Banco de Portugal, Universidade Catolica Portuguesa, Federal Reserve Bank of Chicago and CEPR.

Transcription

1 On te Relevance of Excange Rate Regimes for Stabilization Policy Bernardino Adao, Isabel Correia, and Pedro Teles Banco de Portugal Banco de Portugal, Universidade Catolica Portuguesa and CEPR; Banco de Portugal, Universidade Catolica Portuguesa, Federal Reserve Bank of Cicago and CEPR.

2 ABSTRACT In tis paper, we analyze an economy wit eterogeneous countries wit immobile labor, nominal rigidities and incomplete international assets markets. We sow tat tere are no costs of fixed excange rates, if fiscal policy is used for stabilization. Te result olds independently of te price stickiness. Te assumption of lack of labor mobility is crucial, instead. If labor was mobile across countries, tere would be costs of a monetary union. PRELIMINARY AND INCOMPLETE.

3 I. Introduction Tis paper revisits te issues in te optimal currency area literature, as in Mundell (1961) and a more recent literature on te optimal coice of an excange rate regime. Te issues tat are particularly relevant in te open economy include te asymmetry in socks and te reaction to tese, te lack of mobility of factors, te incompleteness of markets, and te implications of tese conditions for te coice of a monetary regime. Inteliteraturebecauseofsomeformofnominal rigidity, monetary policy as a sort run, stabilization, role, in response to socks tat differ across countries, or tat ave differing effects, because of differences in te extent or type of te nominal rigidity. Because of tis eterogeneity it is common to infer tat tere are costs of coordinated monetary policies, eiter troug a fixed excange rate regime or a monetary union. Tese costs are iger te stronger are te asymmetries, te more severe are te nominal rigidities, te furter is te incompleteness of international asset markets; te less mobile labor is, and, finally, te less able is fiscal policy in effectively stabilizing te national economies (Corsetti, 2005). We sow tat wen bot fiscal and monetary policies are considered jointly wit te same flexibility in response to socks, te loss of te country specific monetary tool is of no cost. Tis is true irrespective of te asymmetry in socks or response to tese and te severity of te nominal rigidities. Te elements tat are crucial in assessing te costs of a single monetary policy are te two last ones in te list by Corsetti, above, but labor mobility works in te opposite way to te conventional wisdom. Fiscal and monetary policy are able to eliminate te costs of a monetary union only if labor is not mobile. We consider a standard cas in advance model were firms may be restricted in te setting of prices. Eac country specializes in te production of an internationally tradeable good wit labor

4 only tat is not mobile across countries. Te consideration of nontradeable goods would not cange te results. Tax instruments are standard state-contingent labor income and consumption taxes. Tere is state-contingent private debt inside eac country in zero net supply and noncontingent nominal public debt in eac currency tat can be traded internationally. Related literature reassesses Milton Friedman s case for excange rate flexibility, as a way of side-stepping te rigidity in relative price movements. Recent examples in te debate are, for instance, Devereux and Engel (2003) and Duarte and Obstfeld (2004). 1 Devereux and Engle (2003) provide an example wit local currency pricing were excange rate flexibility is useless. Duarte and Obstfeld (2004) respond, sowing tat excange rate flexibility, can still be of use in a more complex environment, wit non tradeable goods. Even if excange rate movements cannot affect te relative prices of goods, because of sticky prices and pricing to market, tey can still affect te allocations and improve welfare. Because te optimal regime depends on te degree of excange rate pass-troug, it is important to relax te exogeneity of tat degree. Corsetti and Pesenti (2002) do tis and sow tat tere are two self validating regimes, one wit fixed and anoter wit flexible excange rates. Te flexible excange rate regime obviously provides iger welfare. We add to tis debate by sowing tat te claims inge on te focus on monetary policy only. 2 Once te coice of te excange rate regime is considered in te context of te full coice of policy instruments including tax and debt policy, excange rate flexibility can be replaced wit a gain by fiscal instruments. In particular it is possible to implement te set of allocations under flexible prices wit a fixed excange rate. Cooper and Kempf (2004) make a similar point in a very different context. Tey explicitly model te Mundellian trade-off between te benefits of a monetary union in reducing transaction costs and te costs of te union in te ability to stabilize. Stabilization in teir set up are risk 2

5 saring transfers between agents. If te government is able to stabilize using alternative fiscal instruments, ten tere are no costs of a monetary union. In te same direction, but unable to establis te irrelevance result for te lack of fiscal instruments are papers suc as Gali and Monacelli (2005) and Ferrero (2005). In Gali and Monacelli (2005) te government cooses te optimal level of public consumption in a monetary union wit lump-sum taxes. Ferrero (2005) considers tat lump-sum taxes are not available. Te monetary policy instrument is te interest rate and te fiscal policy consists in coosing state-noncontingent public debt and state-contingent taxes on output by firms. In bot papers it is establised tat tecoiceoffiscal policy elps attaining iger welfare. Te major difference between our set up and te one of Ferrero (2005) is tat we consider not only state-contingent labor income taxes but also consumption taxes. Te idea tat te ability to use fiscal policy for stabilization purposes is essential in assessing te costs of te a single monetary policy is a common old idea, present in te papers just mentioned. We take tis to te extreme, by establising te irrelevance of te regime, once fiscal policy is taken into account. Te assumption of state-contingency of taxes does not ave an obvious parallel in te present institutional arrangements, owever it is a fair assumption wen te object of te analysis is te optimal design of institutions. If tere are fundamental reasons for taxes not to be state contingent, tose reasons probably also affect te coice of monetary policy, and yet te assumption of state-contingent monetary policy is te standard one. Te assumption of state-contingent fiscal policy is also te common one in tis literature on optimal fiscal and monetary policy in closed economies. Oter related literature is on optimal fiscal and monetary policy in small open economies. 3

6 Nicolini and Hevia (2004) consider a small open economy wit flexible excange rates and statecontingent assets. Prices are set in advance. In tat set up te second best, flexible price equilibrium is implementable, but excange rates must move across states. Benigno and Paoli (2004) is oter related work. Te paper proceeds as follows. In Section 2 we present te model. In Section 3, we sow tat te set of implementable allocations in a flexible world were bot prices and excange rates are flexible can be implemented wit constant producer price levels and fixed excange rates. Te result follows tat neiter sticky prices nor te excange rate regime restrict te set of allocations. Section 4 addresses te issue of labor mobility sowing tat wit labor mobility te results are not acieved. Section 5 contains concluding remarks. A. Te Model Te economy as two countries of equal size, te ome country and te foreign country. Tere is for eac of te countries a representative ouseold, a continuum of firms and a government. Eac firm produces a distinct, perisable consumption good. In eac period t =0, 1,..., te economy experiences one of finitely many events s t. Te initial realization s 0 is given. Te set of all possible events in period t is denoted by S t, te istory of tese events up and including to period t, wic we call state at t, (s 0,s 1,...,s t ), is denoted by s t, and te set of all possible states in period t is denoted by S t. Te number of all possible events in period t is #S t and te number of all possible states in period t is #S t. All te relevant variables for tis world economy are a function of te state, s t, but to simplify te notation we do not index formally te variables to te state. Tere are markets for goods, labor, money, state contingent debt and non-state contingent debt. Te labor market is segmented across countries. Te state-contingent debt market 4

7 is segmented across countries and across ouseolds and governments. Te goods and te statenoncontingent debt are tradable across countries and agents. Prices are flexible in all markets. B. Te ouseolds Te preferences of te ome ouseolds are described by te expected utility function: X U = E t β t u (C t,l t ) t=0 wit C t = Cγ,t C1 γ f,t γ γ (1 γ) 1 γ were C,t is te composite consumption of te goods produced at ome and C f,t is te composite consumption of te goods produced in te foreign country. L t is leisure time and is equal to 1 N t, were N t is labor time. Tere is a continuum of goods in te interval [0,1] produced at ome and indexed by i. Tus C,t is defined as Z 1 C,t = 0 C,t (i) θ 1 θ di θ θ 1,θ >1, were C,t (i) is te consumption level of good i, and θ is te elasticity of substitution between any two goods. C f,t is defined similarly, Z 1 C f,t = 0 C f,t (j) θ 1 θ dj θ θ 1,θ >1. Te preferences of te foreign ouseolds are described by an identical expected utility function: X U = E t β t u (Ct,L t ), t=0 5

8 wit Ct = Cγ,t C1 γ f,t γ γ (1 γ) 1 γ were C,t is te foreign ouseolds composite consumption of te goods produced at te ome country and C f,t is te foreign ouseolds composite consumption of te goods produced in te foreign country. We adopt te Lucas timing, in eac period te assets markets open firstandclosebeforete goods markets open. Te representative ouseold of te ome country at te beginning of eac period uses te wealt W t to buy M t (ome money), B,t (ome government noncontingent debt), B f,t (foreign government noncontingent debt) and Z t+1 (ome private contingent debt). Te ome government noncontingent debt pays gross return R t in te domestic currency and te foreign government noncontingent debt pays gross return Rt in te foreign currency. Te normalized priceatdatet of one unit of domestic currency at a particular state at date t +1is z t+1,t. Tere is no government contingent debt and te ome ouseold cannot buy foreign money or foreign contingent debt. Te excange rate between te two currencies is ε t. Tus, te restriction on te assets markets for te ome ouseold is M t + B,t + ε t B f,t + E t Z t+1 z t+1,t W t. (1) and te equivalent restriction for te foreign ouseold is M t + B,t ε t + B f,t + E tz t+1z t+1,t W t. At te ome country tere are taxes on te consumption of ome produced goods, τ,t,onte consumption of foreign produced goods, τ f,t, labor income τ n,t and profits. As te tax on profits is a lump-sum tax it is optimal tat all profits will be taxed away, so tat te net profit iszero. 6

9 Te revenue generated by tis tax is used to subsidize labor in production and it is just enoug to neutralize te mark-up distortion in production. Tere are similar taxes on te foreign country. At te goods markets te ome ouseold faces a cas in advance constraint (1 + τ,t )P,t C,t +(1+τ f,t )ε t P f,t C f,t M t, (2) and te foreign ouseold faces a similar constraint (1 + τ,t )P,t ε t C,t +(1+τ f,t )P f,t C f,t M t. (3) Te wealt ome ouseolds bring to date t +1is W t+1 = M t + B,t R t + ε t+1 B f,t R t + Z t+1 + (1 τ n,t )W t N t (1 + τ,t )P,t C,t (1 + τ f,t )ε t P f,t C f,t. (4) Using (1) and (4) can write te ome ouseold budget constraint more compactly as M t+1 + B,t+1 + ε t+1 B f,t+1 + E t+1 Z t+2 z t+2,t+1 M t + B,t R t + ε t+1 B f,t R t + Z t+1 +(1 τ n,t )W t N t (1 + τ,t )P,t C,t (1 + τ f,t )ε t P f,t C f,t,,alls t, t 0 7

10 Te intertemporal budget constraints for period t for te ome ouseold can be written as X E tq t,t+s+1 (1 + τ,t+s )P,t+s C,t+s +(1+τ f,t+s )ε t+s P s=0 f,t+s C f,t+s (1 τ n,t+s )W t+s N t+s + X µ E Qt,t+s tq t,t+s+1 M t+s 1 W t,alls t, t 0, s=0 Q t,t+s+1 were Q t,t+s β t+s P,t (1+τ,t ) P,t+s (1+τ,t+s ) E t Q t,t +1 W t+1 0. (t+s) (t),t 0, using te no-ponzi games condition lim T Among te first order conditions for te ome and foreign ouseolds are te intertemporal conditions, (t 1) P,t 1 (1 + τ,t 1 ) = βr t 1E t 1 ε t 1 (t 1) P,t 1 (1 + τ,t 1 ) = βr t 1E t 1 (t) P,t (1 + τ,t ) ε t (t) P,t (1 + τ,t ),alls t, t 1, (5),alls t, t 1, (6) " # (t 1) P,t 1 (1 + τ,t 1 ) = βr (t) t 1E t 1 P,t (1 + τ,t ),alls t, t 1, (7) " ε t 1 (t 1) εt P,t 1 (1 + τ,t 1 ) = βr t 1E (t) # t 1 P,t (1 + τ,t ),alls t, t 1, (8) te intratemporal conditions, u L (t) (t) = W t(1 τ n,t ) P,t R t (1 + τ,t ),allst, t 0 (9) (t) f (t) = (1 + τ,t)p,t (1 + τ f,t )ε t Pf,t,alls t, t 0 (10) u L t (t) f (t) = W t (1 τ n,t) P f,t R t (1 + τ f,t ),allst, t 0 (11) (t) f (t) = (1 + τ,t )P,t (1 + τ f,t )ε tpf,t,alls t, t 0 (12) 8

11 Using tese first order conditions, as well as te cas in advance constraints, in te intertemporal budget constraints satisfied wit equality, we get te period t implementability conditions for te ome country X s=0 βs E t uc (t + s) C,t+s + f (t + s) C f,t+s u L (t + s) N t+s = Wt (t) P,t (1 + τ,t ),allst, t 0 and for te foreign country, (13) i s=0 βs E t ³ (t + s) C,t+s + f (t + s) C f,t+s u L (t + s) N u t+s = W C f (t) t Pf,t (1 + τ, t 0 f,t ),allst X (14) C. Te government Te government of eac country includes bot te fiscal autority and te monetary autority. Te ome government issues non state-contingent debt, B,t +B,t, and money, M t s, makes expenditures in te ome consumption good G t, and taxes labor income and private consumption. Te nominal financial responsibilities of te ome government at te start of period t are W g t, wic can be financed by issuing money and public debt M s t + B,t + B,t = Wg t. Te nominal financial responsibilities te ome government brings to te next period are W g t+1 = M s t + R t B,t + R t B,t + P,tG t τ,t P,t C,t τ f,t ε t P f,t C f,t τ n,t W t N t 9

12 We are assuming tat te government taxes all profits of domestic firms and gives te proceeds as a subsidy to production of tose firms. Tese two conditions can be written as M s 0 + B,0 + B,0 = Wg 0 and M s t+1 + B,t+1 + B,t+1 = M s t + R t B,t + R t B,t + P,tG t τ,t P,t C,t τ f,t ε t P f,t C f,t τ n,t W t N t,alls t, t 0. Te ome government period t intertemporal budget constraint is X E tq t,t+s+1 τ,t+s P,t+s C,t+s + τ f,t+s ε t+s P s=0 f,t+s C f,t+s + τ n,t+s W t+s N t+s P,t+s G t+s + X E tm s s=0 t+s (Q t,t+s Q t,t+s+1 )=W g t,allst, t 0. Tere is a similar condition for te foreign country. Te intertemporal budget constraint of te ome country can be obtained by adding up te ome government budget constraint and te ome representative ouseold budget constraint, s=0e t Q t,t+s+1 P,t+s (C,t+s + G t+s )+ε t+s P f,t+s C f,t+s W t+s N t+s = W e t,alls t, t 0, (15) were W e t = W t W g t, are te foreign assets owned by te ome country. 10

13 D. Firms In eac country tere is a continuum of firms in te unit interval. Eac firm produces a distinct, perisable consumption good wit a tecnology tat depends on labor only. Eac ome firm i as te production tecnology Y,t (i) A t N t (i), all s t, t 0, were Y,t (i) is te production of good i, N t (i) is te labor used in te production of good i, and A t is an aggregate tecnology sock in te ome country. Good i can be used for private and public consumption, Y,t (i) =C,t (i)+c,t (i)+g t (i). Tesameistruefortegoodsproducedinte foreigncountry. Eacgoodj produced in te foreign country can be consumed by ouseolds or by te foreign government, Y f,t (j) =C f,t (j) +Cf,t (j) +G t (j). Given price flexibility and tat tere is a labor subsidy, te first order conditions of profit maximization for ome firms are W t P,t = A t,t 0, (16) and for foreign firms are W t P f,t = A t,t 0. (17) E. Equilibrium C,t,C f,t,n t,p,t,w t,r t,τ,t,τ f,t,τ n,t, A flexible-price equilibrium is a vector M S t,m t,b,t,b f,t,b t,z t+1,z t+1,t,ε t C,t,C f,t,n t,p f,t,w t,r t,τ,t,τ f,t,τ n,t, suc tat, Mt S,Mt,B,t,B f,t,b t,zt+1,z t+1,t (a) Given te initial wealt levels, prices and policy te ouseolds coose te relevant quantities tat solve teir problems; 11

14 (b) Firms given prices and policy coose te relevant quantities tat solve teir problems; (c) For initial public debts te governments satisfy teir budget constraints; (d) Te markets are in equilibrium: C,t + C,t + G t = A t N t (18) C f,t + C f,t + G t = A t N t (19) M S t = M t (20) M S t = M t (21) Z t+1 =0 (22) Z t+1 =0 (23) Te equilibrium in te labor and non-contingent bond markets was already imposed. Te next proposition establises tat any flexible price equilibrium allocation can be implemented wit constant prices, constant excange rates and a nominal interest rate common across countries. Proposition 1. Any flexible equilibrium allocation can be implemented wit P,t = P,0, P f,t = P f,0,ε t = ε 0 and R t = R t. Proof: We assume tat te infinite orizon economy is te limit of a sequence of finiteorizon economies, and prove for te finite orizon economy. Witout loss of generality we take t =0, 1. In te beginning of period t =2te asset market opens to liquidate debts. Tis means 12

15 tat te wealt of all agents in period t =2is zero. Te proof involves counting equations and n o unknowns. We take as given an equilibrium allocation C,t,C f,t,n t,c,t,c f,t,n t under flexible prices and excange rates. We sow tat tere are constant prices wit P,t = P,0,P f,t = P f,0, and a fixed excange rate regime wit ε t = ε 0 and R t = R t and a policy tat satisfies te equilibrium equations for tat allocation wic are: (2), (3), and (5)-(23). First, tis allocation satisfies trivially te two feasibility constraints, as it is an equilibrium allocation. For given P,0,P f,0,ε 0 we use te remaining equilibrium conditions to determine te values for te policy vector and remaining prices. Te firms conditions determine W t and W t W t P,0 = A t,t=0, 1 W t P f,0 = A t,t=0, 1. Te period 0 intertemporal budget constraints for te two representative ouseolds are X 1 j=0 βj E 0 uc (j) C,j + f (j) C f,j u L (j) N j = W0 (0) P,0 (1 + τ,0 ) and X 1 i j=0 βj E 0 ³ (j) C,j + f (j) C f,j u L (j) N j = W 0 (0) P,0 ε 0 (1 + τ,0 ) wic are satisfied by appropriately coosing τ,0 and τ,0. Given a common process for te nominal interest rate R t = R t (24) 13

16 to be determined later, and τ,0 and τ,0, can use te following equations (0) (1 + τ,0 ) = βr (1) 0E 0 (1 + τ,1 ) (25) (0) (1 + τ,0 ) = βr 0E 0 (1) (1 + τ,1 ) (26) (1) C,1 + f (1) C f,1 u L (1) N 1 = W 1 (1) P,1 (1 + τ,1 ),s1 S 1 W 2 =0, all s 1 (1) (1) C,1 + f (1) C f,1 u L (1) N 1 = W 1 P,1 (1+τ,1 ),s1 S 1 (27) W 2 =0,s 1 S 1 to determine τ,1, τ,1, W 1 and W 1. Can use te intratemporal conditions u L (t) (t) = W t(1 τ n,t ) P,0 R t (1 + τ,t ),t=0, 1 (t) f (t) = (1 + τ,t)p,0 (1 + τ f,t )ε 0 Pf,0,t=0, 1 u L t (t) f (t) = W t (1 τ n,t) P f,0 R t(1 + τ f,t ),t=0, 1 (t) f (t) = (1 + τ,t )P,0 (1 + τ f,t )ε 0Pf,0,t=0, 1 to determine τ n,t, τ f,t, τ n,t, τ f,t,fort =0, 1. 14

17 Canusetecasinadvanceconstraints (1 + τ,t )P,0 C,t +(1+τ f,t )ε 0 P f,0 C f,t = M t,t=0, 1 (1 + τ,t )P,0 ε 0 C,t +(1+τ f,t )P f,0 C f,t = M t,t=0, 1 to determine M t and M t,fort =0, 1. Can use te ome country intertemporal budget constraints to determine te nominal interest rates R t. Te budget constraints for period t =1are W e 1 = 1 R 1 P,0 (C,1 + G 1 )+ε 0 P f,0 C f,1 W 1 N 1,s 1 S 1 wic give #S 1 interest rates R 1 as a function of te value for W e 1. Given tese values for R 1 te budget constraint for period t =0, W e 0 = 1 R 0 P,0 (C,0 + G 0 )+ε 0 P f,0 C f,0 W 0 N 0 + E 0 Q 0,1 R 1 P,0 (C,1 + G 1 )+ε 0 P f,0 C f,1 W 1 N 1. determines uniquely R 0. Two observations: Notice tat we can support te allocation wit a constant price for any good and a common interest rate wic is a function of te level of te net foreign assets of te ome country in period t =1. Tis, for te case of t =0, 1, gives one degree of freedom for W e 1. Also tere is a degree of freedom in te coice of ε 0. Tis proof olds for any finite orizon economy, t =0,...,T, witt arbitrarily large. Tis means tat te flexible price allocation can be supported by constant prices and constant excange rates and tere is one degree of freedom for ε 0 and #S t 1 15

18 degrees of freedom for W e t for every t =1,...,T. Te discussion of te costs of te excange rate system is interesting only if tere is some type of nominal friction. Te model considered until now as full flexibility of prices and excange rates. We now assume tat prices are sticky in some or in all goods produced. It would appear tat price stickiness, because it introduces restrictions on te setting of prices, would prevent from acieving te allocations in a flexible price equilibrium. However, tose restrictions also give more power to monetary policy. We sow tat tere are fiscal policies and a common monetary policy for te different economies tat can acieve any flexible price equilibrium allocation even wen tere are nominal frictions tat can be different across countries. Tese policies are te ones tat implement te equilibria wit constant prices in te proposition above. Calvo (1983) staggered price setting is a commonly used assumption in te sticky price literature. Every period only a sare of firms is able to optimally set its price. We assume tat te firms set prices in te currency of teir country. We could alternatively ave assumed local currency pricing, but in tat case, te environment would ave to include segmentation of te goods markets. Given te result tat it is possible to implement te allocations under flexible prices wit constant prices and excange rates, te effects of goods market segmentation can also be eliminated. Te sare of firms tat can coose optimally te price can be different across economies. In general tis leads to inefficient differences in prices across firms. Given tat firms in te same country ave te same linear tecnology ten te relative price of te goods tey produce will not be equal to one. Te only case in wic tis will not occur is wen te firmstatavete opportunity of coosing a new price decide to maintain teir price. Te price setting restrictions in tis case will not be binding, te producer price level in eac country will be constant and equal to 16

19 an istorical producer price level. Proposition 1 states tat tere are tax rates, money and interest rates suc tat equilibrium prices can be constant over time and te allocations are te ones in te flexible price economy. Te same reasoning can be applied to any oter form of price stickiness; for instance, to te case were prices are set in advance, wic is anoter frequently used type of price stickiness. Specifically te initial prices P,0 and Pf,0 are exogenously given and te oter period prices P,t and Pf,t may be set in advance for T periods, for a finite T. Again Proposition 1 states tat adding tose restrictions to te flexible price economy does not cange te equilibrium allocation as long as te policy is adjusted conveniently. We ave establised tat under sticky prices it is possible to implement te set of allocations under flexible prices wit constant excange rates. Tis set dominates in terms of welfare te set of allocations under sticky prices. Since agents are eterogeneous, te meaning of welfare dominance is te usual one of a potential Pareto movement were lump sum transfers between agents are implicitly assumed. Tis analysis is in te appendix. A floating excange rate system gives eac country autonomy over its monetary policy. Under a floating excange rate system, monetary policies in eac country can freely respond to te state of te world. However, in a monetary union tere is a unique monetary policy for te members of te union. Tus, tere is a loss of instruments of policy, te excange rate must be constant over time and te nominal interest rate must be equal across countries. Is te loss of tese policy instruments a restriction to acieve te equilibrium allocations of te floating excange rate regime? Proposition 1 provides an answer to tis question. Te discussion above is summarized in te following Corollary. 17

20 Corollary 1. In a world economy wit noncontingent bond markets te excange rate system is irrelevant in implementing te set of allocations under flexible prices, independently of te degree and type of price rigidity. In te particular case of a monetary union in wic te monetary autority cooses te same interest rate for all te members, tere is an aggregate money demand and a distribution of money among countries tat support te equilibrium. Moreover, a common sock in te union does not imply a uniform cange in te distribution of liquidity among te members of te union. II. Labor mobility In te literature of optimal currency areas te lack of labor mobility as been seen as te main cost of a monetary union. A result of tis paper is tat te opposite is true. Labor immobility is a necessary condition for te irrelevance of te excange system wit price rigidity. Full labor mobility implies one additional constraint per state to te equilibrium. Te wage net of taxes must be equal across countries. Te degrees of freedom tat were not used in Proposition 1 to implement te set of flexible price allocations are not enoug to satisfy tese additional constraints. Tis is stated in te Corollary below. Corollary 2. Wen prices are sticky in a fixed excange rate regime (or monetary union) labor immobility is a necessary condition to implement te set of flexible price equilibrium allocations. Proof: Te relation between net wages is given by te intratemporal conditions 18

21 W t (1 τ n,t )= u L (t) P,0 (1 + τ,t )R t, for all s t (t) Wt (1 τ n,t) = u L (t) P t f,0 (1 + τ f,t f (t) )R t, for all s t. Full labor mobility implies W t (1 τ n,t )=W t (1 τ n,t). (28) Tus, we would ave to ave u L (t) P,0 (t) (1 + τ,t )= u L (t) P t f,0 (1 + τ f,t f (t) ) (29) to verify condition (28). Tere are #S t equations of te type (29) but tere are only #S t 2 degrees of freedom on te coice of τ,t and τ f,t since tese policy variables (from te intertemporal conditions) depend on te values of R t 1, and tere are #S t 2 degrees of freedom in determining tese. Terefore te conditions for labor mobility (28) cannot be satisfied. Notice tat te proposition above says tat for a given degree of price stickiness te adoption of a fixed excange rate system (or a monetary union) does not impose a cost wen labor is immobile. Instead, wit labor mobility a monetary union reduces te set of feasible allocations. Of course, for a given excange rate system te elimination of labor immobility increases, in general, te set of feasible allocations. Concluding remarks: In an environment wit nominal rigidities, watever te type of price setting PCP (producer currency pricing) or LCP (local currency pricing), te excange rate regime, weter flexible or fixed excange rates, is irrelevant once fiscal policy instruments are taken into account. Tis is te 19

22 main result of te paper. We also sow tat, in contrast to te conventional wisdom, in order for te costs of te monetary union to be zero labor cannot be mobile. Te irrelevance result we establis is tat te set of implementable allocations under flexible prices can be implemented under sticky prices wit constant excange rates. It can be sown tat for prices set in advance, and more generally for oter price setting restrictions, tat te full set of allocations under sticky prices can be attained wit constant excange rates. Tose allocations are dominated in te sense tat tey would not allow to attain te utility possibilities frontier, for arbitrary Pareto weigts. Tere is a recent literature on fiscal and monetary policy in te open economy imposing arbitrary restrictions on te fiscal instruments, and terefore unable to obtain te irrelevance results. Tere is an analogous debate in te closed economy (see Correia, Nicolini and Teles (2004), Siu (2004), Scmitt-Groe and Uribe (2004), Benigno and Woodford, 2004). One possible objection to our analysis is tat we do not incorporate informational restrictions in te policy coice and also do not take into account lack of ability to commit. Te assumptions of private information on te part of te government and inability to commit in te presence of a time inconsistency problem may justify policy tat does not respond to contingencies, suc as te inflation cap in te analysis in Atey, Atkeson and Keoe (2005). Since te time inconsistency problem is typically more severe in te coice of monetary policy tan fiscal policy, we conjecture tat in tat more deeply founded environment fiscal policy instruments would be less restricted tan monetary ones. A final remark: We sow tat tere are no costs of a monetary union. However an individual country can be better off inside or outside a union depending on te weigts in te union objective function, as well as te structure of te policy game. 20

23 APPENDIX In tis appendix we sow tat for eac allocation under sticky prices tere is an allocation under flexible prices tat gives at least as ig welfare to one country witout reducing te welfare of te oter country. Assuming tat lump sum transfers were feasible between countries, te set of implementable n o allocations under flexible prices C,t,C f,t,n t,c,t,c f,t,n t as well as initial taxes and excange n o rate τ,0,τ,0,ε 0 would be caracterized by te following conditions: X 1 j=0 βj E 0 uc (j) C,j + f (j) C f,j u L (j) N j = W0 (0) P,0 (1 + τ,0 ) X 1 i j=0 βj E 0 ³ (j) C,j + f (j) C f,j u L (j) N j = W 0 (0) P,0 ε 0 (1 + τ,0 ) C,t + C,t + G t = A t N t (A.1) C f,t + C f,t + G t = A t N t (A.2) We do not impose as a restriction te budget constraint between countries, because we allow for transfers between tese. Te remaining equilibrium conditions determine te policy and prices. Denote te set of allocations tat satisfy tese conditions by E. Given Pareto weigts tere will be an optimal allocation tat can be decentralized wit a coice of initial conditions W e 0. Te Pareto weigts can be cosen to be suc tat te optimal allocation is implemented wit te actual initial W e 0. Under sticky prices te set of equilibrium conditions cannot be summarized by a small set of 21

24 n o te implementability conditions as under flexible prices. Te allocations C,t,C f,t,n t,c,t,c f,t,n t are restricted by X 1 j=0 βj E 0 uc (j) C,j + f (j) C f,j u L (j) N j = W0 (0) P,0 (1 + τ,0 ) X 1 i j=0 βj E 0 ³ (j) C,j + f (j) C f,j u L (j) N j = W 0 (0) P,0 ε 0 (1 + τ,0 ) C,t + C,t + G t Z 1 µ P,t (i) θ di = A t N t (A.3) 0 P,t Cf,t + Cf,t + Z 1 µ Pf,t (i) θ G t di = A t Nt 0 P f,t (A.4) were D R ³ 1 P,t (i) θ 0 P,t di 1 and D = R 1 0 ³ P,t (i) P,t θ di 1, as well as all te remaining equilibrium equations. D =1wen P,t(i) P,t =1and D =1wen P f,t(i) P f,t =1. Let te set of allocations tat satisfy tese restrictions be denoted by E s. Te set of allocations under flexible prices dominates te set under sticky prices, meaning tat for eac allocation in E s tere is at least one allocation in E f wit at least one of te goods in larger or equal quantity and none smaller. Te intertemporal budget constraints are te same but te feasibility conditions are different, being A.3 and A.4 more restrictive tan A.1 and A.2, and tere are additional restrictions over E s tat are absent from E f. Moreover, te restrictions over te allocations under sticky prices are exactly te same only wen P,t (i) =P,0 and P f,t (i) =P f,0. REFERENCES [1] Atey, Susan, Andrew Atkeson and Patrick J. Keoe "Te Optimal Degree of Discretion in Monetary Policy." Econometrica, fortcoming. 22

25 [2] Benigno, Gianluca and Paoli "Fiscal and Monetary Policy in a Small Open Economy". Mimeo, L.S.E. [3] Benigno, Pierpaolo and Micael Woodford Optimal Monetary and Fiscal Policy: A Linear Quadratic Approac. In NBER Macroeconomics Annual, edited by. Cambridge, Mass. :MITPress. [4] Benigno, Pierpaolo Optimal Monetary Policy in a Currency Area". J. Intern. Econ. [5] Calvo, Guillermo Staggered Prices in a Utility-Maximizing Framework. J. Monetary Econ. 12: [6] Cooper, Russell and Hubert Kempf "Overturning Mundell: Fiscal Policy in a Monetary Union". Rev. Econ. Stud. 71, [7] Correia, Isabel, Juan Pablo Nicolini and Pedro Teles Optimal Fiscal and Monetary Policy: Equivalence Results. Fed. Reserve Bank Cicago WP (November). [8] Corsetti, Giancarlo "Monetary Policy in Heterogeneous Currency Unions: Reflections Based on a Micro-Founded Model of Optimum Currency Areas," mimeo, Europ. Univ. Inst. [9] Corsetti, Giancarlo and Pesenti "Endogenous pass-troug and Optimal Monetary Policy: A Model of Self Validating Excange Rate Regimes", mimeo, Europ. Univ. Inst. [10] Devereux and Engel "Monetary Policy in te Open Economy Revisited: Excange Rate Flexibility and Price Setting Beaviour". Rev. Econ. Stud. 70, [11] Duarte, Margarida "Monetary Policy and te Adjustment to Country Specific Socks", mimeo, Fed. Res. Bank of Ricmond. 23

26 [12] Duarte, Margarida and Maurice Obstfeld "Monetary Policy in te Open Economy Revisited: Te Case for Excange Rate Flexibility", fortcoming Rev. Econ. Stud.. [13] Duarte, Margarida and Alexander Wollman (2004) "Fiscal Policy and Regional Inflation in a Currency Union", mimeo, Fed. Res. Bank of Ricmond. [14] Ferrero, Andrea "Fiscal and Monetary Rules for a Currency Union". Mimeo, NYU. [15] Friedman, Milton, Te Case for Flexible Excange Rates" in Essays in Positive Economics, Cicago, Il. Univ. of Cicago Press, [16] Gali, Jordi and Tommaso Monacelli "Optimal Fiscal Policy in a Monetary Union", Rev. Econ. Stud., [17] Helpman, Elanan, 1981, "An Exploration in te Teory of Excange Rate Regimes" Journal of Political Economy 89, [18] Mundell, Robert "A Teory of Optimum Currency Areas." Amer. Econ. Rev. 51, [19] Nicolini, Juan Pablo and Constantino Hevia "Optimal Devaluations", mimeo, Univ. Di Tella. [20] Obstfeld, 2004, "Pricing to market, te Interest Rate and te Excange Rate", mimeo, Univ. Calif. Berkeley. [21] Rotemberg, Julio J Sticky Prices in te United States. J. Economic Policy 90:

27 [22] Scmitt-Groé, Stepanie and Martin Uribe Optimal Fiscal and Monetary Policy under Sticky Prices. J. Econ. Teory 114: [23] Siu, Henry Optimal Fiscal and Monetary Policy wit Sticky Prices. J. Monetary Econ. 51: [24] Taylor, Jon Aggregate Dynamics and Staggered Contracts. J. P. E. 88: NOTES Preliminary. We tank participants at te 2005 SED Meetings in Budapest. We gratefully acknowledge financial support of FCT. 1 See also Obstfeld (2004) and Duarte (2004). 2 On recent work on optimal monetary policy in a currency area see Benigno (2004). 25