Fundamental R&D Spillovers and the Internationalization of a Firm s Research Activities. Bernard Franck* and. Robert F. Owen** February 2003

Transcription

1 Fundamental R&D Spllovers and the Internatonalzaton of a Frm s Research Actvtes by Bernard Franck* and Robert F. Owen** February 3 Revsed Verson: Comments are most welcome. JEL classfcaton codes: F15, F3, O3 Key words: fundamental R&D, spllovers, nternatonal locaton, economc ntegraton Acknowledgement: The authors wsh to thank Olver Gaussens and Davd Ulph for a number of nsghtful suggestons. Fnancal support from the Center for Natonal Scentfc Research (CNRS n France s also apprecated. Earler versons of ths paper have been presented at a sesson of the North Amercan Economc and Fnance Assocaton Sesson (NAEFA at the Alled Socal Scence Assocaton Meetngs n Atlanta, January 4-6,, the 9 th European Assocaton for Research n Industral Economcs (EARIE Conference, Madrd, Span, September 5-8,, the French Internatonal Economcs Conference ( GDR at the Unversty of Bordeau, June, the Unversty of Bonn, Unversty of Kel, Unversty of Nantes and the Natonal Unversty of Sngapore. The fnal stage of ths research was undertaken whle the second of the two authors was a Vstng Professor at Yale Unversty. *Faculty of Economcs and Busness Admnstraton, Unversty of Caen and GEMMA (CNRS, Esplanade de la Pa, 143 Caen Cede, France. Telephone numbers: (drect and Fa number: E-mal address: franck@econ.uncaen.fr **LEN-C3E Research Center, Faculty of Economcs and Busness Admnstraton, Unversty of Nantes, Chemn de la Censve du Tertre, B. P. 531, 443 Nantes Cede 3, Telephone Numbers: (drect and Fa number: E-mal address: RobertOwen@compuserve.com 1

2 Fundamental R&D Spllovers and the Internatonalzaton of a Frm s Research Actvtes Abstract A conceptual framework s proposed for analyzng how dfferences n natonal R&D stocks can mpact on a frm s decson to nternatonalze ts R&D actvtes. A central fndng s that the ntegraton of product markets can generate an added ncentve to undertake R&D abroad. A three-stage analyss of a non-cooperatve game s proposed, whch entals cost-reducng process nnovaton n an nternatonal model of duopoly. Each frm s technologcal effcency depends not only on ts nvestment n appled R&D, but also on ts absorpton of domestc and foregn fundamental R&D, as well as the etent to whch the latter are substtutes or complements. In a frst stage, a frm s absorpton of foregn fundamental R&D can be mpacted by a decson to localze R&D actvtes abroad. The nterrelaton between ths decson and ntal producton costs s also eplored. JEL classfcaton codes: F15, F3, O3 Key words: fundamental R&D, spllovers, nternatonal locaton, economc ntegraton

3 I. Introducton It has long been recognzed that research and development, at the level of both countres and frms, can play a crtcal role n eplanng ther economc performance as reflected, for eample, by trade and nvestment shares, as well as endogenous economc growth. Increasng attenton has also been gven to the potental for R&D spllovers mpactng on dverse dmensons of natonal and nternatonal economc performance. Branstetter (1998 and Mohnen (1999 have offered recent surveys of the latter lterature, whle Grlches (199, Nadr (1993, and Mohnen (1996 have consdered the more general role of R&D eternaltes. Yet, the etent to whch the localzaton of R&D actvtes has become globalzed remans a subect of relatvely less attenton for whch there has been lttle formal modelng. 1 Indeed, the relatve lack of attenton to the determnants of knowledge flows contrasts wth the vast lterature relatng to the nternatonal moblty of products, servces and factors of producton. For the most part, estng nvestgatons of the globalzaton of R&D actvtes have been confned to emprcal and polcy analyss often nvolvng case studes and frm surveys. Certan of these studes hghlght the role that dstnctve natonal nnovatve envronments can have n attractng R&D-related foregn drect nvestment. In partcular, Florda (1997 found that a key consderaton accountng for the establshment of foregn-afflated R&D laboratores n the U.S was an obectve to have access to scentfc and techncal 1 However, Sanna-Randacco and Veugelers ( have recently offered a formulaton of the trade-offs that a multnatonal enterprse faces when envsagng the decentralzaton to foregn subsdares of certan R&D actvtes tradtonally undertaken by the parent frm. 3

4 human captal, whle Granstrand (1999 emphaszed the ecellence of Amercan unverstes as a drvng force attractng Japanese R&D. Clearly, f the nternatonalzaton of R&D actvtes enhances frms technologcal compettveness, the nterrelaton between R&D and ndustral performance s rendered nherently more comple. Tradtonally, the lterature on multnatonal enterprses has hghlghted how ntangble assets due to dstnctve technologcal nnovatons n home countres can eplan the compensatng advantage of corporatons n foregn markets. 3 Yet, to the etent that the localzaton of frms R&D actvtes becomes nternatonalzed, there are apparent measurement ssues. Ths suggests potental methodologcal lmtatons n studes of R&D productvty and the determnants of foregn drect nvestment, whch have been largely relant on natonal R&D statstcs. 4 Furthermore, estng emprcal analyss of nternatonal R&D spllovers, such as those proposed by Coe and Helpman (1995, as well as by Coe, Helpman and Hoffmaster (1997, has not made suffcently eplct ether the mcroeconomc underpnnngs of the analyss, nor the structural mechansms by whch alternatve sources of fundamental and appled R&D affect nternatonal economc performance. Presumably reduced form econometrc estmates of technologcal spllovers are senstve to the underlyng specfcatons for such structural mechansms. Representatve other studes on the nternatonalzaton of R&D nclude the contrbutons by Brockhoff (1998, Grandstrand (1999, Kuemerle (1997, Lefebvre and Madeuf (1999, 1, Nos (1999, Patel (1997, as well as Serapo and Dalton ( The etensve lterature on multnatonal corporatons s synthetcally dscussed by Caves ( See, for eample, the studes by Crepon, Duquet, and Maresse (1998, Grlches (199, Grlches and Maresse (199, Maresse (1994 and Mansfeld (1994 relatng to productvty and R&D. The survey of emprcal studes offered by Caves (1996 underscores the role of technologcal advantages n home countres as maor determnants of foregn drect nvestment. 4

5 The obectve of the present research s to offer a conceptual framework for understandng the condtons under whch a frm wll be prompted to localze certan R&D actvtes abroad. A central concern s wth economc ntegraton n goods markets as a factor, whch can eplan the globalzaton of R&D. Ths ssue of the nterrelaton between product market ntegraton and the nternatonalzaton of frms R&D actvtes appears to have been largely neglected n estng analytcal research. Indeed, one characterzaton of the state of estng research s offered by Globerman (1997, who suggested that t s less clear how ncreased nternatonal economc ntegraton wll affect ncentves to decentralze R&D actvtes geographcally, and the relevant lterature s rather confusng on ths ssue. (p. 15 As dscussed n more detal n the net secton, a varety of factors can account for the globalzaton of both fundamental and appled R&D. Wth regard to the former, there have been revolutonary decreases n nternatonal transactons costs resultng from new nformaton and other technologes. In ths paper, however, the focus s on globalzaton of R&D va corporatons decsons to localze nnovatve actvtes abroad. Both demand-sde and supply-sde factors can account for the ncreased pressures for the globalzaton of frms R&D actvtes. The former nclude the need to adopt appled R&D to the dstnctve preferences of consumers n dfferent markets. 5 Whle recognzng the eventual role of such demand-sde factors, the focus n ths research wll be on the role of a specfc supply-sde factor n nfluencng frms decsons to localze 5 Gaussens ( has offered an analyss of certan demand-sde factors n drvng frms to localze R&D actvtes abroad, so as to attract customers and, thereby, mantan ther nternatonal compettveness. 5

6 R&D abroad. 6 In partcular, the concern s wth a need to acqure more advanced and/or complementary forms of fundamental R&D, whch are natonally dstnctve. The organzaton of the rest of ths paper s as follows. The net secton starts by revewng a number of heurstc emprcal ssues relatng to the characterstcs of technologcal nnovaton, along wth ts creaton and dffuson. Ths then offers a pont of departure for a more formalzed framework, whch s proposed for analyzng ssues of how dfferences n natonal stocks of fundamental R&D can mpact on the nternatonal locaton of a frm s R&D actvtes. The proposed analyss entals a three-stage analyss of a strategc game nvolvng a duopoly model of cost-reducng process nnovaton. A frm s technologcal effcency s understood to depend not only on ts nvestment n appled R&D, but also on ts absorpton of domestc and foregn fundamental R&D. In ths paper s thrd secton an analyss of a more specfc formulaton of the model leads to a seres of central analytc propostons regardng the condtons under whch a frm wll localze ts R&D actvtes abroad. More specfcally, the analyss eplores the nterrelaton between the decson to nternatonalze R&D, the degree of nternatonal market segmentaton, and frms relatve ntal compettve postons n terms of ther producton costs. The central fndngs are shown to be robust to alternatve specfcatons regardng whether natonal stocks of fundamental R&D are substtutes or complements. In a concludng secton the prncpal contrbutons of ths research are summarzed, whle a number of concevable etensons of the analyss are also dentfed. 6 The dstncton made here between demand and supply-sde factors s analogous to that suggested by Kuemmerle (1997. In partcular, he dentfed two prmary obectves for classfyng new R&D stes abroad: home-base-augmentng stes and home-base-eplotng stes. He contended that the former were desgned to tap knowledge from compettors and unverstes around the globe, whereas the latter were amed to support manufacturng facltes n foregn countres or to adapt standard products to the demand there (p. 6. 6

7 II. General Analytc Framework A. Introducton The pont of departure for our analyss s a certan number of salent heurstc observatons regardng the nature of R&D. These motvate the prncpal modelng assumptons that wll be subsequently nvoked. Frst, t can be noted that both fundamental and appled R&D have been hstorcally characterzed by a hgh degree of concentraton and locatonal specfcty n frms countres of orgn. Second, the globalzaton of frms R&D actvtes appears, n general, to have developed much more slowly than has been the case for other actvtes, such as those related to producton and marketng. Taken together, these observatons pont to a potental natonal specfcty of R&D. Nonetheless, t needs to be recognzed that the etent to whch R&D has assumed global dmensons depends on the specfc categores of nnovatve actvty. Notably, t s potentally mportant to dstngush between fundamental and appled R&D, as well as between product and process nnovaton. Government sponsored R&D, whch can ental unverstes, publc research nsttutes, and ont ventures between publc nsttutons and ndustry, s undoubtedly a prncpal source of fundamental R&D. There are marked nternatonal dspartes n both the levels and nature of government sponsored R&D. To the etent that these dstnctve characterstcs generate a dffuson of knowledge, whch assumes geographcal dmensons, they can be vewed as gvng rse to natonal stocks of fundamental R&D. Nonetheless, such stocks may have varyng degrees of comparablty 7

8 across countres. When such natonal stocks of fundamental R&D ental characterstcs, whch are substtutes, certan countres may assume technologcally domnant postons. Fundamental R&D can be consdered as consttutng a form of nternatonal sem-publc good, whereby certan foregn frms may be ecluded from fully beneftng from technologcal spllover effects generated from other countres stocks. In partcular, the transfer of fundamental R&D from a country s publc sector to frms nvolves nherent access and transacton costs, whch may be termed learnng costs. Hence, t can be contended that optmal absorpton of fundamental R&D by the prvate sector s enhanced by geographc promty to natonal publc-sector sources of fundamental R&D and nvolves prvate sector nvestment costs. 7 Alternatvely, fundamental R&D, arsng n a gven country, can be consdered to generate postve knowledge eternaltes, whch spllover to the prvate sector both natonally and nternatonally. It s a reasonable presumpton that such spllover effects are heghtened by frms localzng R&D actvtes (labs n a gven source country. 8 Indeed, the acquston of fundamental R&D can be regarded as a necessary condton defnng the capacty of frms to create new products, processes and servces. Thus, appled R&D may be understood to ental the converson at the frm level of basc knowledge nto process and product mprovement. In sum, at an ntal level of smplfcaton, frms can 7 The process of transferrng fundamental R&D can be mpacted by government technology polces, whch am at promotng ts dffuson to the prvate sector. A clear eample was the US government s transfer of nternet technology, whch had arsen from research sponsored by the Department of Defense. 8 Natonal and nternatonal R&D spllovers can arse through the dssemnaton of fundamental knowledge n the form of scentfc presentatons and publcatons. Such knowledge may be dffused asymmetrcally across countres due to dfferences n educatonal and research envronments, as well as governments wllngness to share propretary knowledge nternatonally. In addton, fundamental R&D spllovers undoubtedly capture certan aspects of human captal markets for scentsts and engneers. In partcular, they can arse through dfferent degrees of labor market moblty, as well as through natonal dspartes n the qualty of scentfc tranng. Together these consderatons suggest a natonal specfcty of fundamental knowledge. 8

9 be vewed as prncpally undertakng two dstnct R&D tasks: absorbng fundamental R&D and nvestment n appled R&D for ther commercal use. 9 1 The foregong consderatons hghlght the nherent completes of modelng the nternatonalzaton of frms R&D actvtes. Our analyss proposes an ntal modelng framework that hghlghts certan key aspects of the R&D globalzaton process. As such, the analyss entals smplfyng assumptons, whle only consderng certan dmensons of the nherently comple overall process correspondng to the nternatonalzaton of R&D. In partcular, whle recognzng that the etent to whch R&D stocks n dfferent countres are ether complements or substtutes s crtcal to defnng frms strategc nternatonal locaton decsons, the focus here wll be on a scenaro where stocks of fundamental R&D are substtutes. Smlarly, whle remarkng the potental role that appled R&D spllovers between frms may contrbute to eplanng nternatonal ndustral performance, the concern wll be wth nternatonal spllovers of fundamental R&D. Ther nterrelaton wth appled spllovers s left for subsequent nvestgaton In fact, certan corporatons also undertake path-breakng fundamental research. However, such basc nnovatons may be ether a necessary for undertakng more appled R&D, or a byproduct of research, rather than a prncpal obectve. 1 As ntangble assets, absorbed levels of fundamental R&D and nvestment n appled R&D can be transferred, to varyng degrees, wthn frms - both natonally and nternatonally. However, there are potentally hgh transacton costs and potental rsks assocated wth transferrng technologes between frms. 11 Other supply-sde ratonale for localzng R&D abroad nclude the need to nternalze postve eternaltes from appled R&D spllovers, compettve advantages ganed by access to lower-pad, but nonetheless hghly sklled researchers, as well as ndustral restructurng lnked to market ntegraton. 9

10 B. Characterzaton of the Innovaton Processes A duopoly model of nternatonal technologcal competton n cost-reducng process nnovaton s proposed, where reference wll be made to a domestc and foregn country, and an astersks s used to dstngush varables related to the latter. It s hypotheszed that there s a representatve frm n each country, where the domestc and foregn frms are desgnated, respectvely, by the subscrpts and. There are two forms of R&D actvty - fundamental and appled. Government and unversty sponsored R&D s understood to be the prncpal source of fundamental knowledge creaton and to generate natonal R&D stocks. Frms can be vewed as prncpally undertakng two dstnct R&D tasks. These consst of absorbng fundamental R&D and, then, nvestng n appled R&D. 1 The latter entals the converson by frms of fundamental R&D nto process nnovatons. The two countres fundamental R&D stocks, whch are taken to be eogenously gven and are denoted by X and X*, are potentally dstnctve n terms of ther levels and composton. In lght of ther geographcal separaton and an assumpton that frms must nvest n order to absorb fundamental knowledge, these natonal R&D stocks have certan features of nternatonal sem-publc goods. More specfcally, the proposed analyss dstngushes between alternatve scenaros n whch the two countres fundamental knowledge stocks are ether substtutes or complements. If the two stocks 1 There may be frm-specfc allocatve decsons regardng both the etent of absorpton of fundamental knowledge from publc sector sources and nvestment n fundamental knowledge creaton. As a result, frms fundamental R&D stocks could dffer across frms, sectors, and countres. Consequently, there s the potental for fundamental R&D spllover effects across frms wth dfferent degrees of locatonal specfcty dependng on the mportance of cluster effects at regonal, natonal and nternatonal levels. Nonetheless, our focus wll be on a paradgm where t s the publc sector, whch s the prncpal source of dfferences n natonal R&D stocks. 1

11 are substtutes, but one s larger than the other, there wll be a technologcal gap between the two countres. Each frm has access to an overall fundamental technology base, whch s an amalgam of the natonal R&D stock n ts own country and nternatonal spllovers of fundamental knowledge. It s postulated that there are two key decsons by ether frm, whch determne ts overall resources of fundamental knowledge. The frst of these s whether the frm s wllng to locate ts R&D actvtes abroad, thereby enablng t to nternalze hgher nternatonal spllovers of fundamental knowledge. The second concerns how much t s wllng to nvest n absorbng the avalable natonal and foregn fundamental knowledge stocks. More specfcally, when the two countres R&D stocks are substtutes, a representatve (domestc frm s potental fundamental knowledge base s gven by: 13 ma [X, X + λ ( X* - X] where λ [, 1] Note that λ corresponds to the fundamental R&D spllover parameter n the case of the domestc frm. For epostonal smplcty, t wll be assumed for ths case of substtutablty that the fundamental knowledge stock n the foregn country s hgher than that n the domestc country, and that the localzaton decson by the domestc frm s the only one envsaged. Alternatvely, n the case of complementary R&D stocks, the potental technologcal bases for the domestc and foregn frms are gven by: X + λ X* where λ [, 1] λ* X + X* where λ* [, 1] 13 In order to economze notaton, analogous equatons for the two frms wll only be presented for the domestc one. 11

12 Note that unlke the case of substtutablty t s now not necessary to make any hypothess regardng the relatve values of the R&D stocks, X and X*. Note that the value of the postve spllover parameter, λ, depends on whether that frm localzes part of ts R&D actvtes abroad. In partcular, the spllover parameter equals λ, f the frm does not locate R&D labs n the foregn country. However, f t does undertake R&D abroad t has a easer access to an epanded fundamental knowledge base, whch s captured by a hgher value for the spllover parameter, such that λ 1 > λ. For epostonal clarty, and 1, are used to dstngush, respectvely, the fundamental knowledge base of a frm before, [λ ], and after, [λ 1 ], t has establshed R&D actvtes abroad. A frm s actual capacty to moblze fundamental knowledge, whch s denoted by z, s mpacted by several factors. Frst, ths nnovatve capacty depends on the frm s fundamental knowledge base, whch as dscussed, s generated both natonally and through nternatonal R&D spllovers of fundamental R&D. Second, a frm s acquston of fundamental R&D depends on ts ependtures, desgnated as γ, whch am at absorbng that avalable R&D stock. Thrd, a frm s success n acqurng fundamental knowledge s determned by the actual absorpton process. 14 Taken together, these three factors result n the followng functon determnng a frm s actual, fundamental knowledge capacty: z θ (γ 14 The functonal form, θ(γ, capturng the process by whch a frm absorbs fundamental knowledge, can have a country specfcty. Ths corresponds n part to the effcacy of the structure of unversty-ndustry lnkages and to government polces desgned at promotng the transfer of basc R&D to ndustry. 1

13 Decreasng returns are assumed, so that θ > and θ <. The foregong specfcaton also captures the sem-publc nature of fundamental R&D, snce transferrng t from the publc sectors to frms nvolves nherent access and transacton costs that may be vewed as learnng or, alternatvely, absorpton costs. A frm s overall nvestment n R&D, ρ, entals a combnaton of both the foregong flow ependtures on absorbng fundamental knowledge stocks and ts appled (flow R&D budget, β, such that: ρ γ + β Its effectve technologcal effcency, e, s understood to depend on ts overall ependtures on R&D, ther allocaton between fundamental and appled research, as well as the prevalng technology transformng these nvestments nto reductons n cost. The functonal relaton capturng ths technology process s assumed to be common to both countres, so that: e Φ [ z, β ] Φ [θ(γ, β ] Ths functon s assumed to be ncreasng and concave n the two arguments, z and β. Note that ths formulaton offers a vew of a frm s overall nternatonal technologcal effcency n whch R&D s an ntangble asset whch, whle specfc to each frm, can be used on a worldwde bass wthn a gven corporate structure. Implctly, there s an optmzaton ssue concernng the nternal allocaton of a frm s ependtures between domestc and foregn R&D stes. However, as a smplfcaton, the analyss abstracts from such ssues, snce otherwse solutons are qute ntractable. Nonetheless, the proposed model hghlghts the role that a frm s decson to localze ts R&D actvtes 13

14 abroad can have by generatng a hgher propensty to absorb fundamental knowledge and, thereby, a hgher productvty of nvestments n appled research and development. Effcent management of technologcal resources requres that a frm optmally allocate ts overall ependtures between fundamental R&D absorpton and the assocated appled transformaton of R&D nto process nnovatons. For a gven value of technologcal effcency, ê, ths corresponds to the followng mnmzaton problem: Mn ρ wth respect to γ, β subect to Φ [θ(γ, β ] ê Ths yelds the followng effcent R&D ependture functon: 15 r r r (e, where e r and Thus, more R&D ependtures, r, are necessary n order to acheve ncreased technologcal effcency, e, whle access to a larger base of fundamental R&D,, dampens the need for a frm s overall R&D ependtures. As a consequence, there s an apparent tradeoff between sunk costs lnked to ncreased absorpton capacty, due to 15 Ths functon can be regarded as yeldng effectve levels of process R&D, gven that a frm s appled R&D decsons are postvely mpacted by natonal publc support for fundamental R&D. An equvalent producton functon for effectve technologcal effcency, after cost mnmzaton, could be characterzed as havng the followng general representatve form: e e ( r, e r where,, and. e e r 14

15 localzng R&D abroad, and a frm s overall flow ependtures on R&D. Consstent wth the concavty hypothess characterzng the effectve technologcal effcency functon, e Φ [ z, β ], the followng second-order condtons are taken to apply for the effcent R&D ependture functon: r e r, r and e In addton, for tractablty t wll also be assumed that: e r 3 In sum, a frm s overall R&D effort s vewed, n the current paradgm, as comprsng two key elements:. the absorpton of fundamental R&D, and. ts converson nto appled process nnovatons. Together, these ental the converson of fundamental R&D breakthroughs nto reductons n varable costs of producton, such that for the representatve frm (, wth an ouput level of q, the followng cost functon apples: c (q, e c c c where,, and q e q e Note that ncreased technologcal effcency reduces the margnal cost of producton. C. The Basc Framework of Internatonal Technologcal Competton The proposed analyss of nternatonal duopolstc competton n process nnovaton entals sequental decsons, whch can be treated as three dstnct stages n a non-cooperatve game: 15

16 1. nternatonal localzaton decson n order to acqure fundamental R&D from a technologcally domnant country;. R&D decsons by competng nternatonal duopolsts, whch ental both overall levels of R&D ependture and ther allocaton between the absorpton of fundamental R&D and ts converson, va appled R&D, to process nnovaton; and fnally, 3. product-market competton between two frms. As n the research of Spencer and Brander (1983, a standard metholodogy of backward nducton s used to analyze the determnants of such nternatonal technologcal competton. However, unlke estng research, the proposed analyss admts the addtonal possblty of frm ntally localzng ther R&D actvtes abroad n order to absorb fundamental R&D from abroad. More specfcally, n the fnal stage the duopolsts wll determne ther output levels, q and q, n lght of ther relatve technologcal compettveness and demand condtons n the two markets. The general form of the two frms obectve functons s gven by: Π R (q, q - c (q, e - r (e, Π R (q, q - c (q, e - r (e, The revenue functons, R and R, depend on the demand characterstcs n the two natonal markets, as well as on the etent of market segmentaton. Standard assumptons regardng the form of demand functons wll be made, whle the natonal markets are understood to be ether fully or partally ntegrated nternatonally. In the former case only a sngle overall demand functon needs to be specfed, whereas n the 16

17 latter scenaro two dstnct natonal demand functons are dentfed, whch can be eventually served by frms from both countres. The etent of nternatonal market VHJPHQWDWLRQLVWKHQFDSWXUHGE\DSDUDPHWHU, whch represents the addtonal costs of eportng, rather than sellng n the home market. 16 Under Cournot-Nash assumptons, the outcome of output competton n ths fnal stage wll be reduced form solutons of the general form: q * q (e, e q * q (e, e In the ntermedate stage, the competng nternatonal duopolsts smultaneously determne ther overall levels of effectve technologcal effcency, e and e, under Nash assumptons, whle effcently allocatng these R&D budgets between absorbng fundamental knowledge stocks and undertakng appled cost nnovatons. 17 These nvestment and allocatve decsons are undertaken whle antcpatng the assocated mplcatons for ther relatve cost compettveness n the fnal stage of output competton. These effectve technologcal effcency decsons are n turn dependent on the frms access to fundamental R&D stocks at home and abroad, whch are potentally mpacted by eventual decsons n the frst perod to localze R&D actvtes n the foregn country. The generc form for the assocated reduced form solutons s gven by: e * e (, 16 Although natonal markets are often segmented by asymmetrc trade and other costs, a smplfyng assumpton of unform eport costs between the two natonal markets s made. 17 Snce there s a dualsm between levels of technologcal effcency and corporate R&D ependtures, ananalytcally equvalent formulaton s n terms of overall levels of r and r. Agan, the latter ental ependtures on both absorbng fundamental R&D and on ts converson, through appled R&D, to process nnovaton. 17

18 e * e (, In the frst stage, dfferences between countres n ther stocks of fundamental R&D are understood to potentally generate an ncentve for frms to localze R&D actvtes abroad n order to obtan access to, and thereby absorb, fundamental R&D n the foregn country. Both cases of substtutablty and complementarty n the two countres R&D stocks wll be consdered. In the frst scenaro of substtutablty, the foregn country s understood to be n a technologcally domnant poston, so that X* > X. In a second scenaro, where the fundamental R&D stock of the foregn country s complementary to that avalable n a frm s home country, the analyss wll be lmted to a stuaton where only the nternatonal localzaton decson of the domestc frm s consdered and there s no strategc locatonal response by ts foregn compettor. Thus, the consderably more comple framework of a full game-theoretc analyss at ths frst stage s left for further research. There are apparent market access costs, along wth assocated learnng costs, entaled by localzng abroad n order to absorb foregn fundamental R&D. When only undrectonal localzaton decsons are consdered, so that the analyss relates to entry nto the foregn country, the sunk costs of localzng R&D actvtes abroad are captured, for the representatve domestc frm, by an eogenous varable, S. The decson to localze R&D actvtes abroad wll depend on whether the antcpated gan n profts, resultng from access to an epanded fundamental knowledge base and the assocated ncrease n the frm s technologcal effcency, are hgher than the sunk costs of settng up a R&D lab abroad. Ths leads to the followng crtcal nequalty condton: Π Π ( 1, - Π (, > S 18

19 As prevously noted, the change n the value for the endogenous spllover parameter, λ, plays a key role n mpactng the potental gans from nternatonalzng a frm s R&D actvtes. Indeed, the potental change n a frm s operatng proft, resultng from ts localzng ts R&D actvtes abroad, s at the center of much of the subsequent analyss. Nonetheless, such a change n a frm s operatng profts, Π, s potentally mpacted by not only changes n the spllover parameters, λ and λ 1, but also both absolute and relatve changes n the stocks of fundamental knowledge n ether country, X and X*. 18 III. Model Analyss and Determnaton of Central Analytc Propostons A. Further Model Specfcatons In order to undertake a more detaled analyss of the model, lnearty assumptons are made for both the demand and cost functons. In partcular, the demand functon, when the natonal markets are fully ntegrated, s gven by: Q a - p When there s market segmentaton, the domestc and foregn demand functons are, respectvely: Q 1 a 1 - b 1 p 1 Q a - b p Note that the sum of the slopes, b 1 + b, equals one, whch s numerare used for the slope of the global demand functon. It wll also be assumed that the prce senstvty of 18 An effect of the nformaton technologes has undoubtedly been to facltate the dffuson of fundamental and appled knowledge. Wthn the proposed framework of substtutable R&D stocks, ths could be nterpreted as a narrowng of the technologcal gap, X* - X. For a scenaro of complementary, the globalzaton of technologcal know-how may have resulted n an epanded set of dstnctve natonal R&D stocks. 19

20 demand n the two markets s not too dfferent. More specfcally, that the followng nequalty condtons apply: ½ # b 1 / b # The lnear cost functons for the frms reflect the reducton of costs resultng from ncreases n ther levels of effectve technologcal effcency: c (q, e (c - e q Internatonal market segmentaton s then understood to arse from the addtonal costs, of sellng q * to a foregn market, nstead of at home. These mpact drectly on an eportng frm s cost functon, such that: c (q *, e (c - e + δ q * For such a case of market segmentaton, t wll be demonstrated n Anne I that the epresson for a frm s proft at the Cournot-Nash equlbrum s equvalent to that whch would be obtaned wth a global demand functon, ecept that the assocated value of the ntercept, a, s lower than n the fully ntegrated scenaro. In partcular, t s shown that when the domestc eporter, faces addtonal trade costs of δ, that: a a + δ b - δ b Note that the foregong restrcton on the prce senstvty of demand n the two markets s a necessary condton for a < a. B. General Characterzaton of the Duopoly Equlbrum A detaled analyss of the three stages of nternatonal duopolstc competton s essental n order to establsh the cental propostons of ths research. Usng backward

21 nducton, we start by characterzng the fnal stage of product market competton, where gven ther degree of technologcal compettveness, each frm smultaneously determnes ts output and sales, q, under Cournot-Nash assumptons. In lght of earler specfcatons, the proft of frm then corresponds to: Π ( p c q r M r For notatonal smplcty, the symbol M s used to dentfy a frm s revenues net of varable costs, but not ncludng the fed costs, r, of a frm s R&D ependtures. The latter are determned by the values of e and, whch are taken as gven n ths fnal stage of output competton. In lght of the lnear demand functon, Q a p, t s straghtward to ascertan the followng characterstcs of the Cournot Nash equlbrum: q 1/3 [a c + c ] and M 1/ 9 [a c + c ] Turnng now to the second stage, the R&D decsons of the two frms, e and e, or equvalently r and r, can be analyzed. In lght of the lnear cost functons, c c e and c c e, the followng varable s frst defned: α a c + c. Consequently, the thrd stage equlbrum producton and proft of frm are: q 1/3 [α + e e ] and Π M r 1/ 9 [α + e e ] r ( e, 1

22 Non-cooperatve equlbrum for competton between the two frms n ther effectve technologcal effcences, e and e, s specfed, for frm, by the condton : M e 4 ( α + e e 9 r e Smlarly, the reacton functon for frm corresponds to the relaton: 4 ( α 9 r + e e e These two equatons yeld the equlbrum values of e and e, as functons of each of the frms potental knowledge bases, and. The correspondng second-order condtons are: k 9 4 r e Actually, a more restrctve assumpton s nvoked. Specfcally, t s supposed that the parameters of functon r are such that k > 1. As wll be seen later, ths guarantees that the optmal level of each frm s technologcal effcency, e, s an ncreasng functon of ts potental knowledge base,. A consequence of equlbrum n the second stage s that the proft of frm s a functon of both frms knowledge bases, and. In the ntal stage, frm wll decde whether to localze abroad or not. Such foregn localzaton entals an ncrease n the domestc frm s operatng proft, Π. In a scenaro of substtutable R&D stocks, ths s due to ncreasng from X + λ (X* - X to 1 X + λ 1 ( X* - X. Wth complementary stocks, the correspondng values of are: X + λ X* and 1 X + λ 1 X*.

23 C. Central Analytc Results for Fully Integrated Markets In ths sub-secton a seres of propostons wll be demonstrated on the bass of a more detaled analyss of the three stages of the model. Frst, we consder how changes n the level of frm s fundamental knowledge stock mpact on the equlbrum values of the duopolsts levels of technologcal effcency, producton and profts. In partcular, a further analyss of the second stage yelds the followng: Lemma 1: An ncrease n that frm s fundamental knowledge base,, due to an ncrease n ether the level of ts home stock of fundamental knowledge, X, or n the nternatonal spllover parameter, λ, wll, ceters parbus, ncrease ts effectve technologcal effcency, e, quantty of sales, q, and ts profts, Π. In contrast, the comparable values for ts compettor, e, q, and Π decrease. The demonstratons of these results are based on an analyss of the effects of margnal varaton of the domestc frm knowledge base, d, assumng that ts compettor s knowledge base,, remans constant. Dfferentaton of the equlbrum condtons characterzng each frm s reacton functon n the second stage yelds: k de + de de + k de 9 r d 4 e Ths can be smplfed to: 3

24 k de kk 1 1 de kk r d e r d e In lght of earler assumptons that the second-order cross dervatves of the functon r are negatve, t s easy to see that: de d de, d dq 1 de de, 3 d d d dq, d The foregong effects are llustrated by the changes n the reacton functons, R and R, and assocated Nash equlbra, N and NN, as shown n Fgure 1. 4

25 Fgure 1 The Compettve Gan n Effectve Technologcal Effcency Resultng from an Increase n the Domestc Frm s Knowledge Base e R N R N R e 5

26 6 Furthermore, t follows that: r e e q q r e e r e e q e e q q + Π Π, snce,, r e e q Smlarly, t can be readly shown that an ncrease n the domestc frm s fundamental knowledge base decreases the proftablty of ts foregn compettor: + Π e e q q e e r e e q e e q q Because of the model s basc symmetry, t s also the case that: Π Consequently, the domestc frm s profts, Π, s an ncreasng functon of and a decreasng functon of. The analyss wll now focus on the frst stage when the domestc frm decdes whether to localze ts R&D actvtes abroad. As already dscussed, the assocated crtcal condton apples: Π Π ( 1, - Π (, > S

27 A consequence of Lemma 1 s that, a larger ncremental spllover effect, λ 1 - λ, generated by localzng R&D actvtes abroad, wll generate heghtened net profts,.e. d Π >. It s apparent that such a gan n profts can also be generated by a reducton of the sunk costs of settng up R&D actvtes abroad, S. Based on Lemma 1 t s possble to establsh two key propostons, whch relate to how changes n the domestc frm s profts depend on ts natonal fundamental R&D stock, X, for the alternatve scenaros of substtutablty and complementarty between ths domestc stock and the foregn one. Proposton 1: Let us consder a scenaro where nternatonal stocks of fundamental R&D are substtutes and a frm comes from a country, whch s a technologcal follower. The mpact on a frm s profts from ts localzng R&D actvtes abroad, Π, as a result of an ncrease n ts natonal fundamental R&D stock, X, s potentally ambguous. Notably, d Π / d X depends on ntal value of the fundamental R&D spllover parameter before R&D actvtes are localzed abroad, λ, and on the assocated gan n the nternatonal spllover parameter, λ 1 - λ. For suffcently hgh values of λ 1, the gans from settng up R&D actvtes abroad, Π, wll, ceters parbus, decrease and tend to zero when there s convergence between the domestc and foregn fundamental knowledge stocks,.e. X X*. Consequently, for any gven value for the sunk costs of settng up R&D actvtes abroad, S, there ests a crtcal value of the natonal fundamental R&D stock, X, 7

28 beyond whch the frm wll not localze ts R&D actvtes abroad. Ths crtcal value depends postvely on the ncremental spllover effects, λ 1 - λ, resultng from settng up R&D operatons abroad. Alternatvely, t s apparent that there always ests a suffcently large sunk cost value, S, such that the frm wll not set up R&D actvtes abroad. The demonstraton of the foregong proposton, whch s rather straghtforward, s provded n Append I. The ncremental spllover effects, λ 1 - λ, can be nterpreted as representng the dfferental return to acqurng tact knowledge, whch results from settng up R&D actvtes abroad. On the one hand, the substantal reducton n nternatonal transactons costs, due to advances n nformaton technologes, along wth other factors contrbutng to economc globalzaton, may have facltated the nternatonal dffuson of fundamental knowledge. In the proposed model ths can be nterpreted, ceters parbus, as an ncrease n the ntal spllover parameter λ. On the other hand, the heghtened pace of technologcal change may be reflected by larger dfferentals n countres stocks of fundamental knowledge, X* - X. Such an dea s undoubtedly reflected n polcy debates regardng the dgtal dvde. An apparent mplcaton of Proposton 1 s that such offsettng effects, assocated wth economc globalzaton, may have ambguous mplcatons on the ratonale for localzng R&D abroad. We now eamne how changes n the fundamental R&D stock mpact on a frm s decson to localze R&D abroad for the case of complementary stocks n the two countres. It should be noted that an ncrease n a country s fundamental knowledge 8

29 stock now entals smultaneous ncreases n the knowledge bases of both the domestc and foregn frms. Proposton : Let us consder a scenaro where nternatonal stocks of fundamental R&D are complements. The mpact on a frm s profts from ts localzng R&D actvtes abroad, Π, as a result of an ncrease n ts natonal fundamental R&D stock, X, s agan potentally ambguous. However, gven certan techncal assumptons on the second dervatves of proft functon n relaton to a frm s fundamental knowledge base,, t can be demonstrated that Π s an ncreasng functon of X. Therefore, for any gven value for the sunk costs of settng up R&D actvtes abroad, S, there ests a crtcal value of the natonal fundamental R&D stock, X, under whch the frm wll not localze ts R&D actvtes abroad. Append II provdes the demonstraton of ths second proposton. Note that both Propostons 1 and pont to a crtcal value of a country s R&D stock, X, whch demarcates sub-sets of values of X for whch a frm wll ether undertake R&D actvtes abroad, or not do so. However, as suggested by Fgures a,b, the underlyng mechansms are qute dfferent n the alternatve scenaros of R&D substtutablty and complementarty. More specfcally, the curves correspondng to the ncremental change n profts, Π, are, respectvely, decreasng and ncreasng functons of the natonal 9

30 R&D stock, X. In the former case of substtutablty, the addtonal technologcal advantage arsng from locatng abroad clearly declnes as the two countres R&D stocks converge. Under complementarty, there are two offsettng effects on the home country s relatve technologcal compettveness. Whle the drect mpact of an ncrease n that country s R&D stock s to enhance ts fundamental knowledge base,, there s also an ndrect effect, due to an assocated technologcal spllover to the foregn country. The latter results n an ncreased value of. The techncal assumptons underlyng Proposton ensure that the drect effect ncreasngly domnates the ndrect one, so that the assocated ncremental proft functon n Fgure b s upward slopng. 3

31 Fgures a,b A Comparson of Condtons for Localzng R&D Actvtes Abroad under Alternatve Scenaros Regardng the Relaton between the Natonal Stocks a Substtutablty Π S b Complementarty Foregn localzaton of R&D X X* X Π S X Foregn localzaton of R&D X 31

32 D. The R&D Locatonal Effects of Varatons n Demand and of Changes n Intal Producton Costs In ths sub-secton, the mpact of changes n ntal demand and producton condtons on a frm s propensty to localze R&D actvtes abroad wll be characterzed. The formal analyss starts by consderng, for gven levels of the fundamental knowledge bases and, the effects of varatons n a representatve varable, z, whch mpacts on the equlbrum values of the two frms levels of effectve technologcal effcency e and e. Such varatons generate a change n the proft of the representatve frm. The followng lemma summarzes the prncpal results: Lemma : If dπ (, dz s an ncreasng (decreasng functon of, a rse (fall n the value of z modfes the threshold for the crtcal value of a country s R&D stock, X, such that the representatve frm s more nclned to localze R&D actvtes abroad. The demonstraton of the foregong result starts wth the Taylor epanson for the dervatve of the ncremental effect on profts due to a change n z: 1 d Π dπ (, dπ (, Π d (, 1 ( dz dz dz dz 3

33 wth [, ] 1. d Π (, dπ (, If dz dz then, Π s ncreasng wth z. Thus, when z ncreases, the curve representng the evoluton of Π, as a functon of X, moves upward. Consequently, the threshold value a country s R&D stock, X, moves to the rght (left for the case of substtutable (complementary R&D stocks, as shown n Fgure a (b. The specfc varables whch are understood here to correspond to z are the demand parameter a and the ntal margnal producton costs c and c. In Append dπ III t s demonstrated that under some specfc assumptons dπ, dπ and da are dc dc ncreasng functons of. Ths leads to the followng proposton: Proposton 3: The ntal demand condtons, represented by the parameter a, as well as the margnal costs of producton for the domestc and foregn frm, c and c, play crtcal roles n determnng whether a frm wll localze R&D actvtes abroad. For both scenaros of substtutable or complementary nternatonal stocks of fundamental R&D, ether an ncrease n demand, a fall n the ntal margnal producton cost of frm, or a rse n the ntal margnal producton cost of frm wdens the range of values of the natonal fundamental R&D stock, X, for whch the representatve frm wll localze ts R&D actvtes abroad. 33

34 In other words, when the domestc frm s relatvely more compettve n terms of ts ntal margnal costs of producton, or demand condtons are more favorable, the representatve frm has a greater ncentve to set up R&D n the foregn country. The foregong analyss s llustrated n Fgure 3a,b by the upward movement of the change n proft functon,, for an ncreased value of the parameter a relatve to an value of a. Nonetheless, t s apparent that there are dfferent adustment mechansms, dependng on whether the natonal stocks of R&D are ether substtutes or complements. As shown n Fgure 3a, for a gven level of sunk costs, S, and under the substtutablty assumpton, heghtened demand generates a hgher threshold value of X, X, beyond whch the frm wll not localze abroad. Alternatvely, the mpact of epanded demand costs s to ncrease the crtcal values of sunk costs whch warrant nternatonalzng R&D actvtes from S to S. Fgure 3b llustrates the alternatve scenaro of complementarty n the natonal stocks of fundamental R&D. Snce an ncrease n demand agan generates an upward shft n the ncremental proft functon, the threshold value of X, below whch the domestc frm wll not localze ts actvtes abroad, decreases wth epanded demand. The effect of such ncreased demand on the crtcal values of sunk costs s analogous to that under substtutablty. 34

35 Fgures 3a,b The Impact of Increased Demand on the Incentve to Undertake R&D Actvtes Abroad for Alternatve Scenaros Regardng the Natonal R&D Stocks a Substtutablty Π Π (a Π (a (a < a S SS Foregn localzaton of R&D X X X* X 35

36 b Complementarty S S Π (a Π (a (a < a X X Foregn localzaton of R&D X 36

37 The eplanaton for the fndngs, summarzed n Proposton 3, s agan that, ceters parbus, reductons n a frm s domestc margnal producton costs, as well as ncreases n the margnal costs of ts foregn compettor, nduce a greater ncentve for the domestc frm to produce. Wth such a larger producton base, there s a hgher return from ncreases n the frm s technologcal knowledge base. In ths regard, our analyss hghlghts the assocated ratonale for nternatonalzng a frm s R&D actvtes, n order to absorb more fundamental R&D from abroad and reduce margnal producton costs. E. Reduced Product Market Segmentaton and the Internatonal Locaton of R&D In ths subsecton the focus s on a central ssue of how changes n the etent of nternatonal market segmentaton mpact on the ncentve for R&D actvtes to become more globalzed. The nterrelaton between the mpact of such reductons n trade costs and alternatve scenaros for the substtutablty or complementary between natonal stocks of fundamental R&D wll be characterzed n terms of a central proposton. More specfcally, the analyss focuses on the mplcatons of reducng nternatonal trade costs, whch s captured n the analyss by changes n a parameter, δ. Ths represents the addtonal costs of a frm s eportng, rather than sellng n the home market. 37

38 In Append IV t s shown that, when markets are segmented, the varable cost margn for the representatve frm s smlar to that wth unfed markets, ecept that the demand parameter a must be replaced by a new coeffcent, a. Ths s defned by the equaton a a + a δβ, where β b b. Consequently, the equatons characterzng the equlbrum values for e and e are smlar to those obtaned n subsecton IIIB, descrbng the general characterzaton of the duopoly equlbrum. However, the epressons for α and α wll be replaced by new parameters, whch are represented by α and α, where the followng formulas apply: α a + and c c α a +. It can be seen that heghtened (reduced market ntegraton, as c c reflected by a lower (hgher value for the trade cost parameter, δ, results n hgher (lower values for the demand parameters, a, a and also for α and α. More precsely, the varaton n the degree of market segmentaton dδ entals the followng relaton: dα β dα β dδ. It s shown n Append III that a decrease n trade costs nduces frm to seek hgher levels of technologcal effcency, d e / d δ < f the followng condton s met: k β β >. In that case the margnal varaton of the representatve frm s proft resultng from a decrease of the trade costs s postve and an ncreasng functon of. The foregong reasonng leads to a central fndng n ths research. 38

39 Proposton 4: Let us consder a scenaro where two natonal markets are segmented due to trade costs, δ >, of servng markets abroad, nstead of at home. If the demand condtons n the two countres are such that k β β >, the range of X values, for whch a frm wll localze R&D abroad, ncreases as trade costs are reduced. In partcular, when foregn demand s at least as senstve to prce changes as n the domestc country, so that b b and β β, the above nequalty condton s automatcally satsfed, so that trade lberalzaton always generates a hgher propensty to localze R&D actvtes abroad. Ths follows from the assumpton that k 1. Thus, a central fndng, whch s conveyed n Proposton 4 and the foregong dscusson, s that the probablty of undertakng R&D n the foregn country s hgher wth the ncreased ntegraton of markets. The basc ntuton relates to how an epanded potental market creates an added proft ncentve to mprove a frm s technologcal compettveness. A key nsght s that the heghtened proft assocated wth epanded foregn demand s tself an ncreasng functon of a frm s technologcal effcency, whch, n turn, depends on ts technologcal base. Ceters parbus, the latter s enhanced through the ncreased absorpton of foregn fundamental R&D by localzng R&D actvtes abroad. Alternatvely, undertakng R&D actvtes abroad engenders sunk costs of access to a dstnctve foregn technologcal envronment. Followng the ntegraton of product markets, there are assocated economes of scale, due to the spreadng of such costs across a larger number of consumers. It can be noted that the 39