Monetary Policy in Open Economies: Price Inertia and Inflation Targeting

Transcription

1 Moneary Policy in Open Economies: Price neria and nflaion Targeing Massimiliano Rigon Deparmen of Economics Universiy of Glasgow This version: December 2002 Absrac n his paper we consider a wo-counry model. Each counry is characerised by several differen sources of nominal ineria. This disinguishes our model from ohers in he so called New Open Economy Macroeconomics and makes i a suiable framework wihin which analyse he sabilising properies of moneary policies. We show ha he variance of inflaion induced by domesic inflaionary shocks is lower under CP argeing han when we arge a measure of oupu price inflaion. n fac marke segmenaion and saggered wage and price seing resul in lower and more persisen foreign inflaion responses o a domesic inflaionary shocks. This ineria in foreign price adjusmens is compleely passed hrough ino CP inflaion bu no ino oupu price inflaion. These differences canno be deeced in radiional models ha usually inroduce sluggish adjusmens of domesic oupu prices as he only source of ineria. Furhermore we find a limied role for he exchange rae in affecing he sabilising properies of he rules. JEL: E 52 E58 F4 Key words: moneary policy inflaion argeing open economy exchange rae saggered prices. would like o hank Anon Muscaelli and Campbell Leih for many helpful commens and suggesions. All errors are mine.

2 0. nroducion Much of he conemporary analysis of opimal moneary policy forms par of he emerging macroeconomic consensus as embodied in he New Neo-Classical Synhesis (see Goodfriend and King (997 for a discussion which seeks o incorporae real and nominal rigidiies ino general equilibrium models based on opimising behaviour o provide a coheren framework for he analysis of policy issues. However he vas majoriy of his work is conduced wihin closed economy models and he opimal moneary policy rules ha emerge from his analysis suggess ha Cenral Banks should follow a Taylor rule (993 which ses ineres rae o minimise deviaions of oupu and inflaion from rend and arge respecively wih paricular weigh being given o he inflaion arge (see Woodford (200 for example. is only fairly recenly ha work has begun on assessing he robusness of hese conclusions in he conex of he open economy. n exending he analysis o an open economy a key issue is wha measure of inflaion a cenral bank should arge. n paricular a key poin is wheher consumer price inflaion migh be beer arge han oupu price inflaion. Gali and Monacelli (999 claim ha a welfare opimising moneary policy for a small open economy should aim o sabilise compleely he domesic price inflaion. Similarly Benigno (200 shows ha a policy pursuing domesic inflaion sabiliy is opimal even when financial markes are incomplee. Benigno and Benigno (200a considering wo large economies find ha he opimal combinaion of moneary policies is where boh cenral banks sabilise producer price inflaion. A corollary of heir conclusions is ha if boh cenral banks respond opimally o he deviaions of he producer price inflaion from is planned pah here is no need for furher inernaional moneary policy coordinaion. Similarly Obsfeld and Rogoff (2000 rejec he necessiy of an inernaional moneary compac since i does no provide beer oucome han inward-looking moneary policies se o pursue domesic inflaion sabiliy. Dealing wih a small open economy Clarida e al. (200 claim ha he opimal moneary policies in open economies are isomorphic o hose in closed economies. Essenially all hese papers argue ha moneary policy should seek o minimise he disorions caused by nominal ineria (he only uncompensaed disorion in he model in an aemp o recreae he equilibrium ha would emerge under flexible prices. However hese models are based on he assumpion of complee exchange pass-hrough. n paricular 2

3 hey assume ha prices are se in he producer s currency and ha free-rade ensures ha he law of one-price holds for individual goods and purchasing power pariy holds in erms of consumer price indices. Dealing wih a wo-counry model and allowing for incomplee exchange rae pass-hrough in he seing of impor prices Corsei and Peseni (200 and Corsei and Dedola (200 show ha he exchange rae volailiy can affec welfare. follows ha open economy variables such as he exchange rae should be included in he opimal moneary rule. Similar resuls are obained by Monacelli (999 and Suherland (200 in he conex of a small open economy. Aoki (200 considering a wo-secor model one wih sicky prices and one wih flexible prices- shows ha moneary policy should arge inflaion in he sicky price secor. n our paper we consider a wo-counry model. n each counry here are wo secors: he inermediae goods secor and he final goods secor. nermediae goods are used in he producion of final goods in boh counries. Final goods ener he consumpion baske of domesic and foreign consumers. Furhermore we assume ha workers are monopolisic suppliers of differeniaed labour services and hey se heir wages according o Calvo conracs (983. Producers in boh secors are also monopolisic suppliers of differeniaed goods. More precisely we assume ha marke power allows hem o price discriminae beween domesic and foreign markes. Therefore breaking down he law of one price (LOP we allow for differen price dynamics of he same good in differen counries. Finally since firms in boh secors se prices in buyers currency 2 we inroduce imperfec exchange rae pass-hrough. n fac when a shock occurs and he exchange rae changes only a fracion of firms adjus prices o reac o he exchange rae flucuaions. n his way we inroduce many differen sources of nominal ineria. n each counry we have sluggish adjusmen in nominal wages in prices of domesic and impored inermediae goods and in prices of domesic and impored final goods. This makes our model a paricularly suiable framework wihin which o address he quesion of wha measure of inflaion he cenral bank should arge. n his paper we have chosen o resric ourselves o consider wo alernaives: oupu price inflaion and consumer price index (CP. The firs choice is due he fac ha as already menioned a policy rule formulaed in erms of a measure of oupu prices has been recognised as he opimal one even in open economy. However mos of hese resuls have been derived in The seminal publicaions in his area are Obsfeld and Rogoff ( For a survey of his lieraure see Lane (999. 3

4 model where he sluggishness in oupu price adjusmen is he only source of ineria. CP inflaion has been chosen since i is he measure of inflaion argeed by cenral banks ha implemen an inflaion argeing regime alhough oher measures of inflaion could be more appropriae 3. The exchange rae eners direcly in he definiion of CP inflaion i follows ha under his regime cenral banks implicily reac o change in he real exchange rae. Since he exchange rae reac immediaely o changes in moneary policies while oher nominal variables ypically adjus wih some ineria hen CP inflaion argeing may behave differenly from rules ha arge a measure of oupu price inflaion. Nowihsanding Ball (998 assers ha in open economy cenral banks should arge he real exchange rae and respond o is changes o avoid excessive flucuaions of inflaion and oupu. For his reason we consider rules ha in addiion o eiher oupu price inflaion or CP inflaion arge also he level of he real exchange rae or is changes. The plan of he paper is as follows. Secion oulines he model. n secion 2 we explain how we calibrae our model. Secion 3 deails our resuls and shows ha CP inflaion argeing implies lower volailiy of inflaion han oupu price inflaion argeing. This resuls are due o a lower and more persisen response of foreign good prices o an inflaionary shock in he home counry. Therefore we claim ha he absence of his addiional channel of disorion in previous sudies can lead o some misleading conclusions. n our model wih sources of ineria realisically affecing pricing decisions in he home and foreign marke a differen sages of producion he movemen in he exchange rae has only a limied role in affecing he sabilising properies of he rules wheher hey arge CP or oupu price inflaion. This is in conras o models which make he simplifying assumpion of complee exchange rae pass hrough purchasing power pariy (PPP and a single source of ineria in he pricing of final goods. Secion 4 concludes.. The model This model consiss of wo symmeric counries denominaed as Home (H and Foreign (F. Each counry is inhabied by several differen ypes of agens: consumers final 2 There is a fairly recen bu already vas lieraure on he implicaions of local currency price (LCP assumpion. Examples include Devereux and Engel ( and Bes and Devereux ( Mankiw and Reis (2002 sugges ha he cenral bank should sabilise a price index where he weigh of each secor depends on he secor s characerisics including size cyclical sensiiviy sluggishness of price adjusmen and magniude of secoral shocks. 4

5 good producers inermediae good producers he governmen and he cenral bank. We assume ha in each period a new generaion of consumer is born and ha all consumers face a consan probabiliy of deah. The inroducion of overlapping generaion allows us o derive a well-defined seady sae for consumpion he erms of rade and he ne financial wealh around which he model can be linearised (for a discussion of his poin see Ghironi ( nermediae goods are produced using only domesic labour inpus and sold o boh domesic and foreign producers. The producion funcion of he final good producer combines domesic labour and bundles of domesic and foreign inermediae goods. As wih inermediae goods final goods are sold in boh markes. Therefore he consumpion bundles purchased by households and governmens combine boh domesic and foreign final goods. We assume ha price o marke (PTM is possible and ha prices are se in he buyer s currency. For simpliciy and o allow consumers in boh counries o hold posiive financial asses in equilibrium we assume ha given is public expendiure choices he governmen raises axes o keep he public deb consan 5. Finally he cenral bank is in charge of he moneary policy and ses nominal ineres raes o respond o domesic and foreign shocks o he economy. We now proceed o ouline he model considering firs he problem facing individual consumers before aggregaing across all consumers. We hen urn o he pricing decisions of he represenaive firm in boh inermediae and final good secor. The linearised version of he model required o render i suiable for numerical simulaion is presened in an appendix.. The Consumer s problem Consider a ypical home consumer j in he cohor s who derives uiliy from a baske of consumpion goods ( C( j s and real money balances ( ( js providing labour services ( l( uiliy ( E U ( j s M P and disuiliy from j s. We assume ha he expeced value of he consumer s is obained as follows: 4 Overlapping generaions are also considered in Smes and Wouers ( Since we are no ineresed in considering ineracions beween fiscal and moneary policies we do no allow he governmen o deviae from he zero defici consrain. Moreover insulaing he economy from he effecs of fiscal policies we are able o enhance he consequences of differen moneary policy rules wihou affecing he main conclusions. 5

6 ( ( τ M E U j s = ιρ ln C( j s + χ ln ( j s + k ln( l( j s = τ P ( where ι is he probabiliy of survival and ρ is he consumers discoun rae. We assume ha he parameers χ and k are sricly posiive and ha boh ι and ρ are beween zero and one. The baske of consumpion goods is defined by he following index: where γ ( 0. C ( j s and C ( H C F ( ( γ ( ( j = C j C γ H F j j s are consumpion CES sub-indexes of a coninuum of differeniaed final goods produced respecively in counry H and F: θ θ θ CH j s c h j s dh h= 0 θ θ θ θ C j s = c f j s df f = 0 ( = ( θ F ( ( wih θ (θ > 0 he elasiciy of subsiuion among home (foreign final goods. Given he price of each differeniaed final good he price of any consumpion bundle is obained as he minimum expendiure required o buy one uni of his bundle. Consequenly we have: = θ θ P p ( h dh p ( f H h= 0 where γ ( ( γ ( H ψ = γ γ. θ θ P F = df f = 0 P P = γ ( γ P H F The consumer can hold her financial wealh in he form of home governmen bonds B foreign bonds ( B and money balances. Domesic bonds earn a nominal ineres rae F i foreign bonds a reurn i. Consumers receive also shares in he profis of all domesic firms ( DV ( j s. Furhermore i is assumed ha he consumers receive a premium from perfecly compeiive insurance companies in reurn for heir financial asses should hey die; his effecively raises he rae of reurn from holding financial asses by. Finally he consumer ι receives a wage W ( i for any uni of labour supplied 6 consumes boh domesic and foreign final good bundles pays lump sum axes T( j s and receive lump sum ransfers ( follows ha he consumer budge consrain in nominal erms is given by: ψ TR j s. 6 As i will be explained below workers provide differen labour services. Those who provide a labour service of ype i receive he nominal wage W ( i 6

7 ( ( ( ( ( ( j s + H H + F F + H + F ε = + M j s P C j s P C j s B j s B j s + r + r + BH js + BF js + W il js + Div js T js + TR js ι ι ( ( ( ( ε ( ( ( ( ( M ι where ε is he nominal exchange rae. Deflaing by P we can rewrie i in real erms as follows: ( ( ( ( ( 7 ( P P m j s P m js + C js + C js + b js + b jsε = + H F H F H F P P ι P ( ( ( ( + r + r R + bh js + bf js ε + w( il ( js + div( js τ( js + τr( js ι ι (2 R where ε is he real exchange rae and r ( r is he ex ane real ineres rae paid a ime on home (foreign bonds issued one period earlier. Since he non-arbirage condiion implies ha he usual uncovered ineres pariy (UP condiion mus hold we have: ε R = R + ( + r ( + r ε From he firs order condiions derived from he maximisaion of he expeced uiliy ( under he budge consrain (2 we obain he usual consumpion Euler equaion: ( ρ ( ( E C j r C j + = + The opimisaion also leads o he following money demand funcion: + r m ( j = χ C ( j P + + r P negraing he consumpion Euler equaion forward and subsiuing i ino he ineremporal budge consrain we obain he consumer s consumpion funcion: ( ( + r + r bh ( j + bf ( j + wτ ( j lτ + divτ ( j ττ ( j + τrτ ( j ι ι τ ( ι ( ( ( + ( τ( + τ ( ( τ = τ ι P ( + r ιβ C ( j = w j l j div j j r j χ m j P τ + k k = 0 From he firs order condiions we can also easily derive he consumer s demand for bundles of home and foreign final goods:

8 P CH j = C j P H ( γ ( F and C ( j ( γ C ( j F P = P The domesic demands of a ypical home and foreign final good are given by: ( ( h p = θ ( C h j CH j PH and ( ( f p = θ. ( C f j CF j PF... Labour supply and wage seing We assume ha workers provide differeniaed labour services indexed by i ( 0. Moreover for he sake of simpliciy we assume he same generaion srucure wihin each labour service ype. means ha for any cohor s here are ι s workers for any ype i. Workers of he same ype are represened by a rade union which fixes he same nominal wage for all is members. There are differen rade unions for any ype of labour service. Therefore we label he rade unions wih he same index i. Given he nominal wage W ( i workers flexibly supply he amoun of labour o maximise heir welfare: kc ( i s P l( i s = W i The rade unions are monopolisic supplier of a given ype of labour service. We assume ha in any period each rade union has a consan probabiliy ( z ( W of signing a new wageconrac. Unil a new wage-conrac is signed he nominal wage is fixed. n he appendix we show ha solving he opimisaion problem of he represenaive rade union we have: W% ( j φ = τ = φ τ φ ( zwρ k( l( i W l( j = τ τ φ ( z ρ ( PC W l ( j W where φ > 0 is he elasiciy of subsiuion of labour l( i is he per capia demand of labour service of ype i and C is he per capia consumpion derived in he following secion. The marke power of he rade unions allows hem o se he nominal wages above he discouned sum of marginal coss. Once he nominal wage W % ( i is se he rade union fixes W ( i in τ 8

9 s order o saisfy in each period following consrain: l ( i = ( ι ι l ( i s s= 0. We assume ha he difference beween wha he rade union raises and wha i pays o is members hrough TR W ~ i W i l i. ( ( wages is hen redisribued o all members wih lump sum ransfers: ( ( = τ. 2 Aggregaing across individual consumers By assuming ha each cohor is of size when born a cohor of age τ ι. Therefore he oal size of he populaion is consan and equal o aggregae per capia money demand funcion is given by 7 : + r m = χ C P + r P The aggregae per capia consumpion is: + ιβ P ( ( + C = H F V + + χ r b r b m P where V is he aggregae per capia human wealh afer ax: s V = ( ι ι w ( s l ( s + div ( s T ( s + τ τ τ τ τ s= 0 = τ τ will have a size = τ ι =. The ι τ ( ι ( w( s l ( s + div ( s T ( s k = 0 ( + r τ + k.3 The firms problem Boh he inermediae good secor and he final good secor are populaed by a coninuum of firms producing differeniaed goods indexed by ih ( 0 and ( 0 h respecively. Consequenly we model each producer as a monopolisic compeior ha fixes is prices as a mark up over marginal coss. Moreover we assume ha firms can charge differen prices in 7 We can express all variables in erms of aggregae per capia as follows: consider he generic variable χ ( s hen χ ( ι ι s χ ( js = s= 0 9

10 he home and foreign markes. More precisely we adop he hypohesis of local currency price seing (LCP; in oher words firms se he prices of heir producs in he buyer s currency. Since inermediae good producers and final good producers face a very similar problem we describe in deail only he opimal choice of he represenaive inermediae good producer. The same procedure can be applied o solve he problem for he represenaive firm producing a final good..3. nermediae goods producers We assume ha a ypical inermediae good ( ih is produced using only domesic labour and a linear echnology: ( ih = Al ( ih where A is he home labour produciviy and l ( he following CES index: φ l ( ih = l( i ih φ di j= 0 ih is a composie labour facor defined by Consequenly he nominal marginal coss ( MC faced by he represenaive firm in he inermediae good secor are given by: where W MC = A W is he wage index defined consisenly wih he bundle of labour services: φ φ ( 0 W = W i di Following Chrisiano e al. (200 we assume ha only a fracion of he firms can reopimised in any given period. All he oher firms index imperfecly heir prices o he las period inflaion rae in he marke of heir producs. Define Γ as he degree of indexaion o i he pas inflaion in he domesic marke of home inermediae good. f we assume ha a ime a firm does no re-opimise he prices i charges in he home and foreign markes are respecively: φ φ z 0

11 H H p% ( ih = p% ( ih and p% ( ih = p% ( ih P P P H 2 Γ H θ θ where P ( H = P ih dih and ( H P P H 2 θ θ P = P ih dih are he price indexes of 0 0 domesic inermediae goods in counry H and F respecively. Then he flow of presen and fuure expeced profis ( E τ Π τ in counry H of he represenaive inermediae good producer is: θ ( ih ( ih W ( ih Eτ τ = z where ( ih p ( ih θ τ ϒ ϒ ϒ H H = τ k = 0 + rτ + k P P H PA P H Γ P H H % H P H τ ϒ = Γ H is he aggregae demand in counry H for bundles of home inermediae goods and θ > 0 is he elasiciy of subsiuion across home inermediae goods. Profis maximisaion leads o he following price choice for he home marke: p% τ ( ih θ = θ θ Γ H τ W θ P H z ( P H H = τ k = 0 + rτ+ k PA P H τ Γ ( θ H τ θ P H H z ( P H = τ k = 0 + rτ+ k P P H τ Similarly under he LCP assumpion he opimal choice for he foreign marke is: p% τ ( ih = θ θ ΓH τ W θ P H z ( P H H = τ k = 0 rτ k PA PH τ θ + + ( θ H Γ τ θ H P H z ε ( P H = τ k = 0 + rτ+ k P P τ H where H is he aggregae demand in counry F for home bundles of inermediae goods. We can wrie he price level of home inermediae goods in counry H as follows: Γ θ P H H = H + P H 2 ( ( % ( P z P h z p h θ θ

12 Similarly for he foreign marke we have: Γ θ H P H θ = ( ( ( H + % P z P ih z p ih P H 2 θ.3.2 Final good producers A firm producing final goods combines domesic and foreign inermediae goods and domesic labour services according o he following Cobb-Douglas producion funcion: α ( ( ( ( α [ ] ( β Y h = D BH BF Al where αβ ( 0 and D is he echnology used in he producion of final goods. β BH and BF are bundles of home and foreign inermediae defined by he following CES aggregaors: θ θ θ θ θ θ ( θ ( θ 0 0 BH = ih dih BF = if dif As in he previous secion we can derive he opimal prices ha a domesic final good producer charges in counry H and F respecively: p% τ ( h ( ( ( β ( ( β H F ( αβ α β Γ θ P P D W A τ θ P H zp PH YH τ k 0 rτ k ϑp P = = H τ θ + + = ( H θ θ Γ τ θ Y H P H zp ( PH = τ k = 0 + rτ+ k P P H τ H and p% τ ( h ( ( ( β ( ( β H F ( αβ α β Γ θ P P D W A τ θ P H zp PH YH τ k 0 rτ k ϑp P = = H τ θ + + = ( H θ θ Γ τ θ Y H P H zp ε ( PH = τ k = 0 + rτ+ k P P H τ H 2

13 where ( ( α β ( ( β ϑ = α α β β Γ H ( Γ H β. z p is he probabiliy of no re-opimising while is he degree of indexaion o he pas period inflaion in he home (foreign marke. Y H ( Y H is he aggregae per capia domesic (foreign demand of home bundles of final goods..4 Governmen We assume ha governmen in he domesic economy faces he following real budge consrain where ( g τ + + r b = b + m m P τ is he amoun of axes raises by he governmen g is he governmen s expendiure and b is he amoun of bonds issued by he governmen in period. For he sake of simpliciy we assume ha he baskes of goods purchased by he governmen replicae exacly he privae secor consumpion indexes. As explained above we assume ha he governmen follows a rule o mainain is real deb consan (i.e. b b [ τ P =. implies ha in each period he amoun of axes raised have o saisfy he following consrain: P τ = g + r b m m P.5 Demand side of he economy Before discussing he linearisaion of he model i is useful o specify he cos minimising demands for bundles of inermediae and final goods as well as he demand for labour..5. nermediae goods The represenaive final producer s demand for a domesic inermediae good ih is: ( P ih ( ih = H h P H 3 θ (

14 where ( H h is he demand of bundles of home inermediae goods of a ypical final good producer in counry H. Similarly he demand for he foreign inermediae good if is: ( P ( if θ ( if = F h P F The demand of bundles of domesic inermediae goods of he represenaive home final good producer ( ( H h is obained in wo seps solving he cos minimisaion problem of he final good. Firsly we derive he firm s demand for bundles of inermediae goods ( ( demand for boh home and foreign inpus: where: P = α ( ( ( α P P H F α α ( ( α α ( h ( β ( β β W β ( h w YH = ( β P A D w. Y ( H β h (i.e. he h is he aggregae per capia world demand of he a ypical home final good h. Then we can wrie he demand for bundles of home inermediae goods as follows: ( α ( α α P F h H ( h = α P H D negraing across domesic final good producers we obain: ( ( ( ( ( β α α β α α β α α = w R R Y ( ( ( ( ( β ( ( αβ β ( ( α β + β w H H F H α β A D w where H is he demand for bundles of home inermediae goods in counry H and Y H is he per capia world demand of home final goods bundles. We have also defined: R H PH = and P R F PF =. Similarly he foreign demand for bundles of home inermediae goods is: P ( ( ( ( β α β α α α ( ( ( ( β ( ( 2α 2 αβ+ β ( ( 2α+ αβ = w R R Y β + β α β A D α α β w H H F F 4

15 .5.2 Final goods The aggregae world demand for he final good h is described by he following equaion: Y where Y H ( H counry H and F respecively: θ ( ( θ Y P h ( h = Y P + h Y w H H H PH PH is he aggregae per capia demand for bundles of home final good in PH PH H = H + H = γ + γ P P Y C G C G P H P H H = H + H = ( γ + ( γ P H P H Y Y G C G negraing across domesic firms leads o: Y = Y + Y w H H H.5.3 Labour demand As well as he demand for inermediae goods he labour demand is obained from he cos minimisaion problem of he firms. Therefore he demand for labour service of ype j in he inermediae good ( l ( j is given by: l ( j W ( j φ H + H = W A The demand for labour service of ype k in he final good secor ( l ( l F ( k ( k φ β β w β P YH ( β w β W A D w = k is as follows: The aggregae labour demand for a ypical worker j ( l( j is simply he sum of he previous wo expressions: l ( k ( k w = + 5 φ β β w H + H β P YH ( β w A β W A D

16 The above equaion can be rewrien as follows: ( k β αβ β ( ( ( α β RH RF ( ( α β ( β α ( φ w H + H w l ( k = YH w A + α βα w A D 2. Calibraion n parameerising he model we assume a quarerly daa period and he parameers we choose are given in able (3 along wih he seady sae values hese imply. We do no disinguish beween he elasiciies of demand facing our imperfecly compeiive firms in inermediae and final good secors. The values we choose for θ and θ are aken from Gali e al. (200 and hey imply a price mark up of.. The quarerly discoun rae ρ is slighly lower han ha found in oher sudies (such as Kollman (998 or Roemberg and Woodford (998 for example. The reason for his is ha hese sudies assume infiniely lived consumers. Therefore he usual higher discoun rae is equivalen o an annual real ineres rae of around 3%. Since he overlapping generaion srucure of our model raises he real ineres rae his slighly lower rae of ime preference is consisen wih he same equilibrium real ineres rae found in lieraure. The parameer ι is he probabiliy of survival for our consumers and i implies an average working life of abou 35 years. This seems o be a plausible measure of average ime spen in employmen alhough i is admiedly a high probabiliy of deah if he model is aken lierally. Neverheless such a parameer is necessary o generae a plausible seady sae value of governmen deb relaively o GDP 8. The parameers z and z P are he probabiliies ha a firm in he inermediae good secor and in he final good secor respecively does no re-opimise prices in he nex quarer. The value of 0.66 is aken from Leih and Malley (2002 and i implies ha firms ake on average nine monhs o rese heir prices. They are also consisen wih he esimaes of Gali and Gerler (200. Leih and Malley (op. ci. provide also an esimae of probabiliy z w ha a new wage conrac is se in he nex quarer. The value of 0.74 implies an average lengh of wage conracs of abou one year. 8 This poin is also discussed in Leih and Wren-Lewis (2002. For a furher exploraion of his poin see also Faruqee e al (997 6

17 Finally he degree of indexaion o he pas period inflaion is se equal o 0.3. The value we choose imply ha in he hybrid New Keynesian Phillips curve he weighs associaed o he forward-looking componens and o backward looking componen are approximaely 0.76 and These values are consisen wih he esimaes of Leih and Malley (op. ci. and Gali and Gerler (op. ci.. The seady sae hese parameers imply are shown in able (2. The real ineres rae has an annualised value of 3% and he seady sae raio of deb o GDP is around 70% which is consisen wih he average level of deb in he euro area a he end of 2000 (ECB (200. The raio of governmen spending o GDP is 23%. This value is also consisen wih he daa repored by Gali (994 across OECD economies. Finally he seady sae values of he labour and inermediae good produciviy are chosen in order o obain a labour-income raio of abou 2/3 and a seady sae value of aggregae per capia labour supply equal o /2. 3. neres rae policy rules and shocks n his secion we briefly discuss he policy rules we consider in our policy experimens. n closed economy despie of is simpliciy a Taylor rule seems o provide he bes guidelines for a cenral bank if i aims o sabilise oupu gap and inflaion around rend and arge respecively. However he same degree of consensus has no been reached in open economy. n paricular open economy models arise he issue of wha measure of inflaion should ener a Taylor rule. n his paper we do no aim o specify he bes Taylor rule for our model. The relaive weighs ha oupu gap and inflaion should have in policy rules is sill objec of discussion even hough recen research has moved owards he emphasis of he role of inflaion volailiy in he cenral bank s loss funcion. Therefore he opimal soluion of he inflaion-oupu variabiliy rade-off requires he derivaion of a microfounded welfare funcion which is beyond he scope of his paper. Alhough a erm in oupu gap has o be inroduced in policy rules any choice a his poin would be arbirary. Therefore we have chosen o keep our policy rules as simpler as possible in order o emphasise he consequences of argeing differen measures of inflaion. n fac he properies of he policy rules we implemen do no depend on he choice of no include a erm in oupu gap. The policy rules we choose are repored in he able below: 7

18 i = a π + a π + a ε + a ε R R πh H π ε ε Rules α πη α π α ε α ε Policy rule ( simply arges he oupu price inflaion while policy rule (2 arges CP inflaion. Comparing he dynamics of inflaion and is variance under hese rules allow us o asses some general properies of argeing differen measure of inflaion. Rule (3 is used o rule ou he real exchange rae movemen as a main source of excess inflaion under oupu price inflaion as i will be clear when we discuss he effecs of a supply shock. n order o assess he properies of rules ha reac o movemen in he exchange rae we modify he naive inflaion argeing rules ( and (2 adding a erm for he level of he real exchange rae. Therefore rule (4 arges oupu price inflaion and he real exchange rae while nominal ineres raes in rule (5 respond o CP inflaion and he level of he real exchange rae. Rules (6 and (7 are similar o rules (4 and (5 bu we replace he level of he real exchange rae wih is firs differences. n his way we can conras he properies of hese wo differen ses of rules. n fac here is no consensus in lieraure on how he cenral bank should respond o movemens in he exchange rae. n seing parameers for policy rules (4 and (5 we follow Taylor (200 who claims ha an exchange rae appreciaion should induce he cenral bank o relax moneary policy. However he suggess wo differen ways in which cenral bank can reac o movemens in he exchange raes: in he firs case he cenral bank can adjus nominal ineres raes whenever he real exchange rae is differen from is seady sae equilibrium in he second case he cenral bank responds o changes in he real exchange rae. We consider he firs case wih policy rules (4 and (5 and he second one wih rules (6 and (7. Shocks We consider wo differen ypes of domesic shock. The firs is a negaive shock o home labour produciviy. We assume ha labour produciviy decreases of % for four quarers and 8

19 hen gradually reurns o is seady sae value. The second is a posiive shock o home privae secor s consumpion. Similarly we assume a shock of size % ha lass for one year. Therefore we can evaluae our policy rules under boh supply and demand shocks. 3. Domesic supply shock Before discussing he simulaion resuls of a shock o labour produciviy under differen policy rules i is imporan o esablish he general effecs of his supply shock in our model. Afer a negaive shock o domesic labour produciviy domesic firms in boh secors raise prices o proec heir profis agains he rise in real marginal coss; hey also increase heir demand of labour o offse he effecs of he decline in labour produciviy. The nominal ineres rae rises in response o he increase in he inflaion such ha he real raes rise. Obviously he exac magniude of he rise in he nominal ineres rae depends on he specific ineres rae policy followed by he cenral bank. Consumpion falls as a consequence of he rise in he real ineres rae and his helps o offse he effecs of he negaive supply shock on inflaion. However in he home economy he inflaion rises while oupu in boh secors falls. n conras in he foreign counry he rise in inflaion is accompanied by a rise in real GDP (deflaed by he oupu prices due o he improvemen in he erms of rade. The real exchange rae appreciaes because he response of he domesic moneary auhoriies is iniially more aggressive han he foreign response. The iniial appreciaion of he exchange rae has a negaive impac on he prices of impored goods and his furher offses he iniial inflaionary effecs due o he labour produciviy shock. n fac he real exchange rae appreciaion allows foreign exporers o charge relaively lower prices wihou reducing heir profis. However he subsequen depreciaion of he real exchange rae represens an addiional source of inflaion for he home economy. 3.. Targeing oupu price inflaion vs CP inflaion Under oupu price inflaion argeing he iniial appreciaion of he real exchange rae (fig.5 is followed by a promp depreciaion while under CP argeing he iniial appreciaion is much smaller and he following convergence o he seady sae is slower. The real exchange rae behaviour reflecs he dynamics of he gap beween home and foreign ineres raes 9

20 (fig.6. When he domesic shock occurs CP inflaion in he home counry is mosly due o oupu price inflaion. Similarly CP inflaion in he foreign counry largely reflecs he exporaion of his inflaion abroad. n oher words under oupu price inflaion argeing he iniial response of moneary auhoriies is relaively more aggressive in he home counry and less aggressive in he foreign counry. However excluding he firs quarer when he large appreciaion of he real exchange rae reduces he size of impored inflaion CP inflaion in he couny H is higher under oupu inflaion argeing. n conras CP inflaion in counry F is always higher under CP inflaion argeing afer he firs quarer (fig.. Furhermore in counry H oupu price inflaion is higher under oupu price inflaion han under CP inflaion argeing. The opposie order applies o counry F. The real exchange rae depreciaion soon afer is iniial appreciaion under oupu inflaion argeing does no seem o significanly affec inflaion dynamics alhough i conribues o he inflaionary consequences of he shock. nerpreing he resuls The explanaion of hese resuls lies in he dynamics of real marginal coss. The negaive labour produciviy shock dominaes all oher effecs in he home economy and implies ha he domesic firms marginal coss increase; bu hen he real marginal coss gradually reurn o he seady sae value as he effecs of he shock vanish. n conras in he foreign counry he iniial jump of he real marginal coss can be eiher posiive or negaive. For inermediae good producers he real marginal coss decrease because of he fall in foreign real wages. For a final-good producer hese effecs are offse by rises in prices of impored inermediae goods. As a consequence we observe ha real marginal coss rises for he foreign producers who sell heir good in counry F. However for he final good exporers who can benefi from he real exchange rae appreciaion he real marginal coss iniially fall. is imporan o noe ha he iniial gap beween oupu price inflaion and CP inflaion induces a rise in foreign firms real marginal coss. Therefore whaever is he direcion of he iniial jump foreign firms real marginal coss rise. This pushes he foreign producers o raise prices o proec heir profis agains he rise in he marginal coss. The whole sory can be beer undersood hrough an example Le s consider a firm in counry F ha produces an inermediae good and sell i in he is counry. The firm s coss are given by wages paid o foreign workers. Firms 20

21 deflae nominal wages by he price hey charge in foreign marke while workers evaluae real wages in erms of CP. The shock produces a fall in real wages and a rise in CP inflaion. Foreign workers increase nominal wages o proec heir real wages agains he CP inflaion. This urns ou in a rise in firms real marginal coss ha afer he iniial fall are pushed above he seady sae value. Firms reac o he increase in real marginal coss raising prices o proec heir profis. A similar explanaion also applies o he final good producers. n oher words we can anicipae ha in counry F he domesic inflaion is iniially lower han he impored inflaion bu his order is reversed afer few quarers (hree or four quarers depending on he policy rule. Similarly in he home counry domesic oupu inflaion is he main source of CP inflaion only a he beginning since impored inflaion becomes relaively more significan wihin four quarers. When in he home counry he moneary auhoriies arge oupu price inflaion producers anicipae ha afer he iniial aggressive response moneary policy in he home counry will be less resricive han under CP inflaion argeing. The opposie applies o he foreign counry. The forward looking behaviour of producers hen explains why domesic oupu inflaion and CP inflaion are higher in he home counry when oupu price inflaion is argeed and in he foreign counry when CP inflaion is argeed Rules ha include he real exchange rae n inroducing he real exchange rae erm in policy rules we aim o pursue wo differen resuls. Firsly we wan o esablish how imporan is he depreciaion of he exchange rae afer is iniial appreciaion o explain CP inflaion in home counry. Then we are ineresed in evaluaing wheher policy rules ha include he real exchange rae or changes in he real exchange rae perform beer han rule ha does no provide any explici role for he real exchange rae. nflaionary effecs of he real exchange rae depreciaion The firs experimen aims o evaluae he conribuion of he real exchange rae depreciaion in producing higher CP inflaion in home counry. A reasonable objecion o he differen oucomes in erms of CP inflaion when he moneary auhoriies arge oupu price inflaion raher han CP inflaion is ha mos of he excess inflaion comes from he real exchange rae 2

22 depreciaion afer is iniial appreciaion. Under policy rule (3 moneary auhoriies arge oupu price inflaion and he real exchange rae. We assume ha nominal ineres raes respond quie srongly o deviaions of he exchange rae from he seady sae (we se his parameer equal o. We obain a paern for he real exchange rae ha does no differ significanly from policy rule (2 in which nominal ineres raes respond only o CP inflaion. However CP inflaion under a policy rule (3 ha arges boh oupu price inflaion and he real exchange rae is similar o CP inflaion under a rule ha arges only oupu price inflaion. This allows us o rule ou he real exchange rae as he main source of CP inflaion even in he firs quarers afer he shock and o conclude ha he differen behaviour of inflaion depends on which inflaion rae moneary auhoriies choose o arge. Targeing he real exchange rae Policy rule (4 arges boh oupu price inflaion and he real exchange rae. Nominal ineres raes respond o domesic inflaion as in policy rule ( bu we have added an exra erm o arge also he real exchange rae. Similarly policy rule (5 differs from policy rule (2 since i arges boh CP inflaion and he real exchange rae raher han CP inflaion only. Our findings reveal ha policy rules ha explicily include he real exchange rae perform beer in reducing inflaion as long as he real exchange rae arge conribues o he ighening of moneary policy. n fac he variance of inflaion decreases in foreign counry where he exchange rae argeing implies a more aggressive response o he inflaionary effecs of he shock. n conras he variance of inflaion increases in home economy where he exchange rae sabilisaion requires a relaively less aggressive rise in nominal ineres rae. The rise in variance of inflaion in home counry reveals ha he easing in moneary policy dominaes he benefis coming from he real exchange rae sabilisaion Nominal ineres rae responding o changes in he real exchange rae Under policy rule (6 nominal ineres raes respond o oupu price inflaion and changes in he real exchange rae. This rule akes ino accoun more explicily ha afer an easing in moneary policy due o he real exchange rae appreciaion nominal ineres raes have o rise o offse he inflaionary consequences of he real exchange rae depreciaion. n oher words raher han arge he real exchange rae moneary auhoriies offse he addiional source of 22

23 inflaion due o he real exchange rae depreciaion. The CP inflaion variance under his rule is lower han under rules in which nominal ineres raes respond eiher o oupu price inflaion only ( or boh o oupu price inflaion and he real exchange rae levels (4. The reason of hese findings lies in he rise of nominal ineres raes which is more aggressive han under he oher wo policy rules. As explained above he exchange rae channel does no seem o represen a main source of inflaion. However responding o he exchange rae changes moneary auhoriies respond more aggressively o an inflaionary shock and his induces a fall in variance of inflaion. Finally wih policy rule (7 nominal ineres raes respond o CP inflaion and changes in he real exchange rae. Alhough he variance of inflaion under his rule is slighly lower he behaviour of CP inflaion does no differ significanly from policy rules ha arge CP inflaion alone (2. Our findings are consisen wih resuls of oher sudies. For example Taylor (999 finds ha a policy rule reacing o he exchange rae does no yield a greaer improvemen in performance. The main explanaion for his resul lies on he fac ha he iniial appreciaion of he real exchange rae is much smaller under CP inflaion argeing han under oupu price inflaion argeing. implies ha he subsequen depreciaion has negligible effecs on nominal ineres rae under his policy rule GDP volailiy Afer he labour produciviy shock he GDP falls in counry H (fig.3. Then a GDP sabilising policy requires a moneary expansion while he inflaionary consequences of he shock move he moneary auhoriies in he opposie direcion. Therefore afer a supply shock moneary auhoriies in home counry face a rade-off beween inflaion and oupu sabilisaion. As already explained in our paper we do no aim o calibrae an opimal moneary policy rule. However even he very simply rules we are considering provide some useful insighs. Policy rules ha arge oupu price inflaion imply a relaively aggressive moneary response when he shock occurs. However afer his iniial reacion moneary auhoriies are less aggressive agains inflaion han when hey arge CP inflaion. As a consequence GDP iniially falls more heavily under policy rules ha arge oupu price inflaion bu i also converges faser o is seady sae value. For example policy rule ( responding o oupu price inflaion alone produces he heavies iniial fall in home GDP which is however highes under his rule afer five quarers. The properies of hese differen rules in sabilising GDP derive from he combinaion of hese wo effecs. 23

24 3.2 Domesic demand shock Before discussing he effecs of a shock o domesic consumpion under differen policy rules i is useful o ouline he general implicaions of such a shock in he economy. A domesic real demand shock pushes up oupu; consequenly labour demand as well as real wages increase 9. The rise in real wages increases real marginal coss and induces firms o raise prices o proec heir profis. Under he se of rules we consider he moneary auhoriies in order o offse he inflaionary consequences of he shock raise nominal ineres rae such ha real ineres raes rise. Since during he shock consumers run down he holding of financial wealh when he shock passes privae secor consumpion falls below he seady sae level. Oupu falls below is seady sae level while inflaion is sill posiive because of he ineria in price adjusmens. Since moneary policy in he home counry is relaively more aggressive he real exchange rae appreciaes. The real exchange rae appreciaion raises he relaive price of home goods and his helps o offse he desabilising effecs of he shock. n he foreign counry oupu increases because of he rise in expors while consumpion iniially falls because of he rise in real ineres raes. n fac he excess demand for foreign goods and he rise in impored inflaion induces he foreign moneary auhoriies o raise ineres raes in order o offse he inflaionary consequences of he shock. The iniial fall in foreign consumpion helps o offse he inflaionary effecs of a rise in demand for foreign goods. However because of he increase in privae savings when he shock passes foreign consumpion rises above is seady sae level Targeing oupu price inflaion vs CP inflaion The main conclusions we have drawn for a supply shock are also valid for a shock o privae secor demand. When argeing oupu price inflaion (policy rule ( he moneary auhoriies iniially reac o he shock wih an aggressive moneary policy (fig.7. n he firs year real ineres raes are in fac higher under oupu price inflaion argeing han under CP inflaion argeing (policy rule (2. However he order is reversed afer his period. Nowihsanding he iniial aggressive moneary policy boh CP inflaion and domesic 9 The rise in real wages is easily explained in erms of labour-leisure choice. Since consumpion rises consumers wish o increase heir consumpion of leisure as well as goods. 24

25 inflaion are higher under oupu price inflaion argeing (fig. 2. n he very firs quarer CP inflaion is pracically idenical under hese wo rules because of he deflaionary effecs of he real exchange rae appreciaion. As in he case of a supply shock hese resuls can be undersood by considering he fac ha domesic oupu price inflaion is higher han impored inflaion only in he firs par of he shock. This order is reversed afer abou a year. Then forward looking producers anicipae ha argeing oupu price inflaion moneary policy carry ou a relaively less aggressive moneary policy even hough a he beginning hey seem o reac more srongly. nerpreing he resuls Once again he simples explanaion of hese resuls lies in he dynamics of marginal coss. n he home counry workers iniially raise real wages as a consequence of heir labour-leisure choice. When he shock passes and labour demand falls real wages and consequenly firms real marginal coss reurn gradually o heir seady sae values. ndeed he reurn o he seady sae is relaively fas since as explained above consumpion and labour demands fall below heir seady sae values. n he foreign counry afer he iniial jump real wages decrease. This is due he fac ha he consumers labour-leisure choice works in he opposie direcion such ha he fall in consumpion due o he rise in real ineres raes induces workers o reduce real wages. However when consumpion increases workers demand for higher real wages. n oher words workers behaviour iniially reduces he rise in foreign firms marginal coss before conribuing o he persisence of he inflaionary effecs of he shock Targeing he real exchange rae Under policy rule (4 nominal ineres raes respond o deviaions of oupu price inflaion and he real exchange rae from heir arges. n he home economy he variance of inflaion is lower han in case in which nominal ineres raes respond only o oupu price inflaion. However he fall in variance of inflaion does no come from he relaively less volaile exchange rae under policy rule (4. The real exchange rae afer an iniial appreciaion depreciaes wih respec o is seady sae value 0. Alhough less srong han he iniial 0 The depreciaion of he real exchange rae reflecs he financial condiions of he counries. Foreign consumers hold posiive financial asses and heir consumpion is above he seady sae value. Boh variables converge 25

26 appreciaion he real exchange rae depreciaion is more persisen. Therefore he real exchange rae argeing implies afer an iniial easing in domesic moneary policy a slower reurn of he nominal ineres rae o he seady sae value. n oher words he more aggressive moneary policy reduces he variance of inflaion in he home economy. is ineresing o noice ha in he foreign counry despie of he more aggressive rise in nominal ineres raes CP inflaion is always higher wih policy rules ha arge oupu price inflaion and he real exchange rae (4 han wih rules ( ha arge oupu price inflaion alone. This is explained considering he way in which opimal prices are se. n fac forward-looking producers anicipae ha he real exchange rae argeing will implies a relaively less aggressive moneary policy. However hese resuls are reversed when moneary auhoriies arge CP inflaion and he real exchange arge (policy rule (5. This resul is simply due o he fac ha he real exchange rae depreciaion is insignifican and herefore moneary policy does no induce expecaions of lower inflaion. Nominal ineres raes responding o changes in he exchange raes When nominal ineres raes respond o oupu price inflaion and o changes in he real exchange rae (policy rule (6 he variance of inflaion in he home economy is lower han when oupu price inflaion alone or boh oupu price inflaion and he level of he real exchange rae are argeed. As in he case of a supply shock responding o changes in he real exchange rae implies ha he moneary auhoriies carry ou a relaively more aggressive moneary policy. n fac afer he iniial appreciaion he real exchange rae rapidly depreciaes. Responding o changes in he real exchange rae nominal ineres raes rise. n conras he subsequen appreciaion of he real exchange rae is very slow and is impac on he nominal ineres rae is negligible. For similar reasons he variance of inflaion in foreign counry increases. The same inerpreaion and he same conclusions apply also o policy rule (7 under which he moneary auhoriies arge CP inflaion and respond o changes in he real exchange rae. slowly o heir seady sae value because of he overlapping generaion srucure. The opposie happens o home 26

27 3.2.3 GDP volailiy The variances of GDP due o posiive domesic demand shock (fig.4under differen policy rules can be inerpreed as in he case of a supply shock. However we should noe ha a demand shock does no raise an oupu inflaion sabilisaion rade-off. Boh oupu and inflaion increase afer he shock alhough he shock does no show any persisence on oupu while inflaion reurn slowly o is seady sae value. The variance of GDP in he home counry is minimised when policy rule (6 is implemened. As explained his rule implies he mos aggressive response of moneary policy o an inflaionary shock; since a demand shock move inflaion and oupu move in he same direcion his rule helps o sabilise GDP as well as inflaion. is also ineresing o noice ha he variance of GDP is slighly lower under policy rule ( han policy rule (2. n oher words a pure oupu price inflaion argeing produce a lower variance han when CP inflaion is argeed. The explanaion for his resuls lies on he fac ha he rise in real ineres rae under oupu price inflaion argeing is iniially more aggressive han under CP inflaion argeing. Alhough as explained his iniial moneary policy response is no sufficien o generae expecaion of lower fuure inflaion he rise in real ineres rae helps o offse he effec of he shock on oupu. n fac mos of he variabiliy in oupu is due o i iniial jumping when he shock occurs. When he shock passes oupu immediaely falls. Since under oupu price inflaion moneary policy is aggressive in he very firs par of he shock his helps o offse he iniial rise in oupu and reduce is variance. 4. Conclusions n his paper we have considered a wo-counry model. Each counry is characerised by several differen sources of nominal ineria: sluggish adjusmens in nominal wages in prices of domesic and foreign inermediae and final goods. Moreover we have broken down he hypohesis of complee exchange rae pass-hrough inroducing local currency price seing. Finally marke power allows firms in boh secors o price discriminae beween domesic and foreign markes. n his framework we have analysed he sabilising properies of differen inflaion argeing rules. Our findings reveal ha he variance of inflaion in he home counry consumers whose negaive financial asses posiion forces hem o save and pay back heir debs. 27