Firms entry, monetary policy and the international business cycle

Transcription

1 MPRA Munich Personal RePEc Archive Firms enry, moneary policy and he inernaional business cycle Lilia Cavallari Universiy of Rome III (Ialy) uly 22 Online a hp://mpra.ub.uni-muenchen.de/4876/ MPRA Paper No. 4876, posed 2. Ocober 22 2: UTC

2 Firms enry, moneary policy and he inernaional business cycle Lilia Cavallari Universiy of Rome III Absrac This paper provides a heory of he inernaional business cycle grounded on rms enry and sicky prices. I shows ha under simple moneary rules pro-cyclical enry and couner-cyclical markups can generae ucuaions in macroeconomic aggregaes and rade variables as large as hose observed in he daa while a he same ime providing posiive inernaional comovemens. Boh rms enry and sicky prices are essenial for reproducing he synchronizaion of he business cycles found in he daa. Keywords: rm enry, inernaional business cycle, inernaional comovemens, variable markup, Taylor rule, exchange rae regimes. EL codes: E3; E32; E52 Lilia Cavallari, Universiy of Rome III, DIPES, Via Chiabrera, 99, 45 Rome, Ialy, cavallar@uniroma3.i. I wish o hank wo anonymous referees and he co-edior Giancarlo Corsei for useful suggesions on previous drafs. I also hank paricipans in seminars a CesIfo, Luiss, Universiy of Pavia, Universiy of Tor Vergaa (Inernaional Seminars 2), Universiy of Isanbul (EcoMod 2), Universiy of Cree (ICMAIF 2) and Birmingham Business School. Remaining errors are mine.

3 Inroducion This paper provides a heory of he inernaional business cycle grounded on rms enry and sicky prices. I shows ha under simple moneary rules enry can generae ucuaions in oupu, invesmens, employmen and rade ows close o hose in he daa while a he same ime providing posiive inernaional comovemens. The capaciy o capure esablished facs of he inernaional business cycle overcomes he well-known di culies of sandard models in his regard. As rs shown by Backus, Kehoe and Kydland (992), inernaional business cycle models ypically generae very low or even negaive cross-correlaions (he comovemen puzzle), wih oupu less correlaed han any oher macroeconomic variable across counries (he quaniy anomaly). In addiion, hey fail o mach he couner-cyclical behavior of ne expors found in he daa. These empirical incongruiies arise as a consequence of a srong incenive a work in ari cial economies o use inpus where hey are mos producive. This needs no be he case as long as a business cycle expansion in one counry leads o addiional enry in he rading parner s marke. This paper shows ha rms enry indeed provides a channel for posiive comovemens. I propose a wo-counry dynamic sochasic general equilibrium model wih monopolisic compeiion where producers are subjec o a sunk enry cos, a one-period producion lag and o an exogenous exi shock. Invesmens are represened by enry of new rms. Prior o enry, invesors mus acquire a baske of maerials comprising domesic and foreign goods. Specifying enry coss in erms of goods allows invesmen demand o have a non-negligible componen of impors as in he daa. Laer in he paper, I discuss he implicaions of modelling enry coss in erms of (nonradable) labor. The economy has complee nancial markes and a fully specialized srucure of producion. Risk sharing ogeher wih he assumpion of cosless rade imply ha agens are in principle able o move resources in he mos producive economy. I will argue ha hey have only a moderae incenive o do so as long as prices are sicky and enry coss comprise foreign goods. In he model, nominal rigidiy is capured by a price-seing à la Calvo (983). Moneary policy is represened in he sandard form of a feedback rule as in he Neo-Wicksellian framework (Woodford (23)) and he global naure of he moneary regime is capured by he ineracion of ineres rules followed by he moneary auhoriies in he wo counries. I consider oaing regimes under symmeric Taylor rules, wih or wihou ineres smoohing, and a regime where he exchange rae is xed a all daes. In order o assess he exen o which sicky prices play an essenial role in reproducing he inernaional business cycle, I also consider a exible price equilibrium. Simulaion resuls show ha boh ouward-looking enry coss and sicky prices are essenial for maching he volailiy and synchronizaion of business cycles observed in he daa. Wih exible 2

4 prices or wih labor enry coss, comovemens. are negaive as in Backus e al. (992) and essenially for he same reasons. In he benchmark model, on he conrary, a business cycle expansion in one counry simulaes enry in he rading parner s marke, hereby generaing posiive comovemens. The reason is hreefold. Firs, changes in he erms of rade, by a ecing enry coss, help o bridge he produciviy gap beween counries. Consider for insance a posiive produciviy shock in he home counry. In he face of he shock, he price of home-produced goods falls relaive o he price of foreign-produced goods, deerioraing he home erms of rade. This in urn reduces enry coss in he parner counry (he low produciviy economy), simulaing invesmens in new rms. Clearly, his channel is obscured in a seup wih labor enry coss. Second, he failure o se prices in an opimal way reduces he prospecive pro s from invesing in a new rm and discourages enry compared o a exible price economy. A lower volailiy of invesmens in he benchmark model re ecs a limied abiliy of agens o move resources owards he more producive economy. Las bu no leas, a noiceable di erence wih he alernaive speci caions concerns he behavior of markups. These are couner-cyclical in he benchmark model, pro-cyclical wih labor enry coss and consan wih exible prices. Couner-cyclical markups weaken he incenive o move invesmens owards he more producive economy. The paper conribues o a recen line of research sressing he role of rms dynamics in he business cycle. In a pioneering paper, Cook (22) shows ha couner-cyclical markups can generae posiive comovemens. in a model wih sequenial enry, ime-varying capial uilizaion and incomplee nancial markes. Oher early aemps o model enry in open economy have mainly focused on explaining rade margins and foreign invesmens. In all of hese conribuions, moneary policy is eiher overlooked (as in Ghironi and Méliz (25) and Helpman, Méliz and Yeaple (27), among ohers) or considered as an exogenous source of business cycle variabiliy (as in Russ (27) and Cavallari (27, 2)). Ye, here are good reasons for sudying moneary policy in a model wih rms enry. Recen evidence documens ha a moneary easing, i.e. a drop in he nominal ineres rae, has a posiive impac on he number of rms enering he marke, suggesing ha moneary policy may play a relevan role in a rm s decision wheher o sar-up a new producion uni. 2 There are surprisingly few open economy models ha combine endogenous moneary policy See, among ohers, Ghironi and Méliz (25), Corsei, Marin and Peseni (27, 28) and Bilbiie, Ghironi and Méliz (27, 2). The inroducion of realisic assumpions on rms dynamics amelioraes he capaciy of ari cial economies o mach he business cycle properies of he daa. In a closed economy, Bilbiie, Ghironi and Méliz (27, 2) show ha he momens generaed by heir models wih enry come very close o he daa, ouperforming a ypical xed-enry real business cycle model. 2 See Bergin and Corsei (28), Lewis (29) and Uusküla (2) among ohers. 3

5 and rm enry. The conribuions closer o his paper are Auray, Eyquem and Pouineau (22) and Auray and Eyquem (2). The former focuses on a ransmission mechanism ha may be considered complemenary o he one analyzed here. I emphasizes he role of asse prices in a conex of complee nancial inegraion and labor enry coss. The free enry condiion in he model (equalizing he value of he rm o labor marginal coss) provides a direc link beween asse prices and in aion ha is absen in my seup. This, however, has he unappealing consequence of implying a posiive relaion beween enry and ineres rae innovaions ha is a odds wih he daa. The laer paper considers incomplee nancial markes wih given asse prices. In he model, rm value is ied o an exogenous enry cos and shocks are ransmied hrough changes in he real reurn on asses. An increase in he real reurn on equiy (as afer a posiive produciviy shock) is brough abou by an increase in expeced dividends. Since he real reurns are equalized across counries by arbirage, he increase in expeced dividends in he low produciviy economy requires a fall in he number of enrans. The model fails o mach he posiive cross-correlaion of invesmens observed in he daa. The remainder of he paper is organized as follows. Secion 2 describes he benchmark wocounry model. Secion 3 explains he log-linear soluion of he model. Secion 4 compares simulaion resuls of he benchmark model and alernaive speci caions for enry coss and moneary rules. Secion 5 concludes. The appendix conains he seady sae of he model and he log-linearized equaions. 2 The model The world economy comprises wo counries labelled Home, H, and Foreign, F, each specialized in he producion of one ype of good as in Corsei and Peseni (22). I is populaed by a coninuum of agens of uni mass, where he segmen [; ) belongs o counry H and he segmen ( ] o counry F. A ypical agen in he economy is boh a consumer and a worker: he supplies labor services in a compeiive labor marke and consumes all he goods produced in he world economy. In he Home counry, here is a coninuum of monopolisically compeiive rms, each producing a di eren variey of he Home good h 2 (; N H ), where N H is he number of Home rms. Similarly, in he foreign counry here is a coninuum of rms f 2 (; N F ). The socks of Home and Foreign producers are deermined endogenously in he model. 4

6 2. Preferences In each period, a ypical agen i in counry = H; F derives uiliy from consuming a baske C conaining all he goods produced in he world economy while su ering disuiliy from labor e or, L. Agens maximize he expeced discouned value of ow uiliy U over heir life horizon. Flow uiliy is assumed addiive-separable: U i = C i ' +' + ' L ' i () where > is he iner-emporal elasiciy and ' > is he Frisch elasiciy of labour supply. The consumpion baske C comprises home, C H ; and foreign goods, C F ; : where C H, C F are given by: C = C H C F ( ) (2) C H = " Z N H # ( ) C (h) dh C F = " Z N F # ( ) C (f) df (3) and > denoes he elasiciy of subsiuion across varieies. Consumer price indexes are given by 3 : while producer prices are: P = P H P F (4) P H = " Z N H P (h) dh # ( ) (5) P F = " Z N F P (f) df # ( ) I assume ha he law of one price holds, i.e. P H (h) = "P F (h) and P H (f) = "P F (f), where he nominal exchange rae " is he price of currency F in erms of currency H. Given idenical preferences, purchasing power pariy also holds. In my seup wih enry, he assumpion is less resricive han i 3 For nominal variables a superscrip denoes he currency of denominaion. So, PH F producer price index in Foreign currency. for insance denoes he Home 5

7 migh appear a rs. Firms can in principle insulae he nal price of heir producs from exchange rae changes by leing heir markups vary according o local marke condiions. Simulaion resuls will show ha his is indeed he case as long as prices are sicky. Clearly, he presence of rade fricions would play a role in he decision wheher o access foreign markes in he rs place and evenually wheher o serve hem wih expors or by engaging in invesmens overseas. The analysis of endogenous changes in rade openness or in he mode of accessing foreign markes is beyond he scope of he presen paper. 4 Finally, I de ne he erms of rade of counry F, T, as he price of goods produced in counry F relaive o he price of goods produced in counry H: T = P H F P H H = P F F P F H (6) 2.2 Firms Producers in he world economy face an idenical linear echnology wih labor as he sole facor. Oupu supplied by a rm j = h; f in counry = H; F is given by: y (j) = Z L (j) (7) where Z is a counry-speci c shock o labor produciviy. Prior o enry, rms face an exogenous sunk enry cos (as in Grossman and Helpman (99) and Romer (99), among ohers). 5 In order o sar he producion in period +, a ime a rm needs o purchase fe unis of he following combinaion of Home and Foreign varieies fe = CH C F ; a he price P f; = PH; P F; wih 2 (; ). The cos of enry in unis of he consumpion baske is herefore f e P f; P : In his speci caion, enry requires insalling a bundle of maerials ha may have a di eren composiion han ha of he consumpion baske. Ohers, as Bilbiie e al. (27) and Cavallari (27), specify enry in e ecive labor unis. Enry coss in his case coincide wih labor marginal coss. How o model enry coss is an open quesion. I has implicaions for aggregae accouning: labor coss imply a wedge beween oupu of he consumpion secor and GDP ha is absen wih enry coss in erms of goods. More imporanly, i may a ec he mechanism of moneary ransmission. A moneary easing can in principle lead o an increase or a drop in he cos of enry and herefore 4 In a seup wih exporers and mulinaional rms, Cavallari (2) shows ha he currency of denominaion of inernaional rade a ecs boh dimensions of he decision o serve foreign markes. 5 For a model wih endogenous enry coss see, among ohers, Bergin and Corsei (28) and Arespa (22). 6

8 o opposing responses on he par of enrans. In a closed economy wih labor enry coss, Uusküla (2) shows ha sicky price models predic a posiive relaion beween rms enry and ineres rae innovaions in conras o wha found in he daa. 6 The reason is ha an increase in he ineres rae, by resraining labor demand, reduces real wages and enry coss. A similar mechanism exends o open economies as long as enry coss are enirely non-radable (as labor coss). I is, however, conceivable ha seup coss comprise a non-neglible componen of radable goods. This is cerainly so for invesmen goods in general and one does no see why rs-ime invesmens should be di eren. Clearly, changes in he erms of rade will a ec enry coss in his case. As will be clear soon, a moneary expansion has a posiive e ec on enry wih radable invesmen goods. As in Ghironi and Méliz (25), all rms enered in a given period are able o produce in all subsequen periods unil hey are hi by a deah shock, which occurs wih a consan probabiliy 2 (; ) : Therefore, a rm enered in period will only sar producing a ime +, inroducing a one-period ime-o-build lag ino he model. She will evenually exi wih an exogenous probabiliy. In each period, in addiion o incumben rms here is a nie mass of enrans, N e : Enrans are forward looking and decide o sar a new rm whenever is real value,, given by he presen discouned value of he expeced sream of pro s d s = E " X s=+ C s s=+ C ( ) s+ d s, covers enry coss: The free enry condiion above holds as long as he mass of enrans in posiive. Macroeconomic shocks are assumed o be small enough for his condiion o hold in every period. Noe ha upon enry, rms pro s vary and can even urn negaive for a while (alhough he rm value remains posiive). This is a key di erence relaive o models of fricionless enry. In he absence of sunk # = f e coss, in fac, he free enry condiion requires zero pro s in every period. Finally, he iming of enry and he one-period producion lag imply he following law of moion for producers: P f; P (8) N = ( ) N + Ne; (9) 2.3 Consumers choices I assume complee nancial markes wihin and beween counries. Agens can inves heir wealh in a se of nominal sae-coningen bonds, B; denominaed in he currency of counry H ha span all 6 Uusküla (2) shows ha a % increase in he Federal Funds rae rae leads o a.6% fall in he enry rae. 7

9 he saes of naure. 7 In addiion o sae-coningen bonds, hey hold a share s of a well-diversi ed porfolio of domesic rms. The budge consrain of a ypical home agen is given by: X q H ( + ) BH i P H + s H N H + Ne; H v H BH i + s H v H + d H P H + W H L H i P H C H i () where W is he nominal wage. A similar consrain holds for he foreign economy. Agens choose consumpion, labor e or, share and bond holdings in period so as o maximize uiliy () over heir whole life horizon subjec o a budge consrain as () or is foreign analogue. Consumers opimizaion requires he following rs order condiions: C q (s + ) P C C = + E () P+ = ( ) E d + + v + v C+ (2) C (h) = C (f) = P (h) C PH H (3) P (f) C PF F W P = L ' C (4) Noe ha he Euler equaion for bonds () ogeher wih he no arbirage condiion in inernaional asse markes, q H (s + ) = " q F (s + ), yields he uncovered ineres rae pariy, UIP: E P H C H P H +C H +! P F C F = E P F +C F +! + i F + + i H + The assumpion of complee markes ogeher wih he law of one price and he fac ha consumpion bundles are idenical across counries imply ha consumpion is equalized worldwide, i.e. C H = C F : (5) 7 Each bond pays one uni of he Home currency if sae + 2 occurs a ime +, where is he se of niely saes ha can occur in each period. The price of such a bond a dae is q ( + ). 8

10 2.4 Pricing Goods markes are monopolisically compeiive. Each producer ses he price for is own variey facing he following marke demand: y (h) = y (f) = P (h) T PH C + T fe H Ne; H + fe F Ne; F P (f) T PF C + T fe H Ne; H + fe F Ne; F (6) where C R C idi indicaes world consumpion. I inroduce nominal rigidiies hrough a Calvo-ype conrac. In each period a rm can se a new price wih a xed probabiliy which is he same for all rms, boh incumben rms and new enrans, and is independen of he ime elapsed since he las price change. In every period here will herefore be a share of rms, comprising incumbens and enrans, whose prices are pre-deermined. In a symmeric equilibrium, pre-deermined prices a a given poin in ime coincide wih he average price chosen by rms acive in he previous period. 8 The simplifying assumpion ha new enrans behave like incumben rms is wihou loss of generaliy. Allowing enrans o make heir rs price-seing decision in an opimal way would have only second order e ecs in my seup wih Calvo pricing. 9 I migh have major consequences in a seing where rms face coss of price adjusmen as i would inroduce heerogeneiy in price levels across cohors of rms enered a di eren poins in ime (see Bilbiee e al. (27)). As he number of price-seers ha face no cos of adjusing o a pas pricing decision moves over he cycle, he aggregae degree of price sickiness becomes endogenous. The analysis of endogenous changes in price sickiness is beyond he scope of his paper. Each rm j = h; f ses he price for is own variey so as o maximize he presen discouned 8 The average pre-deermined price for home goods P H H will be: PH H PH; H = N H and similarly for PF: F These properies are used in deriving he Calvo sae equaions below. 9 The pre-deermined price in each period would coincide wih he average price chosen by rms enered in all previous periods and survived o he deah shock: P H H = X ( ) s N E s P H (h) s=2 N 9

11 value of fuure pro s, aking ino accoun marke demand (6) and he probabiliy ha she migh no be able o change he price in he fuure, yielding: P (j) = P E ( ( k= P E k= )) k W +k Z +k y+k (j) P+k C +k ( ( )) k y +k (j) P+k C +k wih = H; F. The above expression can be re-arranged in a more familiar form as: (7) P (j) = W ( ( )) Z + ( ) E P +(j) (8) where he opimal price in each period P (j) depends on curren nominal marginal coss and expeced fuure prices. Clearly, when = opimal pricing implies a consan markup on marginal coss a all daes. Wih >, prices respond less han proporionally o a marginal cos shock, implying variable markups. Changes in markups over he cycle generae a real rigidiy a he rm level. Aggregaing across rms he expressions above and recognizing ha he pre-se price level coincides wih he average marke price in he previous period, yields he following sae equaions: P = N N P + ( ) N P (j) (9) Producer prices in each period depend on curren and previous socks of acive rms. An increase in he number of producers over ime will reduce he aggregae price level everyhing else given. This is a direc consequence of love for variey. A higher number of, say, home varieies raises he value of consumpion per uni of expendiure in home goods. Home producer prices herefore fall. 2.5 Aggregae accouning De ne real GDP in counry = H; F as Y R N marke clearing requires: P (j) y(j)dj where y(j) is given by (6). Goods P 2( ) Y H = T C + T 2 Ne H fe H + Nef F e F Y F = T 2 C + T Ne H fe H + Nef F e F (2) Labor marke clearing implies:

12 L H Z L H i di Z N H y (h) dh L F Z H Z L F idi Z N F y (f) df (2) Z F Aggregaing across agens he budge consrain () and is foreign equivalen, using he equilibrium condiions s + = s equaions: = and assuming ha iniial nancial wealh is zero, yields he accouning Y H C N H e v H = BH H P H (22) where B H H R BH i di and B H F R BH i di: Y F ( )C N F ev F = BH F " P F In open economies, a discrepancy beween oupu and domesic absorpion re ecs ino a change in ne foreign asses (here represened by bonds denominaed in Home currency). Finally, asse marke equilibrium requires B H H = BH F : 2.6 Ineres rules The model is closed by specifying he moneary policy rules in place in he world economy. The moneary insrumen is he one-period risk-free nominal ineres rae, i, and moneary policy belongs o he class of feedback rules: + i = f ( ) (23) where f is a generic funcion and is he informaion se a ime. 3 The log-linear model The model does no provide a closed-form soluion. I is log-linearized around a symmeric seady sae wih zero in aion. In he seady sae, sochasic shocks are mued a all daes, Z =. This secion discusses he main linearized equaions while he Appendix conains he seady sae and he full log-linearizaion. I used Y = W L P + N d in deriving he curren accoun equaions.

13 3. Demand block The aggregae demand block is derived from he log-linear approximaion o he rs order condiions of consumers in he Home and Foreign counries. Consumers allocae heir wealh among consumpion, nominal risk-free securiies and shares. Iner-emporal opimizaion requires ha he marginal rae of subsiuion beween curren and one-period ahead consumpion equalizes he real reurn on nominal asses, boh he risk-free bonds and shares. A rs se of Euler equaions, one for each counry, will herefore describe he dynamic link beween curren and expeced one-period ahead consumpion and relae i o he risk-free reurn in unis of consumpion. A second se of Euler equaions, again one for each counry, will relae he iner-emporal pro le of consumpion o he real reurn on shares. The real value of he rm, which coincides wih he enry cos in equilibrium, is he forward soluion o he Euler equaions for shares. Recognizing ha consumpion risks are perfecly insured in he world economy, he bond Euler equaions in he Home and Foreign counries can be combined, yielding: E b C+ = b C + b i H E H + + b i F E F + (24) where a ha over a variable denoes he logdeviaion from he seady sae, + = ln P+ =P is producer in aion in counry = H; F and E is he expecaion operaor. The above expression says ha an increase in he world real ineres rae, wherever i is originaed, raises he reurn on bonds, herefore making i more aracive o pospone consumpion in he fuure. The de niion of he erms of rade (6) yields he following sae equaion: bt = b T + b" + F H (25) Movemens in he erms of rade around he seady sae are driven by changes in he nominal exchange rae and by cross-counry in aion di erenials. Moneary policy can direcly a ec he erms of rade hrough uncovered ineres pariy: E b" + = bi H bi F (26) 3.2 Supply block The supply block is derived from a log-linear approximaion o he pricing and enry decisions of rms in he Home and Foreign counries ogeher wih a log-linearizaion of agens labor supply. Firs, consider he opimal price (7) for, say, a home variey. Using marke demand (6) and labor 2

14 supply (4), re-arranging and linearizing gives: X E k= ( ) k bp ;+k H + + ( ) T ' b +k + bc +k + + bz +k H ' ' N ' b +k H + P ' b ; H = where P b ;+k H = ln P H (h)=ph;+k H. Noe ha by de niion P b ;+k H = P b ; H kp H +s; namely changes in he real price of a home variey beween and + k coincide wih he variey e ec, he rs addend, less producer in aion over he period. Using he Calvo sae equaion (9), he variey e ec is: s= bp H ; = H + ( )( ) b N H ( )( ) b N H Wih = ; an increase in he number of Home producers raises he real price of Home varieies and he more so he lower he elasiciy of subsiuion. This e ec is dampened wih > : Combining he wo equaions above and re-arranging gives: ( H = ) ( + ') ' + ( ) E H + bt + + bc N ' ( ) ( ) b H ( + ') Z H + N ' ( ) ( ) b H (27) where = ( ( ))( ) ('+) : Producer in aion in he foreign counry is obained in a similar way: F = ( + ') ' bt + + bc N ' ( ) ( ) b F ( + ') Z F + N ' ( ) ( ) b F + ( ) E F + The counry-speci c in aion raes depend on nex period expeced in aion as well as on deviaions of he erms of rade, consumpion, he number of producers and produciviy from heir seady sae values. These deviaions are correlaed wih curren marginal coss. To begin wih, consider an increase in T, i.e. a deerioraion in he home erms of rade. The rise in T swiches world demand in favor of home producs, pushing up labor demand in he home economy. Real wages and marginal coss herefore increase, fuelling in aion. A similar mechanism explains why a rise in world consumpion leads o higher in aion. A rise in home produciviy, on he conrary, direcly reduces marginal coss. The number of producers is relaed o in aion via he variey e ec. An increase 3

15 in he curren sock of producers makes a larger range of home varieies available for consumpion. Because of love for variey, he value of consumpion per uni of expendiure in home varieies raises. Hence producer prices mus fall. The opposing e ec is rue for a rise in N b : In his case, previous period s prices drop and resul ino higher in aion in he curren period. Second, a log-linear approximaion o he number of enrans can be obained from he curren accoun equaions (22) as a funcion of oupu minus absorpion and ne foreign asses: bn H e = bn F e = ( ( )) by H ( ( )) + by F + ( ( )) bc b H ( ) dnfa (28) ( ( )) bc b F ( ) + dnfa where nfa d = B b H B bh and B H = BH H : Noe ha he resource consrain implies a rade-o Y H P H beween invesmens in new varieies and consumpion of exising goods (he coe cien on C is negaive). The law of moion of rms is: bn = ( ) b N + b N e (29) Finally, using he propery ha he aggregae price markup R N P (j) W =Z dj coincides wih he inverse of he labor share, Y P W L, one can subsiue away he real wage in labor supply (4) and ogeher wih he GDP de niion obain an expression for aggregae labor. In log-linear erms, his gives : bl H = ' C b + ' bz H b H + ( ) T b + P b ; H bl F = ' C b + ' bz F b F T b + P b ; F (3) where i is clear ha employmen decreases wih consumpion, because of iner-emporal subsiuion beween leisure and labor, while raising wih he real wage (he erm in brackes). 3.3 Ineres rae rules I consider one regime wih xed exchange raes and wo oaing regimes. The xed regime is a unilaeral peg o he Foreign currency feauring a xed exchange rae a all daes. I is implemened by he ineres rule bi H = bi F &b" wih & > : In he rule, he presence of an exchange arge (normalized o zero) ensures deerminacy. In he oaing regime, moneary policy follows a symmeric Taylor rule bi =. The Taylor 4

16 principle, requiring ha policy-makers reac more han proporionally o in aion, i.e. >, ensures deerminacy. Taylor rules have been exensively analyzed since he seminal paper by Taylor (993). They are empirically plausible, especially in he las few decades when he objecive of price sabiliy has gained a major role in moneary policy-making. In order o accoun for he need o reduce swings in ineres raes in an environmen characerized by long and variable lags in moneary ransmission, I also consider a varian wih ineres rae smoohing, i.e. bi = bi +. For ease of comparisons wih exible price models, I nally consider a Wicksellian regime in which he nominal ineres rae is se so as o reproduce a exible price equilibrium wih zero in aion. The Wicksellian ineres raes ei are given by: ei H = E C+ b C b + ( ) E T+ b T b ei F = E C+ b C b E T+ b T b (3) Wih exible prices, nominal ineres raes mimic changes in he world naural (real) ineres rae. As is well-known, he Wicksellian policy can be implemened recurring o a credible hrea o deviae from a zero in aion arge, i.e. i = ei + # wih # >. 4 Simulaions The model is simulaed using rs-order perurbaion mehods. To begin wih, I consider produciviy shocks as he main source of business cycle volailiy, absracing from ineres rae innovaions. This faciliaes comparisons wih real business cycle models. Nex, I focus on a one-ime innovaion in nominal ineres raes for he purpose of illusraing he mechanism of moneary ransmission. 4. Calibraion I calibrae a US-EMU model in which counry H represens he Unied Saes and counry F he EMU 2. The relaive dimension of hese wo economies is capured by = :6: This parameer also measures he share of domesic goods in US consumpion in he model, while he analogous share in European consumpion is = :4: These values are consisen wih a higher home bias in US consumpion relaive o ha in Europe. As regards he share of domesic goods in US invesmen, I se = :4, in accord wih he fac ha he share of impors in invesmens is higher han ha in consumpion. For robusness, I le vary beween :2 and :8: In he simulaions, periods are inerpreed as quarers and = :99 as usual in quarerly models of he business cycle. The size of he exogenous exi shock is :25 as suggesed by Bilbiie e 5

17 al. (27). The rae of rm disappearance is consisen wih a percen rae of job desrucion per year as found in he US. Moreover, such a moderae rae does no oversae he capaciy of he model o generae persisence. The elasiciy of subsiuion across varieies is equal o 7:88 as in Roemberg and Woodford (999a). This yields a reasonable average markup of approximaely 8 percen. Sudies based on disaggregaed daa usually nd a much lower ; roughly around 4. Simulaions wih a lower elasiciy deliver qualiaively idenical resuls and will no be repored. Oher preference parameers are ' = 2:3 as in Roemberg and Woodford (999a) and = as in Bilbiie e al. (27). I also experimen wih a value of he Frisch elasiciy as high as 6. The degree of nominal rigidiy is esimaed by Galì, Gerler and Lopez-Salido (2). In heir sudy, he value of ranges beween :47 and :66 in he US and beween :67 and :77 in Europe. As suggesed by Benigno and Benigno (28), I ake he middle poins from hese inervals and se = :49 in he US and = :72 in Europe. These values imply an average duraion of nominal conracs of, respecively 2.3 and 3.65 quarers. I also experimen wih a common value of :66 as Roemberg and Woodford (999a), obaining qualiaively idenical resuls. Iniial condiions for produciviy shocks, he erms of rade and he nominal exchange rae do no a ec he dynamics of he model and are se a uniy wihou loss of generaliy. Finally, he vecor of produciviy shocks Z = (Z H ; Z F ) follows a bivariae auoregressive process, Z = AZ + where = ( H ; F ) is disribued normally and independenly over ime wih variance V. The correlaion beween he echnology shocks Z H and Z F is deermined by he o -diagonal elemens of A and V. 4.2 Technology shocks 4.2. Momens This subsecion illusraes he performance of he model in replicaing sylized facs of he inernaional business cycle. Tables and 2 repor saisics of he model s ari cial ime series ogeher wih saisics in he daa. As wih he daa, saisics refer o Hodrey-Presco lered variables wih smoohing parameer of 6: The repored saisics are averages across simulaions. In comparing he model o properies of he daa, he reamen of variey e ecs deserves a paricular aenion. As argued in Ghironi and Méliz (25), empirical relevan variables - as opposed o welfare-consisen variables - ne ou he e ecs of changes in he range of available producs. The reason is he inabiliy of saisical measures of CPI in aion o adjus for availabiliy of new producs as in he welfare-consisen price index. Hence, he daa are closer o he producer These resuls are available upon reques. 6

18 han o he consumer price index. In wha follows, any variable ha in he model is measured in unis of consumpion will be de aed by producer in aion and convered ino unis of oupu (for any variable X in consumpion unis he correced measure will be X R = XP H =PH H ). A similar correcion applies o he real value of household invesmens in new rms, I = H P H H P (h) N H e : The benchmark model feaures sicky prices and enry cos in erms of goods. In his model, moneary policy follows a Taylor rule wih ineres smoohing i = :8i +:3 as in Bilbiee e al. (27). In he exible price economy, moneary policy is given by he Wicksellian rule i = ei +:2. For comparison wih oher models of rms enry, I also consider a varian wih enry coss in labor unis (see he Appendix for linearized equaions). Firs, consider inernaional comovemens. In he daa, comovemens. of oupu, consumpion, invesmen and employmen are srikingly posiive across a large number of counries, alhough cross-correlaions are no oo srong especially in more recen imes (see Ambler e al. (24)). In addiion, inernaional synchronizaion is higher for oupu han for any oher variable, while he synchronizaion of invesmens is larger han ha of employmen. As rs shown by Backus, Kehoe and Kydland (992, 995), here are imporan discrepancies beween hese facs and wha sandard models predic. Real business cycle models ypically generae negaive cross-correlaions (he comovemen puzzle) and a lower correlaion of oupu han ha of any oher macroeconomic aggregae (he quaniy anomaly). Many candidaes have been suggesed o propose a soluion o hese puzzles, ye no agreemen has been reached on wha is he bes way o solve hem. 2 In general, hey have been relaively unsuccessful in nding a soluion o all he anomalies simulaneously. Panel A of Table conains correlaions of Home and Foreign variables in he benchmark model, in a calibraion wih = :8 or wih = :2, in he exible price economy, in he model wih labor enry coss and in he daa for he Unied Saes and Europe from Ambler e al. (24). Panel B conains saisics of Home variables in he hree models above ogeher wih US daa from King and Rebelo (999). To faciliae comparisons, I focus on counry-speci c produciviy shocks wih symmeric sandard deviaion equal o.852, correlaion.258 and persisence.96 as in Backus e al. (992). 2 Successful sraegies comprise, among ohers, he inroducion of non-radable goods, invesmen and consumpion of durable goods, disribuion services, capial marke fricions, adjusmen coss o invesmens as well as governmen spending and ase shocks. 7

19 Table : A: Inernaional Comovemen Benchmark model Flex price model Labor enry coss High Low EU-US daa correlaion of domesic and foreign variables Y R L I B. Business Cycle Properies Benchmark model Flex price model Labor enry coss US daa, KR (999) X Y XY X X Y XY X X Y XY X X Y XY X Y R L I X is he sandard deviaion of variable X, XY is he correlaion of variable X w ih oupu, Y, and X is he auo-correlaion of variable X. The benchmark model (wih sicky prices and enry coss in erms of goods) reproduces he posiive comovemens of oupu, invesmens and employmen found in he daa. 3 In addiion, i maches he ranking in he daa, wih oupu more correlaed han invesmens and invesmens more correlaed han employmen across counries. However, he cross-correlaion of invesmens and employmen is low compared o he daa. Correlaions remain posiive alhough far below hose in he daa when he share of impors in enry coss is eiher very low or very high. In Backus e al. (992), negaive correlaions arise as a consequence of a srong incenive o use inpus where hey are mos producive. In heir model, agens are able o shif subsiuable goods coslessly beween counries and o rade in complee markes for sae coningen claims. They are herefore induced o move producion e or o he counry wih a high echnology shock. A similar incenive is a work in a seup wih enry whenever prices are exible or enry requires hiring workers. No surprisingly, he performance of hese economies in reproducing he inernaional business cycle is very close indeed o ha of Backus e al. (992). A near perfec correlaion of invesmens beween counries re ecs a srong incenive o esablish new rms where produciviy is high (he Home counry in he simulaion). A negaive cross-correlaion of employmen capures he e ec of risk sharing: higher income in he low produciviy economy (he Foreign counry in he simulaion) induces agens o reduce labor supply. The combinaion of hese e ecs leads o a negaive correlaion of oupu beween counries. 3 Ohers have mached he posiive comovemens observed in he daa, for example Kose and Yi (23) and Corsei, Dedola and Leduc (28). Bu he cross-correlaion of oupu in hese models sill falls shor of he empirical ndings. 8

20 In he benchmark model, hree facors work in he direcion of reducing he incenive o move resources owards he high produciviy economy. Firs, a gradual drop in he coss of acquiring maerials for seing up a new rm favors invesmens in he low produciviy economy. This is a key di erence relaive o a seup wih labor enry coss. Second, he failure o se prices in an opimal way reduces he prospecive pro s from invesing in a new rm and discourages enry relaive o a exible price economy. Las bu no leas, invesors realize ha pro s and markups will move upon enry. As will become apparen soon, couner-cyclical markups reduce he incenive o move invesmens owards a more producive economy. Pro-cyclical pro s, on he oher hand, miigae he negaive impac of risk sharing on labor supply, generaing a posiive comovemen of employmen. The abiliy o mach comovemens in he daa does no come a he cos of implausible business cycle properies. Panel B in Table shows ha he benchmark model generaes volailiies of invesmen and employmen in erms of oupu close o hose in he daa. The exible price economy and he model wih labor enry coss, on he conrary, display excessive volailiy of invesmens. The inuiion is ha a lower volailiy of invesmens re ecs a limied abiliy of agens o move producion where i is more producive. Consider now rade variables. Despie ample heerogeneiy across counries, a number of sylized facs emerge wih clariy. Expors and impors are more volaile han oupu, posiively correlaed wih each oher and pro-cyclical, while ne expors are less volaile han oupu and couner-cyclical (Engel and Wang (2)). Table 2 repors saisics of Home real impors, real expors and he raio of ne expors o GDP in he benchmark model (column a), in a calibraion wih = :8 or wih = :2, in he exible price economy (column b), in he model wih labor enry coss (column c) and in US daa from Engel and Wang (2). The paramerizaion of he produciviy shock is as before. Table 2: Trade saisics (a) (b) (c) High Low US daa X Y X XY Y X XY Y X XY Y X XY Y X XY Y Real Impors Real Expors Ne Expors/GDP X is he sandard deviaion of variable X and XY is he correlaion of variable X w ih oupu, Y. U S daa are from E ngel and Wang (2). XY Column a refers o he benchmark model, column b o he exible price economy and column c o he model wih labor enry coss. 9

21 The benchmark model maches he properies of rade variables fairly well. I capures he volailiy and he pro-cyclical behavior of rade ows as well as he couner-cyclical behavior of ne expors (in he model as in he daa, couner-cyclical ne expors derive from a higher correlaion of impors wih GDP han ha of expors). In his respec, i performs beer han sandard inernaional real business cycle models, as Backus e al. (992) and Heahcoe and Perri (22), and in line wih recen models as Corsei, Dedola and Leduc (28) and Engel and Wang (2). The nding is robus o varying he composiion of invesmens goods. In my seup, he volailiy of rade variables depends on he volailiy of demand for consumpion and invesmens goods as well as on he subsiuion beween Home and Foreign goods. In spie of a low elasiciy of subsiuion (equal o in he model) and a low volailiy of consumpion (he sandard deviaion of C relaive o oupu is.75 in he benchmark model), invesmen demand can generae very volaile impors and expors in he benchmark as well as in he oher speci caions. A noiceable di erence is ha expors are couner-cyclical and ne expors are pro-cyclical in he models wih exible prices and wih labor enry coss. This resul re ecs once again a srong incenive o move resources owards he mos producive economy. Falling invesmens in he low produciviy economy, in fac, imply a drop in he demand for Home expors Impulse responses Figure shows impulse response funcions of seleced Home and Foreign variables for a one-sandarddeviaion shock o Home produciviy. The verical axis shows percenage deviaions from he seady sae (a value of, say,. denoes a percen deviaion) and he horizonal axis shows he number of periods afer he shock. For consisency wih second momens, he shock has a persisence of.96. The impulse responses are displayed under a Wicksellian policy (doed line), i = ei +:2 ; and a Taylor smoohing rule (solid line), i = :8i + :3 : Focus on he responses under exible prices (i.e. wih he Wicksellian policy). The posiive shock o Home produciviy creaes a more favorable business environmen, aracing enrans ino he home marke and leading o a gradual increase in he number of producers over ime. 4 A larger number of producers, in urn, rises he relaive price of Home varieies (he variey e ec) ogeher wih marginal coss while markups remain unchanged. Because he shock is persisen, here is also a signi can wealh e ec ha pushes up he demand for boh Home and Foreign goods. As a resul of all hese e ecs, aggregae consumpion and GDP increase in he home counry. 4 The pro-cyclical response of enry is consisen wih an ample evidence. In he US, he cyclical properies of rms enry have been documened by, among ohers, Dunne, Robers and Samuelson (988), Chaerjee and Cooper (993), Campbell (998), Bilbiee e al. (27) and Lewis (29). 2

22 8 x 3 H consumpion.6 H enrans.2 H producers H GDP x 3 H markup x 3 H ineres rae F erms of rade. Nominal exchange rae 2 x 4 F ineres rae F enrans.2 F GDP 5 x 4 F markup Figure : impulse response funcions for a one-sandard-deviaion shock o H produciviy wih sicky prices (solid line) and wih exible prices (doed line) Trade in goods and asses spreads he e ecs of he produciviy shock worldwide. In he face of a home posiive shock, he price of Home-produced goods falls relaive o Foreign-produced goods, deerioraing he home erms of rade (T is above he seady sae for mos of he ransiion). Consequenly, world expendiure swiches in favor of home goods. An analogous shif maerializes in he porfolio of invesors as a consequence of arbirage in nancial markes. In he wake of he produciviy shock, he real reurn on asses (bonds and shares) increases in he world economy. In he high produciviy economy (he Home counry), he increase in he real reurn on shares is brough abou by a decrease in oday s price of equiy (he value of he rm) relaive o omorrow s while he opposie is rue in he low produciviy economy. 5 Therefore rms enry is above he seady sae in he Home counry and below he seady sae in he Foreign counry. As will be clear soon, his needs no be he case when markups (and reurns) move couner-cyclically. Noe ha he response of Foreign enrans is he mirror image of ha of Home enrans. This is a consequence of he fac ha a produciviy shock favors producion of exising goods relaive o he creaion of new varieies. In he foreign counry, he drop in he number of enrans and producers reduces GDP for mos of he ransiion. As already noed, a srong incenive o move resources in he mos 5 Wih exible prices, pro s are a consan share of revenues, d = Y : Therefore, rm s value (he price of N equiy) is given by: = ( ) The real reurn on shares is r+ (v + +d + ) : E " X s=+ 2 C s+ C s ( Y # + N+ )

23 producive economy generaes negaive comovemens beween counries. Comparing he macroeconomic dynamics wih sicky and exible prices reveals a number of ineresing feaures. Consisenly wih he saisics repored in he preceding subsecion and in line wih New-Keynesian models, sicky prices imply signi can deparures from a exible price equilibrium. Firs, he response of enrans is subdued, ranslaing ino a moderae change in he sock of producers over ime. Second, Home markups say below he seady sae for he whole ransiion. In he foreign counry, he response of markups is posiive on impac hen i gradually declines and evenually urns negaive before converging o he seady sae. Markups are herefore couner-cyclical as observed in he daa. 6 7 The behavior of markups is a consequence of rms enry moving prices and marginal coss in opposie direcions. On he one side, an increase in he number of producers, by pushing on labor demand, raises wages and marginal coss. On he oher side, i fosers price compeiion. These e ecs, virually presen in any model wih enry, may be obscured by o seing changes in markups or in oher sources of marginal coss. Wih coss of price adjusmens, for insance, (as in Bilbiee e al.(27), Auray and Eyquem (2) and Auray e al. (22)), he pressure on wages implied by enry is ypically accommodaed by a drop in rms markups. Third, oupu and invesmen spillovers are posiive as in he daa. In order o see why, consider enry behavior in he foreign counry. Markups above he seady sae rise he expeced reurn on invesmens in new rms. Moreover, he Home currency depreciaion reduces he coss of imporing maerials for seing up a new rm. The combinaion of hese e ecs reduces oday s price of equiy relaive o omorrow s, aracing new enrans. My ndings di er from previous models of endogenous enry, as Bilbiie e al. (27) and Auray e al. (22), where he performance of he sicky price model is virually indisinguishable from ha of he exible price economy. In models wih labor enry coss here is a direc link beween asse prices and in aion ha is absen in my seup. Consider, for insance, a emporary ineres rae cu ha reduces he real reurn on bonds and shares. The fall in he reurn on shares is brough abou by an increase in oday s price of equiy relaive o omorrow s. The price of equiy is relaed 6 Sudies based on di eren mehodological approaches converge on he view ha markups are couner-cyclical in major economies. In he US, his is indeed he case for sudies using mosly aggregae daa as Roemberg and Woodford (999b) as well as wo digi indusry level daa as in Bils (987). In a sudy wih 4 OECD counries and indusry level daa, Marins, Scarpea and Pila (996) nd couner-cyclical markups in 52 ou of he 56 cases hey consider. 7 In New-Keynesian models, variable margins of pro s are ypically powered by exogenous price sickiness. For models ha combine variable markups and menu coss see, among ohers, Gopinah and Iskhoki (2) and Bhaaraj and Schoenle (2). Nominal rigidiy is by no means essenial for generaing variable markups. In a seup wih exible prices, Akeson and Bursein (28) show ha rms can discriminae prices across markes by leing heir markups vary based on local marke condiions. Alessandria (29) shows ha consumers search can also deliver variable markups. 22

24 o marginal coss by he free enry condiion in hese models, herefore marginal coss rise, markups fall and, hrough he Phillips curve, in aion rises. Sicky prices will a ec enry only marginally whenever simple moneary rules manage o conrol in aion, as is he case wih Taylor rules. In my seup, insead, he price of equiy is direcly relaed o he cos of acquiring home and foreign invesmen goods. They di er also from models wih exogenous asse prices, as Auray and Eyquem (2). In hese models, shocks are ransmied hrough a change in he expeced reurn on asses. In he face of a posiive produciviy shock, he increase in he real reurn on shares is brough abou by an increase in expeced dividends. In he counry hi by he produciviy shock, markups rise and more rms ener he marke while he opposie occurs in he parner counry (as wih exible prices). In my seup, on he conrary, he behavior of markups is couner-cyclical. Declining markups in high produciviy economies end o amplify de aionary pressures while rising markups in low produciviy economies have he opposie e ec. Moneary auhoriies have herefore an incenive o move ineres raes in a pro-cyclical way in he aemp o sabilize prices (see Figure ). Pro-cyclical ineres raes, in urn, exacerbae exchange rae volailiy via he ineres pariy. This accords wih a large evidence documening ha nominal exchange raes among major currencies rever o heir mean value wih very long lags. 8 In he model, non-saionariy derives from he sae equaion of he erms of rade (25), which splis a given change in he erms of rade ino changes in he nominal exchange rae and in aion di erenials beween counries. Alhough he erms of rade are saionary and rever o he iniial value afer a shock, here is nohing in he oaing regimes considered ha forces he exchange rae owards he iniial seady sae, unless in aion raes are zero a all daes (as wih he Wicksellian policy). Mechanically, rms enry conribues o his non-saionariy by generaing in aion di erenials beween counries. Enry behavior migh in principle be a eced by he exchange rae regime. Simulaing he benchmark model under a unilaeral peg in he Foreign counry, i F = i H :2", I nd ha his is indeed he case. Invesmens and oupu are negaively correlaed beween counries as wih exible prices (no shown in Figure ). The reason is easy o grasp. Fixed exchange raes (combined wih sicky prices) limi he exen o which foreign agens can ake advanage of he Home produciviy shock, especially in he early par of he ransiion. By conras, arbirage in nancial markes requires he real reurn on asses o increase immediaely in boh economies. In oaing regimes, a sharp depreciaion of he Home currency helps o bridge he gap beween high and low produciviy economies. Wih xed exchange raes, on he conrary, adjusmen is brough abou mainly by 8 In a famous paper, Meese and Rogo (983) show ha for major nominal exchange raes agains he dollar a random walk model ouperforms any of he srucural models wihin a one-year forecasing horizon. 23