Monetary Policy and National Divergences in a Heterogeneous Monetary Union

Transcription

1 Journal of Eonomi Integration 4(3), September 9; Monetary Poliy and National Divergene in a Heterogeneou Monetary Union C. Badarau-Semeneu Univerité d Orléan N. Gregoriadi Univerité d Orléan P. Villieu Univerité d Orléan Abtrat In pite of the trutural heterogeneity of the Eurozone, the main objetive of the European Central Bank (ECB) i to preerve prie tability for the union a a whole, and he pay full attention to Union-wide inflation and output, negleting national divergene. In thi paper, we wonder, at a theoretial level, about the oial lo aoiated with uh a entralized objetive, and we how the exitene of an optimal ontrat for the ommon entral bank, whih enure a orret tabilization of national magnitude. Furthermore, we how that oial welfare doe not neearily improve if the ECB worrie about inflation divergene without being onerned about output divergene in the Union. JEL Claifiation : E5, E58, F33 Key Word: monetary poliy, monetary union, optimal ontrat, inflation divergene, output divergene C. Badarau-Semeneu(Correponding author): Laboratoire d Eonomie d Orléan (LEO), Univerité d Orlean, Faulté de Droit, d Eonomie et de Getion, Rue de Bloi BP. 6739, 4567 Orléan Cedex, Frane, Tel: , florina-ritina.emeneu@univ-orlean.fr, N. Gregoriadi: Laboratoire d Eonomié d Orléan (LEO), Univerité d Orlean, Faulté de Droit, d Eonomie et de Getion, Rue de Bloi BP-6739, 4567 Orléan Cedex, Frane, P. Villieu: Laboratoire d Eonomie d Orléan (LEO), Univerité d Orléan, Faulte de Droit, d Eonomie et de Getion, Rue de Bloi BP- 6739, 4567 Orlean Cedex, Frane. 9-Center for International Eonomi, Sejong Intitution, Sejong Univerity, All Right Reerved.

2 Monetary Poliy and National Divergene in a Heterogeneou Monetary Union 49 I. Introdution It i widely reognized that the Euro area i an aymmetri monetary Union ompoed of ountrie with heterogeneou truture of finanial, good and labour market, faing aymmetri hok. The enlargement of the European Monetary Union (EMU) toward the Eatern European ountrie i likely to further amplify thoe heterogeneitie. However, the poliy of the European Central Bank (ECB) mainly foued on prie tability for the whole Euro area, paying attention to the Union-wide output and epeially inflation, but diregarding trutural aymmetrie within the Union. Under thee irumtane the fundamental quetion that arie i whether the poliy of a ommon entral bank hould apture national divergene, and, if o, in whih extent? Thi quetion ha been addreed in the reent literature on the optimal monetary poliy in an aymmetri monetary Union. Firt, empirial reult how that onidering national variable may enhane welfare gain for the Union. In partiular, Briimi & Skotida (8) report that the ECB an ahieve ignifiant gain by taking into aount the heterogeneity of eonomi truture of member ountrie. Akoy, De Grauwe & Dewahter () how that aymmetri hok and divergent propagation of hok in output and inflation are potential aue of tenion, likely to influene the ondut of the ommon monetary poliy. Seond, uing theoretial model, Gro & Hefeker () and De Grauwe & Senega (6) find that the preene of trutural aymmetrie in the interet rate tranmiion require a monetary poliy whih take into aount national data beide aggregate variable. Neverthele, thee tudie onider output divergene only, while the ommon inflation rate i et by monetary poliy. 3 Our Two main ritiim are addreed to the ECB poliy. The firt one onern the abene of an objetive of utaining the eonomi ativity in the monetary poliy lo funtion. The eond one expree a eriou onern over the bear ue of national information and it almot exluive analyi baed on entralized variable. In thi paper, we fou on the eond ritiim. Effetively, the Artile 5 of the Treaty tate that the main objetive of the ECB poliy i to preerve the prie tability, but it reognize that it ould alo ontribute, without prejudie to it primary objetive, to utain the real ativity. Reent empirial data eem to prove that the ECB atually give ome weight to output tabilization (De Grauwe, 7). Thi idea appear in De Grauwe (), Monteforte & Siviero () or Angeloni et al. (), for example. On the ontrary, De Grauwe & Pikorki () onider that poliie baed on union-wide or on national aggregate yield tabilization performane that are quite imilar. Heineman & Hufner (4) how, however, that the onventional Taylor rule that rely olely on Eurozone variable might be biaed by the fat that, in pratie, the member of the Governing Counil of the ECB do not ignore the peifi goal of their home ountry.

3 4 C. Badarau-Semeneu, N. Gregoriadi and P. Villieu tudy extend thi literature in two way. On the one hand, we generalize the reult on the benefit of a monetary poliy baed on national information by ontrolling for inflation divergene. 4 On the other hand, we propoe a imple formulation of the optimal monetary poliy, by mean of an optimal ontrat that an be delivered to the ommon entral bank. We allow for two oure of heterogeneity in the Union: a) a imple trutural aymmetry in the tranmiion hannel of the ommon interet rate to aggregate demand; 5 and b) idioynrati upply and demand hok. 6 Monetary poliy i deigned by a ommon entral bank, only onerned about average variable (inflation and output-gap). In the model, the entral bank poee it own lo funtion (alled entralized lo funtion), whih differ from the Union lo funtion given by the average of national lo funtion (alled ooperative lo funtion). A in previou tudie, ompared to the entralized regime, the ooperative monetary trategy i alway welfare improving. However, the ineffiieny aoiated with a entralized monetary poliy deign an be eaily removed by etting an optimal ontrat for the entral bank. Thi optimal ontrat penalize the ommon entral bank for inflation and output divergene in the Union. The penaltie impoed on inflation (repetively on output) divergene imply orrepond to the relative weight of inflation (repetively output) in the oial welfare funtion. The interpretation of the optimal ontrat i traightforward: if the ommon entral bank i adequately penalized for inflation and output differential, monetary poliy take into aount the partiular ituation of eah ountry, and reahe the Union-wide firt bet. However, thi reult mut reeive ome qualifiation. Firt, the optimal ontrat i not benefiial to all Member-State. Setting a ontrat for the entral bank may be a oure of onflit within the Union, even if it i an optimal one for the Union a a whole. Seond, optimal penaltie take imple value only if the member-tate and the entral bank hare the ame relative preferene for output and inflation 3 Yet, output and inflation divergene are well doumented in the Euro area (ee, e.g. Angeloni & Ehrmann, 4; Muo & Wetermann, 5), and the ECB mainly wonder about inflation divergene, with few or no referene to output divergene (ee ECB, 5, for example). 4 With the notable exeption of Gro & Hefeker (7), the previou tudie do not tudy thi feature 5 In the EMU ountrie, the relative ize of the redit hannel or interet hannel may produe divergent effet of monetary poliy impule (Iing & al., ; Mojon & Peerman, ). The enlargement of EMU will alo inreae unertainty about the tranmiion hannel (Hefeker, 4). 6 Gro & Hefeker () and De Grauwe & Senega (6) onider only ymmetri hok. However, a we will ee, the mix between ymmetri and aymmetri hok trongly affet the form of the entral bank ontrat.

4 Monetary Poliy and National Divergene in a Heterogeneou Monetary Union 4 tabilization. In the oppoite ae, an optimal ontrat an till be found, but it beome more ompliated, and the penaltie are model-dependent. Third, the ommon entral bank may be only onerned with inflation differential. The monetary poliy report of the ECB prove that thi ould be the ae in the Euro area. Under thi aumption, no optimal ontrat exit, but a eond bet ontrat an minimize the Union-wide oial lo funtion. The model how that, if the entral bank ignore output divergene, the eond bet oeffiient for inflation divergene i not neearily poitive. Thu, attempting to redue inflation divergene in a heterogeneou Union doe not neearily repreent an adviable pratie, unle it i upported by an output divergene-oriented devie. Thi reminder of the paper i trutured a follow. Setion II preent the model. Setion III invetigate the ot of a entralized monetary poliy deign, relative to the optimal ooperative olution. In etion IV we ae the optimal ontrat for the ommon entral bank, while in etion V and VI we tudy how the optimal ontrat mut be hanged when the entral bank doe not hare oial preferene for the tabilization of output relative to inflation, and the feature of eond bet ontrat when it diregard output divergene, repetively. The final etion onlude. II. The Model Our model depit a loed Monetary Union made up of a ontinuum of mall open eonomie repreented by the unit interval. 7 All ountrie are of meaure zero and are indexed by i. Supply funtion are defined by: y i απ i + µ i () where π i, y i, µ i relate to the ountry i and define the aggregate upply, the inflation rate and a white noie upply hok with variane, repetively. 8 All variable σµ i 7 We ue a ontinuum of ountrie to enure the ompatibility of our model with the mirofounded framework provided by Gali & Monaelli (8). All reult are obviouly unhanged in a direte um formulation. 8 Compared to Gro & Hefeker () and De Grauwe & Senega (6), we uppoe here that inflation rate may be different aro ountrie. It i an important harateriti of our model, ine we want to tudy the optimal way for the ommon entral bank to take aount of inflation divergene in the Union. Thu, we annot uppoe, a thee author do, that the entral bank diretly ontrol the inflation rate. In ontrat, we mut peify demand funtion and tudy the monetary tranmiion proe.

5 4 C. Badarau-Semeneu, N. Gregoriadi and P. Villieu are peified in log-deviation from their equilibrium level (in partiular, the natural level of output i zero, and all expeted quantitie are et to zero). Thu, relation () depit a Lua upply funtion, in whih equilibrium output an exeed natural produt only when ome urprie are preent, either beaue of an exogenou upply hok or an inflation urprie whih produe an ex pot under-indexation of wage. In order to fou on heterogeneity in the Union, we peify very imple demand funtion. In ountryi, the demand depend on the Union-wide interet rate(r). Sine all expeted quantitie are et to zero, expeted inflation (in deviation from it equilibrium value) i zero, and r denote either the real or the nominal interet rate, onidered the monetary poliy intrument et by the ommon entral bank (hereafter CCB). The demand alo depend on ompetitivene, meaured by the real exhange rate. Sine nominal exhange rate i irrelevant in a loed Monetary Union, ompetitivene pae only through prie differential, namely the relative prie level between ountry i and the other ountrie of the Union. In deviation from equilibrium, prie differential are equivalent to inflation differential (beaue pat equilibrium variable are normalized to zero), o a good indiator of ountry i ompetitivene i the inflation differential: π-π i, where π π i di i the average inflation rate in the Union. Demand funtion are alo affeted by a white d noie demand hok ( µ i ) with variane d : σµ i d y i d β( π ) b i r + µ i π i () In addition to idioynrati hok, we introdue ome trutural heterogeneity in the Union, and more preiely in the monetary poliy tranmiion hannel ( ). 9 In order to deal with «pure» heterogeneity effet, independently of average effet, we define the oeffiient b i in deviation from it mean. Let b b i di be the average interet-elatiity of demand in the Union; we define ( + )b a the ountry-i peifi omponent of the monetary poliy tranmiion hannel, with ε i [, ] and ε i di. In what follow, trutural heterogeneity in the Union will be yntheized by the following index of diperion: Σ ε i di [, ]. b i ε i b i 9 In a eparate Tehnial Appendix (available on requet), we detail the mirofoundation of the equation () and () above. In ynthei, like in Walh () or Gali & Monaelli (8), upply funtion () ome from the maximization of profit by ompetitive firm, with predetermined wage. The demand funtion () an expliitly be derived by introduing light hange in Gali & Monaelli (8). In addition, we diregard publi pending iue; ee for example Minea & Villieu (9).

6 Monetary Poliy and National Divergene in a Heterogeneou Monetary Union 43 All hok µ i (and, more generally, all variable of the model) an be repreented a the um of an average omponent(µ), affeting every ountry in the ame way, and a deviation omponent ( µ i µ i µ ), peifi to the ountry i: µ i µ + µ i (where µ i di ). We deign a ymmetri the omponent of hok that affet every ountry in the ame way (µ, µ d ), and a aymmetri the d peifi omponent of hok ( µ i, µ i ). To olve the model, we write equilibrium in average ( y y d ) and in deviation d ( y i y i ). Appendix A how that equilibrium olution are independent of oeffiient b, o we an normalize thi oeffiient to: b. We obtain the following ymmetri (or average) and aymmetri (or peifi) omponent of inflation: and we an eaily ompute Union produt, on average deviation: π µ d µ r α d µ i µ i π i , i + ε i r α β ( y y i di) (3a) (3b) and in y απ + µ µ d r αµ y i i απ i + µ i d + βµ i , i + αε i r α β (4a) (4b) In equation (4a), we an notie that Union average inome doe not depend on heterogeneity oeffiient(ε i ). Thi i alo the ae for all average variable in the Union. Equation (4b) how that the tranmiion hannel of the ommon interet rate i aymmetri, beaue of the heterogeneity of the Union. We uppoe that eah ountry of the Union i endowed with a oial lo funtion that depend on tabilization of inome and inflation: [ ] L i -- λy i + π i (5) where depit oial preferene for inome relative to inflation tabilization. We alo uppoe that λ i the ame in all ountrie, in order to fou on trutural heterogeneity in the Union. The Union-wide oial lo i: L U L i di (6)

7 44 C. Badarau-Semeneu, N. Gregoriadi and P. Villieu In ontrat with thi oial lo funtion, baed on the average of national lo funtion, we uppoe that the CCB hooe the Union-wide interet rate r, in order to minimize a lo funtion that depend on the tabilization of inome and inflation, baed on the average variable of the Union: L C -- [ λ y + π ] (7) In the Euro zone, for example, the deiion of the ECB are baed on average euro variable and not on national lo funtion (ee the Introdution). In our model, we depit uh a ituation by the fat that the CCB minimize a entralized lo funtion ( L C ) and not the Union-wide oial lo funtion, whih i a ooperative lo funtion ( L U ). We firt uppoe that the CCB hare the oial preferene parameter for the tabilization of output relative to inflation ( λ λ), in order to fou on the impat of entralized veru ooperative deign of monetary poliie. In etion V, we onider the alternative ae in whih the CCB poee ditint preferene ( λ λ). To keep the model imple, we alo hooe to fou exluively on a tabilization problem for monetary poliy, and we ignore a poible inflation bia problem that emerge when the CCB defend an output target higher than the natural produt (here zero). In fat, thi well-known inflation bia an be removed by etting an optimal ontrat that penalize the CCB from inflation deviation, a howed by Walh (995). In our model, the minimization of (7) relative to (6) doe not raie a problem of ytemati bia, but a tabilization problem for monetary poliy. A a reult, the CCB preferene for the tabilization of output and inflation mut be modified, by a kind of quadrati ontrat, ine only quadrati ontrat may affet the tabilization propertie of monetary poliie. The intuition of our reult in etion IV i that the penaltie on inflation and output divergene are preiely a kind of quadrati ontrat. Before analyzing uh ontrat, let u ae the ot of a entralized deiion-making relative to a ooperative one. The heterogeneity of preferene i an important, but ditint, quetion. Our model deribe a Union where there are no preferene onflit, but imply differene in the funtioning of eonomie. Sine we aume a union ompoed of a ontinuum of ountrie (ee footnote 7), an integral appear in the oial lo funtion. However, we mut underline that the reolution and all reult of the model remain unhanged in a monetary union ompoed of a finite number of ountrie, like the EMU. Suh an optimal ontrat reult in a linear penalty on inflation In our model, if i the output target of the ommon entral bank, the optimal penalty for inflation deviation i: λ kα, o that the CCB minimize: L C. -- [ λ ( y k ) + π + π]

8 Monetary Poliy and National Divergene in a Heterogeneou Monetary Union 45 III. The Cot of a Centralized Monetary Poliy Let u now haraterize the ineffiienie aoiated to the minimization of (7) rather than (6), onidering firt that eah Member State of the Union and the CCB hare the ame relative preferene for output and inflation tabilization ( λ λ). The CCB hooe the interet rate by minimizing (7), knowing the value of demand and upply hok. The union-wide interet rate i thu (ee Appendix A): r r u ψ µ + ψ µ d (8) where: ψ λ, ψ, and: λ + α λ. The optimal interet rate, iued by minimizing (6) with repet to r i (Appendix A): + Σ µ + r r u u ψ µ u ψ µ d u + ψ 3 u d ψ 4 Σ µ (9) u u a u where: ψ ψ a λ a, ψ ψ a λ a, ψ 3 λ 3 α u a and ψ 4 α λ a. All along the paper, we ue the notation: a ( α + β), a α Σ and: a λ ( a + a ) ; a well a: λ + α λ, λ β + λ, λ 3 αβλ, and: Σ µ ε i µ i di, d Σ µ ε i µ i ddi. A diret omparion between (8) and (9) allow identifying the ineffiienie in monetary poliy. The reult are ummarized by the following Propoition: Propoition : In a heterogeneou Monetary Union, ymmetri hok have to be le tabilized and aymmetri hok have to be more tabilized than in a homogenou Union. The interet rate poliy obtained by minimizing a entralized lo funtion, depending only on average magnitude, involve an over-reation to ymmetri hok and an inuffiient reation to aymmetri hok. Proof: u Conerning ymmetri hok, ine: a λ a <, we have: ψ < ψ and: ψ u < ψ if Σ >. On the one hand, the reation of interet rate to ymmetri upply hok i exeive with a entralized monetary poliy relative to a ooperative one. A a reult, the Union-wide average produt will be inuffiiently tabilized in (4a), while average inflation will be too muh tabilized in (3a). On the other hand,

9 46 C. Badarau-Semeneu, N. Gregoriadi and P. Villieu in the ooperative regime, demand hok hould be perfetly tabilized if the monetary Union wa homogenou Σ u ( ψ ), but have to be only partially u tabilized in a heterogeneou Union (ine ψ < if Σ > ). Yet, with a entralized lo funtion, the CCB fully tabilize ymmetri demand hok, in pite of heterogeneity. A a reult, average inflation and output in Union are to muh tabilized, to the detriment of the tabilization of deviation ( y i and π i ). Therefore, onerning ymmetri hok, one need a le reative monetary poliy in a heterogeneou monetary Union than in a homogenou Union. Furthermore, by fouing on average variable of the Union, the CCB doe not onider aymmetri hok, while it hould do under the optimal interet poliy u u (ee (8) and (9) where ψ 3 and ψ 4 ). Thu, aymmetri hok are not uffiiently tabilized in the Union. Average output and inflation are not affeted, but the ue of a entralized lo funtion inreae divergene in the area: national quantitie are not properly tabilized. Notie that in a homogenou Monetary Union ( ε i, i), our model would give rie to the well-known equivalene between minimizing L U or L C (Gro & Hefeker, ; De Grauwe & Senega, 6). Thu, if there wa no ro-ountry divergene, monetary authoritie ould rely on a lo funtion baed on area wide variable only, without implying any welfare lo in the Union. In a heterogeneou Union, on the ontrary, the oial lo will be higher with the interet rate rule (8) than with (9). From the Union-wide welfare point of view, what matter i the ex ante (i.e. before knowing the value of hok) value of the oial lo funtion, namely EL U, E denoting the rational expetation operator. To implify the model, we uppoe in the main text that there i no demand hok. 3 So, we heneforth neglet demand hok, by etting from now: d. We will repetively refer to: σµ σµ d, i i and for the variane of ymmetri and aymmetri omponent σµ σ µ σ µi σµ i of upply hok. In addition, to ave notation, we alo uppoe that: i) peifi and average omponent of upply hok are independently ditributed: σ µµi, i, ii) idioynrati upply hok are independently ditributed: 3 Part C of our Tehnial Appendix expliitly prove that the tabilization of demand hok do not raie peifi quetion and the way demand hok are handled an be viewed a a peial ae of upply hok analyi. We thu onentrate our attention on upply hok, whih are a diret laue of onern for monetary poliy. Sine fial poliie are unable to optimally tabilize upply hok in the union, we do not expliitly introdue uh poliie in the model. However, national fial poliie an be viewed a impliit poliie whih perfetly tabilize idioynrati demand hok in the Union, explaining while both demand hok and fial poliie are not preent in the model.

10 Monetary Poliy and National Divergene in a Heterogeneou Monetary Union 47 σ µi µ i i,, and iii) they have the ame variane: σ. 4 µ, i σµ i Therefore, under the optimal interet rate poliy (9), the expeted Union-wide oial lo i: EL U ( r u ) Xσ µ + Xσ µ. Under the entralized poliy (8) the expeted oial lo beome: EL U r u ( ) Yσ µ + Yσ µ. Coeffiient X, X, Y and Y, omputed in Appendix A, are uh that: Y> X, Y X, and we an eaily verify that: EL U ( r u ) < EL U ( r ). Therefore, we obtain the value of the welfare differential: ( EL EL U ( r ) EL U ( r u )) EL U ( Y X)σ µ + α Σ Σ [ σ ( Y X µ + λ 3 σ µ ] )σ µ a λ ( a + α Σ ) () When the Union i heterogeneou, both aymmetri and ymmetri hok are improperly tabilized with a entralized poliymaking, a equation () learly how. A entralized monetary poliy i unable to reat to aymmetri hok, but overreat to ymmetri hok (Propoition ). Symmetri hok are not well tabilized with the entralized poliymaking beaue, in a heterogeneou Union, the multiplier of ymmetri hok differ within the area (ine the ommon interet rate reat to ymmetri hok and the tranmiion hannel of the interet rate to aggregate demand i aymmetri). Thu a entralized monetary poliy annot take aount of thi heterogeneity of multiplier. d EL U Furthermore, we an obtain from equation (): >. Thu, the more dσ heterogeneou the Union i, the higher the relative ot of a entralized poliymaking will be. Thi finding hold independently of the nature of hok (ymmetri or aymmetri). Table imulation learly how that the welfare ot of a entralized monetary poliy (relative to a ooperative one: EL U EL U ) may be quite high, reahing more than % of welfare if the Union i very heterogeneou. It i thu quite obviou that, in a heterogeneou monetary union, the ommon entral bank hould take into aount national divergene. However, propoing Table. Soial Lo Differential (in %) λ λ λ λ For α, β and σ µ σ µ 4 Thee aumption are only notation-aving aumption, with no generality lo; ee Appendix A for the general reolution of the model

11 48 C. Badarau-Semeneu, N. Gregoriadi and P. Villieu the entral banker an aggregate lo funtion defined by the average of the national lo funtion (ee De Grauwe & Senega (6) for example) i diffiult to be aepted, beaue it i too ompliated to repet the tranpareny priniple of the monetary poliy. In thi ontext, the etion III of thi paper earhe for an alternative olution oming from a kind of ontrat for the monetary poliy. IV. Introduing Averion to Divergene in the Central Bank Lo Funtion Thi etion eek for a ontratual olution to the iue of the entralized monetary poliy. Although Walh (995) diued linear ontrat a workaround for the lak of ommitment devie, Herrendorf & Lokwood (997) howed that only quadrati ontrat are optimal to olve a tabilization problem of monetary poliy. In thi model, the ommitment v. diretion iue i not addreed, beaue the problem i only the differene between the oiety preferene and thoe of the CCB, who doe not adequately fight divergene in the Union. Conider that the Union, ating a the prinipal, an delegate monetary poliy to the CCB (the agent ). By etting an optimal ontrat, the prinipal an twit the CCB preferene, to obtain the oial optimum. We deribe uh olution by the fat that, beyond tabilizing average variable in the Union, the CCB attempt to tabilize inflation and inome differential. AU General Formulation of the Problem In the preent model, by fouing exluively on aggregate magnitude, the CCB annot obtain the optimal olution. The goal of the prinipal i to fore the agent (CCB) to be more reative to national divergene, by impoing adequate penaltie (p(.)), o that he minimize: L C ( π i, y i ) + p( π i, y i ). Of oure, if the CCB lo funtion L C ( π i, y i ) i and the oial lo funtion i L U ( π i, y i ), a trivial optimal penalty that ould be added to the CCB lo funtion i: p ( π i, y i ) L U ( π i, y i ) L C ( π i, y i ). Neverthele, uh a penalty would be diffiult to implement, in partiular beaue it depend on CCB preferene that are poibly non-obervable by the prinipal. Thu, we earh for another form of penaltie that rely on imple variable, eay to hek. Suh penaltie hould make the optimal ontrat feaible, verifiable, and ompatible with the tranpareny priniple of monetary poliy. Suppoe for example that the prinipal impoe linear penaltie to the CCB depending on inflation and output differential, meaured a the ro

12 Monetary Poliy and National Divergene in a Heterogeneou Monetary Union 49 etion tandard error of thee variable. 5 The penaltie repreent an additional ot for the CCB and provide an inentive to fight divergene in the Union. 6 The CCB lo funtion beome: L C -- [ λy π θ y y θ π π ] () where and θ π are the penaltie for divergene in the ontrat for the entral θ y banker (or, equally, the oeffiient of averion toward inome and inflation divergene in the CCB lo funtion). In thi etion, we earh for optimal value for and θ π. The following propoition how that we an find a imple optimal θ y ontrat for the CCB. Propoition : If the different Member State of the monetary Union and the CCB hare the ame preferene for tabilization of output and inflation (λ and, repetively), the firt bet olution for monetary poliy an be obtained by an optimal ontrat that penalize the CCB for inflation and output divergene. In the optimal ontrat, the penaltie impoed on national divergene orrepond to the relative weight of eah variable in the oial welfare funtion. Thu, the optimal ontrat for the CCB i uh a: θ y λ and θ π. Proof: By minimizing (6) with repet to r, we obtain: L C () r y y y i π i di i π i r + r r di (a) By minimizing () with repet to r and rearranging, we obtain: L C () r y( λ θ y ) y π( θ π ) π y θ y y i π i di i + + r r r + θ π r π i di r We an eaily oberve that expreion (a) and (b) are idential if (b) θ y λ 5 Defined a: y ( y i y) di and π ( π i π) di 6 Suh penaltie on inflation and output differential look like a quadrati ontrat for entral banker and orrepond to hanging preferene for the tabilization of divergene relative to the tabilization of Union-wide magnitude. One an alo notie the analogy with the analyi of Rogoff (985), in whih relative preferene for the tabilization of output relative to inflation have to be hanged

13 4 C. Badarau-Semeneu, N. Gregoriadi and P. Villieu and θ π, o are lo funtion (6) and (). Thu, under the optimal ontrat, the entralized monetary regime with averion to divergene i effiient and lead to the optimal regime. 7 Propoition how that a imple optimal ontrat for the CCB an enfore the optimal olution. Thi reult i imilar to Walh (995), exept that Walh deal with inflation bia of monetary poliy, while we exluively deal with a tabilization problem. The interpretation of the optimal ontrat i traightforward: for monetary poliy to take aount of Union heterogeneity, one ha to enourage the CCB to feel ome averion to inflation and output divergene. If the degree of averion to divergene i well defined, a in the optimal ontrat, the ommon monetary poliy produe the firt bet. 8 An illutration A we have een, Propoition i etablihed for a general ae. In our model, minimizing () provide the following relation, in plae of (8): + + Σ µ + r r ψ µ ψ µ d ψ 3 d ψ 4 Σ µ (3) with: ψ a Φ, ψ a λ Φ, ψ 3 α ( λ 3 + φ )Φ and: ψ 4 α ( λ + φ )Φ, and we ue the notation: φ α ( θ y λ) + θ π, φ αβ( θ y λ) + θ π, and: Φ ( a + a φ ). One an eaily verify that (3) orrepond to (9) if θ y λ and θ π, and to (8) if θ y θ π. Reintroduing (3) into equilibrium value of inflation and output, we an expre the expeted oial lo EL U for any value of θ y and θ π : EL U r ( ) Zσ, where Coeffiient Z and Z are omputed in Appendix A. 9 µ + Zσ µ The differential of welfare aoiated with a entralized poliymaking ompared to a ooperative one i now: EL EL U ( r ) EL U ( r u ) ( Z X)σ µ + ( Z X)σ µ (4) 7 Notie that thi reult doe not depend on a partiular form of upply or demand funtion: the optimal ontrat in Propoition i not model dependent. 8 Menguy (8) diue an alternative olution to redue the ineffiienie aoiate to the aggregate regime by modifying the weight given to eah ountry in the definition of the CCB aggregate objetive. However, thi olution doe not repreent a firt bet and Badarau & all. (8) howed that the hoie of an optimal ontrat (imilar to thi one) ould improve the oial welfare of the union for all weight ued by the CCB in the definition of the aggregate magnitude.

14 Monetary Poliy and National Divergene in a Heterogeneou Monetary Union 4 where: X a a ( φ ) Φ aα, Z X a [ λ ( α + β)φ + αa φ 3 ] Φ a ; and we ue the notation: φ 3 ( θ y λ) λ( θ π ). Relation (4) learly how that the entralized regime improperly tabilize both ymmetri and idioynrati hok, when the Union i heterogeneou. Let u deal with thee two quetion eparately. Conerning the ymmetri omponent of upply hok, a entralized poliymaking reahe the ame oial lo than the optimal one (X Z) if φ, namely if: θ π θ π ( ) α θ y λ (5) Thi value i the one that minimize the oial lo funtion (del U (r )/dθ π ), if there i no aymmetri hok ( σ µ ). Conerning the aymmetri omponent of upply hok, a entralized poliymaking reahe the ame oial lo than the optimal one if X -Z, namely if: a θ π θ π ( ) + α Ω θ y λ (6) where: Ω a + β( α + β)λ α( α + β)λ + λα a. Thi value minimize the oial lo funtion (del U (r )/dθ π ) if there i no ymmetri hok ( σ µ ). The interetion of (5) and (6) provide the optimal penaltie θ π, whih inure appropriate tabilization of both type of upply hok. a We an notie that: θ π θ π if θ y λ, finding the optimal ontrat of Propoition. But for non-optimal value of the CCB averion for output divergene (that i and ), there i a onflit between tabilizing ymmetri and aymmetri omponent of upply hok. In effet, θ π negatively depend on, while θ π a θ y λ poitively depend on it. θ y Thi harateriti an be explained a follow. With a entralized monetary poliy, the interet rate reat too muh to ymmetri upply hok, a we have een in Propoition. Raiing the penalty on inflation divergene lower the repone of the interet rate to ymmetri hok and ha a tabilizing effet on output differential in the Union (in 4b). Thu, the penalty on output divergene an dereae. For ymmetri upply hok, both penaltie are ubtitutable, thu λ θ y 9 Notie that Z X and Z X, for θ y λ and θ π, and that Z Y and Z Y, for θ y θ π.

15 4 C. Badarau-Semeneu, N. Gregoriadi and P. Villieu θ y and θ y are negatively linked. On the ontrary, for aymmetri upply hok, both penaltie are omplementary and the entralized monetary poliy give rie to an inuffiient tabilization of thee hok. Introduing a penalty on one differential (inflation or output) inreae the variability of the interet rate, thu raiing the other differential. So, a uitable tabilization of both objetive a imultaneouly require θ y and θ π to move in the ame diretion. Thu, if θ y < λ, ituation favoured in etion V, tabilizing ymmetri upply hok all for a higher than one oeffiient of averion to inflation divergene ( θ π > ), but tabilizing aymmetri upply hok require a lower than one oeffiient of a averion to inflation divergene ( θ π < ). The revere i true if θ y < λ. Setion V below tudie the potential onflit between tabilizing ymmetri/aymmetri hok when optimal penaltie annot be implemented. B. National Loe under the Optimal Contrat A entral quetion about the feaibility of the optimal ontrat for the CCB onern it effet on national welfare. Appendix B ompute the welfare u differential of a partiular ountry i, ( EL i EL i EL i ), between a entralized regime without penalty ( θ π θ y ) and the optimal (from the Union-wide point of view) regime with penaltie θ π, and θ y λ. Appendix B alo how that: Sign( EL i ) Sign( ε i ε), where: α( α+ β)σ ε [, ]. ( α+ β) + α Σ Sine ε i di, there i at leat one ountry for whih:. Thu, the ε i < < ε optimal ontrat i not benefiial for all partiipant to the Union. Countrie with high enitivity to the ommon interet rate ( ε i > ε) will prefer the optimal monetary poliy ( EL i > ), but ountrie with low enitivity to the ommon interet rate ( ε i > ε) will prefer the entralized monetary poliy ( EL i > ). Thi reult an be explained a follow. Firt, a we have een, the optimal poliy i le onerned by the tabilization of ymmetri hok than the entralized poliy. Countrie in whih the interet rate elatiity i low ( ε i > ε) prefer a poliy that trongly repond to hok, and are wore under the optimal regime. Seond, the entralized poliy doe not reat to aymmetri hok, while the optimal poliy doe. Country i take benefit from the optimal poliy beaue it tabilize it own aymmetri hok, but at the ame time, uffer from the fat that the Union-wide interet rate reat to hok in other ountrie, whih detabilize ountry i variable. The higher the interet rate elatiity of aggregate demand i, the more the optimal poliy tabilize ountry i idioynrati hok. So, only

16 Monetary Poliy and National Divergene in a Heterogeneou Monetary Union 43 ountrie in whih the interet rate elatiity i high ( ε i > ε) are better under the optimal regime. Therefore, modifying CCB preferene, even to implement the optimal ontrat, an be a oure of potential onflit among Member State. Sine Union-wide benefit exit, thi limitation doe not rule out the interet of an optimal ontrat. The welfare gain for ountrie that take advantage of thi ontrat exeed the welfare lo for the other and, onequently, one ould imagine a ompenation ytem for the lat one. In other word, even if the ontrat i not optimal at a national level, it ould beome benefiial to all member tate of the Union if a ompenation heme ould be implemented. V. The Optimal Contrat with Independent Central Bank Preferene for Output and Inflation Stabilization One important hortoming about Propoition i that the different Member State of the Union and the CCB mut hare the ame preferene. In the oppoite ae, it i till poible to find an optimal ontrat, whih remove the ineffiieny aoiated with a entralized monetary poliy, but thi ontrat i more ompliated and the penaltie toward inflation and output divergene beome modeldependent. Conider now that the CCB poee it own preferene for the tabilization of output relative to inflation, namely: λ λ. The objetive of the CCB beome: L -- [ λ y π θ y y θ π π ] () The interet rule obtained by minimizing of () i analogou to equation (3) below. r r ψ Σ µ d µ + ψ µ + ψ 3 + d ψ 4 Σ µ (3) We uppoe, a uual, that the CCB i more onerned with inflation tabilization than oiety (. λ λ) We ue trivial hange in notation: ψ a Φ, ψ a λ Φ, ψ 3 α ( λ 3 + φ )Φ and ψ 4 α ( λ + φ )Φ, with: φ ( α ( θ y λ ) + θ π ), φ ( αβ( θ y λ ) + θ π ), Φ ( ã + a φ ), and ã λ a λ, λ 3 αβλ, λ + α λ, λ + β λ.

17 44 C. Badarau-Semeneu, N. Gregoriadi and P. Villieu Propoition 3: Suppoe that there are only upply hok ( d. If the CCB σµ σµ d, i) i weight the tabilization of inflation relative to output more than oial preferene in the Union (namely, if λ λ ), the firt bet olution for monetary poliy an be obtained by a ontrat that penalize the CCB from inflation and output divergene in the Union. In the optimal ontrat, the penaltie impoed on inflation (repetively on output) divergene are higher than the relative weight of inflation (repetively output) in the oial welfare funtion. Thu, the optimal θ π ontrat for the CCB i uh a: θ y λ and. Proof: The oial lo reulting from the interet rule (3) i now: EL U r ( ) Z σ µ + Z σ µ, where oeffiient Z and are omputed in Appendix A. The differential of Z welfare aoiated with a entralized poliymaking relative to a ooperative one i: EL EL U ( r ) EL U ( r u ) ( Z X)σ µ + ( X)σ µ Z (4) where: Z X a [ ( )] Φ a α φ α a λ λ a and Z X a [( α + β) [ λ φ + α λ 3 ( λ λ )] + αa φ 3 ] Φ a If λ λ and θ π, the differential of welfare i zero. But if λ, the differential of welfare i poitive even if λ and θ. π Conequently, and θ y θ y λ θ π doe not deribe an optimal ontrat for monetary poliy. Conerning the ymmetri omponent of upply hok ( ), a entralized regime with averion to divergene produe the ame oial lo a the optimal regime if: θ y σ µ λ θ π θ π ( ) a α θ y λ α λ λ a ( ) (5) Conerning the aymmetri omponent of upply hok (i.e. if obtain the ame oial lo under both regime if: We an eaily verify that: Z Z, Z Z if λ λ. We obtain: Z X a α ( λ λ ) and Z X a α ( λ λ ) if θ and. y λ θ π aλ aλ σ µ ), we

18 Monetary Poliy and National Divergene in a Heterogeneou Monetary Union 45 a θ π θ π ( ) + α Ω θ y λ α( α + β)λ 3 ( λ λ) α( α + β)λ 3 + α a λ (6) From (5)-(6), we eaily obtain the value of the oeffiient of averion toward output and inflation divergene under the optimal ontrat. ( α β) + θ y λ λ λ θ π ασ β( α + β) ( ) > λ and ( λ λ ) > (7) The interpretation of Propoition 3 i the following. With independent preferene of the CCB ( λ λ) and entralized poliymaking, monetary poliy i affeted by two biae: one aoiated with the entralized poliymaking and another one aoiated with independent preferene for the tabilization of output relative to inflation. Suffiiently high value of penaltie allow removing thee two biae imultaneouly. Optimal penaltie in relation (7) are the um of optimal penaltie of the previou etion (without independent preferene) and ome extra-penaltie ( θ λ and θ ), whih depend on the gap between the CCB and oial preferene for output tabilization ( λ λ ). Thee extra-penaltie negatively repond to the degree of Union heterogeneity ( Σ ), o that the optimal value of averion toward inflation and output divergene are dereaing funtion of Σ : the more heterogeneou the Union i, the leer the CCB hould worry about inflation and output divergene under the optimal ontrat. 3 Let u examine more loely thi apparent paradox. If the Union wa homogenou, no optimal ontrat ould be reahed, beaue the ommon interet rate annot affet ro-ountrie tandard-error of inflation and output. 4 Thu, no finite value of penaltie θ π or θ y ould totally remove the bia aoiated with the wrong CCB lo funtion, a how the value of penaltie in equation (7), whih tend to infinity. In a heterogeneou Monetary Union, on the ontrary, penaltie on divergene an modify the behaviour of the CCB. In other word, heterogeneity give an intrument for orreting the bia aoiated with the wrong preferene parameter λ. 3 Thee extra-penaltie alo poitively depend on α, β oeffiient, uggeting that higher enibility of the national variable to hok indue more heterogeneity in the model, whih ak for higher penaltie in order to be orreted. 4 If the Union i homogenou, penaltie on divergene annot hange the repone of entralized interet rate (r ) to hok, and the equality r r u an never be reahed with λ λ. Thu, optimal penaltie in (7) go to infinity if Σ. Σ

19 46 C. Badarau-Semeneu, N. Gregoriadi and P. Villieu VI. Seond-Bet Contrat for Monetary Poliy However, the optimal ontrat doe not eem to haraterize the behaviour of the ECB. In the Euro area, the reent monetary poliy debate ha foued on the diffiultie to define a uitable poliy in the preene of inflation differential, but with few referene to inome divergene. Moreover, it eem diffiult to deign monetary poliy in funtion of output-gap differential in EMU, ine thee differential reflet trutural adjutment and athing up of le developed Member State, and are outide the provine of urrent interet rate poliy. Even if inflation divergene alo poe a trutural omponent, they diretly affet the CCB ability to define a good inflation rate for the area, and the ECB doe probably keep more wath on inflation differential than on output differential. In what follow, we earh for a eond bet ontrat, when the CCB hare the oial relative preferene for output and inflation tabilization ( λ λ), a in etion II and III, and worrie about inflation differential, but i not endowed with the optimal degree of averion to output divergene ( θ y θ y λ). In fat, we eek the optimal degree of averion to inflation divergene, given the degree of averion to output divergene (poibly zero). Relation (5) and (6) already exhibit the bet value of θ π in funtion of θ y, in two peial ae: with ymmetri hok only ( σ µ for 5) or with aymmetri hok only ( σ µ for 6). Now, we earh for the bet reation funtion θ π f( θ y ) in the general ae with both ymmetri and aymmetri hok. Notie that the lope of thi reation funtion depend on the relative ize of ymmetri and aymmetri hok, ine the reation funtion i dereaing in the preene of ymmetri hok only (5) and inreaing if there are aymmetri hok only (6). Let u denote by σ σ µ σ µ the ratio of variane of aymmetri to ymmetri hok (i.e. the relative ize of aymmetri to ymmetri hok). With both ymmetri and aymmetri hok, one an expre the degree of averion to inflation divergene ( θ π ) that minimize the welfare differential, for a given oeffiient of averion for output divergene ( ) a: 5 θ y θ π ( ) Θ θ y λ (8) a a + α( a + ( α + β)βλ )[( α + β)λ + αa θ y ]σ Θ In thi expreion: a ( Σ + λ σ) + a α[ ( α + β)λλ + θ y (( α + β)λ + αa λ) ]σ. Relation (8) i obtained by minimizing (4) with repet to θ π, θ y given.

20 Monetary Poliy and National Divergene in a Heterogeneou Monetary Union 47 Coeffiient Θ depend on the variane of ymmetri and aymmetri hok ( σ), but for admiible parameter value, aymmetri hok dominate, even if their variane i very mall ompared to that of ymmetri hok. So, the relation between θ y and θ π i mot probably poitive. Figure, whih repreent θ π a a funtion of θ y, for different ratio σ σ µ σ µ, and for different value of λ, depit thi fat. If there are no aymmetri hok in the model ( σ ), relation (8) i negatively loped, but it beome poitively loped for lower value of σ (a oon a, if λ, for example). σ. Figure. Bet value for θ π in funtion of θ y 6 6 The imulation are alibrated by onidering reaonable value for parameter. Taking into aount the mirofounded determination of the national upply funtion ued in the model, the value of oeffiient α (ee, or 3 in our imulation) reflet tandard value for the labor elatiity of upply (between 3/4 and /3) and are loe to the empirial etimation provided by Hartley & Whitt Jr. (3) for the European ountrie. Empirial etimation for β in Euro ountrie are in the interval. We hooe the medium value β. Under the aumption that the CCB i more onerned with the inflation tabilization than with the output tabilization, we onidered λ <. We generally take a mediumdegree of heterogeneity Σ.5, but onidering different degree of heterogeneity (between.5 and, for example) doe not ignifiantly hange the reult of our imulation.

21 48 C. Badarau-Semeneu, N. Gregoriadi and P. Villieu Furthermore, when the CCB doe not are about output divergene ( θ y ), olving the problem of aymmetri hok may require a negative optimal degree of averion to inflation divergene (ee θ y <, in the graph plaed on the lat two olumn of Figure, for example). Thu, from the Union-wide welfare perpetive, a CCB that worrie about inflation divergene, but neglet output differential might not be a good idea. The model how that a CCB that foue on inflation differential, and diregard output differential may be detrimental to the Union welfare, epeially if the Union i triken by large aymmetri hok (graph on the lat two olumn in Figure ). On the ontrary, in ome ae, if ymmetri hok are large enough ompared to aymmetri hok (graph on the firt olumn in Figure ), a ontrat that penalize the CCB only for inflation divergene ould be benefiial to the Union welfare. Thi analyi prove the importane of taking into aount the nature of hok in aeing the welfare gain aoiated to different intitutional arrangement. VII. Conluion Thi paper tudie the optimal monetary poliy deign in a heterogeneou monetary union with national divergene ariing not only from idioynrati hok but alo from trutural aymmetrie into the tranmiion hannel of monetary poliy among Member State. The main quetion i: Should a CCB in a heterogeneou Monetary Union worry about inflation and output differential? Our anwer i poitive and we how that an optimal ontrat, able to maximize the Union-wide welfare doe exit for the CCB. Thi ontrat impoe penaltie on the CCB for inflation and output divergene in the Union and imply deribe the fat that the CCB mut be fored, impliitly or expliitly, to wath loely over the divergene within the Union. Beide, penalizing the CCB only for inflation divergene i not neearily a better olution than a entralized poliymaking baed only on Union-wide variable. The feature of the optimal ontrat are not muh ompliated than thoe of the optimal ontrat derived by Walh (995) to olve a redibility problem of monetary poliy, whih reult in a linear penalty on inflation. The main differene between the Walh (995) and our tudy i that we addre the tabilization problem of the monetary poliy, uing linear penaltie on inflation and output divergene. All different propoition for the implementation of the Walh

22 Monetary Poliy and National Divergene in a Heterogeneou Monetary Union 49 ontrat in pratie ould be imply tranpoed to diu the implementation of our optimal ontrat. The olution ould be derived from the appointment of a divergene-advere entral banker, a in Rogoff (985), the etting of divergenetarget for the monetary poliy, a in Svenon (997), or the expliit or impliit ontrat for the CCB with divergene oriented penaltie, a in Walh (995). 7 However, the optimal ontrat found in thi paper i open to uual ritiim addreed to ontratual literature in monetary poliy. It implementation i made diffiult, beaue only ome Member State take advantage of thi ontrat, while it i detrimental to the welfare of other. 8 Modifying CCB preferene an therefore be a oure of onflit among Member State of the Union. In our model, trutural heterogeneity i only introdued in the tranmiion of the monetary poliy. However other trutural aymmetrie refleting different level of eonomi development during the athing up proe within the Union ould be alo tudied. Thu, thi work an be viewed a a firt tep toward more general framework. It hould be intereting to extend the preent analyi to an open Monetary Union, to ee how exhange with foreign ountrie affet penaltie on national divergene. Studying more expliitly the different hannel of heterogeneity in the Union ould alo produe intereting reult about the form of the ontrat for the CCB. Finally, we ould invetigate how the optimal ontrat for the CCB in a heterogeneou Union i affeted by the behaviour of national government, in a framework where government minimize their own lo funtion. Suh extenion are unlikely to modify the optimal ontrat for the CCB, whih i not model dependent, but may improve the analyi in a eond bet world. Aknowledgement The author would like to thank Jean-Paul Pollin, Grégory Levieuge and the two anonymou referee for very ueful remark on previou verion of thi paper. The uual dilaimer applie. 7 Penaltie an be of finanial or politial (lo of redibility of the entral bank, onflit with Member State of the Union,...) nature. Walh () diue in ome detail different intitutional arrangement that orrepond in pratie to ontrat for entral banker, in partiular the «Poliy Target Agreement» etablihed in 989 in New Zealand. 9 Furthermore, it i diffiult to identify whih ountrie take benefit from the ontratual olution in pratial term, ine etimation of the interet-elatiity of global demand in the Euro zone are very impreie (ee Mojon & Peerman (), for example).

23 43 C. Badarau-Semeneu, N. Gregoriadi and P. Villieu Reeived 3 Marh 9, Revied 4 May 9, Aepted 8 May 9 Appendix A. Reolution of the Model Optimal interet rate: The firt order ondition for the minimiation of (6) i:. We then ue ε i di and b i di b, implying: b i µ i di b εi µ i di dl U dr d d b i di b and, to write the optimal interet ( + Σ ) b i µ i di b ε i µ i di bσ d µ rate: br u [( α + β) + α Σ ] ( α + β α λ ) µ ( α + β) µ d Σ µ +α d Σ µ λ λ Sine aggregate demand depend on, equilibrium olution are independent of b, and we an normalize b (the ame reaoning applie for the entralized regime). By etting: a ( α + β), a α Σ and a λ ( a + a ), we find equation (9) of the main text. dl Centralized interet rate: The minimization of () ak for: Sine: dr ( b b i )di, ( b b i ) dib Σ, ( b b i )µ i di bσ µ, and: d ( b b i )µ i di bσ d µ, we obtain: α β br + By etting: b, φ α ( θ y λ) + θ π and φ αβ( θ y λ) ( θ π ) we find equation (4) of the paper. If θ y θ π, then λ 3 +φ and λ +φ, and we find relation (8). B. Expeted Soial Lo ( ) ( λ µ d µ ) α ( θ π + θ y α d + [ )Σ µ + ( αλθ y θ π )Σ µ ] ( α + β) λ + α ( θ π + θ y α )Σ Suppoe firt that there i no demand hok µ d d ( µ i ). To olve the model, we ue the ame proedure for all regime: optimal ( ooperative ) regime, entralized regime, entralized regime with averion to divergene for ( λ λ) or ( λ λ). Uing equation (9), (8), (3) and (3) repetively, we obtain the equilibrium value of inflation and output in (3a), (3b), (4a) and (4b), that we replae in the orreponding expeted oial lo. The reolution proedure and notation are detailed in our Tehnial Appendix. Centralized regime: