Basic Research and Industrial Development, Patent Protection, and Growth

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1 Basic Research and Indusrial Developmen, Paen Proecion, and Growh Luca Spinesi Universiè Caholique de Louvain and Universiy of Maceraa December 27 Absrac The empirical analyses show he exisence of srong echnological links beween academic scienific knowledge and indusrial innovaions ha are graned of some form of inellecual propery righs (IPR) such as paens. Since he 8s also new universiies basic worh ideas are graned of paen proecion o reinforce boh he knowledge links and ransmission beween universiy and indusry. Wihin a Schumpeerian endogenous growh model his paper allows boh basic public ideas and privae innovaions o be graned of paen proecion. I is shown ha he marke value s fracion of a new indusrial valuable innovaion appropriaed by a firm, and he subsidy of he indusrial R&D cos are wo equivalen ways o simulae privae R&D effor. However, he higher he marke value s fracion appropriaed by a innovaive firm, he lower he subsidy he posiively affec per capia growh. A main policy implicaion suggess ha -onceipraregranedobasicacademicideas-adifferen regime of paen proecion should be se for privae and public ideas. In paricular, paens should only be graned o very innovaive and fundamenal academic basic ideas. Finally, 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 boh scienific knowledge and echnological innovaions o spur he growh performance of counries is emphasized by boh academic and nonacademic analyses. Boh privae and public insiuions in several developed counries inves large amouns of resources in R&D (see he Naional Science Foundaion repors). Because of knowledge characerisics, firms incurs in large IRES, Place demonesquieu 3, B-1348 Louvain-la-Neuve. Tel +32 () Address for correspondence: Via Sefano Borgia, 84-C7 168 Rome (Ialy). 1

2 fixed R&D coss wih a fundamenal uncerainy and serendipiy for he offsprings of heir effor, herefore hey need o gain some rens when successful in research. A radiional heoreical argumen o guaranee hese economic rens consiss in graning some form of Inellecual Propery Righs (IPR) - such as paens - a new worh innovaions. New knowledge is also creaed in he academy and oher publicly funded insiuions, and since he 8s he U.S. inroduced some form of IPR also for universiy s ideas wih he aim o reinforce he links beween academy and indusry. In paricular, he U.S. adoped several legislaive and insiuional arrangemens o spur he ransfer of public basic discoveries and invenions o he indusrial secor. Among he several legislaive acs he mos influenial has been he Bayh-Dole Ac of he 198. 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, 22). The exisence of large spillovers of new knowledge universiy s flow on he indusrial secor is well documened. 2.Narine al. (1997), and McMillan e al. (2) 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 paper cied by U.S. indusrial paens were firm public science sources. 3 Recenly, David e al. (2) 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. This paper considers he knowledge links beween universiy and indusry wihin a Schumpeerian ladder qualiy framework à la Aghion and Howi (1992, 1998), and Howi (1999, 2). The Schumpeerian growh lieraure considers knowledge accumulaion and echnological progress as he engines of he economic growh. However, in large par of his srand of lieraure policy consiss ino guaranee paen proecion for privae innovaive firms, and o subsidize 1 Ohers legislaive acs in such direcion are he Sevenson-Wydler Technology Innovaion Ac of he (198), 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 (2). 2 See, among ohers, Mokyr (22), Nelson (24), McMillan e al. (2). 3 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. 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. 2

3 heir R&D cos, wihou any direc public invesmen in he R&D secor. 4 This paper disinguishes in he descripion of he R&D secor in ha boh privae and public ideas can be graned of paen proecion, and he spillovers public basic ideas generae on indusry are explicily accouned for. Moreover, as in Aghion and Howi (1996) and in Cozzi and Galli (26), he disincion of he basic and developmen R&D sages is considered. 5 In his se up indusry can conduc boh he basic and developmen sage of he R&D aciviy, while public secor is assumed o only inves in basic research. In fac, he empirical evidence shows ha he developmen sage is he prominen aciviy of he privae research effor, 6 herefore he drasic, ye realisic, assumpion ha public R&D only consiss in basic research programs is inroduced. The universiy s scienific knowledge can be usefully developed by he indusry o creae new commercial valuable innovaive producs. Because public basic ideas are graned of paen proecion, he indusry pays o develop such scienific knowledge. However, in his se up only a successful research firm is assumed o pay for he usefully developed public basic ideas. This assumpion is moivaed by he empirical analyses. Cohen e al. (22) 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, also he high-ech indusries. 7 Therefore, a raional R&D firm gains spillovers from public R&D programs hrough such informal channels. The use of public basic ideas will become eviden only in he momen of a paen applicaion, i.e. only for a successful R&D firm. Once a paen applicaion has deposied by a R&D firm i will have o pay for ha public basic ideas usefully developed for is innovaion. Moreover, he governmen pays an undiffereniaed subsidy o he indusrial R&D effor. I is shown ha boh a higher subsidy o indusrial R&D cos and a lower 4 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, 1999, Ha and Howi, 26). 5 The Science and Engineering Indicaors (SEI, 26) 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. 6 The SEI saes: The federal governmen, esimaed o have found 61,8% of U.S. basic research in 24, 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 26, ch.4 p.13). In addiion, The developmen of new and improved goods, services, and processes is dominaed by indusry, which performed 9.2% of all U.S. developmen in 24. (SEI 26, ch.4 p.13). See also Pavi (21). 7 Cohen e al. (22) 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. 3

4 price paid o develop he paened public basic ideas increase he privae innovaive effor, and he per capia oupu growh rae, while hey reduce he per capia oupu level. Moreover, i is shown ha a lower price paid o develop universiy basic ideas allows a a low subsidy of grealy spur he indusrial innovaive effor and he per capia oupu growh rae. Ye, he subsidy and he price paid o usefully develop public innovaions have some fundamenal differences. The subsidy of he privae R&D cos concerns he cerainy aspec of a R&D process, and i is undiffereniaed beween all he research firms. The price paid for he use of public basic ideas concerns he uncerainy aspec of a R&D process, and i is assumed proporional o he produciviy of he research firms. 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, andjurisprudenial powers of a counry. The subsidy of 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. These resuls have a main policy implicaion. Once IPR are inroduced for public ideas, a differen regime for privae and public innovaions should be inroduced. Paens o public innovaions should be only graned a some radical and very innovaive ideas. In fac, he exisence of IPR for public innovaions generaes a furher cos for he indusry o acquire he licenses from public insiuions. This implies ha a paen design should guaranee a far larger paenabiliy requiremen for public basic ideas han for indusrial innovaions. 8 In fac, a larger paenabiliy requiremen would allow he privae firm o appropriae a higher share of a new produc s marke value. Moreover, his differen regime for he public and privae secor would no resric he echnological ransfer from universiies o indusrial R&D because of he diffuse use of informal channels o access public ideas (see Cohen e al., 22). Finally, hese resuls do no res on he qualiy of universiy research. In fac, he rapid increase in academic paening has provoked new debaes abou he qualiy of hese paens, and abou a indusry-biased universiy research arges induced by he sronger influence of he indusry on scienific research. 9 Recenly, a paper by Cozzi and Galli (27) 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. 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, 24). 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, a lower leading breadh should be graned a public basic innovaions. 9 SeeD EseandPael(27). 4

5 Cozzi and Galli (27) show ha a pro-growh policy consising ino guaranee an inellecual propery proecion for basic half-ideas could no be a he ground of he reforms underaken in he U.S. around he 8s. Moreover, Cozzi and Galli (27) 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 and reinforces Cozzi and Galli s (27) conribuion. The paen-design lieraure, on he oher hand, addresses he quesion of how paen policy for privae innovaions affecs he incenives for indusrial R&D. Recenly, O Donoghue and Zweimuller (24) exend he paen-design lieraure o a general equilibrium 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 universiy scienific knowledge. The paper is organized as follows. Secion 2 ses up he model, secion 3 describes he general equilibrium and he comparaive saics 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 combining a consan inpu, and a coninuum of inermediae goods wih heerogeneous produciviy. In he inermediae secor he firms produce a coninuum of produc lines denoed by N, a a given ime. The inermediae 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. However, a legally imposed disorion render each of hem a local monopoly: his is due o he paen sysem. According o he sandard Schumpeerian approach à la Aghion and Howi (1992 and 1998), new inermediae goods are paened, and each monopoly 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 mass of he inermediae goods is coninuously enlarging hanks o serendipious imiaion as in Howi (2). The R&D secor is composed of boh indusrial (privae firms) and public (universiy) research aciviy. Indusrial R&D consiss ino upgrade he qualiy (or he producion process) of any inermediae produc line (verical innovaion). As said above, a perfecly enforceable paen law allows he privae research firms o gain monopolisic rens for all he effecive duraion of he paen because - as usual in Schumpeerian growh models wih ladder qualiy innovaions - he incumben monopolis can be replaced by he nex innova- 5

6 or along he same produc line. 1 This generaes he Schumpeerian creaive desrucion effec. The exisence of a perfec sock marke channels consumer savings o firms engaged in R&D. Moreover, he governmen employes skilled workers o obain basic knowledge and discoveries. A sochasic share of he sock of basic ideas can be usefully developed by indusry o find a new commercial valuable innovaions and o inroduce new inermediae goods. However, he effec basic ideas produce on he produciviy of privae research firms is heerogeneous beween he produc lines. According o he legislaive acs menioned in he inroducion, academic basic knowledge is graned of inellecual propery righs. 2.1 Basic Framework Le us assume coninuous ime and unbounded horizon. In his economy a mass L > 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 d, wherec is he non negaive consumpion flow of each household. Moreover, each family is endowed wih a uni mass of flow labor ime bearing no disuiliy; r> is he common and consan subjecive rae of ime preference. Populaion growh - i.e. he growh in he number of households - is consan and equal o g L >. The labor marke is perfec and he inelasic supply of labor L is insananeously employed by manufacuring firms and by he R&D secor. Capial markes are assumed o be perfec; he linear insananeous uiliy implies consan real ineres rae always equal o r. Final oupu Y 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 <α<1. x i is he amoun of inermediae good i produced and used as an inpu a a given ime, A i is he produciviy parameer aached a his inermediae good. M is he consan aggregae mass of fixed facor (such as for example, land, minerals, oils, ec.). N [, ) denoes he mass of inermediae produc lines already invened in he economy a dae. Because 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. According o Aghion and Howi (1998), and Howi (1999) we consider he leading-edge echnology, wih an economy-wide leading edge produciviy parameer A max ha exers posiive 1 See Aghion and Howi (1992, 1998), Segersrom (1998), Howi (1999). Cozzi (26) proves ha he sandard Schumpeerian growh models are compaible wih a posiive and finie R&D invesmen by he incumben monopolisic firms. Theanalysisofhispaperis also compaible wih Cozzi s (26) findings. 6

7 R&D spillovers in all inermediae goods. When a new commercial valuable discovery is inroduced along an inermediae produc line i [,N ] (a beer qualiy of an inermediae good is inroduced) he produciviy parameer A i in ha secor jumps o A max. This specificaion incarnaes Aghion and Howi s (1998 ch. 3) and Howi s (1999) iner-secor knowledge spillovers. The echnological fronier A max grows 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 l Ai fi (b ). λ A is a produciviy facor, l Ai = L A N is he per produc line research labor ime, he funcion f i (b ) capures he effec of he per produc line sock of basic knowledge b on he Poisson arrival rae of a new paenable and commercial valuable idea in he produc line i (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 marginal impac of each innovaion on he sock of public knowledge will be σ N,whereσ > 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 Z N λ A l Ai fi (b ) di (2) N Noice ha he sock of basic knowledge accumulaed over ime - and no only he flow of new basic discoveries - affecs he Poisson arrival rae of indusrial innovaions. Moreover, he funcion f i (b ) is assumed o be heerogenous beween he inermediae produc lines, 11 wih f i (b ) b. 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 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 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,wih 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 11 Basic ideas in some produc lines, such as bioechnology, engineering, elecronics, ec., can have an immediae marke applicaion, so ha he spillovers basic ideas produce for he developmen of new markeable producs in such indusry lines can be very high. Insead, basic ideas in ares such as economics, lieraure, anropology, asronomy, ec., can have a far less useful marke applicaion, so ha heir spillovers can be far more low. 12 See Howi (2). In Howi (1999), and Cozzi and Spinesi (25) horizonal innovaion 7

8 imiae β>, hus he aggregae flow of new producs is: Ṅ = βl (3) Sine populaion grows a he consan rae g L, he number of workers per produc line L N converges monoonically o gl β. 2.2 Asse Marke, Inermediae Secor, and Indusrial R&D The indusrial 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.moreover,ar&dfirm incurs a cos for he paened public basic ideas usefully developed, and his cos is here described as a fracion of he commercial value of a new inermediae produc. The fracion of he marke value respecively appropriaed by a R&D firm and by a 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. 13 be he expeced sock marke value of a new inermediae produc appropriaed by a privae R&D firm, and le V b be he expeced sock marke value of a new inermediae produc appropriaed Le V p 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 i V b 1 φi + V b (4) The soluion o his problem gives V p = φ i V,andV b =(1 φ i ) V. The parameer φ i (, 1) represens he insiuional se-up in which he bargaining process akes place. φ i indicaes ha a privae R&D firm pays o use an array of basic ideas which are graned of some form of IPR. The exisence of laws such as he Bayh- Dole Ac - and of oher legislaive arrangemens - heavily 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. 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. 8

9 conribue o deermine he value of he parameer φ i in he economy. 14 The parameer φ i is heerogeneous beween he produc lines. This heerogeneiy is explained because of he heerogeneous spillovers beween he produc lines. In fac, when basic ideas generae a high spillover on he produc line i - i.e. here is a high value for funcion f i (b ) -eachfirm argeing he indusry line i is willing o pay a higher price o develop such paened basic ideas, herefore φ i will be correspondingly lower. This implies ha when he same basic idea can be usefully developed by more han one produc line, he governmen will license ha paened idea a he produc line ha gain a higher spillover, also because i has a higher Poisson arrival rae of innovaions and a lower average inerarrival ime beween wo valuable ideas. Moreover, because of he symmery of he privae R&D firms wihin a produc line, each firm in any line i is willing o pay exacly he same price of any oher firminhesameinermediaeline. 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 produc line i wih relaive produciviy a a dae is rewrien as: w 1 ³ ω µ α 2 a x i = (5) a ω where x ω i a is a labor demand funcion for he manufacuring firm. The labor force employed in he inermediae secor negaively depends on he produciviy-adjused real wage. The R&D is a perfecly compeiive secor, wih free enry and exi. Each verical R&D firm argeing an inermediae produc i chooses is R&D inensiy o maximize φ i V λ A l Aj fi (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 i of he expeced sock marke value of a paenable and commercial valuable idea in he produc line i. The soluion o he above problem is φ i V λ A fi (b )= (1 s) w. Noice ha, he per produc line basic sock knowledge b is aken as given by each individual and firm. Because each R&D firm can inves in any produc line, he same firs order condiion for a maximum profi mushold along any produc line k 6= i, haisφ k V λ A fk (b )=(1 s) w. 14 In his seing, he ighness, he widh and he ease of he inellecual propery righs regime - as measured by φ i - has sudied. A low value of φ i canindicaehaiisexremely 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. 9

10 In equilibrium, each R&D firm mus be indifferen o inves in any inermediae produc line. The indusry lines ha benefi from a higher spillovers - i.e. have a higher f i (b) - will pay a higher price o use he paened basic ideas and herefore hey will appropriae of a lower share φ i of he expeced sock marke value V. This implies he following no-arbirage equaion beween he exising indusry lines: φ i V λ A fi (b )=φ k V λ A fk (b ) (6) ha implies f i (b )= f k (b ) φ i φ. k 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 In he mulisecor economy he R&D arbirage condiion is similar o Aghion-Howi (1998, ch.3, Appendix): (1 s) φ i λ A fi (b ) w = A max = A max Z Z 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 gaτ dτ (7) On he lef hand side of eq. (7) he probabiliy of appropriaing he new innovaion by he auhor has been considered. 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 indusrial R&D and in manufacuring. Le us G (θ) be he disribuion of he basic research abiliy θ, wihθ aking value on, θ,and θ <1. The usual properies G (θ) >, G () =, G θ =1 apply. Since each worker mus be indifferen beween manufacuring and verical research aciviy, i will be w = φ i λa f i(b ) (1 s) V. The addiional no-arbirage condiion beween improving/manufacuring and basic research effor can be wrien as: " w = φ iλ A fi (b ) V = λ B ϕ E (1 s) ³ E where he funcion ϕ A i A max 1 µ # 1 Ai A max θ w = λ B θ w (8) = ϕ (1+σ) represens he spillovers from verical innovaion o basic research produciviy, and λ B ϕ (1 + σ) λ B 15 As proven by Cozzi (25), Howi s (1999) model admis a coninuum of symmeric balanced growh pahs. 1

11 is a produciviy parameer of each public researcher. 16 On he lef hand side of eq. (8) w indicaes he wage of a worker in he indusrial secor - manufacuring and R&D - which in equilibrium mus be equal o he expeced reurns of improving he qualiy of an inermediae produc φ i λ A f i (b ) (1 s) V. The righ hand side of he las par of eq. (8) indicaes he expeced flows reurn o be employed in basic research. Because θ, θ,wih θ 1, he gross salary paid by he public secor is lower han he wage paid by he indusrial R&D laboraory. However, he produciviy erm λ B allows o increase he perceived salary of a public researcher. 17 Le us denoe θ he hreshold value of he basic research abiliy ha saisfies equaliy (8): θ 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 inermediae secor. The higher he basic research alen an individual is endowed wih, he higher he gain o be employed in basic research programs. The no-arbirage equaion (8) deermines he hreshold abiliy value θ = 1, (9) λ B which is consan along he BGP. 18 Each individual endowed of a research abiliy θ>θ will find i profiable o be employed in basic research programs. Hence, in such an economy, for θ>θ, [1 G (θ )] L individuals will choose o be employed in basic research programs. Insead, he individuals endowed wih an abiliy θ θ,haisg(θ ) 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. This in urn changes he populaion employed in basic 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 programs o accumulae basic knowledge P according o he following dynamic law 16 ϕ ( ) can be any posiive funcion of he average relaive produciviy E Ai A max = (1 + σ) See Aghion e. al (25), and he Science and Engineering Indicaors (24, 26) for he empirical evidence of an average higher wage gained in he privae R&D laboraories han in nonprofi/governmen R&D laboraories. The parameer λ B can also posiively depend on public expendiures. 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, a 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 (see D Ese and Pael, 27). 18 Resricion λ 1 < θ <1 is assumed o hold. B 11

12 " Z # θ P = λ B θdg (θ) L = λ B m (θ ) L (1) θ h R i θ where m (θ ) L θ θdg (θ) L is he average condiioned cumulaed basic research effor, λ B is he produciviy of each researcher engaged in basic research programs. Eq. (1) implies ha he sock of basic knowledge P grows a he same rae as he populaion growh rae g L. 2.4 Labor 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) φ i λ A fi (b ) = α x (ω ) r + ga σ + α g (11) A Solving he above equaion for x (ω), he labor force employed in he producion of he op qualiy inermediae good is obained: µ (1 s) x (ω )= r + g A φ i λ A fi (b ) σ + α α 1 α g A (12) 1 α from which, by invering eq. (12), i is possible o deermine he produciviyadjused real wage ω. The labor marke clearing condiion for manufacuring and verical innovaion is: Z 1 G (θ ) L = N l A + N x (ω/a) h (a) da = N l A + N x (ω ) 1+ σ (13) 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 cumulaive disribuion funcion H(a). The labor marke clearing condiion for basic research programs is: [1 G (θ )] L = L B (14) which is a consan fracion of he populaion because he hreshold abiliy parameer θ is consan along he BGP. 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): 12

13 R Y = A max 1 N a x (ω/a)α h (a) da = ³ α da = NAmax = A max N R 1 1 σ a 1 σ α 2 a ω α α 2 ω (1+ ) σ (15) Noice ha, in he ligh of eq.s (15) and (1), he produciviy-adjused fixed facor ren is: re A max =() Y MA max =() N ³ α 2 α ω ³ 1+ σ (16) 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 (1), along he BGP i is obained: p P N = m (θ ) λ B (17) β From eq. (2) he produciviy growh rae becomes (see he Appendix A, poin 2): g A = Ȧmax A max = σ Z N λ A l Ai fi (b) di = σλ A l A F (b, Θ) (18) N Therefore, he labor demand in eq. (12) for he op qualiy inermediae good becomes: (1 s) x (ω) = φ i λ A fi (b) µ r + g A σ + α α 1 α g A 1 α (19) Le us consider boh eq.s (19) and (13), along he raional expecaion equilibrium, a posiive and finie value for he per produc line indusrial research effor exiss: la = 1+ L N G (θ ) r (1 s) φ i λ A fi (b)(1+ ) α σ (1 s) φ i λ A fi(b)(1+ ) α σ ³ 1 σ + α σλ A F ³ b, Θ (2) 13

14 From eq. (2), in order o have a posiive R&D effor he following condiion mus hold along he BGP (his condiion is similar o condiion V in Howi, 1999 and condiion A in Cozzi and Spinesi, 26) The per capia oupu is: g L > β r (1 s) G (θ ) φ i λ A fi (b) Y L = ³ N L Amax ³ 1+ σ α 2 α ω = ³ 1+ σ ³ β g L A max α 1 α ³ 1+ σ α 2 α ω (C) (21) where eq. (15) 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 l A F (b, Θ) (22) In he ligh of eq.s from (17) o (22) he following can be saed: Proposiion 1 Along he raional expecaion BGP, a consan fracion of populaion is employed in he inermediae secor, in he indusrial and public research secor. Along he BGP, an increase eiher in he parameer φ i proporional in all produc lines i 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 Proposiion 1 compares he IPR policy design for boh indusrial and public R&D wih an undiffereniaed subsidy of he indusrial research cos. I is found ha he inellecual appropriaion of a new commercial valuable ideas by he indusrial firms - as summarized by he parameer φ i - and he subsidy of he indusrial R&D cos have he same qualiaive effec on he growh performance of a counry. Ye, some fundamenal differences beween hese wo elemens exis. The policy design of he paen sysem for boh indusrial and public 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 and he environmen in which boh privae and public R&D operae. The subsidy o privae R&D does no shape he insiuional se-up of he economy as he policy design of he inellecual propery righs does, i only direcly affecs he privae R&D coss, and herefore he cerainy aspec of a R&D process. Moreover, he subsidy can be also managed in shor ime horizon. Given hese fundamenal differences beween hese wo elemens, heir effec on he per capia oupu growh rae and level can be differen in magniude, as he following saes: 14

15 Proposiion 2 Whenever condiion (C1) holds along he BGP - i.e. s 1 φ min - 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 value of he parameer φ i in each produc line i [,N ]. Proof. See Appendix C Condiion (C1) implies ha a marginal increase in he subsidy grealy spurs he privae research effor along all he produc lines, and he per capia oupu growh rae. Ye, a marginal increase in he subsidy o privae R&D firms magnifies he rade off beween he per capia oupu growh rae and he per capia oupu level. Noice ha he higher φ min he lower he hreshold subsidy ha grealy affecs he per capia oupu growh rae, and he per capia oupu level. I seems noeworhy o recall ha φ i is a measure of he srengh, ighness and ease of IPR graned o public innovaions. Therefore, proposiion 2 has a main policy implicaion. Once some form of IPR are inroduced for public ideas, wo differen regimes of IPR should be provided for public and privae innovaions. In his framework he differen regime concerns a paen proecion agains fuure innovaors, and herefore i refers o boh paenabiliy requiremen and o paen breadh. 19 O Donoghue and Zweimuller (24) show ha boh a larger paenabiliy requiremen and leading breadh beer off he growh performance of a counry. However, in his seing paens are also graned o public innovaions, and hisrepresensafurhercosforhe indusrial R&D firms. Therefore, a larger paenabiliy requiremen for a public basic idea would reduce he indusrial R&D cos and would beer off he growh performance of a counry. In fac, once paens are graned o only very innovaive and fundamenal public basic ideas, condiion (C1) more easily holds because of a higher value of φ min. This in urn implies ha also a low subsidy o indusrial R&D can grealy spur he innovaive effor of he economy and is per capia oupu growh rae. 4 Conclusions The exisence of srong knowledge links and ransmission beween indusry and academy is widely documened. In paricular, he exisence of large and posiive scienific knowledge spillovers from universiy o indusry is also well documened. Moreover, since he 8s he U.S. and hen oher OECD counries inroduced some form of IPR also for universiy s ideas wih he aim o reinforce he links beween academy and indusry. 19 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 could be considered. In his case, he resuls sugges ha 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 lower leading breadh should be se for public basic innovaions. 15

16 This paper invesigaes on he macroeconomic implicaions of an insiuionally imposed IPR regime for boh academic and indusrial ideas. To his aim a Schumpeerian growh model à la Aghion and Howi (1992, 1998) and à la Howi (1999, 2) is adoped. In he R&D secor, public research programs generae basic ideas ha do no have an immediae commercial value and applicaion. The indusrial R&D firms develops useful academic ideas o inroduce new valuable produc innovaions on he marke. However, a successful R&D firm only appropriaes a fracion of he commercial value of a new paened produc because i pays for he licenses of public basic ideas ha have been usefully developed. Moreover, privae R&D firms obain a subsidy for heir research coss. This paper shows ha he inellecual propery righs and he subsidy o privae R&D coss are wo alernaive ways o finance privae research effor. In fac, boh a higher fracion of a paened produc s marke value appropriaed by a firm and a higher subsidy o R&D cos spur he indusrial innovaive 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. Moreover, a higher fracion of a paened produc s marke value appropriaed by he indusrial firm allows a a low subsidy o grealy spur he innovaive effor and he per capia oupu growh rae. This resul seems remarkable because he policy design of he inellecual propery righs srongly shapes he insiuional se-up of he economy, and i concerns he uncerainy aspec of a R&D process. While he subsidy o indusrial R&D cos does no have an insiuional weigh as he inellecual propery righs has, and i concerns he cerainy aspec of a R&D process. The resuls of he paper generae a remarkable policy implicaion. This paper suggess he inroducion of a differen regime of IPR for indusrial and public innovaions. In fac, alhough paens graned o basic academic ideas can spur he echnological ransfer from universiies o indusry, hey also represen a cos for he privae firms. According o hese consideraions policy should provide IPR o only fundamenal and radical public ideas in order o limi he cos incurred by privae firm o benefi from he use of basic discoveries. 16

17 Appendix A 1. In his par he Poisson arrival rae of verical innovaions has obained. Le us consider he per produc line sock of basic ideas a a given ime, p P N. In his framework only a fracion of academic basic ideas can be usefully developed by indusry o find new commercial valuable inermediae producs. This fracion is assumed o be a coninuous random variable denoed by b, b,wih b m(θ ) λ B β, and cumulaive disribuion funcion (cdf) Ω ( ) common for all i [,N ]. Privae R&D firms gain a posiive spillovers from basic ideas ha have commercial valuable applicaions. These spillovers are measured hrough he funcion f i ( ) in he produc line i. The spillovers funcions f i ( ) for each i [,N ] are assumed bounded above and consans over ime. Therefore he expeced value of spillovers from commercial valuable basic ideas in he produc line i is: f i (b ) E [f i (b )] = Z b f i (b ) dω (b ) (A1) Therefore he expeced Poisson arrival rae of verical innovaion along a produc line i is: R b λ Al Ai f i (b ) dω (b ) di = R b = λ A l Ai f (A2) i (b ) dω (b )=λ A l Ai fi (b ) 2. The no-arbirage equaion in verical R&D beween he produc lines imply f i (b) = φ k φ fk (b). Moreover, a a given ime in he economy here i exis a coninuum N of produc lines. Therefore he echnological fronier growh rae along he symmeric BGP can be rewrien as: R g A = σ N R N λ A l Ai fi (b) di = σ N φ N λ A l k A φ fk (b) dk = i = σ (A3) N λ A l A F (b, Θ) N = σλ A l A F (b, Θ) where F (b, Θ) summarizes he average per produc line spillovers. This funcion is bounded above; Θ > is a proporional facor ha also summarizes he shares φ k for each k. Therefore, all he heerogeneiies in f k (b) and in φ k are capured hrough he funcion F (b, Θ) which is consan over ime because b, f k (b), andφ k are all consan along he BGP. Therefore, along he BGP he echnological fronier growh rae is consan. Moreover, because each average spillovers funcion f i (b) is increasing in b, also F (b, Θ) is increasing in b. Q.E.D. 3. By following he same seps as in Aghion and Howi (1998), he profi flow of any monopolisic firm ha manufacures an inermediae produc i wih produciviy A i is π i = A max 1 α α ω µ α 2 ω 1 1 a = A max π (ω) a 1 where ω w A is he produciviy-adjused real wage, π (ω) is he profi max flow of he inermediae good wih he maximum produciviy parameer A max. 17

18 The expeced sock marke value of he las successful R&D firm ha has produciviy A max is described by he eq. (5) in he ex. The expeced sock marke value of an inermediae produc i wih absolue produciviy A i and relaive produciviy A i A is V max i = V a 1. Therefore, he cumulaive expeced sock marke value of all manufacuring monopolies a a given ime is: Z N Z 1 Z 1 V i di = N V i dh(a) =N V N A max dh(a) = a 1 V 1+ σ (A3) Appendix B The firs par of his Appendix proves he effec of a higher inellecual appropriaion parameer φ i for each produc line on he economic performance of a counry, φ i (, 1) is assumed. The marginal change in he appropriaion parameer is assumed o happen proporionally in all he produc lines, so ha he raio φ i φ k is consan. This proporional change in all he appropriaion parameer φ i has inerpreed as a lower srengh of IPR for public basic ideas. By calculaing a marginal change in all parameers φ i, he change has denoed wih a generic parameer φ. The second par analyses he effec of a higher R&D subsidy. 1. Le us consider he eq. (2). By simply differeniaion along he BGP he following is obained: = 2 ½ L l A r(1 s) α λ A f i (b)(1+ ) σ φ [φ i λ A fi (b)(1+ )] σ 2 N G (θ (1 s) ) r φ i λ A fi (b)(1+ ) α σ (1 s) ( α 1 σ + )σλ α F (b,θ) A φ φ i λ A fi (b)(1+ ) (1 s) σ ( α 1 σ + )σλ α A F (b,θ)λ A fi (b)(1+ ) σ [φ i λ A fi(b)(1+ )] σ 2 (B1) ³ (1 s) where 1+ φ i λ A fi(b)(1+ ) α 1 σ σ + α σλ A F (b, Θ) >, and condiion (C) holds. Because he spillovers are assumed consan in his analysis, hen F( b,θ) φ = N φ k φi φ fk (b)dk =, because we impose a proporional marginal change in each appropriaion parameer φ i such ha φ k φ remains consan. In i fac: F (b,θ) φ R 1 N φ i = N f k (b) dk = = 1 φ i h R N φ k φi fk (b)dk φ = 1 N φi f k (b) dk 1 φ i R N φ k fk (b) dk φ k fk (b)dk φ i = 1 φ i h R N Q.E.D. In eq. (B1) his variaion is simply denoed wih Θ φ i = 1 φ 2 i R N φ k fk (b) dk + f k (b) dk R N i f k (b) dk = because Θ > summarizes all he raios φ k φ in he inegral R N φ k i φ fk (b) dk. Thisimplieshaeq.(B1) i is sricly posiive, i.e. l A φ >. Therefore, along he BGP, a higher inellecual appropriaion parameer φ increases he per produc line privae R&D effor. ¾ 18

19 In order o deermine he effecs of a higher inellecual appropriaion parameer φ on he marke demand for any exising inermediae good, we use he labor marke clearing condiion: N x (ω) L = G (θ ) L +[1 G (θ )] L = N l A + 1+ σ + Nl B (B2) where l B = L B N =[1 G (θ )] L N denoes he per produc line basic research effor. From eq. (8) a consan hreshold abiliy parameer θ is obained. Therefore - along he new BGP wih a higher inellecual appropriaion parameer φ - he per produc line basic research effor [1 G (θ )] L N is consan and equal o [1 G (θ )] g L β. Moreover, eq. (B1) proves ha, along he new BGP, he per produc line verical research effor is higher. Therefore, eq. (B2) necessarily implies a lower marke demand x ω a for each exising inermediae good. Finally, from eq. (21), i immediaely follows ha a higher appropriaion parameer φ deermines a lower per capia oupu level. Q.E.D. The posiive effec of a change in he appropriaion parameer φ on he per capia oupu growh rae is easily proven: g Y/L φ = σλ l A A φ F (b, Θ) > (B3) where he inequaliy follows from eq. (B1). Q.E.D. 2. This par analyses he effec of a change in he subsidy o privae research effor s on he economic performance of he economy; s (, 1) is assumed. From eq. (2) he following is obained: l A s = 2 ½ r α φ i λ A fi(b)(1+ ) L σ ( α 1 σ + )σλ α A F (b,θ) φ i λ A fi (b)(1+ ) σ N G (θ ) r ¾ > (1 s) φ i λ A fi(b)(1+ ) α σ (B4) Therefore, along he BGP a posiive relaionship beween he subsidy o privae research effor s and he per produc line privae R&D labor ime l A is proven. Q.E.D. In order o deermine he effecs of a higher subsidy s on he marke demand for any exising inermediae good, he labor marke clearing condiion (B2) is used. As proven above, along he BGP, he per produc line basic research effor is consan and equal o [1 G (θ )] g L β. Moreover, eq. (B4) proves ha - along he new BGP wih a higher subsidy o privae R&D firms - he per produc line verical research effor is higher. Therefore, eq. (B2) necessarily implies a lower marke demand x ω a for each exising inermediae good. Finally, from eq. (21), i immediaely follows ha a higher subsidy s deermines a lower per capia oupu level. Q.E.D. The posiive effec of a change in he subsidy o privae research effor s on he per capia oupu growh rae is easily proven: 19

20 g Y/L l A = σλ A s φ F (b, Θ) > (B5) where he inequaliy follows from eq. (B4). Q.E.D. Appendix C This Appendix compares he effec of a proporional marginal change in he appropriaion parameer φ i in all produc lines i wih he effec of a marginal change in he subsidy s. Along a new BGP wih a larger value of eiher φ i or s deermines a higher per produc line privae innovaion effor and a higher per capia oupu growh rae. In order o compare he magniude of hese effecs i suffices o consider he eq.s (B1) and (B4). Whenever he following condiion is saisfied l A s l A φ,anincreaseinhesubsidygeneraes he same economic effecs as an increase in he appropriaion parameer, bu he former are higher in magniude. Le us define φ min min {φ i } N i=. Therefore φ min is he produc line ha appropriaes he lowes marke value among he exising produc lines. From eq.s (B1) and (B4), i immediaely follows ha l A s L + N G (θ ) r h i ½ 1 1 s φ i ha is always rue whenever (1 s) φ i λ A fi (b)(1+ ) α σ r α φ i λ A fi(b)(1+ ) + σ l A φ α ( σ 1 + )σλ α A F (b,θ) φ i λ A fi (b)(1+ ) σ if and only if ¾ Q.E.D. s 1 φ min (C1) References [1] Aghion, P., and Howi, P. (1992) A Model of Growh Through Creaive Desrucion. Economerica 6, [2] Aghion, P. and Howi, P. (1998) Endogenous Growh Theory. Cambridge: MIT Press. [3] Cohen, W.M., Nelson, R.R., Walsh, J.P. (22) Links and Impacs: The Influence of Public Research on Indusrial R&D. Managemen Science 48, [4] Arrow, K.J. (1962) The economic Implicaions of Learning by Doing. Review of Economic Sudies 29, [5] Cozzi, G. (25) Self-fulfilling Prophecies and he Composiion of Innovaion. European Economic Review 39,

21 [6] Cozzi, G., and Galli, S. (27) Changing he Research Paening Regime: A Schumpeerian Explanaion. Prin 25 Working Paper Series. [7] David P. A., Bronwyn H. Hall, Toole A. A. (2) Is public R&D a complemen or subsiue for privae R&D? A review of he economeric evidence Research Policy 29, [8] D Ese P., Pael, P. (27) Universiy indusry linkages in he UK: Wha are he facors underlying he variey of ineracions wih indusry? Research Policy 36, [9] Jaffe, A.B., Trajenberg, M., Flows of knowledge from [1] Grossman, G.M., and Helpman, E. (1991) Innovaion and Growh in he Global Economy. Cambridge, MA: MIT Press. [11] Howi, P. (1999) Seady Endogenous Growh wih Populaion and R&D Inpus Growing. Journal of Poliical Economy, 17: [12] Howi, P. (2) Endogenous growh and Cross Counry Income Differences. American Economic Review, 9: [13] Jones, C. (1995) R&D-Based Models of Economic Growh. Journal of Poliical Economy, 13: [14] Jones C. (25) Growh and Ideas, in Aghion P. and Durlauf S. N. eds. Handbook of Economic Growh, Norh-Holland. [15] McMillan S. G., Narin F., Deeds D. L. (2) An Analysis of he Criical Role of Public Science in Innovaion: he case of Bioechnology. Research Policy 29, 1-8. [16] Meron, R.K. (1973) The Sociology of Science: Theoreical and empirical Invesigaions. Universiy of Chicago Press, Chicago. [17] Mokyr, J., (22). The Gifs of Ahena: Hisorical Origins of he Knowledge Economy. Princeon Universiy Press, Princeon. [18] Narin F., Hamilon K. S., Olivasro D. (1997) The Increasing Linkage Beween U.S. Technology and Public Science. Research Policy 26, [19] Nelson, R.R., (24). The marke economy, and he scienific commons. Research Policy 33 (3), [2] O Donoghue, T. (1998) A paenabiliy requiremen for sequenial innovaion. RAND Journal of Economics 29, [21] OECD (22) Benchmarking Science-Indusry Relaionship. OECD, Paris. 21