Asymmetric Labor Market Institutions in the EMU and the Volatility of Inflation and Unemployment Differentials

Transcription

1 D I S C U S S I O N P A P E R S E R I E S IZA DP No Asymmeric Labor Marke Insiuions in he EMU and he Volailiy of Inflaion and Unemploymen Differenials Mirko Abbrii Andreas I. Mueller April 2012 Forschungsinsiu zur Zukunf der Arbei Insiue for he Sudy of Labor

2 Asymmeric Labor Marke Insiuions in he EMU and he Volailiy of Inflaion and Unemploymen Differenials Mirko Abbrii Universidad de Navarra Andreas I. Mueller Columbia Universiy and IZA Discussion Paper No April 2012 IZA P.O. Box Bonn Germany Phone: Fax: Any opinions expressed here are hose of he auhor(s) and no hose of IZA. Research published in his series may include views on policy, bu he insiue iself akes no insiuional policy posiions. The Insiue for he Sudy of Labor (IZA) in Bonn is a local and virual inernaional research cener and a place of communicaion beween science, poliics and business. IZA is an independen nonprofi organizaion suppored by Deusche Pos Foundaion. The cener is associaed wih he Universiy of Bonn and offers a simulaing research environmen hrough is inernaional nework, workshops and conferences, daa service, projec suppor, research visis and docoral program. IZA engages in (i) original and inernaionally compeiive research in all fields of labor economics, (ii) developmen of policy conceps, and (iii) disseminaion of research resuls and conceps o he ineresed public. IZA Discussion Papers ofen represen preliminary work and are circulaed o encourage discussion. Ciaion of such a paper should accoun for is provisional characer. A revised version may be available direcly from he auhor.

3 IZA Discussion Paper No April 2012 ABSTRACT Asymmeric Labor Marke Insiuions in he EMU and he Volailiy of Inflaion and Unemploymen Differenials * How does he asymmery of labor marke insiuions affec he adjusmen of a currency union o shocks? To answer his quesion, his paper ses up a dynamic currency union model wih monopolisic compeiion and sicky prices, hiring fricions and real wage rigidiies. In our analysis, we focus on he differenials in inflaion and unemploymen beween counries, as hey direcly reflec how he currency union responds o shocks. We highligh he following hree resuls: Firs, we show ha i is imporan o disinguish beween differen labor marke rigidiies as hey have opposie effecs on inflaion and unemploymen differenials. Second, we find ha asymmeries in labor marke srucures end o increase he volailiy of boh inflaion and unemploymen differenials. Finally, we show ha i is imporan o ake ino accoun he ineracion beween differen ypes of labor marke rigidiies. Overall, our resuls sugges ha asymmeries in labor marke srucures worsen he adjusmen of a currency union o shocks. JEL Classificaion: E32, E52, F41 Keywords: currency union, labor marke fricions, real wage rigidiies, unemploymen, sicky prices, inflaion differenials Corresponding auhor: Andreas I. Mueller Columbia Business School 824 Uris Hall 3022 Broadway New York, NY USA amueller@columbia.edu * We are very graeful o Charles Wyplosz, Cedric Tille, Pierpaolo Benigno, Lars Calmfors, Per Krusell, John Hassler, Eser Faia, Anonio Moreno, Sephan Fahr, Sefano Manzocchi, Andrea Boiani, Mirella Damiani, Sebasian Weber, Leo de Haan, Thórarinn G. Péursson, René Kallesrup and seminar paricipans a LUISS, GIIS Geneva, he Universiy of Perugia, he Cenral Bank of Iceland, he IIES Sockholm, he ECB, he ASSET conference 2008, he EEA 2008, he Bank of Ialy and he DNB for very helpful commens and ideas. Mirko Abbrii graefully acknowledges financial suppor by Fondazione Cassa di Risparmio di Perugia and he Graduae Insiue, Geneva for suppor during his graduae sudies. Andreas Mueller hanks he Cenral Bank of Iceland for he hospialiy during his summer inernships and he IIES Sockholm for suppor during his graduae sudies. He also graefully acknowledges financial suppor from he Handelsbanken s Research Foundaions.

4 1 Inroducion Recen empirical evidence shows ha inflaion and oupu growh differenials among Euro Area counries are raher sizeable and very persisen over ime 1. This evidence has araced subsanial public aenion, because i suggess ha he adjusmen mechanism in he single currency area may no be working effi cienly. Labor marke rigidiies are ofen blamed as one of he poenial causes behind he asymmeric adjusmen of member counries o economic shocks. The received wisdom is ha here is a need for more flexible labor markes in he conex of he EU, paricularly a he naional and regional levels (ECB Monhly Bullein, May 2005, p. 71) wihou specifying wha labor marke flexibiliy means. Euro Area counries are characerized by heavily regulaed labor markes, generous unemploymen benefi sysems and high unemploymen. Looking only a he European aggregae, however, can be misleading. As documened by Blanchard (2006), Nickell (1997) and Nickell e al. (2001), labor marke insiuions vary considerably across EMU member counries. For example, employmen proecion legislaion is exremely igh in counries like Ialy, Porugal, France and Spain, bu very loose in Ireland. These auhors also documen large heerogeneiy in he degree of wage rigidiy, he degree of unionizaion and in he generosiy of he unemploymen benefi sysems. The aim of he presen paper is o analyze how asymmeric labor marke insiuions affec he volailiy of inflaion and unemploymen differenials in a currency union. For his purpose, we se up a dynamic currency union model ha combines hree key ingrediens: (i) monopolisic compeiion and nominal rigidiies in he goods marke, which serve o give a role o moneary policy; (ii) hiring fricions in he labor marke, which generae involunary unemploymen; (iii) real wage rigidiies, which hinder wage adjusmens and shif he labor marke adjusmen from prices o quaniies. We build on Blanchard and Galí (2010) and inegrae labor marke fricions ino our currency union model by assuming he presence of hiring coss, which increase in he degree of labor marke ighness. Real wage rigidiies are inroduced, following much of he lieraure, by employing a version of Hall s (2005) noion of he wage norm. To carry ou our analysis, we focus on wo ypes of labor marke rigidiies, Unemploymen Rigidiies (UR) and Real Wage Rigidiies (RWR). The former capure insiuions such as employmen proecion legislaion, hiring coss and he maching echnology ha limi he flows in and ou of unemploymen, whereas he laer capure he insiuions ha influence he responsiveness of real wages o economic aciviy. 2 We highligh hree resuls: Firs, we 1 See, e.g., ECB (2003, 2005), Angeloni and Ehrmann (2004), Benalal e al. (2006) for some evidence on inflaion and oupu differenials and for analyses of he poenial causes and policy implicaions. 2 See Abbrii and Weber (2010) for some evidence on he imporance of unemploymen rigidiies and real 1

5 show ha i is imporan o disinguish beween hese wo ypes of rigidiies as hey have opposie effecs on he volailiies of inflaion and unemploymen differenials. Unemploymen rigidiies make i more cosly for firms o hire new workers and shif he adjusmen from quaniies o prices. A higher degree of UR hus increases he volailiy of inflaion differenials bu reduces he volailiy of unemploymen differenials. Real wage rigidiies, which shif he adjusmen from labor prices o labor quaniies, subsanially increase he volailiy of unemploymen differenials bu have lile impac on he volailiy of inflaion differenials. Second, we find ha he volailiy of boh inflaion and unemploymen differenials increase in he degree of asymmery of labor marke rigidiies across counries. The reason is ha differences in labor marke insiuions lead o srong asymmeric responses o common shocks. Finally, we analyze ineracion effecs beween labor marke insiuions and find ha he effecs of he wo rigidiies on inflaion and unemploymen differenials end o offse each oher if hey are posiively correlaed a he counry level, bu reinforce each oher if hey are negaively correlaed. Overall, our resuls sugges ha asymmeries in labor marke srucures worsen he adjusmen mechanism of a currency union o symmeric and asymmeric shocks. A few currency union models have been proposed in recen years (see, among ohers, Benigno, 2004, Galí and Monacelli, 2008, and Benigno and Lopez-Salido, 2006). The lieraure has focused on he implicaions of differen degrees of nominal rigidiies in member counries. The main resul is ha, when asymmeries in he degree of price sickiness are presen, an inflaion argeing sraegy ha gives higher weigh o inflaion in he "sicky price" region is nearly opimal (Benigno, 2004). Mos of hese works assume perfecly compeiive labor markes and hus ignore a fundamenal source of asymmery among member counries, namely he wide heerogeneiy in European labor marke insiuions. Campolmi and Faia (2011) are he firs o inegrae labor markes fricions "à la Morensen- Pissarides" ino a currency union model. Their paper, which sudies he link beween inflaion volailiy and unemploymen insurance coverage, represens an imporan firs sep owards an undersanding of how he ransmission mechanism of moneary policy works in he presence of asymmeries in he srucure of labor markes. 3 Our paper differs from heir analysis in hree imporan aspecs: Firs, we ake a differen perspecive on labor markes, as we disinguish beween he wo ypes of labor marke rigidiies menioned above. Second, we focus our analysis on he volailiy of differenials, which direcly reflec how shocks are absorbed in he currency union, whereas hey analyze differences in he volailiy of inflaion wage rigidiies for business cycle flucuaions in OECD counries. 3 Oher conribuions relaed o our paper, bu wih a differen focus, include Andersen and Seneca (2010), Poilly and Sahuc (2008), Dellas and Tavlas (2005) and Fahr and Smes (2010). 2

6 across member counries. Finally, we also analyze he effec of labor marke insiuions on he volailiy of unemploymen differenials. More precisely, we analyze flucuaions of unemploymen in deviaions from he effi cien allocaion and hus focus he aenion on ineffi cien allocaions in he labor marke. This disincion is imporan because in a currency union ha is hi by symmeric and asymmeric shocks, flucuaions in unemploymen are no necessarily effi cien. The remainder of he paper is organized as follows. Secion 2 describes he model. Secion 3 discusses he calibraion sraegy. Secion 4 sudies he dynamics of he model under differen calibraions. Secion 5 concludes. 2 The Model A currency union is a group of regions or counries sharing he same currency, wih a single cenral bank eniled o conduc moneary policy 4. To keep hings simple, we consider a currency union consising of wo regions, Home and Foreign, of he same size (normalized o 1). Each economy, which is populaed by idenical, infiniively lived households, is specialized in he producion of a bundle of differeniaed goods. Producion of hese goods akes place in wo secors. Wholesale firms produce inermediae goods in compeiive markes and sell heir oupu o monopolisic reailers. Reailers ransform he inermediae goods ino final goods and sell hem o he households. Price rigidiies arise a he reail level, while hiring fricions in he inermediae goods secor. There is no migraion across regions. Capial markes are complee. Wages are se in individual bargaining beween he employer and he employee. Counries are symmeric for everyhing apar from labor marke insiuions 5. 4 The basic framework of he currency union is inspired by Benigno (2004) and Galí and Monacelli (2008). The srucure of he labor marke builds on Blanchard and Galí (2010). The complee derivaion of he model is described in he Appendix, which is available on he corresponding auhor s webpage. 5 We deviae from Campolmi and Faia in wo imporan respecs: Firs, we use Blanchard and Galí s framework insead of a Morensen-Pissarides ype search-maching model. Krause, Lopez-Salido and Lubik (2008b), however, demonsraed ha he wo models are basically equivalen, and hus all our resuls would carry over o a search-maching model. Second, Campolmi and Faia s model feaures endogenous job desrucion. As argued furher below, we believe ha inroducing his addiional channel of adjusmen would no change our resuls. In fac, in a model wih endogenous job desrucion, rigidiies such as firing coss have he same effecs on unemploymen and inflaion as wha we capure wih he erm unemploymen rigidiy (UR) in a model wihou endogenous job desrucion. For deails, see foonoe 15 regarding Zanei (2010) and Thomas and Zanei (2009). 3

7 2.1 Assumpions Preferences The represenaive household in counry i (i = H or F ) maximizes a sandard lifeime uiliy, which depends on he household s consumpion and disuiliy of work: E 0 =0 { ( ) β C 1 σ N H 1+φ } Ω 1 σ χ, E 0 β Ω 1 + φ =0 { C 1 σ 1 σ χ ( ) N F 1+φ } 1 + φ where variables wih sar refer o he foreign counry. N i denoes he number of employed individuals in he represenaive household of counry i while Ω i denoes shocks o he household s discoun facor (preference shocks) 6. C and C are he composie consumpion indexes for he home and foreign counry respecively, defined as: C = ( C H ) 1 α ( C F ) α (1 α) 1 α α α, C = ( C F, ) 1 α ( C H, ) α (1) (1 α) 1 α α α (2) where C H is he quaniy of he good produced a Home and consumed by home residens, while C H, denoes he quaniy of he good produced a Home and consumed by foreign residens. These consumpion bundles are given by he usual CES aggregaor wih elasiciy of subsiuion beween varieies ɛ. α [0, 1] is he weigh on he impored goods in he uiliy of privae consumpion. Uiliy maximizaion for he home household is subjec o a sequence of budge consrains which, condiional on opimal allocaion of expendiures across varieies, is given by 7 : { } P C + E Q,+1 V+1 H V H + W H N H + Π H where P = ( ) P H 1 α ( ) P F α is he home CPI index, V H is he nominal payoff in period of he porfolio held a he end of period 1 and Q,+1 is he sochasic discoun facor for one-period ahead nominal payoffs, which is common across counries. W H is he nominal wage and Π H denoes he profis received by he home households, ne of lump-sum axes. P H and P F are he Dixi-Sigliz domesic price indexes of he home and foreign counries. 6 We model he preference shock as in Smes and Wouers (2003). 7 Implici in he budge consrain is he assumpion ha he law of one price holds across he union. 4

8 2.1.2 The Terms of Trade and he Real Exchange Rae We define he bilaeral erms of rade beween he home and foreign counry as he raio of he price of goods produced in counry F over he price of goods produced in counry H: S = P F P H (3) As he law of one price holds for all goods, which implies P F = P F, and P H CPI and he domesic price indexes in he wo regions are relaed according o: P = P H (S ) α, P = P F (S ) α = P H,, he The real exchange rae RER is defined as he raio beween foreign and home CPIs and is relaed o he erms of rade according o: RER = P P = (S ) 1 2α Technology In each counry here are wo secors of producion: a reail secor and a wholesale secor. The reail secor is composed by a coninuum of monopolisic reailers indexed by z [0, 1], each producing one differeniaed consumpion good. All reailers share he same echnology, which ransforms one uni of inermediae goods ino one uni of reail goods: Y i (z) = X i (z) where X i (z) is he quaniy of he inermediae good bough by reailer z in counry i. The inermediae good is produced by a large number of perfecly compeiive firms, indexed by j [0, 1], using labor as he only inpu: X(j) i = A i N i (j) where he variables A i represen he sae of echnology in counry i. In each period a fracion δ i of he employed lose heir job and join he unemploymen pool. Employmen in firm j evolves according o: N i (j) = (1 δ i )N 1 i (j) + h i (j) 5

9 where h i (j) is he number of new hires for firm j in counry i Labor Marke Flows and Hiring Coss We assume all unemployed in he family look for a job. Aggregae hiring in counry i, h i 1 0 hi (j)dj, evolves according o: h i = N i (1 δ i )N i 1 where N i 1 0 N i (j)dj denoes aggregae employmen. The number of searching workers who are available for hire, U i, is defined as U i = 1 (1 δ i )N i 1 and we define unemploymen in our model as he fracion of he populaion who are lef wihou a job afer hiring akes place, u i = 1 N i. Labor marke fricions are inroduced by assuming ha hiring labor is cosly. Following Blanchard and Galí (2010), we define he labor marke ighness index as he raio of aggregae hires o he number of searching individuals, x i hi, and we assume ha uni U i recruimen coss are an increasing funcion of he labor marke ighness index: G i = A i B i ( x i ) ϕ where ϕ > 0 and B i is a posiive consan. Noe ha from he viewpoin of he unemployed x i can be inerpreed as he probabiliy of finding a new job. 2.2 Equilibrium under Flexible Prices Price Seing The inermediae good produced a Home is sold o home reailers a relaive price µ H = P I,, P H wih P I, being he nominal price of he inermediae good. The problem of he wholesale firm is o maximize profis by choosing opimally he number of workers i would like o hire in each period. Profi maximizaion gives he firs order condiion: µ H A H = w H,R (S ) α { } + G H (1 δ H )E β,+1 G H +1 (4) where w H,R β,+1 = β Ω +1 Ω = W H P ( C+1 is he real wage expressed in erms of he consumpion good and where ) σ ( ) S α. C S +1 Equaion (4) saes ha he real marginal revenue produc 6

10 of labor (he lef-hand side) has o equal is real marginal cos, ha now includes no only real wages bu also a componen associaed wih hiring coss. This new componen is composed of wo erms. The firs, G H, represens he addiional cos he firm faces o hire a new worker; he second - he las erm in (4) - reflecs he savings in fuure hiring coss resuling from increasing he number of employees oday. Under flexible prices, he opimal price seing rule of final goods firms akes he form of a mark-up over he real marginal coss: P H (z) P H = ɛ ɛ 1 µh and hus in a symmeric equilibrium, where P H (z) = P H seing implies µ H = ɛ 1 ɛ for all. I follows ha under flexible prices: w H,R (S ) α { } = A H µ H G H + (1 δ H )E β,+1 G H +1 for all z [0, 1], he opimal price where µ H is he inverse of he mark-up. A similar condiion hold for he foreign counry. (5) Wage Deerminaion We inroduce real wage rigidiy by employing a version of Hall s (2005) noion of wage norm. A wage norm may arise as a resul of social convenions ha consrain wage adjusmen. One way o model his is o assume ha he real wage w H,R is a weighed average of he Nash bargained wage w H,Nash and a wage norm w H, which is assumed o be he wage prevailing in seady sae. Specifically: where γ and γ ( w H,R = w H,Nash ) 1 γ ( ) ( w H γ, w F,R = w F,Nash ) 1 γ ( w F ) γ (6) are indexes of he real wage rigidiies presen in he home and foreign economy, wih γ [0, 1] and γ [0, 1]. One can show ha he Nash bargained wage is deermined as: w H,Nash (S ) α = mrs + η { { [ ]}} G H (1 δ H )E β,+1 (1 x H +1 )G H +1 (7) 7

11 ( ) where η is he relaive weigh of workers in he Nash bargaining and mrs = χc σ N H φ (S ) α denoes he marginal rae of subsiuion beween consumpion and leisure 8. The Nash wage rule (7) ogeher wih equaions (6) and (5) deermines he evoluion of unemploymen under flexible prices. Similar condiions hold for he foreign counry Inernaional Risk Sharing and Marke Clearing Households have access o a complee se of coningen claims, raded inernaionally. Combining he firs order condiions for sae coningen securiies in he wo counries, we ge: S 1 2α = ψ u (C ) u (C ) where ψ is a consan, reflecing iniial condiions regarding relaive ne asse posiions. To keep hings simple, we assume ψ = 1. Throughou our analysis we assume home bias in consumpion, i.e. α < 1/2, and hus movemens in he erms of rade are refleced in differen consumpion raes. The clearing of all markes implies, for he home and foreign counry respecively, where D H 1 ( P H (z) 0 Y G H h H = ϖ C D H ; Y G F h F = ϖ C D F (9) P H ) ɛ dz and D F 1 ( P F (z) 0 P F (8) ) ɛ dz are measures of price disorions and ϖ and ϖ capure he expendiure swiching effec of erms of rade flucuaions The Effi cien Equilibrium In a currency union wih asymmeric shocks, no all flucuaions in economic aciviy are ineffi cien. In order o deermine he ineffi cien porion of unemploymen and oupu flucuaions, his secion briefly characerizes he condiions under which he decenralized allo- 8 We follow Blanchard and Galí (2010) and absrac from unemploymen benefis. Inroducing unemploymen benefis in our model, he wage rule would become: { w H,Nash (S ) α = mrs + b + η G H (1 δ H { [ )E β,+1 (1 x H +1 )G H ]} } +1 where b is he unemploymen benefi (expressed in domesic prices). Campolmi and Faia (2011) exensively sudy he effec of differences in b on inflaion differenials inside a currency union. They find ha counries wih higher replacemen raes end o have a lower volailiy of inflaion and marginal coss. Unemploymen benefis mainly limi wage variaions and hus have he opposie effec of UR in our model. 9 Specifically, ϖ = S α ϱ = ( 1 1 σ ) (1 2α). [ (1 α) + αs ϱ ( Ω Ω ) 1 σ ] and ϖ = (S ) α [α (S ) ϱ ( Ω Ω ) 1 σ + (1 α) ], where 8

12 caion is effi cien. The consrained effi cien allocaion is found by assuming ha he social planner maximizes he welfare of he union, aking as given he echnological consrains and he hiring fricions ha are presen in he decenralized economy (see he Appendix for deails). Comparing he soluion of he social planner s problem wih he decenralized equilibrium under flexible prices leads o he following resul. Proposiion 1 Under flexible prices, he decenralized equilibrium corresponds o he consrained effi cien equilibrium if hree condiions are saisfied: 1. Monopolisic disorions in he final goods marke are eliminaed hrough a producion subsidy; 2. The Hosios condiion holds, i.e. ϕ = η; 3. Real wages are fully flexible, i.e. γ i = 0 for i = H, F. Proof. See he Appendix. Proposiion 1 highlighs he disorions ha characerize he real side of he economy: monopolisic disorions in he goods marke, search exernaliies in he labor marke, and real wage rigidiies. In he following we assume, as i is common pracice 10, ha he firs wo condiions are me, so ha he seady sae of he decenralized allocaion corresponds o he effi cien one, and focus on real wage rigidiies as he main source of deviaion of he flexible price allocaion from he effi cien allocaion. 2.3 Equilibrium under Sicky Prices We inroduce nominal price rigidiy ino reailers maximizaion problem using he formalism à la Calvo (1983), where each period firms may rese heir prices wih a probabiliy 1 θ. Thus we obain he New Keynesian Phillips curve, which is wrien in log-linear form as: ˆπ H = βe ˆπ H +1 + λ p mc H (10) where ˆπ H is domesic (i.e. producer prices ) inflaion, mc H = ˆµ H represens he log deviaion of real marginal coss from is seady sae value and λ p = (1 βθ)(1 θ)/θ. Noe ha while (10) looks like he sandard New Keynesian Phillips curve, he dynamics of he real marginal coss are now subsanially differen, as hey are deeply affeced by he labor marke insiuions. In fac, log-linearizing equaion (4) we can rewrie marginal coss as: mc H = w (S)α µ ( ŵ H,R + αŝ â H ) + gϕ µ ˆxH β(1 δ H ) g } µ E {ˆβ,+1 + a H +1 + ϕˆx H +1 (11) 10 See, e.g., Blanchard and Galí (2010), Ravenna and Walsh (2010) and Thomas (2008). 9

13 where variables wih ha denoe log-deviaions from seady sae, variables wihou subscrip seady sae values, µ is equal o he inverse of he mark-up of reailers and g is he seady sae value of uni hiring coss G H. Marginal coss depend no only on he evoluion of real wages, erms of rade and produciviy, as in he sandard New Keynesian model; hey also depend on curren labor marke condiions (x H ) and on he fuure labor marke condiions, as capured by he las erm on he righ-hand side Log-linearized Equilibrium Dynamics Before characerizing he equilibrium dynamics, le us define ˆX as he deviaion of a variable X around is seady sae value. Le us also define X as he (sochasic) effi cien equilibrium level of ˆX and X ˆX X as he effi ciency gap, i.e. he gap beween he acual level ˆX and is effi cien counerpar. Finally, we define union-wide variables as ˆX U ˆX H + ˆX F 2. Our currency union model is quie rich, bu sill racable, as i can be characerized in few equaions. The demand side of he model is sandard. The evoluion of he aggregae consumpion gap a he union level is capured by he union-wide IS equaion: c U = E c U +1 1 σ (î E ˆπ U +1 r ) (12) where ˆπ U is union-wide inflaion, r = σ ( ) E c U +1 c U + (1 ρf ) ˆΩ U is he naural real ineres rae and î he common nominal ineres rae. Noe ha he preference shock leads o higher curren consumpion relaive o fuure consumpion, as i makes individuals discoun he fuure more heavily. While he real ineres rae affecs aggregae consumpion, erms of rade movemens disribue consumpion among he wo counries: c c = (1 2α) s (13) σ Using he approximaion ñ i = ũi (1 u i ), he marke clearing condiions can be expressed as: c = τ 0 ũ H τ 1 ũ H 1 (α + ζ s ) s (14) c = τ F 0 ũ F τ F 1 ũ F 1 + (α + ζ s) s (15) 11 Under he baseline calibraion, he acual values of he marginal coss are: ( mc H =.988 ŵ H,R + αŝ â H ) { )} ˆx H.960E (ˆβ,+1 + a H +1 + ˆx H +1 I can be shown ha he weigh on curren and fuure labor marke condiions (he erm in curled brackes) lies in beween he values of Blanchard and Galí (2010) and Krause, Lopez-Salido and Lubik (2008a,b). 10

14 where τ i 0 = 1 gi (1+ϕ i ) N i (1 δ i g i ), τ i 1 = gi (1 δi )(1+ϕi (1 x)) and where he parameers ζ N i (1 δ i g i ) i s are zero for σ = 1 and posiive bu small for σ > Noe ha movemens in he erms of rade lead o changes in consumpion a Home and Foreign, and his effec is larger he smaller he degree of home bias in consumpion (i.e. he larger is α). The aggregae supply equaions for Home and Foreign are: ˆπ H = βe ˆπ H +1 h 0 ũ H + h L ũ H 1 + h F E ũ H +1 + h F S E s +1 + h 0S s γh T ˆT H (16) ˆπ F = βe ˆπ F +1 h 0ũ F + h Lũ F 1 + h F E ũ F +1 h F SE s +1 h 0S s γ h T ˆT F (17) where he coeffi ciens h are funcions of he srucural parameers characerizing he wo economies 13, and he erm ˆT i inroduces an endogenous rade-off of moneary policy beween inflaion sabilizaion and unemploymen gap sabilizaion. This rade-off is generaed by he presence of real wage rigidiies which make he response of real wages dynamically ineffi cien (see, e.g., Blanchard and Galí, 2010) and follows: ˆT H = κ 0 ū H + κ L ū H 1 + κ F ū H +1 + κ SF s +1 κ S s + κ D ˆΩ κ D ˆΩ + κ A â H A similar condiion holds for he foreign counry. Wih compleely flexible real wages (i.e. γ = 0), wages and marginal coss move in proporion o a disribued lag of employmen and erms of rade gaps, and produciviy shocks do no ener as a separae erm in he Phillips curve. On he conrary, in he presence of real wage rigidiies (i.e. γ > 0), produciviy shocks ener as a negaive cos push shock because wages do no move enough o absorb he impac of he shock, and his ranslaes ino ineffi cien allocaions in he produc and labor markes. Preference shocks also ener as a cos push shock, mainly because hey affec how firms and workers discoun he fuure value of an employmen relaionship, bu hese effecs can be shown o be quaniaively small. Noe also ha he Phillips Curves depend posiively on he curren and fuure evoluion of he erms of rade, because he erms of rade no only disribue producion among member saes, bu also affec he wage schedule and he firms marginal coss (see equaions 7 and 11). From he definiion of he erms of rade S = P F P H we ge: ŝ ŝ 1 = ˆπ F ˆπ H (18) Finally, we assume ha he cenral bank ses he nominal ineres rae by reacing o 12 αs Specifically, ζ s = ϱ αs ϱ +(1 α) ϱ and ζ αs s = ϱ αs ϱ +(1 α) ϱ, wih ϱ = ( ) 1 1 σ (1 2α). 13 The expression for he parameers is given in he Appendix. 11

15 union inflaion ˆπ U and he oupu gap ỹ U, according o he following moneary policy rule: î = ω R î 1 + (1 ω R ) (ω πˆπ U + ω y ỹ U ) + ε (19) where ω R capures he degree of ineres rae smoohing and ε m is a moneary policy shock. Equaions (12)-(19), ogeher wih he evoluion of he variables under he effi cien allocaion, characerize our equilibrium dynamics. 3 Calibraion In our baseline calibraion, we assume ha Home and Foreign are perfecly symmeric. The parameers are consisen wih hose sandard in he New Keynesian lieraure. Parameer Value Preferences Discoun rae β Annual real ineres rae of 3.3% Elasiciy of in. subsiuion σ 1 Log uiliy Labor supply elasiciy φ i 0 Homogeneous ases for leisure Share of impored goods α 0.25 Campolmi and Faia (2011) Labor marke Job finding rae x i 0.45 Monhly rae of 0.18 Job separaion rae δ i Reconciles u i = 8% and x i = 0.45 Aggregae hiring coss gh 0.01Y Walsh (2005), Blanchard and Galí (2010) Elasiciy of hiring cos funcion, ϕ i 1 Blanchard and Galí (2010) Relaive bargaining power η i 1 Blanchard and Galí (2010) Price and wage rigidiies Price rigidiy, θ 0.66 Average price duraion of 3 quarers Real wage rigidiy γ i 0.5 Blanchard and Galí (2010) Moneary policy Response o inflaion ω π 1.5 Chrisoffel, Kueser and Linzer (2009) 0.5 Oupu gap ω y Chrisoffel, Kueser and Linzer (2009) 4 Ineres rae smoohing ω R 0.85 Chrisoffel, Kueser and Linzer (2009) Shocks Sd. deviaion ineres rae shock σ ɛ 0.1% Thomas and Zanei (2009) Auocorr. produciviy shocks ρ i a 0.95 Sahuc and Smes (2008) Corr. produciviy shocks ρ σa Backus e al. (1992) Sd. deviaion produciviy shock σ i a 0.624% Smes and Wouers (2003) Auocorr. preference shocks ρ i Ω 0.85 Smes and Wouers (2003) Corr. preference shocks ρ σω Same as corr. produciviy shock Sd. deviaion preference shocks σ i Ω 0.392% Smes and Wouers (2003) Table 1: Baseline calibraion 12

16 Preferences: Time is aken as quarers. The discoun facor β is se o 0.992, which implies a riskless annual reurn of abou 3.3 percen. In he baseline calibraion, he uiliy is log in consumpion (σ = 1). We assume he labor supply elasiciy o be φ i = 0. This is consisen wih our model if he members of he household have homogenous ases for leisure. The home bias parameer α, represening he share of impored goods on oal consumpion, is se o Technology: Following Blanchard and Galí (2010) we se he parameer ϕ i in he hiring cos funcion, represening he sensiiviy of hiring coss o labor marke condiions, o be ϕ i = 1. The seady sae level of produciviy A i is normalized o 1. The degree of price rigidiy θ i is se equal o 0.66, consisen wih daa on price duraion. Following Campolmi and Faia (2011) and Blanchard and Galí (2010), we se he degree of real wage rigidiy γ i equal o 0.5. Shocks: The sandard deviaion of he produciviy shock, and he persisence and sandard deviaion of preference shocks are respecively σ i a = , ρ Ω = 0.85 and σ i Ω = , as in he esimaes of Smes and Wouers (2003) for he Euro Area. The persisence of he produciviy shock is se o he sandard value of ρ a = 0.95, which is also consisen wih he esimaes of Sahuc and Smes (2008). Following Backus, Kehoe and Kydland (1992) we se he correlaion beween he produciviy shocks ρ σa o Since we do no have daa on he correlaion of preference shocks across counries, in he baseline calibraion we use he same value as for produciviy shocks. For he moneary policy we use a simple rule reacing o inflaion wih an elasiciy ω π of 1.5, o he oupu gap wih an elasiciy ω y of 0.5 and a persisence in ineres raes 4 ω R = The sandard deviaion of moneary policy shocks is se o 0.001, consisen wih he esimaes by Thomas and Zanei (2009). The labor marke: In he baseline calibraion, we se unemploymen in counry i o be u i = 0.08, which maches roughly he average unemploymen rae in Europe. The job-finding rae x i is se o 0.45, which corresponds o a monhly rae of Given u i and x i, i is possible o deermine he separaion rae using he relaion δ i = u i x i / ((1 u i ) (1 x i )). We obain a value δ i = The relaive bargaining power η i is se o 1, which implies ha firms and workers have he same bargaining power. The scaling parameer B i is chosen such ha hiring coss represen a 1 percen fracion of seady sae oupu, as in Walsh (2005). The parameers χ i can hen be deermined using seady sae ideniies. In our analysis in he nex secion, we disinguish beween wo ypes of labor marke imperfecions: Unemploymen Rigidiies (UR), which capure he insiuions - such as em- 14 As in Chrisoffel, Kueser and Linzer (2009), we divide he weigh on he oupu gap ω y by 4 because we do no annualize he ineres rae. 13

17 ploymen proecion legislaion, hiring coss and he maching echnology - ha limi he flows in and ou of unemploymen; and Real Wage Rigidiies (RWR), inended o capure all he insiuions - including wage norms, wage indexaion and he wage bargaining mechanism and legislaion - which influence he responsiveness of real wages o economic aciviy. To sudy he role of differen degrees of RWR, we simulae he model varying γ i from 0.25 o Calibraing he degree of UR is a more challenging ask, as he overall degree of rigidiy in he labor marke does no depend only on one parameer bu on he enire configuraion of he labor marke. Following Blanchard and Galí (2010), we define a labor marke as flexible when he job-finding and he separaion rae are high; he opposie holds in a scleroic labor marke. The following abulaion shows he parameers implied by our calibraion sraegy: Index of Rigidiy=0 Index of Rigidiy=1 UR x i = 0.7 / δ i = 0.12 / u i = 0.05 x i = 0.2 / δ i = 0.03 / u i = 0.11 RWR γ i = 0.25 γ i = 0.75 As our UR index increases from 0 o 1, he job-finding rae decreases from 0.7 o 0.2, he separaion rae decreases from 0.12 o 0.03 and he unemploymen rae increases from 0.05 o Noe ha we keep consan oal hiring coss in seady sae as percenage of GDP. This implies ha marginal hiring coss are higher in labor markes wih low hiring raes (i.e. high UR). This is consisen wih a view of "scleroic" economies characerized by insiuional consrains on he hiring process. 15 refers o an economy wih UR = 0.5 and RW R = 0.5. Noe also ha our baseline calibraion Simulaions of he model under he baseline calibraion show ha he volailiies of he model are close o he daa. The sandard deviaion of oupu, inflaion and unemploymen of he Euro Area are 0.85, 0.5 and 4.59, compared o 0.83, 0.43 and 4.63 in our model Zanei (2010) and Thomas and Zanei (2009) inroduce firing coss in a closed economy search and maching model and find ha firing coss increase inflaion volailiy bu reduce oupu volailiy. In a reduced form bu inuiive way, our calibraion of unemploymen rigidiies also capures hese firing coss: we find ha increasing unemploymen rigidiies has he same effecs on inflaion and oupu volailiies as firing coss in Zanei (2010) and Thomas and Zanei (2009). 16 The sandard deviaions of acual Euro Area daa are aken from Chrisoffel, Kueser and Linzer (2009), who use quarerly daa for he Euro Area from 1984Q1 o 2006Q4. Boh daa and model are derended wih an HP filer (λ = 1600). In order o faciliae he comparison, inflaion is compued in a year o year base = log P log P 4 ) and he volailiy of unemploymen is calculaed in percenage erms. (ˆπ yoy 14

18 4 The Dynamics of he Currency Union In his secion we sudy how differen labor marke srucures are likely o affec he funcioning of a currency union. The main focus is on he evoluion of inflaion and unemploymen differenials because hey direcly reflec how shocks are absorbed in he moneary area. Labor marke rigidiies can affec hese differenials in wo main ways. Firs, he presence of labor marke rigidiies may affec he size and persisence of unemploymen and inflaion differenials following asymmeric shocks. Second, symmeric shocks may have asymmeric effecs when he wo regions have differen labor marke srucures. How do hese effecs operae? Are hey likely o be imporan or negligible? To answer hese quesions, we simulae he dynamic behavior of he model in response o hree ypes of shocks: produciviy shocks (symmeric and asymmeric), preference shocks (symmeric and asymmeric) and moneary policy shocks. 4.1 Labor Marke Rigidiies and he Phillips Curve To gain some inuiion on how labor marke srucures influence he adjusmen mechanism of member counries o shocks, i is helpful o look a he Phillips curve, which we rewrie here for convenience: ˆπ H = βe ˆπ H +1 h 0 ũ H + h L ũ H 1 + h F E ũ H +1 + h F S E s +1 + h 0S s γh T ˆT H Labor marke rigidiies affec he supply side of member counries hrough heir impac on he parameers h. We concenrae our aenion on he wo key parameers: The "slope coeffi cien" h 0, which capures he elasiciy of inflaion o unemploymen changes. 17 The "rade-off coeffi cien" γh T, which deermines o wha exen produciviy and preference shocks ener as cos push shocks in he Phillips curve (hrough ˆT H ). Figure 1 shows how he slope coeffi cien changes for varying degrees of UR and RWR. A higher degree of unemploymen rigidiy has a srong, posiive and non-linear effec on he slope of he Phillips Curve. The reason is ha wih lower job-finding raes and separaions employmen adjuss less easily o changing labor marke condiions. This in urn implies ha marginal coss and hence inflaion become more sensiive o unemploymen changes. Real 17 In our calibraions, he parameers on lagged (h L ) and fuure unemploymen (h F ) are small relaive o h 0. Therefore, we follow Ravenna and Walsh (2008) and refer o h 0 as he slope of he Phillips curve. While his is an approximaion, we believe i o be useful o develop inuiion ha will hold hroughou he paper. 15

19 Slope of PC Slope of PC 6 5 Low RWR Baseline High RWR 6 5 Low UR Baseline High UR Index of UR Index of RWR Figure 1: Labor Marke Rigidiies and he Slope of he Phillips Curve wage rigidiies have he opposie effec on h 0 : higher degrees of RWR lower he sensiiviy of real wages and inflaion o unemploymen changes. Noe also ha he sensiiviy of he slope o RWR is much smaller han o UR, and becomes sizeable only when UR are high. This suggess ha here may be imporan ineracion effecs beween differen ypes of labor marke rigidiies. While UR have a dominan role in explaining he size of he slope coeffi cien h 0, RWR are he main deerminan of he rade-off coeffi cien γh T 18. In paricular, noe ha when γ 0, preference and produciviy shocks aler he endogenous wedge ˆT H cos push shocks in he Phillips curve. and hus ener as 4.2 Labor Marke Rigidiies and Inflaion and Unemploymen Differenials To assess how he dynamics of he currency union depend on he underlying labor marke srucure, we simulae he economy for differen degrees of UR and RWR. Specifically, in his firs exercise we change eiher he degree of UR or he degree of RWR for boh counries a he same ime. This allows us o undersand how he average degree of labor marke rigidiy in he moneary union affecs inflaion and unemploymen differenials. We define he inflaion differenial as ˆπ D = ˆπ H ˆπ F and he unemploymen differenial as ũ D = ũ H ũ F. Noe ha he unemploymen differenial is expressed in erms of he deviaion from he effi cien allocaion, and hus any deviaion from zero reflecs ineffi ciencies in he adjusmen process of he currency union. Figure 2 shows he resuls of his exercise. A higher degree of UR increases he volail- 18 The effec of URs on γh T is found o be negligible. 16

20 sd sd (a) The Volailiy of Inflaion Differenials UR RWR (b) The Volailiy of Unemploymen Differenials UR RWR Index of Rigidiy Index of Rigidiy Figure 2: Labor Marke Rigidiies and he Volailiy of Differenials iy of he inflaion differenial, bu reduces he volailiy of he unemploymen differenial. Unemploymen rigidiies make i more cosly for firms o hire new workers and induce firms o absorb shocks hrough an increase in prices. A higher degree of RWR, on he conrary, srongly increases he volailiy of he unemploymen differenial, because, as in Hall (2005), wage rigidiies increase he responsiveness of profis and hus hirings o shocks. The effec of real wage rigidiies on he inflaion differenial is insead small and he slope is sensiive o calibraion choices 19. Labor marke rigidiies are ofen blamed as one of he possible causes of large and longlasing inflaion and unemploymen differenials in he European Moneary Union. resuls, however, sugges ha i is crucial o disinguish among he insiuions ha consrain he quaniy adjusmen (UR) from he ones ha consrain he price adjusmen (RWR) in he labor marke, as hese may have very differen implicaions. Resul 1 (Labor Marke Rigidiies and he Volailiy of Differenials): UR and RWR have differen effecs on he volailiy of inflaion and unemploymen differenials: UR increase he volailiy of he inflaion differenial bu reduce he volailiy of he unemploymen differenial, while RWR increase he volailiy of he unemploymen differenial bu have lile effec on he volailiy of he inflaion differenial. 19 As can be seen from Appendix Table A, he effec of RWR on he volailiy of inflaion differenials depends on he calibraion of he model and he shock processes ha hi he economy. In general, RWR have a small effec on he volailiy of inflaion differenials because hey have wo offseing effecs on marginal coss: on he one hand, hey reduce he volailiy of wages, bu on he oher hand, hey increase he volailiy of hiring, unemploymen, labor marke ighness and hus marginal hiring coss (i.e. he second componen of he marginal cos equaion (4); see Krause and Lubik (2007) for a horough assessmen of his issue in a closed economy seing). Our 17

21 sd sd (a) The Volailiy of Inflaion Differenials Asymmeric UR Asymmeric RWR (b) The Volailiy of Unemploymen Differenials Asymmeric UR Asymmeric RWR Index of Asymmery Index of Asymmery Figure 3: Asymmeric Labor Marke Rigidiies and he Volailiy of Differenials 4.3 The Imporance of Asymmeries in Labor Marke Rigidiies We furher analyze how labor marke asymmeries affec he volailiy of differenials, holding he average degree of UR and RWR consan. For his purpose, we consruc an index of asymmery ha sars ou a 0 where boh counries are perfecly symmeric (he baseline calibraion). As he index increases owards 1, he wo counries become increasingly differen bu he average degree of UR and RWR does no change. 20 The following abulaion shows he values of he underlying parameers: Complee Symmery: Index=0 Srong Asymmery: Index=1 x H = x F = 0.45 x H = 0.2 / x F = 0.7 Asymmeric UR δ H = δ F = 0.07 δ H = 0.03 / δ F = 0.12 Asymmeric RWR γ = γ = 0.5 γ = 0.75 / γ = 0.25 Figure 3 shows ha he volailiy of inflaion and unemploymen differenials is increasing in asymmeries in boh UR and RWR. Asymmeries in he degree of real wage rigidiy are found o increase subsanially he volailiy of he unemploymen differenial. Asymmeric unemploymen rigidiies have insead a sronger effec on he volailiy of he inflaion differenial, which is relaed o he fac ha in he presence of high UR firms adjus o shocks by adjusing prices raher han quaniies. Overall, hese resuls sugges ha asymmeries in labor marke srucures worsen he adjusmen of a currency union o shocks. The reason for his resul is simple and inuiive: when asymmeries are presen, sym- 20 See Benigno (2004) and Andersen and Seneca (2010) for similar assumpions. 18

22 meric shocks are ransmied differenly across member counries and, as a consequence, inflaion and unemploymen differenials arise. This resul is remarkably robus as long as he correlaion of shocks across counries is high enough. When he correlaion of produciviy and preference shocks is lower han in he baseline calibraion, he volailiy of differenials is sill increasing, excep for he volailiy of he unemploymen differenial, which is slighly decreasing in he degree of asymmery in UR. Noice, however, ha i is likely ha hese shocks are more srongly correlaed across members of he EMU han in our baseline calibraion (ρ σa = 0.258) because our baseline calibraion is based on an esimae of ρ σa beween he U.S. and a European aggregae (see Backus, Kehoe and Kydland, 1992). Resul 2 (Asymmeric Labor Marke Rigidiies and he Volailiy of Differenials): Unless shocks are very weakly correlaed across member counries, asymmeries in UR and RWR increase he volailiy of inflaion and unemploymen differenials in a currency union. This suggess ha asymmeries in labor markes worsen he adjusmen of a currency union o shocks. 4.4 Ineracions Beween Labor Marke Rigidiies Table 2. The volailiies of he differenials and he ineracion beween asymmeries Panel A: baseline sd(πd ) sd(ud ) sd(πu ) sd(uu ) Symmeric currency union Asymmeric UR Asymmeric RWR Asymmeric UR + RWR (Complemens) Asymmeric UR + RWR (Subsiues) Panel B: simulaions wih perfecly correlaed shocks sd(πd ) sd(ud ) sd(πu ) sd(uu ) Symmeric currency union Asymmeric UR Asymmeric RWR Asymmeric UR + RWR (Complemens) Asymmeric UR + RWR (Subsiues) Noe: all series are unfilered and inflaion is annualized. How imporan are ineracion effecs beween differen ypes of labor marke rigidiies? Panel A of Table 2 shows he volailiy of inflaion and unemploymen differenials for a currency union characerized by asymmeries in boh UR and RWR. The symmeric currency 19

23 union follows he baseline calibraion, whereas "Asymmeric UR" and "Asymmeric RWR" in rows 2 and 3 represen a currency union where he corresponding index of asymmery is se o 1. The resuls confirm he Resul 2 in he previous secion. The rows 4 and 5 of Panel A sudy he ineracions beween asymmeries in UR and asymmeries in RWR, where "complemens" characerizes a currency union where he home counry has boh low UR and low RWR (and, similarly, he foreign counry has boh high UR and high RWR). "Subsiues", on he oher hand, characerizes a currency union where he home counry has low UR and high RWR and he foreign counry high UR and low RWR. The resuls show ha when rigidiies are complemens a he counry level, he volailiy of inflaion and unemploymen differenials is somewhere in beween he numbers of he currency union characerized by asymmeries in unemploymen rigidiies and he currency union characerized by asymmeries in real wage rigidiy. In conras, he adjusmen mechanism of he currency union is much worse when labor marke rigidiies are subsiues a he counry level, as he volailiy of he inflaion and he unemploymen differenial (as well as he volailiy of he union variables) is higher han for any oher economy. This suggess ha when rigidiies are subsiues, heir effecs end o reinforce each oher, whereas when hey are complemens he effecs of asymmeries end o offse each oher. Panel B furher analyzes he resuls of simulaions where we assume ha all shocks are perfecly correlaed across counries. As expeced, he inflaion and unemploymen differenial are zero a all imes when he home and he foreign counry are idenical (he symmeric case). When he counries have asymmeric labor marke srucures, however, he volailiy of hese differenials increase dramaically. Moreover, when asymmeries are subsiues, he volailiy of unemploymen differenials is highes when shocks are perfecly correlaed (i.e., compared o he corresponding numbers in Panel A). This is somewha surprising as asymmeric shocks are compleely absen here as a source of volaile differenials. Thus, if labor marke insiuions are asymmeric across counries, he coss of a currency union migh be subsanial even in he presence of highly correlaed shocks across counries. Resul 3 (Ineracions beween Labor Marke Rigidiies): There are imporan ineracion effecs beween asymmeries in UR and asymmeries in RWR: when hese rigidiies are subsiues, heir effecs reinforce each oher, whereas when hey are complemens heir effecs end o offse each oher. 5 Conclusion This paper invesigaes how asymmeric labor marke insiuions affec he adjusmen of a currency union o shocks. In our analysis, we focus on wo ypes of labor marke 20

24 rigidiies, Unemploymen Rigidiies (UR) and Real Wage Rigidiies (RWR). The former capure insiuions such as employmen proecion legislaion, hiring coss and he maching echnology ha limi he flows in and ou of unemploymen, whereas he laer capure insiuions ha influence he responsiveness of real wages o economic aciviy. Three main conclusions emerge from our analysis: Firs, he wo ypes of labor marke rigidiies have very differen effecs on he incenives for firms o rese prices and hus on he Phillips curve. A higher degree of unemploymen rigidiies makes he Phillips curve seeper whereas real wage rigidiies make he Phillips curve flaer. The basic inuiion is ha inflaion is more sensiive o labor marke condiions when firms adjus prices raher han quaniies in response o shocks. Second, labor marke rigidiies have a srong impac on he adjusmen mechanism of he currency union o shocks. We find ha unemploymen rigidiies increase he volailiy of he inflaion differenial bu reduce he volailiy of he unemploymen differenial, while real wage rigidiies increase he volailiy of he unemploymen differenial and have lile effec on he volailiy of he inflaion differenial. Asymmeries in unemploymen and real wage rigidiies across counries, however, increase he volailiy of boh inflaion and unemploymen differenials, mainly because differen labor marke insiuions lead o srong asymmeric responses o common shocks. Finally, we sudy ineracion effecs beween hese wo rigidiies. We define rigidiies as "complemens" when unemploymen and real wage rigidiies are posiively correlaed a he counry level, and as "subsiues" when hey are negaively correlaed a he counry level. We find ha he effecs of he rigidiies end o offse each oher when hey occur in complemens, bu hey reinforce each oher when hey are subsiues. This is an ineresing resul and furher underlines he imporance of disinguishing beween differen ypes of labor marke rigidiies. Overall, our resuls sugges ha asymmeries in labor marke srucures worsen he adjusmen mechanism of a currency union o symmeric and asymmeric shocks. Therefore, i may be opimal o coordinae labor marke reforms across he member counries of a currency union and o limi he degree of asymmery in labor marke rigidiies. Anoher imporan consideraion is ha, in he presence of asymmeric labor marke srucures, moneary policy shocks hemselves creae erms of rade movemens and are a source of differenials. The quesion hen is wheher he cenral bank can exploi hese asymmeries and gain from responding sysemaically o differenials. Our model absracs from a number of issues, such as imperfec insurance markes for unemploymen risk, ha make welfare comparisons and hus he derivaion of he opimal policy diffi cul. Neverheless, we hink ha hese are imporan issues and we leave i o fuure research o ackle hese quesions. 21