Exports and foreign direct investments in an endogenous-entry model with real and nominal uncertainty

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1 Expors and foreign direc invesmens in an endogenous-enry model wih real and nominal uncerainy Lilia Cavallari Universiy of Rome III Absrac Drawing on a racable DSGE model wih nominal rigidiy, his paper sudies he implicaions of rms enry in domesic and foreign markes for he inernaional business cycle. The paper shows ha he decision o ener a new marke as well as he choice wheher o inves a home or abroad depend on global moneary and produciviy condiions. I nd ha a domesic moneary expansion migh favor or deer sar-up invesmens, depending on wheher he poenial enran is a naional or a mulinaional rm. Moreover, a srucural policy change, as an increase in he degree of moneary sabilizaion, has a posiive impac on rend invesmens in all secors. Firms dynamics, in urn, ampli es consumpion and employmen spillovers in he world economy. I sress ha his may have non-negligible consequences for welfare. Keywords: mulinaional rms, endogenous enry, moneary policy, FDI JEL codes: F4 Inroducion The remendous growh in rade and FDI ows ha has occurred in he pas wo decades has changed he srucure of macroeconomic inerdependence in he global economy, especially among similar, indusrialized counries and beween hese and newly emerging economies (see UNCTAD, 7). Consequenly, a growing ineres has been devoed o sudies of he inernaional business Lilia Cavallari, Universiy of Rome III, DIPES, Via C. Chiabrera, 99, 45 Rome, Ialy, cavallar@uniroma3.i. The auhor wishes o hank an anonymous referee and paricipans in seminars a he Universiy of Prague (European Economic and Finance Sociey Annual Conference 8), LUISS, Perugia (Socieà Ialiana degli Economisi, Annual Conference 8) and Milano Bicocca (II Ineric Conference on Endogenous Marke Srucure).

2 cycle where macroeconomic inerdependence is endogenous. on rade relaions, overlooking inernaional linkages hrough FDI ows. Mos conribuions, however, focus This paper aims o ll he gap and invesigae boh dimensions of macroeconomic inerdependence by focusing on he role of producers enry in domesic and foreign markes for he ransmission of moneary policy and produciviy shocks around he world. For his purpose, i proposes a racable DSGE model wih nominal rigidiy ha incorporaes he endogenous deerminaion of he number of rms ha decide o ener a new marke a home or abroad. Firms are allowed o choose wheher o serve foreign markes hrough expors or engage in direc invesmens overseas. 3 The paper conribues o a recen srand of research analyzing he implicaions of rms enry and produc creaion for moneary policy and he business cycle dynamics. 4 A general nding in his lieraure is ha sicky prices can disor enry behavior in a number of ways, hereby creaing a new role for moneary policy in welfare maximizaion. I is argued ha well-designed moneary rules can eliminae he incenive on he par of rms o (excessively) conrac exensive margins in cyclical downurns and help replicae he business cycle dynamics ha would prevail wih exible prices. Moreover, enry and exi of rms can a ec moneary ransmission hrough a variey of channels. Bilbiie, Ghironi and Méliz, 7 sress he relevance of asse pricing in spreading he e ecs of moneary policy. The nancing of sar-up invesmens urns ou o be negaively associaed wih a moneary expansion in heir model. Ohers, as Bergin and Corsei, 5 and Lewis, 6, focus on he real cos of new produc creaion, suggesing ha moneary policy would raher boos enry (as i appears o be he case in he daa). These conribuions, as mos models in his area, refer o closed economies. Russ, 7 and Cavallari, 7 develop open economy models wih endogenous enry ha are closes o he one sudied here. Russ focuses on foreign invesmens by mulinaional corporaions in a seing wih heerogeneous rms à la Méliz, 3. Cavallari considers a represenaive- rm model wih endogenous rade and foreign invesmens. These conribuions poin o di eren mo- Open economy models wih endogenous enry include, among ohers, Ghironi and Méliz, 5, Corsei, Peseni and Marin, 7, Bergin, Glick and Taylor, 6 and Bergin and Glick, 3, 5 and 7. Russ, 7 and Cavallari, 7 provide noable excepions. In a framework wih a xed number of rms, see also Cavallari, 8. 3 Helpman, Méliz and Yeaple, 4, have pionereed a fas-growing lieraure ha invesigaes he general equilibrium consequences of alernaive modes of foreign marke access. Helpman, 6, provides a comprehensive survey of conribuions in his area. 4 A non-exhausive lis of conribuions in his area includes Bilbiie, Ghironi and Méliz, 7, Bergin and Corsei, 5, Lewis, 6, Elkouri and Mancini Gri oli, 6 and Barensen and Waller, 7. These sudies refer o closed economies.

3 ives behind why moneary policy migh in principle arac or deer foreign invesmens. The former sresses wheher moneary uncerainy originaes a home or abroad as a key deerminan of he percepion of exchange rae risk on he par of poenial invesors conemplaing o engage in invesmens overseas. The laer focuses on he degree of moneary sabilizaion, showing ha invesmens migh be sub-opimally low when sabilizaion is no complee. Di erenly from previous conribuions, his paper ness wihin a uni ed framework boh he decision of rms wheher o ener a marke a home or abroad (as in Russ, 7) and wheher o serve foreign cusomers hrough rade or by engaging in direc invesmens overseas (as in Cavallari, 7). To his end, he model in Cavallari, 7 is exended so as o encompass rms ha operae on domesic markes only, endogenizing he size of he non-radable secor. This in urn allows domesic demand o play a role (along wih foreign demand) in he decision wheher o serve foreign markes in he rs place. In addiion, he model can accoun for movemens of rms beween he raded and he non-raded secor as hose sressed in he lieraure showing ha a relevan fracion of he growh in rade volumes occurs a he exensive margin, wih expors of new producs and previously nonraded goods (see Kehoe and Ruhl, ). 5 The paper proposes a way of exploring he mechanisms behind such observaions in a simple macro model where rms are idenical in all respecs excep for he marke demand hey face. I provides an illusraion of how he dynamics of rms across and wihin secors can help improve our undersanding of macroeconomic inerdependence. Remarkably, I nd ha rms enry in domesic and foreign markes depends on curren moneary and produciviy condiions a home and abroad. The major role of exernal shocks is a novely in he lieraure and a consequence of sricly inerdependen invesmen decisions wihin and across secors. A rise in home produciviy, for insance, is shown o a ec rms invesmens well beyond he domesic borders, by discouraging overseas invesmens of home mulinaional rms in favor of domesic invesmens in he foreign counry. I furher argue ha a moneary expansion migh have conrasing e ecs on domesic and foreign invesmens as a resul of heir di eren degree of exposure o exchange rae risk. In my seup wih pre-deermined prices and exible enry coss, a moneary easing is associaed wih higher enry coss and a boosing demand, wih clearly opposing e ecs on he araciveness of new invesmens. An expansion a home is found o favor domesic invesmens a he expense of direc invesmens by foreign mulinaionals whenever exchange rae pass-hrough is no complee. The nding is a consequence of movemens in he exchange rae ha reduce he foreign-currency revenues of invesmens 5 See also Bernard and Jensen,. Based on a panel of US manufacuring rms beween 987 and 997, hey show ha on average 3.9% of non-exporing rms begin o expor in any given year in he sample and.6 % of exporers sop o rade. 3

4 below enry coss, hereby discouraging foreign invesmens. Exi of foreign mulinaionals from home markes, in urn, improves he prospecive pro s of home invesors, crowding-in domesic invesmens. Moneary policy can a ec enry decisions also by changing he percepion of macroeconomic risks on he par of poenial invesors. A more acive moneary policy, as capured by a rise in moneary volailiy or an increase in he covariance wih produciviy shocks, is found o have a permanen e ec on he level of invesmens in all secors of he economy. A couner-cyclical moneary policy, in fac, helps sabilize marginal coss and hence reduce he risks associaed wih pre-se prices. Accouning for rms dynamics allows o emphasize a new propagaion mechanism in he inernaional business cycle arising from cross-counry di erences in rms inegraion sraegies. When he number of producers is endogenous, high-produciviy economies end o arac domesic and foreign invesmens, supplying he wides range of produc varieies. Firms in low-produciviy economies, on he conrary, will nd i convenien o inves abroad, serving foreign cusomers mainly hrough local a liaes of mulinaional corporaions. As a consequence of massive enry in home markes, he relaive price of home producs will fall, i.e. he home counry experiences a deerioraion in is erms of rade. The nding is reminiscen of he well-known immiserizing growh by Bhagwai, 958, showing ha a sharp deerioraion in he erms of rade of a growing economy migh reduce welfare. Ye, in my model falling erms of rade are he resul of asymmeries in rms inegraion sraegies over he business cycle. A cavea o my ndings is ha he endency owards falling prices migh be aenuaed in secors characerized by high dispersion of produciviy across rms. The rise in he number of producers would hen come wih a drop in average produciviy. The quesion provides an ineresing ground for furher research. Finally, I compare consumpion and employmen spillovers wih and wihou enry e ecs in a number of numerical exercises. The inuiion ha endogenous enry ampli es he propagaion of moneary and produciviy shocks is con rmed in all calibraions. Take, for insance, a global moneary expansion. The moneary easing, wherever i is originaed, is associaed wih a rise in world-wide consumpion and employmen. Inernaional spillovers, however, are higher when exensive margins are allowed o move relaive o he model wih a xed number of rms. The paper is srucured as follows. Secion models he world economy. Secion 3 derives he sicky-price equilibrium of he log-linearized model. Secion 4 provides numerical simulaions ha help address poenial ambiguiies in he analyical resuls. Secion 5 concludes. 4

5 The model. Preferences Expeced lifeime uiliy of a ypical home agen i is given by: i = E X = U i (C i ; M i P ; Li ) () where ow uiliy U is a posiive funcion of real consumpion, C, and real money balances, M=P; a negaive funcion of labor e or, L; and is he discoun facor. In order o keep algebraic complexiy a a bare minimum, I adop he addiively-separable speci caion: U i (C i ; M i P ; Li ) = log C i + log M i P L i () Foreign agens preferences are expressed in an analogous way, bu are de ned over consumpion of goods sold in he foreign counry, C ; foreign money balances, M =P, and foreign labor, L. Each agen in he world economy consumes a baske ha comprises radable and non-radable goods, C T and C N, respecively, as follows: C = C = C T C N ( ) (3) C T C N ( ) wih (; ): Goods markes are characerized by monopoly disorions due o less han perfec subsiuabiliy among di ereniaed varieies. Traded goods consumed in he home counry are de ned over a coninuum of varieies of mass N X ; where N X is he number of foreign exporers, and are indexed by f X (; N X ): Traded goods consumed abroad are de ned over a mass N X of varieies indexed by h X (; N X ), where N X is he number of home expor rms. Consumpion of radables is herefore given by: C T = C T = Z N X Z NX C(f X ) ( ) dfx C (h X ) ( ) dhx (4) Consumers preferences for non-raded goods are de ned in a similar way: 5

6 C N = C N = Z ND " Z N D Z ND C(h D ) +N MN hd + C(f MN ) fmn N D Z N C(f D ) D +N MN fd + ND ( ) # C(h MN ) ( ) hmn (5) where N D and NMN are, respecively, he number of home rms and foreign mulinaionals in he home non-raded secor and a similar inerpreaion holds for ND and N MN. The number of rms acive in he world economy in each period will be deermined endogenously in he model. The assumpion of a uniary elasiciy of subsiuion in consumpion beween radables and non-radables in (4) is made for ease of simpliciy in order o keep he model linear (in logs) as in Obsfeld and Rogo, b. A uniary elasiciy migh be a relaively high number compared o some esimaes suggesed in he lieraure. 6 This migh imply oo small ucuaions in he heoreical erms of rade relaive o hose observed in he daa (a higher elasiciy requires a lower price change in order o accommodae a given change in quaniies). In my seup wih endogenous invesmens, however, ucuaions in he erms of rade are inensi ed by movemens of rms beween he expor and he non-raded secor. As i will be apparen below, asymmeric inegraion sraegies on he par of rms acive in world markes can lead o sharp movemens in he erms of rade over ime.. Technology I associae each rm wih an individual variey, so ha a rm, say, h D is he sole producer of he corresponding variey of he home non-raded good. There will herefore be hree classes of rms consisen wih preferences (4) and (5), namely expor rms, domesic rms and a liaes of foreign mulinaional enerprises. Firms are idenical in all oher respecs. The assumpion of homogeneous rms has he major advanage of providing closed-form analyical soluions wih no need o resor o a paricular aggregaion mehod. On he ip side, i leaves undeermined which rm belongs o which class. This, however, does no appear oo limiing given he emphasis of he paper on he macro implicaions of enry. Technology is linear and labor is he only inpu. The represenaive rm locaed in he home counry faces he following producion funcion: Y (!) = AL (!) 6 Lane and Milesi Ferrei, 4 derive a value for he elasiciy beween radables and non-radables as low as.5. The esimaed elasiciy is even lower for relaively closed economies as he US, Europe and Japan. Ohers, as Osry and Reinhar, 99 provide esimaes in he range beween.6 and.3 for a sample of developing counries. 6

7 where Y (!) is oupu of variey! (; h D + h X + f MN ) ; L he labor inpu and A is a sochasic erm capuring home labor produciviy. Similarly, in he foreign counry echnology is given by: Y (! ) = A L (! ) where! (; f D + f X + h MN ) :.3 Enry Enry in boh he raded and he non-raded secor is cosly. Enry coss comprise a one-period lag in invesmen, as rms mus pay he xed cos a he beginning of each period in order o sar producion in he subsequen period. Enry coss are denominaed in he currency of he counry where he invesmen is locaed, so ha all rms esablishing a new plan in he home counry, comprising foreign mulinaionals, face enry coss equal o q in home currency. Similarly, new invesmens on he foreign soil enail he cos q in foreign currency. The enry cos for each class of rms is measured in unis of labor as follows: q j = W A N j q MN = W A N MN (6) qj = W A N j q MNj = W A N MN where j = (D; X); W is he nominal wage in home currency, W he nominal wage in foreign currency and is a measure of he concaviy of he cos funcion. As sressed by Corsei, Marin and Peseni, 8, a high value of capures he growing di culy of enering a marke when he number of direc compeiors increases. In addiion o enry coss, raded goods also enail iceberg-ype ranspor coss, so ha for one uni of he nal good o arrive a a foreign desinaion > unis mus be sen. These shipping coss capure a variey of (variable) coss associaed wih inernaional rade. 7.4 Individual and governmen s budge consrains In each period, he represenaive agen holds home currency, wo inernaional bonds, B i and B i, respecively denominaed in home and foreign currency, and shares in all ypes of domesic rms, s j. He receives labor income from rms acive on he home soil, a share in he pro s of home 7 Tari barriers range on average beween 4 and 5 per cen of he price of raded goods. Trade coss - including ari and non-ari barriers, shipping and disribuion coss - vary grealy across classes of goods. 7

8 naional and mulinaional rms, j, and pays non-disorionary ne axes, T, o he governmen. The budge consrain of agen i is herefore: where i and i B i + + " B i + + M i + + X j=d;x;mn " B i ( + i +) + M i + W L i + X Z Nj j=d;x;mn s j q j dh j B i ( + i + )+ (7) Z Nj s j j dh j P i C i are, respecively, home and foreign nominal ineres raes and " is he nominal exchange rae de ned as unis of home currency for one uni of foreign currency. The governmen simply rebaes all seignorage revenue in lump-sum ransfers o households, so ha is budge consrain is as follows: T i Z M i M i di + Z T i di = (8).5 The equilibrium allocaion The equilibrium in he world economy is characerized as follows. Given he sochasic processes driving moneary policies and produciviy, and given he iniial holdings of bonds, money and shares, he equilibrium is a se of processes for he nominal exchange rae ", he number of rms acive in he world economy (N j and Nj ), he home allocaions and prices ( L, C, P and W ) and heir foreign counerpars (L, C, P and W ) such ha a) consumers opimaliy condiions are sais ed, b) rms pro s are maximized, c) he free enry condiions are me, d) markes for each asse, each good and for labor clear and e) he resource consrains are sais ed..5. Consumers rs order condiions Agens choose consumpion, labor e or, money, bond and share holdings in each period so as o maximize heir life-ime uiliy () subjec o he budge consrain (7). The rs order condiions for home agens are: C(h D ) = ( ) P C p(hd ) (9) P N P N C(f X ) = P C P T C (f MN ) = ( p(fx ) () P T ) P C p(fmn ) () P N P N 8

9 W = P C () M P = C + i + q D = E P +C + P C D+ (h D ) q X = E P +C + P C X+ (h X ) " q MN = E P +C + P C MN+ (h MN ) (3) i + (4) (5) (6) where P T ; P N prices de ned as follows: P C = E (( + i + )) (7) P+ C + " = E " + + i + (8) P C and P are indices for, respecively, raded goods, non-raded goods and consumer P = P T P N (9) P T = P N = Z N X Z ND p(f X ) df X p(h D ) dh D + Z ND +N MN N D p(f MN ) df MN () where p(f X ) and p(f MN ) are he prices for varieies f X and f MN, respecively, of he foreign good and p(h D ) is he price of variey h D of he home good. Combining he Euler equaions (7) and (8) and money demand (3), i is possible o de ne an index of he home moneary sance P C such ha a moneary expansion, i.e. a rise in ; is associaed wih a lower ineres rae. Similarly, P C represens foreign moneary policy..5. Pro maximizaion I allow for nominal rigidiies by assuming ha rms se prices a he beginning of each period, before shocks and enry occur, and are commied o mee marke demand a he given price for he whole period. 8 Firms ac as monopolisic compeiors and choose prices so as o maximize expeced 8 Firms commimen applies as long as pre-se prices do no fall shor of marginal coss. In wha follows, he domain of real and nominal shocks is resriced so ha he paricipaion consrain is always sais ed. 9

10 pro s given marke demand, (9), () or (). Firms acive in foreign markes also ake he degree of exchange rae pass-hrough as given, hereby leing he nal price of heir produc vary wih he exchange rae a a consan elasiciy equal o : 9 In his seing, a value of = corresponds o local currency pricing, namely a siuaion where prices are pre-deermined in he consumers currency and do no respond o movemens in he exchange rae. The case = corresponds o producers currency pricing. Opimal pre-deermined prices are given by: p (h D ) = E ( A ) E ( ) p (f MN ) = E ( " A ) " E ( " )) p (f D ) = E ( ) A E ( ) p (f X ) = E " ( " ) A ) E ( " p (h MN ) = E ( " ) A " E ( " ) p (h X ) = E ( " ) A " E ( " ) () where = ( ) is he usual mark-up. Noe ha prese prices incorporae a premium over expeced marginal coss as a hedge agains he risk of a fuure drop in pro s. Expeced pro s, in fac, depend on he fuure realizaions of marginal coss, =A a home and =A in he foreign counry, as well as on he covariance beween hese variables and nominal spending, respecively, and. In foreign markes, he premium also depends on he expeced movemens in he exchange rae and heir implicaions for nal (consumers ) prices. Consider, for insance, a home rm serving foreign cusomers eiher hrough expors or via foreign invesmens. Oher hings being equal, he premium in he foreign-currency price of her producs will be higher as long as she expecs he domesic currency o appreciae, a fall in ", hereby reducing sales revenue in foreign currency. Depending on he degree of exchange rae pass-hrough, he appreciaion may also a ec expeced pro s hrough a change in foreign demand. Wih sicky prices, mark-ups are ime-varying ex-pos. Any unexpeced increase in marginal coss, as due for insance o a fall in produciviy or a rise in nominal wages, will have no consequences for marke demand as long as prices are xed, hereby reducing pro margins. As usual wih CES preferences, pro s are proporional o overall spending in each secor. In he home counry, he pro s of domesic rms and foreign mulinaionals are given by: 9 This is equivalen o saying ha rms opimally choose he price for expors and mulinaional sales in heir own currency, recognizing ha he nal price may vary wih he exchange rae as in Corsei and Peseni, 5. Empirical evidence on raded good prices, as documened by, among ohers, Goldberg and Kneer, 997, Engel, 999, Parsley and Wei, and Campa and Goldberg, 5 poins o a degree of exchange rae pass-hrough ino impor prices which is higher han zero on average alhough far below uniy. Lipsey, 999 documens ha mulinaional rms also engage in subsanial pricing-o-marke hrough heir a liaes abroad.

11 (h D ) = D ( ) () ND + N NMN (f MN ) = (h X ) = MN " X N X ( ) ND + N NMN where D X MN N p(h D ) p(h D ) A " p(h X ) " p(h X ) p(h D ) p(f MN ) " p (f MN ) p(h D ) A A " p (f MN ) p(h D ) and similar expressions hold in he foreign economy. As already noed, (he inverse of) pro margins j vary wih nominal and produciviy shocks as long as prices are xed. Wih exible prices, insead, pro margins would be consan a he level =..5.3 Free enry condiions Each home rm will ener a domesic or a foreign marke as long as he expeced presen value of operaing pro s in he subsequen period, on he righ hand side, will cover enry coss, on he lef hand side: q D = E + q X = E + " qmn = E " A + p + (h D ) " + p + (h X ) + " + p + (h MN ) C + (h D ) A + + A + C+ (h X ) C + (h MN ) (3) Opimal exible prices are simply given by: implying J = : p(h D ) = p(f MN ) = "p (h X ) p (f D ) = p (h MN ) = p(f X) " = = A A

12 and similar relaions hold for foreign rms. Subsiuing pro s () and enry coss (6) ino he equaions above and re-arranging, yields: N + D = N + X = N + MN = E D + + E N + "+ A E + + E X + E MN + E N + + ( E MN + E D + ) A E ( " ( ) A E "+ + + E MN + " E D + + " + ) + " E ( " )! (4)!.5.4 Aggregae resource consrains Asse markes equilibrium requires ha inernaional bonds are in zero ne supply: Z B i di + Z B i di = Z B i di + Z B i di = (5) Goods marke clearing in he world economy requires ha world supply and demand for each ype of good are equalized: N D Y (h D ) N X Y (h X ) N MN Y (h MN ) Z Z Z C(h D )di C (h X )di C (h MN )di Finally, equilibrium in he labor marke yields: N DY (f D ) N XY (f X ) Z Z C (f D )di (6) N MNY (f MN ) C(f X )di Z C(f MN )di L NX Y (h X ) + N D Y (h D ) + NMN A Y (f MN ) + N + D + N + X L A + N + MN N X Y (f X ) + ND Y (f D ) + N MN Y (h MN ) + N + D + N + X + N + MN (7) where L = R Li di and L = R Li di are, respecively, he home and foreign labor force: Aggregaing he budge consrains (7) across agens and using he governmen (8) and resource consrains (6) and (7), yields he balance of paymens in home currency: "P T C T P T C T + N MN " MN N MN MN N MN "q MN + N MNq MN = (8)

13 where iniial bond holdings are assumed o be zero in each counry, i.e. B = B = : As usual in he class of models ha use log uiliy, inernaional asse rade is redundan, implying ha bond holdings will be zero in any poin in ime provided iniial non-moneary wealh is zero as well. The rs wo addends in he expression above consiue he rade balance, i.e. home expors less home impors. The hird erm is he reurn on he invesmens of home mulinaional corporaions abroad and he fourh erm is he dividends of foreign mulinaionals a home, heir di erence is herefore ne facor paymens. The sum of he rade balance and ne facor paymens consiues he curren accoun. The las wo erms are he nancing of foreign direc invesmens owards and from he home economy and heir di erence is he capial accoun of he balance of paymens. Subsiuing demands (), pro s () and enry cos (6) ino he aggregae accouning equaion (8), gives a useful expression for he nominal exchange rae as a funcion of real and nominal shocks: " = + + MN ( )N MN (N MN +N ( )N MN MN ( N N MN N D ) +N D ) (N MN ) + A (N MN ) + A The expression above, ogeher wih he free enry condiions (4), capure macroeconomic dynamics in he home economy. (9).6 Soluion sraegy In wha follows, i is assumed ha moneary policy and produciviy shocks are lognormal disribued variables de nes as: where m, m ; a and a = e m = e m A = e a A = e a are random variables wih a join Normal disribuion. Wihou loss of generaliy, he sochasic processes for moneary policy and produciviy are hypohesized symmeric across counries wih means, respecively, m and a and variances m and a. 3 A log-linearized version of he model will describe he macroeconomic dynamics of he world economy in he neighborhood of a symmeric seady sae where all shocks are mued, i.e. where m = m = a = a =. For noaional convenience, lower-case leers will denoe he log deviaion of As poined by Corsei and Peseni,, a balanced curren accoun is he resul of hree hypohesis: i) a Cobb-Douglas consumpion index ii) logarihmic uiliy in consumpion and iii) zero iniial ne asses. 3 Cross-counry asymmeries in cyclical condiions can sill be capured by he covariances am and a m. 3

14 he corresponding upper-case variables, so ha, for insance, c = log C of he exchange rae for which e = log " log ": log C; wih he excepion 3 Macroeconomic dynamics 3. Enry and he nominal exchange rae The percen change in he nominal exchange rae is given by (see Appendix A for analyical deails): e = a (m m ) + a (a a ) + a ( am a m) (3) where he consans a ; a and a are de ned as follows: a = a = h + ( ) + ( ) i h ( ) + i ( ) ( ) h i + ( ) ( ) + + ( ) ( ) ( + ) a = a n h io + ( ) + + ( ) ( ) In my seup wih endogenous invesmens, he nominal exchange rae moves in response o a wide range of cyclical ucuaions comprising cross-counry di erences in moneary policy and produciviy. A rise in, say, home produciviy, i.e. an increase in a, a ecs boh he curren and he capial accoun of he balance of paymens, wih opposing e ecs on he exchange rae. Wih sicky prices, he main implicaion of he produciviy rise will be an (unexpeced) increase in he pro s of all rms esablished on he home soil, including he local subsidiaries of foreign mulinaionals. As long as mulinaional pro s are ransferred abroad, he domesic currency will end o depreciae. On he oher side, however, higher produciviy reduces enry coss in home markes, hereby aracing foreign direc invesmens and appreciaing he domesic currency. In my speci caion, hese wo e ecs exacly cancel ou wih linear enry coss, i.e. when = : I sress ha he exchange rae moves one o one wih cross-counry di erences in moneary policy in his case. In general, for posiive values of, he ne e ec of he produciviy rise is a priori ambiguous. 4 Moreover, he exchange rae migh under-reac o global moneary condiions and even urn negaive, i.e. a. In order o see why, consider a one percen moneary expansion a home. 4 The coe cien a urns negaive for a very low value of and a very high value of. 4

15 Absen mulinaional aciviies, he main exernal implicaion of he moneary easing would be a one percen increase in he value of home impors. In equilibrium, he value of expors mus rise by he same amoun, implying ha he nominal exchange rae will need o depreciae by exacly one percen (recall ha he rade balance is equal o " ; so ha e = m m 5 ). This is no necessarily he case when here are foreign invesmens. On he one side, in fac, he moneary expansion booss demand in home markes, creaing a more favorable environmen for foreign rms esablished on he home soil and for hose conemplaing a sar-up. On he oher side, however, i in aes nominal coss, hereby reducing curren and prospecive pro s. In my speci caion, hese poenially o seing e ecs happen o cancel ou exacly when pass-hrough is complee, i.e. wih = ; leing he exchange rae move one o one wih relaive moneary policy. 6 I nally sress ha he consan erm in equaion (3) can be inerpreed as capuring rend movemens. The nominal exchange rae ucuaes around is seady sae value, displaying no rend, as long as cyclical condiions are compleely symmeric across counries, i.e. when am = a m : Trend movemens also disappear when exchange rae changes have no consequences for nal prices, namely when = : The dynamics of sar-up invesmens in he home counry is as follows: n D = n X = n MN = ( + ) + a + X ( + ) + a a + a a + ( a ) (m m ) + D + a a + [a a + ( a ) (m m )] + MN (3) where j are consans enirely deermined by uncerainy: D = 4 m a + + a ( ) ( am a m ) + ) ( (a m + a a) ( ) (a m + a a) + (a am + a a) MN = D + a ( am a m ) 3 5 X = m a + a ( am a m ) Remarkably, equaions (3) show ha curren moneary policy shocks can a ec he araciveness of invesing in one s naive marke as compared wih overseas. In order o see he poin, focus on a home moneary expansion, i.e. an increase in m. The moneary easing, by raising nominal coss 5 Noe ha he amoun of currency depreciaion does no depend on exchange rae pass-hrough. The adjusmen will ake place wih unchanged rade ows in a very low pass-hrough scenario, i.e. when = : 6 I is immediae o verify ha a = when = : 5

16 in home currency, makes a sar-up in he home economy more expensive. This will clearly deer invesmens. The rise in m; on he oher side, booss demand in home markes, hereby aracing domesic as well as foreign invesors. As i will be apparen soon, which one of hese wo opposing e ecs will acually prevail crucially depends on wheher poenial invesors are naive or foreigners. Wih a uniary demand elasiciy as in he raded secor he wo e ecs discussed above exacly cancel ou. A one percen moneary policy shock will lead o a proporional increase in boh enry coss and prospecive pro s, implying ha expor rms will have no incenive o engage in sar-up aciviies. 7 This is no o say, however, ha moneary policy has no bearing on invesmens in he raded secor. Various dimensions of moneary uncerainy, as volailiy and he covariance wih produciviy shocks, are relevan for a rm conemplaing o inves. Equaion (3) shows ha a symmeric world-wide increase in moneary volailiy, i.e. a rise in m, leads o an upward movemen in rend invesmens by expor rms, X. The nding migh appear odd a rs sigh. In a seup wih nominal rigidiy, however, invesors migh bene from higher volailiy on he ground ha i faciliaes changes in world spending and relaive prices ha would oherwise be di cul o achieve. The same reasoning applies o he invesmens of domesic and mulinaional rms. In addiion, rend invesmens for all classes of rms are posiively associaed wih a rise in he covariance am ; re ecing a higher degree of cyclical sabilizaion. A couner-cyclical policy in fac will help reduce he variabiliy of marginal coss and herefore he risks associaed wih pre-deermined prices. In he non-raded secor, he home expansion migh favor invesmens by domesic rms a he expense of direc invesmens by foreign mulinaionals. In my speci caion, his happens whenever exchange rae pass-hrough is no complee. In order o see why, consider a foreign mulinaional conemplaing o open an a liae in he home counry before he moneary expansion akes place. The poenial invesor will balance as usual prospecive pro s and enry coss in is own currency. Since shocks are iid and fuure pro s are calculaed using he sochasic discoun facor = +, he curren moneary easing will a ec her decisions only hrough he exchange rae. As he home currency, say, depreciaes, he expeced pro s of he overseas a liae will fall (precisely, by a percen). The depreciaion, on he oher side, will help reduce enry coss in foreign currency, alhough no as much as necessary (enry cos will hike by a percen). The ne e ec is clearly lower or equal o zero depending on : Noe ha foreign invesmens are deerred even when he home currency appreciaes. Exi of foreign mulinaionals, in urn, improves he prospecive pro s 7 A uniary demand elasiciy implies ha he percen rise in foreign demand (equal o a ) coincides wih he percen drop in he expor price, leaving revenues (and pro s) in home currency unchanged. Expeced pro s, which are calculaed using he sochasic discoun facor +, herefore raise as much as enry coss (precisely, by one percen). 6

17 of heir compeiors in he non-raded secor, crowding-in invesmens by domesic rms. I is worh sressing ha he opposed conclusions hold when he moneary easing originaes abroad. In his case, on op of he e ecs already menioned (wih elasiciies, respecively, equal o a for pro s and a for coss), foreign mulinaionals will bene from discouning fuure pro s a a lower ineres rae (exacly, by one per cen). They will herefore anicipae an increase in he value of heir overseas asses whenever < ; nding i convenien o engage in invesmens abroad. Enry of foreign invesors, in urn, will crowd-ou domesic invesmens. The argumen ha he origin of moneary policy maers for he araciveness of invesing in one s naive counry as compared wih overseas is reminiscen of a similar nding in Russ, 7. The resuls in he wo papers, however, are quie disinc. In her framework, overseas invesmens respond o crosscounry di erences in moneary volailiy. In my seup, all rms incorporae ino heir invesmen decisions he fac ha moneary policy can a ec nominal marginal coss. This in urn implies ha curren moneary shocks can play a role along wih srucural dimensions of moneary uncerainy in re-direcing invesmens across counries and secors as well inside he boundaries of he rm. I nally sress ha invesmens in he non-raded secor depend on produciviy shocks all over he world. Clearly, a rise in home produciviy, by reducing enry coss in home markes, will end o encourage all ypes of invesmens a home. More surprisingly, invesmens also reac o a change in produciviy abroad. The nding is a consequence of sricly inerdependen invesmen decisions boh across and wihin secors. A rise in a will induce foreign rms o op in favor of expors raher han direc invesmens, implying ha n MN will fall. Exi of foreign mulinaionals, in urn, will weaken compeiion in he home non-raded secor, favoring naive invesors. 3. Consumpion and employmen The dynamics of consumpion and employmen is given by: l = m + m a + ( + ) X j=d;x;mn n j + c = m p ' m e + nd n MN + X j=d;x;mn n j (3) nx (33) Global moneary condiions are he main deerminan of movemens in consumpion and employmen, as one would expec in a seing where moneary policy conrols nominal spending and oupu accommodaes any change in aggregae demand. Produciviy shocks can a ec consumpion only indirecly, hrough enry and he nominal exchange rae. 8 8 The minor role of supply shocks in driving aggregae consumpion and oupu is consisen wih he so-called New Keynesian view of he business cycle, as synhesised by Clarida, Galì and Gerler,

18 Moneary policy is ransmied in he world economy hrough changes in world demand and he erms of rade. An easing of he global moneary sance, wherever i is originaed, booss world demand and oupu and re-direcs expendiure across counries. Direc consumpion spillovers, as capured by e in (33), depend on he pricing sraegies of rms acive in foreign markes and will be large in a high pass-hrough environmen. 9 Over ime, indirec spillovers will also maerialize hrough a change in he number of rms serving domesic and foreign markes. Worldwide employmen needs o increase as well when a moneary expansion is in place so as o provide a larger amoun of goods for consumpion. In my seup wih endogenous enry, he rise in world employmen is he resul of an increase in inensive margins, i.e. oupu per rm, as well as in exensive margins. 4 Numerical simulaions The purpose of his secion is o provide a quaniaive illusraion of rms dynamics and inernaional spillovers in he wake of moneary policy and produciviy shocks. I will consider he percen change of key endogenous variables around he seady sae when a one percen shock o moneary policy and produciviy occurs. In he benchmark model, parameers are calibraed as follows. The discoun facor is se equal o.99, which corresponds o an ineres rae of % a he convenional quarerly frequency (4% per year). The elasiciy of subsiuion among varieies is se a, implying a mark-up rae of roughly %, as suggesed by esimaes based on aggregaed daa. I also experimen wih a higher elasiciy (and a lower mark-up) in he radiion of sudies ha use microeconomic daa, leing be equal o 5 or. Noice ha he elasiciy of subsiuion beween raded and non-raded goods, equal o uniy in he model above, is lower han he elasiciy across varieies, consisenly wih ample empirical evidence. Obsfeld and Rogo, a argue ha a uni elasiciy is a reasonable base case and he empirical lieraure would suppor even a lower esimae (and herefore a higher disance relaive o ). In my calibraion, he di erence beween he elasiciy across varieies and he elasiciy beween raded and non-raded goods can vary from wo o en imes, as in Obsfeld and Rogo, 5. The share of radable goods in consumpion is se a.5, roughly corresponding o he dimension of he non-raded secor ha we acually observe in OECD economies. The degree of exchange rae pass-hrough is = :6, consisenly wih he ndings in Engel and Rogers, The depreciaion of he home currency, by deerioraing he home erms of rade, swiches world expendiure in favor of home goods. Since domesic prices are pre-deermined, home consumer prices rise and foreign consumer prices fall wih he depreciaion of he exchange rae, hereby raising consumpion in boh counries. 8

19 and Campa and Goldberg, 5. The concaviy of he cos funcion is he mos di cul parameer o calibrae. Corsei, Peseni and Marin, 8 sugges a value of = :5. I will also allow for higher (more conservaive) values of. Table conains he response of n D, n MN, c, l, heir foreign analogues and e o a one percen deviaion of moneary policy from seady sae. The values in parenhesis refer o he log change of he corresponding variable in he model wih no enry (enries equal o zero are no repored). Table : e ecs of a % change in m n D n MN n D n MN e c l c l benchmark (.77).45 (.54).9 ().55 (.46).8 () = (.7).6 (.9).67 ().4 (.).33 () = (-.58).8 (.35).3 ().9 (-.35).68 () = (.77).47 (.54).89 ().53 (.46). () = (.77).48 (.54).93 ().5 (.46).7 () A home moneary expansion is generally associaed wih a less han proporional depreciaion of he domesic currency. As already noed, he exchange rae migh even respond in he wrong direcion, as i is he case in he model wih no enry when =. The appreciaion in his case is a consequence of a sharp decline in he pro s of foreign mulinaionals esablished on he home soil, leading o a fall in ne pro ou ows. The e ec maerializes in highly compeiive markes, where pro margins are small. A depreciaion of he home currency reduces he relaive price of goods produced on he home soil, shifing global demand owards home producs (wih uni elasiciy) and raising world consumpion. Noice ha changes in world consumpion, c + c, coincide wih changes in world moneary policy, m + m. Relaive consumpion, c movemens in real money balances. c, insead, can ucuae over ime as a resul of cross-counry Moneary policy can a ec prices in he world economy hrough he nominal exchange rae as well as by in uencing enry behavior. A depreciaing currency makes impored goods more expensive, hereby raising consumers prices in home currency. Enry (exi) of new rms in domesic markes, In he model wih no enry, he response of he nominal exchange rae o moneary and real shocks is as follows: de dm = de dm = + ( ) [ ] + ( ) [ ( )] de da = de da = ( ) ( ) + ( ) [ ( )] 9

20 by fosering (weakening) compeiion, will dampen (amplify) he in aionary consequences of he moneary expansion over ime. In all simulaions, rms dynamics appears o play a remarkable role in spreading he e ecs of moneary policy, wih higher consumpion spillovers under endogenous enry as compared o he model wih no enry. The boos in global demand following a home expansion can be accommodaed hrough a change in boh inensive and exensive margins in he world economy. In he benchmark model, here will be a iny.6% increase in he number of domesic rms and an % fall in he number of foreign mulinaionals acive on he home soil, while he opposie occurs in he foreign counry. New invesmens are more reacive o moneary policy in highly compeiive markes, where even small pro opporuniies induce large changes in rms dynamics. Wih =, for insance, he overall number of rms esablished a home reduces by 45%: Oupu per rm, on he conrary, will move from a low of 77% wih = up o almos % when eiher enry coss are exremely high or compeiion is weak. Adjusmen a he exensive margin becomes progressively less relevan as enry coss rise and i almos disappears wih = : Now, consider Table, displaying he e ecs of a one percen change in home produciviy. Table : e ecs of a % change in a n D n X n MN n D n MN e c l c l benchmark (.58) -.3 (-.35).3 (-).3 (.7) -.35 = (.7) -.49 (-.4).33 (-).49 (.7) -.3 = (3.97) -.34 (-.38).58 (-).34 (.59) -.86 = (.58) -.6 (-.35).3 (-).6 (.9) -.54 = (.58) -. (-.35).3 (-). (.) The boos in home produciviy aracs new invesmens on he home soil in boh he raded and he non-raded secor. The overall increase in sar-up aciviies a home remains subsanial even when enry coss are very high. Noice ha he share of home rms ha decide o serve foreign markes hrough expor rises a he expense of hose engaging in foreign invesmens (he opposie holds in he foreign counry). The e ec is paricularly srong in markes wih higher degrees of compeiion. I sress ha aracing foreign invesors, however, does no come wihou coss. In all simulaions, he domesic currency depreciaes in high-produciviy economies as a resul of massive ou ows of mulinaional pro s. In he model wih no enry, where here are no compensaing FDI in ows, his e ec may become exremely srong and lead o a fall in real consumpion as high as %. The combined e ec of enry in home markes and a depreciaing currency worsen he

21 home erms of rade, reducing consumpion in real erms. The apparenly paradoxical nding ha high produciviy may deeriorae welfare is reminiscen of he immiserizing growh by Bhagwai, 958. In my model, he deerioraion of he erms of rade is exacerbaed by he decision of rms o move invesmens owards high produciviy economies. In a conex where produciviy is rmspeci c, however, enry migh raher increase prices. Over ime, as more rms ener a marke, he average produciviy in ha marke declines, resuling in higher prices. On his ground, one could expec immiserizing growh o be relevan in secors where produciviy dispersion is low. The quesion deserves furher invesigaion. In his respec, combining rms heerogeneiy and cyclical asymmery wihin a macro model provides an ineresing ground for fuure research. 5 Conclusions This paper has provided a simple DSGE model wih nominal rigidiy and endogenous enry by naional and mulinaional rms wih he aim of exploring he implicaions of producers enry for moneary policy and business cycle dynamics. The main achievemens of he paper can be summarized as follows. Firs, I show ha boh he decision wheher o engage in sar-up invesmens and he choice wheher o inves a home or abroad depend on various dimensions of moneary policy. A domesic moneary expansion is found o arac he invesmens of rms ha are no exposed o exchange rae risk, as hose operaing in markes locaed in heir own counry. Foreign direc invesmens, on he conrary, migh be discouraged by exchange rae ucuaions ha reduce he value of he overseas asses of mulinaional enerprises. Moreover, I nd ha a rise in world moneary volailiy as well as he move owards cyclical sabilizaion may have a posiive impac on rend invesmens in boh he raded and he non-raded secor. The resul is a consequence of reducing he macroeconomic risks associaed wih pre-deermined prices when a couner-cyclical moneary policy is in place. Second, I nd ha world-wide produciviy condiions can in uence no only foreign invesmens, as one migh expec, bu also domesic invesmens. The major role of exernal shocks in he nonraded secor is a consequence of sricly inerdependen invesmen decisions wihin and across secors. Finally, inernaional consumpion and employmen spillovers are magni ed in a seup wih en- The poin is made in Méliz, 3. I hank he referee for suggesing his poin. Helpman, Méliz and Yeaple, 4 documen ample variabiliy in he measures of produciviy heerogeneiy across secors. In he US, for insance, dispersion is he highes in Tobacco, Elecronics, Transpor equipmens and Oher elecronics and he lowes in Pulp and paper, Glass, Oher indusrial equipmens and Indusrial chemicals.

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25 6 Appendix A This appendix illusraes how o derive equaion (3) in he main ex. Wihou loss of generaliy, I convenienly normalize previous period shocks so ha he share of exporers and mulinaionals is symmeric across counries and re-wrie he equilibrium in he balance of paymen as follows: 8 < + ( " = : + ( ) MN + N ) [ MN ( + N )] A N MN + A (N MN ) + Using a rs order Taylor approximaion around he seady sae, he above equaion can be expressed in erms of percen changes of he original variables as follows: e = m m + 4 ( N N + ( ) ( + ) n MN n MN 9 = ; 3 ) MN MN 5 (34) + ( ) (a a ) where + ( ) ( ). Similarly, approximaion of he free-enry condiions a home (4) and heir analogues abroad gives: n D = n D = n MN = n MN = n X = n X = 4 a ( + ) 4 a ( + ) 4 ( + ) 4 ( + ) ( + ) a ( + ) E N + + E D + + E MN + (m e m + E (e + )) + E D + + E MN + (m e m + E (e + )) E N a E X + E (e + ) E N ++ E N + a + E MN + + D (m e m + E (e + )) 3 a + E MN + + D (m e m + E (e + )) E X + + E (e + ) 3 5 (35) 3 5 5