Comparative Advantage in Innovation and Production

Transcription

1 Comparatve Advantage n Innovaton and Producton Marano Somale y Prnceton Unversty November 204 Abstract Ths paper develops a mult-country, general equlbrum, sem endogenous growth model of nnovaton and trade n whch specalzaton n nnovaton and producton are jontly determned. The dstnctve element of the model s the ablty of the agents to drect ther research e orts to spec c goods, n a context of heterogeneous nnovaton capabltes across countres and contemporaneous decreasng returns to R&D. The model features a two-way relatonshp between trade and technology absent n standard quanttatve Rcadan trade models. I calbrate the model usng a sample of 29 countres and 8 manufacturng ndustres and quantfy the mportance of endogenous adjustments n technology. I nd that endogenous adjustments n technology due to drected research can account for up to 52.8% of the observed varance n comparatve advantage n producton. In addton, the model suggests that standard Rcardan models overestmate the reductons n real ncome from ncreases n trade costs and underestmate the ncrement n real ncome due to trade lberalzatons. Vst for the latest verson of the paper. y I am ndebted to Stephen Reddng, Esteban Ross-Hansberg and Gene Grossman for gudance, encouragement and support. I also bene ted from conversatons wth Eduardo Morales and Ferdnando Monte. I would lke to thank the Internatonal Economcs Secton at Prnceton Unversty for nancal support.

2 Introducton Ever snce the wrtngs of Davd Rcardo, the relatonshp between technology and trade has featured promnently n economc analyss. Tradtonal Rcardan theores of trade have emphaszed the role of technologcal d erences across countres n generatng the observed specalzaton patterns n producton and trade. The lterature followng ths tradton typcally has been concerned wth the e ects of those technologcal d erences and consequently t has manly used statc models n whch technology s exogenous to analyze a myrad of topcs such as the patterns of producton and trade, the welfare gans from trade, the e ects of exogenous technologcal progress and the e ect of the d uson of technology, among others. Moreover, snce the semnal contrbuton of Eaton and Kortum (2002), we have a rch set of trade models that ncorporate the man nsghts from the Rcardan theory of trade n a context of many goods and many countres and that lend themselves to easy quanttatve mplementaton, allowng the researcher to go beyond the qualtatve analyss that prevous models permtted. 2 However, the state of producton technology at any gven moment n tme s hardly exogenous, but a consequence of past nnovatons. For long, economsts have emphaszed the economc nature of nnovaton actvty and the role of expected pro ts n shapng the amount and drecton of nnovaton e orts. In the words of Schmookler: "...nventon s largely an economc actvty, whch lke other economc actvtes, s pursued for gan." 3 In hs semnal work on techncal change n varous captal good ndustres, Inventon and Economc Growth (966), Schmookler provdes evdence about the mportance of demand and the expected market sze for an nnovaton as determnants of nventon actvty. Snce then, a large number of emprcal studes have provded evdence n support of Smookler s deas. 4 The dscusson n the prevous paragraph mples that n the case of an open economy, not only does technology a ect the patterns of trade as n the standard Rcardan model, but also trade can a ect nnovaton and technology through the changes n the expected market sze for an nnovaton that t nduces. In partcular, n an economy n whch research e orts can be drected to d erent goods, trade-nduced changes n the expected market sze for nventons generate a reallocaton of research e orts from those goods n whch the market contracts towards those goods n whch the market expands, provdng an addtonal margn through whch economes can adjust to changes n the tradng envronment. Although the relatonshp between trade and nnovaton has been extensvely studed snce the poneerng contrbutons of Grossman and Helpman (989, 990, 99) and Rvera-Batz and Romer (99), lttle attenton has been gven to the e ects of drected research across goods n the quanttatve trade lterature. 5 Grossman and Helpman (995) survey the lterature that follows ths tradton. 2 Eaton and Kortum (202) survey the quanttatve trade lterature that extends the model n Eaton and Kortum (2002). 3 Schmookler, Inventon and Economc Growth, 966, p Just to menton a few examples, Newell, Ja ee and Stavns (999) show that the type of nnovaton on the typcal ar condtoner (AC) sold at Sears shfted from nnovatons that reduced the prce of ACs n the perod to nnovatons that made them more energy-e cent n the perod , whch they argue was the consequence of the rse n energy prces n the later perod. Acemoglu and Lnn (2004) and Cerda (2007) use changes n demographc trends as a source of exogenous varaton n the market sze of d erent types of drugs; they nd that the e ect on nnovaton of these changes n market sze are economcally mportant. 5 In a context n whch techncal change complements factors of producton, Acemoglu (998, 2002, 2003) studes the e ects drected techncal change on factor rewards. 2

3 The purpose of ths paper s to study the two-way relatonshp between trade and technology that emerges n a context of endogenous nnovaton and drected research, and to assess qualtatvely and quanttatvely the mplcatons of drected research for nnovaton, producton and trade specalzaton patterns. One of the challenges n the quanttatve assessment of ths new margn s that the postve correlatons n the nnovaton, producton and export specalzaton patterns observed n the data are of lttle help to dsentangle the mportance of the e ects of trade on technology. The reason for ths s that such correlatons characterze both a world wth drected research and a world n whch the trade envronment does not a ect the drecton of techncal change. 6 A potental approach to deal wth ths ssue s to nd a natural experment n whch an exogenous shock a ects only the tradng condtons of a country, and use that shock to solate the e ects of trade on nnovaton and technology. 7 Leavng asde the d cultes of ndng such natural experment, ths approach cannot be used to evaluate the consequences of other counterfactual shocks on nnovaton, producton and trade patterns, nor does t permt to study the welfare mplcatons of the addtonal margn of adjustment ntroduced by drected research. To overcome these d cultes, I buld on Eaton and Kortum (200) and on recent developments n the statc quanttatve trade lterature to develop a mult-country, general equlbrum, sem-endogenous growth model of nnovaton and trade n whch specalzaton n nnovaton and producton are jontly determned. The dstnctve element of the model s the ablty of agents to drect ther research e orts to spec c goods n a context n whch countres d er n ther exogenous nnovaton capabltes; ths new element bulds nto the model the two-way relatonshp between trade and technology that s the focus of ths paper. The sem-endogenous nature of techncal change n ths model mples that all the e ects of drected research are re ected n the levels of the varables of nterest n the balanced growth path (BGP), wth no e ect on BGP-growth rates. These level e ects are the focus of ths paper. I use the model to dsentangle the e ects of trade on technology and to study some questons that standard Rcardan quanttatve models and reduced-form approaches are not sutable to answer. How mportant s the feedback from demand and market sze to technology? How s comparatve advantage n producton determned n ths context? How are the specalzaton patterns of nnovaton, producton and trade determned? How does ths addtonal margn a ect our conclusons regardng the e ects of trade lberalzaton on producton, trade ows and welfare? The model features contemporaneous decreasng returns n R&D, whch are parsmonously captured by a sngle parameter common to all countres and goods. Decreasng returns n R&D are an mportant element of the model snce they control the mportance of the addtonal margn of adjustment ntroduced by drected research; the weaker the decreasng returns n R&D, the stronger the endogenous adjustment n technology n response to changes n the envronment. Ths mples that under the structure of the model, dsentanglng the mportance of each drecton n the two-way relatonshp between technology and trade reduces to the determnaton of the value of the sngle parameter capturng the decreasng returns to R&D. 6 Usng R&D expedtures or patents counts as measures of nnovaton actvty, the data shows that countres nnovate relatvely more n those sectors where they produce and export relatvely more. 7 See Bustos (2008) and Lleeva and Tre er (200) for studes that use exogenous varatons n tar s to analyze the e ect on rms technology spendng decsons. 3

4 To estmate the decreasng returns n R&D I use a structural relatonshp of the model that captures the dstnctve element ntroduced by drected research,.e., the endogenous and jont determnaton of manufacturng technology and trade ows. Usng cross-sectonal producton and trade data, I estmate ths relatonshp usng two method of moments estmators that yeld lower and upper bounds for the degree of decreasng returns n R&D. As an overdent caton check for ths estmaton strategy, I use a dynamc mplcaton of the model that relates the growth rate of ncome per capta n the BGP to the growth rate of research employment and the degree of decreasng returns n R&D. These alternatve approaches yeld smlar results. The model presents some convenent features that facltate ts quanttatve mplementaton. Frst, n the BGP, the model nests the benchmark Rcardan model wth no nnovaton as a specal case. More spec cally, when R&D possbltes are elmnated, the model reduces at the aggregate level to a multndustry verson of Eaton and Kortum (2002) (henceforth EK model.) 8 In addton, both models share the same structure n the cross-secton. Ths mples that many of the methods developed n the lterature to estmate mult-ndustry versons of the EK model can also be appled to ths model. In partcular, ths feature of the model allows me to use the methods developed n Costnot, Donaldson and Komunjer (20) to estmate comparatve advantage n producton, whch s a necessary nput n the estmaton of the degree of decreasng returns n R&D. Second, relatve to such a benchmark model wth no nnovaton, the present model adds only one addtonal parameter to the total number of parameters needed to be estmated to evaluate counterfactual predctons across BGPs. Moreover, armed wth an estmate of the parameter capturng the decreasng returns to R&D, any method used to estmate the countres manufacturng productvtes n the model wth no nnovaton can be used to recover countres nnovaton capabltes. Consequently, all the addtonal estmaton burden mposed by the ntroducton of drected research reles on the estmaton of decreasng returns to R&D. Thrd, the fact that the models wth and wthout nnovaton share the same cross-sectonal structure mples that both models perform equally well n matchng trade and producton data n the cross-secton. Moreover, both models can be estmated to match exactly the data and to share all exogenous parameters and manufacturng technologes. Nevertheless, even f the two models are set up n ths way, they stll d er n ther counterfactual predctons regardng the changes n trade ows, manufacturng technology and welfare assocated wth d erent shocks, all of whch are relevant dmensons for polcy analyss. When performng counterfactual analyss across BGPs, I extend the approach popularzed by Deckle, Eaton and Kortum (2007) (henceforth DEK) to nclude the e ect of nnovaton and drected research and solve the BGP of the model n changes. When the model s solved n changes, only a subset of parameters s needed to perform any gven counterfactual evaluaton. In partcular, ths approach does not rely on estmates of unobserved structural parameters such as nnovaton capabltes or trade costs. In addton, the system of equatons of the model n changes encompasses the system of equatons correspondng to a mult-ndustry EK model as a specal case. Ths mples that armed wth an estmate of the parameter 8 More spec cally, the model reduces to a mult-ndustry verson of Bernard, Eaton, Jensen and Kortum (2003). However, these models have equvalent reduced-forms at the aggregate level n terms of the determnaton of wages, producton and trade ows. 4

5 capturng the decreasng returns n R&D, performng counterfactual analyss n the model wth drected research does not mpose any addtonal data requrement over the benchmark model wth no nnovaton. I calbrate the model usng a sample of 29 countres and 8 manufacturng ndustres and I use t to quantfy the mportance of drected research on technology, producton and trade ows. I decompose comparatve advantage n the observed open equlbrum nto exogenous and endogenous components. Under the benchmark calbraton for the decreasng returns n R&D, I nd that the endogenous adjustments n technology due to drected research can account for up to 52.8% of the observed varance n comparatve advantage n producton. In addton, the estmated endogenous component of comparatve advantage n producton s tghtly connected to relatve domestc demand condtons, whch accordng to the theory, s ndcatve of the presence of hgh trade frctons. I use the model to explore quanttatvely two counterfactual stuatons: () I explore the changes n real ncome as countres move to autarky. The model shows that all countres su er a reducton n ther real ncome. Relatve to the model wth drected research, the standard model wth no nnovaton tends to overestmate the reductons n real ncome, although the d erences between models appear to be modest. On average, the reductons n real ncome predcted by the model wth drected research represent 93% of those predcted by the model wth no nnovaton. The man reason for the modest d erences n the predcted changes n real ncome s the presence of hgh trade frctons n the observed open equlbrum, whch reduces the scope for specalzaton n nnovaton. () I examne the e ects of a 25% reducton n trade costs. The ntroducton of drected research has relatvely mportant e ects on the model s predctons regardng the changes n trade ows and market shares. The predcted changes n trade ows n the model wth no nnovaton can explan a lttle more than a thrd of the varaton n the correspondng changes n the model wth drected research. In addton, the model wth no nnovaton tends to underestmate the magntude of the changes n market shares. Accordng to the model, all countres enjoy an ncrease n ther real ncome. Relatve to the model wth drected research, the standard model wth no nnovaton tends to underestmate the ncreases n real ncome, although the d erences are also modest n ths case. The ncreases n real ncome n the presence of drected research are on average 2% hgher than n the case of no nnovaton. Ths paper s related to the large endogenous and sem-endogenous growth lterature analyzng the effects of trade on the pace of endogenous techncal change. Among these studes we can menton Grossman and Helpman (989, 990, 99), Rvera-Batz (99), Taylor (993), Jones (995), Eaton and Kortum (200). The man departure from ths lterature n ths paper s the focus on drected research across goods and the quanttatve focus of the analyss. Ths paper s also related to Arkolaks, Ramondo, Rodrguez-Clare and Yeaple (203). They develop a quanttatve sngle-ndustry model of multnatonal producton and trade n whch countres d er n ther manufacturng and nnovaton productvtes and n whch rms can separate the locaton of ther nnovaton and producton actvtes. They use the model to study the e ects of openness on the specalzaton n nnovaton or producton patterns and they analyze the role of multnatonal producton as a vehcle through whch ths nternatonal specalzaton takes place. In contrast, n ths paper countres can drect ther research e orts to d erent goods n the economy but cannot separate ther nnovaton and 5

6 producton locatons. In a context n whch countres d er n ther nnovaton capabltes across the dfferent goods n the economy, I analyze the e ects of trade on the nnovaton and producton specalzaton patterns across the goods n the economy. Fnally, ths paper s related to a rapdly growng lterature that use statc mult-sectors Rcardan quanttatve trade models that buld on Eaton and Kortum (2002). Among these studes we can menton Arkolaks, Costnot and Rodrguez-Clare (202), Calendo and Parro (204), Chor (200), Costnot, Donaldson and Komunjer (202), Donaldson (202), Levchenko and Zhang (204a, 204b), Shkher (20). The fundamental d erence between these studes and ths paper s the treatment of technology. Whle n all the above mentoned studes technology s exogenous, n ths paper technology s endogenous and t s a ected by trade. 2 The Model In ths secton I buld on Eaton and Kortum (200) to develop a mult-country, dynamc, general equlbrum model of nnovaton and trade n whch specalzaton n nnovaton and producton are jontly determned. The dstnctve element of the model s the ablty of the agents n any country to drect ther research e orts to spec c goods n a context n whch nnovaton capabltes vary across goods and countres. The model s a sem-endogenous growth model and as such, aggregate growth rates n the balanced growth path (BGP) are not a ected by trade or standard polces such as taxes, R&D subsdes; ths mples that all of the new endogenous adjustments n the nnovaton process nduced by drected research are re ected n the levels of manufacturng technology n the BGP. In the rest of ths secton I descrbe the components of the model and I provde a characterzaton of the market equlbrum, leavng for the next secton the analyss of the BGP. 2. Basc Envronment Tme s contnuous and s ndexed by t 2 [0; ). The world conssts of N countres. Country s populated by a contnuum of dentcal and n ntely lved households, each of them wth L t members at tme t. The mass of households s normalzed to one such that L t also represents total populaton at tme t. The representatve household n every country grows at the exogenously gven rate n,.e., L t L 0 e nt. Labor s the only factor of producton and ts total nelastc supply at tme t s gven by the populaton sze L t. There are two sectors n the economy, a manufacturng sector and a research sector. The manufacturng sector produces a xed set of nal goods takng the level of technology as gven, whle the research sector nvests n R&D to mprove the technology of nal goods. 9 Labor s perfectly moble across sectors wthn a country but s mmoble across countres. R&D and Productvty. The goal of R&D actvty s to obtan new producton technques that mprove the e cency wth whch nal goods are produced. To capture the dea of drected research, I dvde the set of nal goods n ndustres and allow countres to drect ther research e orts toward 9 Alternatvely, R&D could mprove the qualty of the product. Both spec caton are equvalent for the purposes of the present paper. 6

7 the d erent ndustres. Formally, there s a xed set of ndustres wth a contnuum of goods n each ndustry. A nal good n the economy s dent ed by the par (z; ) 2 [0; ], where dent es the ndustry to whch the good belongs and z dent es the good wthn the ndustry. Country can drect ts research e orts to any ndustry, but not to any spec c good wthn the ndustry. I assume that countres d er n ther research productvtes across ndustres. Spec cally, deas regardng new technques arrve to ndvdual rms n country targetng ndustry as a Posson process wth arrval, rate l R; t where s a parameter representng the ndustry spec c research productvty of country, l R; t s the total number of researchers employed by the representatve rm and 2 (0; ) s a parameter that captures the extent of contemporaneous decreasng returns n research. I assume that there s a xed set of research rms targetng ndustry and I normalze the mass of ths set to one. The partcular functonal form assumed for the arrval rate of R&D has two advantages: () t captures the contemporaneous decreasng returns n R&D parsmonously through ; and () ts Inada condton together wth no free entry guarantee that all ndustry are targeted n equlbrum n any country. 0 Nevertheless, the case of constant returns to scale and free entry can be obtaned as the lmt. The ablty to drect research across ndustres s the new mechansm ntroduced n ths paper, and t wll be responsble for all the endogenous adjustments of technology to shocks that are the focus of the analyss n the present paper. In ths context, the parameter s of fundamental mportance snce t determnes the relevance of the new mechansm, wth hgher values of assocated wth stronger adjustments through the new margn. An dea s the realzaton of two random varables Z and X. The realzaton of Z ndcates the good z wthn ndustry to whch t apples, whle the realzaton of X ndcates the e cency x of the new technque n the producton of the correspondng good. The e cency of a technque ndcates how many unts of nal output are obtaned per unt of labor,.e., q xl. Throughout the rest of the analyss I assume that Z has a unform dstrbuton over [0; ] and X has a Pareto dstrbuton wth cdf H (x) x. As the result of the R&D process descrbed above, the arrval of deas regardng new producton technques for any nal good (z; ) n country has thefollowng characterstcs: () t follows an nhomogeneous Posson process P (z; ; ) wth arrval rate L R; t where L, R; t denotes the total number of researchers targetng ndustry at tme t; () for any par (z; ; ) ; (z 0 ; 0 ; 0 ) such that (z; ; ) 6 (z 0 ; 0 ; 0 ), P (z; ; ) and P (z 0 ; 0 ; 0 ) are ndependent. The total number of technques for good (z; ) dscovered up to tme t n country s then a random varable dstrbuted Posson wth parameter T t Z t L R; s ds: () The e cency of the best and second best technques up to tme t for a good n ndustry are random 0 No free entry n R&D mples that research rms make postve pro ts n equlbrum. However, the presence of pro ts per se does not a ect the results of the paper. Alternatvely, I could have assumed free entry and that R&D requres the combnaton of labor and a xed factor that s spec c to each country and ndustry. Wth these mod catons, the pro ts n the model presented n the text would become rents of the spec c factors n the alternatve model. In the extreme case of 0 no nnovaton takes place and the addtonal margn of adjusment s not opperatonal. 7

8 varables X ;() t ; X ;(2) t wth jont cdf gven by 2 F t (x ; x 2 ) Pr X ;() h + T t t x ; X ;(2) t x 2 x2 x e T t x 2 for x x 2. (2) Assumng a law of large numbers across the contnuum of goods wthn each ndustry, F t also represents the cdf of the jont dstrbuton of the best and second best technques across goods wthn ndustry n country. 3 Gven ts de nton and ts role n (2), throughout the paper I wll refer to T t nterchangeably as the stock of deas or the level of manufacturng technology of country n ndustry. are Preferences. The representatve household s preferences over streams of per-capta consumpton " Z U E 0 e t (C t L t ) L t 0 dt # " Z E 0 e 0 t C t where s the nverse of the ntertemporal elastcty of substtuton, tme preference, and for > 0. Z C C t exp log t d Z C t 0 c t (z) dz dt # (3) n s the e ectve rate of Market Structure and Geography. Although the detals of the market structure n both sectors and ts consequences are analyzed later, here I provde an overvew that serves as a gude through the exposton. All the assumptons regardng the market structure are completely standard n the lterature. As dscussed above, at any gven moment n tme there are many alternatve technques n each country to produce a gven nal good (z; ) that d er n ther respectve e cences. The owners of these technques around the world engage n prce competton n the market of good (z; ) n each country. As the result of ths competton, the producer wth the lowest margnal cost of servng that market becomes the only suppler of the good to that market and charges the mnmum between the monopoly prce and the maxmum prce that keeps compettors at bay. 4 In sum, the manufacturng sector s characterzed by Bertrand competton n the market of each nal good, and monopolstc competton among producers of nal goods wthn an ndustry. Entrepreneurs n the research sector nance ther R&D actvty ssung equty clams that pay nothng 2 See Appendx C.. for a proof. 3 Throughout the analyss I assume that T 0 s su cently hgh for all and, such that we can safely consder that (2) s vald for x x 2 0. All the results n the paper are derved under ths assumpton. In Appendx C.. I show that the d erence between F above and a cdf F 0 gven by (2) but wth support x x 2 0 becomes neglgble as T t. 4 The monopoly prce s the optmal prce charged by a monopoly that faces the resdual so-elastc demand correspondng to good (z; ). (4) (5) 8

9 f research e orts fal to mprove upon the state of the art technque for some good, but enttle ther holders to the stream of future monopoly pro ts f research succeeds. I assume that producton technques generated by the R&D actvty can be used only n the manufacturng sector of the country where they were developed, rulng out nternatonal lcensng and multnatonal corporatons. In order to abstract from ssues regardng ntertemporal trade and foregn ownershp of domestc rms, I assume that nancal assets are not traded. Ths assumpton mples that each country must nance all R&D that takes place wthn ts borders from domestc savngs, and that trade s balanced every perod. 5 However, consumers of country can freely borrow and lend at the rsk free domestc nterest rate r t. Geographc barrers are modeled n the standard ceberg formulaton, whereby j unts of a good must be shpped from country n order for unt to arrve to country j, wth j > f 6 j and. Throughout the analyss I use w t to denote the wage of country n perod t and set the wage of some country j as the numerare, w jt for all t. 2.2 Market Equlbrum 2.2. Demand The representatve household n country maxmzes ts preferences subject to ts budget constrant. Gven that preferences are addtvely separable over tme, we can dvde the consumer s problem nto a statc and a dynamc problem. The statc problem n each perod t nvolves the optmal allocaton of total expendture E t among the d erent goods n the economy. For a gven level of expendture E t allocated to ndustry, the expendture on ndvdual goods wthn that ndustry mpled by the CES lower ter utlty functon s E t (z) E t [p t (z) P t ] ; (6) h R where P t 0 p t (z) dz s the deal prce ndex of goods n ndustry. The upper ter Cobb-Douglas utlty functon mples that the share of total expendture allocated to ndustry n country s,.e., E t E t : (7) Gven the prce ndces of each ndustry, the aggregate prce ndex s From the dual problem of the statc problem we get Z P t exp log P t d : (8) Z E t C tp t, E t C t P t, and E t E td: (9) The dynamc problem nvolves the optmal allocaton of expendture across tme subject to an ntertem- 5 Exogenous trade de cts/supluses can be ntroduced wthout a ectng the qualtatve results presented n the paper. 9

10 poral budget constrant. The soluton to ths problem s characterzed by the famlar Euler equaton ec t h r t Pt e ; (0) where e X t d log (X t ) dt, together wth transversalty condtons on bonds holdngs, Manufacturng Sector The problem of the rms n the manufacturng sector s completely statc: at any tme t rms hre labor, produce, set prces and make ther export decsons takng as gven the level of technology and the demand condtons at the tme. At any moment n tme, the dstrbuton of manufacturng productvtes, the demand and the market structure n each ndustry of goods are as n Bernard, Eaton, Jensen and Kortum (2003) (henceforth BEJK.) Ths mples that, n the cross-secton, the structure of costs, markups and prces at the ndustry level are also as n BEJK. For ths reason, when descrbng the structure of the model wthn an ndustry, I descrbe those aspects of the model that are central to the purpose of ths paper, relegatng nonessental dervatons and proofs to the appendx. 6 Trade Shares and Prces. Bertrand competton mples that country buys each good from the cheapest source around the world. The cost dstrbutons I. n Appendx C..2 mply that the fracton of goods from ndustry that country j buys from country at tme t; jt, s jt T t w j : () jt In the prevous expresson, jt s a cost parameter that summarzes how manufacturng technology around the world, wages around the world and trade costs govern the dstrbuton of the cost of servng market n country j; t s gven by jt NX T kt w k kj : (2) k Gven that the dstrbuton of prces n each ndustry s ndependent of the source country, () also represents the fracton of country j s total expendture n ndustry that s allocated to goods from country. Fnally, the exact prce ndex for ndustry n country s P t B P ( t) ; (3) where B P s a constant that depends only on parameters.7 Cost Share n Revenues. In any ndustry, the share of total producton costs (ncludng trade 6 See Appendx C..2 for a dscusson of the determnaton of costs, markups and prces. n h o 7 Spec cally, B P +2 + m ( ) ( ) : See Appendx C..3 for a dervaton of (3). [ ( )] 0

11 costs) n country j s total expendture s ( + ). 8 Intutvely, a lower value of corresponds to a fatter upper tal of the Pareto dstrbuton from whch the e cency of a new technque s drawn. Ths mples that, on average, the cost reductons assocated wth a successful new technque are hgher for lower values of. 9 Consequently, low values of translate nto hgher average markups and a hgher (lower) share of pro ts (costs) n total revenue. Gven that the dstrbuton of costs and markups s ndependent of the source country, the share of total producton costs n country s sales to country j s also gven by ( + ). Snce ths s true for any destnaton country j, we obtan w t L q; t + R t; (4) where L q; t ; R t are the total number of workers employed and the total revenues/sales generated by country s manufacturng rms n ndustry ; respectvely. Fnally, market clearng at the ndustry level mples that the total revenue of country s rms producng goods n ndustry, R t, equals the world expendture on ndustry--goods produced n country, Research Sector R t NX jte jt. (5) j Frms n the research sector nvest n R&D to obtan new producton technques that mprove the e cency wth whch nal goods are produced. Research rms nance ther R&D actvty ssung equty clams that pay nothng f research e orts fal to mprove upon the state of the art technque for some good, but enttle ther holders to the stream of future pro ts f research succeeds. Gven that no nancal assets are traded, the savngs of domestc households are the only source of nancng for research rms. Gven that there s a contnuum [0; ] of dentcal rms drectng ther research e orts to ndustry, and that the rsks assocated wth the R&D e orts are ndependent across rms, well-dvers ed equty holders can obtan a determnstc return from ther equty nvestment. Consequently, the equlbrum prce of the equty clams ssued by the research rms equals ther expected return. Let V jt denote the expected present value at tme t of the stochastc future stream of pro ts generated by an dea from country n country j, condtonal on the dea beatng the state of the art n country j at tme t. Then V Z jt E t e t R s t rudu js (z) ds ; where js (z) are the pro ts at tme s of the rm producng good (z; ) n country j. Notce that the expected pro ts generated n country j at any future tme s > t are equal to average pro ts at s, multpled by the probablty at tme t that the dea s stll the state of the art n that country at tme s, wth ths probablty gven by jt js.20 Usng ths together wth the fact that the share of pro ts n the sales to 8 See Appendx C..4 for a proof. 9 A new technque s successful f t becomes the most e cent technque to serve the domestc market. 20 See Appendx C..5 for a proof.

12 country j s ( + ), the last expresson becomes 2 V jt Z t e R s t [r u + b ju]du E js ds: (6) + As the last expresson clearly shows, n evaluatng V jt, future average pro ts must be dscounted at the augmented rate r u + b ju. As more deas are dscovered and the technologcal fronter n country j grows, some of the rms servng that market at tme t are drven out of busness by more e cent rms. Ths endogenous termnaton probablty that reduces the expected value of pro ts of any rm producng at tme t s captured by the addtonal term b ju n the dscount rate. Gven that the prce of an equty clam ssued by a research rm equals ts expected value, any research rm maxmzes the expected returns from the R&D actvty. On the one hand, for any rm n country usng l R; t researchers to target ndustry, the expected bene t over the nterval dt s (l R; t ) h PN T t j jtv jt dt, where l R; t dt s the probablty of havng and dea n the nterval dt, T t s the probablty that the dea beats the technologcal fronter n country and jt s the probablty of beatng the state of the art technque n country j condtonal on beatng the fronter n country. On the other hand, the costs for the rm are smply the wages pad to researchers w t l R; t. The rst-order condton that characterzes the soluton to ths problem for each ndvdual rm yelds the aggregate pro t maxmzaton n research condton w t L R; t T t 2 NX 4 jtv jt j 3 5 (7) for all, where L R; t s the total number of researchers targetng ndustry. It s worth mentonng that, n ths settng, research rms make postve pro ts n equlbrum. However, the presence of these pro ts does not a ect the households savng decsons nor the drecton of nnovaton e orts n the economy Closng the Model and De nton of Equlbrum Balanced Trade. Snce there s no trade n nancal assets, households n country can save only n equty clams ssued by the domestc research sector. Consequently, at any moment n tme, total ncome s equal to the sum of total expendture n nal goods and total purchases of domestc equty clams Z h R t + R; t Z + w t L R; t d I td + E t ; where R t R R t d s the total revenue generated by manufacturng rms,22 R; t are the total pro ts generated by the research rms n ndustry and I t s the total value of household s purchases of equty 2 From the analyss of the costs share n revenues we know that the total producton costs n country s sales to country j s gven by ( + ), whch mples that the share of pro ts s ( + ). 22 Recall that R t q; t + w tl q; t, where q; t are total pro ts generated by manufacturng rms n class. 2

13 clams ssued by research rms n ndustry. Notcng that by de nton, the total revenue of research rms n ndustry s equal to I t, the last expresson mples that trade s balanced every perod23 R t E t : (8) Labor Market Clearng. The labor market clearng condton requres that the sum of the total number of producton workers and researchers allocated to all ndustres equals the total endowment of labor at each moment n tme. Recallng that L q; t represents the producton workers employed n ndustry and that L R; t denotes the total number of researchers drectng ther research e orts to the same ndustry, the labor market clearng condton can be wrtten as Z L t h L q; t + L R; t d: (9) In the rest of the paper I use L t ; Lq t ; LR t to denote total workers devoted to ndustry, total workers employed n the manufacturng sector and total workers employed as researchers respectvely,.e., L t L q; t + L R; t ; L q t Z Z L q; t d; L R t L R; t d: Havng descrbed all the components of the economy, we can now state a formal de nton of the equlbrum. De nton A market equlbrum s a set of functons r t ; w t ; P t ; R t, E t, C t : [0; ) R + and C t ; P t ; R t, E t, V t ; Lq; t ; L R; t ; T t : [0; ) R + for each country ; :::; N such that condtons (),(6)-(9) hold. 3 Balanced Growth Path In ths secton I wll focus on the balanced growth path of the economy n whch P t ; R t, E t, C t, C t ; P t ; R t, E t, V t ; Lq; t ; L R; t ; T t grow at constant rates for all countres and ndustres. As a general rule, throughout the rest of the paper I omt the subscrpt t when referrng to the BGP-level of varables that are constant n the BGP. 3. Solvng for the BGP Growth Rates and Research Intensty. In the model presented n the last secton, growth rates n the BGP depend only on the exogenous rate of populaton growth and technologcal parameters. In partcular, BGP-growth rates are not a ected by trade or standard polces such as taxes, R&D subsdes, etc; a feature that s common to sem-endogenous growth models. Ths means that the e ects of trade through the new margn of adjustment ntroduced by drected research wll only a ect the BGP-levels of 23 Trade s not requred to be balanced n each ndustry, mplyng that n general R t 6 E t. 3

14 varables of nterest such as technology, consumpton, prce level, etc. These level-e ects are the focus of the analyss n ths paper. For ths reason, I start the analyss of the BGP wth Lemma, whch descrbes those elements n the model that are not a ected by the addtonal margn of adjustment proposed n ths model. Lemma In any balanced growth path of ths economy the followng condton holds: () wages, trade shares and nterest rates are constant; () the nterest rate s the same across countres: r t r [n + n] + n () growth rates are gven by 24 el q; t e L R; t e R t e V jt n; e T t n; e Pt n; e Ct n + n (v) the research ntensty L R; t L t s constant and t s the same for all ndustres and countres: (n; ; ; ; ) LR; t L t 2 n 2 n + [r ( ) n] Proof. See Appendx C.2.. A hgher rate of populaton growth n rases the expected pro ts from R&D through a hgher expected ncrease n the sze of the market for successful deas, leadng to more nnovaton and growth as we can see n (). Hgh values of and low values of are assocated wth better R&D possbltes snce they represent weaker decreasng returns n R&D and a fatter upper tal of the dstrbuton from whch the e cency of an dea s drawn, respectvely. These better R&D possbltes are re ected n hgher growth rates for the stock of deas, and the consumpton aggregator as we can see n (). The rst two terms n the expresson for the nterest rate n () represent the real nterest rate, whle the last term s the change n the prce level. Notce that the expresson n brackets n the rst term of () s just the growth rate of the consumpton aggregator, Ct e. The hgher C e t s, the steeper s the expected ncrease n consumpton over tme, whch leads ndvduals wantng to smooth ther consumpton to ncrease ther borrowng at any gven rate, pushng up the equlbrum real nterest rate. A few thngs from Lemma are worth emphaszng. Frst, notce that country sze, research productvty and openness have no e ect on the BGP-growth rates or the BGP-research ntensty. Second, the results of Lemma are vald for any number of ndustres, ncludng the sngle ndustry case; ths means that extenson of the model to allow for multple ndustres and drected research has no e ect on BGP s growth rates, nterest rates or the research ntensty. Consequently, all the addtonal e ects on 24 For any varable X, Xt e X _ tx t denotes ts nstantaneous growth rate. 4

15 the nnovaton process brought about by the addtonal margn of adjustment emphaszed n ths paper are re ected on the levels of manufacturng technology, a topc to whch I turn next. Drected Research and Endogenous Manufacturng Technology. Let us now turn to the analyss of the new dstnctve feature of the model wth nnovaton and drected research: the endogenety of the BGP-dstrbuton of levels of manufacturng technology across ndustres. R&D nvestment decsons are made by pro t maxmzng rms who wegh the costs and the expected bene ts from those nvestments. A fundamental factor a ectng the expected bene ts of R&D s the expected sze of the market for a future nnovaton. For ths reason, a key varable n the study of the determnants of country s BGP-levels of technology s ts market share n ndustry, R;, de ned as the rato of country s total sales n ndustry, R t ; to the world expendture n the same ndustry, E t,.e., R; R t E t. 25 As shown later, R; s constant n the BGP, and consequently t also represents the fracton of present and future pro ts generated by world expendture on ndustry accrung to rms n country. Wth ths de nton n mnd, we can combne the de nton of T e t, Lemma., and (7) to get26 T t B T h R; V t w (20) where V t s the present value of pro ts generated by the stream of world expendture fe s g st n the ndustry; and B T n 2 s a constant. The last equaton clearly shows all the elements a ectng the BGP-level of manufacturng technology n any gven ndustry: the research productvty of the country n the ndustry, 27 ; the sze of the market captured by country s rms, R; V t ; and the R&D-nput costs gven by the wage pad to researchers w. The e ects of and w on T t are straghtforward: everythng else equal, a hgher research productvty or lower R&D-nput costs nduce more nnovaton that s ultmately re ected n a hgher manufacturng productvty. To understand the e ect of the actual market sze captured by country s rms, notce that n the BGP, R; V t also represents the expected present value of pro ts for an dea from country that surpasses the domestc fronter. 28 Consequently a larger market R; V t nduces more nnovaton whch s re ected n a hgher T t. It should be clear that equaton (20) s an equlbrum relatonshp between endogenous varables and as such, t does not allow to connect drectly T t to exogenous parameters.29 Nevertheless, t helps understand how the dstrbuton of the BGP-levels of manufacturng technology across ndustres s determned. Spec cally, t dent es the research productvty, the market sze captured by country s rms R; V t ; and the cost of researchers w, as the only aggregate channels through whch all exogenous parameters of the model can a ect manufacturng productvty. In partcular, factors such as openness, comparatve advantage n nnovaton, country sze and home market e ects, 30 all a ect T t through ther e ect on 25 E t P N E t. 26 See Appendx C.2.2 for a dervaton. 27 The relatnshp between T t and n (20) captures only the drect e ect of on T t, wthout consderng the potental ndrect e ects through R; V t w. 28 The domestc fronter s determned by the most e cent technques dscovered n the country of reference. 29 In fact, no closed form solutons exst for T t n terms of prmtves except for the autarky case. 30 See Appendx C.2.9 for a formal dscusson of home market e ects n ths model. 5

16 R; V t and w. Notce that the dervaton of equaton (20) does not depend on the number of ndustres n the model, mplyng that t s also vald for the sngle ndustry case n whch the addtonal margn of adjustment ntroduced by drected research s not operatonal. However, there s a fundamental d erence between the sngle-ndustry and the mult-ndustry case that cannot be apprecated clearly from equaton (20): when, and no drected research takes places, the degree of openness has no e ect on the BGP-level of technology. The reason for ths s that for any country, openness brngs about two opposng e ects on nnovaton: on the one hand, there s a postve e ect on nnovaton granted by the easer access to foregn markets experenced by domestc rms; on the other hand, there s a negatve e ect on nnovaton caused by the ncreased competton faced by those same rms n ther domestc markets. In the sngle-ndustry case, these two opposng e ects exactly cancel out, leavng the BGP-level of manufacturng technology unchanged. In contrast, n the mult-ndustry case, when a country opens up to trade t reallocates ts research e orts towards those ndustres n whch t has comparatve advantage. Ths reallocaton of resources mples that the two opposng e ects on nnovaton descrbed above do not cancel out at the ndustry level, and consequently openness has an e ect on the dstrbuton of BGP-levels of manufacturng technology. These e ects can be seen more clearly wth the help of the next equaton that shows how the BGPlevel of manufacturng technology relates to the resources allocated to each ndustry. Lettng L t L t denote the share of the total labor force allocated to ndustry, the de nton of T b t and ponts and v of Lemma yeld 3 T t BT 0 [ L t ] ; (2) where B 0 T (n) s a constant. The last equaton s partcularly helpful n showng how openness can have an e ect on the level of manufacturng technology n the presence of drected research. To see ths consder rst the snglendustry case, n whch there s no drected research by constructon. In ths case, all the resources must be allocated to the unque exstng ndustry regardless of the degree of openness,.e., for the only ndustry n the economy. Consequently, equaton (2) mples that n the sngle-ndustry case, the BGP-level of technology of a country depends only on ts research productvty and on the sze of ts labor force, T t B0 T L t, and t s not a ected by trade. In contrast, n the mult-ndustry case wth drected research, not only does trade a ect the allocaton of producton across ndustres a feature present n almost any trade model, but also t a ects the allocaton of research e orts across those ndustres, whch s ultmately re ected n the dstrbuton of BGP-levels of manufacturng technology as we can see from (2). The e ects of specalzaton and trade on the allocaton of resources across ndustres n the BGP can 3 See Appendx C.2.3 for the dervaton. 6

17 be seen wth the help of the next equaton 32 R; R R; E; ; (22) where the varable E t E t s the share of world expendture allocated to ndustry, R R t R t s the share of country n world output 33, and E; E t E t s the share of country s expendture n world expendture n the ndustry. The rst equalty n (22) clearly shows the e ects of specalzaton and world demand on manufacturng technology. On the one hand, notce that the rato R; R can be nterpreted as a measure of specalzaton: a value of ths rato above one means that country contrbutes more to world output n ndustry than what t does to total world output, re ectng a specalzaton n producton and R&D that s the result of more prmtve supply and demand factors such as comparatve advantage n nnovaton, geography and relatvely large domestc market n the ndustry, among others. On the other hand, re ects the e ects of world demand on : a greater world demand for goods n ndustry -as captured by - s assocated wth more producton and R&D n that ndustry n every country, leadng to a worldwde hgher BGP-level of the manufacturng technology n the ndustry. The second equalty n (22) s partcularly useful n understandng the e ects of trade on and T t. To see ths consder rst ts mplcatons for an autarkc economy. In autarky, whatever a country produces n an ndustry must be consumed n the domestc market,.e., producton must equal expendture n every ndustry or R; E; for all. In ths case, the allocaton of resources across ndustres s drven only by demand condtons n country as captured by. In contrast, when a country trades wth the world, trade does not need to be balanced n each ndustry and the rato R; E; can d er from one: f R; E; > (< ), then country s a net exporter (mporter) n that ndustry and ts level of technology s hgher (lower) n that ndustry relatve to an autarkc economy that shares the same fundamental parameters. Fnally, equatons (2) and (22) clearly show the fundamental role played by the parameter n controllng the relevance of the new margn emphaszed n ths paper: the weaker the decreasng returns to R&D are (hgh ), the stronger the endogenous e ects of drected research on manufacturng technology. Exstence of a Balanced Growth Path. The next proposton gathers all the equatons from whch the BGP of ths economy s obtaned and guarantees the exstence of a soluton. Although the system can be smpl ed even further, the system of equatons presented n the proposton clearly dent es the new elements of the model and facltates the comparson wth a benchmark model wth no drected research. Proposton The balanced growth path values correspondng to trade shares j; countres market shares R; and R, countres expendture shares E; and E, world-wde ndustres expendture shares 32 See Appendx C.2.4 for the dervaton. 33 In the de nton of R, Rt denotes country s total output, Rt R R td; and R t denotes world output, R t P N Rt. The letter R n ths notaton stands for revenue. 7

18 , countres levels of manufacturng technology T t followng system of equatons and wages w are obtaned as a soluton to the T t w Z j j P (23.) R N k T kt w R; d kj (23.5) NX NX R; j E; j (23.2) j E j (23.6) j E R (23.3) E; E (23.7) " # T t R; B0 T R L t (23.4) R w L t P N j w (23.8) L t j (23) for all,. Moreover, for 2 (0; ) a soluton to the system exsts wth R; > 0 for all ;. Proof. See Appendx C.2.5. The presentaton of the system of equatons (23) n Proposton allows us to dstngush two set of equatons. The set of equatons n the rst column represent structural equatons of the model stated prevously n the text but now expressed n terms of shares: the rst lne reproduces the expresson for trade shares obtaned n (); the second lne corresponds to equaton (5) that represents the market clearng condton for the output of each country n each ndustry; the thrd lne s the balanced trade condton (8); and the fourth lne combnes the technology relatonshps (2) and (22). The set of equatons n the second column express all the relatonshps between expendture shares, E; ; E ; market shares R; ; R, ndustres shares n world demand and wages w that follow mmedately from ther de ntons. Proposton clearly shows the two-way relatonshp between manufacturng technology and market shares n the present model. One drecton of ths relatonshp, whch s present n any Rcardan model of trade, goes from technology levels to market shares as we can see from equatons (23.) and (23.2). The second drecton of ths relatonshp, whch s the dstnctve element of the model wth drected research, goes from market shares to manufacturng technology. Ths re ects the feedback from underlyng supply and demand condtons to nnovaton as we can apprecate from equaton (23.4). Notce that wth the excepton of equaton (23.4), the rest of the system (23) contans the exact same equlbrum equatons correspondng to a mult-ndustry benchmark model wth no endogenous nnovaton, n whch the dstrbuton of rms productvtes wthn an ndustry s gven by (2) for some exogenous scale parameter T t, and n whch the structure of the manufacturng sector s the same as n the present model. 34 Relatve to such a benchmark, Proposton shows that the e ect of the new 34 The no nnovaton benchmark model descrbed corresponds to the case of a mult-ndustry BEJK (2003) model n whch the parameter s the same across ndustres. It also share the same equlbrum equatons wth a mult-ndustry EK(2002) model wth common across ndustres. Some studes usng models wth ths structure nclude Costnot, Donaldson and Komunjer (20), Chor (200) and Shkher (20), among others. 8