Knowledge licensing in a Model of R&D-driven Endogenous Growth

Transcription

1 Knowledge licensing in a Model of R&D-driven Endogenous Growth Vahagn Jerbashian Universitat de Barcelona June 2016

2 Early growth theory One of the seminal papers, Solow (1957) discusses how physical capital accumulation can affect short- and long-run welfare Solow uses neoclassical framework/production function Y = F (K, AL) where A stands for labor augmenting technology F is homogeneous of degree 1 in capital K and labor L

3 Microeconomics: Homogeneity of degree 1 Homogeneity of degree 1 in K and L is motivated by standard replication argument given that K and L are rival inputs Rival goods: whose use by one prevents the use by other Replication argument: in order to double output firm needs to hire twice more K and L Homogeneity of degree 1 supports competitive equilibrium; in equilibrium firms hire K and L and make zero profits Euler thoerem: Y = F K K + F L L

4 Implication of homogeneity of degree 1 That F is homogenous of degree 1 in K and L implies that the accumulation of K bears decreasing returns Ceteris paribus, as capital K increases the returns to its accumulation decline to zero In long-run as long as A is fixed output per capita y = Y L constant is This is not in line with the observation that many developed countries grow at relatively constant rates (Kaldor stylized facts) In order to encompass this A needs to grow

5 Can A grow endogenously a neoclassical model? In neoclassical framework F is homogenous of degree 1 in K and L This implies that All revenues are spent compensating K and L and A cannot be compensated Therefore, A cannot be accumulated endogenously (by firms/market mechanisms) Solow (1957) assumes therefore that A grows exogenously He acknowledges that this is a significant shortcoming since changes in A involve trade-offs e.g., time and physical resources allocated to research

6 Early endogenous growth theory - Romer (1986) In a seminal paper, Romer (1986) endogenizes the accumulation of A assuming that the latter is proportional to the stock of physical capital (per capita) Romer (1986) assumes that in equilibrium A = K L Microeconomics: there are learning-by-doing externalities; labor learns and becomes more productive interacting with capital

7 Early endogenous growth theory - Lucas (1988) Lucas (1988) interprets AL as human capital H endogenizes the accumulation of A assuming that the household does it through schooling household allocates part of human capital to production (u Y H) and part to schooling (u H H) Y = F (K, u Y H) H = λu H H u Y + u H 1

8 Issues in Romer (1986) and Lucas (1988) In Romer (1986) changes in A are still exogenous/not driven by (rational) decisions of agents In Lucas (1988) it is hard to motivate the linear structure of schooling function human capital is a rival input; constant returns to it might not be justified

9 Romer (1990) In Romer (1990) private firms intentional investments in R&D are the driver of long-run growth and welfare R&D generates knowledge that can be used for subsequent innovations Knowledge is not rival and is partly non-excludable Non-excludable: there are knowledge spillovers and R&D builds on a pool of knowledge Excludable: firms can use it in order to secure (at least temporary) monopoly position in product market

10 Micreconomics/structure - Romer (1990) Final goods sector Intermediate/capital goods sector A Y = (u Y L) 1 σ x σ (i)di intermediate goods (x) producers are price setters production of 1 unit of an intermediate good requires 1 unit of final goods 0

11 Micreconomics/structure - Romer (1990) R&D sector researchers produce blueprints of intermediate goods research builds on previous knowledge (which is non-rival good! here it is also non-excludable in R&D) A = λa(u A L)

12 Micreconomics/structure - Romer (1990) There is free entry into intermediate goods industry in order to enter the industry an entrepreneur needs to buy a blueprint it borrows the resources for that investment from household at the market interest rate r

13 Motivation - Non-rivalry and partly excludability Rivalry of a good is purely technological attribute Knowledge as non-rival good because its use by a firm or a person does not preclude its use by another Excludability, however, depends also on the legal framework and detection mechanisms

14 Motivation - Interpretation of the assumption Partly non-excludability: patenting and patent enforcement frameworks and mechanisms for detection of patent infringements are imperfect They are weak since firms or researchers can avoid citing or paying license fees for current patents while generating new patents They are strong to the extent that firms can maintain exclusive rights on their type of good that is part of the patents

15 Motivation - Patenting in high-tech industries In high-tech industries (e.g., ISIC 32) patenting and patent enforcement frameworks and mechanisms for detection of patent infringements seem to be not so imperfect In these industries citing, licensing, and establishing consortiums for exchanging patents is common and has played and currently plays significant role for innovation Grindley & Teece (1997), Hagedoorn (1993, 2002), Shapiro (2001), Clark, Piccolo, Stanton & Tyson (2001) e.g., establishment of RCA Corporation patent consortium in the Radio, Television and Communication Equipment industry

16 Motivation - High-tech industries contribution to growth High-tech industries are the top private R&D performers and have significant contribution to economic growth Helpman (1998), Jorgenson, Ho & Stiroh (2005)

17 Objectives - Knowledge licensing This project models knowledge (patent) licensing between high-tech firms in an endogenous growth framework Shows how market concentration, intensity of competition, and the type of competition (Cournot or Bertrand) in high-tech industry can matter for innovation in that industry and aggregate performance Compares the inference to setups with no exchange of knowledge between high-tech firms and/or knowledge spillovers

18 Objectives - Externalities This project also models externalities from the use of high-tech goods and assesses their impact on innovation in high-tech industry and aggregate performance

19 Two-sector growth model Two sectors: Final goods sector and High-tech industry Final goods sector Final goods are homogenous Y Final goods producers form the demand for high-tech goods High-tech industry The use of high-tech goods creates positive externalities in final goods production Firms produce differentiated goods {x} and set prices {p x } Each firm can invest in R&D which improves its knowledge on production process (or quality of x) Firms can license their knowledge

20 The problem of final goods producers (1) The problem of a representative final goods producer is max π Y = Y P X X wl Y {x j } N j=1,l Y s.t. Y = X X σ L 1 σ Y ε N X = j=1 x ε 1 ε j ε 1

21 The problem of final goods producers (2) I assume that in equilibrium and in equilibrium 1 σ > µ 0, 1 > σ > 0, ε > 1 X = X µ

22 High-tech goods production The knowledge of the production process of a high-tech firm is measured by its productivity λ Each firm has its knowledge of the production process The production function of a high-tech good x is x = λl x

23 R&D processes High-tech firms can engage in R&D for accumulating knowledge and increasing λ In order to improve its knowledge a firm needs to hire researchers L r Researchers use the current knowledge of the firm in order to create a better one process innovation: the firms are able to produce more of x quality upgrade: the firms are able to produce the same amount of higher quality x I consider 3 different settings for R&D processes

24 R&D process S.1 (1) S.1: Knowledge licensing In this setup knowledge can be licensed If a high-tech firm decides to license knowledge from other firms, researchers combine it with the knowledge available in the firm in order to produce new knowledge The knowledge available in the firm is (the only) essential input in the knowledge accumulation process of the firm

25 R&D process S.1 (2) Considering for example the j-th firm, R&D process is given by [ N ] λ j = ξ (u i,j λ i ) α λ 1 α j L rj i=1 where u i,j is the share of knowledge of i-th firm (λ i ) that the j-th firm licenses, and u j,j 1 Elaborate

26 R&D process S.2 (1) S.2: Inter-firm exchange of knowledge inter- and intra-firm knowledge spillovers In R&D process researchers do not fully internalize the use of the knowledge available in the firm and have external benefits from it Researchers have external benefits also from complementary knowledge which spills over from remaining high-tech firms They combine this knowledge with the knowledge available in the firm while generating new knowledge

27 R&D process S.2 (2) R&D process is given by λ j = ξ Λλ 1 α j L rj

28 R&D process S.2 (2) R&D process is given by where in equilibrium I assume that λ j = ξ Λλ 1 α j L rj Λ = N i=1 λ α i

29 R&D process S.3 (1) S.3: No inter-firm exchange of knowledge intra-firm knowledge spillovers In R&D process the researchers do not fully internalize the use of previous knowledge and have external benefits from it These external benefits increase the productivity of researchers R&D process is given by λ j = ξ λλ 1 α j L rj ξ > 0, 1 > α > 0

30 R&D process S.3 (2) In equilibrium I assume that λ = λ α j Elaborate

31 High-tech firms problem(s) The j-th producer s problem is max Cournot: L xj,l rj,{u j,i,u i,j} N i=1;(i j) Bertrand: p xj,l rj,{u j,i,u i,j} N i=1;(i j) s.t. p xj = σy x ε 1 ε 1 π j = p xj x j w ( L xj x j, λ j j ( N i=1 V j (t) = ) 1 x ε 1 ε i + L rj ) + N i=1,i j + t π j (τ) exp p uj,i λ j (u j,i λ j ) τ t r(s)ds dτ N i=1,i j p ui,j λ i (u i,j λ i )

32 Labor demand S.1-3 cases The j-th high-tech firm s demand for labor for production and R&D are ( w = λ j p xj 1 1 ) e j w = q λj where e j is the perceived elasticity of substitution Elaborate λ j L rj

33 Demand for and supply of knowledge, S.1 In S.1 case high-tech firm s demand for and supply of knowledge are ( ) 1 α λj p ui,j λ i = q λj ξα L u i,j λ, i j rj i u j,i = 1, i j

34 Returns on knowledge accumulation, S.1 If there is cross-licensing (S.1) high-tech firm s returns on knowledge accumulation are q λj = r ek j 1 p xj L xj + λ j N p uj,i λ + j u j,i q λj e j q λj λ j q λj i=1,i j λ j N ( ) ui,j λ α i = ξl rj 1 + (1 α) λ j i=1,i j λ j

35 Returns on knowledge accumulation, S.2-3 If there is no knowledge licensing (S.2-3) high-tech firm s returns on knowledge accumulation are ( q λj e k j 1 p xj = r L xj + λ ) j q λj e j q λj λ j λ j λ j = (1 α) λ j λ j

36 Households There is a continuum of identical and infinitely lived households of mass one Each household is endowed with constant amount of labour L The household s optimality problem is max U = + 0 s.t. A = ra + wl C θ > 0, ρ (0, 1) C 1 θ 1 exp( ρt)dt 1 θ

37 Couple of definitions Define b k = ek 1 e k, k = C, B D k = σ ( e k 1 ) e k σ { 1 for S.3 I N = N otherwise

38 Properties of equilibrium I focus on symmetric equilibrium It can be shown that in decentralized equilibrium the economy jumps to balanced growth path

39 Labor force allocations and growth rates (1) It can be shown that in decentralized equilibrium labor force allocations to production of final goods, high-tech goods and R&D are NL r = N ξd k IN N L ρ ξi N (θ 1) (σ + µ) + α + D k N [(θ 1) (σ + µ) + α] L + k ξi NL x = D N ρ (θ 1) (σ + µ) + α + D k L Y = 1 σ σb k N [(θ 1) (σ + µ) + α] L + Dk (θ 1) (σ + µ) + α + D k ξi N ρ

40 Labor force allocations and growth rates (2) The growth rates of final output and knowledge/productivity are g Y = (σ + µ) g λ g λ = ξi N L r = ξd k I N N L ρ (θ 1) (σ + µ) + α + D k

41 Some comparative statics It can be easily shown that g λ NL r NL x L Y g Y ε C B σ µ α + +

42 Comparative statics with respect N It can be easily shown that

43 More on knowledge accumulation S.3 Another interpretation for λ is that spillovers are from average knowlege ( ) 1 N λ = λ α i N i=1 This masks the complementarity between knowledge of different high-tech firms This knowledge accumulation process implies non-decreasing returns at firm level Example: Firm that started with tabulating machines and reached to producing supercomputers and AI systems (e.g., IBM) Back to S.3 (2)

44 Perceived elasticity of substitution It can be shown that under Bertrand competition [ ] (ε 1) p 1 ε ej B x e j = ε j N i=1 p1 ε x i and under Cournot competition Back to S.1-3 e C j e j = ε 1 + x ε 1 ε j (ε 1) N i=1 x ε 1 ε i 1

45 R&D process S.1 This R&D process can be rewritten as λ j = ξ N i=1,i j (u i,j λ i ) α + λ α j λ 1 α j L rj Back to S.1 (2)