Extensive and intensive margins and the choice of exchange rate regimes

Transcription

1 Exensive and inensive margins and he choice of exchange rae regimes Hamano M. and Picard P.M. July 212 Absrac This paper sudies how he choice of fixed or flexible exchange rae regimes is affeced by he exisence of inensive and exensive margins. Using a conemporaneous enry model, only exensive margins vary under fixed exchange rae regimes following a demand shock. In such a case, he choice resuls from he balance beween he lower average number, higher volailiy in exensive margins and heir sronger congruence wih preferences. Fixed exchange rae regimes are hus preferred for high enough labor supply elasiciies. In conras, when enry is lagged because households smooh heir consumpion by lending/supplying heir funds o firms, boh inensive and exensive margins flucuae. In such a case, exensive margins have a negaive conribuion o welfare hrough heir lower average and higher volailiy. Insead, he congruence beween preferences and inensive margins brings a posiive conribuion o welfare. In his general seing, fixed exchange rae regimes are less likely o be suppored for a larger se of parameers when produc varieies are less alike i.e. when consumers express a higher preference for produc diversiy). Keywords: Firm enry, Exchange rae sysem JEL classificaion: E22, E52, L16 1 Inroducion Since Friedman 1953), he inernaional and moneary economics lieraure has widely sudied he ransmission of inernaional shocks wihin he producion secor. Accordingly, he adopion of a pegging policy This projec has been suppored by he gran F2R-CRE-PUL-1EGQH a he Universiy of Luxembourg. Universiy of Luxembourg, CREA, L-1511 Luxembourg, Luxembourg. Conac address: Faculy of Law, Economics and Finance, Universiy of Luxembourg, 162a, avenue de la Faïencerie, L-1511 Luxembourg. Tel.: masahige.hamano@uni.lu. Universiy of Luxembourg, CREA, Luxembourg, and Universié caholique de Louvain, CORE, Louvain-la-Neuve, Belgium. Conac address: Faculy of Law, Economics and Finance, Universiy of Luxembourg, 162a, avenue de la Faïencerie, L-1511 Luxembourg. Tel.: ; fax: pierre.picard@uni.lu. 1

2 or a common currency union shifs mos adjusmens o he real side of he economy. Flexible exchange raes, on he oher hand, correc relaive price misalignmens and absorb macroeconomic shocks. Adjusmens on he real side of he economy consis no only of he expansion and conracion of exising firms, bu also he enry and exi of firms. Thus shocks are ransmied hrough boh inensive and exensive margins of producion and rade. The choice of fixed or flexible exchange rae regimes is herefore likely o be affeced by he way hose margins respond o shocks. While previous lieraure has mainly focused on he role of inensive margins on his choice, he presen paper aims o sudy he role of exensive margins. This paper sudies he coss and benefis of fixed and flexible exchange rae regimes in a general equilibrium model ha includes wo counries, money holdings, an elasic labor supply, sochasic exogenous demand shocks and endogenous inensive and exensive margins. Firms produce and sell differeniaed producs under monopolisic compeiion. They ener or exis by comparing operaional profis wih coss of enry. Wages are assumed o be sicky for one period. Money maers in he economy beyond a mere uni of accoun under such nominal rigidiies. Thus, moneary policy may have an impac on boh exensive as well as inensive margins. Wihou any sae-coningen financial asses inernaionally held, he choice of exchange rae regimes becomes criical for welfare. Acceping closed form soluions, he model allows us o discuss he effec of asymmerical demand shocks on inensive and exensive margins and on he choice of exchange rae regimes. In paricular, we compare wo models. In he firs, households can smooh heir consumpion only by money savings. In he second, hey can addiionally smooh heir consumpion by lending/supplying heir funds o firms. The consumpion smoohing behavior hrough fuure exensive margins in he laer case has a crucial implicaion under fixed exchange rae regimes: while invesmen and firm enry are aligned wih demand shocks in he firs case, firm enry lags behaind demand shocks in he second case as a resul of moneary reacion. Our resuls are as follows. In general, he loss of he exchange rae insrumen requires adjusmen in exensive as well as inensive margins following a demand shock. When here is no possibiliy of consumpion smoohing hrough new firm creaion, he adjusmen arises only in exensive margins. As a resul, exensive margins are procyclical and have a lower average and higher variance under a fixed regime. Ye, such procyclical movemens in exensive margins raise welfare because hey are provided a he very momen of he shif of preference. The choice of a fixed exchange rae regime mus herefore accoun for is coss he lower mean level of and higher variabiliy in exensive margins) and is benefis he sronger congruence beween preference and produc diversiy). These coss decrease wih higher labor supply elasiciies. When households can smooh heir consumpion hrough he fuure number of firms, inensive margins flucuae on impac of a demand shock while exensive margins arise wih one period of lag. This is due 2

3 o he moneary reacion under fixed exchange rae regimes. Hence, on he one hand, we have a posiive congruence effec under fixed regimes on inensive margins. On he oher hand, because of his lag beween invesmen and producion of exensive margins, he enry of firms and new produc varieies is no necessarily concomian wih consumers ases. As a resul, he welfare cos, arising from a smaller average of and higher volailiy in exensive margins, remains. As in he firs case, we show ha fixed regimes are preferable under high enough labor supply elasiciies. Imporanly, we also show ha fixed exchange rae regimes are suppored for a smaller se of parameers when households are allowed o save and inves in he form of firm creaion. This is furher he case when produc varieies are less alike, hence consumers express a higher preference for produc diversiy. The mean and variance effec in exensive margins has indeed a higher impac on households welfare when consumers aach a higher imporance o produc diversiy. In his paper, here is neiher inernaional borrowing and lending nor fiscal ransfer. 1 Risk sharing across counries is herefore imperfec and he flexible price allocaion realized under flexible exchange rae regimes deviaes from ha obained under complee asse markes. 2 The Pareo efficien allocaion would se he produc supply or diversiy according o changes in ase for each counry s producs and o redisribue hose margins appropriaely across counries. However, alhough flexible exchange raes correc relaive prices and realize higher average producion and lower volailiy, hey fail o ensure ha produc supply and diversiy align wih consumer preferences. By conras, fixed exchange rae regimes have he opposie properies. Our conribuion relaes o he lieraure in he following way. Firs of all, our model and resuls can be compared wih Devereux24) s conribuion qualifying he prevailing view ha exchange raes are he mos imporan shock absorbers. Discussing a saic economy wih wo counries, wo varieies, wage rigidiies and consan reurns o scale, Devereux shows ha fixed exchange raes are more welfare improving han flexible one, when he elasiciy of labor supply is sufficienly high. Our model exends his model o full dynamics, increasing reurns o scale, monopolisic compeiion and he enry and exi of firms. The exension allows us o discuss he role of he balance beween inensive and exensive margins in welfare ranking. Comparing resuls, i urns ou ha, when households canno make invesmen choices for firm creaion, he choice of an exchange rae regime is he same in Devereux 24) as our model. The forces a play are, however, differen since produc subsiuabiliy and love of produc diversiy drive he welfare effecs of exensive margins in his paper. Our resuls differ when households can inves by 1 This corresponds o siuaions where governmens are unable o organize significan ransfers beween counries and where households and/or governmens are unable o use he inernaional credi marke in he long run because of various borrowing consrains e.g. credi consrains for households, Maasrich reay for E.U. counries, I.M.F. consrains for developing counries). The 211 Greece-EU crisis is a good illusraion of he difficulies of organizing inernaional ransfers and access o credi markes. 2 The deviaion is called a demand imbalance in he lieraure Corsei e al. 21a, 21b). See also Hamano 29a, 29b) for relaed opics of risk sharing and exensive margins. 3

4 holding shares of new firms. This paper also presens and discusses a formal decomposiion of he welfare conribuion of he wo margins. The presen paper emphasizes he mechanisms hrough which inensive and exensive margins can be accounable for he choice of exchange rae regimes. Our approach conrass wih he classical lieraure, where firms enry is driven solely by real facors such as produciviy and populaion shocks Krugman 198, 1991; Meliz 23; Ghironi and Meliz 25). In his insance, Naknoi 28a,28b) s conribuion is very close o ours. Naknoi analyzes how differen exchange rae regimes can impac exensive margins hrough endogenous radabiliy based on a Ricardian comparaive advanage. 3 While relocaion of firms beween radable and non-radable secors arises in her model, our model accommodaes free enry condiions and exporing by all firms. Because he secoral relocaion of firms is insananeous in response o shocks in Naknoi s model, here are none of he welfare coss ha could arise from he mismach beween ase and exensive margins under fixed regimes. Baldwin and Nino 26) and Bergin and Lin 21) also look a he impac of a common currency on exensive margins. They, however, aach a special role o fixed coss and absrac away from moneary issues. Finally, our paper builds upon he so-called New Open Economy Macroeconomics see, for insance, Obsfeld and Rogoff 1995, Corsei e al. 21b). While his lieraure has focused on opimal moneary policies under complee financial markes, i is new beginning o invesigae hose policies under incomplee financial markes, as we do in his paper. This approach is also followed by Ching 23) and Picard and Worrall 29), who consider moneary ransfers wihin currency unions ha correc for he incompleeness of financial markes. The srucure of he paper is as follows. Secions 2 and 3 presen and discuss he model and equilibrium. Secions 4 and 5 discuss he choices of exchange rae regimes when enry is eiher conemporaneous or lagged wih invesmen. Secion 6 concludes. 2 Model The presen model discusses he welfare coss and benefis of exchange rae regimes beween wo counries, Home and Foreign. Foreign variables are denoed wih aserisks.) Each counry is inhabied by a uni mass of households who are differeniaed only in erms of heir labor services. Wages are se by households one period in advance of producion. There are no fiscal ransfers and no borrowing and lending across counries. We describe he domesic counry Home). The same descripion holds for Foreign. Households In every ime period, each household i [, 1] consumes goods in a domesic se X and a foreign se Z of differeniaed varieies. I also holds a quaniy of money M i) and supplies l i) labor unis worked hours). The household maximizes is expeced ineremporal uiliy, E = β U where 3 Ineracion beween exensive margins and moneary policy has been invesigaed in a closed economy. See for insance, Bergin and Corsei 28), Bilbiie, Ghironi and Meliz 27), Lewis 29) and Bilbiie, Fujiwara and Ghironi 211). 4

5 β, 1) is a common discoun rae and where uiliy in period is given by he following wo-ier uiliy funcion: where and X i) = x i, ω) 1 ω X U i) = ln C i) + χ ln M i) κ [l i)] P 1 + ψ ) α X i) Z i) C i) = α 1 α ) 1 dω ) α and Z i) = z i, υ) 1 υ Z ) 1 dυ In his definiion, P is he consumer price index, and M i) /P is household i s real money holding. The parameer ψ measures he inverse of he Frisch) elasiciy of labor supply while he parameers χ and κ measure he inensiy of preferences owards real money holdings and individual labor supply worked hours) respecively. We call C i) he composie bundle and X i) and Z i) he consumpion baskes of domesic and foreign produc. While x i, ω) denoes is consumpion of domesic varieies ω X, z i, υ) denoes he consumpion of foreign varieies υ Z. Under he above preferences Dixi and Sigliz, 1977), he parameer > 1 measures he elasiciy of subsiuion among varieies wihin he same consumpion baske and also he inverse of) love for produc diversiy wihin his baske. The parameers α, α ) where α 1 α, 1) measures he preference beween he wo consumpion baskes. Following Devereux 24), we will consider ha he economy is hi by demand shocks so ha α follows an i.i.d. sochasic process which is symmerically disribued around a mean equal o 1/2. A Home household supplies is labor and earns an income w i)l i) where w i) is is hourly wage. In addiion o spending is income on he above produc varieies and holding money, he household can inves in domesic firms. We consider wo modes. In he firs, firm invesmen and enry occur in he same ime period so ha m =. In he second, invesmen occurs one period before enry as a resul of share holding choice by households -ha is m = 1. The household can herefore inves in a firm ha produces he variey ω X +m ha become available eiher wihin he same period m = ) or wihin he nex period m = 1). The household budge consrain is hen given by p ω) x i, ω) dω + p υ) z i, υ) dυ + s i, ω) q ω) dω + M i) ω X υ Z ω X +m = w i)l i) + s m i, ω) d ω) dω + M 1 i) ω X where p ω) and p υ) are he domesic) prices of Home and Foreign varieies ω X and υ Z. In his expression q ω) denoes he price a dae for a share of a firm ha eners a dae and produces variey ω X +m a dae + m, while d ω) denoes he dividend paid by an incumben producer ω X a period. Household i spends a share s i, ω) on he sock of an enering firm ω X +m and receives he share s m i, ω) of he dividend paid by every incumben producer ω X. 5

6 Firms Firms aciviies are described as follows. Consider a Home firm ha produces a differeniaed variey ω X under increasing reurns o scale and sells is producs under monopolisic compeiion a dae. We assume ha o produce is oupu he firm mus spend on esablishmen aciviies e.g. building a producion plan) a he ime period m where m =, 1. Every firm employs a se of horizonally differeniaed labor services. To make his more precise, we assume ha each household i [, 1] offers a differeniaed labor service and ha every firm ω demands he quaniies of labor services l i, ω) and e i, ω), for is producion and seup aciviies, respecively. To produce y ω) unis of oupus, he firm uses he se of labor services given by whereas i uses 1 y ω) = 1 f = l i, ω 1 1 θ 1 θ di e m i, ω 1 1 θ 1 θ di for is esablishmen aciviies a dae m. In hose expressions, θ > 1 is he elasiciy of subsiuion among he differen labor services. The firm pays a dividend o is shareholders. This dividend is equal o he conemporaneous operaional profi ha includes sales and producion cos: d ω) = p ω) y ω) The seup cos is equal o 1 e m i, ω) w m i)di. Markes and governmens is variey by boh domesic and foreign consumers: y ω) = 1 1) 2) l i, ω) w i)di 3) When produc markes clear, each firm s supply equals he demand for 1 x ω, i) di + 1 x ω, j) dj, ω X where he superscrip denoes foreign consumpion and j denoes each foreign household. Similarly, when labor markes clear, each household s labor supply equals he demand by firms: l i) = l i, ω) dω + ω X e i, ω) dω, ω X +m i [, 1] In equilibrium, rade mus be balanced so ha he value of domesic impors equaes he value of expors. We ge 1 ε p ν) z ν, i) dνdi = p ω) x ω, j) dωdj ν Z ω X where ε is he exchange rae namely, he price of one uni of foreign money in erms of he domesic currency), p ν) is he price of foreign variey ν Z denominaed in he foreign currency, and x ω, j) is he foreign demand for he domesic variey ω X. Finally, he cenral bank supplies an amoun of money M. When he money marke clears, he money supply is equal o is demand so ha M = M i) di

7 Symmeric condiions hold for he foreign counry. Wages are sicky during one ime period. We define he equilibrium as follows: i) each household i chooses a plan of money holding {M i)} =, consumpion profiles {x i, ), z i, )} =, sock marke posiions {s i, )} = and wages {w +1i))} = applying in he nex period, ha maximize is ineremporal uiliy subjec o is per-period budge consrain, ii) each firm ω X chooses is produc price p ω) and is labor demands l i, ω) and e i, ω) ha maximizes is profi, iii) he local sock marke clears so ha firms ener as long as hey raise a sock price q ω) ha mees fuure expeced dividends and iv) producs, labor and money markes clear in every period. The money supply is se by each cenral bank wih he objecive of eiher a fixed or flexible exchange rae. 3 Equilibrium We here describe he equilibrium choices by households and firms and deermine he marke equilibrium condiions for any exogenous moneary policy. Equilibrium condiions will be applied o he moneary policies of fixed and flexible exchange rae regimes in he nex secions. For he sake of conciseness, we here discuss he cases of conemporaneous and lagged enry ogeher, equilibrium condiions being idenical or similar. We finish by discussing equilibrium welfare. Household choices In period, he household i chooses is consumpion profiles x i, ), z i, )), money holding M i) and share holdings s i). varieies can be compued as where Firs, is opimal consumpion of home and foreign ) ) p ω) p ν) x i, ω) = X i) and z i, ν) = Z i) P X, are he chosen consumpion baskes and P Z, X i) = α P C i) P X, and Z i) = 1 α ) P C i) P Z, P X, = p ω dω ω X 1 and P Z, = p ν dν ν Z are he price indexes for hose baskes. Finally, he consumer price index is given by 1 P = P α X, P 1 α Z, Second, he household s opimal money holdings and share of sock are expressed as he following real money demand equaion. M i) P = C i) χ 1 E Λ,+1 i) 4) 7

8 for m = and 1, where P C i) Λ,+1 i) = β P +1 C +1 i) denoes he endogenous discoun rae beween and + 1. While he equilibrium share of sock should be such ha sock prices equal dividends q ω) = d ω)) when m =, he opimal share of sock is given by he following Euler equaion when m = 1: q ω) = E Λ,+1 i) d +1 ω). 5) Firms decisions Firms produce under monopolisic compeiion. Consider a firm ω X ha chooses is price and labor demand a dae. I maximizes is dividend paymen 3) wih respec o p ω) and l, ω) subjec o he producion funcion 1). The cos-minimizing demand for labor services is hen equal o l i, ω) = w i)/w ) θ y ω) i where 1 W w i θ 1 θ di is he wage index, common for all domesic firms. Considering he following iso-elasic demand for is variey y ω) = 1 x i, ω)di + he firm ses is opimal price 1 ) [ x p ω) 1 j, ω)di = X i) di + p ω) = P X, 1 W 1 ] X j) dj which is he same for all domesic varieies. Taking ino accoun he above condiions, he firm s dividend is equal o d = p ω) y ω) /. Firm i also minimizes is seup cos 1 e m i, ω) w m i)di. Is cos-minimizing demand for labor services is equal o e m i, ω) = w m i)/w m ) θ f, which resuls in a cos W m f. Wage seing In his paper we consider wages ha are sicky. The households se heir wages one ime period in advance. Accordingly, a dae, a domesic household i ses he wage w +1 i) ha maximizes is expeced uiliy E U +1 i) subjec o nex period s budge consrain and nex period s balance beween labor supply and demand: l +1 i) = ω X +1 l +1 i, ω)dw + ω X +1+m e +1 i, ω)dw. In he laer expression, he firs and second erms respecively represen he labor demands for producion aciviies a dae +1 and for seup aciviies a dae +1 by he firms producing a dae +1+m, m =, 1. As seen above, his labor demand is a iso-elasic funcion of w i). One can show ha he household ses is wage such ha is expeced disuiliy of a marginal work effor, κθw +1 i) 1 E l +1 i), equals is expeced uiliy from he associaed increase in consumpion, θ 1) E [l +1 i) / P +1 C +1 i))]. Hence, w +1 i) = κ θ E l +1 i) θ 1 E [l +1 i) / P +1 C +1 i))] 6) 8

9 Local sock marke equilibrium The equilibrium in he local sock marke depends on invesmen iming. When a firm eners and esablishes producion in he same period as is sales m = ), i asks a sock price of q ω) = W f and pays a dividend of d ω) = p ω) y ω) /. Since q ω) = d ω) when m =, he sock marke clears when p ω) y ω) / = W f. By conras, when a firm eners and invess in he period before is sales m = 1), i asks a sock price of q 1 ω) = W 1 f and pays a dividend of d ω) = p ω) y ω) /. The Euler equaion 5) becomes W 1 f = E 1 Λ 1, p ω) y ω) / 7) Produc marke equilibrium The above analysis shows ha households make he same choices and firms he same decisions wihin each counry. This symmery allows us o dispense wih householdand firm-specific noaions. We can now drop he reference o i and ω, ν) wihou any ambiguiy. The produc marke clear when rade is balanced. The balanced rade condiion yields he exchange rae, ε = 1 α ) P C α P C, which simply compares he value of impors numeraor) o he value of expors denominaor). Given he above relaionships, we can readily deermine he dividends and wages as well as he exensive and inensive margins. Le N be he mass of firms ω X ha produce in he domesic counry. Wih he above balanced rade condiion, each domesic firm s dividend is successively given by d = 1 p y = 1 Wages, exensive and inensive margins α [P C + ε P C ] = 1 P C. 8) N N On he one hand, consider a firm ha eners and ses is producion up in he same period as is sales m = ). We know ha d = p y / = W f so ha he exensive and inensive margins are given by N = 1 P C W f and y = W f p = 1) f 9) As usual in Dixi-Sigliz models, he inensive margin is consan while he exensive margin absorbs all shock variabiliy. The equilibrium labor supply is deermined as follows. Consider he wage and labor services supplied in period + 1. The labor marke clears if l +1 = N +1 l +1 + N +1 e +1 = N +1 y +1 + N +1 f = P +1C +1 W +1 where we successively used 1), 2) and 9). Plugging his value of labor supply ino he wage equaion 6) yields he wage index W +1 = κ θ [E P +1 C +1 ) ] 1 θ 1 9

10 Ceeris paribus, he wage increases if he disuiliy from work increases higher κ) or heir labor services become weaker subsiues lower θ). In addiion, i increases wih a higher volailiy of fuure nominal expendiures P +1 C +1 when ψ >. On he oher hand, consider a firm ha eners and invess in he period before is sales m = 1). Then, he dividend is given by d = p y / and he share price by he Euler equaion 7). The laer condiion yields he exensive margin as N = E 1Λ 1, P C W 1 f = β P 1 C 1 W 1 f, 1) while he former yields he inensive margin y = 1 P C 1. 11) W N Boh margins respond o shocks. In paricular he exensive margin responds o he previous period s economic condiion whereas he inensive margin responds o he curren condiions. Noe ha he number of firms which appear as a consequence of households consumpion smoohing across ime falls wih more impaien invesors smaller β). When he labor marke clears, he labor supply is equal o labor demand. So, using 1), 2), 1) and 11), we ge he equilibrium labor supply as l +1 = N +1 l +1 + N +2 e +1 = N +1 y +1 + N +2 f = 1 + β Plugging his value of labor supply ino he wage equaion 6) yields he wage W +1 = κ θ θ β P +1 C +1 W +1 ) ψ [E P +1 C +1 ) ] 1 As above, he wage increases wih higher disuiliy from work higher κ) and less subsiuable labor services lower θ). In addiion, he wage increases wih higher impaience lower β). This is because he exensive margin decreases, leading o a decrease in he remuneraion from seup aciviies. A he limi, where β 1, he wage coincides o ha under conemporaneous enry assumpion m = ). Welfare working The household s uiliy is he sum of is uiliy from consumpion and disuiliy from U R l = ln C κk m 1 + ψ, where k m, m =, 1 are wo consans 4 and he uiliy from real money balance is U M = χ ln M P. 4 For m =, k = 1 + ψ) 1 θ 1) θ 1 ψ 1 + β) ψ while for m = 1, k 1 = k 1 + β) /).. 1

11 Following Obsfeld and Rogoff 1995), we assume ha he laer uiliy can be negleced χ ). The household s consumpion can be compued as C = α N 1 α N 1 α y α ) α y α ) α, 12) where α = 1 α. This consumpion level has he same expression in he conemporaneous enry model. Noe ha, using he equilibrium labor supply and aking he expecaion of U R, he expeced work disuiliy second erm in U R ) is found o be consan and idenical across exchange rae regimes. Wha maers for welfare is he expeced uiliy from consumpion he firs erm in U R ). where The ineremporal expeced uiliy from consumpion a period = is equal o = β E ln C E ln C = E α ln y + E 1 α ) ln y + 1 [E α ln N + E 1 α ) ln N ] + cs In fac, he firs and second and fourh and fifh erms in he above expression are he same because of he symmery of α s disribuion. Thus developing he erms, he expeced consumpion will acually depend on E α E ln y + covα, ln y ) + 1 [E α E ln N + covα, ln N )] 13) This expression presens ses of facors ha affec domesic welfare. On he one hand, domesic welfare rises wih he log of expeced domesic producion and diversiy firs and hird erms). The log of expeced inensive and exensive margins can rise wih heir mean level and fall wih heir higher volailiy. 5 On he oher hand, domesic welfare also depends on he congruence beween domesic consumers preferences and he inensive and exensive margins second and fourh erms in 13)). Specifically, he welfare effec of produc diversiy depends on, ha measures boh he elasiciy of subsiuion and he preference for variey. 4 Exchange rae sysems and conemporaneous enry As in Corsei and Peseni 25, 29), we define he moneary sance as µ P C The moneary sance is here derived from 4) as µ = M /χ E Λ,+1 ), which, afer subsiuing for Λ,+1, yields he following recursive ideniy: µ = M χ 1 βµ E µ 1 +1). ) 5 For insance, one can make he following approximaion for small demand shocks: E ln y ln y 1 2 var y y and ) E ln N ln N 1 2 var N. N 11

12 This ideniy solves o µ = 1 1 χ 1/M ) + s=1 βs E 1/M +s ). So, he curren moneary sance is a funcion of he curren and expeced fuure money supply. As a resul, he exchange rae can be expressed in erms of he moneary sance as ε = α µ. α In he domesic counry, he equilibrium wages, exensive and inensive margins are hen compued as see more variables in Appendix Table A1) where is a consan. W = ξ E 1 µ, N = 1 f µ ξ κ θ θ 1 µ and y = 1 µ W W N We can make several commens from hose expressions. Firs, wages are sicky and depend on he expecaion of he moneary sance. A given wages, exensive margins increase proporionally wih he moneary sance. An expansion of domesic money supply simulaes curren expendiure on consumpion goods and increases local firms profi, which riggers he enry of new produc varieies. This effec is similar o he one discussed in Bergin and Corsei 28). Second, he expansion of he domesic money supply also simulaes producion scales of incumbens bu he laer are exacly cancelled ou by he business sealing effec of new enrans. Indeed, given he above equaliies, we ge y = f 1). Third, ) i is shown below ha E 1 µ 1 is an increasing funcion of ψ and he variance of µ. Therefore, wages increase wih weaker labor supply elasiciy ψ 1 and larger variance in moneary sance when ψ >. A larger variance in µ amplifies he flucuaions in consumers produc demands and herefore firms labor demands. This enices workers o claim higher wages in compensaion for fuure wage uncerainy, hence increases firms coss. As a resul of hese higher wages, he number of firms falls. However, when he labor supply is infiniely elasic ψ = ), he variabiliy of moneary sance does no maer in wage seing behavior. In a flexible exchange rae regime, he domesic and foreign money supply M, M ) are consan for all ime periods, so ha he moneary sance is given as µ = µ = 2µ where µ is a consan. The exchange rae becomes ε = α /α. Replacing P C wih µ = 2µ in he above expressions, we can compue he equilibrium wage, exensive and inensive margins as W = µ ξ, N = 1 fξ and y = 1) f In his regime, no only are wages bu also exensive and inensive margins consan and independen of shock disribuions. The exchange rae perfecly absorbs he effecs of demand shocks on wages and margins. This is he allocaion of producion ha would prevail in an economy wihou wage rigidiies. 12

13 In a fixed exchange rae regime, he domesic and foreign money supply M, M ) are se so ha he exchange rae ε equals 1. This means ha moneary auhoriies ake procyclical moneary sances such as µ = 2µ α and µ = 2µ α. Le A E s j αs for s > j, which is larger han E α = 1/2. A increases wih increased variance in α. Replacing P C by µ in he above expressions, we can compue wages, exensive and inensive margins as follows: W = 2µ ξa, N = 1 α fξ A and y = 1) f On he one hand, wages are consan bu depend on shock disribuions hrough A). Wages coincide under flexible and fixed exchange rae regimes when labor supply is perfecly elasic ψ = A = 1/2). Since W rises wih A, wages increase wih he shock variance and wih he lower labor supply elasiciy larger ψ). On he oher hand, exensive margins respond o shocks. Higher demand for local goods riggers firm enry under procyclical moneary policy. Finally, exensive margins fall wih A. Indeed, a higher shock variance or a lower labor supply elasiciy increases wages and herefore reduces firms incenives o ener in he marke. Compared o he flexible exchange rae regime, he domesic expeced welfare a = under fixed exchange raes differs only from is exensive margins N. Hence, using 13), he condiion wih which a fixed regime is suppored compared o a flexible regime is given by [ E α E ln α 1 A + covα, ln α ] A ) > 14) The firs erm in he bracke represens he welfare loss under fixed exchange raes. Provided a disribuion of α, his erm can be furher negaive wih a lower labor supply elasiciy ψ 1 hrough A. As i has been menioned, he lower labor supply elasiciy and resuling higher wages reduce furher he equilibrium level of exensive margins under fixed regime. The second erm is sricly posiive and measures he gains from he congruence beween domesic preferences and domesic produc diversiy. Because A is a consan, his erm is equal o covα, ln α ). In expression 14), he choice of exchange rae regime is independen from he love for variey. Only he elasiciy of labor supply ψ 1 maers hrough he erms in A. A ψ =, we have ha A = E α so ha expression 14) is proporional o covα, ln α ), which is sricly posiive, hence supporing fixed exchange rae regimes. I is shown below ha A increases in ψ so ha he above expression falls below zero as ψ increases from zero o infiniy. Therefore here exiss a unique hreshold ψ below which 14) is posiive and above which i is negaive. Proposiion 1 In he conemporaneous enry model, here exiss a labor elasiciy hreshold ψ 1 such ha a fixed exchange rae sysem is preferred for labor elasiciies ψ 1 larger han ψ 1. 13

14 Proof. We need o show ha A is an increasing funcion of ψ and is negaive for large ψ. Le G : [1 α, α] [, 1] be he cumulaive disribuion of α where α [1/2, 1] is he upper bound of he disribuion. We firs show ha da/dψ >. Indeed, le fψ) A = α dgα), which is lower han one because α < 1 for all α and is an increasing funcion as f ψ) = 1 + ψ) α ψ dgα) >. Then, we compue ha d lna/dψ = d/dψ) [ ln fψ/)] = d/dψ) [ 1 + ψ) 1 ln fψ) ] = 1 + ψ) 2 ln fψ)+) 1 f ψ)/fψ), which is posiive because each erm is posiive in he las expression. Since d lna/dψ = A 1 da/dψ, i mus be ha da/dψ >. Second, expanding he covariance erm, he bracke in expression 14) is equal o E α E ln α E α E ln A + E α ln α E α E ln α, which simplifies o E α ln α ln A). The laer expression is negaive because ln α < ln A = ln α for ψ. Indeed, we successively ge lim ψ ln A = lim ψ ln [ E α ] 1 = lim ψ ln [ α lim ψ ln [ α 1 α α/α) α dgα ) ] 1 1 α α dgα) ] 1. Since lim ψ α /α ) = for any α < α, he laer expression becomes lim ψ ln [ α gα) ] 1 = ln α+ lim ψ [1/ 1 + ψ)] ln gα) = ln α. Inuiively, on he one hand, fixed exchange rae regimes are definiely preferred because hey realize an ideal composiion of produc diversiy in he consumpion baske following a shif in preferences. On he oher hand, however, fixed regimes are less likely suppored since hey increase he variabiliy of produc diversiy and reduce he equilibrium mean level of exensive margins. The laer negaive effec on welfare, arising from higher equilibrium wages, becomes srong when he labor supply is less elasic. This resul has been highlighed in Devereux 24) in a saic economy wih wo differeniaed goods where adjusmens ake place solely hrough inensive margins. Our resul simply shows ha he exensive margins have he same effec as inensive margins. We now discuss he more realisic model where exensive and inensive margin coexis hrough households s saving decision. = 5 Exchange rae sysems and lagged enry We now consider he siuaion in which households save and inves one par of curren wealh in he form of fuure produc diversiy in order o smooh heir consumpion. As before, he exchange rae is a funcion of moneary sances, ε = α /α )µ /µ ), which allows us o compue he following equilibrium wages, exensive and inensive margins see oher variables in Appendix Table A2) where is a consan. W = ξφ E 1 µ, N +1 = β f 1 + β φ µ and y = 1 µ, W W N ) ψ 14

15 Given he saving and invesmen behavior of households, he expansion of curren moneary sance booss he number of firms in he nex period. Higher nominal expendiure simulaed by an expansion of moneary sance increases firms discouned expeced operaional profis while enry coss remain unchanged because of wage sickiness. As a resul, he enry of firms which produce wih one period lag is induced. Since he number of firms behaves exacly as a sae variable, he curren producion scale also expands wih an expansion of he curren moneary sance. Hence, here is no business sealing effec following curren demand shocks. In he flexible exchange rae regime, he domesic and foreign money supply are consan for all ime periods so ha he moneary sance is again µ = µ = 2µ and he exchange rae is equal o ε = α /α. Replacing P C by µ = 2µ in he above expressions, we ge W = µ ξφ, N = βφ fξ and y = 1) f β. As in he conemporaneous enry model, he exchange rae perfecly absorbs he effecs of demand shocks on wages and margins so ha he laer remain consan. In he fixed exchange rae regime, he domesic and foreign money supplies are se o mainain a fixed exchange rae ε = 1. Moneary sances are procyclical and hen equal o µ = 2µ α and µ = 2µ α. Replacing P C by µ in he above expressions, he wages, he equilibrium exensive and inensive margins are compued as follows: W = 2µ ξφa, N +1 = β α fξ A and y = 1) f β As before, wages rise wih he higher variance of he shocks larger A) and lower elasiciy of labor supply larger ψ). α α 1 Conrary o he conemporaneous enry model, boh he exensive and inensive margins here respond o shocks under fixed exchange rae regimes. The fuure exensive margins vary wih curren period shocks due o he procyclical feaure of moneary policy. The inensive margins adap o boh he curren and previous period demand shocks which deermine he curren number of firms. We can now compare welfare under he wo regimes. Welfare differences sem from boh exensive and inensive margins. Hence, using 13), he fixed exchange rae regime supporing condiion is given by E α E ln α α 1 + covα, ln α α 1 ) + [ E α E ln α 1 1 A + covα, ln α ] 1 A ) >. The firs erm reflecs he impac of he mean and variance of inensive margins. Since demand shocks are i.i.d., his erm is nil. In expecaion, he mean and variance effec of curren demand shocks is cancelled ou by he mean and variance effec of exensive margins a he same period. The second erm measures he congruence of presen preferences and presen supply of each domesic produc. Wih i.i.d. shocks, his erm simplifies o cov,α, ln α ) >, which reflecs he benefi of a congruence beween preferences and supplies of each produc under fixed exchange rae regimes. The las square bracke 15

16 expresses he same rade-off in he cos and benefi of exensive margins. The firs erm is he mean and variance effec of exensive margins, negaive under fixed exchange rae regimes. This cos can be, however, compensaed by a higher labor supply elasiciy larger ψ 1 ) hrough A. Since demand shocks are i.i.d., he second erm in he bracke is nil. Pas movemens in firm enry and exi, hence he resuling flucuaions in produc diversiy, canno be relaed o presen preferences and do no bring any congruence benefi. The above condiion simplifies o covα, ln α ) + 1 E α E ln α 1 A > 15) which decreases in A and herefore in ψ lower labor supply elasiciy). By he same argumen as for Proposiion 1, he expression 15) acceps a unique roo ψ 1. Since expression 15) is smaller han 14) by he erm covα, ln α )/ 1) and increases in, his roo ψ 1 is smaller han ψ and ha increases wih larger. Proposiion 2 In he lagged enry model here exiss a labor elasiciy hreshold ψ 1 1 such ha a fixed exchange rae sysem is preferred for ψ 1 > ψ1 1. The labor elasiciy hreshold ψ 1 1 is larger han ψ 1 and falls as rises. In his proposiion, he fixed exchange rae sysem is less likely suppored for a given value of labor elasiciy if consumers express a higher love for produc diversiy higher 1/ 1)). While he ideal composiion of inensive margins can be achieved under fixed exchange rae regimes, he cos arising from he lower mean level and higher variabiliy of exensive margins has a larger impac on heir welfare when households aach a higher imporance o produc diversiy. The above poin is summarized in Figure 1. When he value on he verical axis exceeds he uniy, a flexible sysem is suppored. In he figure, he case where = coincides o he welfare ranking obained wih a conemporaneous enry economy and discussed in Devereux 24). 6 Conclusion This paper sudies how he choice of fixed or flexible exchange rae regimes is affeced by he exisence of inensive and exensive margins. When here is no consumpion smoohing hough he fuure number of produc varieies, inensive margins do no change following he shock and only exensive margins vary under fixed regimes. In such a case, he choice resuls from he balance beween he lower average number of produc varieies and higher volailiy in exensive margins and heir sronger congruence wih preferences. Fixed exchange rae regimes are preferred for high enough labor supply elasiciies. In conras,when enry is lagged as a resul of households consumpion smoohing by lending/supplying heir funds o firms in addiion o money savings, boh inensive and exensive margins vary under fixed 16

17 = =12 =6 = Figure 1: Welfare comparison beween fixed and flexible exchange rae sysem wih differen values of he elasiciy of labor supply ψ 1 and subsiuion. 17

18 regimes. In such a case, exensive margins have a negaive conribuion o welfare hrough heir lower average and higher volailiy while he congruence beween preference and inensive margins brings a posiive conribuion o welfare. In such a general seing, fixed exchange rae regimes are less likely o be suppored for a larger se of parameers when produc varieies are less alike and consumers express a higher preference for produc variey. References [1] Baldwin, R.E., Nino, V.D., 26. Euros and Zeros: The Common Currency Effec on Trade in New Goods. NBER Working Papers Naional Bureau of Economic Research, Inc.17 [2] Bergin, P., Lin, C.Y., 21. The Dynamic Effecs of Currency Union on Trade. NBER Working Papers Naional Bureau of Economic Research, Inc. [3] Bergin, P.R., Corsei, G., 28. The exensive margin and moneary policy. Journal of Moneary Economics 55, [4] Bilbiie, F.O., Fujiwara, I., Ghironi, F., 211. Opimal Moneary Policy wih Endogenous Enry and Produc Variey. NBER Working Papers Naional Bureau of Economic Research, Inc. [5] Bilbiie, F., Ghironi, F., Meliz, M., 27. Moneary policy and business cycles wih endogenous enry and produc variey, in: NBER Macroeconomics Annual 27, Volume 22. Naional Bureau of Economic Research, Inc. NBER Chapers, pp [6] Ching, S., Devereux, M.B., 23. Mundell revisied: a simple approach o he coss and benefis of a single currency area. Review of Inernaional Economics 11, [7] Corsei, G., Dedola, L., Leduc, S., 21a. Demand Imbalances, Excange Raes Misalignmen and Moneary Policy. Technical Repor. mimeo. [8] Corsei, G., Dedola, L., Leduc, S., 21b. Opimal moneary policy in open economies, in: Friedman, B.M., Woodford, M. Eds.), Handbook of Moneary Economics. Elsevier. volume 3 of Handbook of Moneary Economics. chaper 16, pp [9] Corsei, G., Peseni, P., 25. Inernaional dimensions of opimal moneary policy. Journal of Moneary Economics 52, [1] Corsei, G., Peseni, P., 29. The simple geomery of ransmission and sabilizaion in closed and open economies, [11] Devereux, M.B., 24. Should he exchange rae be a shock absorber? Journal of Inernaional Economics 62,

19 [12] Dixi, A.K., Sigliz, J.E., Monopolisic compeiion and opimum produc diversiy. American Economic Review 67, [13] Friedman, M., The Case for Flexible Exchange Raes. Chicago Universiy Press, Chicago. [14] Ghironi, F., Meliz, M.J., 25. Inernaional rade and macroeconomic dynamics wih heerogeneous firms. The Quarerly Journal of Economics 12, [15] Hamano, M., 29a. The consumpion-real exchange rae anomaly wih exensive margin. Mimeo Universiy of Rennes1. [16] Hamano, M., 29b. Inernaional equiy and bond posiions in a DSGE model wih endogenous variey risk in consumpion. Mimeo Universiy of Rennes1. [17] Krugman, P., 198. Scale economies, produc differeniaion, and he paern of rade. American Economic Review 7, [18] Krugman, P., Increasing reurns and economic geography. Journal of Poliical Economy 99, [19] Lewis, V., 29. Opimal moneary policy and firm enry. Research series Naional Bank of Belgium. [2] Meliz, M.J., 23. The impac of rade on inra-indusry reallocaions and aggregae indusry produciviy. Economerica 71, [21] Naknoi, K., 28a. The Benefi of Exchange Rae Flexibiliy, Trade Openness and Exensive Margin. Purdue Universiy Economics Working Papers Purdue Universiy, Deparmen of Economics. [22] Naknoi, K., 28b. Real exchange rae.ucuaions, endogenous radabiliy and exchange rae regimes. Journal of Moneary Economics 55, [23] Obsfeld, M., Rogoff, K., Exchange rae dynamics redux. Journal of Poliical Economy 13, [24] Picard, P.M., Worrall, T., 29. Currency Unions and Inernaional Assisance. CREA Discussion Paper Series 9-1. Cener for Research in Economic Analysis, Universiy of Luxembourg. 19

20 Appendix A: Opimal choice of households The problem can be saed in erms of he following opimizaion of he Lagrangian funcion L i): E = β {U + λ i)[w i)l i) + s m i, ω) d ω) dω + M 1 i) ω X P C i) s i, ω) q ω) dω M ]} ω X +m wih respec o {x i, ω), z j, ν), M i), s i, ω), w i)} = where λ i) denoes he Lagrangian muliplier associaed wih he flow budge consrain a ime. Noe ha P C i) = ω X p ω) x i, ω)dω + υ Z p υ) z i, υ)dυ. The firs order condiion wih respec o C i) yields 1 C i) λ i)p = 16) So, λ i) represens he marginal uiliy semming from one addiional uni of nominal wealh. The above expression is idenical for boh models wih m =, 1. The firs order condiion wih respec o M i) yields The firs order condiion wih respec o s i, ω) gives χ M i) λ i) + βe λ +1 i) = 17) λ i)q ω) + βe d +1 ω) λ +1 i) = The marginal uiliy of nominal wealh a is equal o he discouned marginal uiliy a + 1. This condiion is redundan when m =. The household also ses he fuure wage w +1 i) a knowing he demand funcion for her labor service l +1 i). The firs order condiion wih respec o w +1 i) yields κθ E l +1 i) w +1 i) θ 1) E [λ +1 i)l +1 i)] = Accordingly, he expeced disuiliy of a marginal work effor is equal o he expeced consumpion uiliy of he associaed marginal wage increase. We can summarize he soluions for he conemporenous and lagged enry models m =, 1 for any exchange rae in he following ables: 2

21 Home variables Foreign variables C = α Φ N 1+ 1)1 α 1 ) y Φ N )α l = µ W N = 1 y = 1 p = d = 1 ) α y α 1 α α C = 1 α ) Φ ε = 1 α α l = µ W µ W f N = 1 µ W N = 1) f y = 1 µ µ µ W f µ W N 1 W p = 1 W µ N q = W f W = ξ E 1 µ d = 1 µ N q = W f = ξ W E 1 µ µ = P C µ = P C Table A1: Soluion in conemporenous enry model m = ) = 1) f Home variables Foreign variables C = α Φ N 1+ 1)1 α 1 ) y Φ N )α l = N = β 1+β y = 1 p = d = 1 1 α α C = 1 α ) Φ µ α µ 1+β ε = 1 α ) α y α ) µ W l = µ 1 W 1f N = β µ W N y = 1 µ 1 W 1 f µ W N 1 W p = 1 W µ N q = W f W = ξφ E 1 µ d = 1 µ N q = W f = ξφ µ = P C µ = P C Table A2: Soluion in lagged enry model m = 1) W ) µ W E 1 µ 21