Frank Smets a and Raf Wouters b. European Central Bank, D Frankfurt am Main, GERMANY

Transcription

1 Forhcoming in Journal of Moneary Economics Openness, imperfec exchange rae pass-hrough and moneary policy Frank Smes a and Raf Wouers b a European enral Bank, D-63 Frankfur am Main, GERMANY b Naional Bank of Belgium, B- Brussels, BELGIUM Absrac This paper analyses he implicaions of imperfec exchange rae pass-hrough for opimal moneary policy in a linearised open-economy dynamic general equilibrium model calibraed o euro area daa. Imperfec exchange rae pass hrough is modelled by assuming sicky impor price behaviour. The degree of domesic and impor price sickiness is esimaed by reproducing he empirical idenified impulse response of a moneary policy and exchange rae shock condiional on he response of oupu, ne rade and he exchange rae. I is shown ha a cenral bank ha wans o minimise he resource coss of saggered price seing will aim a minimising a weighed average of domesic and impor price inflaion. Key words: moneary policy, open economies; exchange rae pass-hrough JEL: E58-F4 orresponding auhor: Frank Smes, Direcorae General Research, European enral Bank, D-63 Frankfur am Main, Germany; Telephone: ; Fax: ; frank.smes@ecb.in. This paper has been prepared for he 2 arnegie-rocheser onference on Public Policy. The views expressed are solely our own and do no necessarily reflec hose of he European enral Bank or he Naional Bank of Belgium. Frank.Smes@ecb.in and Rafael.Wouers@nbb.be. We hank Dale Henderson, our discussan, B. Mcallum, he edior, and seminar paricipans a Boson ollege, Harvard Universiy, Bonn Universiy and Humbold Universiy in Berlin for very useful commens. J:\Projecs\openraf\Open economy R JME.doc

2 . Inroducion Over he las six years a large lieraure (he so-called New Open Economy Macroeconomics, NOEM ) has developed examining he opimal conduc of moneary policy in a class of open-economy dynamic general equilibrium models ha feaure imperfec compeiion and nominal rigidiies. One of he models ha recenly has araced a lo of aenion is he one of Gali and Monacelli (2). This model combines he open economy feaures of he NOEM, wih he elegance of he benchmark New-Keynesian closed economy model as, for example, analysed in Woodford (999b). One of he sriking findings in Gali and Monacelli (2) is ha he welfare resuls obained in he basic New-Keynesian model carry over o is open economy counerpar. Welfare opimising moneary policy resuls in a complee sabilisaion of he domesic price level. In paricular, here is no rade off beween oupu gap sabilisaion and domesic price sabiliy and here is no need for an explici consideraion of he exchange rae. 2 This resul has proven o be relaively robus wih respec o cerain exensions of he model. For example, in a wo-counry se-up Benigno and Benigno (2) have shown ha a policy pursuing domesic price sabiliy can be considered as he opimal oucome in a Nash game beween he moneary auhoriies in wo counries. Similarly, Obsfeld and Rogoff (2b) have rejeced he necessiy of a new inernaional compac on he basis of he argumen ha policies geared a domesic price sabiliy deliver oucomes ha are close o he firs bes. In anoher exension, Benigno (2) shows ha achieving domesic price sabiliy coninues o characerise he opimal moneary policy when inernaional financial markes are incomplee. One feaure ha characerises all he models discussed above is he assumpion of perfec exchange rae pass-hrough. There is, however, a lo of empirical evidence ha changes in nominal exchange raes affec impor prices only gradually. Recenly, ampa and Goldberg (2) esimaed pass-hrough equaions for 25 OED counries over he period 975 o 999. They find ha hey can rejec he hypohesis of complee shor-run pass-hrough in 22 of he 25 counries. In conras, long-run elasiiciies are generally closer o one; ampa and Goldberg (2) rejec long-run pass-hrough equal o one in only 9 of he 25 counries. 3 Based on an empirical analysis of inernaional prices for wo magazines, Ghosh and Wolf (2) argue ha sicky prices or menu coss are a beer explanaion for imperfec pass-hrough han sraegic pricing or inernaional produc differeniaion. onsisenly wih he findings of ampa and Goldberg (2), hey find complee long-run pass-hrough, which ypically holds in heories based on sicky prices, bu does no hold in heories of inernaional produc differeniaion. 2 3 The seminal publicaions in he area are Obsfeld and Rogoff (995, 996). Oher noable conribuions include Bes and Devereux (997,998), Kollmann (2a,b), Gali and Monacelli (2), Ghironi (2a,b), Benigno and Benigno (2), hari, Kehoe and McGraan (2), Mcallum and Nelson (999), orsei and Peseni (2, 2). This lieraure parallels an abundan lieraure on opimal moneary policy in closed economy dynamic general equilibrium models. See, for example, he volume edied by Taylor (999). See Woodford (999b) for a clear and horough analysis of his resul. The seminal papers are King and Wolman (999), Goodfriend and King (997) and Roemberg and Woodford (997). Oher recen evidence on imperfec exchange rae pass-hrough can be found in Mcarhy (999). Page 2 of 32

3 In his paper, we explore he implicaions of sicky impor prices and imperfec exchange rae pass-hrough for opimal moneary policy. This is done in hree seps. In he firs sep, we develop a compleely microfounded model for an open economy wih sicky domesic and impor prices, which akes he inernaional ineres rae, prices and oupu as given. This model differs from he benchmark model in Gali and Monacelli (2) in wo imporan ways. Firs, as in Monacelli (999), we inroduce a monopolisically compeiive impor goods secor wih sicky prices. Firms in his secor impor a homogenous foreign good a a given world price and produce a differeniaed impor good for he domesic marke. Following alvo (983) and capuring he presence of menu coss, impor firms are only allowed o change heir price when hey receive a random price signal. In line wih he empirical evidence discussed above, he assumpion of sicky impor prices implies a gradual adjusmen of impor prices o he level implied by he law of one price. In addiion, following he suggesion by Mcallum and Nelson (2), we allow impored goods o be used boh in consumpion and producion. Second, following Ghironi (2b), we inroduce Blanchard- Yaari-ype overlapping generaions ino he Gali and Monacelli (2) model. 4 This allows us o derive a well-defined saionary seady-sae for consumpion, he erms of rade and ne foreign asses, around which he model can be linearised. I also allows for a poenially imporan role of he curren accoun and ne foreign asses in he dynamics of he economy, which we do no furher explore in his paper. 5 In he second sep, we calibrae a linearised version of he model using euro area daa. As our analysis focuses on he implicaions of imperfec pass-hrough for opimal moneary policy, our calibraion exercise concenraes on esimaing he degree of price sickiness in he domesic and impored goods secors. In order o do so, we use a new esimaion mehodology. Using a VAR on euro area daa, we esimae he effecs of a moneary policy shock on domesic and impor prices and on he hree variables ha drive hose prices: oupu, ne expors and he exchange rae. ondiional on he response of he hree driving variables and on oher srucural parameers of he model, we can hen esimae he degree of price sickiness in he domesic and impored goods secor by minimising a measure of he disance beween he empirical and he model-based impulse responses of domesic and impor price inflaion o he moneary policy shock. The resuls of his exercise sugges wo conclusions. Firs, here is a considerable degree of price sickiness in euro area impor prices, consisen wih he findings menioned above. Second, he degree of sickiness in impor prices is no significanly differen from ha in domesic prices. In he hird and final sep, we hen analyse he implicaions of sicky impor prices for opimal moneary policy in he calibraed model. We assume ha he cenral bank s mandae is o minimise he disorions ha arise from saggered price seing in he domesic and impored goods secor. Following Woodford (999b), we show ha he oupu cos of hese disorions is proporional o he relaive price variabiliy in he respecive secors, which in urn is proporional o he variance of price inflaion in ha secor. The resuling loss funcion can herefore be wrien as a weighed average of he variance of domesic and impor price inflaion, where he relaive weigh depends on he degree of openness of he economy (or he relaive 4 5 More specifically, we use he discree-ime version developed in Frenkel and Razin (987). For a horough discussion of his poin, see Ghironi (2b). Page 3 of 32

4 imporance of boh secors in consumpion and producion) and he relaive degree of price sickiness. As impor price inflaion will depend on he gap beween he sicky impor price and he foreign price denominaed in local currency, one imporan implicaion of his analysis is he inroducion of an explici reason for he sabilisaion of he nominal exchange rae in response o oher shocks han hose ha affec foreign prices. The reason is ha such movemens in he nominal exchange rae creae relaive price disorions in he impored goods secor. Anoher imporan implicaion is ha he combinaion of sicky domesic and impor prices makes he achievemen of he flexible price oucome no longer feasible, even if he cenral bank only cares abou domesic inflaion sabilisaion. The reason is ha imperfec exchange rae pass-hrough makes he exchange rae channel less effecive. As a resul more of he adjusmen needs o be born by he domesic ineres rae channel which primarily affecs domesic demand. These findings echo he analysis in Erceg, Henderson and Levin (2), who come o similar conclusions focusing on he radeoff beween he sabilisaion of sicky price and wage inflaion in a closed economy. We discuss he opimal policy response o a domesic produciviy shock, a world demand shock and an exchange rae shock. Overall, he resuls show ha an exclusive focus on he sabilisaion of domesic prices is no longer opimal, when impor prices are sicky and he exchange rae pass-hrough is gradual. A number of papers have analysed moneary policy behaviour in he presence of imperfec exchange rae pass-hrough. For example, Devereux and Engel (2) examine he implicaions of local currency pricing in he conex of he Obsfeld-Rogoff model and argue ha in conras o he findings of Obsfeld and Rogoff (2b) in his case opimal moneary policy in response o real shocks is fully consisen wih fixed exchange raes. Oher papers are Monacelli (999), Baini, Harrison and Millard (2), Devereux (2) and Adolfson (2). Those papers analyse he performance of simple moneary policy rules in he presence of imperfec exchange rae pass-hrough. However, hey do no consider he coss of imperfec pass-hrough and as such ignore he explici role for exchange rae sabilisaion ha i implies. This parly explains why he conclusions are someimes differen. For example, Devereux (2) finds ha a rule ha sabilises non-raded goods price inflaion performs he bes, in paricular when pass-hrough is limied. However, he welfare judgemen is based on an ad hoc examinaion of he volailiy of oupu, consumpion and inflaion. As we show in his paper, in he presence of sicky prices in boh he domesic and he impored goods secor, he response of oupu and consumpion will indeed be less han in he flexible price oucome when a produciviy shock his. However, his response is sub-opimal. Anoher example is Adolfson (2), who analyses he impac of incomplee exchange rae pass-hrough when he cenral bank minimises a sandard loss funcion in inflaion, he oupu gap and ineres rae changes. Adolfson (2) finds ha lower pass-hrough leads o higher exchange rae volailiy. However, also his resul depends on he fac ha exchange rae sabilisaion does no explicily ener he loss funcion. Our resuls are mos similar o hose obained by orsei and Peseni (2). In a model wih predeermined domesic and foreign prices based on orsei and Peseni (2), hey show ha he opimal policy is o minimise he expeced value of a PI-weighed average of mark-ups charged in he domesic marke by domesic and foreign producers. The reasons for doing so are differen from hose in our model. In orsei and Peseni (2), risk-averse producers respond o he variabiliy of profis from a specific marke by increasing he ex-ane price charged in ha marke. Policy makers can defend domesic Page 4 of 32

5 consumers welfare by commiing o sabilise producers profis around heir equilibrium flex-price level. orsei and Peseni (2) also find ha a low degree of pass-hrough severely consrains he abiliy of moneary policy o move he economy owards he flexible price allocaion. 6 The remainder of he paper is organised as follows. In Secion 2 we develop he heoreical model, derive is seady sae and a log-linearised version. In Secion 3, we derive and discuss he loss funcion of he cenral bank, which is based on a minimisaion of he resource cos of inefficien relaive price variabiliy in he domesic and impored goods secor. Secion 4 presens he calibraion of he model. We firs esimae a VAR using synheic euro area daa over he period This VAR is used o derive he empirical impulse response funcion of a moneary policy shock and an exchange rae shock on he euro area economy (Secion 4.). In Secion 4.2 he srucural parameers of he price seing processes are esimaed. Secion 5 analyses he opimal moneary policy response under discreion o a produciviy, world demand and exchange rae shock. Finally, we make some concluding remarks in Secion An open-economy model wih sicky domesic and impored goods prices In his secion, we develop a dynamic, micro-founded model for an open economy wih sicky domesic and impor prices ha akes he foreign ineres rae, prices and oupu as given. The domesic monopolisically compeiive goods marke is modelled as in he closed-economy models of Roemberg and Woodford (997) and larida, Gali and Gerler (999). The consumpion and savings decisions, on he oher hand, are derived along he lines of he discree-ime version of he Blanchard-Yaari overlapping-generaions model as developed by Frenkel and Razin (989). 7 Using an overlapping-generaions framework allows us o derive a saionary seady-sae for consumpion, he erms of rade and ne foreign asses in an economy which akes he world real ineres rae as given. 8 Imperfec exchange rae pass-hrough is modelled as he resul of sicky impor price seing raher han from an explici model of opimal price differeniaion Suherland (2) shows ha hese resuls are o some exen dependen on he linear specificaion of leisure in he uiliy funcion. See Blanchard (985). See, for example, Ghironi (2a) for an applicaion of he Blanchard-Yaari framework o an open economy wih price rigidiies. Alernaive approaches o obaining a saionary seady sae in a small open economy are discussed in Schmi-Grohe and Uribe (2). Page 5 of 32

6 2. onsumpion and labour supply decisions 2.. The households consumpion and labour supply decisions The objecive of he represenaive household of generaion i is o maximise he expeced uiliy flow derived from consumpion and from providing labour services: 9 ( i σ κ + ω ) ( i L ) j β j ϑ + = σ j j + ω + j where β is he discoun facor, ϑ is he consan probabiliy of households o survive, i () is he consumpion of he aggregae consumpion baske by household i, L i is he labour services provided by he household i, (/σ ) is he ineremporal elasiciy of subsiuion in consumpion and ω is he elasiciy of marginal disuiliy wih respec o labour supply. As in Frenkel and Razin (989), households have a finie life expecaion. A perfec insurance marke inheris consumers' financial wealh coningen on heir deah and redisribues his in proporion o financial wealh. As a resul he effecive cos of borrowing or reurns on savings relevan for individual decisions is muliplied by ϑ. Household i s ineremporal budge consrain is given by: i i e F B + = ( + * R ) ( + R ) ϑ [ e i F + i B + W i L D F P + Div + Div T ] i i (2) where B represen he holdings of domesic one-period governmen bonds issued on a discoun basis wih an ineres rae R, F denoe he holdings of one-period bonds issued by he res of he world in foreign currency wih an ineres rae, R *, Div D and Div F are respecively he dividends disribued by he domesic goods producers and he impor secor, T i is a lump-sum governmen ax. I is assumed ha inernaional markes are incomplee, i.e. here is no perfec inernaional risk sharing. Maximising he household s expeced uiliy flow wih respec o i, i L, i B and i F subjec o his budge consrain, gives he familiar firs-order condiions which can be expressed as he uncovered ineres rae pariy (UIRP) condiion and generaion i s consumpion Euler equaion and labour supply funcion: + R e = + + * R e i σ + + i = β P + ( ) R / P (3) (4) 9 For simpliciy, we do no analyse money demand which could be inroduced by puing money in he uiliy funcion. Given separabiliy, he resuling money demand funcion would be compleely recursive o he res of he model discussed. As we will evenually linearise he model, we analyse he model under he assumpion of cerainy equivalence and leave ou he expecaions operaors from he sar. Page 6 of 32

7 ω i ( L ) ( ) i σ W = (5) κ P i Using he UIRP condiion (3) and he following expressions for financial wealh ( A ), and human wealh i ( H ), i i i A = e F + B, (6) H i i j j i h j = k = h j R = + ϑ +, (7) ( + + k) where i h is oal household non-ineres income and defined as he budge consrain can be wrien as i i i [ h P A ] + R A + ϑ i i D F i h = W L + Div + Div T, i + =. (8) Solving equaion (8) forward and using equaion (4), consumpion of household i can also be wrien as a fracion of oal wealh: [ H A ] i i P = Φ + i where he propensiy o consume ou of wealh, defined as j σ = = ( + ) = + j Φ β + σ j j ϑ k RR k σ, () is consan over generaions and RR is he ex-ane real ineres rae, given by: RR = P ( + R ) + / P For logarihmic preferences he propensiy o consume is consan and equals βϑ. For more general isoelasic preferences i is a funcion of he expeced real reurn on financial wealh Aggregaion Aggregaing equaions (8) and (9) over he generaions alive a ime, yields he macro-economic consumpion and wealh equaions: [ H ] P = Φ + A (2) A + = ( + R )[ h P + A ], (3) from which he following macro-economic consumpion funcion can be derived (9) () An aggregae variable, X, is defined as X i i = ( ϑ ) ϑ X i=, where i refers o he generaion born a period -i. Page 7 of 32

8 Page 8 of 32 Φ + = P A RR / ) ( ) ( ϑ ϑ β σ, (4) Equaion (4) shows ha due o he overlapping-generaions naure of our model, aggregae consumpion is a funcion no only of expeced consumpion, bu also of he real sock of financial wealh. The ineres rae effec remains neverheless unchanged. In he remainder of he paper, we will assume ha he governmen deb B always equals zero in equilibrium. This implies ha in every period he governmen expendiures on subsidies o firms equal ne ransfers o households. Aggregaion of he labour supply equaion (5) yields he following relaionship: ( ) ( ) i i i P W L ω ω σ ω ϑ ϑ κ = = ) ( (5) In general, aggregae labour supply will depend on he disribuion of consumpion over he differen generaions and hus on he wealh disribuion. However, as in he seady sae ha we will describe below all generaions have zero ne foreign asses and as a resul he same seady sae consumpion, he linearised version of his expression will only depend on aggregae variables (see secion 2.4) The demand for domesic and impored goods The overall consumpion baske is a ES aggregae of he domesic and impor good bundles: ( ) ( ),, ) ( + = η η η η η η α α F D (6) where η is he elasiciy of subsiuion beween domesic and foreign goods and α deermines he seady sae share of impored goods in oal consumpion. The demand for he domesic and impored composie good derived from expendiure minimisaion is given by: 2 P P D D η α =,, ) ( (7) P P F F η α =,, (8) where he aggregae price index is defined as: ( ) ( ) η η η α α + =,, ) ( P P P F D (9) 2 Here we suppress he index i since he individual and aggregae demand equaions are idenical.

9 Each composie good is iself a bundle of differeniaed goods: θ θ θ = ι k, k, θ dι for k=d,f. (2) The elasiciy of subsiuion beween any wo differeniaed goods, θ, is assumed o be greaer han one. The demand for each differeniaed good ι is hen given by: Pk,, Pk, ι = ι θ k k, (2) where ( ) = ι θ θ Pk, Pk, dι (22) and ι P k, is he price of he differeniaed good for k=d,f. 2.2 Producion and price-seing decisions 2.2. Firms producing domesic goods In he domesic good producing secor, firm ι ransforms homogenous labour and he impor good bundle ino a differeniaed domesic oupu good. 3 Following a Leonief-echnology, he impored inermediae good is used in a fixed proporion, α Y, of oupu: Y ι D, ι υ L = min( α Y I, α ι F, Y ) (23) where υ is an aggregae produciviy shock and in producion: θ ( ) θ I = m I F, F, dm os minimisaion implies ha: ι ι ι υl I F, YD, = = αy αy I F, is an index over differeniaed impored goods used (24) (25) Nominal profis of firm ι are hen given by: 3 For a horough discussion of he imporance of allowing for inermediae impored inpus in open economy models, see Mcallum and Nelson (2). Page 9 of 32

10 ι ι Ξ P M ι H, = ( D, ) Y D, (26) where he marginal cos is a funcion of aggregae produciviy and he facor coss, he wage and he impor price. Moreover, he marginal cos is idenical across firms: W M, = ( α Y ) + αy PF. (27) υ The demand for good ι is he sum of demand by domesic consumers and he demand by he compeiive expor secor which bundles he differeniaed domesic goods ino a homogenous expor good: ι θ P ι ι ι* D, Y D, = D, + D, = D, + PD, [ X ] Following alvo (983), firms are no allowed o change heir prices unless hey receive a random pricechange signal. The probabiliy ha a given price can be re-opimised in any paricular period is consan and is given by ( ξ D ). Following hrisiano e al (2), prices of firms ha do no receive a price signal are imperfecly indexed o las period s inflaion rae in domesic good prices. The degree of indexaion is given by he parameer γ D ( γ D ). γ D ι PD, ι PD, = P D, (29) P D, 2 (28) Profi opimisaion by producers ha are allowed o re-opimise heir prices a ime resuls in he following firs-order condiion: j ξ ι j = j DY D j M θ j ( ) N k R, + + = + + k P D, = ( τ )( θ ) γ P j ξ ι D j, + j = j DY D j k ( R k ) + P, = + + D, Equaion (3) shows ha he new price se by firm ι, a ime, is a mark-up over he expeced fuure marginal coss. If prices are perfecly flexible ( ξ D = ), he mark-up is a consan and equal o θ. We will assume ha firms are subsidised (τ ) in such a way ha in seady sae he markup is zero. Wih sicky prices he mark-up becomes variable over ime when he economy is hi by ( τ )( θ ) exogenous shocks. D (3) The definiion of he price index in equaion (22) implies ha is law of moion is given by: θ γ,, ( ) N PD D D D P D, PD, 2 D θ ( ) ξ PD, = P + ξ ( ) θ (3) Page of 32

11 Aggregaing equaion (28) over he monopolisic domesic goods producers and using equaion (7) and he equivalen equaion for expored goods yields he overall domesic goods marke equilibrium equaion: η P D, Y D, = δ P, + ( α ) X, (32) P θ P ι where δ D, P, = dι is a measure of relaive price dispersion in he domesic good secor. Equaion PD, (32) illusraes he real resource cos of relaive price dispersion in he domesic goods secor. As he measure of relaive price dispersion will always be greaer han or equal o one (which is is seady-sae value when all prices of he differeniaed goods are equal) and rise wih he variance of domesic prices, i shows ha higher variabiliy implies ha for given aggregae oupu here will be less aggregae consumpion Firms imporing foreign goods The impor secor consiss of firms ha impor a homogenous good produced abroad and urn i ino a differeniaed impor good for he home marke using a linear producion echnology. As in he domesic good secor, impor firms are only allowed o change heir price in response o a change in he exchange rae or he foreign price when hey receive a random price-change signal. The consan probabiliy of receiving such a signal is ( ξf ). As before, we also assume ha prices of impor firms ha do no receive a price signal are indexed o las period s inflaion rae in impor goods prices. When an imporing firm m is allowed o change is impor price, i does so o opimise he presen discouned value of is profi flow subjec o he demand consrain: m θ m θ m P F P F,, Y F, = Y F, = F, + F, PF, PF, ( I ) For simpliciy, we assume he same elasiciy of subsiuion beween differeniaed goods in he domesic good and impor secor. As in he case of he domesic good producers, his resuls in an expression for he opimal seing of he new impor price: [ P e ] j ξ ι * j = j FY θ F j F j j ( ) N k R, +, + + = + + k P F, = ( τ )( θ ) γ P j ξ ι F j, + j = j F Y F j k ( R k ) + P, = + + F, Again we assume ha he subsidy rae, τ, is se such ha he mark-up is zero in seady sae. Wih flexible impor prices ( ξ F = ), he imporing firms simply se he domesic sales price equal o he marginal cos, which in urn equals he foreign currency price ranslaed in domesic currency: F (33) (34) Page of 32

12 * PF, = PF, e (35) This siuaion is equivalen o he radiional assumpion of Producer urrency Pricing (PP). Sicky impor prices lead o an imperfec pass-hrough of changes in he exchange rae and he foreign oupu price on impor prices. The aggregae domesic impor price becomes: F θ ( ) ξ PF, P = P + ( ξ ( P ) P γ θ F, F F, F ) F, 2 N F, θ (36) In order o preserve symmery, we also assume ha foreign impor firms use he domesic expor good o produce a differeniaed expor good for he foreign marke. The expor demand for he domesic good is given by: η P *, D * X = * (37) P F, where * is foreign consumpion and * P D, is he price of he composie expor good abroad. Wih perfec exchange rae pass-hrough, he foreign expor price equals he domesic price in foreign currency, P D *, = PD, e. Wih imperfec exchange rae pass-hrough due o sicky expor prices, he foreign expor price will adjus only gradually o deviaions from he law of one price. 2.3 The seady-sae analysis In his secion, we analyse he non-sochasic seady-sae of he model in which domesic and impor prices are sabilised. I is easy o show ha his seady-sae is also he flexible price non-sochasic seady sae. Below we will use his seady sae as he poin around which o linearise he model. Firs, assuming ha he foreign and domesic real ineres rae equal he inverse of he rae of ime preference ( β = RR ) and ha inflaion is sabilised a zero, he propensiy o consume ou of wealh is given by: σ Φ = ϑβ σ RR σ = ϑβ Using he aggregae consumpion equaion (4), he definiion of wealh and he law of moion for human wealh, seady-sae consumpion can be derived as a funcion of he seady-sae erms of rade ( T O T = P D P F ) and oupu:4 (38) H RR PF PD PF PD = Φ = Φ ( αy ) Y = ( αy ) Y, (39) P RR ϑ PD P PD P 4 Noe ha P D P is a monoonic posiive funcion of he erms of rade. When = α η, P D P = TOT. Page 2 of 32

13 The second equaliy follows from he fac ha in seady sae non-ineres income equals he seady sae wage bill, which in urn equals he seady sae value of oupu minus he value of impored inermediae goods. The las equaliy follows from he assumpion ha β = RR. In seady sae, higher poenial oupu and an improved erms of rade increase consumpion. The assumpion ha ha he real rade balance and he real ne foreign asse posiion are equal o zero in seady sae. β = RR also implies Nex, we examine he seady sae relaionship beween oupu and he erms of rade from he demand side. From equaion (32) and (37), he following seady-sae relaionship can be derived: η η PD PD * Y = ( α ) +. (4) P PF Using equaion (39), a negaive relaionship beween he seady-sae erms of rade and seady-sae oupu follows: η PD P F * Y = η ( )( P TO T ) D α αy P Finally, in order o characerise he seady-sae oupu and erms-of-rade, we also need o consider he supply side. In a seady sae wih consan prices, no sochasic shocks and an appropriae subsidy o producion, all prices se domesically will equal marginal cos. Moreover, he assumpion ha β = RR also implies ha consumpion will be equal across generaions. As a resul, in seady sae he labour supply equaion (5) will equal: ω σ W = κpl. (42) ombining his wih he aggregae producion funcion derived from (25), he seady sae versions of equaions (27) and (3), he expression for seady sae consumpion derived above, gives he following seady-sae supply equaion: ( α TO T ) + ω σ σ + ω υ P κy = D Y. (43) αy P In his open economy here are hree effecs of an increase in he erms of rade on he supply of domesic oupu. Firs, an increase in he price of domesic goods versus foreign goods has a direc negaive impac on he marginal cos as impored inermediae goods become cheaper. This has a posiive impac on seadysae oupu. Second, an increase in he price of domesic goods relaive o impored goods will also reduce producer wages for given consumpion wages and hereby reduce he real marginal cos. Also his effec on oupu is posiive. Third, an improvemen in he erms of rade also leads o increased consumpion hrough is posiive effec on real wealh. This reduces he marginal uiliy of an addiional uni of consumpion and leads workers o reduce heir supply of labour. This has a posiive effec on he marginal cos and a negaive one on oupu. The overall erms-of-rade effec will depend on he coefficien of relaive risk aversion. If σ >, hen he supply curve will have a negaive slope. However, i can also be shown ha he slope of (4) Page 3 of 32

14 he seady-sae supply curve will be seeper han ha of he seady-sae demand curve. Also noe ha an increase in produciviy (i.e. a rise in υ ) shifs he supply curve o he righ. If σ =, he supply curve is verical. In ha case, a permanen increase in world demand leads o an improvemen of he erms of rade, while oupu remains consan. A permanen increase in produciviy leads o a rise in oupu and a fall in he erms of rade. The seady-sae discussed in his secion characerises boh he seady sae under flexible prices and he one under sicky prices when inflaion is compleely sabilised. In wha follows we will analyse small deviaions around his seady sae. 2.4 The linearised open-economy model In his secion we linearise he model discussed in Secion around he seady sae discussed in Secion 2.3. In addiion, we normalise he seady sae erms of rade o be one. Linearisaion of equaion (3) yields he following uncovered ineres rae pariy condiion: eˆ * = eˆ ˆ ˆ + + R R, (44) where he las erm capures sochasic deviaions around he world real ineres rae. In he res of he paper, his shock will be inerpreed as a emporary change in he risk premium on domesic currency asses. Linearisaion of equaion () yields a version of he Fisher equaion: [ Pˆ Pˆ ] RRˆ = Rˆ + Around a seady sae wih β RR = and zero ne wealh, he linearisaion of he consumpion funcion yields: ˆ ˆ ˆ ( ϑ) ~ = RR Φa +, (46) σ ϑ where a~ = d ( A P ) is he deviaion of real ne foreign asses from seady sae as a percenage of seady sae consumpion. Variaions in he propensiy o consume are of second order around his seady sae and can herefore be negleced. The corresponding ne foreign asse accumulaion equaion is given by: ~ = ( + RR ) a~ + Yˆ ˆ ( Pˆ + e ) a +, (45) α + α + Y D. (47) αy The linearisaion of he aggregae labour supply funcion (5) and he producion funcion (25) yields: Wˆ = Pˆ + ωyˆ + σˆ ωυˆ (48) Subsiuing equaions (48) in he linearised domesic price seing equaions resul in he following expression for domesic price inflaion ( π ˆ ˆ ˆ D, = PD, PD, ): Page 4 of 32

15 πˆ D, β γ = D πˆ D, + + πˆ D, + βγ + βγ ( βξ )(ξ ξ ( + βγ ) D D D D [( (α )(α ))( P ˆ Pˆ ) ( α )(( ω + σ ) Yˆ σ ( Yˆ ˆ )) + ( α )( + ω) νˆ ] Y D, F, Y Domesic inflaion depends on pas and expeced fuure inflaion and he curren real marginal cos, which iself is a funcion of oupu, he rade balance, he price of impored inpus relaive o he price of domesic goods and he produciviy shock. When γ D =, his equaion revers o he sandard purely forwardlooking Phillips curve. In oher words, he degree of indexaion deermines how backward looking he inflaion process is. The elasiciy of inflaion wih respec o changes in he marginal cos depends mainly on he degree of price sickiness. Similarly, impor price inflaion ( π ˆ ˆ ˆ F, = PF, PF, ) is deermined by: β γ D D ( βξ ) )( ξ Y [ ˆ eˆ ] F F F ˆ F, = πˆ F, + + πˆ F, P F F F, + + βγ + βγ + βγ F ξf π ) (49), (5) where we have assumed ha he foreign price level is consan. Linearisaion of he goods marke equilibrium equaion yields: Yˆ = ηα ( α )( αy )( Pˆ D Pˆ F Y ˆ,, ) + ( α )(α ). (5) ( Y ( Y ) ) Pˆ * D ( ( )( Y )) ˆ * η α + α α, + α α Finally, he consumer price level is given by: Pˆ = ( α ) Pˆ + α Pˆ D, F, (52) Wih perfec exchange rae pass-hrough in he foreign marke, he foreign expor price will be equal o he domesic price in foreign currency: Pˆ * D, = Pˆ D, + eˆ. In he simulaions repored in Secion 5 we will assume imperfec exchange rae pass-hrough in foreign expor prices (in analogy wih he impored goods * * secor). In ha case expor price inflaion ( π ˆ, ˆ, ˆ X = PD PD, ) is given by: β γ ( βξ )(ξ [ Pˆ Pˆ eˆ ] F F F * ˆ X, = πˆ X, + + πˆ X, D, D, + βγ F + βγ F + βγ F ξf π Adding a policy reacion funcion for he nominal ineres rae closes he sysem. The linear model conaining equaions (45) o (53) can be furher reduced o a dynamic sysem in six variables: he real exchange rae, he erms of rade, consumpion, ne foreign asses, domesic price inflaion and impored price inflaion. The sochasics depends on hree exogenous shocks: a produciviy shock, a foreign demand shock and an exchange rae risk premium shock. Before discussing opimal moneary policy in he calibraed open economy model of Secion 4, i may be worh discussing he various ransmission channels of moneary policy in his economy. In he closed economy model of Roemberg and Woodford (997) he only channel of moneary policy is he ineremporal subsiuion effec of changes in he ineres rae on spending. This channel is also presened in ) (53) Page 5 of 32

16 his model. In he open-economy model discussed in his secion, here are addiional ransmission channels ha work hrough he effecs of changes in he exchange rae on he erms of rade. ombining equaions (49) and (5), one can show ha changes in he erms of rade have wo imporan effecs on real marginal cos and hus inflaion. Firs, an improvemen of he erms of rade will reduce boh domesic and foreign demand for domesically produced goods. This will have a negaive impac on domesic oupu and reduce he marginal cos of producing an addiional uni of oupu. The reducion in marginal cos will be refleced in a fall in domesic inflaion. Second, an improvemen in he erms of rade has a direc negaive effec on he real marginal cos hrough he price of impored inermediae goods and because i increases producer prices relaive o consumpion prices which affec he nominal cos of producing an addiional uni. The size of his effec will of course depend on he degree of openness of he economy. I is easy o show ha his effec is similar wheher impored goods are used as inermediae or final consumpion goods. Finally, changes in he erms of rade also have a wealh effec on consumpion which is enhanced hrough he effec on ne foreign asses. As can be seen from equaion (47), an improvemen in he erms of rade will lead o an accumulaion of ne foreign asses which ener he consumpion funcion because of he overlapping generaions srucure. Higher consumpion will in urn have a posiive impac on prices boh hrough is direc impac on labour supply and hrough is impac on he demand for domesic producs. When he ineremporal elasiciy of subsiuion is small enough, his effec may dominae he oher negaive erms of rade effecs. 3. The cenral bank s loss funcion In his secion we discuss he cenral bank s objecive funcion ha we will use o analyse opimal moneary policy. Raher han assuming he sandard quadraic loss funcion in inflaion and he oupu gap as is done in a large par of he lieraure on opimal moneary policy, we wan o relae he cenral bank s objecive funcion o he underlying model and he welfare of he consumers. Because of he overlapping generaions srucure a full-blown derivaion of he cenral bank s loss funcion from consumers uiliy as in Roemberg and Woodford (997) is raher complicaed. 5 We will herefore assume a more limied mandae for he cenral bank. In our model wih saggered prices in boh secors, boh domesic and impored price inflaion give rise o resource misallocaion across monopolisic compeiive secors ha are oherwise similar. We will assume ha he cenral bank aims a minimising hose disorions ha arise from inflaion. To derive he loss funcion of he cenral bank we proceed in hree seps. Firs, we firs derive a measure of he resource cos ha is due o relaive price variabiliy. Then we show ha hese resource coss are proporional o he variabiliy of prices in he monopolisic domesic and impor good secors. Finally, we relae he variabiliy of prices o he variance of inflaion and he change in inflaion as in Woodford (999), Seinsson (2) and Amao and Laubach (2). 5 For a derivaion of a welfare based loss funcion in a similar OLG model wihou sicky prices, see Ghironi (2c). Benigno (2) is an example of a full-blown welfare analysis in a wo-counry model. Page 6 of 32

17 In order o illusrae he resource cos of relaive price variabiliy, i is useful o sar from expression (6) for he aggregae consumpion bundle and relae he consumpion bundle o he real resource cos in erms of unis of oupu and ne impors ha are needed o produce i. This can be done by subsiuing he aggregaion of equaion (28) and (33) ino equaion (6). This yields: Y = ( α ) δd, where η η M X + α δ F, η η η η IF, θ θ i P i D, P δd, = di and F, δf, = di denoe he resource cos of relaive price P D, P F, variabiliy in he domesic and impored good secors respecively. Boh measures are one in seady sae, when all prices are sabilised and equal o he average price in he secor, and become greaer han one when individual prices deviae from he average price. Equaion (54) illusraes ha for given unis of oupu produced a home and foreign goods impored, aggregae consumpion will be higher, he lower hese measures of relaive price variabiliy. In wha follows, we will assume ha he cenral bank ries o minimise a weighed average of he resource coss due o relaive price variabiliy in he domesic and impored good secors. The relaive weigh is assumed o be proporional o he relaive elasiciy of aggregae consumpion wih respec o a change in he wo resource coss (δ ). Taking he derivaives of equaion (54) wih respec o evaluaing hem a he seady sae, he following elasiciies are derived: w D = and w F = α α + Y + α Y (54) δ D, and δ F, and. (55) The weighs depend solely on he parameers characerising he openness of he economy. The higher he share of impored goods in consumpion and in producion, he greaer he weigh on relaive price variabiliy in he impored good secor in he cenral bank s loss funcion. In he nex sep, we can link he resource cos δ o he variabiliy of relaive prices in he monopolisic secor by aking a second-order Taylor expansion around he seady sae. This yields: 2 i δ ˆ k, = ( + θ ) Var i Pˆ k, for k = D, F. (56) 2 A higher relaive price variabiliy increases he resource cos; by how much depends on he degree of monopolisic compeiion. The higher he degree of compeiion or he lower he marke power of firms (he lower he mark-up), he higher he resource cos. The inuiive reason for his is ha he higher he degree of subsiuabiliy beween differeniaed goods, he more demand and oupu will respond o changes in relaive prices ha arise from inflaion. As he efficien allocaion is one where equal quaniies of he differeniaed goods are produced and consumed, his is indicaive of a worse resource misallocaion. However, as we have assumed he same degree of subsiuabiliy beween differeniaed goods in he Page 7 of 32

18 domesic and impor secor, he degree of monopolisic compeiion will no feaure in he weighs a he end of his secion. Finally, following Woodford (999), Amao and Laubach (2) and Seinsson (2), we can relae he uncondiional variance of relaive prices in boh secors o he uncondiional variance of he inflaion rae and is change, as follows: i ξk ( γ k )( ξkγ k ) ξkγ k ( ξk ( γ k ) + ) Var i P k, = Varπk, + Var π 2 2 k, for k = D, F (57) ( ξk ) ( ξk ) Equaion (57) shows ha he weigh on inflaion in he domesic and impored goods secor will depend on he degree of price sickiness (ξ ) and he degree of price indexaion (γ ). A higher degree of price sickiness will increase he weigh on inflaion in ha secor. 6 The degree of price indexaion primarily deermines he relaive weigh of he level of inflaion as opposed o he change in he inflaion rae. Wihou indexaion, γ k =, only he variance of inflaion maers: i ξ Var k i P k, = Varπ 2 k,. (58) ( ξk ) Wih perfec indexaion o pas inflaion, γ k =, only he change in inflaion needs o be sabilised: i ξ Var k i P k, = Var π 2 k,. (59) ( ξk ) In summary, in he res of his paper we will assume ha he cenral bank minimises he following weighed average of he variance in inflaion and he change in inflaion in boh domesic price and impor price inflaion: [ w Varπ + w Var π ] αy L = wπ Varπ D, + w π Var π D, + α π F, π F, D D + (6) F F αy where he weighs are deermined by hose in equaion (57). 4. Empirical calibraion of he open-economy model In order o analyse he opimal policy response o he shocks affecing he economy, we need o calibrae he parameers of he model. Given ha he weighs in he objecive funcion of he cenral bank are crucially dependen on he parameers governing he domesic and impor inflaion process, we concenrae he empirical calibraion of he model on hese parameers. This calibraion is done on he basis of euro area macro-economic daa. In he lieraure, here are basically wo ways of esimaing he parameers of price sickiness ( ξ D, ξ F ) and indexaion ( γ D, γ F ) feauring in equaions (49) and (5). One way is due o Roemberg and 6 This resul was highlighed by Benigno (999), who argued ha argeing a weighed average of secoral inflaion where he weighs depend on he degree of price sickiness came close o achieving he firs-bes oucome. See also Benigno and Lopez- Salido (2) for an empirical applicaion o he euro area. Page 8 of 32

19 Woodford (997) and hrisiano e al (2) and consiss of esimaing he effecs of a moneary policy shock using an empirical mehodology such as idenified VARs and esimaing/calibraing a subse of he srucural parameers such ha he heoreical impulse responses mach as closely as possible he empirical ones. For example, using his mehodology, Roemberg and Woodford (997) calibrae he alvo parameer of price sickiness o be.66 in US daa. 7 One problem wih his mehodology is ha he esimaion of he parameers of ineres will depend on he full srucure of he model. This poin is highlighed by hrisiano e al (2). 8 These auhors show ha he esimaed degree of price sickiness crucially depends on how he real economy and in paricular he marginal cos is modelled. They show ha he esimaed degree of price sickiness falls quie considerably and is no significanly differen from zero if nominal wages are modelled as being sicky. Even allowing for sicky wages, he esimaed degree of price sickiness varies from.34 o.54 depending on how he res of he economy is modelled regarding habi formaion in consumpion, adjusmen coss in invesmen and variable capial uilisaion. As combining he open economy feaures of he model in his paper wih a realisic modelling of he persisence in he res of he economy is beyond he scope of his paper, using his mehodology in he curren model would naurally bias our esimaes upward. A second way of esimaing he price parameers is o esimae equaions (49) and (5) direcly using insrumenal variable echniques as in Gali and Gerler (2) and Sbordone (998). For example, using GMM mehods, Gali, Gerler and Lopez-Salido (2) find ha he degree of price sickiness in he euro area lies beween.79 and.92 depending on he specificaion of echnology. This mehodology works quie well for he pricing equaion esimaed in hose papers because under he assumpions of he model he real marginal cos can be measured by he wage share and is herefore direcly observable. However, under more general condiions his may no be he case. Moreover, for oher prices such as wages or impor prices, such a sraighforward empirical counerpar o he driving facors may no easily be found. In such a case, one needs o ake a sand on how o measure he unobservable variables ha ener he driving variables, such as, for example, preference shocks. For example, Sbordone (2) assumes ha preference shocks follow a random walk. Such an assumpion regarding he naure of he preference shock appears o be quie arbirary and is likely o affec he resuls considerably. In his paper we use a mehodology o calibrae he price parameers, which combines feaures of boh mehods. As in Roemberg and Woodford (997) and hrisiano e al (2), we use empirical impulse response funcions of domesic and impor price inflaion o a moneary policy shock o calibrae he sickiness parameers. However, as in Sbordone (2) we ake he process driving he fundamenal facors enering he pricing equaions as given. Tha is, in esimaing he sickiness parameers we ake he response of oupu, ne rade and he exchange rae as given and minimise he squared difference beween he implied heoreical response of domesic and impor price inflaion o he shock and is empirical counerpar. This mehodology alleviaes he criicism of he firs mehodology ha he esimaed sickiness will depend 7 8 In a previous version of his paper, we applied he same mehodology o an open economy model for he euro area. See Smes and Wouers (2). See also Dosey and King (2). Page 9 of 32

20 crucially on how he real side of he economy is modelled, by aking he response of he driving facors as given. I also alleviaes he difficulies of he second mehodology wih he idenificaion and measuremen of unobserved shocks, by doing he analysis condiional on an idenified srucural shock (in our case a moneary policy). Of course, his mehodology does no solve all problems. Firs, he resuls may depend on he idenificaion of he moneary policy shock. To check he sensiiviy we also examine he sensiiviy of he resuls o an alernaive exchange rae shock. Second, he form of he error-correcion erm ha appears in equaions (49) and (5) does depend on cerain assumpions regarding echnologies and preferences. The res of his secion repors he resuls of his calibraion exercise. In he nex subsecion, we esimae an unresriced VAR and discuss he idenificaion mehod for obaining he impulse response funcions of he wo srucural shocks: a moneary policy shock and an exchange rae shock. In Secion 4.2. we calibrae he model of Secion 2 and esimae he price sickiness parameers using he mehodology discussed above. 4.. A VAR model esimaed on synheic euro area daa From he hree pricing equaions, (49), (5) and (52), i is clear ha hree variables are driving he vecor of prices: oupu, ne rade and he exchange rae. In order o esimae he sickiness parameers, in a firs sep we herefore esimae a 6x6 VAR sysem for he euro area over he period 977: o 999:4 conaining real GDP, ne rade as a percenage of GDP, domesic PI inflaion, a shor-erm nominal ineres rae, he real effecive exchange rae (re ) and impor price inflaion. 9 The US-dollar 3-monh ineres rae, US GDP and PI-inflaion rae and world commodiy-prices ener he VAR as exogenous variables in order o conrol for world condiions. 2 As in much of he lieraure on he effecs of moneary policy using VARs (see, for example, hrisiano, Eichenbaum and Evans (999)), he impulse-response of he endogenous variables o a moneary policy shock and an exchange rae shock are idenified by using a holeski decomposiion. The implici idenifying assumpion is ha changes in moneary policy have only a lagged effec on oupu and domesic prices, bu may have an immediae impac on he exchange rae and herefore impor prices. The immediae impac effec of a moneary policy shock hrough impor prices on PI-inflaion is assumed o be negligible. The exchange rae shock is idenified as he shock o he exchange rae equaion. Inser Figure Esimaed response o a moneary policy shock (Euro area daa: ) 9 2 The synheic euro area variables are consruced in Fagan e al (2). One problem wih he impor price series is ha i also includes inra euro area rade which accouns for abou half of gross impors. This will end o bias he degree of price sickiness in impor prices upward. The VAR is esimaed wih quarerly dummies, bu wihou a ime rend. Two lags appear o be sufficien o make he residuals whie noise. Page 2 of 32

21 The empirical impulse responses for a moneary policy are given by he solid lines in Figure. The bounds represen wo imes he sandard error of a boosrap exercise. The esimaed impulse response funcions appear o broadly conform wih oher evidence on he ransmission mechanism in he euro area. 2 The effecs of he exchange rae shock are shown in Figure 2. Inser Figure 2 Esimaed response o an exchange rae shock (Euro area daa: ) Boh impulse responses conain significan informaion on how inflaion in impor and consumer prices reacs o he wo shocks. This informaion allows us o esimae he relaive sickiness in he heoreical price equaions, using he impulse responses of he oher macro-economic variables ha were idenified by he model as he driving forces behind he price dynamics Esimaing he price sickiness parameers In order o esimae he parameers ha deermine he sickiness of domesic and impored prices ( ξ D, ξf, γ D, γ F ), we firs need o calibrae he oher parameers ha appear in he pricing equaions (49) and (5): he labour supply elasiciy (ω ), he ineremporal elasiciy of subsiuion (σ ), he share of inermediae impors in producion ( α Y ), he share of impors in final consumpion ( α ) and he rae of ime preference ( β ). As in many oher papers, we calibrae he rae of ime preference o be equal o.99, which implies a 4 percen seady sae real ineres rae given he assumed quarerly frequency of he model. The share of oal impors in GDP ( α + α Y ) is calibraed o be approximaely equal o is hisorical average for he euro area, which is abou 5%. 22 In a recen paper, Mcallum and Nelson (2) have argued ha reaing impors as inermediae inpus raher han final consumpion goods improves he empirical fi (in paricular regarding he cross-correlaions beween he exchange rae and prices) of open economy models. As we do no have inpu/oupu daa ha allow us o deermine how much of he impors is used as an inermediae good in producion and how much is used for consumpion, we ake he assumpion ha all impors are used in inermediae producion as our benchmark (i.e. α = ). For he ineremporal elasiciy of subsiuion, we assume log uiliy, which implies an elasiciy of one. This elasiciy is close o he one esimaed by asares (2) on euro area daa on he basis of a srucural consumpion equaion. 23 The mos difficul parameer o calibrae is he elasiciy of labour supply. I is well known ha in models wihou sicky wages or oher fricions ha cause a slow and gradual response of he 2 22 See, for example, Peersman and Smes (2). This is also close o he number ha is obained when we include his parameer in he esimaion. 23 asares (2) esimaes an inverse elasiciy of subsiuion of.25. Page 2 of 32