NBER WORKING PAPER SERIES PRODUCTIVITY SPILLOVERS, TERMS OF TRADE AND THE HOME MARKET EFFECT. Giancarlo Corsetti Philippe Martin Paolo Pesenti

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1 NBER WORKING PAPER SERIES PRODUCTIVITY SPILLOVERS, TERMS OF TRADE AND THE HOME MARKET EFFECT Giancarlo Corsei Philippe Marin Paolo Peseni Working Paper 65 hp:// NATIONAL BUREAU OF ECONOMIC RESEARCH 050 Massachuses Avenue Cambridge, MA 0238 March 2005 We hank Péer Benkzúr, Caroline Bes, Fabio Ghironi, Marc Meliz, Assaf Razin, Jaume Venura, and seminar paricipans a CEPR, Pompeu Fabra Universiy, Tel-Aviv Universiy, Triniy College in Dublin, AEA and SED Meeings for useful commens. Corsei s work is par of a Research Nework on The Analysis of Inernaional Capial Markes: Undersanding Europe s Role in he Global Economy, funded by he European Commission under he Research Training Nework Programme (Conrac No. HPRN-CT ). Marin s work is par of a CEPR Research Nework on Specializaion Versus Diversificaion: The Microeconomics of Regional Developmen and he Spaial Propagaion of Macroeconomic Shocks in Europe, funded by he European Commission under he Research Training Nework Programme (Conrac No: HPRN-CT ). The views expressed here are hose of he auhors, and do no necessarily reflec he posiion of he Federal Reserve Bank of New York, he Federal Reserve Sysem, or any oher insiuion wih which he auhors are affiliaed. The views expressed herein are hose of he auhor(s) and do no necessarily reflec he views of he Naional Bureau of Economic Research by Giancarlo Corsei, Philippe Marin, and Paolo Peseni. All righs reserved. Shor secions of ex, no o exceed wo paragraphs, may be quoed wihou explici permission provided ha full credi, including noice, is given o he source.

2 Produciviy Spillovers, Terms of Trade and he Home Marke Effec Giancarlo Corsei, Philippe Marin, and Paolo Peseni NBER Working Paper No. 65 March 2005 JEL No. F4, F32 ABSTRACT This paper analyzes he welfare implicaions of inernaional spillovers relaed o produciviy gains, changes in marke size, or governmen spending. We inroduce rade coss and endogenous varieies in a wo-counry general-equilibrium model wih monopolisic compeiion, drawing a disincion beween produciviy gains ha enhance manufacuring efficiency, and gains ha lower he cos of firms' enry and produc differeniaion. Our model suggess ha counries wih lower manufacuring coss have higher GDP bu supply a smaller number of goods a a lower inernaional price. Counries wih lower enry and differeniaion coss also have higher GDP, bu supply a larger array of goods a improved erms of rade. The sign of he inernaional welfare spillovers depends on erms of rade, bu also on consumers' ase for variey. Higher domesic demand has macroeconomic implicaions ha are similar o hose of a reducion in firms' enry coss. Giancarlo Corsei Rober Schuman Cenre European Universiy Insiue Via dei Rocceini 9 I 5006 San Domenico di Fiesole Ialy giancarlo.corsei@iue.i Philippe Marin CERAS ENS, 48 Boulevard Jourdan 7504 Paris, France marin-p@enpc.fr Paolo A. Peseni Federal Reserve Bank of New York 333 Libery Sree New York, NY 0045 and NBER paolo.peseni@ny.frb.org

3 Inroducion A common view in rade and growh heory is ha he increased supply of producs by a fas-growing economy mus be absorbed by inernaional markes a falling prices, causing a deerioraion of is erms of rade. The e ecs of produciviy gains are hen ransmied posiively o he counry s rading parners worldwide, hanks o movemens in inernaional relaive prices. Underlying his view is he assumpion ha he se of commodiies produced in he global economy and he number of produc varieies raded inernaionally are given and ime-invarian. When such assumpions are relaxed, as in Krugman (989), he ene ha rapidly growing counries mus experience a deerioraion of heir erms of rade becomes quesionable. The argumen is ha counries can change he aribues of heir producs: produc diversi caion can reduce or preven alogeher he fall in heir observed relaive prices. Moreover, wih an endogenous se of producs, he inernaional spillovers of produciviy gains are no exclusively driven by relaive price movemens. The counry s rade parners are hur by higher impor prices, bu also bene from he availabiliy of more varieies of goods. The ne welfare e ecs from hese wo compeing forces depend on he relaive magniude of monopoly power of a counry on is erms of rade, as well as consumers preferences for variey. These consideraions raise imporan issues in he de niion and use of appropriae welfare-based price indices, as heir produc baskes should re ec variaions in he array and qualiy of goods available o consumers (a poin sressed by Feensra (994) and more recenly by Broda and Weinsein (2004a,b) among ohers). This paper provides a sylized analysis of he welfare implicaions of inernaional spillovers. We analyze he deerminans of he erms of rade and he world paern of producion wihin he framework of a wo-counry macroeconomic model wih imperfecly compeiive produc markes. We le he se of varieies produced in each counry o be endogenous, and explicily ake ino accoun he welfare implicaions of variaions in he availabiliy of produc varieies and changes in consumpion baskes. We allow for ransacion coss in inernaional rade which induce home bias in consumpion, generaing deviaions from purchasing This paern of inernaional ransmission is clearly consisen wih he Harrod-Balassa-Samuelson hypohesis. According o his hypohesis, counries wih higher produciviy growh in he radable secor should experience an increase in he relaive price of heir nonradable goods. Provided ha he elasiciy of subsiuion across radables produced a home and abroad is su cienly high, hese counries will also experience an appreciaion of heir real exchange raes. Thus high produciviy growh in radables may simulaneously cause appreciaion of he real exchange rae, and weakening of he erms of rade. To he exen ha faser produciviy growh ranslaes ino faser oupu expansion, an imporan implicaion of he associaion of higher growh wih deerioraing erms of rade is ha inernaional rade conribues o a sable world income disribuion, as emphasized by Acemoglu and Venura (2002).

4 power pariy (PPP) even hough all goods are radable. Our framework hus encompasses he main elemens of rade models ha sudy he home marke e ec. 2 I also conribues o he recen bu fas-growing lieraure on general-equilibrium open-economy macroeconomic models wih endogenous radabiliy and produc innovaion, including Bergin and Glick (2003) and Ghironi and Meliz (2004) among ohers. We analyze inernaional produciviy di erenials by drawing a disincion beween produciviy in manufacuring he ypical de niion of produciviy in sandard macro models of inernaional ransmission and produciviy relaed o he abiliy of creaing new produc varieies and new rms. This disincion plays a crucial role in our analysis of he inernaional ransmission, as produciviy gains have very di eren implicaions for he equilibrium allocaion depending on wheher hey reduce he coss of manufacuring goods, or he coss of rms s enry and produc di ereniaion. When he number of produc varieies is endogenous, one may expec ha counries wih higher producion e ciency in manufacuring end o supply he wides array of goods. We show ha his is no necessarily he case. Under realisic assumpions abou parameers values, rms compeiion in more producive counries drives down prices and pro s, hus reducing he incenive for rms o sar producing new goods. Hence, he range of goods varieies supplied by domesic rms falls, driving down he overall supply of varieies in he world economy. Alhough higher e ciency raises he scale of producion of domesic rms, domesic households bene from produciviy gains mainly in erms of lower labor e ors. The counry experiences a deerioraion of is erms of rade and a depreciaion of is real exchange rae. Conversely, when produciviy gains reduce he coss of inroducing new varieies and operaing new rms, he number of produc varieies supplied by domesic rms and available o consumers worldwide rises, while he counry s erms of rade improve. If he real exchange rae is convenionally measured wihou accouning for he greaer availabiliy of goods varieies, he counry also experiences a real appreciaion. Overall, hen, esablishing wheher produciviy improvemens a ec he producion process as opposed o he coss of creaing varieies and rms is crucial o predicing heir e ec on rade volumes, erms of rade, and he real exchange rae. Recen empirical evidence 2 When produc markes are imperfecly compeiive and inernaionally segmened, local demand condiions have a di eren impac on he pro s of rms locaed in di eren counries. Because of rade coss, rms producing in he marke wih he sronger demand can ake advanage of local marke condiions beer han rms producing elsewhere. Wihou enry, pro s for he rms locaed in he counry wih he larger markes would increase relaive o rms abroad. When enry is possible, he sronger marke condiions induce he creaion of new rms producing new varieies. According o he home marke e ec, a change in demand for domesically produced goods raises he number of varieies more han proporionally, and/or raises domesic facor prices. 2

5 by Debaere and Lee (2004) appears o corroborae hese resuls: hey show ha produciviy improvemens induced by R&D as well as an increase in a counry s per capia GDP relaive o is rading parners have a posiive impac on he erms of rade. Since boh measures are relaed o changing varieies in he heoreical and empirical lieraure, his suggess ha fas oupu expansion need no necessarily imply a drop in a counry s erms of rade. Faser relaive oupu growh no induced by R&D has however a negaive impac on erms of rade. Our model also predics ha, ceeris paribus, counries wih a larger marke size (and herefore demand) supply a larger fracion of world goods, and have sronger erms of rade. Again, his predicion of he model is consisen wih empirical evidence. The model suggess ha oupu and consumpion in hese counries are high relaive o he res of he world, bu heir real exchange rae (appropriaely measured as o accoun for produc varieies) ends o be weaker. Analogously, when governmen spending is biased owards domesic goods, counries wih a larger scal secor have higher GDP, appreciaed erms of rade, bu weaker real exchange rae. High public consumpion is associaed wih high privae consumpion. The inernaional spillovers from domesic produciviy gains and surges in demand depend in par on he sign and size of relaive price movemens. In general, foreign households are beer o if hey can buy impors a lower prices he poin sressed by radiional models of he inernaional ransmission. Wih endogenous paerns of producion, however, anoher imporan deerminan of welfare is consumers ase for variey. Even if produciviy gains in manufacuring in one counry lower he inernaional price of he goods supplied by ha counry s rms, our model poins ou ha he number of varieies produced worldwide end o fall as price compeiion drives down pro s. Ulimaely, foreign agens bene from lower impor prices, bu hey may be worse o overall due o he reduced availabiliy of consumpion varieies. Conversely, even if lower enry coss end o raise he inernaional price of a counry s producs, he associaed rise in he number of varieies available o consumers worldwide may make foreign households beer o provided ha heir preference for produc variey is srong enough. Trade liberalizaion ha reduces cross-border rade coss bene s consumers via lower prices (higher real incomes). However, our model also emphasizes ha e ciency gains from deeper economic inegraion may resul in a lower array of goods available o consumers. This raises he issue of wheher world welfare could fall if consumers highly value variey a poin ofen sressed in he debae on he e ecs of globalizaion. We will show ha his is no he case: for any degree of love for varieies, our model predics ha he gains from 3

6 lower prices are always larger ha he coss associaed wih a possible conracion in he se of goods supplied world wide. All goods are radable in our model, so ha our framework di ers from boh he radiional Balassa-Samuelson view and is re-inerpreaion by Ghironi and Meliz (2004). As in he laer conribuion, we race he implicaions of using price indices ha fail o accoun for produc varieies, providing examples in which inappropriae indices of he real exchange rae would provide misleading informaion. I is worh noing ha in our model full radabiliy need no coincide wih free rade. In fac, wihou fricions in inernaional rade he real exchange rae would be consan in our seup, no deviaion from PPP would ever appear, and he naure of produciviy innovaions would no maer. Secion 2 presens he model seup. Secion 3 discusses is equilibrium properies. Secion 4 analyzes produciviy di erenials. Secion 5 sudies asymmeries in marke size, including he role of governmen spending. Secion 6 uses numerical examples o shed ligh on welfare resuls. Secion 7 concludes. 2 The model The world economy consiss of wo counries, Home and Foreign Foreign variables are denoed wih a sar. In each counry here are households, rms, and a governmen. Households consume a baske of di ereniaed radable goods. They love variey of goods: hey demand any brand of boh domesically produced and impored goods available in he marke. They supply labor o domesic rms only bu own claims on rms pro s worldwide. Labor is no mobile across borders. There are L households in he Home counry and L households in he Foreign counry. Over he ime frame relevan for analysis (period ), agens se up rms and creae new varieies of goods. Firms in boh counries produce goods for boh domesic and expor markes, using labor as he only inpu in producion. The varieies produced by rms operaing in he Home counry are de ned over a coninuum of mass n and indexed by h 2 [0; n ]. Similarly, Foreign varieies are indexed by f 2 [0; n ]. The number of varieies produced in each counry is endogenously deermined in he model. There is free enry in he goods secor, bu rms face xed enry coss o sar producion of a paricular variey. The enry coss consis of wages paid o he labor employed in seing up a rm. Firms in boh counries operae under condiions of monopolisic compeiion, so ha each rm produces one variey only. Hence, an increase in n corresponds o boh he inroducion of new varieies in he Home counry, and he creaion of new Home rms. A he end of period he (human) capial invesed in he creaion of a speci c 4

7 variey fully depreciaes and he producion process resars wih new enry of rms. Governmens are assumed o purchase goods from naional rms only. heir expendiures wih lump-sum ne axes. 2. Firms They nance To produce nal goods for he domesic and he expor markes, rms have access o a linear echnology in labor. The producion funcion of he represenaive Home rm producing a speci c variey h is: Y (h) `(h) () where Y (h) is he oupu of variey h, `(h) is labor used in is producion, and is a counry-speci c labor produciviy innovaion ha is common o all Home rms. Similarly, in he Foreign counry we have: Y (f) ` (f) (2) To sar he producion of a variey h in he Home counry, a rm needs o employ unis of Home labor. The rm hus faces a xed cos q(h): q (h) w (3) where w is he wage rae and is labor produciviy in he aciviies required o sar a rm. 3 Similarly, he enry cos in he Foreign counry is: q (f) w (4) E ciency in seing up a rm does no necessarily coincide wih produciviy in manufacuring. Thus, in general di ers from. From he vanage poin of a new rm, i is never pro able o produce a brand h or f already supplied by oher rms, raher han inroducing a new good variey. Hence in equilibrium rms are monopolisic suppliers of one good only. Variey h is sold o domesic agens (boh privae and public) or expored o foreign households. Shipping goods abroad enails ransporaion iceberg coss, denoed by and expressed in unis of he expor good. The resource consrain for variey h is herefore: Y (h) L C (h) + ( + ) L C (h) + G (h) (5) 3 I would be possible o inroduce alernaive parameerizaions of he enry coss, even hough hey would leave subsanially unalered our qualiaive resuls. For insance, one could consider a convex enry cos as an increasing funcion of he overall number of varieies. In his case he Foreign enry cos would depend on he number of Home varieies, adding a negaive inernaional spillover o he analysis. 5

8 where C (h) is consumpion of good h by he represenaive Home residen, C (h) is consumpion of good h by he represenaive Foreign residen, and G (h) is Home governmen purchases of good h. Similarly, he resource consrain faced by he Foreign rm producing good f is: Y (f) L ( + ) C (f) + L C (f) + G (f) (6) Le p (h) denoe he Home-currency price of one uni of good h sold in he domesic marke, and p (f) he Home-currency price of impors f. Similarly p (h) is he Foreigncurrency price of variey h impored by he Foreign counry and p (f) is he Foreigncurrency price of variey f sold in he Foreign counry. Also, le " denoe he nominal exchange rae, de ned as Home currency per uni of Foreign currency. Using he above noaion, Home-currency operaing pro s are: (h) p (h) L C (h) + " p (h) L C (h) + p (h) G (h) w ` (h) (7) Accouning for (5) and (), he opimal prices p (h) and p (h) charged by he Home rm o maximize is pro s (7) solve: (L C (h) + G (h) + p (h) 0 L C (h) + G (h) (8) " + " p (L (h) ( + ) C (h) L C 0: (h) (9) Similar expressions hold for (f), p (f) and p (f). 2.2 Households and governmen The uiliy of he represenaive naional household is a posiive funcion of consumpion C and a negaive funcion of labor e or `. As household preferences are de ned over a very large se of goods, uiliy is a well-de ned (and non-decreasing) funcion of all goods available in he marke. Focusing on Home counry residens, uiliy in period is: 4 U C where C is a composie good ha includes all varieies: ` (0) C A " Z n 0 Z n C (h) dh + C (f) 0 df # () 4 In our model we assume consan marginal disuiliy of labor, corresponding o an in nie Frisch elasiciy of labor (he laer is de ned as he elasiciy of labor suppply relaive o he wage, keeping consan he marginal uiliy of consumpion). I can be shown ha our resuls remain qualiaively unchanged under alernaive speci caions wih a lower ( nie) Frisch elasiciy. 6

9 and he erm A is de ned as: A (n + n ) : (2) In he expressions above, he parameers and denoe, respecively, he elasiciies of ineremporal and inraemporal (i.e., across varieies) subsiuion, wih > 0 and, and he parameer measures he degree of consumers love for variey. Precisely, as shown by Benassy (996), represens he marginal uiliy gain from spreading a given amoun of consumpion on a baske ha includes one addiional good variey. Consumers preferences for variey play an imporan role in our analysis, especially in deermining he sign of inernaional spillovers. Noe ha if we se ( ), expression () would be equivalen o he sandard Dixi-Sigliz consumpion index. In his case, he marginal uiliy of variey would be ( ), i.e. i would be sricly ied o elasiciy of subsiuion (which in equilibrium deermines he size of he markups in he produc marke). However, here is no paricular reason for adoping a welfare merics based on an arbirary and mechanical link beween he elasiciy of subsiuion among goods and individual preferences for goods variey. 5 reamen of hese wo dimensions of consumers preferences. The budge consrain for he represenaive Home household is: Z n 0 Our formulaion allows for a separae Z n p (h) C (h) dh + p (f) C (f) df + I w ` + T (3) 0 where T are lump-sum ne axes denominaed in Home currency, I is households invesmen in rms ( nancing enry coss) and is oal dividends revenue. We assume ha markes are incomplee. Wihou loss of generaliy, we also posi ha households are endowed wih a well-diversi ed inernaional porfolio of claims on rms pro s, so ha hey nance he same fracion of he cos of creaing new varieies in each counry. 6 Home households inves in a diversi ed porfolio of rms: I L + L Z n 0 Z n q (h) dh + " 0 q (f) df! Formally, In reurn, each Home household receives an equal share of pro s of all rms in he world economy: L + L Z n 0 Z n (h) dh + " 0 (f) df! (4) : (5) 5 This is discussed in he working paper version (974) of Dixi and Sigliz (977), as well as by Benassy (996). 6 This is in conras wih he sandard assumpion ha households only own and nance domesic rms. As long as free enry is assumed, posiing complee home bias in equiy porfolio would no aler our resuls. 7

10 The represenaive Home household maximizes (0) wih respec o C (h), C (f), and ` subjec o (3). The rs order condiions yield: C (h) A C (f) A where P is he uiliy-based consumer price index: p (h) C (6) P p (f) C (7) P w P C (8) P A " Z n 0 Z n p (h) dh + p (f) 0 df # (9) Wihou loss of generaliy, in wha follows we choose he appropriae nominal unis of accoun such ha w, so ha: C P : (20) As domesic households provide labor in a compeiive marke boh for rms sar-up and producion aciviies, he resource consrain in he Home labor marke is: L ` Z n Similar expressions hold in he Foreign counry. 0 Y (h) dh + n : (2) We posi ha he governmens spend only on local varieies and balance heir budges every period. The Home governmen budge consrain is herefore: Z n 0 p (h) G (h) dh L T (22) For simpliciy, we assume ha public demand for each speci c variey has he same price elasiciy as privae demand, so ha: p (h) G (h) G ; P G; G (f)! p (f) PG; G (23) where G and G denoe oal public consumpion in he wo counries and P G and P G are governmen spending de aors which involve only prices of domesically-produced varieies: 7 P G; n Z n 0 p (h) " dh, P G; n Z n 0 p (f) df # (24) 7 This speci caion deliberaely assumes ha governmens do no care abou variey, ha is, he parameer in public preferences in equal o one. This has no rs-order impac on our resuls as long as we analyze shocks around an iniial equilibrium where governmen expendiures are zero. 8

11 2.3 Prices Subsiuing expressions (6), (7), (23) and heir Foreign analogs in (8) and (9), we derive he prices charged by Home rms as markups over marginal coss, equal in our seup o labor coss per uni of produc: Similar expressions hold in he Foreign counry: p (h) w p (25) " p (h) w ( + ) p ( + ) (26) p (f) p (f) " w w p (27) ( + ) p ( + ) (28) Noe ha produciviy gains (higher a or ) lower marginal coss and reduce produc prices proporionally. The equilibrium uiliy-based Consumer Price Indices (CPIs) are de ned as he minimum expendiures required o purchase one uni of he baskes C and C, and are equal o: P p B A ; P p B A (29) where: B n + n (" p p ) ; B n + n (" p p ) ; (30) and, borrowing a familiar noaion from he inernaional rade lieraure, ( + ). The parameer is posiive and less han one; he case 0 corresponds o in nie rade coss and he case o zero rade coss. Finally, as governmens spend only on domesic varieies, in equilibrium he public consumpion indices P G and PG are simply: P G; p ; P G; p (3) 3 Firms pro s and produc varieies in he global economy 3. Free enry and he balance of paymens In his secion we characerize he model soluion, and commen on he equilibrium link beween pro s and he creaion of new varieies. To sar wih, using (6), (7), (20), and (29), we can wrie he operaing pro s earned by imperfecly compeiive rms as follows: (h) A p 4 L + L " (p p ) 5 + p G (32) B B 8 The privae individual demands for he h and f goods in he Home counry are: 9

12 (f) A p 2 4 L B + L " (p p ) B where and denoe rms pro s in heir own currencies p G (33) Noe ha wih consan markups, we can express he pro s of he represenaive rm in boh counries as a consan fracion of global sales. Wih sricly posiive rade coss (i.e., < ), we can use he expressions for pro s o shed ligh on some crucial dimensions of he ransmission mechanism furher sudied below. Firs, holding he number of varieies and relaive prices consan, an increase in Home marke size (an increase in L) raises operaing pro s a Home more han abroad. This is he Home marke e ec analyzed in rade models. Second, everyhing else consan, an increase in he number of Home rms lowers Home pro s more han Foreign pro s. This is because rade coss parially shield Foreign rms from compeiion by Home rms. Third, holding he number of Foreign and Home goods consan, a depreciaion of he Home currency (an increase in ) raises pro s a Home. This is he compeiive e ec of real depreciaions: Home-produced goods become cheaper, and heir demand increases. Finally, for a given exchange rae and number of rms, a produciviy innovaion in he manufacuring secor a Home (an increase in ) corresponds o a drop in p p, wih opposie e ecs on Home pro s. By charging lower prices, Home rms become relaively more compeiive and experience an increase in sales. However, because all Home rms experience he same rise in produciviy, and charge he same lower price, when he ineremporal elasiciy of subsiuion is less han one, sales revenue decreases overall. 9 Wih free enry, opimal invesmen in new varieies implies ha he value of a rm is equal o he cos of creaing a variey, and in equilibrium his mus be equal o he value of operaing pro s. Thus compeiion in he goods marke implies he following free enry C (h) A P p A p B C (f) A P (" p ( + )) A ( + ) (" p p) p B. Similarly, in he Foreign counry: C C (f) A P p A p and B and (h) A P (p ( + ) " ) A ( + ) (" p p) p B. 9 One may conjecure ha hese resuls depend on he assumpion of in nie Frisch elasiciy. As labor supply becomes more inelasic, domesic agens may ake advanage of produciviy gains in manufacuring by increasing he array of goods supplied by domesic rms (hence by creaing new rms). Noably, his is no he case: wih a less elasic labor supply, he e ec of higher manufacuring produciviy on he global number of varieies is weaker, bu remains negaive as long as he ineremporal elasiciy of subsiuion is less han. 0

13 condiions: q (34) q (35) I follows ha, in equilibrium, a fall in enry coss mus ranslae ino a corresponding fall in operaing pro s. When <, he mechanism of adjusmen requires a rise in he number of varieies supplied by domesic rms, driving pro s down. Noe also ha, as pro s are proporional o global sales, he level of enry coss pins down rms size. Using his resul, we can wrie he size of each rm as a funcion of produciviy levels and as well as he elasiciy : Y (h) ( ) : (36) I follows ha Home GDP per capia can be wrien simply as w ` n (L ), and Home employmen per capia is ` n (L ). These expressions will be useful in he analysis o follow. Aggregaing privae and public budge consrains in any of he wo counries, we can wrie he balance of paymens in erms of Home currency as follows: 2 4 p n L " (p p ) p n L " (p p ) A L n L + L B + L " n L + L + L q n L + L L " q n L + L B (37) The rs wo erms are Home expors less Home impors, boh inclusive of rade coss heir di erence is herefore he rade balance. The hird erm corresponds o ne pro s paid by Home rms o Foreign households, he fourh erm o ne pro s paid by Foreign rms o Home households heir di erence represening ne facor paymens. The balance of hese four erms is he curren accoun. The sum of he las wo erms is he capial accoun, i.e. he nancing of Home rms by Foreign households minus he nancing of Foreign rms by Home agens. Using he balance of paymen equilibrium (37), he wo free enry condiions (34) and (35), as well as he equaions for pro s (32) and (33), i can be checked ha equilibrium pro s are: L n P + p G (38) L n P + p G (39) where P P C is oal domesic expendiure.

14 The above expressions highligh ha an increase in he number of varieies has wo e ecs on pro s via consumpion demand. On he one hand, i leads o a fall in he price of curren consumpion P (as de ned in (29)) by, he marginal welfare gain of goods diversiy. The fall in he price index induces ineremporal subsiuion ino curren consumpion by ( )( ), raising demand and pro s. On he oher hand, an increase in he number of goods implies inraemporal subsiuion away from exising goods, measured by a negaive e ec on demand. The ne e ec is herefore given by., wih Choosing a benchmark value for is no obvious, as we are no aware of any empirical/quaniaive work on he subjec. However, he assumpion ha consumers value diversiy, ha is, >, is no very srong. When >, an increase in he number of goods does lower curren consumpion and herefore lowers sales and pro s if < ( ). A su cien condiion for such inequaliy o hold is ha he ineremporal elasiciy of subsiuion is no larger han corresponding o benchmark values o be found in he lieraure, whereas he ineremporal elasiciy of subsiuion is usually se beween and /2. In he res of he paper, unless oherwise saed, we will carry ou our analysis under he mainained assumpion ha: < Implicaions of rade reforms Recalling ha q, q, p ( ) and p ( ), he sysem of hree equaions (34), (35) and (37) deermine he hree endogenous variables ", n and n as a funcion of he exogenous variables,,,, L, L, G and G for given parameers,,, and. I is sraighforward o verify ha if L L and G G 0, here is a symmeric equilibrium such ha " and n n. In wha follows, we ake his equilibrium as he baseline in our comparaive saics exercises. This symmeric equilibrium is characerized as follows: p p ( ), w w, ` ` n. Noe also ha: P P n: The number of varieies produced by each counry is: n + 2 ( )( ) () ( ) ( ) ( + ) ( )( ) (40) This expression suggess an ineresing resul on he e ecs of rade liberalizaion, de ned as lower rade coss which in our model correspond o a higher. Namely, when he ineremporal elasiciy of subsiuion is less han one, rade liberalizaion acually reduces he number of varieies supplied a he world level. This conrass wih he predicion of 0 In he sandard Dixi-Sigliz model where ( ), he condiion is > >. Inuiively, his implies ha goods are subsiues in he Edgeworh-Pareo sense. 2

15 he sandard Krugman model wih rade-induced variey expansion. Recenly, Baldwin and Forslid (2004) have discussed a similar resul in a model wih rms heerogeneiy afer Meliz (2003). The above expression however makes i clear ha he fall in good varieies afer liberalizaion does no depend on rms heerogeneiy. In general, rade liberalizaion has wo opposie e ecs: on he one hand i raises demand for goods, increases pro s and herefore induces enry. This e ec of raising is capured by he numeraor of he expression (32) for Home pro s. On he oher hand, rade liberalizaion (if symmeric on boh impors and expors) induces more compeiion by rms abroad. This e ec is capured by he presence of in he erms a he denominaor of equaion (32). The number of varieies produced and raded by Home rms falls wih rade liberalizaion when (a) < ( ), so ha pro s are decreasing in he number of varieies and (b) <, so ha he decrease in he price index induced by rade liberalizaion does no lead o a large jump in curren consumpion. 4 Domesic and inernaional implicaions of produciviy di erenials In his and he following secions, we analyze he mechanism of inernaional ransmission wih endogenous produc varieies, by di ereniaing he equilibrium condiions (34), (35) and (37) around a symmeric equilibrium. We consider only shocks o Home exogenous variables, wih he undersanding ha similar resuls hold wih respec o changes in Foreign variables. Consider rs he deerminans of he overall number of varieies available o households worldwide: [ + ( )] dn + dn n dl + dg n ( ) d + d (4) The number of varieies in he global economy unambiguously rises wih a larger Home marke size, higher Home governmen spending on Home goods, and gains in e ciency in seing up rms and creaing new goods in he Home counry. Noably, he e ecs of gains in manufacuring produciviy depend on he size of he ineremporal elasiciy of subsiuion: he global number of varieies falls when <, rises oherwise. We will discuss he inuiion underlying his resul below. For he ime being, i is worh noing ha a produciviy innovaion ha a ecs boh manufacuring coss and enry coss symmerically, i.e. d d, unambiguously leads o enry. Also, oher hings equal, exchange rae movemens do no a ec he global number of varieies: in our symmeric world economy, changes in he exchange rae a ec symmerically bu wih opposie sign 3

16 sales and pro s in boh counries, wihou global e ecs. One may reasonably expec ha counries wih higher produciviy be he world suppliers of mos good varieies, sold abroad a a relaively low inernaional price. In wha follows, we will show ha his is no necessarily he case. A crucial issue in his respec is he disincion beween produciviy in manufacuring, and e ciency gains reducing he coss of seing up rms and inroducing new varieies. In our framework, counries wih higher produciviy in manufacuring acually charge lower inernaional prices (i.e., heir erms of rade deeriorae), bu supply a smaller (no a larger) se of goods o world markes. This is because higher compeiion in he produc marke drives goods prices and Home suppliers pro s down. For a given cos of seing up a rm, lower goods prices and pro s lead o marke exi. Such compeiion e ec is somewha mued abroad, o he exen ha Foreign rms are shielded by rade coss. Conversely, gains in e ciency relaed o innovaion and rms creaion improve a counry s erms of rade, and raise he number of varieies, boh domesically and globally. In his case higher produciviy does no spur more inensive compeiion in a given se of goods markes, bu leads rms o compee by expanding he array of goods and services provided. Inuiively, inroducing a new good when agens prefer varieies implies ha demand rises in line wih supply. More e cien counries will hus be able o expand heir expors, wihou su ering a deerioraion of heir erms of rade. In he Foreign counry, more compeiion by Home rms can be parly o se by higher global demand. The ne e ec on enry and employmen is herefore ambiguous. 4. Produciviy gains in manufacuring We rs focus on gains in manufacuring produciviy by he Home counry, i.e. an increase in. We have already seen in (4) ha, as long as <, gains in Home manufacuring produciviy reduce he number of goods produced worldwide. Their implicaions for he inernaional allocaion of producion are summarized by he following expressions: dn ( ) ( ) 2 ( ) < 0 (42) n d 2 [ + ( )] 2 ( ) dn ( ) ( ) 2 ( ) + (43) n d 2 [ + ( )] 2 ( ) where: (2 ) [ ( )] > 0: (44) Gains in Home manufacuring produciviy unambiguously reduce he number of varieies supplied by Home rms, alhough heir scale of producion rises (see (36)). e ec on he number of Foreign rms is ambiguous. I is negaive in he Dixi-Sigliz case, The 4

17 ( ), or when rade coss are low enough, as srong compeiion by Home rms grealy reduces Foreign producers pro s. In any case, i can be veri ed ha he number of varieies always falls more a Home han in he Foreign counry. To shed ligh on hese resuls, i is useful o conras heir micro and macro dimensions. From he vanage poin of an individual Home rm, produciviy gains ha reduce he marginal coss of producion are an opporuniy for rms o expand heir marke share and pro s via a reducion in he price of heir producs. However, wih an economy-wide produciviy innovaion, all Home rms simulaneously experience he same fall in marginal coss: hey all compee wih each oher by cuing prices. As discussed above, a fall in he price of consumpion a ecs aggregae consumpion demand wih elasiciy : When his elasiciy is below one, lower prices ranslae ino lower pro s for he Home rms. For given enry coss, lower pro s reduce he number of varieies produced by Home rms. Conversely, when >, a fall in prices raises demand more han proporionally, driving up pro s and herefore he number of varieies supplied in equilibrium. There is no change in Home varieies when. Since we scale nominal variables by equaing wage rae o he consan parameer, nominal exchange rae movemens index he relaive price of labor. Our rs resul is ha Home labor becomes more expensive he nominal exchange rae appreciaes in response o produciviy innovaions: d" d [( ) ( ) + ( ) ( + )] ( ) < 0: (45) Noe ha he e ec is sronger, he higher he rade coss. Noneheless, he erms of rade deeriorae. De ning T OT p (p " ), we have: dt OT d d" d < 0: (46) Even if Home labor is relaively more expensive han Foreign labor, marginal coss and herefore he price of domesic goods fall wih produciviy gains, more han o seing he nominal exchange rae appreciaion. I can also be checked ha wih zero rade coss (i.e. when approaches ) i mus be he case ha dt OT d. Le RER denoe he welfare-based real exchange rae, i.e., RER " P P. The real exchange rae also depreciaes, moving in he opposie direcion relaive o he nominal In our model, all rms supply goods o boh he domesic and he foreign markes, hence enry and exi a naional level correspond one-o-one o enry and exi in he expor markes. Allowing for rm-speci c produciviies (as in Ghironi and Meliz (2004)) inroduces he possibiliy ha some good be endogenously non-raded in equilibrium, depending on prices and produciviy levels. In his case, enry and exi in he expor markes may di er from enry and exi of rms locaed in he Home counry. Wha our analysis highlighs is he aggregae e ec on oal supply, which is someimes blurred in analyses sressing heerogeneiy. 5

18 exchange rae: drer RER d ( ) ( ) > 0 (47) In oher words, movemens in he real exchange rae are dominaed by he relaive movemen of price indices (raher han by he movemen in he nominal exchange rae). he Home marke, he welfare-based price index falls in response o produciviy gains in manufacuring: dp P d dn < 0 (48) n d This resul is due boh o a fall in he price of domesic goods and impor prices (he laer because of exchange rae appreciaion), and o he direc impac of an increase in goods variey on he welfare-based price index. Symmerically, he response of he welfare-based price index in he Foreign counry o changes in is: dp P d The sign here is generally ambiguous, bu we noe ha P In dn (49) n d decreases when rade coss and/or love for variey are su cienly low ( is high, is low enough). Inuiively, wih low rade coss, sronger compeiion by more e cien Home rms drives down goods prices and causes exi in he Foreign marke. The overall e ec is a drop in he CPI, unless variey is srongly preferred by consumers. Recen lieraure has emphasized poenial measuremen problems ha arise when consumpion baskes are no properly consruced so o accoun for (endogenous) changes in he number of goods varieies (see Feensra (994) and Broda and Weinsein (2004a,b) among ohers). Ghironi and Meliz (2004) carry ou a numerical assessmen of he gap beween heoreically-consisen real exchange raes, and wha hey dub empirical exchange raes based on price indices ha simply average prices over a xed bundle of varieies. In he same spiri, we se dn d dn d 0 in he above expressions, and denoe he resuling price index a Home and abroad wih e P and e P, respecively. If we used hese price indices in compuing he real exchange rae (ha is, de ning ]RER " e P e P ), he e ec of a produciviy innovaion would sill be a depreciaion, bu a a lower rae: ]RER d ]RER + d" > 0 (50) d + d We conclude by noing ha wihou rade coss, i.e. wih, he real exchange rae (independenly of he CPI de niion) would always be consan, i.e., PPP would hold. Bu rade coss generae home bias in consumpion, hus produciviy di erences induce deviaions from PPP despie he fac ha in our framework all goods are raded. 6

19 4.2 E ciency gains in creaing new rms and new goods Consider now he e ecs of produciviy gains ha reduce coss in he aciviies a he origin of new rms and varieies. An analysis of his ype of e ecs is obviously absen in sandard models wihou enry, whereas produciviy is con ned o he manufacuring secor. We have seen in equaion (4) above ha lower enry coss raise he number of varieies supplied a he global level. Bu he worldwide disribuion of varieies clearly changes. The counry-speci c e ecs of changes in he level of are given by: dn ( ) ( ) > 0 (5) n d 2 [ + ( )] 2 ( ) dn ( ) + 2 ( ) (52) n d 2 [ + ( )] 2 ( ) The rs expression is unambiguously posiive: more goods are produced by he Home counry. In he Foreign counry, insead, he e ec is generally ambiguous. I can be veri ed ha he number of varieies supplied by Foreign rms decreases in he Dixi-Sigliz case, ( ) ; or when rade coss are low enough. Trade inegraion (a higher ) ampli es he e ec of lower enry coss on he Home supply of varieies. This is because new enry a Home raises compeiion worldwide, he more so he lower rade coss. Wih low rade coss, compeiion by Home producers unambiguously drives Foreign rms pro s down. To analyze he equilibrium response of relaive prices, we rs observe ha marginal coss and herefore p and p are no a eced by. however, srenghens: The Home nominal exchange rae, d" d ( ) ( ) + ( ) ( + ) < 0: (53) Given p and p, he erms of rade move one-o-one wih he nominal exchange rae: he counry wih lower coss of enry experiences an equilibrium appreciaion of he erms of rade. The response of he nominal exchange rae is sronger, he higher rade coss are his is so because high rade coss raise he rae of appreciaion required o bring abou he equilibrium change in relaive demand for goods. Alhough boh he nominal exchange rae and he erms of rade become sronger, he welfare-based real exchange rae acually depreciaes: drer RER d ( ) > 0 (54) The weakening of he real exchange rae is enirely due o he increase in he number of varieies, re ecing he imporan propery of welfare-based price indices discussed above: a wider array of varieies per se reduces he CPI. 7

20 I follows ha, when produciviy a ecs he cos of creaing new varieies, he sign of our comparaive saics resuls will crucially depend on which measure of real exchange rae is used, i.e. wheher his is he welfare-based RER or he empirically relevan ]RER. In fac, a measure of he real exchange rae based on price indices ha fail o accoun for changes in he number of varieies would move in he opposie direcion relaive o he welfare-based real exchange rae, i.e., i would poin o a real exchange rae appreciaion: d ]RER d" < 0: (55) ]RER d + d The use of an inappropriae index would hus provide severely biased informaion. In he Home marke, he response of he welfare-based CPI o changes in is negaive: dp dn < 0: (56) P d n d Impor prices fall wih a sronger currency. The higher availabiliy of produc varieies also reduces he welfare-based price index. The response of he CPI in he Foreign counry is insead ambiguous: dp P d dn (57) n d Once again, he Foreign price index falls when rade coss and/or love for variey are suf- cienly low ( is high, is high enough). In hese cases Foreign consumers face higher impor prices, bu he adverse erms of rade e ecs on he welfare-based price index is more han compensaed by a higher array of goods resuling in a lower CPI. 4.3 A comparison We have seen above ha improvemens in produciviy in Home manufacuring, and asymmeric e ciency gains reducing Home enry coss relaive o Foreign coss have quie di eren equilibrium implicaions. Consider for insance he comovemens in GDP per capia and relaive prices prediced by he model. Since he raio of Home o Foreign GDP per capia can be wrien as:l n (" L n ), i is easy o verify ha relaive GDP is increasing in boh and. However, a rise in Home GDP relaive o Foreign GDP may be associaed wih eiher an appreciaion or a depreciaion of he real exchange rae depending on which ype of innovaion akes place. Predicions reminiscen of Balassa-Samuelson richer counries have a sronger real exchange rae are generaed by innovaions o, bu only if price indices are no properly adjused for changes in produc varieies. In his case, he (empirically relevan) exchange rae would unambiguously appreciae wih a rise in relaive GDP driven by higher produciviy in creaing rms and new goods. 8

21 Mos crucially, he implicaions for he erms of rade are widely di eren: he erms of rade deeriorae in response o an increase in produciviy ha lowers marginal coss in producion, while improves if produciviy gains reduce he cos of rms enry. The laer e ec dominaes if d d. 2 These resuls quesion he sandard predicion ha higher growh raes lead o deerioraing he erms of rade. Disinguishing beween -ype and -ype produciviies is a di cul and challenging empirical ask. Recen empirical sudies have appealed o he inuiion in Krugman (989), and aemped o measure he e ec on he erms of rade of an increase in he supply of goods, as opposed o an increase in he varieies of goods supplied in he world markes. In a quie elaboraed panel sudy, Debaere and Lee (2004) indeed nd a posiive associaion beween higher spending in R&D and sronger erms of rade. In his respec, he model in his paper provides a heoreical framework o concepualize and moivae similar empirical exercises. 3 5 Asymmeries in marke size In his secion we analyze he implicaions of marke size, revisiing some resuls of he rade lieraure on he Home marke e ec. In is original formulaion ha can be raced back o Krugman (980), he Home marke e ec represens he more-han-proporional impac of an increase in marke size on he number of varieies produced domesically, in he presence of rade coss and holding labor supply and real exchange rae consan. In wha follows we cas he analysis of marke size asymmeries here measured by L L in he conex of our general-equilibrium analysis wih endogenous inernaional prices and labor supply. Nex, we compare hese resuls wih he e ecs of asymmeries in governmen spending across counries. 5. Labor force and privae expendiure Consider rs he general-equilibrium implicaions of a relaively larger Home marke on he number of varieies produced worldwide and in each counry. Equaion (4) above shows ha an increase in L raises he number of varieies supplied a he global level. The 2 In his case, he erms of rade improve by ( ) ( ). 3 In our model goods price elasiciies do no depend on he number of rms and varieies. One may consider an exension of he model esablishing such a link. However, while improving he realism of our speci caion, we do no expec such an exension o overurn our main resuls. For insance, o he exen ha a produciviy gain ha leads o exi also reduces he price elasiciy of exising rms, erms of rade movemens are likely o be aenuaed in equilibrium, bu no overurned. 9

22 counry-speci c e ecs are given by: dn n dl dn n dl ( ) + 2 [ + ( )] 2 ( ) 2 [ + ( )] ( ) 2 ( ) ( ) 2 ( ) > 0 (58a) (58b) The rs expression above is always posiive: he Home counry always experiences an increase in he number of varieies produced locally. According o he Home marke e ec, as long as rade coss are posiive and <, 4 an increase in Home demand raises rms incenive o ener ino he Home marke. The lower he rade coss, he easier is o inves in he high-demand counry and sill expor o he oher marke: he advanage relaed o marke size is hen ampli ed by small rade coss (higher ). I follows ha marke size e ecs are sronger in economies ha are more closely inegraed. In he Foreign counry, he e ec of a larger Home marke is ambiguous, crucially depending on rade coss. When rade coss are low enough, compeiion by a larger number of Home rms is so srong ha Foreign rms exi he marke. Observe ha when he uiliy from consumpion is logarihmic ( ), a larger Home marke size L raises n one o one, bu leaves n una eced: from he viewpoin of Foreign producers he posiive implicaions of a larger Home marke are exacly o se by he increasing compeiion by a larger number of Home rms. In our model, goods prices in domesic currency respond only o changes in produciviy and wage raes, bu no o changes in marke size. We can herefore analyze erms of rade direcions by looking exclusively a movemens in he nominal exchange rae: d" ( ) ( ) ( ) < 0 (59) dl [2 ( )] ( + ) A large Home marke appreciaes he Home currency, and herefore improves he Home erms of rade p (p " ). As regards facor prices, i raises Home wages and labor coss relaive o heir Foreign counerpars. Noe ha his e ec vanishes when rade coss approach zero ( goes o ). In his case erms of rade and relaive facor prices are consan since he increase in impors due o a larger marke is exacly compensaed by he increase in Home expors following he creaion of new varieies. A higher marke size lowers he welfare-based Home CPI: dp dn < 0 (60) P dl n dl This resul re ecs lower impor prices (because of he exchange rae appreciaion) as well as he larger se of goods available o consumers. As regards he Foreign price index, he 4 In he case in which is exacly equal o no Home marke e ec arises and he locaion of producion of varieies is indeerminae. 20

23 impac is ambiguous: dp P dl dn (6) n dl The sign of he above expression is negaive when rade coss are low enough and/or consumers have a srong ase for variey. In his case, he increase in he global number of varieies more han compensaes he deerioraion of he Foreign counry s erms of rade. Using he above welfare-based price indices, i is easy o show ha a larger marke size unambiguously depreciaes he Home currency in real erms: drer RER dl ( ) ( )( ) + ( ) ( + ) d" > 0 (62) dl Noe ha he inernaional price of consumpion moves in he opposie direcion relaive o he inernaional price of producs: a weaker real exchange rae corresponds o sronger erms of rade. Conversely, using he empirically relevan price indices e P and e P o compue he real exchange rae ]RER, we would have a real appreciaion: d ]RER d" < 0 (63) ]RER dl + dl If he real exchange rae is no correcly measured, changes in marke size move he real exchange rae and he erms of rade in he same direcion. 5.2 Governmen spending Do counries wih higher governmen spending have a sronger real exchange rae? Does governmen spending srenghen he compeiive posiion of domesic producers by creaing a larger marke for heir producs? In his secion we use our general-equilibrium model o address hese issues. Noe ha asymmeries in public spending are qualiaively di eren from he asymmeries in counry size discussed above in wo imporan respecs. Firs, di erences in L a ec boh goods demand and he labor force he laer e ec is obviously absen in an analysis of governmen spending G. Second, we assume ha public consumpion falls enirely on domesically produced goods, while he (endogenous) home bias in privae consumpion expendiure associaed wih an increase in L is much less pronounced. We sar our analysis by considering he e ec of variaions in Home governmen spending on he number of varieies: dn n dg dn n dg + 2 ( ) + 2 ( ) 2 ( ) [ + ( )] > 0 (64) + 2 ( ) 2 ( ) + 2 ( ) [ + ( )] Under sandard assumpions on elasiciies, a larger governmen spending is associaed wih a higher number of rms in he Home counry. The number of rms in he Foreign counry (65) 2