A Model of Innovation, Standardization, and Imitation: the Effects of Intellectual Property Rights Protection Taro Akiyama, Yuichi Furukawa International Graduate School of Social Sciences, Yokohama National University, Tokiwadai 79-4, Hodogaya, Yokohama 240-8501, JAPAN
1 Introduction In recent years, the literature on product cycle models has made remarkable progress. However, while Raymond Vernon’s (1966) original view of the product cycle emphasizes the role for standardization of production technologies in the international transfer of technology from an innovative region (the North) to an imitative region (the South), most models in the literature have not focused on standardization as an integral factor in technology transfer (Krugman, 1979; Helpman, 1993; Glass and Saggi, 2002). 1 A most recent exception is the model of Antr`as (2005), although the rates of innovation and standardization are exogenous in this model. An important contribution of our paper is to present a product cycle model in which both innovation and standardization are endogenous. Departing from the two-region variety expansion model of Helpman (1993), we assume that newly introduced products in the North can be transferred to the South only after the technologies for these products are standardized. Our modification makes the model much more akin to Vernon’s (1966) original formulation and theoretical work capturing his idea. 2 Vernon (1966) argues that newly introduced goods are initially manufactured in the country where they are first developed (the North), and the locus of production can be shifted to the South only when the production technique has been standardized by the original innovator in the North. We shed light on this consideration by assuming that goods are produced using two types of technology: a complicated, hard-to-learn technology and a simple, easier-tolearn (easier-to-use) technology. We associate the latter with standardized technology. Corresponding
author: Tel.: +81-422-53-5853; fax: +81-422-53-5853. E-mail address:
[email protected] (Yuichi Furukawa). 1 See also Grossman and Helpman (1991), Lai (1998), Parello (2005), and Dinopoulos and Segerstrom (2006). 2 Antr` a s (2005) shows that when the good is sufficiently standardized, manufacturing shifts from the North to the South.
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We adopt the simplest way to model the standardization of production technologies: a standardized technology is less costly owing to its simplicity. 3 The product cycle we consider below is as follows. A newly introduced product is initially manufactured with a non-standardized, hard-to-learn technology in the North. Once standardization of the production technology is driven by a voluntary decision made by the original innovator, this innovator manufactures his/her product using a standardized technology in the North until it has been imitated by the South. In line with the Vernon–Antr`as view, the South imitates only innovators who have standardized their technologies. Thus, in our model, while Northern monopolists who have already standardized their technologies are at risk of being imitated by the South, they enjoy lower costs of production than the non-standardized innovators at the cost of safety from imitation (they may lose their market power). As the South imitates products that are manufactured using standardized technology, the locus of production shifts to the less developed South. Our model differs from Helpman (1993) essentially in that we allow for this type of standardization of production techniques in the technology transfer process. We apply our simple framework to examine the effects of strengthening intellectual property rights (IPR) protection in the South, which we associate with a decrease in the rate of imitation, as in Helpman (1993). 4 In the model, since only products that have been standardized can be imitated by the South, tighter IPR protection in the South stimulates an incentive to standardize, by keeping Northern producers who have already standardized their technologies safer from imitation. It follows that stronger IPR protection increases the number of standardized products that can be imitated and thereby the fraction of products that are actually imitated and manufactured in the South. Previous studies in the literature could not address this mechanism of standardization, through which strengthening of IPR enhances the transfer of technology, since they neither incorporate the process of standardization nor treat it as endogenous. An interesting result of our model is that the long-run rate of innovation may increase with tightening of IPR. This result, which contrasts sharply with that of Helpman (1993), arises because stronger IPR protection, by enhancing international technology transfer, relaxes resource scarcity in the North through contraction of the fraction of products manufactured in the North (less production remains in the North). The smaller fraction of Northern products leaves more resources for innovation, so that tightening IPR increases the rate of innovation in the North. In addition, the enhanced international technology transfer, implying that more production is shifted to the South, increases the demand for Southern labor. Therefore, an increase in IPR protection increases the relative wage, or terms of trade, of the South. The force behind this result is closely related to the decision-making of North3 An alternative model approach is, for example, to define the standardization of technology as an increase in the factor intensity of low-tech inputs, as in Antr`as (2005). This makes model analyses very complex, while we consider that it does not qualitatively change the results obtained. 4 The enforcement of intellectual property laws, which is often raised in public policy discussions, has been a critical issue, especially in trade relations between developed and developing countries, as reflected, for example, in the Trade Related Aspects of Intellectual Property Rights (TRIPs) agreement under the World Trade Organization.
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ern monopolists on whether to standardize or not. This is the key assumption of our model. As mentioned above, IPR protection in the South affects only producers who have already standardized their technologies. It follows that stronger IPR changes the decision-making of Northern monopolists by stimulating the incentive to standardize their production techniques. Although tighter IPR protection, implying a reduction in the rate of imitation, has a negative effect on technology transfer in existing models, it has a positive effect owing to the increased number of standardized products that can be imitated in our model. As a consequence of enhanced standardization in our model, tighter IPR can enhance international technology transfer and thus the rate of innovation. However, for economies with much stronger IPR protection, the effects of IPR will be altered. In such economies, standardized innovators are sufficiently safe from imitation, so that all the innovators standardize their technologies immediately after the introduction of their products in this case (i.e., the rate of standardization is constant at unity). Thus, the decision-making of Northern innovators on whether to standardize their technology no longer exists. This case is much closer to Helpman’s (1993) economy, since the role of standardization disappears here. As a result, for economies with stronger IPR protection, the effects of IPR are quite opposite to those in the case of weaker protection, and rather akin to those of Helpman (1993). That is, stronger IPR reduces the long-run rates of innovation and international technology transfer, and negatively affects the South’s terms of trade. These results can be summarized as follows. There is an inverted-U relationship between innovation and IPR protection in this economy: IPR protection that is too strong or too weak negatively affects the incentive to innovate; rather, a balanced approach is required to enhance long-run innovation and subsequent long-run growth. In addition, for the rate of technology transfer and the South’s relative wage, an inverted-U relationship to IPR protection is evident in the model. We also show that the long-run welfare of both regions increases with tightening of IPR protection if the protection is very weak to start with: both the South and North can gain from stronger IPR. This result suggests, interestingly, that policies that require developing countries to strengthen IPR protection (e.g., TRIPs agreement) may enhance both developing and developed countries: depending on the conditions (if IPR is hardly protected in developing countries), a strengthening of IPR protection can be good for all regions. The remainder of the paper is structured as follows. Section 2 presents a product cycle model with standardization as the integral factor for international technology transfer. Section 3 presents the equilibrium conditions of the model and examines the effects of IPR. Section 4 summarizes the main results presented in Section 3 and Section 5 provides a few policy implications and concludes.
2 The Model This section describes the basic model based on Helpman (1993), who constructs a tworegion variety expansion model with exogenous imitation by the South. Our model essentially differs from Helpman (1993) only in the following. We allow for two types of 3
production technology: standardized and yet-to-be standardized technology. Production technologies of Northern innovators are standardized only by voluntary decisions they make themselves. Time is continuous and indexed by t, and extends from zero to infinity. Two regions exist, the innovative North and the imitative South. There is a continuum of differentiated consumption products. At any date, only a subset of them, 0 n t , is available in the marketplace. The economy initially inherits a given number of available varieties, n0 , and expands over time through the entry process into R&D activity in the North. Each product (or variety) is indexed by j, and thus j 0 n. The two regions differ in their technological capabilities. While the North introduces new products endogenously, the South costlessly imitates Northern products that are manufactured with technologies that have already been standardized at the rate m n˙ S 1 α nN , where α denotes the fraction of products for which the technology has not been standardized by their original innovators in the North, n S denotes the number of products that have already been imitated, 5 and nN denotes the number of products that have not been imitated yet; n n S nN .6 Imitation by the South is the only channel of international technology transfer in this model, as in Helpman (1993). The product cycle we consider, which is much more akin to the Vernon–Antr`as model, can be summarized as follows: the North first innovates and new goods are manufactured in this country. Next, the original innovators in the North standardize their own production technology. Finally, the South imitates the standardized Northern goods. We assume here that the Northern innovators who have not standardized their technologies can not be imitated by the South (safe from imitation), but their marginal (or average) cost is higher than for standardized technologies. On the other hand, we assume that Northern innovators who have already standardized their technologies can manufacture their products at a lower marginal/average cost owing to the simplicity of the technology, but can be imitated by the South and then are at risk of losing their monopoly power by imitation. Hence, 1 α n N , which is the number of products manufactured with standardized technologies, is equal to the number of products that can be imitated by the South, while α n N is the number of yet-to-be standardized products that the South can not imitate. For simplicity, we assume that standardizing technologies is costless.7 In this model we interpret a reduction in production costs as standardization of the production techniques: technological standardization is defined as the transition from a complex technology to a simple, easy-to-use technology that enables users of this is apparent below, 1 α nN is the number of products that the South can imitate. specification on costless imitation would be incomplete, since it does not capture the mechanism through which patent policies by the Southern government affects the rate of imitation in the South. However, it is useful to analyze various important issues owing to its simplicity. The costless specification of imitation has been used by many authors, such as Grossman and Helpman (1991), Lai (1998), Eaton and Kortum (1999), and Kwan and Lai (2003). In addition, costly imitation would make the model more complicated and the analysis more difficult without altering the basic conclusion of this paper: stronger IPR may be better for the long-run rate of innovation. 7 While we can show that our results do not change when we allow for a costly standardization process, the analysis of costly standardization models is much more complex. Our companion paper, Akiyama and Furukawa (2006), which constructs a product cycle model with costly standardization, shows similar results to the current paper. While the model in Akiyama and Furukawa (2006) is so complex that the results depend on numerical calculations, the current paper solves the model analytically. 5 As
6 Our
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technology to manufacture a product more efficiently (i.e., less costly). This view is very simple and tractable, but, of course, has limitations because it does not capture the role of the factor intensity of high-tech inputs (e.g., skilled labor). 8 Nevertheless, it will prove to be useful to clarify a number of important issues. The rate of imitation, m, can be interpreted as the hazard rate of the Poisson process, at which the monopoly power of the Northern innovators who have standardized their technologies disappears at the next date. In Section 2.3 we describe details of the imitation rate, m.
2.1 Consumption Individuals in both regions have identical preferences. In the economy that we consider, individuals in region i i S N supply L i units of labor inelastically 9 and consume n nS nN differentiated products. At any date they choose consumption and saving so as to maximize: ∞
U
0
e ρ t ln ut dt ,
(1)
where ρ 0 denotes the subjective discount rate and ln u t denotes the instantaneous utility at date t, which depends on the composite of differentiated varieties and takes the form of symmetric constant elasticity of substitution (CES): nt
ut
0
xt j
σ 1 σ
σσ 1 dj
,
σ
1,
(2)
where xt j denotes consumption of product j at time t. Owing to the CES specification, static optimization implies that the demand functions exhibit a constant price elasticity, σ 1: x j p j σ
E , P1 σ
(3)
where p j denotes the price of product j, E 0n p jx jd j denotes aggregate spending on differentiated products, and P is the price index that satisfies nt
P
p j
1 σ
1 1σ dj
.
(4)
0
Using (2) and (3), we have the following indirect utility function: ln u ln E lnP .
(5)
8 The
literature often associates standardization with an increase in the factor intensity of low-tech inputs, and it emphasizes the link transferability and the intensity of low-tech inputs (Vernon, 1966; Antr`a s, 2005; Thoenig and Verdier, 2005). However, since an increase in the low-tech intensity can decrease average costs because low-tech inputs are frequently lower priced, it would be possible to extend our simple formulation by identifying standardization as an increase in the intensity of low-tech (lower-priced) inputs. Such an extension would not change our results qualitatively. 9 Indexes S and N represent the South and North, respectively.
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This equation implies that the instantaneous utility depends on real spending, E P. A Northern consumer maximizes welfare with preferences (1) and indirect utility (5) subject to an intertemporal budget constraint. It is well known that the dynamic optimization problem has a solution that yields the equation: E˙ N EN
rN ρ ,
(6)
where E N represents consumption spending of Northern consumers and r N is the nominal rate of interest. Following Helpman (1993), we assume that financial capital does not flow between the two regions, so that the investment in R&D is equal to the domestic savings in the North. Then the trade account is balanced at all times owing to the absence of international capital flows: E N nnS p jx j d j. Note that product j 0 nS is manufactured in the South and product j n S n in the North. The South spends all of its income on consumption goods because there is no international capital flow and thus no investment takes place in the South: per capita expenditure on consumption in the South is equal to the Southern wage rate.
2.2 Production As defined above, a standardized technology is less costly than non-standardized technology, but it can be imitated by the South. Thus, Northern innovators who have already standardized their technologies can manufacture their products at a lower average cost, but their monopoly power can disappear, depending on the rate of imitation, m. The South can not imitate the products manufactured by Northern innovators who have not standardized their technologies yet. That is, standardized manufacturers face an uncertainty created by laxly enforced domestic laws and regulations on patents in the South in return for more efficient technology. 10 More specifically, if a Northern manufacturer who invents a product with index j has standardized his/her technology, product j is manufactured with λ λ 0 1 units of labor per unit output, while the market power held by innovator j disappears at the next time point of the hazard rate, m. On the other hand, a Northern manufacturer is subject to a higher cost when he/she has not standardized his/her technology yet. We normalize this higher cost to one unit of labor, and, noting λ 1, standardization leads to a cost reduction in our model. Owing to the constant price elasticity σ 1, 11 a Northern innovator charges the following monopoly price for technology that is already standardized (as long as the
10 In
the current model, standardization is described as rational behavior by the original innovator. This specification is much closer to Vernon’ (1966) original vision. However, Arrow (1962) shows that in a monopolistic sector, an original innovator (an incumbent) has little incentive to further innovate or improve his/her own production technology because monopoly rents are secured without any effort (the Arrow effect). In line with Arrow (1962), Akiyama and Furukawa (2006) construct a product cycle model with endogenous innovation and standardization, in which innovators and standardizers are explicitly distinguished. The results of the current paper and of Akiyama and Furukawa (2006) are similar. 11 See the demand functions in Eq. (3).
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product has not been imitated yet): pˆN
σλ N w , σ 1
(7)
where wN represents the wage rate in the North, and then the marginal cost for standardized Northern innovators is λ w N . For technology that is not standardized yet, a Northern innovator charges: pN
σ wN , σ 1
(8)
where the marginal cost for Northern innovators who have not standardized is w N λ wN . Clearly, pN pˆN λ pˆN holds.12 Assuming that products that have already been imitated are available to all Southern producers, imitated products are competitively produced in the South. In that event, the price of the remaining n S products is equal to the marginal cost in the South: pS λ wS ,
(9)
where wS is the wage rate in the South. We assume that the wage rate is higher in the North.13 Hence, the prices of products in the North are also higher; p N pˆN pS . From the demand functions, (3), and the prices in the North, (7) and (8), we have xˆN λ σ xN . Let xˆN and xN denote the per product consumption of a standardized Northern product and of a Northern product that is yet to be standardized. Using this relationship, we can express the temporary profits for both standardized and yet to be standardized products as:
πˆ
λ 1 σ p N x N σ
and
π
p N xN , σ
(10)
respectively. Since λ 1 σ 1, the profit for standardized products is higher than for non-standardized products: πˆ π . Note again that α 0 1 denotes the proportion of non-standardized Northern manufacture. It follows that n N products that have not been imitated are monopolistically priced above Northern wages, α t nN products have yet to be standardized (highly priced, not imitated), and 1 α n N products of n N are standardized (lowly priced, easily imitated).14 Using the above prices ofproducts, we rewrite the condition for the lack of international capital mobility, E N nnS p jx jd j, as: EN
α nN pN xN 1 α nN pˆN xˆN ,
(11)
12 We
here assume implicitly that Northern innovators manufacture their products at home: we do not deal with foreign direct investment or multinational firms. 13 This assumption ensures that imitated products are manufactured in the South. 14 We consider the process of innovation, standardization, and imitation to be irreversible: that is, Northern innovators who standardize their own technology never use the non-standardized technology again. Specifically, we impose n˙ α n˙ N , which assures that the gross increase in the number of standardized products, 1 ˙α nN n˙ S , is not negative, noting n α nN 1 α nN nS . It is easy to verify that this condition is always satisfied near a balanced growth path (shown in the Appendix).
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from which we obtain the Northern spending on consumption as: EN
nN pN xN α λ 1 σ 1 α .
(12)
This equation, combined with (10), implies that the temporary profits in the North depend on the share of non-standardized products in the North, α , the Northern spending, E N , and the number of the Northern products, n N :
π
EN . σ nN α λ 1 σ 1 α
(13)
2.3 Imitation We have already defined the Poisson arrival rate of imitation for the South as n˙ S 1 α nN , denoted by m. We assume that this Poisson hazard rate is composed of two parts: m μ K, as in Lai (1998). μ 0 is a policy parameter determined by the Southern government, while K is determined by the technologies. In this model we can interpret a strengthening of IPR as a decline in μ ; good patent laws and stronger legal enforcement by the Southern government imply a slower pace of imitation. Of all imitative actions taken by the South, a fraction μ escapes monitoring by the patent authority. That is, lower μ implies tighter IPR protection. When μ 0, patent laws are perfectly enforced. When μ ∞, no enforcement of patent laws exists. K is assumed to be determined by the technologies (i.e., by how quickly a newly invented technology can be understood and imitated by the South). Departing from Lai (1998), we assume that K is endogenously determined by the relative knowledge stock of the South. Specifically, we assume that the technological difference between the North and the South determines the pace of imitation: a higher level of knowledge accumulation in the South relative to the North implies a faster pace of imitation. We therefore specify the technological variable K as K S K N , in which K S is the cumulative stock of knowledge of the South, and K N of the North. In a standard manner, these are taken to equal n S and n, respectively: then m μ n S n. Using nS n nN , the law of motion for n S can hence be written as: n˙ S μ 1 nˆ N 1 α nN ,
(14)
where nˆ N nN n denotes the fraction of products that have not been imitated (and are thus manufactured in the North). Eq. (14) states that, when more knowledge capital is accumulated in the South relative to the North (i.e., smaller nˆ N ), imitation in the South becomes more active and, as a result, more production transfers internationally (i.e., larger n˙ S ). In addition, the stronger the IPR protection (i.e., lower μ ), the lower is technology transfer, as in Helpman (1993).
2.4 Innovation Assume that innovating a new product requires bK N units of labor as inputs. If investment in innovation takes place, the reward from this activity cannot exceed its expenditure in equilibrium: innovation values w N bn. This is because free entry, which we assume in this paper, produces an unbounded demand for labor by innovators. 8
There are two types of Northern innovators: those who have standardized their technology and those who have not yet standardized. Since a non-standardized product cannot be imitated by the South (market power does not disappear), the value of a nonstandardized innovator, V , satisfies the following Bellman equation (see Grossman and Helpman, 1991 for details): rtN Vt
πt V˙t .
(15)
The market power of a standardized product that has not been imitated ceases to exist with the probability mdt of being imitated in the next time interval of length dt. Using m μ 1 nˆ N , arbitrage in asset markets for standardized innovators implies the following Bellman equation: rN Vˆ λ 1 σ π Vˆ˙ μ 1 nˆ N Vˆ , (16) t
t
t
t
t
t
where Vˆt represents the value of an innovator who has already standardized his/her technology. Innovators will not opt to standardize their technologies when Vˆt Vt : newly introduced products are all manufactured with the yet to be standardized technology, and standardization never takes place, or equivalently 1 α n N nS stays constant and α 0. When this condition does not hold, Northern innovators may choose to standardize their production techniques and to produce using less costly techniques, which can be imitated: 1 α n N nS can increase. In particular, in the case of Vˆ V , all innovators, on introducing a new product to the market, start producing with standardized production techniques: α 0. The dynamics of n is then:
n˙
α n˙ N n˙ N n˙S
when Vˆ when Vˆ
V
V
,
(17)
reflecting n α nN 1 α nN nS .
2.5 Labor We denote by Li the labor force of region i, i N, S. Then we can express the labor market clearing conditions as:
λ xS nS LS , x αn N
N
(18)
λ xˆ 1 α n N
N
N
bg L ,
(19)
where xS is the per product consumption of a product that has been imitated and is manufactured in the South, and g n˙n is the rate of innovation. The first term on the left-hand side of the latter equation represents employment in manufacturing nonstandardized products, the second term represents employment in manufacturing standardized products, and the third term represents employment in innovation. Using (7), (8), (12) and the free entry condition, max V Vˆ bwN n, we can rewrite this labor market condition for the North (19) as:
σ 1 EN σ nV
g
LN . b
(20)
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3 Equilibrium In a balanced growth path (BGP), for i N, S, n, n i , wi , and E i grow at a constant rate, g£ : g£ n˙n n˙ N nN n˙ S nS in a BGP. In addition, α , r, V , and Vˆ are constant. As α is constant and n˙ n n˙ N nN along a BGP, Vˆ V cannot be compatible with the existence of a BGP, as is apparent from (17). 15 We should therefore impose a restriction, Vˆ V .
3.1 Case with Both Standardized and Non-standardized Technologies To shed light on the role of standardization, we first focus on a situation whereby nN Northern products are manufactured with both standardized and non-standardized techniques in the BGP: Northern innovators are indifferent on whether to standardize or not. That is, in this case Vˆ V .16 To analyze the dynamic equilibrium, it is useful to define a new variable, v E N σ nV . From (13) and Vˆ V , the two Bellman equations, (15) and (16), can be reduced to a single expression:
α
1 1 λ σ 1
v
μ nˆ N 1
nˆ N
,
(21)
from which we have the dynamics of V as follows, noting (13) and (15) again. r N V˙ V λˆ μ 1 nˆ N , where we define λˆ λ σ 1 1 λ σ 1 . Combined with the Euler equation (6), we can derive from this equation the following law of motion for v: v˙ v
λˆ μ 1 nˆ N ρ g .
(22)
Next, we need to describe the dynamic evolution of nˆ N . By definition, n˙ N n˙ n˙ S . From (14), we have n˙ N nN gnˆ N μ 1 α 1 nˆ N . We thus have the following dynamic equation for nˆ N : n˙ˆ N g1 nˆ N μ 1 α 1 nˆ N . N nˆ nˆN Substituting (21) into this expression, we can derive the following law of motion for nˆ N : g1 nˆ N ˆ v n˙ˆ N λ μ 1 n ˆN N . (23) N nˆ nˆN nˆ
15 Since α is constant along a BGP, (17) implies that n˙ α n ˙N when Vˆ V . Along a BGP, n˙ n equals n˙N nN . Then, if Vˆ V , α nˆ N equals unity. This is a contradiction with the structure of the model, since nˆN 1 and α 1. 16 In Section 3.2 we discuss the case of V ˆ V , in which case, no sooner do all innovators introduce their products into the market than they standardize their technologies (i.e., α 0). Comparative statistics analysis in this case is essentially no different from that of Helpman (1993), as shown in Section 3.2. This is because in this case the rate of standardization is constant at unity and thus the presence of standardization, which is the crucial assumption of this paper, hardly affects the economy. While the only difference between the case of Vˆ V and Helpman’s (1993) economy is that we assume that the rate of imitation depends on the relative knowledge of the South, nS n, it does not affect our results qualitatively (allowance for the standardization process plays the most important role in the model), but makes the analysis tractable.
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Figure 1: Transitional dynamics Finally, together with v E N σ nV , the labor market condition for the North, (20), implies: g
LN b
σ 1v .
(24)
It follows that Eqs. (22)–(24) form an autonomous system of two differential equations in v nˆ N . In this system, nˆ N is a state variable, while v is a jumpable variable. Figure 1 depicts the phase diagram for this system. 17 The locus of v˙ 0 is represented by v
1
σ 1
ρ
while the locus of n˙ˆ N
v
LN b
λˆ μ 1 nˆ N
,
(25)
0 is represented by
1 nˆ N LN b λˆ μ nˆ N
.
σ σ 1nˆ N
(26)
These two loci intersect once at a point v £ n£ , which indicates the unique BGP equilibrium. The term “once” implies the uniqueness of the BGP. It is well known that 17 For simplicity, we assume that LS bσ σ μ 1 λ σ 1 σ 1σ 1 holds. This ensures that, for any point nˆN v , the wage rate in the North is higher than in the South. The labor market condition for the North
can derive the following expression: xN (21), this equation implies: wN wS
σ
1σ 1 1 λ σ 1 LS b μσ σ 1 nˆN 2
LN bg . nN α λ 1 σ 1 α
Together with xS LS λ nS , (8), (9), (20), and
σ1 .
This equation, together with the prices (8) and (9), implies that wN wS holds if and only if LS bσ σ μ 1 λ σ 1 σ 1σ 1 holds. While we can loosen this condition, we impose it for simplicity.
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paths that do not converge to this BGP cannot satisfy requirements in the model, such as the transversality condition. Hence, since this BGP is a saddle point (a proof appears in the Appendix), the saddle path converging to the BGP is a unique equilibrium path. From (25) and (26), we can determine the BGP, v £ n£ , uniquely: v£
LN b ρ λˆ μ ρ , ρ σ λˆ μ ρ
n£
LN b σ λˆ μ ρ . ρ σ λˆ μ ρ
(27)
Together with (24), this equation derives the BGP rate of innovation as: g£
λˆ μ LN b ρ σ 1λˆ μ ρ . ρ σ λˆ μ ρ
(28)
Before we proceed to an inspection of this equation, it is helpful to state the restrictions that need to be imposed on the parameters. Various situations are a priori possible. As represented in Figure 1, we restrict ourselves here to the most interesting case, whereby α is not equal to zero in a BGP, and then an interior BGP, α £ 0 1, still exists (both standardized and non-standardized technologies are used in production): that is, Vˆ V holds.18 The parameter values determine whether α £ exceeds zero. The case of α £ 0 requires that μ is not too small: the protection of IPR is not too strong. Specifically, we define the threshold value of μ as μˆ . Why is there such a lower bound of μ in the model? Tighter IPR protection reduces the cost of standardizing a technology by decreasing the rate of imitation. It follows that a reduction in μ (strengthening of IPR) stimulates an incentive to standardize. Then for a sufficiently small μ , it is not likely that innovators will leave non-standardized technology in place: there could exist a threshold value of μ below which all innovators choose to standardize once their products are introduced into the market. The Appendix formally describes the above discussion, and gives a formal definition of μˆ . We assume μ μˆ to ensure the possibility of Vˆ V . In summary, an economy in which IPR protection is not too strong in the South (i.e., μ μˆ ) allows for both standardized and non-standardized technologies to be used in Northern production (α 1). In addition, we need two restrictions on the parameters to ensure the existence and feasibility of a non-trivial BGP, v £ n£ . First, the following is a feasibility condition that assures that 0 n£ 1 holds:
μ
LN b σ ρ λˆ σ .
If we assume that μˆ LN b σ ρ λˆ σ , two restrictions on μ can be reduced to a single expression as follows: (A1)
μ μˆ .
that the case of α 1 is not possible in a BGP. α 1 implies the absence of standardized Northern products that can be imitated. It follows that n˙S is always zero: imitation never takes place. This violates a requirement for a BGP; n, nN , and nS grow at the constant rate, g . In fact, the Appendix shows that, under the assumption of positive growth imposed below (see (A2)), α cannot exceed unity in the BGP: α 1 necessarily holds. 18 Note
12
While we maintain this assumption μˆ LN b σρ λˆ σ for simplicity, the implications of this paper would not be altered without this simplification. Second, the long-run rate of innovation, g £ LN b σ 1v£ , needs to be positive for a non-trivial BGP, v £ n£ . Assume that the North innovates at a positive rate for any μ : LN b
(A2)
ρ σ 1 .
This restriction implies that the effective labor supply is sufficiently large to ensure g£ 0. A formal discussion of these conditions is in the Appendix. We are now ready to run comparative static experiments and clarify their impacts in the case of Vˆ V , which is characterized by the assumptions (A1) and (A2). We assume (A1) and (A2) in this subsection to focus on the case of Vˆ V . Note again that we interpret a reduction in μ as a strengthening of IPR protection; m μ K. Our interest is hence in the effect of μ on the rate of innovation. We have first established that the rate of innovation must increase on impact. Differentiating (27) and (28), we obtain:
∂ g£ ∂μ ∂ n£ ∂μ
λˆ ρ σ 1LN b ρ Λ
λˆ σ LN b ρ Λ
0,
(29)
0,
(30)
0.
(31)
where
2
Λ ρ σ λˆ μ ρ
It follows from (29) and (30) that the long-run rate of innovation increases and the longrun fraction of products that have not been imitated decreases in response to stronger IPR protection (captured by a reduction in μ ). Since this result is important, it should be stated as a proposition: Proposition 1 ∂ g£ ∂ μ
0 and ∂ n£ ∂ μ
0.
This proposition shows that, in the case of weak protection (i.e., assumption (A1)), strengthening of IPR protection is always better for growth in the long run: strengthening IPR in the South stimulates Northern innovation in the long run. It also shows that stronger IPR in the South accelerates international technology transfer from the North to the South in the long run. This result on the long-run innovation sharply contrasts with that of most existing models in the literature. 19 Helpman (1993), for example, 20 shows that strengthening of IPR protection, by depressing the international transfer of technology, tightens the Northern resource constraint. The scarcity of Northern resources reduces employment in R&D and hence lowers the rate of innovation in the long run. 19 A
recent exception is Lai (1998). also Glass and Saggi (1998) and Grossman and Helpman (1991).
20 See
13
Why does stronger protection enhance the long-run growth in our model? What is the difference between most existing models and ours? The answer to these questions is related to the process of standardization. To understand the intuition behind our contrasting result, we derive the first-order response of the BGP fraction of products that have been standardized and not been imitated, 1 α , (which we define as the rate of standardization) to changes in μ . Taking account of conditions (A1) and (A2), we calculate from (21) and (27):
∂ 1 α £ ρ LN b σ λˆ μ ρ LN bλˆ μ ρ ρ σ 1λˆ μ ρ 0 , (32) £2 ∂μ μ n Λ namely, a strengthening of IPR protection (a decrease in μ ) increases the long-run rate of standardization, as well as the long-run rate of innovation. This is because stronger IPR protection makes innovators who have standardized their technologies safer from imitation,21 and thus stimulates the incentive to standardize. In addition, its impact spreads to international technology transfer: the increased rate of standardization implies an increase in the number of Northern products that can be imitated, and hence enhances the international transfer of technology, which is driven by Southern imitation, since only the products that have been standardized can be imitated by the South. Specifically, the long-run fraction of (already imitated) Southern products, 1 n £ , increases with a strengthening of IPR protection: ∂ 1 n £∂ μ 0 holds, as is apparent from (27). As a result, the resource scarcity in the North is relaxed (Northern employment in manufacturing, bσ 1v £ , decreases),22 decreased Northern production leaves more resources for innovation, and finally the rate of innovation increases. We have established that the long-run rate of innovation increases as a result of stronger IPR protection. We turn now to the short-run effect of IPR. For simplicity, following Helpman (1993), we restrict ourselves to economies that are initially in a BGP; nˆ N 0 n£ . Taking into account this initial condition, we can calculate the firstorder response of v nˆ N to changes in μ on the transitional paths from a log-linearized system of (22)–(24) around the BGP (proof appears in the Appendix):
∂ vt 1 ∂ v £ γ e ε2 t ∂ n £ vt £ ∂μ v£ ∂ μ n ∂μ N t ∂ n£ ∂ nˆN t n ˆ ε t 1 e 2 , ∂μ n£ ∂ μ
∂ n£ ρ γ e ε2 t vt ∂ μ σ v£ n£
,
(33) (34)
where ε2 0 and γ 0. From Proposition 1 and (34), the fraction of products that have not been imitated yet decreases with a tightening of IPR protection (a reduction in μ ) at every point in time (except for t 0: tighter IPR stimulates international technology transfer from the North to the South at all times. While tighter IPR protection must increase the rate of innovation in the long run, as shown in Proposition 1, (24) and (33) imply that it would decrease temporarily. This implies the following proposition: Proposition 2 A tightening of IPR protection also encourages international technology transfer in the short run. The short-run effect on the rate of innovation is ambiguous. 21 This 22 Note
effect can be detected by comparing (15) with (16). ∂ v ∂ μ 0.
14
Table 1: Effects of strengthening IPR protection in the case of Vˆ
V
We have established in Propositions 1 and 2 that a strengthening of IPR protection initially decreases the rate of innovation, but that the rate of innovation subsequently increases. Finally, our remaining interest is to examine the effect on the relative wage. The relative wage of the North, w N wS , can be represented as follows (see footnote 17): wN wS
σ 1σ 1 1 λ σ 1 LS bμσ σ 1 nˆ N 2
σ1 ,
(35)
which exceeds 1. Eq. (35) implies that the Northern relative wage, w N wS , decreases as μ 1 n£ 2 increases along the BGP. Then we calculate:
£2 ˆ ∂ 1 n ρ σ 1 λ μσ μ 1 n£ 2 ˆ ∂μ ρ σ λ μ ρ
0,
where this inequality is ensured by assumption (A1). From this expression, we can verify that the long-run response of w N wS to μ is positive: that is,
∂ wN wS ∂μ
0.
It follows that the relative wage of the South, w S wN , increases as a result of a tightening of IPR protection (a decrease in μ ). Proposition 3 Stronger IPR protection leads to a higher wage in the South relative to the North in the long run. The economic intuition behind this result is as follows. As shown in Proposition 1, tighter IPR, by stimulating the incentive for Northern innovators to standardize, encourages the international transfer of technology from the South to the North. In other words, a strengthening of IPR protection leads to the shift of more production to the South, increasing the demand for labor in the South. As a consequence, the wage, or terms of trade, of the South increases when IPR protection is tightened.
15
We can also derive the short-run response of the relative wage to tighter IPR protection. When t 0, ∂ nˆ N ∂ μ 0 holds (see (34)). Taking account of this we have:
∂ μ 1 nˆ N 02 1 nˆ N 02 0 , when t 0 ∂μ
(36)
which, combined with (35), implies that a strengthening of IPR protection initially decreases the relative wage of the South (i.e. ∂ w N 0wS 0∂ μ 0), but that the relative wage of the South subsequently rises. A summary of Propositions 1–3 is shown in Table 1. These propositions also prove the following theorem: Theorem 1 Under assumptions (A1) and (A2), both standardized and non-standardized technologies take place, α 0 1. A strengthening of IPR protection enhances the international transfer of technology from the North to the South at every point in time (except for t 0), and increases the rate of innovation and the relative wage (terms of trade) of the South in the long run. Our result suggests a role for tightening of IPR protection in the South as a growthenhancing policy, as well as a policy that encourages the transfer of technology. This contrasts with results of most studies (e.g., Grossman and Helpman, 1991; Helpman, 1993; Glass and Saggi, 2001). 23 An important exception is Lai (1998). However, while Lai (1998) shows that if multinationalization is the channel for international production transfer, stronger protection enhances growth and production transfer, we use imitation by the South as the channel for transfer. In our model, the decision-making of Northern innovators on whether to standardize plays an essential role in the result that stronger protection is better for long-run growth, unlike in Lai (1998). We also suggest that the South would benefit from stronger IPR protection. In the model, stronger IPR affects both regions through two channels. First, it increases the long-run rate of innovation and then benefits both regions via its effect on product availability in the long run. Second, since it improves the terms of trade of the South (Proposition 3), the South gains as a result. Stronger protection benefits the South through any channel in the long run. It follows that stronger IPR may benefit the South as well as the North. Does the South in fact gain from stronger IPR? The answer to this question is that it can. To develop this result, we consider two economies that begin in a BGP: nˆ N 0 n£ . One inherits a higher μ and the other a lower μ . Comparing these two economies, we can say that the South benefits from stronger IPR if the Southern welfare in the economy with a lower μ is higher than in the economy with a higher μ . 24
23 Recent studies, such as by Dinopoulos and Segerstrom (2006) and Parello (2005), extend the semiendogenous growth model of Segerstrom (1998). These models do not have a scale-effect property to allow for North–South trade. Their conclusions, in line with Segerstrom (1998), are also different from ours: the long-run rate of innovation depends only on the rate of population growth and the R&D difficulty parameter, and thus a strengthening of IPR protection leads to no change in the long-run innovation rate. 24 We ignore here the short-run impact in welfare evaluation. A proper welfare evaluation requires the impacts on the entire transitional dynamics, not only on the BGP values, as indicated in Helpman (1993).
16
Before we proceed any further, it is useful to rewrite the price index equation (4). Substituting the prices (7), (8), (9) into (4), the price index can be represented by: P n1
1
σ
1 nˆ N pS 1 σ nˆ N pN 1 σ λ 1 σ 1 λ 1 σ α
1 1σ
.
(37)
Together with (21) and (27), this expression implies that the long-run price index is: 1 P£ n 1 σ
£ S 1 σ λˆ μ ρ pN 1 σ 1 n p
1 1σ .
λˆ μ
(38)
While welfare is higher when real spending, E P, is higher, a decrease in the equilibrium fraction of products that have not been imitated benefits every consumer for a given nominal expenditure level. This is because, other things being equal, a decrease in n£ reduces the price index through improved interregional allocation of production and increases real spending. 25 That is, encouragement of technology transfer benefits all consumers. Note that the South spends all of its income on consumption because there are no international flows of financial capital and no investment takes place in the South. In this case, consumer spending per worker in the South equals wS λ 1 pS . It follows from Eqs. (5), (35), and (38), and the fact that ln nt lnn 0 0t gsds, that the BGP instantaneous utility of Southern workers equals ln uS
ln n0 g£t σ 1
1
σ 1
ln 1 n£ ΔS ,
(39)
where ΔS δ S μ 1
δ
S
σ
b1 λ
λˆ μ ρ ρ σ λˆ μ ρ 2σ 1
σ
σ 1 1 σ 1
σ 1L
N
,
S σ 1 σ
b ρ L
2
(40) .
(41)
These expressions imply that a tightening of IPR protection affects the instantaneous welfare of the South through several channels. The first is the product availability (i.e., welfare increases with the number of available products). The effect of product availability is captured by the term ln n 0 g£t σ 1 in (39), through which strengthening IPR protection (a reduction in μ ) positively affects the Southern temporary utility.26 Other channels are captured by the term ln 1 n£ ΔS σ 1, through which real spending positively affects the welfare of the South. The effect of real spending is determined by changes that emerge from the terms of trade and international technology transfer. We have established in Propositions 2 and 3 that stronger IPR enhances the international transfer of production (i.e., ∂ 1 α ∂ μ 0) and improves the terms of trade of the South in the long run (i.e., ∂ w S wN ∂ μ 0). As already mentioned above, the South can benefit from a strengthening of IPR protection, since these forces are all good for the South (product availability, international allocation of production, terms of trade). The following proposition formally states that this is actually the case (see the Appendix for a proof). 25 Note 26 This
that λˆ μ ρ λˆ μ 0 1 holds and that pN is because ∂ g ∂ μ 0 (Proposition 1).
17
pS is necessarily satisfied.
Proposition 4 For economies with weaker IPR protection, a tightening of IPR protection benefits the long-run welfare of the South. Here we impose the restriction that IPR protection is initially weak for simplicity of proof, while we believe that it is possible to show the same result without any such assumptions. Our belief is based on the fact that, even if nothing is added, we still cannot provide numerical examples whereby the South loses from stronger IPR protection. The analysis for the Northern welfare is more difficult, since investment in R&D takes place in the North. Note again that the absence of international flows of financial capital implies that the North finances investment in R&D from domestic savings, or equivalently, the trade account is always balanced: E N α nN pN xN 1 α nN pˆN xˆN (see (11)). Combined with the labor market condition for the North, (19), this expression can be rewritten as E N pN LN bg. Thus, spending per Northern worker is equal to pN 1 bgLN , in which bgL N is the savings (and investment) rate. We then can express the instantaneous utility in the BGP as follows: ln u
N
ln n0 g£t σ 1
bg£ ln 1 N L
λˆ μ ρ ln Δ σ 1 λˆ μ 1
N
,
(42)
where
δ N μ σ 1 σ 1 n£ 2 σ σ , δ N LS λ 1 σ 1bλ σ 1 . ΔN
(43) (44)
The second term in (42) represents the effect of savings on the instantaneous utility: the current utility from consumption is lower when the savings rate is higher. The North may suffer from stronger IPR because the North’s terms of trade decline as a result of IPR strengthening. However, the fact is that it does not: both the North and the South can gain from stronger IPR protection. The following proposition states this formally (proof appears in the Appendix). Proposition 5 For economies that begin and stay in the BGP with weaker IPR protection, a tightening of IPR protection benefits the long-run welfare of the North. Propositions 4 and 5 show that stronger IPR increases the long-run welfare of both the North and the South. As a result of stronger IPR, fewer resources are devoted to production in the North, and thus the long-run rate of innovation increases. Both regions therefore gain via the effect on product availability, but the effect on terms of trade hurts the North. Interestingly, for economies with weak protection, the effect on the product availability dominates: then the long-run welfare of the North increases with a tightening of IPR. Propositions 4 and 5 prove the following theorem. Theorem 2 Under assumptions (A1) and (A2), for economies with weaker IPR protection, all regions gain in the long run from a strengthening of IPR protection in the South. This theorem is quite striking: strengthening of IPR protection improves the welfare of the two regions in the long run whenever IPR protection is not sufficient. Together with Theorem 1, it suggests a role for stronger IPR as a preferred policy for 18
innovation, international technology transfer, and the long-run welfare of both regions: there is no loser from stronger protection in the long run.
3.2 Case without Non-standardized Technologies We now turn to the case of Vˆ V . In this case, the time at which an innovator introduces his/her product into the market is the time at which he/she standardizes the production technology. Then, all Northern monopolists manufacture their products using standardized technology. Taking into account the fact that V˙ˆ V˙ along the BGP, we can rewrite Vˆ V using Eqs. (13), (15), and (16) as: 1 λ σ 1 v£ n£
μ 1 n£ ,
(45)
where we redefine v as v E N σ nVˆ . Under assumption (A2), Vˆ V holds in a neighborhood of the BGP: all monopolists standardize their technologies; α 0. In a neighborhood of the BGP, two differential equations in the case of Vˆ V , (22) and (23), must be changed in the case of Vˆ V as follows. Eq. (16), combined with (6) and (13), implies: v˙ v
v nˆ N
μ 1 nˆ N ρ g ,
(46)
reflecting α 0. This differential equation corresponds to (22). Noting α 0, another differential equation, (23), can be rewritten as: n˙ˆ N nˆ N
g1 nˆ N μ 1 nˆN . nˆN
(47)
In the case of Vˆ V , a dynamic path of v nˆ N , which is the market equilibrium of this economy, satisfies these two differential equations and the labor market condition (20). These equations, together with v˙ n˙ˆ N 0, determine BGP levels of g, nˆ N , and v: g£ μ n£
N μ LN b LN b μ ρ L b , n£ , v£ . σ μ σ 1ρ σ μ σ 1ρ σ μ σ 1ρ (48)
Using these expressions, the condition required for the current case (45) can be expressed by: (A3)
μ μˆ ,
noting the definition of the threshold level of μ , μˆ , presented in the Appendix (D). The economic intuition behind (A3) is as follows. In economies with stronger IPR (lower rates of imitation, μ ), standardized monopolists are sufficiently safe from imitation, so that their expected instantaneous return, λ 1 σ π μ 1 nˆ N , is high enough to dominate that of non-standardized monopolists, π . As a result, for lower μ (i.e., μ μˆ ), all innovators standardize their technology at the same time as they introduce their 19
products. In addition, using these expressions, we can easily show that the BGP is a saddle point in a linearized version of the system, (46) and (47), and hence the BGP is also locally saddle-path-stable in the case of μ μˆ . In addition, we need to impose the following condition to ensure n £ 1: (A4)
LN b
ρ σ 1 μσ .
We assume (A3) and (A4) to focus on the case of Vˆ V until the end of this section. From Eq. (48), we can establish the following proposition: Proposition 6 A tightening of IPR protection decreases the rate of innovation and the rate of technology transfer in the long run. These long-run effects in economies with weak protection (μ μˆ ) are quite opposite to those with strong protection (μ μˆ ); see Propositions 1 and 6. Rather, an economy with μ μˆ is similar to that of Helpman (1993), who shows the same result: stronger IPR hurts the long-run innovation. The logic behind Proposition 6 is as follows. As in Helpman (1993), tighter IPR and the resulting decrease in the rate of imitation depress international technology transfer when imitation is the only channel of transfer in the model. More production remains in the North, and thus the North’s resource scarcity becomes tighter. Finally, fewer resources are devoted to the R&D sector. Economies with lower μ do not have the mechanism whereby stronger IPR enhances the rate of standardization, because the rate of standardization 1 α is constant at unity in such economies. The role of standardization in determining the effects of IPR therefore ceases to exist in economies with stronger IPR protection: economies with stronger IPR protection are similar to Helpman’s (1993) economy. Next, we examine the short-run effects of IPR. In much the same method of proof as for Proposition 2 (see Eqs. (33), (34) and (48), and the Appendix), we can show the following proposition. Proposition 7 A tightening of IPR protection also depresses the international technology transfer in the short run. The short-run effect on the rate of innovation is ambiguous. Propositions 6 and 7 state that the effects of IPR protection, both short-run and longrun, vary across economies with different levels of IPR protection (i.e., economies with μ μˆ and μ μˆ ). From Eqs. (35) and (48), we also determine the response of the relative wage: Proposition 8 Stronger IPR protection leads to a lower wage in the South relative to the North in the long run. Contrary to the case of Vˆ V , the standardization process has little effect on economic performance, so that tighter IPR directly decreases the international transfer of technology from the South to the North in the long run (Proposition 6). It follows that stronger IPR leads to the shift of less production to the South, a decreased demand for Southern labor, and thus a lower wage for the South. In addition, it is easy to
20
Table 2: Effects of a strengthening of IPR protection in the case of Vˆ
V
verify that the short-run response of the relative wage for the South is negative (i.e., ∂ wN 0wS 0∂ μ 0) in this case, as well as in the case of Vˆ V .27 Propositions 6–8 are summarized in Table 2 and prove the following theorem. Theorem 3 Under assumptions (A3) and (A4), all innovators standardize their technologies immediately, and thus α 0. A strengthening of IPR protection depresses the international transfer of technology from the North to the South at every point in time (except for t 0), and decreases the rate of innovation and the relative wage (terms of trade) of the South in the long run. Theorem 3, which contrasts sharply with Theorem 1, implies that an economy with Vˆ V , in which all innovators standardize their own technologies, is very similar to the Helpman (1993) economy. As mentioned above, this is because in such an economy the rate of standardization, 1 α , is fixed to be unity and our model differs from Helpman (1993) essentially in that we allow for standardization of production technologies in the process of international technology transfer. Our remaining interest in this section is in the long-run welfare of both regions. Propositions 6–9 indicate that the South cannot gain from tighter IPR protection in the long run, since this worsens both product availability and the South’s terms of trade. Using α 0 and (37), the instantaneous utility of the South along the BGP (39) remains the same: ln uS
ln n0 g£t σ 1
1 ln 1 n£ ΔS , σ 1
where ΔS and δ S must be modified as follows: ΔS δ S n£ μ 1 n£ 2
σ 1 σ
,
δ σ 1 1 b LS 1 λ σ 1 σ 1 S
(49) σ
.
(50)
A reduction in μ decreases the BGP rate of innovation g £ and the BGP rate of technology transfer 1 n £ . In addition, we can easily show that, as μ is sufficiently small (IPR protection is strong enough), the response of Δ S is also negative; ∂ ΔS ∂ μ 0. Therefore, we have proven the following proposition: 27 See
Eq. (36).
21
Proposition 9 For economies with strong IPR protection, tightening of IPR protection hurts the long-run welfare of the South. This result is different from Proposition 4, which asserts that, for economies with weak IPR protection, a tightening of IPR increases the BGP welfare. This is because in the case of Vˆ V , stronger IPR decreases the international transfer of production and innovation, as in Helpman (1993). We next need to replace Eq. (42), which describes the BGP welfare of the North in the case with non-standardized technologies, with:
ln uN
lnn0 g£t bg£ ln 1 N σ 1 L
1
σ 1
ln 1 n£
pN pS
σ 1
λ 1 σ n£ . (51)
Using Eqs. (35) and (48), we can show that, as μ converges to zero, both g £ and n£ converge to finite values, but p N pS converges to ∞. It follows that for economies with sufficiently small μ , the BGP welfare of the North is downward sloping as a function of μ . Then we have: Proposition 10 For economies with strong IPR protection, a tightening of IPR protection benefits the long-run welfare of the North. While IPR protection negatively affects product availability and positively affects the North’s relative wage, the latter effect dominates when the protection is strong enough. Propositions 9–10 can prove the following theorem: Theorem 4 Under assumptions (A3) and (A4), for economies with stronger IPR protection, the South loses in the long run from a strengthening of IPR protection in the South, but the North gains from this.
4 Results The results presented in the previous section are summarized by four theorems (Theorems 1–4), two tables (Tables 1 and 2), and four assumptions (A1–A4). In this section we briefly review these results. We first should assume that the effective labor force takes an intermediate value: LN b ρ σ 1 ρ σ 1 μσ , which ensures the feasibility and non-negative growth of the BGP (A2 and A4). In the economy there is a threshold level of IPR protection, μˆ (A1 and A3). All innovators standardize their technologies immediately after the introduction of new products when IPR protection is strong enough; μ μˆ . This is because stronger IPR decreases the risk of being imitated for standardized innovators, and thus, for sufficiently strong IPR, standardized monopolists are much safer from imitation (their expected returns are much larger), so that all innovators choose to standardize their technologies. In this case, the rate of standardization is fixed to be unity, 1 α £ 1. Meanwhile, in the case of weaker IPR protection (μ μˆ ), both standardized and non-standardized innovators exist, or the value of an innovator who has already standardized his/her technology is equal to that of an innovator who has not yet standardized: then the rate of standardization is not fixed and is flexible, 0 1 α £ 1. 22
Figure 2: IPR protection, innovation, and standardization in the long run The effects of IPR protection differ in these two cases. In the case of weaker protection (μ μˆ ), a strengthening of IPR protection in the South enhances standardization, the international transfer of technology, and innovation in the long run. As we have already mentioned, stronger IPR makes standardized producers in the North safer from imitation, encouraging standardization. The number of Northern products that can be imitated by the South increases as a result of enhanced standardization, stimulating international technology transfer. More production shifts to the South, which leaves more resources for innovation in the North. Also, the enhanced international transfer of technology leads to an increase in the demand for Southern labor, so that the long-run relative wage of the South increases as a result of a strengthening of IPR protection. We also clarify the effect of stronger IPR on the long-run welfare of both regions. For economies that inherit sufficiently weak IPR protection in the South, strengthening of IPR protection increases the long-run welfare of both regions: if IPR in the South is too weak, everyone can gain from the strengthening of IPR in the long run. In the case of stronger protection (μ μˆ ), the properties of the economy are similar to Helpman’s (1993). A strengthening of IPR in the South depresses the international transfer of technology and innovation in the long run. This result is much more akin to that of Helpman (1993), since the rate of standardization is fixed to be unity, and thus incorporating standardization into the model has little impact on the economy. The intuition is as follows. As in Helpman (1993), stronger IPR simply leaves more production in the North by encouraging imitation, so that this tightens the resource scarcity of the North and fewer resources are devoted to innovation. In addition, enhanced technology transfer implies a decrease in the long-run wage of the South. These effects seem to be negative for the South: in fact, for economies that inherit sufficiently strong IPR protection in the South, strengthening of IPR protection decreases the long-run welfare of the South, whereas the North can gain from this because the effects on product availability (by innovation) and the relative wage are all positive for the North. In summary, the long-run rates of innovation, technology transfer, and standard-
23
Figure 3: BGP welfare of both regions ization have an inverted U-shaped configuration as functions as μ (an inverse measure of IPR protection), as depicted in Figure 2. The long-run welfare of the South may have an inverted-U shape as a function of μ , while the Northern welfare may be a downward-sloping configuration; see also Figure 3. 28
5 Implications and Concluding Remarks An important contribution of this paper is to present a natural extension of the influential product cycle model of Helpman (1993) by allowing for standardization of production techniques, which is one of the main features in Vernon’s (1966) original view and in which the current model differs from Helpman (1993) essentially. 29 We show that many of the economic variables (i.e., innovation, standardization, technology transfer, and wage inequality) have a single-peak configuration as a function of IPR protection in the long run, whereas Helpman (1993) shows that they have downward configurations. The model considered in this paper presents a mechanism whereby tightening of IPR in the South enhances long-run innovation in the North, by focusing on the standardization process. We use this model to show many interesting results, which sharply contrast with those of Helpman (1993). Our results suggest that IPR protection that is too strong or too weak negatively affects the incentive to innovate in the North; rather, a balanced approach is required for innovation. We also suggest, interestingly, that for economies with protection that is too weak in the South, tightening of IPR benefits both the South and the North in the long run. In this case, no one loses from a tightening of IPR in the long run. Contrary to Helpman (1993) and some dynamic product-cycle models (e.g., Glass and 28 We do not clarify the configuration of the BGP welfare of both regions for intermediate values of μ . The dotted lines in Figure 3 are associated with such a range. We calculate a number of numerical examples to clarify the configurations of BGP welfare. A representative example, which appears most frequently in our calculations, is depicted as the dotted line in Figure 3. 29 It can be considered that the current model includes Helpman’s economy as a specific case characterized by stronger protection and a fixed rate of standardization. When the rate of standardization is fixed to be 1 (a fully standardized economy), our economy seems to be almost the same as Helpman’s.
24
Saggi, 2002), our result emphasizes the role of IPR in the South as a growth-enhancing policy, and also indicates that stronger IPR encourages the welfare of both regions in the long run if IPR protection is initially too weak. All the agents in both the South and the North can gain from a tightening of IPR protection if IPR protection is initially weakly enforced. The broader issue of IPR has been at the center of many of the policy debates in recent decades (as reflected, for example, in the establishment of TRIPs agreement), and thus these results on IPR can help to inform current policy discussions on trade relations, innovation, and the development of countries across the world. One important policy implication of this paper is that policies that force stronger IPR enforcement on developing countries (e.g., TRIPs) may improve the welfare of developing countries themselves, and not just developed countries, depending on the circumstances (if IPR is weakly protected in the South). If IPR enforcement hardly takes place in developing countries, governments in such countries should reform their patent systems to strengthen IPR protection for themselves. This also enhances innovation and technology transfer, as well as the welfare of the North, in the case of much weaker initial protection. In this case, strengthening of IPR protection is good for all.
25
Appendix (A) Proof that the BGP is saddle-path-stable We log-linearize the system of (22)–(24) around the BGP, v £ b£ , represented by (27):
z11 z12 ζ ζ˙ , η z21 z22 η˙
(S) where
ζ
ln v ln v£ ,
η
ln nˆ N lnn£ ,
and z11 σ 1v£ 0 , z12 λˆ μ n£ 0 ,
σ v£ 0 , n£ σ v£ LN z22 λˆ μ n£ £ £ . n bn
z21 σ 1v£
Using (27), the determinant of the coefficient matrix Z z i j can be represented by:
Z
LN b
σ λˆ μ ρ .
The feasibility condition (A1) implies that this determinant is negative: Z 0. We can therefore conclude that it has one positive and one negative eigenvalue. This means that the dynamic system is saddle-path-stable, confirming the qualitative conclusion of the phase diagram shown in Figure 1. (B) Comparative statics for the stable saddle path Solving the characteristic equation Z ε I 0, the two eigenvalues are:
ε1
1 1 z11 z22 B 2
2
,
ε2
1 1 z11 z22 B 2
2
,
where B z11 z22 2 4Z 0, noting Z 0. Since Z 0 implies that the two eigenvalues are of opposite sign, ε 1 0 and ε2 0 hold. The general solution of the log-linearized system (S) can be represented as:
ζ t A1 γ11 eε1t A2γ12 eε2t , η t A1 γ21 eε1t A2 γ22 eε2t , where 1 t γ11 γ21 and 2 t γ12 γ22 are the eigenvectors corresponding to ε 1 and ε2 , respectively, and A 1 and A2 are arbitrary constants, which are determined as the solution of the initial value problem. While η is a state variable, η 0 η 0 is given 26
as an initial condition. In addition, the transversality condition works as a boundary condition: η ∞ 0 on the stable saddle path, or equivalently, nˆ N ∞ n£ . Using these two conditions, we have the two arbitrary constants A 1 0, and A2 η0 γ22 , reflecting the fact that ε 1 0 and ε2 0 hold. By normalizing the eigenvector as γ12 γ and γ22 1, we can represent the particular solution as:
ζ t η0 γ eε2t , η t η0 eε2t . We now turn to determination of the eigenvector, γ 1. By definition,
z11 z21
z12 z22
γ 1
ε2
γ 1
.
Then we determine γ as
γ
z12 ε2 z11
ε2 z22 z21
0,
reflecting z11 0, z12 0, and ε2 0. We combine the particular solutions shown above to obtain the following policy function:
ζ η γη , from which we can easily show that, around the BGP, ζ ¼ η γ 0. By definition of ζ and η , we can establish the following result. Result: The stable saddle path is
upward sloping; v ¼ nˆ N γ v£ n£ γ nˆ N γ 1 0. Next, we characterize the impact of a reduction in μ (a strengthening of IPR protection) on the transitional paths of v and nˆ N . Following Helpman (1993), we consider economies that are initially on the BGP: nˆ N 0 n£ and then η0 0. Under this restriction, we can first calculate the first-order response of ζ t η t to changes in μ by differentiating the above particular solutions ζ t and η t with respect to μ : (a) (b)
∂ ζ t γ e ε2 t ∂ n £ , ∂μ n£ ∂ μ ∂ η t e ε2 t ∂ n £ , ∂μ n£ ∂ μ
while ignoring the impact of μ on ε 2 and γ , and taking into account the definition of η0 , η0 ln nˆ N 0 lnn£ . Using the definition of ζ and η , we obtain: (c) (d)
∂ ζ t ∂ vt ∂ μ ∂ v£ ∂ μ £ , ∂μ vt v ∂ η t ∂ nˆ N t ∂ μ ∂ n£ ∂ μ £ . ∂μ nˆ N t n
27
Using the initial condition nˆ N 0 n£ and ∂ v£ ∂ μ imply the following expressions.
∂ vt 1 ∂ v £ γ e ε2 t ∂ n £ vt £ ∂μ v£ ∂ μ n ∂μ N N £ ∂ nˆ t ε2 t nˆ t ∂ n 1 e , ∂μ n£ ∂ μ
ρ σ ∂ n£ ∂ μ , Eqs. (a)–(d)
∂ n£ ρ γ e ε2 t vt ∂ μ σ v£ n£
,
from which we obtain:
∂ v0 ∂ v£ γ v£ ∂ n£ £ , ∂μ ∂μ n ∂μ ∂ nˆN 0 0 , μ reflecting v0 v£ eζ 0 v£ .
(C) ½
Using Eqs. (21) and (27), α £ 1 implies
ρ σ 1λˆ μ ρ λˆ μ ρ σ λˆ ρ
LN b , ρ σ λˆ ρ
which, together with the feasibility condition (A1), implies
λˆ μ ρ λˆ μ
LN b . ρ σ 1
This inequality is always satisfied because the positivity condition (A2) implies that LN bρ σ 1 1, and λˆ μ ρ λˆ μ 1. (D) The threshold value of , ˆ
We restrict ourselves in the model to the case with α £ 0 1. We prove here that there exists a threshold value of μ , μˆ , which satisfies α £ 0 for all μ μˆ . Using Eqs. (21) and (27) and noting conditions (A1) and (A2), α £ 0 can be expressed as a quadratic function of μ : (m)
f μ a1 μ 2 a2 μ a3 0 ,
where a1 λˆ σ ,
a2 λˆ ρ σ 1 ρσ
LN b , 1 λ σ 1
a3 ρ 2 σ 1 .
It is easy to verify that the function f is a convex function and then f ¼ 0 implies a minimum value of f : a 2 2a1 is a unique minimum point of f , which is assured to be positive by the positive growth condition (A2). In addition, the minimum of f
28
is negative; f a2 2a1 0, and f is an increasing function for μ follows that if we define
μˆ
a2 a22 4a1 a31 2 2a1
a 22a1. It
,
then the above inequality (m), or equivalently α £ 0, always holds for all μ that satisfy μ μˆ .
¾ ´¼ ½µ £ We first check n 1 using (27). Clearly, n £ 1 if and only if ρ σ λˆ μ ρ 0, which can be rewritten as μ ρ σ 1 λˆ σ . Next, we turn to the condition for n £ 0. Taking account of μ ρ σ 1 λˆ σ , n£ 0 implies μ LN b ρσ λˆ σ . We (E) Feasibility condition (A1);
can reduce these two conditions to a single expression because ρ σ 1 L N b ρσ . That is, it suffices to impose μ LN b ρσ λˆ σ for n£ 0 1. (F) Positive growth condition (A2); ¼, for any It is straightforward to prove this using (28) and condition (A1).
(G) Irreversible process of innovation and standardization: n˙ n˙ N Since α is constant and g £ n˙ n n˙ N nN holds in the BGP, n˙ α n˙ N implies
g£ α £ n£ g£ , which is always satisfied, noting g £ 0, α £ 1, and n£ 1.
(H) Proof of Proposition 4 It suffices to prove that Δ S in (39) decreases as a result of a reduction in μ , since £ ∂ g ∂ μ and ∂ 1 n£ ∂ μ are negative (Proposition 1). Differentiating Δ S with respect to μ , we obtain:
∂ ΔS ∂μ
δ S σ 1 μ 1 σ 1
2σ 1 ρ σ λˆ μ ρ σ 1 Θ ,
where Θ σ σ 1λˆ μ 2 σ 1 σ 2 ρ λˆ μ ρ 2 σ 1 . It is easy to verify that there exists a threshold value of μ , above which Θ must exceed zero: for sufficiently large values of μ (implying for sufficiently weak protection of IPR), Θ 0. It follows that Δ S decreases with μ for an economy with weak protection of IPR. (I) Proof of Proposition 5 We calculate: Ψ
∂ ∂μ
∞ 0
e ρ t
g£ t bg£ ln 1 N σ 1 L
dt
g£μ 1 bLN ρ ρ σ 1 1 bg£ LN
.
In addition, it is easy to verify from (28) that g £ LN b ρ σ 1σ as μ ∞. ˆ 0 as μ ∞. Moreover, it is straightforward It follows from g £μ 0 that Ψ Ψ to prove that ∂ ∂ μ Δ N λˆ μ ρ λˆ μ 0 as μ ∞. It suffices to prove this proposition. 29
REFERENCES Akiyama, T., Furukawa, Y., 2006. Innovation, Standardization, and Imitation in the Product Cycle Model. Mimeo., Yokohama National University. Antr`as, P., 2005. “Incomplete Contracts and the Product Cycle,” American Economic Review 95 (4), 1054–1073. Arrow, K., 1962. Economic Welfare and the Allocation of Resources for Invention. In: Nelson, R (ed), The Rate and Direction of Inventive Activity, Princeton University Press, Princeton, NJ. Dinopoulos, E., Segerstrom, P., 2006. North–South Trade and Economic Growth. Mimeo., University of Florida, Stockholm School of Economics. Eaton, J., Kortum, S., 1999. International Technology Diffusion: Theory and Measurement. International Economic Review 40, 537–570. Glass, A. J., Saggi, K., 2002. Intellectual Property Rights and Foreign Direct Investment. Journal of International Economics 56, 387–410. Grossman, G., Helpman, E., 1991. Innovation and Growth in the Global Economy. MIT Press, Cambridge, MS (chapter 11, 12). Helpman, E., 1993. Innovation, Imitation, and Intellectual Property Rights. Econometrica 61, 1247–1280. Krugman, P. R., 1979. A Model of Innovation, Technology Transfer, and the World Distribution of Income. Journal of Political Economy 87, 253–266. Kwan, Y. K., Lai, E. L.-C., 2003. Intellectual Property Rights Protection and Endogenous Economic Growth. Journal of Economic Dynamics and Control 27, 853– 873. Lai, E. L.-C., 1998. International Intellectual Property Rights Protection and the Rate of Product Innovation. Journal of Development Economics 55, 133–153. Parello, C. P., 2005. Endogenous Imitation and Intellectual Property. Mimeo., Universit´e Catholique de Louvain. Segerstrom, P., 1998. Endogenous Growth without Scale Effects. American Economic Review 88, 1290–1310. Thoenig, M., Verdier, T., 2005. A Theory of Defensive Skill-Biased Innovation and Globalization. American Economic Review 93, 709–728. Vernon, R., 1966. International Investment and International Trade in the Product Cycle. Quarterly Journal of Economics 80 (2), 190–207.
30
v •
LN b + ρ σ −1
v=0
v∗ LN b
σ
LN b + ρ − λˆμ σ −1
•
nˆ N = 0
n∗
Figure 1. Transitional dynamics
1
nˆ N
The long-run rate of innovation, g ∗
1
The long-run rate of standardization, 1 − α ∗
Fully standardized
μˆ
μ Partially standardized
Figure 2. IPR protection, innovation, and standardization in the long run
BGP welfare of the North
BGP welfare of the South
Fully standardized
μˆ
μ Partially standardized
Figure 3. BGP welfare of both regions
Rate of innovation Rate of production transfer Relative wage of the South
the short run ambiguous increase decrease
the long run increase increase increase
Table 1: Effects of a strengthening of IPR protection in the case of Vˆ
Rate of innovation Rate of production transfer Relative wage of the South
the short run ambiguous decrease decrease
the long run decrease decrease decrease
Table 2: Effects of a strengthening of IPR protection in the case of Vˆ
1
V
V
