Imbalances and Fiscal Policy in a Monetary Union

Transcription

1 Imbalances and Fiscal Policy in a Moneary Union Job marke paper Ida Hjorsø Ocober 2011 Absrac The Eurozone crisis has iniiaed a debae on he imporance of inernaional imbalances for policy making. In his paper, I sudy how inernaional financial fricions lead o inernaional imbalances and affec he opimal conduc of fiscal policy in a wo-counry, wo-good DSGE model of a moneary union. I show ha he presence of inernaional imbalances affecs he opimal conduc of cooperaive fiscal policies when he inernaionally raded goods are complemens: Governmen expendiures opimally play a cross-counry risk sharing role. The cross-counry insurance role of fiscal policy is in conflic wih he domesic sabilizaion role. Tha is, domesic macroeconomic sabilizaion is no sufficien for achieving inernaional macroeconomic sabilizaion. Opimal fiscal policy consis in seing governmen expendiures such as o reduce inernaional imbalances a he expense of higher domesic inefficiencies. I am graeful o Giancarlo Corsei, Russell Cooper, Evi Pappa, and Gianluca Benigno. I would also like o hank Nobuhiro Kiyoaki, Alber Marce, and Meixing Dai for helpful commens. All errors are my responsibiliy only. European Universiy Insiue 1

2 1 Inroducion The inernaional imbalances wihin he European Economic and Moneary Union (EMU), illusraed by large curren accoun imbalances and deb differences across counries, are widely seen as one of he main reasons for he Eurozone crisis. This crisis has poined ou he ensions beween naional and inernaional policy objecives, and has recas he debae over fiscal policy making wihin moneary unions. In he absence of alernaive, poenially more suiable policy insrumens, i could be desirable o use naional fiscal policies o address inernaional imbalances. In his paper, I invesigae wheher i is indeed opimal o use naional governmen spending o conain he inernaional demand imbalances which arise in he presence of inernaional financial fricions in a moneary union. Tha is, I examine he poenial cross-counry insurance role of fiscal policies in a moneary union. Wihin a wo-counry, wo-good model of a moneary union, I show ha he inernaional ransmission of produciviy shocks and governmen spending and he resuling opimal fiscal policy is dependen on he srucure of he inernaional financial markes. Financial fricions are modelled in he spiri of P. Benigno (2001) who analyses he effecs of inernaional financial fricions for opimal moneary policy. 1 Governmen spending, he fiscal policy insrumen, yields uiliy o agens and shifs demand owards he domesically produced good, hereby affecing oupu, inflaion and inernaional imbalances. Under realisic assumpions, I show ha when inernaional financial markes are incomplee and bond yields are deb-elasic - replicaing he recen siuaion wihin he EMU - fiscal policy opimally adjuss such as o reduce inernaional demand imbalances i.e. i acs as a cross-counry insurance ool. Higher consumpion risk sharing is achieved hrough relaive price movemens: changes in governmen spending induce inflaionary pressure by shifing demand and hus affec he real exchange rae and relaive consumpion demand. The relaive imporance of he disorions arising due o inernaionally incomplee markes for he fiscal policy maker is shown o be very sensiive o he rade elasiciy: he lower he rade elasiciy, he more imporan is i for he policy maker o limi inernaional demand imbalances. The rade elasiciy deermines he relaive imporance of he income and subsiuion effecs of price changes. Hence, a change in prices in one counry will eiher improve is curren accoun or deeriorae i dependen on he rade elasiciy. As a resul, he effecs of fiscal policy on inernaional imbalances, achieved hrough price changes, differ according o he rade elasiciy. For fiscal policy o effecively improve risk sharing across counries i mus be able o affec consumpion and he real exchange rae in opposie direcions. Since hese variables are affeced in he same direcion by fiscal policy under subsiuabiliy of he raded goods, decreasing he inernaional demand imbalances requires large and cosly changes in governmen spending. Hence, under high rade elasiciies, he opimal response of governmen expendiures o a produciviy shock consiss in sabilizing he naional economies, no in redressing he cross-counry demand imbalances arising due o inernaional financial fricions. However, under low rade elasiciies, he fiscal policy maker opimally acs such as o reduce hem; since governmen spending leads o changes in consumpion and he real exchange rae which go in opposie direcions, i is possible for he fiscal policy maker o improve risk sharing wihou oo large coss in erms of deviaions from he opimal spending composiion. Tha is, when he inernaionally raded goods are complemens, he fiscal policy maker opimally ses policy such as o avoid large deviaions from full consumpion risk sharing across counries: governmen expendiures play he role of a cross-counry insurance ool. Ineresingly, wihin a moneary union where he raded goods are complemens, i is opimal o reduce cross-counry imbalances a he expense of larger naional inefficiencies, indicaing ha he bes oucome for he union as a whole consiss in sabilizing union- 1 Noe ha on he conrary o P. Benigno (2001), I assume ha he financial fricions are symmeric across counries, and ha home bias in consumpion may be presen, leading o deviaions from PPP. 2

3 wide imbalances a he expense of naional imbalances. To my knowledge, he consequences for fiscal policy of cross-counry imbalances resuling from inernaional financial fricions has no been addressed in he lieraure. The New Open Economy Macroeconomic (NOEM) lieraure, iniiaed by Obsfeld and Rogoff (1995), has invesigaed he relaion beween inernaional financial fricions and he inernaional ransmission of governmen spending shocks. Suherland (1996) is he firs o consider he effecs of inernaional financial fricions on he ransmission of fiscal policy wihin a NOEM framework. He invesigaes he effecs of inernaional porfolio adjusmen coss for he ransmission of governmen spending shocks in a wo-counry model wih flexible exchange raes. Pierdzioch (2004) and Koenig and Zeyneloglu (2010) carry ou similar exercises wihin a currency union. These analyses focus on he inernaional ransmission of fiscal policy. However, incomplee financial markes across counries do no only affec he ransmission of shocks and policies bu also creae inefficiencies. These inefficiencies poenially affec welfare, and migh hus have imporan implicaions for opimal policy - also fiscal policy. Some recen conribuions o he inernaional lieraure, such as Obsfeld and Rogoff (2002), P. Benigno (2009), or Corsei e al. (2011) consider he effecs of inernaionally incomplee markes for opimal moneary policy. However, hese auhors leave aside he analysis of he moneary and fiscal ineracion, of he rade-off faced by he fiscal policy maker, and of he consequences for opimal fiscal policy, issues ha I address here. Wihin a moneary union where counries migh be hi by asymmeric shocks, he implicaions of inernaional financial fricions may be paricularly imporan for he opimal conduc of fiscal policy because moneary policy is no available o address hese shocks. Boh Beesma and Jensen (2005) and Gali and Monacelli (2008) poin ou he imporance of he assumpion of perfec risk-sharing wihin heir analyses of opimal fiscal policy in a moneary union. However, hey do no invesigae he consequences of imperfec risk sharing in heir research. I fill his gap in he lieraure and show ha when naional moneary policies canno complemen fiscal policies in redressing cross-counry imbalances, he fiscal policy maker faces an imporan rade-off which canno be characerized by domesic objecives: he mus chose wheher o sabilize oupu gaps, inflaion, or limi he inefficiencies arising due o inernaional financial fricions - hereby facing an addiional objecive, absen under complee markes. One implicaion of inernaional financial fricions for he opimal conduc of fiscal policy wihin a moneary union is hus ha opimal policies canno be achieved by focusing on domesic objecives exclusively. My analysis has imporan implicaions for he conduc of fiscal policy wihin he EMU. I show ha, under realisic assumpions, he opimal cooperaive fiscal policy in a moneary union consiss in reducing inernaional imbalances, a he expense of larger domesic inefficiencies. Since reducing he laer consiues he main objecive of naional fiscal policy makers in he EMU, his research indicaes ha rehinking fiscal policy could resul in welfare gains for he union as a whole. In he following secion, I presen he moneary union framework wihin which I address he issue of inernaional financial fricions for he conduc of fiscal policy. Then, in secion 3, I describe he Ramsey policy problem and relae he Ramsey allocaion o he efficien allocaion. In secion 4, I consider he implicaions of inernaional financial fricions for opimal fiscal policy by invesigaing he opimal response of governmen expendiures o a counry-specific echnology shock. The robusness of he resuls o differen ypes of counry-specific shocks and he sensiiviy wih respec o he chosen calibraion are invesigaed in secion 5. Finally, I conclude he paper. 3

4 2 The Model 2.1 Households The world is composed of wo counries, denoed H (Home) and F (Foreign). There are respecively n and 1 n households in each of hese counries. In he following, I will focus on he agens in he home counry. 2 Households ge uiliy from privae consumpion and governmen expendiures (respecively c and G), bu disuiliy from work (l), and herefore a household s uiliy is given by v = E 0 X =0 h i β U C (c ) + U G (G ) U L (l ) (1) where β is he discoun facor. The funcional forms are as follows: U C (c ) = c1 σ 1 1 σ U G (G ) = χ G1 σ 1 1 σ U L (l ) = l1+η 1 + η where σ > 0 is he inverse of he ineremporal elasiciy of subsiuion and he relaive risk aversion coefficien, η > 0 is he inverse of he Frisch labor-supply elasiciy, and χ is he weigh given o public consumpion relaive o privae consumpion The differeniaed goods produced by firms h and f in counry H and F respecively, c (h) and c (f), are assembled by a Dixi-Sigliz aggregaor ino he composie goods denoed respecively C H, and C F,:»Z n C H, = 0 θ»z c (h) θ 1 θ 1 1 θ dh, CF, = n θ c (f) θ 1 θ 1 θ df Consumpion is a CES index of consumpion of he goods produced a Home and he goods produced in he Foreign counry» C = a 1 φ 1 φ H C φ H, + (1 a H) 1 φ C φ 1 φ F, φ φ 1, 0 < ah < 1, φ > 0, (2) where he consan elasiciy of subsiuion beween he home and foreign goods, also called he rade elasiciy, is denoed φ. The rade elasiciy is an imporan deerminan of he ransmission of shocks and policies beween counries. I herefore plays a crucial role in deermining opimal fiscal policy. a H is he weigh given o consumpion of he home goods, whereas 1 a H is he weigh aached o consumpion of he foreign goods. If a H > n, hen a home bias in consumpion is presen. The presence of home bias resuls in deviaions from purchasing power pariy, even when he law of one price holds. Given ha households choose heir relaive consumpion demand such as o maximize uiliy for given expendiures, he domesic demand for respecively home and foreign goods are: «φ PH, C H, = a H C, (3) P 2 Analogous relaions hold for he agens in he foreign counry, unless oherwise specified. 4

5 where P H and P F C F, = (1 a H) PF, P «φ C. (4) respecively denoe he price of he domesically produced generic good C H and he foreign good C F, whereas P and P denoe he respecive prices of he domesic and foreign consumpion baskes C and C. The consumpion-based price indices are defined analogously o he consumpion bundles: where P = P =»Z n P H, = 0 h a HP 1 φ H, i + (1 a H)P 1 φ 1 1 φ F,, (5) h i (1 a H)P H,1 φ + a HPF, 1 φ 1 φ 1. (6) 1»Z p (h) 1 θ 1 θ 1 1 dh, PF, = p (f) 1 θ 1 θ df n The erms of rade are defined as he raio beween he price of impors and expors: T OT P F, P H,, whereas he real exchange rae is defined as he price of he foreign consumpion bundle in erms of he home consumpion good: Q P P (7) Households face complee financial markes a he domesic level, and firms profis are equally disribued among domesic households (because hey all hold an equal share of each domesic firm) such ha a represenaive household exiss wihin each counry. However, households are subjec o fricions a he inernaional level: only a nominal risk-free one-period bond wih deb-elasic yield is raded across counries. The yield of he bond is higher he higher is a counry s deb relaive o he seady sae level, as in Schmi-Grohe and Uribe (2003). Apar from implying saionariy of he seady sae, modelling financial fricions hrough a deb-elasic yield on bonds allows for yield differences across counries which mimic hose recenly observed across counries in he EMU. Indeed, he model can replicae he recen siuaion in which iner alia Greek, Spanish, Irish, Poruguese and Ialian bonds have experienced a wide yield spread relaive o German bonds. In order o model he deb-dependen ineres raes, I assume ha bonds can only be raded inernaionally hrough inermediaries. The inermediaries in counries wih curren accoun surpluses demand a higher yield on bonds which are issued by counries wih higher deb levels, because of an underlying risk of defaul ha is increasing in deb 3. The addiional ren hus exraced by he inermediaries by lending o indebed counries (i.e. counries wih a curren accoun defici) is colleced and disribued o households wihin he curren accoun surplus counry as lump-sum ransfers. To illusrae he mechanism of he deb-elasic yield, consider he siuaion in which Home bond B H, P holdings are above heir seady sae level i.e. > B H P, ha is, he Foreign counry has issued (excessive) deb. In ha case, he Foreign yield is muliplied by a funcion Φ(B F,/P ) (he premium) which depends posiively on he deviaion of Foreign deb (Φ (B F,/P ) < 0) and saisfies Φ( B F ) = 1; he domesic ineres rae is decreased, since i is muliplied by Φ(B P H,/P ) < 1. Hence, a yield spread across he counries arise, and i is increasing in he difference beween he counries deb levels, or curren accouns. The yield premium associaed wih holding bonds is assumed o be linear in he excessive borrowing/lending (in deviaions from he seady sae value). An example of a funcion saisfying he requiremens above is Φ(B F,/P ) = 1 δb F,/P, wih δ 0. Labor is immobile beween counries bu perfecly mobile wihin counries such ha wages are idenical across households wihin a counry. I follows ha labor supply and consumpion decisions are 3 Noe, however, ha in equilibrium defaul never occurs. 5

6 idenical for all households wihin each counry. Every period, he represenaive household uses is labor income, is wealh accumulaed in bonds, profis of firms in he domesic economy, and he lump-sum ransfers resuling from inermediaion aciviies, o purchase consumpion and bonds and pay lump-sum axes. I assume ha individual households do no inernalize he effec of changes in heir own bond holdings on he yield, i.e. hey ake he funcion Φ(.) as given. In he home counry, he household budge consrain hus amouns o: b w c + + T = l + b [ P (1 + i )Φ(B H,/P ) P P Φ(B F,/P ) 1] B F, + profis (8) (1 + i )P where P is he CPI, i denoes he nominal ineres received in period + 1 on a bond purchased in period, w is he wage rae, and l is he hours worked by he household, T denoes he lump-sum axes paid by he household, and B H, = R n bdh and 0 BF, = R 1 n b df. The firs-order condiions of he represenaive domesic household can be aggregaed o yield: βe [ C σ i 1 C σ ] = π +1 Φ(B H,/P ) (9) (10) L η C σ = W P (11) The firs wo equaions are he Euler equaions, deermining he ineremporal allocaion of consumpion. The hird equaion is he labor supply equaion saing ha in equilibrium, he marginal uiliy of consumpion obained from an exra hour of work mus equal he marginal disuiliy of working ha exra hour. 2.2 Firms Firms are monopolisically compeiive, and se prices in a saggered fashion a la Calvo-Yun, ha is rese heir price a a ime-independen random frequency. More specifically, each firm faces he probabiliy 1 α of geing he possibiliy o rese heir price every period. Firms are owned by domesic households, and all firms wihin a counry are idenical in ha heir echnology is such ha oupu is linear in labor, and depends on an aggregae counry-specific produciviy shock denoed A: Y (h) = A L (h). The maximisaion problem of he firm producing good h is: max E p (h) X s=0 α s µ,+s[((1 τ)p (h) W+s A +s )y,+s(h)] subjec o demand: y,+s(h) = ( p(h) ) θ (C H,+s + G +s) + ( p (h) ) θ C P H,+s PH,+s H,+s where µ,+s is he sochasic discoun facor of he firm, and τ is a ax on producion. Given ha he firms are owned by he households heir discoun facor is idenical o he discoun facor of he P U C,. represenaive household: µ,+s = β s U C,+s P +s The resuling firs order condiions imply ha prices are se according o expecaions of fuure 6

7 marginal coss and demand in he following way: p (h) = P C σ +s θ s=0 (αβ)s (θ 1)(1 τ) C σ +s (αβ)s P s=0 W +s P +s A +s y,+s(h) P +s y,+s(h) (12) Because all firms ha ge o rese heir price in a given period face he same expecaions of marginal coss and demand, hey all se he same price. Hence he following condiion holds: P H, = [αp 1 θ H, 1 + (1 α)p (h) 1 θ ] 1 1 θ ( p(h) ) 1 θ = 1 απθ 1 H, P H, 1 α (13) where π H, P H, P H, 1. Aggregaing across firms, Disp Y H, = A L where Disp R n 0 ( p (h) P H, ) θ dh is a measure of he degree of price dispersion. This erm is always larger or equal o uniy 4. The evoluion of price dispersion is dependen on inflaion in he following way: Disp = (1 α)[ 1 απθ 1 H, 1 α ] θ (1 θ) + απh,disp θ 1 (14) The price seing process of firms hus inroduces dynamics ino he framework, and is disorionary in ha price dispersion among firms resul. Noe ha if firms operae in an environmen wih perfecly flexible prices, he represenaive domesic firm ses is price o equal a consan markup over marginal coss, ha is he real wage rae adjused for produciviy: P H, P = θ 1 W (θ 1)(1 τ) A P 2.3 Moneary and fiscal policies Moneary and fiscal policies are se simulaneously by a Ramsey planner. I absrac from moneary fricions and can hus consider a cashless economy as in Woodford (2003). Neverheless, moneary policy affecs he real economy because of he presence of nominal rigidiies, and hrough is effec on he deb burden of counries Fiscal policy Fiscal policy is defined as he pah of governmen expendiures. These are assumed o be financed by lump-sum axaion and (non sae-coningen) bond issuance. 6 governmen spending raher han on is financing in he presen paper. 7 4 Proof: Le v (h) = ( p,h P H, ) 1 θ, such ha Disp = R n 0 ( p,h P H, ) θ dh = R n 0 v(h) θ θ 1 dh. 1 Tha is, I focus on he effecs of Recall ha P H, = [ R n 0 p(h)1 θ ] 1 θ dh 5. I follows ha R n 0 ( p (h) ) P 1 θ dh = 1 [ R n H, 0 ( p (h) ) P 1 θ dh] θ 1 = 1, or, equivalenly H, ha [ R n 0 v(h)dh] θ θ 1 = 1. Noing ha f(v(h)) = v(h) θ 1 θ is a convex funcion we can apply Jensen s inequaliy, and hereby conclude ha Disp = R n 0 v(h) θ 1 θ dh [ R n 0 v(h)dh] θ θ 1 = 1. 6 I absrac from any implicaions of fiscal policy ha relaes o disorionary axaion issues. This is reasonable if he pah of governmen expendiures can be considered as independen of he financing of i. 7 See e.g. Ferrero (2009) for he role played by disorionary axaion and governmen deb θ 7

8 Governmen demand is enirely direced owards domesically produced goods which are assembled by he governmen ino a composie public good denoed G:»Z n G = 0 θ c (h) θ 1 θ 1 θ dh The echnology used by he governmen in order o assemble he goods is differen from he echnology available o he privae agens, and herefore he good G and he good C H yield differen levels of uiliy o households. The fiscal auhoriies impose a subsidy on producion which eliminaes monopolisic disorions in he seady sae: τ = 1. Hence, under appropriaely chosen governmen expendiure levels and zero 1 θ inflaion, he seady sae will be efficien. Noe ha he subsidy is fixed: hough i does consiue an expendiure for he governmen, i does no consiue a policy insrumen ha can be changed in he face of shocks. Fiscal and moneary policy is se such as o maximize welfare from he view-poin of he moneary union as a whole. More specifically, policies are se in a consrained Ramsey opimal way: A supranaional policy maker ses a pah for he common moneary policy insrumen and for governmen expendiures in each counry such as o maximize he populaion-weighed welfare of he moneary union, given he privae secor s firs order condiions and he naional governmens budge consrains. Imposing ha in equilibrium, he bonds marke mus clear meaning ha B H, + B F, = 0, and using ha R n p(h)y(h)dh = PH,YH, renders he governmen budge consrain: 0 A similar budge consrain holds for he Foreign governmen: τy H, + T = G (15) τ Y F, + T = G (16) Moneary policy Wihin he moneary union, he nominal exchange rae is normalized o uniy and does herefore no consiue a policy insrumen. The moneary policy insrumen is he union-wide nominal ineres rae paid on one-period bonds (more precisely on an inernaionally raded one-period bond). 8 Whereas moneary policy is neural under flexible prices wihin he described framework, i plays a role in he presence of nominal rigidiies. Moneary policy (he common nominal ineres rae) is se simulaneously wih fiscal policy and such as o be Ramsey opimal from a imeless perspecive. 2.4 Marke Clearing and Aggregaion Given he menioned privae and public demand, aggregae demand facing domesic producers amouns o: Y H, = a H PH, P «φ C + 1 n n a H P H, P «φ C + G (17) 8 As explained in Woodford (2003) (p. 239, foonoe 4), In a cashless economy he cenral bank achieves is operaing arge for i by adjusing he ineres rae i m paid on he moneary base; an arbirage relaion hen requires ha i = i m in any equilibrium, given a posiive supply of base money a all imes. Here I simplify by supposing ha he cenral bank can direcly conrol he shor-erm marke rae i... 8

9 and aggregae demand for he foreign good amouns o: Y F, = n (1 ah) 1 n PF, P «φ P «φ F, C + a H C P + G (18) Oupu is demand-deermined in equilibrium, and, hence, he above equaion can also be viewed as a goods marke clearing condiion. Equilibrium on he financial markes requires ha bonds and asses are in zero ne supply: B H, + B F, = 0 (19) When here is no complee rade in asses across counries, hen consumpion risk is no fully shared across counries. I is herefore necessary o keep rack of he evoluion of he curren accoun. Under a single inernaionally raded bond, he household s budge consrain and he governmen s budge consrain can be combined o yield an aggregae resource consrain, characerizing he evoluion of he curren accoun. The Home aggregae resource consrain is: B H, C + P (1 + i = PH, (Y H, G ) + 1 B H, [ )Φ(B H,/P ) π P 1 Φ(B F,/P ) 1] B F, P Q (20) (1 + i ) P Wihin he model developed above, opimal moneary and fiscal policy will depend on he rade-off facing he Ramsey policy maker. In he following secion, I will describe he Ramsey policy maker s problem, define he efficien allocaion, and characerize he rade-off faced by he Ramsey policy maker when deviaions from his efficien allocaion occur. 3 Ramsey Opimal Policy 3.1 The Ramsey planner s problem I analyse he effecs of inernaional financial fricions and he resuling inernaional imbalances for Ramsey opimal policy from a imeless perspecive. 9 The policy insrumens available o he Ramsey planner are he union-wide nominal ineres rae and Home and Foreign governmen spending. The Ramsey planner chooses a sequence of policies which maximize union-wide welfare subjec o privae secor opimizaion, he governmen budge consrains and he resource consrains, given he iniial condiions (I 1) and he conemporaneous shocks (Ω ). The Ramsey problem hus is: max E i (Ω,I 1 ),G (Ω,I 1 ),G (Ω,I 1 ) s.. X s=0 β s [nu(c +s, G +s, L +s) + (1 n)u (C +s, G +s, L +s)] (5), (6), (7), (9), (11), (15), (16), (12), (13), (14), (17), (18), (19) and Foreign counerpars Solving he above problem corresponds o aking derivaives of he Lagrangian figuring in appendix A wih respec o all endogenous variables and lagrange mulipliers. The Ramsey allocaion does generally no coincide wih he firs-bes allocaion. Only when no disorions are presen and prices are flexible can he Ramsey planner se policies which susain he 9 This implies ha he policy maker canno deviae from commimens made previously, cf. Woodford (2003) 9

10 social planner s soluion. 10 This efficien allocaion consiues a naural benchmark for evaluaing differen policies, and helps characerize he rade-off faced by he Ramsey policy maker. 3.2 The efficien allocaion - a benchmark In his secion, I characerize he efficien allocaion defined as he equilibrium which yields he highes possible union-wide welfare in he absence of any disorions. This allocaion can be suppored as a decenralized equilibrium under complee markes, flexible prices and appropriae subsidies eliminaing monopolisic compeiion according o he second welfare heorem. The efficien allocaion will serve as a benchmark in order o undersand how he rade-off faced by he policy maker is affeced by he inernaional financial markes srucure. The efficien allocaion derived from maximizaion of union-wide uiliy subjec o privae-secor opimizaion, governmen budge consrains, and firm echnology, in he absence of disorions, is characerized by he following equaions: χg σ = PH, C σ (21) P χg σ = P F, C σ P (22) C σ C σ = P (23) P Tha is, he policy maker aims a achieving he opimal composiion of spending relaing privae and public consumpion wihin each counry (equaions (21) and (22)) as well as full consumpion risk sharing (equaion (23)). Full risk sharing resuls from equalizaion of he marginal uiliy of consumpion and is marginal cos, he laer being measured by he foreign marginal uiliy of consumpion imes he relaive price. I is useful o define deviaions from he opimal spending composiion and from full risk sharing by gaps. The spending composiion gaps are defined as Ggap χg σ PH, C σ and Ggap χg σ P P F, C σ P (24) The demand gap defining deviaions from full risk sharing is described by he equaion: Dgap C σ C σ P P (25) When nominal fricions are presen and markes are incomplee, he Ramsey policy maker faces a rade-off which can be characerized in erms of deviaions from he efficien oupu level, from he opimal spending composiion level, and from full risk sharing, i.e. in erms of oupu gaps, spending composiion gaps and demand gap. 3.3 Targeing rules - an analyical characerizaion of opimal policy The rade-off faced by he policy maker can be illusraed by his loss funcion. The loss funcion can be ransformed ino a quadraic argeing rule in which he relaive weighs aached o minimizing he differen inefficiencies illusrae he relaive imporance of each objecive. In he case where he 10 The Ramsey planner ses he policy insrumens such as o increase common welfare - consrained by privae agens behavior and naional governmen budge consrains. Tha is, he canno ransfer funds from one counry o he oher direcly. Could he do so, hen he firs-bes allocaion could be obained a all poins in ime, whaever shocks hi. However, given ha his is no possible, he firs-bes allocaion can generally no be obained when a counry-specific shock his. 10

11 counries are symmeric and χ 0, he argeing rule can be wrien as: where L 0 = E 0 X =0 λ C((Ĉ C ) 2 + (Ĉ C ) 2 ) + λ T ( ˆT T ) 2 + λ DDgap 2 + λ CT ( ˆT T )((Ĉ C ) (Ĉ C )) + λ π(π 2 H, + π 2 F,) +.i.p. + ( O ) 3 λ C = η + σ λ T = ah(1 ah)(η + σ)[4ah(1 ah)η(1 + 2φ2 σ 2 ) + 2φσ 2 η] σ 2 [σ + η 3a H(1 a H)η] λ D = 1 (η + σ) ηah(1 ah) 2 λ CT = 8aH(1 ah)η(η + σ)( 1 + σφ)(ah 1/2) 2 σ[σ + η 3a H(1 a H)η] 2(η + σ)αθ(ηθ + 1) λ π = (3a 2 Hη + σ + η 3aHη)(1 αβ)(1 α) and.i.p. denoes erms independen of policy, and ( O ) 3 denoe erms of order 3 or higher. A iled variable denoes he efficien deviaion of ha variable from seady sae. 11 The demand gap (Dgap) eners he argeing rule showing ha deviaions from full risk sharing across counries are disorionary and reduce welfare. The coefficien in fron of he demand gap, assigning he relaive weigh of his policy objecive relaive o he oher objecives, is dependen on he degree of home bias, as well as on he ineremporal elasiciies of labor and consumpion, and on he rade elasiciy, 12 confirming he findings in Corsei e al (2011): openness and elasiciies play a key role in shaping he policy rade-offs in open economies wih incomplee markes. The relaive weigh of he demand gap is increasing in he degree of home bias a H and decreasing in he rade elasicy φ. The reason for his relaes o he fac ha redirecing demand from one counry o he oher requires larger price deviaions he higher he degree of home bias and he lower he rade elasiciy. Hence, i is opimal, in order o avoid large deviaions from full risk sharing, o allow relaive price changes o a larger degree he higher he degree of home bias and he lower he rade elasiciy. As a resul he weigh on he demand imbalances relaive o he weigh on he erms of rade rises wih he degree of home bias and falls wih he rade elasiciy. As illusraed by he argeing rule, he relaive imporance of he gaps and he resuling radeoff faced by he policy maker differ according o he inernaional financial markes srucure and o he inernaional goods marke srucure. In order o undersand he implicaions for opimal policy, I engage in numerical analysis in he following secions. More specifically, I invesigae he rade-off facing he fiscal policy maker wihin he specified framework by sudying he impulse responses following a counry-specific echnology shock. 11 If governmen spending was presen he G-gaps would also ener he rule. For simpliciy, hey do no figure in he argeing rule. For deails on he derivaion of he argeing rule, please refer o he echnical appendix on he auhor s homepage. 12 Even hough he rade elasiciy does no figure in he coefficien on he D-gap, i eners he coefficien on he erms of rade and hus affecs he relaive weigh assigned o eiher of hose objecives. 11

12 4 A Numerical Invesigaion of Opimal Policy in a Moneary Union 4.1 Soluion mehod and Parameerizaion The recursive soluion o he Ramsey problem consiss in policy funcions describing he response of he nominal ineres rae and he governmen spending levels o iniial condiions and curren disurbances. However, he form of he policy funcions are undeermined and herefore a closed-form soluion does no exis. We can neverheless approximae he policy funcions around some specified seady sae. By using he mehod of undeermined coefficiens (perurbaion mehods), based on he knowledge of he derivaives of he equilibrium equaions a he seady sae, he model above can be solved by approximaing he soluion o he policy funcions. The seady sae around which he policy funcions are approximaed is he symmeric zero-inflaion seady sae in which monopolisic disorions are eliminaed hrough appropriae subsidies. The approximaed policy funcions hus found are used for he numerical analysis carried ou in his secion. 13 The parameer values used hroughou his secion figure in he Table 1. Mos of hem are quie sandard in he business cycle lieraure, and realisic for he EMU. 14 The populaion of each of he counries are assumed o be idenical. The discoun facor is se such ha he seady sae annual real ineres rae is 4 percen. The Frisch elasiciy of labor is se equal o 0.5. The inverse of he ineremporal elasiciy of subsiuion, he risk aversion coefficien, is se o 1.5 in he benchmark calibraion following Smes and Wouers (2003). χ is equal o 1/3 such ha in seady sae privae consumpion is hree imes larger han governmen consumpion. The degree of home bias is se o 0.9, implying ha he seady sae impor raio is 10 percen. The elasiciy of subsiuion beween goods produced wihin a counry is se equal o 7.66 such as o ensure a mark-up of 15 percen. On average prices are sicky for a year: α = This value is in line wih he GMM-esimaes found by boh Gali e al. (2001) and he Bayesian DSGE esimaions carried ou by Smes and Wouers (2003). 15 Since he inernaional rade elasiciy is an imporan deerminan of he equilibrium dynamics of he model presened in secion 2, and hus of he rade-off faced by he policy maker, and since he empirical lieraure has no reached a consensus as o plausible values for ha parameer, I consider differen possible values for his elasiciy. Whereas large values have been prediced by he inernaional rade lieraure and by microeconomic sudies, a relaively low rade elasiciy, close o 1/2, corresponds o he esimaes found in he inernaional macroeconomic lieraure, see e.g. Hooper e al. (2000) or Corsei e al. (2008). I hus consider values in he [0.5; 4] range for he rade elasiciy. In he incomplee markes model, δ, he sensiiviy of he bond yield o deb is se such as o roughly mimic he observed yield differences across he EMU before he deb crisis. 16 As compared o he former lieraure on he fiscal and moneary policy ineracion in a moneary union, he calibraion here depars on several poins: Boh Gali and Monacelli (2008) as well as Beesma and Jensen (2005) assume no home bias in consumpion, and a uniary rade elasiciy. The assumpion of no home bias rules ou deviaions from PPP (and hus changes in he real exchange 13 I use code developed by Levin e al (2004) o compue he Ramsey opimal policies. 14 The parameer values used are wihin he range of esimaes found by Smes and Wouers (2003) by engaging in Bayesian esimaion of a DSGE model of he euro area, or follow Benigno (2004) who calibraes his model o he EMU. See also Gali and Monacelli (2008). 15 The degree of price sickiness is assumed o be idenical across counries in he benchmark calibraion, bu I also carry ou an experimen in which price sickiness differs across counries, mimicking poenial differences in price rigidiies across regions wihin he EMU as noed iner alia by Benigno (2004). See he appendix available on he auhor s homepage. 16 The esimaes vary quie a lo from counry o counry and from year o year. The benchmark parameerizaion of δ is a raher conservaive value when comparing o recen years. 12

13 rae), whereas a uniary rade elasiciy simplifies heir models considerably. Furhermore, Gali and Monacelli (2008) consider he knife-edge case of log-uiliy in consumpion, which ogeher wih a uniary rade elasiciy implies ha here are no spillovers across counries. The calibraion chosen here can be considered as being somewha beer suied for considering realisic equilibrium dynamics wihin he EMU. Table 1: Parameer values in benchmark case Populaion in counry H n 0.5 Discoun facor β /4 Inverse of he elasiciy of labor supply η 2 Risk aversion coefficien σ 1.5 Degree of home bias a H 0.9 Price sickiness coefficien α 0.75 Weigh on governmen expendiures χ 1/3 Inraemporal elasiciy of subsiuion θ 7.66 Trade elasiciy φ [0.5; 4] Yield sensiiviy o deb δ 0.05 The following process is assumed for he echnology shocks: " # " # " # log A log A 1 = + log A log A 1 " v v # (26) where v and v are whie noise processes wih sandard deviaions In he following, he parameer values lised above are used in order o invesigae he effecs of inernaional financial fricions for he rade-off faced by he policy maker, and he resuling opimal moneary-fiscal policy mix. Firs, I analyze he opimal policy response o counry-specific shocks when prices are flexible. Then, I show how he rade-off changes when nominal rigidiies are presen. 4.2 Opimal policy under flexible prices When prices are flexible and markes complee, hen he efficien allocaion can be implemened. In ha case, fiscal policy does no play a sabilizaion role: governmen spending is se such as o saisfy he opimal spending composiion. If, insead, inernaional financial markes are incomplee, i migh be opimal o use he fiscal policy insrumens such as o reduce he disorions associaed wih inernaional financial fricions. The derived argeing rule indeed showed he Dgap o be an objecive for he cooperaive policy maker. The opimaliy of using fiscal policies for his objecive, ha is, o reduce inernaional imbalances, depends on he fiscal ransmission mechanism which is shaped by he rade elasiciy. To undersand he mechanism, consider he effec of governmen spending. A change in governmen spending affecs marginal coss hrough is effec on aggregae demand and hus labor demand. Under flexible prices, producer prices are se a a consan mark-up over marginal coss, and hus he change in governmen spending affecs prices. The induced change in he erms of rade affecs relaive income and hus relaive consumpion demand differenly depending on wheher he inernaionally raded goods are subsiues or complemens in uiliy. Indeed, he rade elasiciy deermines he movemens in income following a change in he erms of rade induced by fiscal policy. Under a high rade elasiciy he effecs of governmen spending on relaive consumpion and price movemens are such ha large deviaions of governmen spending from is opimal spending composiion level are required in order o achieve a given reducion in inernaional demand imbalances. 13

14 Consider he effec of an increase in Home governmen spending, shifing demand owards he Home good, and hus increasing inflaionary pressure a Home. The laer implies a fall in he real exchange σ C rae and a fall in relaive Home income. Since he demand gap is defined as Dgap C 1 Q, he fac ha fiscal policy affecs boh of he erms defining he Dgap in similar direcions implies ha i is raher difficul o narrow he demand gap using he fiscal policy insrumen - a leas wihou large coss in erms of governmen spending gaps. And, hence, i is no opimal o reduce he demand gap using fiscal policy when he rade elasiciy is large, as Figure 1 shows. Figure 1 depics he opimal policy response o a one sandard deviaion shock o produciviy in counry H. Due o he resuling fall in marginal coss, producer prices fall in he Home counry. Since he subsiuion effec of he price change dominaes he income effec, Home agens become emporarily richer and he curren accoun urns posiive. Prices move less han under complee markes in order o conain he rise in he curren accoun a he expense of oupu gaps. This illusraes he fac ha he efficien allocaion, characerized by a zero demand gap and zero oupu gaps, canno be achieved in he face of counry-specific shocks. As already poined ou, opimal fiscal policy does no consis in reducing he demand gap since he coss associaed wih doing so, in erms of deviaions from he opimal spending composiion, are oo large. 14

15 Figure 1: Opimal policy under subsiuabiliy (φ = 4). The impulse responses are hose following a one-sandard deviaion shock o produciviy in counry H. H, Ramsey fisc pol refers o he response of Home variables under Ramsey fiscal and moneary policy. H, op spend comp refers o he response of Home variables in he case where moneary policy is Ramsey opimal whereas governmen expendiures are se a heir opimal spending composiion level, i.e. such as o close he spending composiion gap. CM refers o he case of complee markes. For all variables, excep for he annualized real ineres raes, deviaions are shown relaive o heir seady sae level. The real ineres raes depiced are no idenical o he bond yields which depend on deb levels. The opimal fiscal policy response o a produciviy shock o counry H is in line wih he predicions from he argeing rule derived in secion 3.3. Indeed, he argeing rule indicaes ha he cross-counry insurance role of fiscal policy migh be raher small when he raded goods are subsiues. In combinaion wih he limied effeciveness of fiscal policy in reducing inernaional imbalances, his refrains fiscal policy from acing as a cross-counry insurance ool. However, he derived argeing rule implies a larger risk-sharing role for fiscal policy when he raded goods are complemens. The numerical exercise confirms his: The inernaional imbalances affec he rade-off o a larger exen under a low rade elasiciy, cf. Figure 2. Figure 2 depics he opimal policy response o a Home TFP shock under complemenariy of he raded goods. Whereas he Home agens were made relaively richer by he TFP shock under a high rade elasiciy, he TFP shock makes hem emporarily poorer under a low rade elasiciy: he dominaion of he income effec implies ha he fall in prices riggered by he TFP shock resuls in lower income. Hence, he curren accoun is negaive. Prices reac more aggressively o a Home echnology shock such as o reain inernaional imbalances: The Home real ineres rae falls furher han under complee markes, hereby increasing demand for he Home good, and he Foreign real 15

16 ineres rae rises such as o decrease demand in counry F. Price adjusmens hus limi he curren accoun imbalances by also increase Home oupu above he complee markes level and reduce Foreign oupu below is efficien level. The imbalances are hus curbed a he expense of oupu gaps which are of he opposie sign of hose appearing under subsiuabiliy of he goods. In a moneary union he fiscal policy maker faces a rade-off beween using governmen spending such as o reduce he oupu gaps a he expense of higher inernaional imbalances and using i in order o decrease inernaional imbalances a he expense of higher oupu gaps. The rade-off faced by he policy maker is illusraed by he presence of domesic inefficiencies (he oupu gaps) and inernaional imbalances (he D-gap) in Figure On he one hand, closing he posiive oupu gap in H and he negaive oupu gap in F requires a decrease in relaive Home governmen expendiures; on he oher hand, closing he posiive relaive demand gap requires an increase in relaive domesic governmen expendiures. As he impulse responses below show, he rade-off facing he policy maker is opimally iled owards correcing he relaive demand imbalances arising due o inernaional financial fricions: Governmen expendiures are opimally increased a Home (relaive o he case where hey are passively se o saisfy he opimal spending composiion) and decreased in F such as o reduce he demand gap a he expense of larger oupu gaps and spending composiion gaps. Hence, under a low rade elasiciy, fiscal policy plays a risk-sharing role which clearly overshadows is sabilizaion role. Governmen expendiures hus opimally follow a very differen pah han hey would were markes complee, or were hey simply se a he opimal spending composiion level. The reason why i is opimal o use fiscal policy o reduce inernaional imbalances raher han naional inefficiencies is simple. Whereas he fiscal insrumens, namely governmen spending, are raher ineffecive in reducing inefficiencies associaed wih inernaionally incomplee markes under subsiuable goods, hey can improve risk sharing wihou high coss in erms of deviaions from he opimal spending composiion level under complemenary goods. Indeed, a rise in governmen spending leads o a rise in relaive prices and a rise in relaive consumpion (raher han a fall in relaive consumpion under subsiuabiliy). Hence, an improvemen in risk sharing across counries can be obained a he expense of raher small deviaions from he opimal spending composiion under complemenariy of he inernaionally raded goods: fiscal policy is more effecive in reducing inernaional demand imbalances. Combined wih a relaively large weigh on he Dgap in he argeing rule of he policy maker, he incenive o use fiscal policy for his purpose, raher han in order o sabilize domesic objecives, is hus high under complemenariy of he inernaionally raded goods. And, indeed, opimal fiscal policy consiss in reducing inernaional imbalances a he expense of larger domesic inefficiencies as illusraed in Figure In he case where he counries do no form a moneary union, opimal fiscal policy leads o a reducion in all inefficiencies. Fiscal policy canno achieve he same wihin a moneary union because he oupu gaps are of differen signs han under flexible exchange raes, cf. appendix on he auhor s homepage. 16

17 Figure 2: Opimal policy under complemenariy (φ = 0.5). See noes for Figure 1. The srand of he NOEM lieraure which considers he presence of inernaional financial markes incompleeness has mosly come o he conclusion ha he gains from aking ino accoun he srucure of inernaional financial markes are raher small, cf. e.g. P. Benigno (2001). 18 As a resul he policy maker need no care much abou he inernaional financial markes srucure when seing policies, bu should simply focus on domesic arges. Above, I have shown ha his is no so under a low rade elasiciy, in a moneary union wih flexible prices: opimal policy consiss in reducing he demand imbalances due o inernaionally incomplee markes a he expense of larger domesic inefficiencies (oupu gaps). Since inflaion per se does no resul in disorions which are relevan for he policy maker under flexible prices, i is opimal o le prices and governmen expendiures adjus such as o narrow a welfare-weighed combinaion of he oupu gaps, he relaive demand gap and he opimal spending composiion gaps. When prices are se in a saggered way as described in secion 2, however, inflaion leads o inefficien price dispersion across firms wihin a counry. The New-Keynesian lieraure has emphasized he imporance of sabilizing oupu gaps and inflaion in his environmen. More 18 The gains from aking ino accoun financial markes have been shown o be non-exisen in some special cases as poined ou by Cole and Obsfeld (1991) and Corsei and Peseni (2001). Recenly, Corsei e al (2011) is one among a few excepions o poin ou ha he inernaional financial markes srucure migh have imporan consequences for opimal policy. 17

18 specifically, Beesma and Jensen (2005) as well as Gali and Monacelli (2008) poin ou he oupu and inflaion sabilizaion role of governmen expendiures wihin a moneary union wih complee markes. When prices are sicky and inernaional financial fricions are presen, here migh be conflics beween achieving oupu sabilizaion, inflaion sabilizaion, and cross-counry insurance. In he following I sudy which policy objecives are conflicing, and which goal is he mos imporan for a benevolen policy maker. 4.3 Opimal fiscal policy under sicky prices The resuls found in he previous secion go hrough when nominal rigidiies are presen. The radeoff faced by he fiscal policy maker is no very much affeced by he srucure of inernaional financial markes under a high rade elasiciy, and governmen spending coninues o be inefficien as a crosscounry insurance ool. However, when he rade elasiciy is low, governmen expendiures can play a risk-sharing role. Subsiuabiliy. In order o undersand he rade-off faced by he Ramsey policy maker, consider he effecs of a posiive Home TFP shock. The nominal ineres rae is opimally decreased such as o ensure a union-wide increase in demand o couner-ac he fall in prices due o he increased oupu supply. Since he real exchange rae is fixed and prices are sicky, relaive prices will no adjus sufficienly o ensure he efficien level of oupu. Oupu gaps and inflaion are hus non-zero. Under complee markes, fiscal policy faces a rade-off beween closing oupu gaps and reducing inflaion, as emphasized in Beesma and Jensen (2005). For example, by increasing Home governmen spending, he fiscal policy maker can reduce he deflaionary pressure on Home prices resuling from he increase in TFP, bu only a he expense of a higher oupu gap: he reduced fall in Home prices reduces he subsiuion owards he Home good, and since he subsiuion effec dominaes he income effec of he price change, Home oupu falls furher below is efficien level. A similar rade-off applies o he Foreign counry s fiscal policy. Hence, he opimal moneary-fiscal policy mix canno achieve he firs-bes allocaion under sicky prices. In he presence of inernaional financial fricions, he conduc of opimal policy is alered, showing he imporance of he disorions semming from incomplee markes. The main difference perains o he fac ha price changes are opimally much lower under incomplee markes implying higher oupu gaps, see Figure 3. The fac ha prices fall less in counry H following he TFP shock no only decreases disorions arising due o price changes, bu also implies a lower subsiuion owards he Home good, hus lower income in counry H. Since counry H agens have become relaively rich following he posiive Home TFP shock under a high rade elasiciy, he curren accoun has urned posiive: Home agens lend o Foreign agens. The lower price changes, achieved a he expense of higher oupu gaps, ensure ha curren accoun imbalances leading o disorionary demand gaps do no become oo large. An acive use of governmen spending only leads o minor changes, cf. Figure 3. This is so because governmen spending is a raher inefficien risk-sharing ool, as already noed in he case of flexible prices Indeed, domesic governmen expendiures are se o be above heir opimal spending composiion level in he firs periods such as o decrease deflaionary pressures a home, and vice-versa in counry F. When inflaion becomes posiive, governmen expendiures fall below heir opimal spending composiion level such as o dampen inflaionary pressures. Whereas he iniial increase in home governmen spending and decrease in foreign governmen spending reduce he oupu gaps and he demand gap, he subsequen reversal has he opposie effec. This indicaes ha governmen expendiures are firs and foremos se such as o sabilize inflaion, under a high rade elasiciy. 18

19 Figure 3: Opimal policy under sicky prices and high rade elasiciy (φ = 4). See noes for Figure 1. The impulse responses above show ha financial marke incompleeness only plays a minor role for opimal fiscal policy when he rade elasiciy is high. However, his is no a general resul. Indeed, as under he flexible prices, he above resul changes dramaically when he rade elasiciy is low. Complemenariy. In he face of a emporary posiive Home TFP shock, aggregae Home producer prices do no fall sufficienly under sicky prices in he firs periods. Home firms hus make large profis on aggregae during hese firs periods where firms readjus heir prices. As a resul, Home agens become relaively richer in he shor erm following a produciviy shock. Only afer prices have adjused do heir income fall and will hey hus wish o borrow. The curren accoun hen urns negaive. When he inernaionally raded goods are complemens, he presence of inernaional financial fricions leads o larger - bu conained - price movemens and hus more aggressive responses of he real ineres raes. Prices vary more such as o conain inernaional imbalances: he resuling shor erm increase in he Home real ineres rae reains Home lending in he firs periods. Following, he H real ineres rae falls implying higher income in counry H and hus less borrowing. Boh in he shor erm and in he long erm, moneary policy hus acs such as o reain curren accoun imbalances, a he expense of higher disorions associaed wih price changes and higher oupu gaps. When fiscal policy is allowed o adjus opimally, i is increased in Home and decreased in he Foreign 19