1 Journa of Internationa Economics 56 (2002) ocate/ econbase Inteectua property rights and foreign direct investment Amy Joceyn Gass *, Kama aggi a, b a Department of Economics, Texas A&M University, Coege tation, TX 77843, UA b Department of Economics, outhern Methodist University, Daas, TX 75275, UA Received 25 June 1999; received in revised form 5 eptember 2000; accepted 9 January 2001 Abstract This paper deveops a product cyce mode with endogenous innovation, imitation, and foreign direct investment (FDI). We use this mode to determine how stronger inteectua property rights (IPR) protection in the outh affects innovation, imitation and FDI. We find that stronger IPR protection keeps mutinationas safer from imitation, but no more so than Northern firms. Instead, the increased difficuty of imitation generates resource wasting and imitation disincentive effects that reduce both FDI and innovation. The greater resources absorbed in imitation crowd out FDI. Reduced FDI then transmits resource scarcity in the outh back to the North and consequenty contracts innovation Esevier cience B.V. A rights reserved. Keywords: Innovation; Imitation; Inteectua property rights; Foreign direct investment; Product cyces JEL cassification: F21; F43; O31; O34 1. Introduction In recent years, the iterature on product cyce modes has made some important strides. Yet whie Vernon s (1966) origina vision of the product cyce assigns a centra roe to foreign direct investment (FDI), most modes capturing his ideas cast imitation as the ony channe of internationa technoogy transfer from an innovating region (the North) to an imitating region (the outh) see Krugman *Corresponding author. Te.: ; fax: E-mai address: (A.J. Gass) / 02/ $ see front matter 2002 Esevier cience B.V. A rights reserved. PII: (01)
2 388 A.J. Gass, K. aggi / Journa of Internationa Economics 56 (2002) (1979), Grossman and Hepman (1991) and egerstrom et a. (1990). Two recent exceptions are Hepman (1993) and Lai (1998); however, imitation is exogenous in these modes. An important contribution of our paper is to provide a product cyce mode in 1 which innovation, imitation, and FDI are a endogenous. tarting from the quaity adders mode of Grossman and Hepman (1991), we determine the composition of internationa technoogy transfer between imitation and FDI. A common perception is that due to oca knowedge spiovers, outhern firms can more easiy imitate the products of mutinationas producing in the outh reative to firms producing in the North. We formaize this idea by assuming that the costs of imitating a mutinationa s product are ower than costs of imitating a Northern firm s product. By distinguishing between imitation that targets the products of Northern firms and imitation that targets the products of mutinationas, we are abe to determine the effects of parameter changes on the imitation exposure of mutinationas reative to Northern firms. We appy our mode to determine the effects of increased inteectua property rights (IPR) protection in the outh, which we assume increases the cost of imitation due to stricter uniqueness requirements. This increased cost resuts in an endogenous decine in imitation. Whie products ike books, videos and compact disks receive much press about conficts over IPR protection, imitating most products is not so simpe. Empirica evidence indicates that imitation is a costy activity for a wide range of high technoogy goods, such as chemicas, drugs, eectronics and machinery. For exampe, Mansfied et a. (1981) finds that the costs of imitation average 65% of the costs of innovation, and very few products were beow 20%. ince outhern firms must devote substantia effort to backward engineering products prior to producing imitations, IPR protection may affect the effort required by specifying how simiar an imitation can be to the origina. We find that stronger outhern IPR protection makes mutinationas more secure from imitation in absoute terms but no more secure from imitation reative to successfu innovators sti producing in the North. Consequenty, stronger outhern IPR protection does not ater the expected profit stream from becoming a mutinationa reative to remaining a Northern firm and hence does not encourage FDI. The past iterature coud not address reative imitation exposure because imitation was exogenous. An interesting resut of our mode is that FDI decreases with a strengthening of outhern IPR protection. This resut arises because an increase in the cost of imitation crowds out FDI through tighter outhern resource scarcity. Less efficient imitation absorbs more outhern resources despite the reduction in the rate of imitation stemming from the reduced profitabiity of imitation. Additionay, the 1 Here, FDI is endogenousy determined through costy adaptation of technoogies, unike in Gass and aggi (1999) where FDI opportunities arrived exogenousy.
3 A.J. Gass, K. aggi / Journa of Internationa Economics 56 (2002) contraction in FDI tightens Northern resource scarcity. Increased Northern production eaves fewer resources for innovation, so the rate of innovation fas. To highight the forces behind our resuts, we show that an increased cost of imitation has both an imitation disincentive effect simiar to a tax on imitation and a resource wasting effect simiar to a reduction in the outhern abor suppy. These two effects reinforce each other in reducing FDI and innovation. This decomposition demonstrates that even if the resource wasting consequences of stronger IPR protection were not present, the reduced incentive for imitation woud sti generate a reduction in FDI and innovation. 2. Product cyces with endogenous FDI We begin with a description of the mode. Consumers ive in either the North or the outh, and choose from a continuum of products avaiabe at different quaity eves. Due to assumed differences in the technoogica capabiities of the two countries, Northern firms push forward the quaity frontier of existing products through innovation, whie outhern firms pursue the quaity frontier through imitation. The increased utiity from higher quaity eves of products wi be shown to drive innovation, whie cost savings wi drive imitation and FDI. Northern firms, by becoming mutinationas, can shift their production to the outh Consumers The specification of the consumer s probem foows Grossman and Hepman (1991). Consumers choose from a continuum of products j [ [0, 1]. Quaity eve m m of product j provides quaity qmsj d;. By the definition of quaity improve- m ment, new generations are better than the od: qmsd j. qm21sd j. m A products start at time t 5 0 at quaity eve m 5 0, so the base 0 quaity is q0sjd A consumer from country i [ hn, j has additivey separabe intertempora preferences given by ifetime utiity ` 2rt U 5Ee og u (t)dt, (1) i 0 i where r is the common subjective discount factor. Instantaneous utiity is 1 m og u i(t) 5E ogo sd x im( j, t)dj, (2) m 0
4 390 A.J. Gass, K. aggi / Journa of Internationa Economics 56 (2002) where x im( j, t) is consumption by consumers from country i of quaity eve m of product j at time t. Consumers maximize ifetime utiity subject to an intertempora budget constraint. ince preferences are homothetic, aggregate demand is found by maximizing ifetime utiity subject to the aggregate intertempora budget constraint ` ` 2R(t) 2R(t) i i i 0 0 t 0 i Ee E (t)dt # A (0) 1Ee Y (t)dt, (3) where R(t) 5 e r(s) ds is the cumuative interest rate up to time t and A (0) is the aggregate vaue of initia asset hodings by consumers from country i. Individuas hod assets in the form of ownership in firms, but with a diversified portfoio, any capita osses appear as capita gains esewhere so ony initia asset hodings remain. Aggregate abor income of a consumers from country i is Y (t) 5 Lw(t), i i i where w i(t) is the wage in country i at time t and Li is the abor suppy there, so Lw(t) i i is tota abor income in country i at time t. Aggregate expenditure of a consumers in country i is 1 F G E (t) 5E O p ( j, t)x ( j, t) dj, (4) i m im m 0 where p m( j, t) is the price of quaity eve m of product j at time t, and Et is dis aggregate expenditure of consumers in country i, where overa aggregate expenditure is E(t) 5 E N(t) 1 E (t). Due to assumed free trade, price eves do not vary across countries. A consumer s maximization probem can be broken into three stages: the aocation of ifetime weath across time, the aocation of expenditure at each instant across products, and the aocation of expenditure at each instant for each product across avaiabe quaity eves. In the fina stage, consumers aocate expenditure for each product at each instant to the quaity eve m( j, t) offering the m owest quaity-adjusted price, p m( j, t)/. Consumers are indifferent between quaity eve m and quaity eve m 2 1 if the reative price equas the quaity difference p m( j, t)/p m21( j, t) 5. ette indifference in favor of the higher quaity eve so the quaity eve seected is unique. Ony the highest quaity eve avaiabe wi se in equiibrium. In the second stage, consumers then eveny spread expenditure across the unit measure of a products, Eisj, td5 Et, is d as the easticity of substitution between any two products is constant at unity. Consumers demand x im ( j, t) 5 E i(t)/p m ( j, t) units of quaity eve m( j, t) of product j and no units of other quaity eves of that product. In the first stage, consumers eveny spread ifetime expenditure across time, Et5 isd E i, as the utiity function for each consumer is time separabe and the aggregate price eve wi be shown to not vary across time og p m ( j, t) 5 og p m ( j). ince aggregate expenditure is constant across time, the interest rate at each
5 A.J. Gass, K. aggi / Journa of Internationa Economics 56 (2002) point in time refects the discount rate rt sd5 r, sor(t) 5 rt in the intertempora budget constraint Research and deveopment The premium consumers are wiing to pay for quaity gives firms an incentive to improve the quaity of existing products. Our mode shares the properties of endogenous and costy R&D with Grossman and Hepman (1991), but we introduce severa unique features to capture the roe of mutinationa firms. Firsty, we aow Northern firms to adapt technoogies so that they can produce in the outh. econdy, we aow imitation targeting a mutinationa s product to be easier than imitation targeting a Northern firm s product. To produce a quaity eve of a product, a firm must first devote resources to designing it. We mode innovation success as a continuous Poisson process so that innovation resembes a ottery: at each point in time, firms pay a cost for a chance at winning a payoff. Assume undertaking R&D intensity i for a time interva dt requires aidt units of abor at cost waidt and eads to success with probabiity idt (subscripts suppressed). A higher investment in innovation yieds a higher probabiity of success, but no eve of investment in innovation can guarantee success. Ony the current eve of innovation activity determines the chance of innovation success, since innovation is memory-ess for simpicity. The potentia for quaity improvement is unbounded. Assume R&D races occur simutaneousy for a products, with a innovating firms abe to target the quaity eve m 1 1 above the current highest quaity eve m and a imitating firms abe to target the current highest quaity eve m for each product. Finay, assume free entry into R&D, with an endess poo of potentia innovators and imitators. In our mode, the process of adapting techniques for outhern production resembes the process of conducting R&D. The resource requirements are an in innovation, af in adaptation, s1 1 kda in imitation targeting a Northern firm s 2 product, and s1 1 kdga in imitation targeting a mutinationa s product. The corresponding R&D intensities are i, i, i, and i. N F N F Higher eves of k can be viewed as representing a strengthening of IPR protection: outhern firms must spend more resources for a given imitation 3 intensity. tronger IPR protection can reduce imitation efficiency through various channes. Firms may need to add traits to the product that distinguish the imitation 2 ubscripts denote the type of firms (Northern, FDI/mutinationa or outhern) that can produce the highest quaity eve avaiabe of a product if R&D is successfu. 3 We distinguish imitation from copying (or pirating), which is iega dupication of a protected product design.
6 392 A.J. Gass, K. aggi / Journa of Internationa Economics 56 (2002) in the view of ega authorities. Proonged ega battes may be required to prove that a product is sufficienty unique. As IPR protection is strengthened, aspects of the design that woud have been copied may have to be innovated anew. Thus, k can be thought of as measuring how much of the design must be unique to satisfy the standard. In our mode, due to Bertrand behavior in product markets, once a quaity eve of a product has been invented, another Northern firm never invents the same quaity eve. imiary, once a quaity eve has been imitated, another outhern firm never imitates the same quaity eve. For simpicity, we do not aow Northern innovation to target other Northern firms by making the necessary assumptions for such innovation to fai to earn the market rate of return. Innovators can be separated into two groups: eaders and foowers. Leaders are firms who deveoped the most recent quaity improvement; foowers are a other firms. Leaders are ikey to enjoy a cost advantage in designing the next highest quaity eve due to their experience in having successfuy designed the current highest quaity eve, as spiovers are apt to be incompete. Assume the resource requirement in innovation for foowers is sufficienty arge reative to the resource requirement in innovation for eaders so that innovation is undertaken ony by the firm that made the previous innovation for that product. Aso assume the quaity increment is sufficienty arge that Northern eaders do not undertake further innovation unti their most recent innovation has been imitated. Thus, innovation targets products produced by outhern firms whie imitation targets products produced by Northern firms and mutinationas. Our mode distinguishes between imitation that targets mutinationas and imitation that targets Northern firms. We assume that the resource requirement in imitation is ower when targeting mutinationas compared to Northern firms: g, 1. This assumption refects the idea that outhern imitation of brands produced through FDI in the outh may be easier than imitation of brands produced in the North due to arger knowedge spiovers. Moving production in cose proximity to outhern firms trying to imitate a product may ower the cost of imitation, since outhern firms can more easiy earn about the production techniques of mutinationas than those of Northern firms. A outhern firm targeting a mutinationa s product can hire away some of the mutinationa s workers, spy on the mutinationa s production faciities or use simiar means of acquiring information more feasibe with proximity. Aso, mutinationas have aready made adaptations for the outhern economic environment that have the side effect of making successfu imitation easier to accompish for outhern firms. When undertaking R&D, a firm endures costs waidt and gains an expected 4 A ega imitation must be sufficienty distinct from the origina innovation according to an ABC ± ABD C ± D rue, where at east one significant aspect of the production process or design must differ.
7 A.J. Gass, K. aggi / Journa of Internationa Economics 56 (2002) reward vidt (subscripts suppressed). Each firm chooses its intensity of innovation i to maximize its expected gain from R&D ` 2sr 1idt v 2 wa maxee sv 2 wadidt 5max ]] i max sv 2 wadi, (5) r 1 i i$0 i$0 i$0 0 where v denotes the reward to successfu R&D, the vaue of a firm in the appropriate product market where the firm produces if successfu in R&D. The 2it term e captures the probabiity that no other firm wi have succeeded in R&D in the same industry prior to time t, and i is the R&D intensity of other firms (taken as given). Each nonproducing firm chooses its R&D intensity to maximize the difference between the expected reward and the costs of R&D. Firms engage in innovation with nonnegative intensity whenever the expected gains are no ess than their costs. To generate finite rates of innovation, expected gains must not exceed their cost, with equaity when innovation occurs with positive intensity v N# wa N, i N. 0 vn5 wa N (6) and simiary for imitation of Northern firms v N # s1 1 kda, i N. 0 vn 5s1 1 kda (7) and imitation of mutinationas v F # s1 1 kga d, i F. 0 vf 5s1 1 kga d, (8) where we have normaized the outhern wage to one w5 1, so that w 5 wn is the reative wage. Northern firms aso optimay choose how hard to attempt to adapt their production techniques for use in the outh, so by simiar ogic, the cost of adaptation must equa the expected reward when the adaptation intensity is positive vf2 v N# a F, i F. 0 vf2 vn5 a F. (9) When successfu at adapting its technoogy for outhern production, a firm experiences the capita gain vf2 v N$ 0, the difference between the vaue of a mutinationa and the vaue of a Northern firm. The adaptation process required to achieve ower costs through FDI resembes process R&D: expenses are incurred to achieve a ower margina cost of production Production outhern firms are exposed to ony innovation since further imitation is not immediatey possibe, whie Northern firms and mutinationas are exposed to ony imitation since further innovation has been assumed prohibitivey costy. D
8 394 A.J. Gass, K. aggi / Journa of Internationa Economics 56 (2002) A Northern firm successfu in innovating over a product produced by a outhern firm earns the reward pn1 i F(vF2 vn2 a F) pn vn 5]]]]]]] 5 ]], (10) r 1 i r 1 i N where pn is instantaneous profits for a Northern firm and the simpification imposes (9) assuming i F. 0. Once successfu in adaptation, its vaue becomes p F N vf 5 ]], (11) r 1 i F where pf is instantaneous profits for a mutinationa. Meanwhie, a outhern firm successfu in imitating a brand produced by a Northern firm earns the reward p N vn 5 ]], (12) r 1 i N whie a outhern firm successfu in imitating a brand produced by a mutinationa earns the reward p F vf 5 ]], (13) r 1 i N where pn and pf are simiary defined. The effective discount rate is the subjective discount rate r pus the probabiity that the profit stream wi end due to imitation or innovation. Labor is the ony factor of production, and production is assumed to exhibit constant returns to scae. Normaize the unit abor requirement in production to 1 in each country. However, we assume that the unit abor requirement for mutinationas is greater than one ( z. 1), so that mutinationas face higher production costs reative to outhern firms. Mutinationas experience ogistica difficuties when coordinating decisions over arge distances and suffer from their ack of famiiarity with the outhern economic environment. The theory of the mutinationa firm emphasizes that mutinationas need advantages based on superior product design, advertising, or reputation to offset operating cost disadvantages reative to native firms: see Markusen (1995). Once successfu in R&D, each firm chooses its price p to maximize its profits p 5sp 2 cx, d where c is margina cost and x is saes. Under Bertrand competition, the market outcomes depend on the extent of competition from rivas priced out of the market. Each producing firm chooses a imit price that just keeps its riva from earning a positive profit from production (this price equas the second highest margina cost in quaity-adjusted terms). Firms that have just succeeded in innovation have a one-quaity eve ead over the former producer; they choose a price equa to the quaity increment times their riva s margina cost. When competing against a outhern firm, a Northern firm charges price p 5 and N makes saes xn 5 E/ with margina cost cn 5 w, yieding instantaneous profits
9 A.J. Gass, K. aggi / Journa of Internationa Economics 56 (2002) w pn 5 E1 2] D. (14) When competing against a outhern firm, a mutinationa charges price pf 5 and makes saes xf 5 E/ with margina cost cf 5 z, yieding instantaneous profits D z pf 5 E 1 2 ]. (15) For Northern production to be profitabe (p N. 0), the quaity increment must be arge enough to exceed the reative wage in equiibrium (. w), which wi impy. z, as needed for p F. 0. The equiibrium vaue of the reative wage (24) wi be derived shorty. Firms that have just succeeded in imitation have no quaity ead over the former producer; they choose a price equa to their riva s margina cost. When competing against a Northern firm, a outhern firm charges price pn 5 w and makes saes xn 5 E/w with margina cost cn 5 1, yieding instantaneous profits D 1 pn 5 E 1 2 ]. (16) w When competing against a mutinationa, a outhern firm charges price pf 5 z and makes saes xf 5 E/z with margina cost cf 5 1, yieding instantaneous profits 1 pf 5 E1 2 ] D. (17) z outhern production with mutinationa rivas is profitabe (p F. 0) because outhern firms are assumed to have a cost advantage reative to mutinationas (z. 1). We wi show that z. 1 aso impies that the reative wage wi exceed one (w. 1), which ensures that p N Resource constraints Let nn denote the measure of Northern production, nf the measure of mutinationa production, nn the measure of outhern production with Northern rivas, and nf the measure of outhern production with mutinationa rivas (each as a fraction of a production so the measures sum to one). Define the measure of outhern production as n ; nn1 n F. In each country, the fixed suppy of abor is aocated between R&D and production. For equiibrium in each abor market, the demand for abor must equa the suppy of abor in each country. In the North, abor demand for innovation is a i n and for production is n E/ N N N E aninn1 nn] 5 L N. (18)
10 396 A.J. Gass, K. aggi / Journa of Internationa Economics 56 (2002) In the outh, abor demand for imitation is s1 1 kdafinnn1 gifn Fg, for adapta- tion is ifan F N and for production is ne/ F 1 nne/w 1 nfe/z nn nf nf 1 1 k a innn1 gifnf 1 afifnn1] 1] 1] E 5 L. (19) w z s d f g F G The usua steady-state conditions for market measures to remain constant (that fows in equa fows out) ifnn5 ifn F, ifnf5 inn F, innn5 innn and sum to one n1 nf 1 nn5 1 compete the mode teady-state system We focus on steady-state equiibria and begin with the case where a four R&D activities occur so that internationa technoogy transfer occurs through both imitation and FDI. In ection 3 we estabish resuts for this equiibrium and in ection 4 we show that they aso hod for equiibria with ony FDI or ony imitation as the channe of internationa technoogy transfer. If a four R&D activities occur i F. 0, i N. 0, i F. 0, and i N. 0, our mode is a system of six equations. The four vauation conditions are gathered beow from the appropriate profits and vaues of producing firms: innovation vauation condition from (6), (10) and (14) w E1 2] D 5 wansr 1 i Nd (20) adaptation vauation condition from (6), (9), (11) and (15) D z E 1 2] 5saF 1 wandsr 1 i Fd (21) imitation of Northern firms vauation condition from (7), (12) and (16) 1 E1 2] D5s1 1 kdasr 1 i Nd (22) w and imitation of mutinationas vauation condition from (8), (13) and (17) 1 E1 2] D5s1 1 kga d sr 1 i Nd. (23) z The other two equations are the resource constraints (18) and (19). The two imitation vauation conditions (22) and (23) are soved for the reative wage gz w 5 ]]]]. (24) gz 2sz 2 1d The ower cost of imitation targeting mutinationas reative to Northern firms (g, 1) impies production costs are higher for Northern firms than for mutina-
11 A.J. Gass, K. aggi / Journa of Internationa Economics 56 (2002) tionas (w. z ). Aso, wages are higher in the North than the outh (w. 1) since z. 1 by assumption. In the imit as z 1, the reative wage goes to one, w 1. From (24), outhern IPR protection does not affect the reative wage and neither 5 does a tax on imitation or a reduction in outhern resources. Define the cost of adaptation reative to innovation as u ; a F/wa N. Next sove the innovation and adaptation vauation conditions (20) and (21) for the reative effective discount rate D D r 1 if 1 2 z j ;]] 5 ]] ]]. (25) r 1 i 1 1u 2 w N The reative effective discount rate is the degree that mutinationa profits are defated reative to the profits of Northern firms due to differences in exposure to imitation. In the imit as z 1, g 1 and u 1, the reative effective discount rate goes to one, j 1. Our mode conforms to the perception that mutinationas face greater exposure to imitation than Northern firms (Mansfied, 1994; Hepman, 1993) when Northern firms face sufficienty sight adaptation costs w 2 z j. 1 u, u ;]]. (26) 2 w The threshod eve u for j 5 1 stipuates that adaptation reative to innovation costs equas the cost reduction margin from adaptation (w 2 z ) reative to the 6 profit margin from innovation ( 2 w). Whie the greater exposure of mutinationas to imitation does in part refect our assumption that their products are easier to imitate, it is nonetheess a resut (provided u, u ). By encompassing both the Grossman and Hepman (1991) imitation product cyce and the Vernon (1966) FDI product cyce (see Fig. 1), our mode determines the fraction of technoogy transferred to the outh through imitation rather than FDI. To expore the consequences of outhern IPR protection on the rate of innovation and fows of FDI to the outh, we first define these measures of interest and transate the system into these variabes. Let h be the fraction of a product cyces, and hence the fraction of internationa technoogy transfer, that occurs through imitation of Northern firms. Define the rate of innovation as the intensity of innovation times the measure of outhern production i ; inn, which captures the frequency of product cyces. imiary, define the rate of imitation as the sum of imitation targeting Northern firms and mutinationas m ; i n 1 i n. In the steady-state equiibrium, the N N F F rate of innovation must equa the rate of imitation, i 5 m, so that production shifts to the outh at the same rate as production returns to the North. Define the fow of FDI as the adaptation intensity times the measure of Northern 5 This invariance ikey depends on the assumed constant returns to scae in R&D. 6 For z 5 6/5, 5 4, and w 5 3/2, the threshod is u 5 3/255 12%.
12 398 A.J. Gass, K. aggi / Journa of Internationa Economics 56 (2002) Fig. 1. Product cyce composition. production f ; ifn N. Of a the i 5 m fows in the product cyce, m N; innn5hi occur through imitation of Northern firms and f 5s1 2hdi5 ifn F ; mf occur through FDI (and then imitation of mutinationas). In addition to the fow of FDI f, the measure of mutinationa production nf can aso be used as a gauge of the extent of FDI. The soutions for the reative wage (24) and the reative effective discount rate (25) take the pace of the vauation conditions for adaptation (21) and imitation of mutinationas (23), eaving four remaining equations: the Northern resource constraint (18), outhern resource constraint (19), innovation vauation condition (20) and imitation vauation condition (22). Making substitutions for hi N, i F, i N, n F, n, n N, nfj into the four remaining equations achieves a system in the four remaining endogenous variabes: aggregate expenditure E, the measure of Northern production n N, the rate of innovation i, and the fraction of a product cyces that occur through imitation h. The equiibrium can be seen graphicay by soving the innovation and imitation vauation equations for E and nn and then inserting these expressions into the Northern and outhern resource constraints. The two resource constraints then determine the rate of innovation i and the fraction of internationa technoogy transfer that occurs through imitation of Northern firms h as in Fig. 2. The Northern resource constraint LN is downward soping (arger h requires sower i) whie the outhern resource constraint L is upward soping (arger h permits faster i). A arger h dictates that a smaer fraction of products that have not yet been imitated are produced in the outh (through FDI) reative to the North
13 A.J. Gass, K. aggi / Journa of Internationa Economics 56 (2002) Fig. 2. Resource constraint shifts. (n R; n F/nN fas). With more abor demand for production in the North and ess in the outh, Northern resources support a smaer rate of innovation, whie outhern resources support a arger one. The equiibrium vaues of i and h occur at the intersection of LN and L. Introduce a mutipicative term s1 1 td on the right-hand (cost) side of the imitation vauation conditions (22) and (23) to represent a tax on imitation and introduce a mutipicative term s1 2 cd on the right-hand (suppy) side of the outhern resource constraint (19) to represent a reduction in outhern resources. In the next section, we wi reate the effects of changes in k to those of changes in t and c. 3. Inteectua property rights protection We now determine how strengthening IPR protection in the outh, through increasing the costs of imitation, affects the imitation exposure of mutinationas reative to Northern firms, the composition of internationa technoogy transfer, 7 FDI, imitation and innovation. We aso show that the reduced efficiency of imitation due to stronger outhern IPR protection is equivaent to a tax on imitation combined with a reduction in outhern resources. 7 Additiona detais on the derivation of our resuts appear in an Appendix avaiabe on the web at economics.sbs.ohio-state.edu/ pdf/ gass/ iprsup.pdf.
14 400 A.J. Gass, K. aggi / Journa of Internationa Economics 56 (2002) Reative imitation exposure First note that stronger outhern IPR protection increases the profit incentive for Northern firms to undertake FDI in the outh ony if imitation of mutinationas fas reative to imitation of Northern firms as a resut. Our mode is the first to determine the intensities of imitation targeting the products of mutinationas and Northern firms in order to estabish whether stronger outhern IPRs wi increase the reative return to conducting FDI. From (25), it is obvious that the reative effective discount rate is invariant to 8 the strength of outhern IPR protection k. The vaue of a mutinationa reative to a Northern firm refects reative profits defated by the reative effective discount rate vf p F/ sr 1 ifd pr v R ;] 5]]]] 5 ]. (27) v p / sr 1 i d j N N N ince the instantaneous profits of a mutinationa reative to a Northern firm are not affected F G z p E 1 2] F 2 z p R ;] 5]]]] w 5 ]], (28) pn ] 2 w EF1 2 G a strengthening of outhern IPR protection does not affect the reative imitation 9 exposure faced by mutinationas. Proposition 1. The imitation exposure of mutinationas reative to Northern firms is independent of a strengthening of outhern IPR protection, a tax on imitation, or a reduction in outhern resources. Whie mutinationas become safer from imitation with a strengthening of outhern IPR protection, so do Northern firms. The intensity of imitation targeting the products of Northern firms decreases in z 2 1 i z 2 1 i ]] 5]] D] 5 2 ]] D],0, (29) k wj k wj D as i/ k 52i/D, 0 (see Proposition 4). 8 This invariance ikey depends on stronger outhern IPR protection raising the costs of imitation to the same degree when targeting the product of a Northern firm as when targeting the product of a mutinationa. 9 Appying the equiibrium reative effective discount rate (25) to the reative mutinationa to Northern profits (28), the higher profits of mutinationas reative to Northern firms refect the additiona costs of adaptation and any greater exposure to imitation p 5 js1 1u d. 1. R
15 A.J. Gass, K. aggi / Journa of Internationa Economics 56 (2002) Composition of internationa technoogy transfer ince mutipe channes of internationa technoogy transfer are active in this equiibrium of our mode, we can study the effect of a strengthening of IPR protection on the composition of internationa technoogy transfer between imitation and FDI. We find that the fraction of technoogy fowing to the outh through imitation expands with stronger outhern IPR protection h ] 2s1 2h w d ] 5 ]]]].0, (30) k D where the denominator is 1 EnN1 2] DF1 1uj] 2 1DG z w D ; 1 1 ]]]]]]]]].1. (31) ga jhi For future reference, note that, in addition to other factors, the extent that the denominator D exceeds one is reated to the extent that: adaptation costs exist (u. 0), mutinationas are easier to imitate than Northern firms (g, 1), and mutinationas suffer a cost disadvantage reative to outhern firms ( z. 1). Proposition 2. The fraction of internationa technoogy transfer that occurs through imitation of Northern firms increases with a strengthening of outhern IPR protection, a tax on imitation, or a reduction in outhern resources. outhern imitation absorbs more resources when outhern IPRs are strengthened due to imitation becoming more difficut. outhern resource demand in imitation is R L ; s1 1 kda ih1 f gs1 2h dg. (32) Differentiating with respect to k yieds: R L i h ]] f s dg ] s d] k k k 5 ah h 1 g 1 2h i 1 D 1 i 1 2 g J. 0. (33) The second term is ceary positive and represents the shift toward more difficut imitation of Northern firms. The first term is positive: innovation fas by ess than the rate of innovation u i/ ku 52i/D, i because D. 1 in (31) see Proposition 4. Within the first term, the portion invoving i represents each unit of imitation using more resources and the term invoving i/ k represents the reduction in the overa eve of imitation (therefore using fewer resources). With greater outhern resources demanded for imitation, abor demand for production must be shifted from the outh to the North to restore equiibrium. When products cyce through imitation, they generate more abor demand for
16 402 A.J. Gass, K. aggi / Journa of Internationa Economics 56 (2002) production in the North reative to the outh than when products cyce through FDI: n R; n F/nN decines in h. With FDI, production occurs in the outh that woud have occurred in the North in the absence of FDI Foreign direct investment We find that stronger outhern IPR protection discourages FDI. FDI fows are the fraction of a product cyces that occur through imitation times the frequency of product cyces f 5s1 2hdi. ince the rate of innovation i fas (Proposition 4) and a arger fraction of internationa technoogy transfer occurs through imitation h (Proposition 2), the fows of FDI to the outh douby fa F G D f i h i i ] 52]]]] w ] 5]] 52 ] ],0. (34) k ] k w k w D 1 2 s1 2h d The measure of mutinationa production n F, an aternative measure of FDI, aso decreases nf h ] 52hjfs1 2 nfd1 n F( 2 z ) 1 1 g], 0. (35) k k Thus, FDI decines with stronger outhern IPR protection. We further find that the rate of imitation of Northern firms m N; innn5hi actuay increases mn i i ]] 52] 21D] 5] 21 D]. 0. (36) k w k w D Whie product cyces occur more sowy due to the sower rate of innovation, more 10 of them occur through imitation, and this positive effect dominates. Proposition 3. FDI fows to the outh decrease whie fows of production to the outh through imitation of Northern firms increase with a strengthening of outhern IPR protection, a tax on imitation, or a reduction in outhern resources Innovation and imitation We find that stronger outhern IPR protection discourages innovation in our mode. tronger outhern IPR protection shifts internationa technoogy transfer toward imitation of Northern firms, which shifts abor demand for production from the outh to the North. Resource scarcity in the outh is transmitted back to the North and impinges on innovation 10 Whie imitation substitutes for FDI in transferring technoogy to the outh, the substitution is incompete as the tota fows of technoogy to the outh m 1 f 5 i fa (Proposition 4). N
17 A.J. Gass, K. aggi / Journa of Internationa Economics 56 (2002) i i h i ] 52 ]]]] ] 52 ],0. (37) k k D ] 2s1 2h w d Proposition 4. The rates of innovation and imitation decrease with a strengthening of outhern IPR protection, a tax on imitation, or a reduction in outhern resources. The positive effect on the fraction of product cyces that occur through imitation h and negative effect on the rate of innovation i can be seen graphicay in Fig. 2. tronger IPR protection in the outh (increase in k) shifts the outhern resource constraint down to Lk (smaer i for a given h) due to the arger resource requirements in imitation. The Northern resource constraint is unaffected. Thus the equiibrium shifts down aong the downward-soping Northern resource constraint to arger h and smaer i. Whie the increased cost of imitation does reduce incentives for imitation, the tota resources devoted to imitation increase, increasing resource scarcity in the outh. The parameters used to construct Fig. 2 are Northern abor suppy L 5 3, N outhern abor suppy L5 6, resource requirement in innovation an5 3, resource requirement in imitation a 5 2, resource requirement in imitation of mutination- as reative to Northern firms g 5 1/25 50%, resource requirement in adaptation reative to imitation u 5 1/ %, cost disadvantage of mutinationas reative to outhern firms z 5 6/ 5, subjective discount rate r 5 1/ 20, and quaity increment 5 4. The initia equiibrium is for k 5 0, c 5 0 and t 5 0. In the 11 subsequent equiibrium outhern IPRs are strengthened to k951/ 5 in Lk. Tabe 1 shows how the equiibrium vaues are affected: for a cases in Tabe 1, mutinationas are exposed to sighty more imitation than are Northern firms j These cacuations confirm that there is indeed an equiibrium with a four types of R&D active, and that k can be shifted without disturbing the type of equiibrium, provided that the shift is not too arge. For these parameters, we can increase k to ] k 5 143/ or decrease k to ] k 5297/ Tabe 1 Both FDI and imitation product cyces k i h E w nn n nf f % % 33.8% 66.2% % % 40.1% 48.1% % % 45.6% 32.3% % % 50.2% 19.2% % % 54.0% 8.2% % % 57.0% 0% 0 11 The other shifts depicted are c951/5 for Ls and t951/5 for Lt.
18 404 A.J. Gass, K. aggi / Journa of Internationa Economics 56 (2002) and sti achieve an interior soution. Further numerica exampes iustrating the equiibria for other vaues of k are provided in ection Decomposition Fig. 2 aso iustrates that when k, t or c (depicted by Lk, Lt and Ls) are increased to the same degree, the effects of k are in the same direction but between the smaer effects of a tax on imitation t h/ t f/ t m N / t i/ t h 1 2h ]] 5]] 5]]] 5]] 5] 1 ]],1 (38) h/ k f/ k m / k i/ k w z N and the arger effects of a reduction in outhern resources c in magnitude h/ c f/ c m N/ c i/ c L 1 ]] 5]] 5]]] 5]] 5]] 1 2 ].1. (39) h/ k f/ k m / k i/ k ia g z N The effect of c is a proportionate reduction in the entire outhern abor suppy, whie k invoves an expansion in abor demand of ony the abor engaged in imitation. An increase in k combines resource wasting and imitation disincentive effects, which reinforce each other in owering i and raising h. A reduction in outhern resources (an increase in c) captures the resource wasting effect. When outhern resources contract, more product cyces must occur through imitation of Northern firms. A higher fraction of product cyces occurring through imitation h reduces abor demand in outhern production by keeping more production back in the North (n F/nN fas) and shifting outhern production toward higher priced products with ower saes (n F /nn fas). Aso, a ower rate of innovation i reduces abor demand in R&D in both countries to restore equiibrium. Thus, the composition of internationa technoogy transfer h adjusts the distribution of abor demand across countries, whie the speed of the product cyces i adjusts the overa eve of abor demand. A tax on imitation (an increase in t) captures the imitation disincentive effect. The reduction in the rate of innovation heps both conserve outhern resources in imitation and restore the equaity between the expected benefits of imitation and the greater costs of imitation. When the rate of innovation fas, a successfu imitation earns a onger expected duration of profits due to the reduced probabiity of innovation terminating the profit stream. The increase in the reward to imitation needed to offset its increased cost due to the tax is aso accompished through an increase in aggregate spending, which increases profits. However, the increase in aggregate spending increases abor demand primariy in the outh due to more ower priced production occurring there, impying arger saes. The extent that the D Imitation costs at the upper bound are s1 1k d/11k s d5 256% of imitation costs at the ower ] bound. 12 ]
19 A.J. Gass, K. aggi / Journa of Internationa Economics 56 (2002) increase in abor demand occurs disproportionatey in the outh must be offset by increasing the importance of imitation of Northern firms in the product cyce, as h serves the function of reaocating abor demand across the two countries. 4. Other equiibria Now we turn to considering equiibria for parameters such that one form of imitation or the other does not occur in equiibrium. As a resut, in these equiibria, ony one of the two types of product cyces occurs, either FDI or imitation. We find, however, that our resuts do not depend on the type of equiibrium that emerges Imitation cyce ony Here we consider the equiibrium of the mode in which ony innovation and imitation of Northern firms occur (with no FDI and no imitation of mutinationas). The Northern abor constraint is E ani 1 nn] 5 L N. (40) The outhern abor constraint is s1 1 kdaiw 1s1 2 nnde5 Lw. (41) The vauation condition for innovation is w EnN1 2] D 5 wansrnn1 i d. (42) The vauation condition for imitation targeting a Northern firm s product is Es1 2 n dsw2 1d5s1 1 kda frs1 2 n d1 i g, (43) N N where i 5 inn5 inn5 m is the rate of innovation, which equas the rate of imitation and nn 5 n for notationa ease. The system determines he, w, i, n Nj. The vauation condition for adaptation (21) must be an inequaity, with rewards 13 ess than costs. Using comparative statics techniques, we find that an increase in outhern IPR protection decreases the rate of innovation i i ] 52 ]]]],0, (44) k 2 w 1 1]]] ww2 s 1d 13 The mode here is essentiay the same as Gass (1997) but with ony one quaity eve of each product seing in equiibrium.
20 406 A.J. Gass, K. aggi / Journa of Internationa Economics 56 (2002) decreases the reative wage D w 2 w i ] 5 ]] ],0, (45) k i k increases the measure of Northern production D nn 2 w i ] 52nNs1 2 n Nd]] ]. 0, (46) k wi k and increases aggregate expenditure. In this equiibrium, any force that reduces the rate of imitation aso reduces the rate of innovation, since the two rates are equa. These resuts mirror those of Grossman and Hepman s (1991) inefficient Northern foowers equiibrium, if the effect of decreasing the outhern abor suppy is combined with taxing imitation in the spirit of our decomposition resut. imiary, Hepman (1993) and Lai (1998) find that a reduction in the intensity of imitation 14 eads to a sower rate of innovation. Tabe 2 shows equiibria with ony the imitation product cyce that arise for arge vaues of k.k. ] For k 5k, ] the reward to adaptation exceeds its costs according to the vauation condition (21), so ower eves of k #k] do not support an equiibrium with ony the imitation product cyce the FDI cyce aso 15 emerges FDI cyce ony Now we consider the equiibrium of the mode in which ony innovation, FDI, and imitation of mutinationas occur (with no imitation of Northern firms). The Northern abor constraint is E ani 1s1 2 nf2 nd] 5 L N. (47) Tabe 2 Ony imitation product cyce k i h E w nn n nf f % % 57.0% 0% % % 54.6% 0% % % 52.6% 0% % % 51.7% 0% 0 14 In simiar spirit, Tayor (1994) shows that faiure to protect foreign patents reduces R&D by causing innovators to use inferior technoogies. Aoki and Prusa (1993) find that discriminatory protection based on where a firm is ocated may decrease R&D. 15 Rewards exceed costs by 144 for these parameters (at k 5k ] ).