IPR for Public and Private Innovations, and Growth

Transcription

1 IPR for Public and Privae Innovaions, and Growh L. Spinesi Discussion Paper Déparemen des Sciences Économiques de l'universié caholique de Louvain

2 IPR for Public and Privae Innovaions, and Growh Luca Spinesi Universiè Caholique de Louvain and Universiy of Maceraa May 28, 2007 Absrac The empirical analyses show ha public and privae R&D are srongly inerwined. On he one hand, he exisence of large direc spillovers from public R&D o privae indusry has exensively proven. Ye, boh a subsiuabiliy and complemenariy relaionship beween privae and public R&D invesmen has been found. From an insiuional poin of view, o simulae he echnology ransfer from public R&D o privae indusry he U.S. adoped an uniform paen policy for public funded research, such as ha guaraneed by he Bayh-Dole Ac. This paper conribues o explain his empirical evidence. Wihin a neo-schumpeerian endogenous growh model, i is shown ha he inellecual appropriaion share of a new commercial valuable idea by privae firms and he subsidy of privae R&D cos are wo equivalen ways o simulae privae R&D effor, and hey affec in he same way he endogenous per capia oupu growh rae. The exisence of a rade off beween he per capia oupu growh rae and level has found. The main policy implicaion of hese resuls consiss ino guaranee wo differen regimes of IPR for indusrial and public innovaions. Furhermore, i is shown ha he large direc spillovers from public R&D o privae indusry allows o have beer growh performance even if public R&D invesmen crowds ou privae innovaive effor. Again a rade off beween he per capia oupu growh rae and level has found. Keywords: Inellecual Propery Righs, Privae and Public R&D, Growh JEL classificaion: O31, O34, O38 1 Inroducion The role of he echnological progress and of he Research and Developmen (R&D) invesmens for he growh performance of a counry is emphasized by IRES, Place de Monesquieu 3, B-1348 Louvain-la-Neuve. Tel +32 (0) Address for correspondence: Via Sefano Borgia, 84-C Rome (Ialy). luca.spinesi@unimc.i 1

3 boh academic and non-academic analyses. In several developed counries boh privae and public insiuions inves large amouns of resources in R&D (see he Naional Science Foundaion repors). In such counries inellecual propery righs (IPR) - ofen in he form of a paens - have graned a he offsprings of he R&D effor. Since he 80s he U.S. adoped several legislaive and insiuional arrangemens o reinforce he ies beween public and privae R&D, and o spur he echnology ransfer of discoveries and invenions from public research o privae indusry. Among he several legislaive acs he mos influenial has been he Bayh-Dole Ac of he This Ac insiued an uniform federal paen policy for universiies and small businesses under which hey obained he righs o any paens resuling from grans and conracs funded by any federal agency and o licence hese paens on an exclusive or non-exclusive basis. 1 Based on he belief ha legislaive arrangemens such as he Bayh- Dole Ac enhance he echnology ransfer and he academic conribuions o innovaion and growh in he U.S., similar legislaion is being considered in oher OECD counries (OECD, 2002). The exisence of inerrelaions beween public and privae R&D is also proven by he empirical evidence. The empirical analyses show ha privae firms benefi of large spillovers from public discoveries and innovaions (direc spillovers), whaever is heir effec on he privae innovaive effor. Narin e al. (1997), and McMillan e al. (2000) show ha, for he U.S. indusry, relying in exernal sources of knowledge ceners on public science. In paricular, Narin e al. (1997) show ha during he , 73% of he scienific papercied by U.S. indusrial paens were firm public science sources. From a heoreical poin of view hese spillovers are explained boh hrough he inrinsic naure of knowledge as a nonrival inpu (see Arrow 1962) and he Meron s issue of prioriy of scienific discoveries. 2 Furhermore, some empirical analyses sudy he effec of public R&D invesmen in simulaing privae research effor. Recenly, David e al. (2000) also find he exisence of large and direc spillovers from public R&D o privae indusry, and he same auhors mainain ha hese spillovers...ofen are held o enhance privae secor producive capabiliies, and, specifically, o encourage applied R&D invesmens by firms ha lead o echnological innovaions - from which will flow fuure sreams of producer and consumer surpluses. 3 1 Ohers legislaive acs in such direcion are he Sevenson-Wydler Technology Innovaion Ac of he (1980), he Small Business Innovaion Developmen Ac (1982), he Naional Cooperaive Research Ac (1984), he Federal Technology Transfer Ac (1986), he Naional Cooperaive Research and Producion Ac (1993), he Technology Transfer and Commercializaion Ac (2000). 2 Meron (1973) argued ha - wihin he non marke rewards srucure - he goal of scieniss is o esablish he prioriy of discovery by being he firs o announce an advance in knowledge. Therefore, he rewards o prioriy are he recogniion awarded by he scienific communiy for being he firs. 3 The same auhors mainain: Several recen economeric sudies, for example, documen posiive, saisically significan spillovers effecs via he simulaion of privae R&D invesmen by publicly funded addiions o he sock of scienific knowledge. See also Leyden and Link (1991). Oher macro empirical works ha show he exisence of complemenariy beween publicly funded R&D and privae R&D are Levy (1990), Robson (1993), Diamond 2

4 Ye, his complemenariy relaionship beween public and privae R&D invesmens is no general, in fac he empirical analysis also shows he exisence of a subsiuabiliy relaionship beween privae and public R&D invesmen. 4 Therefore, he empirical evidence shows ha privae and public R&D effors are sricly inerwined. The exisence of large direc spillovers from public R&D o privae indusry has exensively proven. Ye, a clear subsiuabiliycomplemenariy relaionship beween public and privae research effor is no proven. Moreover, he insiuional se-up of a counry in he form of IPR can affec he ies beween privae and public R&D. This paper considers hese inerrelaions, and i sheds ligh o explain he empirical evidence menioned above. To his aim a neo-schumpeerian growh framework à la Aghion and Howi (1992, 1998), and Howi (1999, 2000) is adoped. The neo-schumpeerian growh lieraure considers innovaion, knowledge accumulaion, and echnological progress as he engines of he economic growh. In large par of he neo-schumpeerian lieraure policy consiss ino guaranee paen proecion a he privae innovaive firms and o subsidize heir R&D cos, wihou any direc presence of he governmen in he R&D secor. 5 The paen-design lieraure, on he oher hand, addresses he quesion of how does paen policy affec incenives for indusrial R&D. Recenly, O Donoghue and Zweimuller (2004) exend he paen-design lieraure o a general equilibrium framework. However, also hese auhors only pay aenion a he effec on he indusrial R&D. This paper disinguishes in he descripion of he R&D secor, where boh he privae and public secors inves in R&D. In his framework he indusrial secor can conduc boh he basic and developmen sage of he R&D aciviy, 6 while he public secor invess in basic research. Because he empirical evidence shows ha he developmen sage is he prominen aciviy of he privae research effor, 7 he drasic, ye realisic, assumpion ha public R&D only consiss in (1998), Von Tunzelmann and Marin (1998). 4 David e al. (2000) remark ha empirical evidence on public R&D as complemen or subsiue for privae R&D is no conclusive; in fac he auhors mainain:...available empirical evidence on he issue remains raher shor of being conclusive, o say a leas. 5 The heoreical conclusions are no univocal. Some heoreical and empirical analyses conclude ha policy has posiive effec on boh per capia oupu growh rae and on per capia oupu level. The alernaive view concludes ha policy is ineffecive on per-capia oupu growh rae, even if i can produce posiive effecs on he per capia oupu level (see Jones 1995, 1999). Alhough a recen empirical analysis by Ha and Howi (2006) seems o consider public policy effecive even on he per capia growh rae of counries, a conclusive resul, boh heoreical and empirical, can no be again obained. 6 The Science and Engineering Indicaors (SEI, 2006) by he Naional Science Foundaion defines as basic he research aimed o gain more comprehensive knowledge or undersanding of he subjec under sudy wihou specific applicaion in minds. The developmen sage is defined as he sysemaic use of he knowledge or undersanding gained from research direced oward he producion of useful maerials, devices, sysems, or mehods, including he design and developmen of prooypes and processes. 7 The SEI saes: The federal governmen, esimaed o have found 61,8% of U.S. basic research in 2004, has hisorically been he primary source of suppor for basic research...indusry devoed only an esimaed 4,8% of is oal R&D suppor o basic research in ha year. (SEI 2006, ch.4 p.13). In addiion, The developmen of new and improved goods, services, and 3

5 basic research programs is inroduced. Furhermore, he innovaions of boh public and indusrial R&D are graned of paen proecion. Public research inroduces new basic discoveries a share of which can be usefully developed by he privae indusry o creae a new commercial valuable produc. This share can be assumed o be sochasic. The indusrial secor pays he licenses o develop he paened public innovaions. Therefore, i will only appropriae a share of he final marke value of a new produc. This paper sudies he macroeconomic implicaions of he inerplay beween indusrial and public invesmens in R&D. The resuls show ha he subsidy o privae R&D cos and he inellecual appropriaion s share of a commercial valuable idea by a privae R&D firm are wo - in some sense - equivalen ways o finance he indusrial R&D effor. In fac, boh hese ways increase he privae innovaive effor and he per capia oupu growh rae, while hey reduce he per capia oupu level. Ye, he subsidy and he inellecual appropriaion of a new idea have some fundamenal differences The subsidy of he privae R&D cos concerns he cerainy aspec of a R&D process, while he inellecual appropriaion s share of a commercial valuable idea concerns he uncerainy aspec of a R&D process. Furhermore, he subsidy and he inellecual appropriaion have deep differences from an insiuional poin of view. The inellecual appropriaion of new ideas concerns boh public and privae research aciviy, and he policy design of he IPR involves he poliical, execuive, legal, and jurisprudenial powers of a counry. The subsidy o privae research cos does no deeply shape he insiuional se-up of a counry as he IPR policy design does, and i can also be used as a fine-uning policy insrumen. Alhough he mere inroducion of some form of IPR regime for public innovaions reveals o be an efficien way o simulae boh he privae innovaive effor and he per capia oupu growh rae of a counry. A policy implicaion is ha - once IPR are inroduced for public innovaions - a differen regime for privae and public innovaions should be inroduced. Paens o public innovaions should be only graned o some radical and very innovaive ideas. In fac, he exisence of IPR for public innovaions generaes a furher R&D cos for he indusrial secor o acquire he licenses from public insiuions. This implies ha a paen design should guaranee a larger paenabiliy requiremen and a lower leading breadh for public basic ideas han for indusrial innovaions. 8 In fac, a larger paenabiliy requiremen and a lower leading breadh boh allow he privae firm o appropriae of a higher share of a new produc s marke processes is dominaed by indusry, which performed 90.2% of all U.S. developmen in (SEI 2006, ch.4 p.13). 8 The paenabiliy requiremen is a minimum innovaion size required o receive a paen. A paen breadh s pu resricions on he producs oher firms can produce wihou a license. In paricular, he leading breadh limis fuure innovaors by specifying superior producs ha oher firms can no produce (see O Donoghue, 1998, and O Donoghue and Zweimuller, 2004). Basedonhesedefiniions, he leading breadh could only concern a new markeable produc, and i could no apply a a basic innovaion ha - by is own definiion - does no have an immediae and specific marke applicaion. However, if he leading breadh also applies a a basic innovaion, he policy implicaion of he paper follows. 4

6 value. The policy o gran paens a few and very radical basic innovaions for he public secor does no resric he echnological ransfer from universiies o indusrial R&D. In fac, he empirical analyses show ha he privae secor uses many channels o access public and universiies discoveries. Cohen e al. (2002) find ha he mos imporan channels o access publicly funded research are publicaions, conferences, informal ineracions raher han more insiuional channels such as paens, licenses, and cooperaive venures. These resuls refer o all indusrial secors, even he high-ech indusries. 9 Recenly, a paper by Cozzi and Galli (2007) focuses on he sequenial naure of he innovaion process wihin a dynamic general equilibrium framework. Their paper considers a wo sage innovaion process, and i evaluaes he condiions under which IPR should be exended o basic discoveries ha does no have an immediae and specific markeable applicaion and a commercial value. Cozzi and Galli (2007) show ha a pro-growh policy consising ino guaranee an inellecual propery proecion for basic half-ideas was a he ground of he reforms underaken in he U.S. around he 80s. Moreover, Cozzi and Galli (2007) explicily deermine he marke value of a basic half-idea. The focus of his paper is on he srengh and widh of paens graned o public R&D, once paen proecion for public innovaion already exiss in a counry. Therefore, his paper complemens Cozzi and Galli s (2007) conribuion. O Donoghue and Zweimuller (2004) sudy he general equilibrium implicaions of a larger paen proecion agains fuure innovaors wihin a neo-shumpeerian growh framework. Their resuls show ha boh a larger paenabiliy requiremen and a larger leading breadh spur he privae innovaive effor, and herefore he per capia oupu growh rae. However, heir work does no consider neiher he role of he public R&D invesmen nor a paen proecion for public innovaions. Furhermore, and differenly from Cozzi and Galli (2007), his paper shows how he mixed empirical evidence abou he subsiuabiliy-complemenariy relaionship beween public and privae R&D invesmen can be explained. I is shown ha a higher public invesmen in R&D can eiher crowd ou or complemen privae R&D effor. The subsiuabiliy-complemenariy relaionship beween public and privae R&D invesmen depends on he srucural parameers of he economy, on he populaion growh rae, and on he inensiy hrough which privae and public R&D affec he probabiliy o find a new commercial valuable idea. In paricular, i is shown ha whenever populaion growh rae is no high enough, a higher public R&D invesmen divers oo much resources from he privae secor - boh manufacuring and R&D - and hus i crowds ou privae R&D invesmen. The effec on he per capia oupu growh rae depends on he direc spillovers public innovaions generae on he privae indusry. As indicaed above, he exisence of large and posiive spillovers from public R&D o privae indusry has found by he empirical analysis. This paper 9 Cohen e al. (2002) find ha he pharmaceuical indusry more heavily conveys public research knowledge hrough paens and licenses. However, he same auhors mainain ha even in his indusry informal channels and open science are sill more imporan in conveying public R&D discoveries. 5

7 proves ha - because of hese large spillovers - a higher public invesmen in R&D beer off he growh performance of a counry. These resuls are reinforced when populaion growh rae is high enough, so ha a higher public R&D invesmen only crowds ou he manufacuring resources, while i complemens he privae innovaive effor. Finally, he exisence of a rade-off beween he per capia oupu growh rae and level has found. This rade-off is sronger when a complemenariy relaionship beween privae and public R&D exiss. The paper is organized as follows. Secion 2 ses up he model, secion 3 describes he general equilibrium resuls, secion 4 concludes. 2 The Model This economy is composed of a final good secor, of an inermediae good secor, and of a R&D secor. As in Aghion and Howi (1992, 1998), compeiive firms produce a homogeneous final consumpion good by using a fixedinpu,anda coninuum of inermediae goods wih heerogeneous produciviy. Inermediae secor produces a coninuum of producs denoed by N a a given ime 0. The mass of inermediae goods is coninuously enlarging hanks o serendipious imiaion as in Howi (2000). The manufacuring secor is characerized by free enry and exi, and by a consan reurns o scale echnology: workers can be hired by a coninuum of firms ha produce heir inermediae goods on a one o one basis from labor. A legally imposed disorion - he Paen Sysem - renders each of hem a local monopoly. According o he sandard Schumpeerian approach à la Aghion and Howi (1992 and 1998), each inermediae monopolisic firm is challenged by ousider R&D firms rying o inven and paen a beer produc and - due o insananeous price compeiion - drive he former monopolis ou of he marke. The R&D secor is composed of boh privae and public research. Privae R&D consiss ino upgrade he qualiy (or he producion process) of he inermediae producs (verical innovaion). As said above, a perfecly enforceable paen law allows he researcher o gain monopolisic rens for all he effecive duraion of he paen, because - as usual in neo-schumpeerian growh models wih verical innovaion - he incumben monopolis can be replaced by he nex innovaor in he same produc line. 10 Therefore, i generaes he Schumpeerian creaive desrucion effec. The exisence of a perfec sock marke channels consumer savings o firms engaged in R&D. Moreover, he R&D secor is composed of public research: he governmen employes skilled workers o obain basic innovaions and discoveries. According o he legislaive acs menioned in he inroducion, paens are graned o basic innovaions. These basic innovaions are developed by privae R&D firms o find a new commercial valuable innovaion and o inroduce new inermediae goods. 10 See Aghion and Howi (1992, 1998), Segersrom (1998), Howi (1999). Cozzi (2007) proves ha he sandard neo-schumpeerian growh models are compaible wih a posiive and finie R&D invesmen by he incumben monopolisic firms. Theanalysisofhispaper is also compaible wih Cozzi s (2007) findings. 6

8 2.1 Basic Framework Le us assume coninuous ime and unbounded horizon. In his economy a mass L > 0 of infiniely lived families exiss. Each family has an idenical preference for non-negaive consumpion flows represened by he ineremporal uiliy funcion R e r C 0 d, wherec is he non negaive consumpion flow of each household, r>0is he common and consan subjecive rae of ime preference. The linear insananeous uiliy implies consan real ineres rae always equal o r. Moreover, each family is endowed wih a uni mass of flow labor ime bearing no disuiliy. Populaion growh is consan and equal o g L > 0. The labor marke is perfec and he inelasic supply of labor L is insananeously employed by manufacuring firms and by he R&D secor. Final oupu is produced by perfecly compeiive firms combining he fixed facor wih a large variey of inermediae goods, ha is: Z N Y = M A i x α idi (1) wih 0 <α<1. x i is he amoun of inermediae good i produced and used as an inpu a a given ime 0, anda i is he produciviy parameer of he curren version of ha good. M is he aggregae mass of fixed facor (such as for example, land, minerals, oils, ec.). N [0, ) denoes he mass of inermediae goods already invened in he economy a dae 0. Since in each secor insananeous Berrand compeiion guaranees ha only he mos advanced paen holder will be producing, N also denoes he mass of acive inermediae good indusries. The elasiciy of subsiuion beween inermediae producs is equal o ε 1 > 1. The perfecly compeing R&D firms ry o achieve and appropriae he nex generaion of any inermediae good (verical innovaion process). According o Aghion and Howi (1998), and Howi (1999) he leading-edge echnology has considered, wih an economy-wide leading edge produciviy parameer A max ha exers posiive R&D spillovers in all inermediae goods. When a new commercial valuable discovery is inroduced ino an inermediae produc line i (a beer qualiy of ha inermediae good is inroduced) he produciviy parameer A i in ha line jumps o A max.thisspecificaion incarnaes Aghion and Howi s (1998 ch. 3) and Howi s (1999) iner-secor knowledge spillovers. The echnological fronier A max grows deerminisically a a rae proporional o he per produc line rae of verical innovaions. The Poisson arrival rae of verical innovaions in any produc line i is λ A f (l A,b ). λ A is a produciviy facor, l A = L A N is he per produc line research labor ime, b = B N is he per produc line sock of basic knowledge ha can be usefully developed o generae a new paenable and commercial valuable idea in any produc line i. The funcion f (l A,b ) capures he effec of he wo R&D effors, privae and public, ino generae a new markeable produc and herefore o increase he echnological fronier (see he appendix A, poin 1). As he economy develops an increasing number of inermediae goods, an innovaion of a given size in any produc line will have a smaller impac on he aggregae economy; hence he 0 7

9 marginal impac of each innovaion on he sock of public knowledge will be σ N, where σ>1 is a proporionaliy facor. The aggregae flow of verical innovaions is he number of inermediae goods N imes he expeced flow of verical innovaions per indusry line. The economy-wide rae of verical echnological progress is described by he following: g A = Ȧmax A max = σ ZN λ A f (l A,b )=σλ A f (l A,b ) (2) N 0 The generic specificaion of f ( ) leaves room o many ways hrough which he sock of basic knowledge affecs he produciviy of privae R&D. As an example, only a share of he sock of basic knowledge can be usefully developed, and/or he duplicaion argumen can be applied boh o privae innovaive effor and o basic discoveries. 11 Therefore, a new beer qualiy version of any inermediae produc is he resul of privae innovaion ha renders markeable and commercial valuable he offsprings of boh public basic and privae research effor. According o his framework, in equilibrium we will observe an ever-evolving inersecoral disribuion of he absolue produciviy parameers A i,wihvalues ranging from 0 o A max. Defining a A i A, we can concenrae on he max relaive inersecoral disribuion, ha - as shown in Aghion and Howi (1998, ch. 3) and in Howi (1999) - converges o he unique saionary disribuion of relaive produciviy parameers - a - characerized by cumulaive disribuion funcion H (a) =a 1 σ,wih0 a 1. Every ime a beer qualiy of an inermediae good is inroduced ino he economy, he absolue disribuion will be re-scaled righward because he echnological process rises o A max. The mass of inermediae producs grows as a resul of serendipious imiaion, no deliberae innovaion. 12 Each person has he same propensiy o imiae >0, hus he aggregae flow of new producs is: Ṅ = L (3) Sine populaion grows a he consan rae g L, he number of workers per produc line L N converges monoonically o g L. 11 The per produc line sock of basic ideas b encompasses all discoveries ha can be useful o privae indusry in a wide meaning. I includes all basic ideas ha help each privae economic agen o have new ideas, insighs, developmens, ec. Since inellecual propery righs for public R&D ideas exis - a share of he sock of basic discoveries b has obained a paen gran - he privae firm incurs a cos o use paened basic discoveries. Noice ha he spillovers per produc line basic discoveries have on he produciviy of privae research effor concerns he sock of basic knowledge accumulaed over ime, and no only he flow of new basic discoveries. Hence, he sock of basic ideas can be used for he developmen of differen versions of an inermediae produc. 12 See Howi (2000). In Howi (1999), and Cozzi and Spinesi (2005) horizonal innovaion is moivaed by he same profi seeking objecives as qualiy improving innovaion. The resuls of his paper are no qualiaively affeced by his specificaion for horizonal innovaion. 8

10 2.2 Asse Marke, Manufacuring, and Verical R&D The privae and public research effor allows o increase he echnological fronier. As remarked in he inroducion, a public basic idea does no have an immediae and specific commercial applicaion, and i will be developed by he indusrial R&D secor o find a new markeable inermediae produc. Therefore, he commercial value of a new inermediae produc is given by he firm s expeced sock marke value ha monopolizes he commercializaion of he new inermediae produc. Le V be he expeced sock marke value of a new inermediae produc wih maximum produciviy A max. Theprivaefirm pays for he use of paened public basic ideas, and herefore i will appropriae a share of he commercial value of he new inermediae produc. The share of he marke value respecively appropriaed by he privae R&D firm and by he public research uni ha have conribued o inroduce he new inermediae produc is described as a Nash-bargaining soluion beween hese wo forces. The bargaining process is described as aking place beween a represenaive firm and a public insiuion from which he righs on he paened basic innovaions are acquired. Because of he symmery in he R&D secor, each R&D firm behaves symmerically. 13 Le V p be he expeced sock marke value of a new inermediae produc appropriaed by he privae R&D firm, and le V b be he expeced sock marke value of a new inermediae produc appropriaed by he public insiuion, wih V = V p + V b. The expeced sock marke value appropriaed by privae and public innovaors is he soluion o he following: max s.. V = V p V p,v b (V p ) φ V b 1 φ + V b (4) The soluion o his problem gives V p = φv,andv b =(1 φ) V. The parameer φ (0, 1) represens he insiuional se-up in which he bargaining process akes place. 14 The exisence of laws such as he Bayh-Dole Ac - and of oher legislaive arrangemens - heavily conribue o deermine he value of he parameer φ in he economy. In fac, φ indicaes ha a privae R&D firm 13 Because of he macroeconomic framework of his paper, he bargaining process is here described wih a cenralized se-up. A represenaive firm bargains wih a cenralized public insiuion o buy he righs on a sock of basic ideas per uni of ime. This sock can be usefully developed by privae R&D firms. 14 As shown by Cozzi and Galli (2007) he mere inroducion of IPR for public basic ideas can beer off he growh performance of a counry. In his paper he ighness and he ease of he IPR regime - as measured by φ - has sudied. Therefore, φ < 1 is assumed. On he oher hand a low value of φ can indicae ha i is exremely easy for public R&D o obain paen grans for any basic innovaion. This implies ha privae firms mus pay o also use basic discoveries ha have a very low innovaive power. When φ =0any incenive for privae R&D effor disappears, i.e. l A =0. Therefore, φ>0 is assumed. Noice ha, in his macroeconomic se-up, he share (1 φ) appropriaed by he public secor can encompass differen public paens all useful o develop a new inermediae produc, and no jus one paened basic public idea. As indicaed in he Appendix A, poin 1, he per produc line sock of basic innovaions graned of paen proecion can be a random variable p [0, p] wih 9

11 pays o use basic ideas which are graned of some form of IPR. In wha follows he parameer φ is assumed consan wihin each inermediae produc line and beween hem. Because he break-down of he bargaining process beween privae and public insiuions gives a zero value a boh of hem, a leas one firm will buy he basic paened ideas. In fac, because of he symmery, all R&D firms will pay he same price for he basic ideas and hey will appropriae of a share φ of he expeced commercial value of an innovaion V. On he oher hand, he governmen will have he incenive o license he same basic ideas a leasaoneprivaer&dfirm. Each verical R&D firm argeing an inermediae produc i chooses is R&D inensiy o maximize φv λ A ψ (l Aj,b ) (1 s) w l Aj,wherel Aj is he labor ime flow employed by he verical R&D firm j a ime, s is he subsidy o privae research. Raional individuals and firms know hey will appropriae a fracion φ of he expeced sock marke value of a paenable and commercial valuable idea. Noice ha, he per produc line basic sock knowledge is aken as given by each individual and firm. This condiion deermines he opimal choice l Aj = laj for each R&D firm (see he appendix A, poin 2). Applying Aghion and Howi s (1992 and 1998) mehods, he inermediae good i producion level ha maximizes he monopolis profis a ime is µ α 2 1 A i x i = M, because he disribuion of relaive produciviies is unchanging, we do no classify he secors by heir index i bu by heir relaive produciviy a A i A. max Defining he produciviy-adjused real wage as ω w A and normalizing he max fixed facor o one (ha is posiing M =1) he insananeous labor demand funcion for a secor wih relaive produciviy a a dae is rewrien as: ³ ω x i = a w µ α 2 a ω 1 where x ω i a is a labor demand funcion for he manufacuring firm. The labor force employed in he manufacuring secor negaively depends on he produciviy-adjused real wage. We will focus on he symmeric seady sae, ha is x i = x, l Ai = l A,ec., for every inermediae produc line i. 15 Because he R&D secor is characerized by free enry and exi, in equilibrium he following condiion mus hold for a successful R&D firm: φv λ A ψ laj,b (1 s) w laj =0(see he appendix A, poin 2). This condiion can be rewrien as: p acommoncdff (p). Therefore, each produc line has he same average value p = pdf (p). Because of he inersecoral knowledge spillovers and by he Law of large numbers, he share of he per produc line paened public ideas acquired by he indusrial secor is deerminisic. 15 As proven by Cozzi (2005), Howi s (1999) model admis a coninuum of symmeric balanced growh pahs. 0 (5) 10

12 w = φλ Aψ laj,b (1 s) laj V (6) Therefore, in a he mulisecor economy a condiion very similar o he manufacuring-r&d no-arbirage equaion as in Aghion and Howi (1998) has obained. Noice ha, in eq. (6) he wage paid o a researcher in he indusrial R&D laboraory w is proporional o he average Poisson arrival rae of innovaion of he indusrial R&D laboraory iself, i.e. is proporional o λ Aψ(l Aj,b ) l. Aj By following he same seps as in Aghion and Howi (1998, ch. 3, Appendix) from eq. (6) i follows: (1 s) laj ³ w = V = A max φλ A ψ laj,b = A max Z 0 Z 0 e (r+g A/σ)τ π (ωe g Aτ ) dτ = e (r+g A/σ)τ 1 α α ω x (ω) e α g Aτ dτ (7) On he righ hand side of eq. (7) he discoun rae (r + g A /σ), andheprofi flows A max π (ωe gaτ ) accruing o a successful innovaor from dae o infiniy have been considered. 2.3 Public R&D Populaion differs in he basic research abiliy, while here are no qualiy differences among workers employed in verical R&D and in manufacuring. Le us G (θ) be he cumulaive disribuion funcion (cdf) of he basic research abiliy θ, wihθ aking value on 0, θ and θ 1. The usual properies G 0 (θ) > 0, G (0) = 0, G θ =1apply. Since each worker mus be indifferen beween manufacuring and verical research aciviy, i will be w = φλ Aψ(lAj,b ) (1 s)l V Aj. The addiional no-arbirage condiion beween improving/manufacuring and basic research effor can be wrien as: " w = λ B ϕ E where he funcion ϕ E ³ Ai A max µ # 1 Ai A max θ 0 w = λ B θ 0 w (8) 1 represens he spillovers from verical innovaion o basic research, and λ B ϕ (1 + σ) λ B. 16 Thelefhandsideofeq. (8) indicaes he expeced reurns of manufacuring and improving he qualiy of an inermediae produc. The righ hand side of he las par of eq. (8) indicaes he expeced flows reurn o be employed in basic research. Because 16 ϕ ( ) can be any posiive funcion of he average relaive produciviy E Ai A max = (1 + σ) 1. 11

13 θ 0, θ, he research gross salary paid by he public secor is lower han he wage paid by he indusrial R&D laboraory. 17 The parameer λ B allows o increase he perceived salary of a public researcher. In his framework he parameer λ B also posiively depends on public expendiures. 18 Le us denoe θ 0 he hreshold value of he basic research abiliy ha saisfies equaliy (8): θ 0 abiliy researchers are indifferen beween rying o improve he qualiy of one of he exising inermediae goods, o be employed in basic research, and o be employed in he manufacuring secor. The higher he basic research alen an individual is endowed wih, he higher he gain o be employed in basic research. The no-arbirage equaion (8) deermines he hreshold abiliy value θ 0 = 1, (9) λ B which is consan along he BGP. 19 Each individual endowed of a research abiliy θ>θ 0 will find i profiable o be employed in basic research. Hence, in such an economy, for θ>θ 0, [1 G (θ 0 )] L individuals will choose o be employed in basic research. Insead, he individuals endowed wih an abiliy θ θ 0,haisG(θ 0 ) L, will decide eiher o inroduce a beer qualiy of he exising inermediae goods, or o work in he manufacuring secor. A policy ha affecs he produciviy of basic research effor also affecs he hreshold abiliy parameer θ 0. Thisinurnchangeshepopulaionemployedinbasic research programs, and herefore he per produc line sock of basic knowledge. This implies ha he insiuional se-up can affec in differen ways he inerplay beween public and privae research effor. The governmen conducs basic research o accumulae basic knowledge B according o he following dynamic law " Z # θ Ḃ = λ B θg 0 (θ) dθ L = λ B m (θ 0 ) L (10) θ 0 h R i θ where m (θ 0 ) L θ 0 θg 0 (θ) dθ L is he expeced condiioned cumulaed basic research effor, λ B is he produciviy of each researcher engaged in basic research. Eq. (10) implies ha he sock of basic knowledge B is accumulaed a he same rae as he populaion growh rae g L. 17 See Aghion e. al (2005), and he Science and Engineering Indicaors (2004, 2006) for he empirical evidence of an average higher wage gained in he privae R&D laboraories han in nonprofi/governmen R&D laboraories. 18 To fix ideas, he public expendiures affec he qualiy of laboraories equipmen, because higher public expendiures allow o have higher qualiy of equipmen. This affec he expeced and perceived gain of a public researcher. Moreover, public researcher ofen obains some financial suppor from a variey of insiuions above heir conracual gross salary. These elemens conribue o increase he expeced gain of a public researcher I assumed ha < θ 1. λ B 12

14 The governmen uses proceeds from basic innovaions o finance he public research and o subsidize verical R&D firms. The public balanced budge in each insan of ime requires (see Appendix A, poin 3): m (θ 0 ) L w + sw N l A + E (A max ) L = = N d (1 φ) V + τ (A max (11) ) L The lef hand side of eq. (11) represens public oulays o finance boh privae and public R&D effor. m (θ 0 ) L w are he oal oulays for he wages paid a researchers employed in public research, sw N l A are he oal oulays o subsidize privae research effor, E (A max ) L indicaes he public expendiures ha are proporional o he leading-edge produciviy parameer and o populaion. The righ hand side of eq. (11) indicaes he oal proceeds of he public secor. The governmen appropriaes a fracion (1 φ) of he expeced sock marke value of a markeable paened idea V from boh successful and unsuccessful R&D firms, d indicaes he per produc line number of he ousider R&D firms. The parameer τ is a lump-sum ax ha is proporional o leading-edge echnology parameer A max Labor and Asse Marke Equilibrium Each researcher endogenously decides o allocae her research labor ime o invenive or o manufacuring aciviy. Plugging hese resuls in he manufacuring/verical R&D arbirage condiion (7), and solving he inegral yields: (1 s) laj ³ α x (ω) = φλ A ψ laj,b r + g A σ + α g A (12) Solving he above equaion for x (ω), he labor force employed in he producion of he op qualiy inermediae good is obained: x (ω) = (1 s) l Aj ³ φλ A ψ laj,b µ r + g A σ + α α 1 α g A 1 α (13) from which, by invering eq. (13), i is possible o deermine he produciviyadjused real wage ω. The labor marke clearing condiion for manufacuring and verical innovaion is: 20 In his framework all variables are proporional o he leading-edge produciviy parameer A max. Along he BGP, he per capia consumpion grows over ime a he same rae as he per capia final oupu Y. In fac, he final oupu is also he unique and homogeneous L consumpion good of he economy. Moreover, he linear preferences imply a consan pah of he per capia consumpion over ime. These wo elemens imply ha - along he BGP - wha is consan over ime is he produciviy-adjused per capia consumpion. Therefore, also a lump-sum ax mus be proporional o he leading-edge produciviy parameer A max. 13

15 Z 1 G (θ 0 ) L = N l A + N x (ω/a) h (a) da = N l A + N x (ω) 0 1+ σ (14) where x (ω/a) is he labor demand funcion of a produc line wih relaive produciviy parameer a a he dae, andh(a) is he densiy funcion of he relaive produciviies cumulaive disribuion funcion H(a). The labor marke clearing condiion for basic research is: [1 G (θ 0 )] L = L B (15) which - because he hreshold abiliy parameer θ 0 is consan along he BGP - is a consan fracion of he populaion. From eq. (1), and reclassifying inermediae goods by heir relaive produciviies, he aggregae GDP can be wrien as (see Aghion and Howi 1998, ch. 3, and Howi 1999): R Y = A max 1 N 0 a x (ω/a)α h (a) da = ³ α da = N A max = A max N R σ a 1 σ α 2 a ω α α 2 ω (1+ ) σ (16) Noice ha, in he ligh of eq.s (16) and (1), he produciviy-adjused fixed facor ren is: re Y A max =() MA max =() N x α (ω) ³ =() 1+ σ N ³ α 2 α ω ³ 1+ σ (17) Therefore, he fixed facor ren increases in he number of inermediae goods, simply because hey complemen i in he producion of he final good; and i decreases in he produciviy-adjused real wage. 3 General Equilibrium The economy has a unique raional expecaion equilibrium on which raional individuals insananeously jump on. From now onward he ime index is eliminaed for he sake of noaional simpliciy. Le us consider he law of moion of he basic knowledge (10), along he BGP i is obained: b B N = m (θ 0) λ B (18) Therefore, he labor demand in eq. (13) for he op qualiy inermediae good becomes: 14

16 (1 s) laj x (ω) = ³ φλ A ψ laj, m(θ 0) λ B µ r + g A σ + α α 1 α g A 1 α (19) Le us consider boh eq.s (19) and (14), along he raional expecaion equilibrium, a posiive and finie value for he per produc line verical research effor exiss such ha: l A = L N G (θ 0) ³ (1 s)laj φλ A ψ(laj,b) r + g A σ + α ³ 1+ σ g A α (20) where, along he BGP, b = m(θ 0) λ B. From eq. (20) he per produc line privae research effor is obained (see he Appendix B). The per capia oupu is: N Y L = ³ L Amax x α (ω) 1+ σ = ³ g L A max ³ 1+ σ α 2 α ω (21) where eq. (16) has been used. Therefore, he per capia oupu growh rae is equal o he echnological fronier growh rae: g Y/L = g A = σλ A f (l A,b) (22) By considering he eq.s from (18) o (22) he following can be saed: Proposiion 1 Along he raional expecaion BGP, a consan fracion of populaion is employed in manufacuring, privae and public research. Along he BGP, an increase eiher in he privae inellecual appropriaion parameer φ or in he subsidy s posiively affecs he per capia oupu growh rae and negaively affecs he per capia oupu level. Proof. See Appendix B and C The indusrial inellecual appropriaion s share of a new commercial valuable idea and he subsidy of he privae R&D cos are wo alernaive ways o finance indusrial research effor. Ye, some fundamenal differences beween hese wo ways exis. The policy design of he IPR regime of valuable ideas concerns he uncerainy aspec of a R&D process and i involves he poliical, execuive, jurisprudenial auhoriies of a counry. Therefore, his policy design srongly shapes he insiuional se-up in which boh privae and public R&D operae. The subsidy of he indusrial R&D cos does no shape he insiuional se-up of he economy as he policy design of he IPR does, and i only direcly affecs he privae R&D cos, and herefore he cerainy aspec of a R&D process. Moreover, he subsidy can be also managed in shor ime horizon. 15

17 Given hesefundamenal differences beween he IPR regime and he suppor of indusrial R&D cos, and he subsidy o R&D, boh he indusrial inellecual appropriaion share φ and he subsidy s spur he per produc line verical research effor. However, his effec can be differen in magniude, as he following saes: Proposiion 2 Whenever condiion (D1) holds along he BGP wih a public balanced budge - i.e. s 1 φ - a larger subsidy would produce a higher per capia oupu growh rae and a lower per capia oupu level han wha could be obained from a higher privae inellecual appropriaion parameer φ. Proof. See Appendix D Le us consider he public balanced budge along he BGP: )L g L m (θ 0 )+s l A + e = = (1 φ)(1 s)l Aj φλ A ψ(laj,b ) d + τ g L (23) where e E(Amax A max N = E g L is a consan erm, and l A is he per produc line verical labor ime research effor. Eq. (23) allows o obain he ax rae τ such ha equaliy s =1 φ holds. Once his equaliy holds along he BGP, a marginal increase in he subsidy grealy spurs he indusrial research effor and he per capia oupu growh rae. Ye, a marginal increase in he subsidy magnifies he rade-off beween he per capia oupu growh rae and he per capia oupu level. Noice ha he higher φ he lower he hreshold subsidy s ha grealy affecs he per capia oupu growh rae and he per capia oupu level. This means ha he larger he privae appropriaion share of he expeced sock marke value of a new commercial valuable idea, he lower he subsidy o spur he indusrial invesmen in R&D and he growh rae of a counry. Because φ is a measure of he srengh, ighness and ease of IPR graned o public innovaions, proposiion 2 has a main policy implicaion. Once some form of IPR are inroduced for public ideas, wo differen regimes of IPR agains fuure innovaors should be provided for public and privae innovaions. In paricular, he differen regime concerns in his framework a paen proecion agains fuure innovaors, and herefore i refers o boh paenabiliy requiremen and o paen breadh. 21 O Donoghue and Zweimuller (2004) show ha boh a larger paenabiliy requiremen and leading breadh beer off he growh performance of a counry. This paper shows ha because paened basic ideas are a cos for a privae R&D firm, a larger paenabiliy requiremen for a public basic idea reduces he indusrial R&D cos and beer off he growh performance of a counry. Insead, a larger leading breadh for a public basic innovaion generaes a cos of licences for boh universiies and privae firms, and his discourages he R&D effor. Therefore, a larger paenabiliy requiremen and a 21 Because he leading breadh limis fuure innovaors by specifying superior producs ha oher firms can no produce, i could no apply a a basic idea ha does no have an immediae and specific marke applicaion. However, o be as general as possible, also a leading breadh for non markeable basic ideas has considered. 16

18 lower leading breadh should be se for public basic ideas han for indusrial innovaions. In his way, a higher value of he parameer φ can be obained, and herefore also a low subsidy of he indusrial R&D cos grealy spurs he innovaive effor and he per capia oupu growh rae of a counry. Le us now suppose ha he offsprings of public research also depends on public expendiures e. 22 As proven in he Appendix E, whenever he populaion grows a a high enough rae, a larger per produc line public expendiures e in basic R&D programs spurs he privae R&D invesmen. This in urn implies a higher per capia oupu growh rae and a lower per capia oupu level. The resuls are summarized in he following Proposiion 3 When condiion (E4) holds along he BGP a higher public invesmen in R&D deermines: a) a higher per produc line indusrial R&D effor; b) a higher per capia oupu growh rae; c) a lower per capia oupu level. Proof. See Appendix E When he public secor invess resources in public R&D o endow researchers of beer equipmen and insrumens, more alened researchers will find i profiable o work in ha research programs. A larger proporion of he populaion will choose o be employed in public research. This in urn can also spur he privae research effor and invesmen o gain from a higher produciviy of basicresearch. Theposiiveeffec of a higher public expendiure on he per capia oupu growh rae is hen magnified from boh hese elemens. On he oher hand, he workforce employed in he manufacuring secor - as well as he demand for each inermediae monopolisic firm - will be lower along he new BGP. Therefore, also he negaive effec on he per capia oupu level has magnified from a higher public expendiure in basic R&D. These resuls also depend on a hreshold for he populaion growh rae. When he populaion growh rae is no high enough, an increase in he public expendiure o finance public R&D discourages he indusrial research effor and reduces he per capia oupu level (see he Appendix E). In fac, a larger fracion of he populaion will find i profiable o work in public R&D, and a lower facion of he populaion will be employed in boh manufacuring and privae R&D. Ye, in his case he populaion growh rae is no high enough o compensae he privae firm for he reduced marke demand of an inermediae produc. This in urn implies a lower privae innovaive effor due o a oo low marke demand for each inermediae good. In his case, he final effec on he per capia oupu growh rae is no univocal and i depends on he relaive 22 We can hink o e as public invesmen in maerial goods used in he public R&D programs, such as more producive machineries, more modern laboraory equipmen, libraries, laes compuers and sofware programs, ec. These expendiures can increase he produciviy of each R&D worker employed in public research. Therefore λ B = λ B (e), wih λ B > 0. This e means ha he produciviy of each researcher in finding new basic discoveries depends on her personal abiliy, and i is also posiively affeced by he equipmen, libraries, machineries, ec. she works wih. Moreover, a higher public expendiure can concern larger financial suppor and research funds for each researcher, so ha all hese elemens increase he salary gained by public researchers above he conracual salary w. 17

19 srengh of basic discoveries and of privae effor in he funcion f la,b. In fac, if he spillovers of basic discoveries o he Poisson arrival rae of innovaion are srong enough o compensae he reducion in he privae innovaive effor, he per capia oupu growh rae rises. Therefore, also he exisence of a rade-off beween he per capia oupu growh rae and he per capia oupu level depends on he spillovers srengh ha basic discoveries produce on he innovaive capaciy of privae R&D firms. Noice ha hese resuls depends on a populaion growh rae hreshold ha is deermined by he srucural and insiuional parameers of he economy. Moreover, hese resuls conribue o explain he mixed subsiuabiliy/complemenariy relaionship beween privae and public R&D invesmen. 4 Conclusions Since he 80s he U.S. adoped several legislaive acs o spur he ransfer of knowledge and innovaions from public funded research programs o privae indusry. The mos influenial legislaive ac has been he Bayh-Dole Ac of he 1980 ha creaed an uniform federal paen policy ha allowed universiies and small businesses o reain righs o any paens resuling from governmen and federal agency funded research and o licence hese paens on an exclusive or non-exclusive basis. Based on he belief ha legislaive arrangemens such as he Bayh-Dole Ac enhance he echnology ransfer and he academic conribuions o innovaion and growh in he U.S., similar legislaion is being considered in oher OECD counries. Srong inerwined relaionships beween privae and public R&D have documened by he empirical evidence. On he one hand, he exisence of large spillovers from public research aciviy owards privae indusry is widely recognized. On he oher hand, boh a complemenariy and subsiuabiliy relaionship beween public and privae R&D invesmen has been found. This paper invesigaes on he macroeconomic implicaions of he ies beween public and privae R&D and i sheds ligh o explain he empirical evidence jus menioned. To his aim a neo-schumpeerian growh model à la Aghion and Howi (1992, 1998) and à la Howi (1999, 2000) has been adoped. In he R&D secor, public research generae basic ideas ha do no have an immediae and specific commercial value and applicaion. According o he insiuional se-up of he U.S., IPR are graned a hese basic ideas. The privae R&D secor pays for licenses on such basic paened innovaions and i develops hese basic ideas o inroduce a beer inermediae produc in he markeplace. Therefore, he indusrial secor appropriaes a share of he final commercial value of each produc, being anoher share paid a he public secor for he licenses on he usefully developed paened basic ideas. Moreover, an indusrial R&D firm obains a subsidy for is research cos. This paper shows ha he IPR and he subsidy o privae R&D cos are wo alernaive ways o finance he privae research effor. Boh he inellecual appropriaion parameer and he subsidy o R&D spur he privae innovaive 18

20 effor. This in urn generaes a rade off beween he per capia oupu growh rae and level, by increasing he former and reducing he second. This resul seems remarkable because he policy design of he IPR srongly shapes he insiuional se-up of he economy, and i concerns he uncerainy aspec of a R&D process. While he subsidy of he privae R&D cos does no have an insiuional weigh as he IPR has, and i concerns he cerainy aspec of a R&D process. An imporan policy implicaion concerns he IPR regime. Once he IPR are also graned a public ideas, wo differen regimes of IPR agains fuure innovaors should be provided for public and indusrial innovaions. In paricular, a larger paenabiliy requiremen and a lower leading breadh should be graned for basic public ideas han for indusrial innovaions. This policy allows a a low subsidy o privae R&D cos o grealy spur he innovaive effor and he per capia oupu growh rae of he economy. Moreover, i is shown ha public invesmens in R&D can explain he mixed empirical evidence abou he subsiuabiliy-complemenariy relaionship beween public and privae innovaive effor. Iisshownhaanincreaseinhe public invesmen in R&D can eiher crowd ou or complemen privae R&D effor. The subsiuabiliy-complemenariy relaionship beween public and privae R&D effor depends on he srucural parameers of he economy and on he populaion growh rae. When populaion grows a a high enough pace, a higher public invesmen in R&D complemens he indusrial research effor and i only crowds ou he demand for each inermediae produc. This in urn generaes a rade off beween he per capia oupu growh and level. However, because he exisence of large and posiive direc spillovers from public R&D o privae indusry has found by he empirical analyses, he his paper shows ha a higher public invesmen beer off he growh performance of a counry whaever is he relaionship beween privae and public R&D invesmens, eiher subsiuabiliy or complemenariy. 19