North, β, is set equal to 1, and so is the measure of the human capital used in R&D, hN. In this way, one can think of these productivity measures in the South as the relative ones when compared to the North. The benchmark values of policy parameters τ and η are set at a level 15% higher than the values of the free flows of goods and ideas, respectively, i.e. at 1.15. These parameters are varied as a policy experiment evaluation. The remaining parameters, (hS, δ, ϕ) are set at values which allow the model to match the following moments of the macro data: 1) 1.5–2.5% growth of the economy 2) Northern relative wage of 2.1 (World Bank, International Comparison Program database, online edition, 2009) 3) Up to 10% share of resources devoted to R&D relative to GDP in the North (average for OECD countries; National Science Foundation, US, http://www.nsf.gov/statistics) The resulting parameter values are 0.08 for the innovativeness parameter δ, 0.27 for the Southern human capital parameter hS, and 0.25 for ϕ which measures the effect of the quality level on labor productivity in manufacturing as well as prices.

The Northern equilibrium condition in the no-trade and the trade scenarios, respectively, is given by " # hN g l ρ þ γ A α ð1−ϕÞ A ¼ βγ ð1−α Þ þ α δ g l þ γA α ð1−ϕÞ ! " # T −d g þγ T α ð1−ϕÞÞ hN g l ρ þ γ α ð1−ϕÞ 1−e ð l T ¼ βγ ð1−α Þ þ α : δ g l þ γT α ð1−ϕÞ 1−e−dðρþγT α ð1−ϕÞÞ In the trade equilibrium, as d → ∞, the quality jump approaches its no-trade scenario value, i.e. " # hN g l ρ þ γT α ð1−ϕÞ T ¼ γ ð1−α Þ þ α : δβ g l þ γ T α ð1−ϕÞ On the other hand, with d → 0, it follows that lim

T 1−e−dðgl þγ αð1−ϕÞÞ gl þ γ T α ð1−ϕÞ ¼ T ρ þ γT α ð1−ϕÞ 1−e−dðρþγ αð1−ϕÞÞ

and

hN gl T ¼γ : δβ

As the term in squared parenthesis is larger than 1 with ρ > gl, γ becomes larger compared to the one with d → ∞. Therefore, the Northern condition slopes downward as it rotates, and lies to the left relative to its counterpart in the no-trade scenario. Appendix D. Welfare effects of opening to trade Welfare in the North in the no-trade and trade scenarios, respectively, is given by
" nN ðgl þγαð1−ϕÞÞ #1−α α 1−α 1 e A U N ¼ moα LN −mN ð1−α Þ βγ hN g l þ γα ð1−ϕÞ with no trade in goods, and  1  α −dðg l þγα ð1−ϕÞÞ α
" nN ðgl þγαð1−ϕÞÞ #1−α α 1 þ ωτ 1−α −1 e 1−α 1 e T  α  −dðg þγαð1−ϕÞÞ  U N ¼ moα LN −mN ð1−α Þ βγ  l hN gl þ γα ð1−ϕÞ 1 þ ω1−α −1 e

in the trade scenario. The last term in the trade expression relates to the terms of trade and the range of varieties produced, and it is larger than 1 for trade costs that are not too high. The second squared bracket term represents the aggregate quality index. The quality index in

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T. Borota / Journal of International Economics 87 (2012) 365–376

Welfare effects of openness, South (−−)

hand, lowers the welfare gains of opening to trade in both regions, as it reduces the incentives for R&D and the effect of trade on the size of the quality jump. The gains are eliminated for α > 0.98, i.e. monopolistic mark-up lower than 2%. More importantly, the positive welfare result proves to be sensitive to the level of the trade cost in the two regions. While the welfare effect is positive in both the North and the South with the benchmark value of parameters (a 4% gain in the South and 13% in the North), the gains diminish with a larger τ. A trade cost higher than the cutoff eliminate the welfare gains of transition from autarky to trade in the two regions. When the number of varieties (n) is set such that the resulting GDP levels correspond to the data, the numerical exercise shows that the cutoff levels of τ are 1.16 and 1.26, for the South and the North, respectively. The welfare gains in the two regions are presented in Fig. 7.

70 60

welfare change in %

50 40 30 20 10 0 −10 −20 −30

References

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

tau Fig. 7. The effect of trade cost on welfare gain from opening.

the North increases with opening to trade due to an increase in γ, provided that the number of varieties (n) is large enough to satisfy n(gl + γα(1 − ϕ)) > 1. On the other hand, the first squared bracket term in the welfare expression is the manufacturing labor which decreases with opening to trade. Therefore, the direction of change in the welfare is determined by the prevailing effect, i.e. an increase in aggregate quality and access to cheap varieties from the South vs. the decrease in manufacturing labor and thus lower production. With costless trade, the numerical solution shows that the positive effect dominates and the welfare increases even with a very small increase in the aggregate quality index (the case of n(gl + γα(1 − ϕ)) → 1). The welfare gains of opening to trade in the North are 7.5%. The welfare in the South in the no-trade and the trade scenarios, respectively, is given by A US

1−α α

¼ mo


" ðnN −dÞðgl þγα ð1−ϕÞÞ #1−α α 1 e LS −mS ð1−α Þ θðdÞγ hS g l þ γα ð1−ϕÞ

with no trade in goods, and   1 α α dðg þγα ð1−ϕÞÞ
" ðnN −dÞðgl þγαð1−ϕÞÞ #1−α α 1 þ ½τωα−1 e l −1 1−α 1 e T U S ¼ moα LS −mS ð1−α Þ θðdÞγ  α  hS gl þ γα ð1−ϕÞ 1 þ ωα−1 edðgl þγαð1−ϕÞÞ −1

in the trade scenario. The aggregate quality index of varieties consumed in the South increases as consumers now have access to high quality goods, but also due to the increase in γ (provided that n(gl + γα(1 − ϕ)) > 1). However, the welfare is a function of quantities consumed as well. The range of qualities produced in the South decreases (higher d), and the change in welfare will depend on whether the increased production for export in the South allows for enough high quality import to compensate for the increase in the price index. The numerical solution shows that the consumption of high quality varieties produced in the North and larger production in the South more than compensate for the unfavorable terms of trade, and thus the welfare in the South increases with opening to trade. With a very small increase in the quality index (n(gl + γα(1 − ϕ)) → 1), the welfare increases by 21%. The robustness of the positive welfare result is maintained for substantial changes in all R&D parameters (β, hN, hS, δ, η), the interest rate r, and the population size and growth (L and gL). A higher value of α (higher elasticity of substitution between varieties), on the other

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