Endogenous IPR and Economic Growth

Transcription

1 Endogenous IPR and Economic Growth Andreas Schäfer University of Leipzig Maik T. Schneider ETH Zurich Preliminary version 8. May 2008 Abstract Why are intellectual property rights in some countries higher than in others and what does this imply for economic growth? This paper takes a fresh look at this question by developing a growth model with international trade in which governments endogenously determine the country s level of IPR-protection. We study the countries incentives for international IPRprotection and relate the results to empirical observations and the recent debate on the international harmonization of IPR-protection such as via TRIPS within the World Trade Organization. JEL Code: F10, F13, O10, O30 Keywords: Trade, Endogenous Growth, Intellectual Property Rights, Differential Game Correspondence: Institute of Theoretical Economics / Macroeconomics Marschnerstr. 31, D Leipzig. schaefer@wifa.uni-leipzig.de. Center of Economic Research at ETH, Zurich ZUE D , Zurich - Switzerland. E- mail:schneider@mip.mtec.ethz.ch.

2 1 Introduction Why are intellectual property rights in some countries higher than in others and what does this imply for economic growth? The most part of the literature sought to answer this question by assuming IPR-protection as exogenous and putting forth a comparative statics argument. In this paper, we take a fresh look at the question by developing a growth model with international trade in which governments endogenously determine the country s level of IPR-protection. In autarky, each country faces the well known trade off between static welfare losses due to monopoly power of intermediate producers and the dynamic gains from new innovations. When opening up the economy, this trade off becomes richer as now additional profits can be made by exporting new technologies via foreign direct investment to the foreign country. This gives incentives to increase the domestic level of property rights protection. On the other hand, the economy receives new technologies from outside and hence the need to innovate oneself decreases. As intellectual property rights protection of foreign technologies additionally increases the deadweight loss, this effect tends to decrease the level of IPR s granted. In the model, the countries differ in their technological level, and population size. Accordingly, which of the described effects prevails depends on the countries characteristics relative to each other. We find that identical economies lower their level of IPR s compared to the autarky scenario. If the countries differ in their market sizes that is their populations, the bigger economy will increase its IPR protection and the smaller economy will lower it. Furthermore, if both countries differ not only in their population sizes as just describes but also in their levels of technology in the sense that the bigger economy is also technologically inferior compared to the smaller economy, the effect reverses. The smaller economy will increase its IPR protection and the bigger economy will lower it compared to the symmetric freetrade scenario. By far we are not the first to examine the question of optimal intellectual property protection. However, there are only few papers that consider endogenous IPR-protection. Eicher (2008) examines private investments to enforce intellectual property rights protection in a closed economy taking formal institutions such as the existence of a patent office as given. In contrast, we focus on a country s government to provide intellectual property right enforcement. Although we do not neglect that private investments might be necessary for effective IPR-enforcement, we argue that the central institution-builder is the national authority. In a sense, our approach is complementary to that of Eicher (2008) in that the state s provision of IPR-protection shapes the productivity of private investment to enforce protection. The paper closest to ours is Grossman and Lai (2004). They also examine a policy game of two open economies with respect to the protection of intellectual 2

3 property. However, their model does not allow for positive long run growth. Although we incorporate some of the assumptions of Grossman and Lai (2004) into our model, our aim was (i) to recast the question in a Romer-type growth model with two open economies and (ii) to avoid some of their assumptions that we found not very realistic, such as an exogenous market size independent of the population size and their income. As we show our framework provides different results such as market size in combination with the relative state of technology determines the IPR policy which seem to better reflect the empirical evidence as in Ginarte and Park (1997). The paper is structured as follows. In section 2 we introduce the general modelframework. We shortly illustrate the classical trade-off in a closed economy before moving to the main focus of our paper, which is the analysis of the incentives to protect intellectual property in open economies. Section 3 concludes. 2 The Model Our analysis builds on a variety expanding growth framework of the Romer (1990)- type. We deviate from the standard assumptions in two points. One is that we assume increasing marginal costs of innovation and the other that we proxy a country s human capital by its technology stock. Additionally, we take the assumption of linear instantaneous utility from Grossman and Lai (2004), as well as the assumption that in each period the government can choose a level of intellectual property rights enforcement ω(t). That is, with probability ω the patent is enforced, whereas with probability 1 ω it is not. Different from Grossman and Lai (2004), however, we assume infinite patent length. The next subsections describe the model in more detail. 2.1 The closed economy Final goods production The final good Y is produced by using Labor L and a range of intermediates supplied either on fully competitive markets or under monopolistic competition Y = AL 1 α [ Nm 0 Nc ] x α m + x α c. (1) 0 3

4 2.1.2 Intermediate production Each intermediate good i [0,N j (t)] is produced by a monopolist or an imitator using final output Y. Final output Y is chosen as the numeraire, such that p Y =1 implying constant marginal production costs of machines equal to unity. Therefore the price p m (i) for one intermediate i offered under monopolistic competition in a symmetric equilibrium is given by p m (i) = 1 α (2) whereas the competitive price of an imitated product is given by p c (i) =1. (3) Hence, if the government fails to protect intellectual property there are zero profits in the market for intermediate i. 1 As monopoly pricing implies on the other hand that p(i) = 1 α, demand for this type of machine reads x j,m (i) =LA α α 1 α. (4) Consequently under full patent protection, the monopoly profit flow accrues to ( ) 1 α π j,m (i) = α α A 1 α L. (5) α If an intermediate is copied and, hence, sold at the competitive price p c (i) =1, demand increases up to x j,c (i) =LA α α 1 α, (6) and profits are zero. Taking patent enforcement into account, we can write N m (t) =ω(t) N(t) and N c (t) =[1 ω(t)] N(t). A symmetric equilibrium on the market for intermediates implies that p c (i) =p c =1, p m (i) =p m =1/α, x(i) c = x c, and x(i) m = x m i, and consequently yields [ Y (t) =A 1 2α 1 α α 1 α LN(t) ω(t)+[1 ω(t)](α 1 This is a normalization in order to make the model tractable. ] α 1 α 1). (7) 4

5 2.1.3 Research and Development We use the lab-equipment approach to model the research sector. Each agent in the economy can invest in research equipment to invent new ideas that are licensed out to the intermediate producers. In contrast to the standard literature, we assume that lab-equipment faces decreasing returns within a period. That is, an additional investment in research yields less new ideas. In particular, we assume the following cost function: ζ(η(t)) = δη(t) 2 L (8) N where δ is an exogenously given productivity parameter and N L is supposed to reflect the economy s average level of human capital. This implies that the labequipment can be more productively used the lower δ and the higher the average level of human capital. The assumption of decreasing returns in research investment can be justified in several ways. First, when thinking of each agent running its own research lab, it seems very natural to think of investment to have decreasing returns as further equipment may not be used as efficiently. Second, looking at it from an aggregate perspective, it may also reflect heterogeneity in the cost of research projects. A similar argument can be found in e.g. Scotchmer (2004) (ch. 11). Third, one could also interpret the aggregate cost function in the sense that agents are heterogeneous with respect to research ability. Hence the most able invest first producing a high number of ideas whereas the less talented cannot use the lab-equipment as productively, leading to an increasing cost function in the aggregate. Each new idea receives a patent of infinite length that is enforced with probability ω(t). Accordingly, the expected value of an invention is E[V i ](t) = t π(i)ω(t )exp[ t 0 r(t )dt ]dt. (9) Optimality requires that each agent s marginal costs for another invention must equal its expected value. Consequently, each agent invents η(t) =E[V i ](t) N (10) 2δL new ideas Households and the Government s Problem The representative household wishes to maximize overall utility, U, where as already mentioned above instantaneous utility is assumed to be linear. The objective function of the representative households therefore reads as 5

6 U = 0 c(t)exp[ ρt]dt. (11) Each household inelastically supplies one unit of labor to final good production and decides how much to spend for R&D. The budget constraint and the law of motion of the technology stock can be written as c(t) = y(t) x(t) ζ(η(t)), (12) Ṅ = E[V i ](t) N 2δ. (13) Lower case letters indicate per capita variables. As due to the linear instantaneous utility function we must have that r = ρ, the household s problem is already solved by the decision on R&D-investment for a given path of IPR-enforcement {ω(t)} t R+. This path is decided on by a benevolent government that strives to maximize the representative agents utility. Accordingly, the government solves max U = {ω(t)} t R+ 0 c(t)exp[ ρt]dt. (14) s.t. c(t) = y(t) x(t) ζ(e[v i ](t) N ), 2δL (15) N = E[V i ](t) N 2δ. (16) The necessary conditions ( H c H =0and N = λ) imply Using (9) and (17), we yield λ(t) = e ρt 2δ c(t) ( ) E[Vi ](t) 1 ω(t) ω(t) (17) λ(t) = e ρt c(t)+λ(t) E[V i](t). 2δ (18) λ(t) =e ρt [ ω(t)π rl ] 2δr π A 1 1 α (αm α c ), (19) 6

7 where α c = α α 1 α α 1 1 α and αm = α 2α 1 α α 2 1 α. Taking a closer look at (19), we observe that the shadow price at t equals the discounted difference between the present value of profits stemming from innovations which is increasing in the enforcement of intellectual property rights, ω, and the dead weight loss stemming from the monopoly distortion. In light of (18), r = ρ, differentiation of (19) with respect to time, and appropriate substitutions, we yield with χ = δr 2 π A 1 1 α L2r 2 δ[α m α c + παc 2r 2 δ ]. ω aut = 2r[δrπ ± πδχ] π 2, (20) 2.2 Open Economy We now examine how incentives for IPR-protection change in an open economy. In our model, open means that intermediate firms are allowed to invest in the foreign country in production facilities where they produce the intermediate good they hold a patent on and sell the products to the foreign country s final good sector. Our analysis considers a setting with two economies (j and k) which potentially differ with respect to their population size L, their labor productivity A and their technological level N. In principle, c.p. two things change relative to the closed economy: The incentive to invest in R&D increases as patents yield additional profits and final good production becomes more productive as this sector can produce with a greater variety of intermediate goods. To be more precise, the first effect is reflected by a higher expected value of inventions: t E[V j i ](t) = [π j (i)ω j (t )+π k (i)ω k (t )] exp[ r(t )dt ]dt. (21) t 0 Given the R&D-cost function ζ j (η j (t)) = δη j (t) 2 L j, (22) N j the total number of inventions in country j at time t is L j η j (t) =E[V j i ](t)n j 2δ. (23) 7

8 (a)(b) (c) Figure 1: Effect of variations in: (a) factor productivity A, (b) population L, and (c) on R&D-costs δ, on the endogenous protection of IPRs in the closed economy. Note that we have not assumed international knowledge spillovers from FDI. That is, a country s average level of human capital depends on the number of technologies that have been invented in that country. How great spillovers from FDI 8

9 are is still an open issue. For simplicity, we neglected them in this basic setting and explore the implications of full spillovers at the end of the paper. The second effect is simply that the number of new varieties in final good production increases: Y j (t) =A 1 1 α j ] α 2α 1 α Lj [N j (t)+n k (t)] [ω j (t)+[1 ω j (t)](α α 1 α 1). (24) These observations reveal that the incentives for R&D and the deadweight losses due to IPR-protection also depend on the other economy s IPR-policy. Hence, the two governments play a dynamic policy game, which we will now analyze The Government s Problem in the Open Economy We assume that both governments can fully commit to future IPR-protection. In this way, we are looking for open-loop Nash-equilibria of the policy game. Both players take the path of IPR-protection in the other country as given and maximize their representative agents utility. max U j = {ω j (t)} t R+ 0 c j (t)exp[ ρt]dt. (25) s.t. c j (t) = N j N k y j (t) x j (t)+π k π j ζ(e[v j i L j L j ),(26) j 2δL j N j = E[V j i ](t)n j 2δ, (27) N k = E[Vi k ](t) N k 2δ. (28) Let s define the relative state of country j s technology as n = N j N i. Consequently, country i s Hamiltonian reads as H i = N i {e ρt 1 α [(1 + n)ai (α c + ω i (α m α c )) n π j ω i π i + ω j E2 ]+λ E } L i L i 4δL i 2δ and of country j accordingly, 1 9

10 { H j = N j e ρt [( 1 1 n +1)A 1 α j (α c + ω j (α m α c )) + ω iπ i L j ω jπ j nl j E2 4δL j ]+λ E 2δ } Optimizing the Hamiltonians i, j leads us to the following set of equations which defines implicitly the reaction functions - that is (ω i,ω j) and (ω j,ω i) - for optimal IPRs in country i and j given the decision of the respective trading partner with 2r2 δχ i π i = (1+n)L i ψ i π i ω i n + ω j π j 1 4δL i (E) 2 nψ i + ω iπ i n χ i E r (29) L i π i 2r2 δχ j = ( 1 π j n +1)L jψ j + π i ω i ω jπ j n 1 (E) 2 4δL j ψ j n + ω jπ j nl j χ j E r π j, (30) 1 1 α χ i (1 + n)ai L i (α m α c ) π i n 1 E π i 2δL i r χ j ( 1 1 n +1)A 1 α j L j (α m α c ) π j n 1 E π j 2δL j r and 1 1 α ψ k Ak (α c + ω k (α m α c )) k = i, j. Obviously, the Nash-equilibrium (ωi,ω j ) is given by the solution to (29) and (30). What are the effects of trade on the optimal choice of IPRs? We first consider two identical economies. Both economies face the same trade-off between dynamic gains and monopolistic distortions as the closed economy. In addition, however, trade opening induces a market size effect such that 10

11 aut open Figure 2: Effect of trade opening on IPRs for two identical economies. profits of technology owners increase which makes innovations more profitable. On the other hand, each economy can copy foreign products and lower the dead weight loss stemming from the monopoly distortion. At the end, each generates a positive externality to foreign technology owners and increases the home country s 11

12 Figure 3: Effect of trade opening on IPRs for two countries with different market sizes: L j >L i. dead-weight loss by increasing the enforcement of IPRs. Hence, both countries face an incentive to free-ride on each other s IPR protection. This effect together with the market size effect induces both countries to lower their IPRs compared 12

13 Figure 4: Effect of trade opening on IPRs for two countries with different market sizes and different states of technology: L j >L i and n<1. to the closed economy case (see Figure 2). More interesting, however, is the case when both countries differ in their market sizes and/or their relative states of technology. The former is represented by L in our model and the latter by n. If the the 13

14 foreign country j is technologically inferior, we set n < 1. In Figure 2 we illustrate the effect of different market sizes, in the sense that the population of country i is smaller than country j s. Obviously, country i gains through trade opening a larger market than country j. Given an identical state of technology in both countries (n =1), profits for technology owners increase by more than the dead-weight loss in country i, and vice versa in country j. This effect, induces country i to lower its IPRs compared to the symmetric case (see Figure 1), where the opposite is true for country j. But happens now if country j is larger in terms of market size but also technologically more backward (n <1) compared to country i? This case is illustrated in Figure 3. Apparently, the just described effect reverses. Now the smaller but technologically leading country i increases its IPR enforcement compared to both country j and the symmetric case. Obviously, the relative backwardness of country j makes it for country j s government more profitable to lower the dead weight loss as its gains through the market effect are smaller. 3 Conclusions In this paper we show, the interaction of IPR-policies in an open economy. To this end we employ a growth model of the Romer-type enriched by the endogenous protection of IPR s. In a relatively simple open loop game, both governments choose optimal IPR strategies in response to the optimal strategy of their trading partner. Our main results can be summarized as follows: Free trade lowers the level of IPR s. In an open economy, the smaller economy represented by its population size sets a lower level of IPR protection. This effect reverses, however, if the bigger economy is technologically more backward compared to its smaller trading partner. References Eicher, T. and C. Garcia-Penalosa (2008), Endogenous Strength of Intellectual Property Rights: Implications for Economic Development and Growth, European Economic Review, Vol. 52, No. 2, Grossman, G.M. and E.C. Lai (2004), International Protection of Intellectual Property, American Economic Review, Vol. 94, No. 5, Ginarte, J.C. and W.G. Park (1997), Determinants of Patent Rights: A crossnational study, research Policy, Vol. 26,

15 Romer, P.M. (1990), Endogenous Technological Change, Journal of Political Economy, Vol. 98, Scotchmer, S. (2004), Innovation and Incentives, MIT Press, Cambridge MA. 15