Expectations and Exchange Rate Policy

Transcription

1 Rober M. La Follee School of Public Affairs a he Universiy of Wisconsin-Madison Working Paper Series La Follee School Working Paper No hp:// Expecaions and Exchange Rae Policy Michael B. Devereux Deparmen of Economics, Universiy of Briish Columbia Charles Engel La Follee School of Public Affairs, Universiy of Wisconsin-Madison, and he Naional Bureau of Economic Research Rober M. La Follee School of Public Affairs 225 Observaory Drive, Madison, Wisconsin Phone: / Fax: info@lafollee.wisc.edu / hp:// The La Follee School akes no sand on policy issues; opinions expressed wihin hese papers reflec he views of individual researchers and auhors.

2 Expecaions and Exchange Rae Policy Michael B. Devereux UBC Charles Engel Wisconsin January 2, 2006 Preliminary Draf Absrac Boh empirical evidence and heoreical discussion has long emphasized he impac of `news on exchange raes. In mos exchange rae models, he exchange rae acs as an asse price, and as such responds o news abou fuure reurns on asses. Bu he exchange rae also plays a role in deermining he relaive price of non-durable goods. In his paper we argue ha hese wo roles may conflic wih one anoher when nominal goods prices are sicky. If news abou fuure asse reurns causes movemens in curren exchange raes, hen when nominal prices are slow o adjus, his may cause changes in curren relaive goods prices ha have no efficiency raionale. In his sense, anicipaions of fuure shocks o fundamenals can cause curren exchange rae misalignmens. We ouline a series of models in which an opimal policy eliminaes news shocks on exchange raes.

3 Much of analysis of open economy macroeconomics in he pas 30 years has been buil on he foundaion ha exchange raes are asse prices and ha some goods prices adjus more slowly han asse prices. If his is rue, i means ha exchange raes wear wo has: They are asse prices ha deermine he relaive price of wo monies, bu hey also are imporan in deermining he relaive prices of goods in inernaional markes in he shor run. For example, if expor prices are sicky in he exporing currency, hen nominal exchange rae movemens direcly change he erms of rade. While of course he lieraure has recognized his dual role for exchange rae movemens, i has no recognized he implicaion for exchange-rae or moneary policy. Asse prices move primarily in response o news ha alers expecaions of he fuure. Mos exchange rae movemens in he shor run reflec changes in expecaions abou fuure moneary or real condiions. Bu fuure expecaions should no be he primary deerminan of he relaive price of nondurable goods. Those relaive prices ough o reflec curren levels of demand and supply. So, news ha causes nominal exchange raes o jump may have undesirable allocaional effecs as he news leads o inefficien changes in he relaive prices of goods. I may be ha conrolling exchange raes dampening heir response o news is an imporan objecive for moneary policy. The asse marke approach o exchange raes has long recognized ha exchange rae movemens are primarily driven by news ha changes expecaions. For example, he survey of he field by Frenkel and Mussa (985, p. 726) in he Handbook of Inernaional Economics saes: These facs sugges ha exchange raes should be viewed as prices of durable asses deermined in organized markes (like sock and commodiy exchanges) in which curren prices reflec he marke s expecaion concerning presen and fuure economic condiions relevan for deermining he appropriae values of hese durable asses, and in which price changes are 2

4 largely unpredicable and reflec primarily new informaion ha alers expecaions concerning hese presen and fuure economic condiions. In heir monograph, Foundaions of Inernaional Macroeconomics, Obsfeld and Rogoff (996, p. 529) sae One very imporan and quie robus insigh is ha he nominal exchange rae mus be viewed as an asse price. Like oher asses, he exchange rae depends on expecaions of fuure variables. A he same ime, a broad par of he lieraure has acceped, as Dornbusch (976, pp 6-62) pus i, he fac of differenial adjusmen speeds in goods and asse markes. Indeed, i was his difference in he speed of adjusmen ha led Milon Friedman (953, p. 65) o advocae for flexible exchange raes: If inernal prices were as flexible as exchange raes, i would make lile economic difference wheher adjusmens were brough abou by changes in exchange raes or equivalen changes in inernal prices. Bu his condiion is clearly no fulfilled A leas in he modern world, inernal prices are highly inflexible. Friedman s case for flexible exchange raes was derived, however, in a world in which capial flows were absen. In his world, he exchange rae would deermine he erms of rade, bu i was no forward looking and did no reflec expecaions of he fuure as would an asse price. Bu when he exchange rae changes are primarily driven by news, he erms of rade or oher inernaional prices may be badly misaligned in he shor run. The misalignmen of relaive prices is a he hear of he moneary policy analysis in modern macroeconomic models of inflaion argeing. Woodford (2003, p. 2-3) explains when prices are no consanly adjused, insabiliy of he general level of prices creaes discrepancies beween relaive prices owing o he absence of perfec synchronizaion in he adjusmen of he prices of differen goods. These relaive-price disorions lead in urn o an inefficien secoral allocaion of resources, even when he aggregae level of oupu is correc. 3

5 Here, we are focusing on possibly severe misalignmens in relaive prices, when large changes in exchange raes are caused by changes in expecaions. This disorion would no be presen if all goods prices changed flexibly. Then relaive prices would no be forced o incorporae hese expecaions effecs, and nominal goods prices would reac (efficienly) o news abou he fuure. To help focus he cenral idea of his paper, i is useful o make a lis of hings we are no saying:. We are no saying ha oher models of moneary policy in open economies have no modeled exchange raes as asse prices. They have. Bu all of hose models assume ha he only source of news abou he fuure is curren and pas shocks o he economy. Our cenral insigh is ha moneary policy mus reac o news ha moves exchange raes. In exising models, he only news ha his he marke is shocks o curren economic variables. By argeing curren economic variables in hose models, moneary policy does effecively arge he news. Bu in a realisic model, agens have many oher sources of informaion han simply shocks o curren macro aggregaes. Targeing he aggregaes does no achieve he goal of offseing he influence of news on relaive prices. Our model explicily allows agens o have informaion abou he fuure ha is differen han shocks o he curren level of macro variables. 2. We are no looking a differences in he informaion se of he marke and policy makers. While ha may be an ineresing area for sudy, i is no our primary concern. To make his clear, we model he marke and policy makers as having he same informaion. 3. The problem we have pinpoined is no one of excess volailiy in asse prices. We do no consruc a model in which here is noise or bubbles in asse prices. Insead, we model he exchange rae as he no-bubble soluion o a forward-looking difference equaion, so i is 4

6 modeled as an efficien, raional expecaions, presen discouned value of expeced fuure fundamenals. Indeed, as Wes (988) has demonsraed, he more news he marke has, he smaller he variance of innovaions in he exchange rae. Noneheless, i is he influence of ha news on exchange raes ha concerns us. Our inuiion is ha movemens in nominal exchange raes caused by noise or bubbles would also be inefficien, bu we purposely pu aside ha issue for ohers o sudy. 4. We are no saying ha exchange raes are he only asse price ha could be of concern o policy makers. We have no invesigaed oher asse prices, such as equiy prices. Bu our inuiion is ha exchange raes are differen. Exchange raes are he only asse price whose movemen direcly causes a change in he relaive price of wo non-durables ha have fixed nominal prices. Tha happens because nominal prices of differen goods (or he same good sold in differen locaions) can be sicky in differen currencies. Flucuaions in oher asse prices cause a change in he price of a durable (e.g., equiy prices are he price of capial) relaive o he price of a non-durable. A leas in some circumsances, ha flucuaion is no a concern of moneary policy. As Woodford (2003, p. 3) explains, Large movemens in frequenly adjused prices and sock prices are among he mos flexible can insead be allowed wih ou raising such concerns, and if allowing hem o move makes possible greaer sabiliy of he sicky prices, such insabiliy of flexible prices is desirable. 5. Our concerns abou how news influences exchange raes and affecs relaive goods prices does no depend on wheher inernaionally raded goods prices are se in he producers currencies (PCP) or he consumers currencies (LCP). Some of our earlier work (Devereux and Engel, 2003, 2004) has focused on ha issue, in models where news was no imporan. Bu we se aside ha dispue here. If here is PCP, hen nominal exchange rae changes (arising from 5

7 news of he fuure) can lead o inefficien changes in he erms of rade. If here is LCP, hese nominal exchange rae changes lead o inefficien deviaions from he law of one price. 6. We are no saying ha a policy of fixed nominal exchange raes is opimal. Firs of all, in response o radiional conemporaneous disurbances (non-news shocks), exchange rae adjusmen may be desirable. Bu even wih news shocks alone, our resuls generally say no necessarily ha exchange raes should be fixed, bu ha unanicipaed movemens in exchange raes should be eliminaed. In fac, anicipaed movemens in exchange raes may play a vial role in faciliaing relaive price movemens afer a news shock. In general, our poin is ha news shocks can lead o relaive price disorions ha are ranslaed hrough exchange rae changes, and hese shocks should be a arge of policy. Technically, our model is exceedingly simple. The cenral idea is based on he propery ha efficien relaive prices of non-durable goods depend only on curren fundamenals, and should no be direcly linked o news abou fuure fundamenals. This propery is saisfied in mos recen general equilibrium exchange rae models. In fac, he cleares saemen of independence of curren allocaions on fuure fundamenals is in Barro and King (984). They show ha in general equilibrium models wih ime-addiive uiliy and absening invesmen, curren (efficien) equilibrium allocaions are independen of expecaions abou fuure fundamenals. This resul exends o an open economy where markes are sufficienly complee o suppor a ime-invarian risk sharing rule. Bu, in he presence of sicky nominal prices, his dichoomy beween curren allocaions and fuure fundamenals no longer necessarily holds. When prices canno adjus, any news shocks ha affec he curren exchange rae auomaically affec relaive prices. Bu in general, his is inefficien, and he moneary auhoriy should ake acion o dampen or eliminae he impac of news shocks on curren allocaions. 6

8 Secion presens some empirical evidence on he imporance of news in moving exchange raes. Secion 2 hen explains in a general conex why prices of nondurables should no ac like asse prices and reflec expecaions of fuure fundamenals. The res of he paper demonsraes he logic of argeing shocks o exchange raes caused by news in wo differen models. Secion 3 describes he firs model, in which prices are pre-se one period in advance, and can fully adjus afer one period. In his model, we find ha an opimal moneary policy in face of news shocks is o mainain a fixed exchange rae. Secion 4 hen exends he model o allow gradual price adjusmen. The exended model no longer calls for a fixed exchange rae, bu implies ha an opimal moneary rule eliminaes he impac of news shocks on he exchange rae. In secion 5, we build a more realisic model wih invesmen. Opimal invesmen decisions are forward looking, so in his model i is no longer sricly rue ha curren relaive goods prices should no depend on fuure produciviy shocks. Noneheless, under sandard parameerizaions, our conclusions are no alered opimal moneary policy should no only arge inflaion bu also ry o eliminae he effec of news on exchange raes. Secion. Empirical Evidence on he Effec of Expecaions on Exchange-Rae Volailiy Several recen empirical papers have emphasized he role of news in driving exchange raes. Engel and Wes (2005) demonsrae ha sandard exchange rae models do no in fac imply ha exchange rae changes should be predicable using curren values of fundamenal variables, or even necessarily srongly correlaed wih conemporaneous changes in fundamenals. Insead, hey show ha a esable hypohesis of he models is ha he news ha is incorporaed in exchange raes should help he exchange rae forecas fuure macroeconomic variables. They find empirical evidence o suppor ha posiion. 7

9 Andersen, e. al. (2003) use six years ( ) of real-ime quoaions from he foreign exchange marke o assess he impac of macroeconomic news on exchange raes. They measure news as he difference beween announced values of macro variables (payroll employmen, rade balance, reail sales, ec.) and a survey measure of he marke s expecaion of hese announcemens. They find ha exchange raes reac significanly o hese announcemens, and over 5-minue windows, a simple OLS regression of he exchange rae on he news yields high R 2 values: ofen around 0.3 and someimes approaching 0.6. While he emphasis in Andersen, e. al. is on he shor-run influence of news on exchange raes, Faus, e. al. (2005) use real-ime daa and informaion from he erm srucure of ineres raes o examine how news announcemen affec expecaions of long-run exchange rae changes. They find ha news announcemens abou U.S. real or nominal aciviy move exchange raes and also influence longer-erm ineres raes, wih he maximum effec 2-years. They argue ha he effec on longerm raes migh reflec he response of long-run changes in expeced currency depreciaion. Here we provide some alernaive evidence on he effec of changes in expecaions on exchange raes. In paricular, we consider models in which he exchange rae can be expressed as a presen discouned value of curren and fuure fundamenals. The log of he exchange rae is deermined by: (.) Here, j I + j j= 0 x = ( b) b E( f I ) 0< b <. f measures he economic fundamenals ha drive he log of he exchange rae. The discoun facor is b. (.2) I represens he informaion se of agens. I is helpful o rewrie his as: x f ( b) b E( f f I ). = + j I + j j= Our models sugges ha moneary policy should have as one objecive he sabilizaion of 8

10 innovaions (unexpeced changes) in he second erm on he righ-hand-side of equaion (2). Tha is, moneary policy should work o offse he effecs of news shocks on exchange raes ha work hrough unexpeced changes in fuure fundamenals relaive o he curren fundamenal. How imporan is his second erm in driving exchange rae innovaions relaive o he effec of innovaions in he curren fundamenal? We would like o know how much of he variance of unexpeced changes in x I can be aribued o innovaions in he curren fundamenals, f. Tha is, we would like o calculae var( f E( f I )) (.3) η. var( x E( x I )) I I Our premise is ha innovaions in curren fundamenals do no conribue much o he variance in he innovaions in x I. We believe ha i is mosly news abou fuure fundamenals ha causes variaion in x I. If our hypohesis is correc, hen η should be small. However, i seems hopeless o measure he variances in he numeraor and denominaor of equaion (.3), because we do no have he informaion available o he marke in forming is expecaions. We can calculae a measure of he expeced discouned sum of curren and fuure fundamenals based on he informaion se available o he economerician,. Define H (.4) j H + j j= 0 x = ( b) b E( f H ). Bu as Wes (988) shows, we can only consruc upper bounds for he variances in equaion (.3). Tha is, from Wes, we have var( f E( f I )) < var( f E( f H )) var( x E( x I )) < var( x E( x H )). I I I I Having an upper bound on boh he numeraor and he denominaor does no help us even 9

11 esablish an upper bound on η. We could follow he mehod of Campbell and Shiller (987), and impose ha he log of he exchange rae exacly equals x I. Their mehods hen allow one o exrac he relevan informaion in I because ha informaion is refleced in exchange rae movemens. Bu as Engel and Wes (2005) argue, ha approach requires ha we have measures of all he relevan fundamenals ha drive he exchange rae. While one migh plausibly argue ha he fundamenals for some asse prices such as equiies are compleely observable ex pos (ha is, dividends are observable), i is much less plausible o asser ha we can observe all he fundamenals ha drive exchange raes, which include such variables as money demand shocks, produciviy shocks, ec. If he fundamenals are no ex pos observable, we canno apply he procedures of Campbell and Shiller (987). We can, however, rely on a resul of Engel and Wes (2004) o ge a measure of he denominaor of η from equaion (.3). They show ha as he discoun facor ges large ( b ), he economerician s measure of he variance of innovaions in he presen value is approximaely equal o he variance based on he marke s informaion se: var( x E( x I )) var( x E( x H )). I I I I Even hough he economerician canno replicae he informaion se of he marke, he can accuraely measure he variance of he innovaion in he discouned sum when he discoun facor is large. Engel and Wes show ha in pracice he discoun facors implied by common empirical models are large enough ha he approximaion is a good one. Engel and Wes (2004) proceed o show ha he volailiy of innovaions in he acual exchange rae is approximaely wice he size of var( xi E( xi H )) for U.S. exchange raes 0

12 relaive o oher G7 counries using wo familiar models of exchange raes. The firs is a moneary model, in which he observed fundamenal is measured as f = m y ( m y ), he log of he money/oupu raio in he U.S. relaive o anoher counry. The fundamenals in his model correspond approximaely o hose in our model in secion 3. The second is a model based on a Taylor rule for moneary policy, in which he fundamenal can be wrien as eiher f = p p, he difference in he log of U.S. versus foreign-counry prices, or f = p p + ( i i ), he sum of he log of he price level and he ineres rae in he U.S. relaive o anoher counry. Engel and Wes (2005) demonsrae how hese fundamenals are derived from he underlying model. These fundamenals correspond o he ones in our model in secions 4 and 5. The fac ha exchange raes innovaions are more volaile han innovaions in he discouned sum of curren and expeced fuure fundamenals indicaes eiher ha here are fundamenals ha are no included, or ha exchange raes may be driven by non-fundamenal sources. Our objecive here is no o ask wheher economic fundamenals from radiional models can accoun for exchange rae volailiy. Insead, we ake he models as given, and simply ry o measure η. Using he Engel-Wes heorem, we can approximaely calculae he variance in he denominaor of equaion (.3). As we have noed, we can calculae an upper bound on he variance in he numeraor, and hence can calculae an upper bound for η. Table repors our measure of η for he fundamenals considered by Engel and Wes (2004), for various values of he discoun facor, b. In calculaing hese saisics, we ake he economerician s informaion se o be only curren and lagged values of he fundamenals, f. Engel and Wes (2004) rely on a resul of Engel and Wes (2005) o show ha innovaions in he log of he exchange rae can be measured approximaely by change in he log of he exchange rae when he discoun facor is near one.

13 We esimae an auoregression wih four lags (in all cases) on each measure of he fundamenals. From hese, we calculae our esimaes of var( f E( f H )) and var( xi E( xi H )). We use he same daa used in Engel and Wes (2004, 2005). I is quarerly daa, 973:- 2003:. 2 The US is he home counry, and we measure he fundamenals relaive o he oher G7 counries. The money supplies are seasonally adjused M (excep for UK, for which we use M4) from he OECD Main Economic Indicaors. The US money supply daa is correced for sweeps, as described in Engel and Wes (2004), using daa from he Federal Reserve Bank of S. Louis. We use seasonally adjused GDP from he same source (excep for Germany, which combines daa from he IMF s Inernaional Financial Saisics (IFS) wih he OECD daa.) The ineres raes are 3-monh Eurocurrency reurns aken from Daasream. The consumer prices are from he IFS. While he esimaed value of η varies from counry o counry, ypically we find ha i is around More precisely, he average across all counries and all measures of he fundamenals, in he case of b = 0.99 is The average is slighly higher for lower values of b and lower for higher values of b. Tha is, mos of he surprise movemen in he discouned sum ha is supposed o deermine exchange raes comes from innovaions in expeced fuure values of fundamenals raher han unexpeced changes in curren values. I is imporan o noe ha he upper bounds for η repored in Table migh be crude upper bounds. Tha is, innovaions in he curren fundamenals migh conribue much less o innovaions in x I han he numbers repored in his Table. For example, during 2005, he Federal Reserve raised he Fed Funds rae by 25 basis poins all seven imes ha he FOMC has me (so far.) Fed Funds fuures indicaed before each meeing ha here was virual cerainy 2 In a few cases, he ime span differs because of daa availabiliy. See Engel and Wes (2005) for daa spans. 2

14 ha he Fed would raise raes. Tha is, here was essenially no innovaion in he curren fundamenal he ineres rae on he FOMC meeing days. Bu clearly he Fed s policy decisions are imporan for exchange raes, and ha is refleced in movemens in he exchange raes on hose FOMC days. The exchange rae, however, was no changing because of any surprise in he curren fundamenal. The news ha hi he marke came in he announcemens of he Fed s assessmen of marke condiions, which in urn impared news abou fuure ineres rae changes. Our measure of he variance in he innovaions in he curren fundamenal, var( f E( f H )), is a crude one because he marke uses much more informaion han four quarerly lags of he fundamenals o form is expecaions. For example, i does no even use he Fed funds fuure raes o help capure he marke s informaion abou fuure ineres raes, and so we end o overesimae he variance of innovaions in curren fundamenals. Secion 2. A General Resul The echnical resul of he paper ress on an insigh ino dynamic general equilibrium models firs discussed by Barro and King (984). In a closed economy model wih ime-addiive uiliy and wihou endogenous invesmen, hey show ha all real allocaions and relaive prices are deermined solely by conemporaneous fundamenals. Tha is, here are no inrinsic ineremporal links beween periods, and no persisence in he effecs of shocks, apar from ha due o persisence in he shocks hemselves. An equilibrium allocaion in heir model is Pareo efficien, since here is a represenaive individual and all prices are fully flexible. I follows ha, in an economy wih sicky prices, if an opimal moneary policy is designed o replicae he flexible price equilibrium, i should insulae curren allocaions and relaive prices agains shocks ha come in he form of announcemens abou fuure fundamenals. 3

15 We develop his basic inuiion wihin he sandard wo-counry environmen of recen open economy macroeconomic models. We firs se ou a general version of he model, o illusrae he logic of Barro and King wihin our framework. We hen apply his model o wo paricular ypes of price seing environmens one where prices are pre-se one period ahead, for jus one period, and hen o an environmen of Calvo-ype saggered pricing. In each case, we idenify one or more opimal moneary policy rules o deal wih news shocks. Alhough he analyical resuls rely on he sric separaion across periods, we do no argue ha i be aken lierally. There are a number of facors ha give rise o efficien links beween curren allocaions or relaive prices and fuure fundamenals shocks. One obvious channel is invesmen. Bu we argue ha even once we allow for his linkage, our cenral resul, ha he curren exchange rae response o announcemens abou fuure fundamenals should be dampened, will sill hold in a quaniaive sense. An exension of he model o allow for endogenous invesmen esablishes his poin. The Basic Model Take a general example of an open economy macro model. Say ha here are wo equally sized counries: home and foreign, where in each counry, he measure of households is normalized o one. In each counry, households maximize expeced lifeime uiliy aking prices and wages as given. Households consume raded goods, consiuing a mix of home and foreign goods, and a non-raded good, produced and consumed only in he domesic counry. Firms are monopolisic and maximize uiliy for heir owners. Say ha consumer preferences are: ϒ= E, 0< β <, 0 = 0 β υ where υ = UC (, L) + VM ( / P ), wih U > 0, U2 < 0, U < 0, U22 < 0. Here C represens aggregae consumpion, L is labor supply, and M / P are real money balances. Aggregae 4

16 consumpion C is a funcion of non-raded consumpion and raded consumpion; C = C( C, C ). Traded consumpion is also a funcion of home and foreign raded good N T consumpion; C = C( C, C ). Each funcion is homogenous of degree, and each argumen of T H F hese funcions is a homogenous of degree funcion of a coninuum of differeniaed individual goods, wih consan elasiciy of subsiuion λ across varieies. The price index P reflecs he weighs implied by he consumpion aggregaor, and P= P( P, P ) = P( P, P ( P, P )), where N T N T H F again each funcion is homogenous of degree. Firms are monopolisic compeiors, and se prices as a markup over marginal cos. Assume firs ha all prices are fully flexible. In addiion, le he producion echnologies of ypical firms in he raded and non-raded secors of he economy be (ignoring firm specific noaion): Y = θ L, Y = θ L. N N H H Thus, here is a common echnology shock o boh secors, and he only inpu o producion is labor. Finally, we assume ha here exiss a full se of sae coningen asses for sharing consumpion risk across counries. There is only one ype of fundamenal shock in his model, a shock o he counry specific echnologies. Bu he argumen may be easily generalized o oher shocks. I is sraighforward o show ha he equilibrium of his economy, where all households wihin a counry and all firms wihin a secor are idenical, may be represened by he following condiions (leing foreign variables be denoed wih an aserisk). PH λ U( C, L) θ (2.) =, P λ U ( C, ) (2.2) θ L = P (, ) P P C, N N T 2 L 5

17 (2.3) (2.4) θ L = P( P, P ) P ( P, P ) C + P ( P, P ) P ( P, P ) C, H N T T H F N T T H F SP U( C, L) =Λ U( C, L). P Equaion (2.) relaes he equilibrium real price for home goods o he price-cos markup imes he firm s marginal cos, represened by he raio of he real wage o he echnology variable. Since non-raded and raded goods share he same echnology, and labor is mobile across secors, his condiion is he same for boh secors (so ha PN = P ). Equaions (2.2) and (2.3) represen H marke clearing in he home non-raded and raded goods marke, respecively, where he noaion P (, PN P T) represens he firs derivaive of he price index wih respec o he firs argumen, ec. Finally, (2.4) represens he risk-sharing condiion across counries, relaing marginal uiliies o he real exchange rae (where is he nominal exchange rae), for a imeinvarian consan Λ. S Equaions (2.)-(2.3), heir analogues for he foreign economy, and equaion (2.4) represen a general equilibrium in seven equaions ha deermine he endogenous variables (where ildes denoe equilibrium values); C C L L L L,, N, H, N, H, SP and τ = P F H, he erms of rade. The key feaure of his soluion is ha i represens a mapping from conemporaneous echnology shocks θ and θ o he equilibrium values of endogenous variables. More paricularly, fuure echnology shocks have no impac on allocaions or he erms of rade. In fac, he sysem (2.)-(2.4) conains no pas or fuure variables a all. The following resul hen immediaely follows. If nominal prices P H and are sicky, and he moneary auhoriy follows a rule aimed o susain he flexible price equilibrium of he model described by (2.2)- P F 6

18 (2.4), hen i mus necessarily choose a value of he nominal exchange rae ha is independen of unanicipaed curren announcemens abou fuure echnology shocks (or news shocks). If his were no he case, hen news shocks would affec he curren erms of rade, and allocaions would be pushed away from he flexible price equilibrium of he model. We now explore he implicaion of his resul in a number of seings where prices are sicky. Secion 3. A Model wih One-period Price Seing. We now apply his resul o a model where prices are pre-se for one period. The model is a simple exension of Devereux and Engel (2003) (henceforh DE) and is based also on Duare and Obsfeld (2005). We le: ε ρ χ M υ = C + ηl, ρ > 0, ε > 0, ρ ε P and γ γ CC T N, C = C ( ) T = C γ γ HC F. The parameer γ represens he share of non-raded goods γ ( γ) γ γ in consumpion. The price indices P are defined by P = PT P N, PT = PH PF. Following Beaudry and Porier (2003), we assume ha echnology shocks have a componen ha is known one period in advance of he shock. Thus, for he home counry, we assume ha he echnology shock is θ = θθ, θ = exp( v ), θ = exp( u ), 2 2 where v and u are normally disribued, wih mean zero, and variance 2 σ v and 2 σ u respecively. The criical feaure of he echnology process is ha he innovaion in θ becomes known one period in advance, i.e. a ime -. On he oher hand, he componen θ 2, is realized a he same 7

19 ime as i becomes known 3. The implicaion of his assumpion is ha households and firms will know, one period in advance, par of fuure echnology innovaions. Hence, since, in his version of he model, prices are pre-se for only one period, prices for fuure periods can fully adjus o a forecas in he echnology shock. Bu prices for he curren period, based on period - informaion, canno adjus o he shock. The soluion o he model follows closely ha of DE. An approximaion o he money marke equilibrium may be wrien as: ρ (3.) m ( ) p = c Ep+ + ρec + p ρc +Γ ε iε m where Γ m is a consan, and lower-case leers refer o logs of he respecive variables. An analogous condiion may be derived for he foreign counry. The opimal rade-off beween consumpion and leisure implies: W (3.2) = η. ρ PC The risk sharing condiion implies: (3.3) SP P C Γ 0 C = ρ. 3 Beaudry and Porier (2003) assume ha he forecasable componen of echnology is permanen. Here we assume ha i is ransiory. This makes lile difference o he resuls of his secion. In secion 4, some of deails of he resuls are alered in he presence of a permanen forecasable echnology shock, alhough he cenral resul (eliminaing surprise exchange rae changes) is unchanged. 8

20 Price Seing Prices for period are se one period in advance, based on period - informaion ses. Firms choose prices o maximize profis using he sochasic discoun facor of heir owners. We allow for expored goods prices o be se eiher in he firm s own currency (producer currency pricing, or PCP) or in foreign currency (local currency pricing, or LCP). Equilibrium The goods marke equilibrium in he home counry non-raded goods secor is: PC (3.4) θln = ( γ), P N where L N represens employmen in he non-raded goods secor. In he raded goods secor, for he PCP pricing environmen, he equilibrium condiion is ( L is employmen in he home raded goods secor): H (3.5) θ L H PC S P C = γ + 2 PH PH. Wih LCP he goods-marke equilibrium in he home raded goods secor is wrien as: (3.6) θ L H PC P C = γ + 2 P H PH. The difference beween (3.5) and (3.6) is due o he fac ha in he laer case here are separae pre-se prices of home goods in domesic currency (for domesic sales) and foreign currency (for expor). Flexible-Price Soluion Wih flexible prices, we may apply he condiions (2.)-(2.4) o solve for consumpion and he erms of rade as: 9

21 λη = λ ρ.5γ+ γ.5γ (3.7) C ( θ θ ) ρ (3.8) τ =Γ γ θ 0 θ Wihou non-raded goods, consumpion would be equalized across counries. Generally however, wih γ<, home consumpion is more sensiive o a home echnology shock han o a foreign echnology shock. Moneary Policy Rules Money supply of each counry is given by: (3.9) m = m + µ + δ (3.0) m = m + µ + δ. Moneary policy rules are designed o respond o unanicipaed shocks, so E ( µ ) = E ( µ ) = 0, and E = = will hold. Here µ ( µ ) is an addiion o 2( δ ) E 2( δ ) 0 he ime informaion se, while δ ( δ ) is an addiion o he ime - informaion se. Noe ha his assumpion means ha condiionally (on ime informaion) expeced money growh will vary over ime, alhough he uncondiional expecaion of money growh is zero. This moneary rule is designed so ha he µ componen reacs o curren u shocks, while he δ componen reacs o fuure v shocks, which are announced oday. Exchange Rae and Consumpion under PCP Wih PCP pricing, he law of one price holds for raded goods. Hence, from (2.4): (3.) ( γ ) ( c E c) = ( c E c ) + ( s E s). ρ Unanicipaed changes in he exchange rae will affec he real exchange rae, and herefore 20

22 relaive consumpion levels, o he exen ha hey aler he inernaional relaive price of nonraded goods, which in his model, is also equal o he erms of rade. Since prices fully adjus afer one period, he expeced real allocaions from nex period on will be governed by (3.7) and (3.8). Therefore: (3.2) Ec + E c+ = ( 0.5 γ ) v+.5 γ v ρ. There are no expeced changes in nominal ineres raes from ime period +2 onwards, since he news shock is hen dissipaed, and in expecaion, he money sock is consan. We can hen use his propery and he period + version of (3.), o obain: (3.3) ρ Ep + E p+ = Em + E m+ ( Ec + E c+ ) ε. ρ( + i) = δ + Em E m ( Ec + E c+ ) ( + εi) Now, puing (3.), (3.2), and (3.3) ogeher wih (3.), and using he analogous equaions for he foreign counry, leads o he exchange rae (3.4) ( ε ) i ( γ )( v v ) + δ δ ( + iε ) ( m E m) ( m E m ) ( + iε ) s E s = + + i( γ( ε)) + i( γ( ε)) The exchange rae is he sum of wo elemens. Firs, here are revisions o curren fundamenals, i.e. unanicipaed movemens in relaive money growh across he home and foreign counry. The second elemen is fuure fundamenals, capured by he second erm in (3.4). This is explained as follows. When v > v, here is a shock o fuure home produciviy ha exceeds ha o fuure foreign produciviy. If in addiion γ <, his mus increase anicipaed consumpion a home more han in he foreign counry, since home residens consumpion is more sensiive o home produciviy in he presence of a non-raded goods secor. From (3.), 2

23 holding he curren moneary innovaion consan, a rise in expeced fuure home relaive consumpion will increase he home nominal ineres rae, relaive o he foreign nominal ineres rae, when ε >. This will reduce demand for money a home relaive o he foreign counry, and as a resul here is an unanicipaed home currency depreciaion. Finally, fuure fundamenals also incorporae fuure changes in he relaive money supplies, δ δ, which can be forecased based on announcemens of fuure relaive echnology growh raes. Noe ha he key feaure of his mechanism is ha he exchange rae responds o fuure fundamenals, raher han curren fundamenals. Tha is, he ime + produciviy shock becomes known a ime, and generaes `news, which leads he curren exchange rae o move, and he resuling changes in he expeced fuure money supply have a similar effec. There are no changes in curren supply or demand variables, however. How do home and foreign consumpion raes respond o fuure produciviy shocks? Again from he money marke clearing condiion (3.), we can derive he expression for he unexpeced response of home and foreign consumpion, respecively, as: γ ( ε ) i δ = ( + i) ( + iε ) ρ (3.5) c E c φ ( m E m ) ( s E s ) ( Ec E c ) + + γ ( ε ) i δ = ( + i) ( + iε ) ρ (3.6) c E c φ ( m E m ) ( s E s) ( Ec + E c+ ) + iε where φ = ρ + i. We may explain hese expressions as follows. Take equaion (3.5), and imagine ha here is an anicipaed posiive home counry produciviy shock. Then here is a rise in expeced fuure home consumpion, which will end o raise nominal ineres raes when ε >. This causes an excess supply of home money, and would lead o an unanicipaed rise in curren home 22

24 consumpion. Agains his, however, is he fac ha he anicipaed home produciviy shock causes an exchange rae depreciaion, when ε >. This reduces real money supply, and ends o reduce home consumpion. The ne effec on curren period home consumpion may be posiive or negaive. When ε < he reasoning goes he oher way. The impac of fuure money supply changes are sraighforward a posiive δ represens an expeced fuure moneary expansion, which raises nominal ineres raes and raises curren consumpion. Local-Currency Pricing (LCP) Under local-currency pricing, he law of one price will no generally hold. Since wih LCP all domesic and foreign nominal goods prices are pre-deermined, he CPI s of each counry are also predeermined. Then, from (3.3), we ge: (3.7) ( c E c) = ( c E c ) + ( s E s) ρ The behavior of expeced period + consumpion is he same as in (3.7), since LCP and PCP are equivalen o one anoher afer prices have fully adjused. For he same reason, equaion (3.3) is he same as before. Then, using (3.7), (3.7), (3.3), and he money marke equilibrium condiions (3.) for each counry, gives: (3.8) + iε ( ε ) i s E s = ( m E m) ( m E m ) + ( γ )( v v ) + δ δ + i ( + i) ( + iε ) This differs from expression (3.4) due o he fac ha price levels are predeermined under LCP. Bu qualiaively, we ge a similar message. The exchange rae is a funcion of curren and fuure fundamenals. A fuure produciviy shock, which becomes known oday, represens `news, which impacs on he curren exchange rae. The size of his effec depends on he size of he 23

25 non-raded goods secor, as well as he size of ε. The impac of fuure produciviy shocks on consumpion is given by: ( ε ) i δ = + + ( + i) ( + iε ) ρ (3.9) c E c φ( m E m ) ( Ec E c ) + + ( ε ) i δ = + + ( + i) ( + iε ) ρ (3.20) c E c φ( m E m ) ( Ec + E c+ ) These effecs are equivalen o he PCP case, save for he absence of he exchange rae from (3.9) and (3.20), since movemens in he exchange rae no longer direcly impac on CPI values. Bu again, as in he PCP case, we have announcemens effecs of fuure produciviy shocks influencing curren consumpion. This case also allows us o be more precise regarding he impac of fuure produciviy shocks. Whenever ε >, a rise in fuure home or foreign produciviy will lead o a rise in curren consumpion. This happens because here is no secondary channel of he iniial ineres rae increase arising from he fuure produciviy shock, as exiss in he PCP case. Opimal Moneary Policy wih News Shocks So far we have no been specific abou he moneary policy response o curren or anicipaed fuure produciviy shocks. Implici in he analysis above is ha curren produciviy shocks (i.e. shocks o θ 2 ) have no impac on eiher he exchange rae or consumpion, independen of he endogenous response of moneary policy. Bu, following he analysis of DE, here are clear welfare reasons why moneary policy should be designed o ensure he efficien response of he real economy o curren produciviy shocks in he presence of sicky prices. The opimal values for he moneary policy response o curren produciviy shocks are similar o hose analyzed in DE and Duare and Obsfeld (2005). For he PCP model, he moneary policy responses in he home and foreign currency can perfecly replicae he flexible price equilibrium. 24

26 For he LCP model, given he absence of exchange rae pass-hrough, he flexible price equilibrium canno be susained. The opimal moneary policy response ensures ha consumpion responds o curren produciviy shocks as in he flexible price equilibrium, bu he exchange rae responds by less han in he flexible price equilibrium. In face of anicipaed fuure produciviy shocks however, he raionale for an opimal policy response becomes less clear. When here is a shock o θ +, which by assumpion is observed a ime, hen prices have he chance o respond fully before he shock akes effec. In ha case, here is no reason for moneary policy o be used in order o ensure he efficien adjusmen of he period + allocaions o he produciviy shock. Bu he key feaure of our examples above, and he cenral message of he paper, is ha hese anicipaed fuure shocks will affec he economy in he presen. Tha is, by impacing on ineres raes and exchange raes, curren consumpion will be moved away from is flexible price equilibrium, given by (2.9). The reason is ha, while fuure prices have ime o adjus o he shock ha occurs in period +, curren prices canno reac o he announcemen. To he exen ha he announcemen effecs shif curren allocaions away from heir flexible price equilibrium, hey are undesirable, and an opimal moneary policy can be devised o deal wih his. The naure of he opimal moneary policy for fuure produciviy shocks urns ou o be he same, for boh ypes of pricing. Thus, we can sae: Resul : Le he moneary policy rules be defined as δ = av 0 + av δ = av + av 0. Then for boh LCP and PCP, he opimal moneary rule is described by 25

27 a ( ε ) i γ = a = ( ) ( + iε ) 2 0 ( ε ) i γ a = a0 =. ( + iε ) 2 Proof: These rules eliminae he impac of fuure produciviy shocks on curren consumpion in boh counries. Therefore, employmen is also unchanged. Therefore he rules susain he flexible price equilibrium, in face of announced fuure produciviy shocks. Resul 2: The opimal moneary rules from Resul preven he exchange rae from responding o fuure produciviy shocks. Proof: By inspecion. Resul 2 is in a sense he more ineresing one. Sandard Opimal Currency Area (OCA) reasoning suggess ha i is efficien o allow he exchange rae o respond o counry specific produciviy shocks. We find, in he absence of a moneary response, ha indeed he exchange rae will respond o announcemens of counry specific produciviy shocks. The direcion of movemen depends on he size of ε. For ε >, he exchange rae will depreciae in response o an announced fuure home produciviy expansion. I is emping o inerpre his movemen along efficiency (or OCA) lines he fuure home produciviy expansion should cause a home counry erms of rade deerioraion. Hence, he response of agens in financial markes, forecasing his, leads o an immediae nominal exchange rae depreciaion. Bu he problem wih his reasoning is ha he immediae response of he curren nominal exchange rae causes a change in he curren real exchange rae (by differen degrees in he PCP and LCP environmens), because curren nominal prices canno respond o he announced fuure shock. In he absence of a curren (as opposed o fuure) produciviy shock, however, here is no efficiency reason for he real exchange rae o move a all. In fac, movemens in he real 26

28 exchange rae are associaed wih welfare losses since hey push consumpion and employmen away from heir efficien levels. Thus, in a sicky price environmen, when he exchange rae responds o `news, here is no guaranee ha i will do so in an efficien manner. Indeed, in our model, he opimal moneary rule should preven he exchange rae from responding o news shocks a all. The criical requiremen is ha here no be any unanicipaed movemens in he exchange rae. Tha is he ime exchange rae will be known in ime -. Given he form of he moneary rules defined here, we can acually go beyond his, and esablish ha under hese rules he exchange rae is fixed over ime (when all shocks are observed in advance). To see his, noe ha s = ρ( c c ) + p p ρε ( ) i = ( c c ) + m m ( + iε ) ρε ( ) i ( ε ) i( γ ) = ( c c ) + m m + ( v v ) + δ δ ( + iε) ( + iε) ρε ( ) i = ( c c ) + m m ( + iε ) = s The firs equaliy comes direcly from he risk sharing condiion (2.5). The second comes from he soluions for period + prices discussed before equaion (3.3). The hird equaliy comes from a decomposiion of money growh and consumpion growh, while he fourh uses he opimal money rule of Resul. Hence, he moneary auhoriy follows a rule in which nex period s money supply responds o fuure produciviy shocks leing, nominal price levels ake he full burden of adjusing he fuure real exchange rae o he produciviy shocks, and keeping he exchange rae fixed over ime. From a welfare perspecive however, his is no necessary. The efficien allocaion could jus as easily be aained by a policy which prevens he curren exchange rae 27

29 from reacing o news shocks, bu allowing par of he real exchange rae adjusmen o occur via movemens in he fuure nominal exchange rae. Thus, here could be expeced changes in he exchange rae over ime. These changes would no be cosly, because prices can adjus over he same ime frame. The criical ingredien in he analysis is ha fuure produciviy shocks do no generae surprise movemens in he curren nominal exchange rae. Of course he model is quie sylized, since we have assumed ha all prices can adjus before he news akes effec. Bu his is no necessarily unrealisic. A an anecdoal level, we see he exchange rae responding o all ypes of poenial evens (e.g. effecs of Social Securiy changes ha may affec he budge defici in 5 or more years ime) ha may occur much furher in he fuure han would be relevan for business cycle frequencies. These exchange rae movemens are no necessarily desirable, because we have o recognize ha he response o fuure shocks may no be consisen wih he currenly desired srucure of relaive prices. Neverheless, we now urn o an exended version of he model, which assumes ha nominal prices mus be adjused gradually raher han all a once. Secion 4. Exension o Gradual Price Adjusmen We now exend he model o allow gradual price adjusmen using he Calvo specificaion where only a given fracion of firms may adjus heir prices wihin a period, and ex ane, all firms have an equal chance of price adjusmen. The specificaion for households and firms is unchanged excep for he price seing rule. For simpliciy, we focus only on he PCP pricing case. In addiion, o make he analysis comparable o he previous model, we follow Roemberg and Woodford (997) in assuming ha a firm ha has an opporuniy o change is price mus se is price for period wih informaion based on period -. Tha is, prices ha are 28

30 adjused are se one period in advance, as in he previous model. Unlike he previous model however, no all prices are adjused in every period. Assume ha all firms in boh counries have a probabiliy κ of receiving an opporuniy o change heir price in any period. Then he newly se price for any home counry firm in he non-raded goods secor ha can change is price for period is given by (4.) P N W E λ P Y = λ C ρ i + i λ + i ( βκ) N+ i N+ i i= 0 θ + i P+ i ρ i λ C+ i E ( βκ) PN+ iyn+ i i= 0 P+ i Using sandard properies of he Calvo price seing scheme, we may wrie he non-raded goods price index as (4.2) P = κp + ( κ) P N N N Now, aking a linear approximaion of (4.) and (4.2) around a zero-inflaion seady sae, and puing he wo condiions ogeher, we may obain he convenional forward looking inflaion equaion, given by (4.3) π = ϕe ( w p u v ) + βe π N N N + Since he marginal cos facing firms in he home counry raded goods secor is idenical o ha of he non-raded good firm, o a linear approximaion he price inflaion equaion for raded goods will be idenical o (4.3). We hen follow he convenion of referring o inflaion in he home goods price (eiher raded or non-raded) as π. To conform o he sandard in he lieraure, we assume now ha he moneary auhoriies follow an ineres rae rule raher han a rule for he money supply. The gross nominal ineres rae in he home economy may be read off he Euler equaion as: 29

31 (4.4) R C P = β C E P ρ ρ + + Again, aking a linear approximaion around a seady sae, gives us: γ (4.5) r = r + ρe( c+ c) + Eπ+ + E ( τ+ τ ) 2 Where τ = p + s p is he home counry erms of rade. f h Assume ha he moneary auhoriy follows an ineres rae rule given by: (4.6) r = r + σπ + δ where E δ = 0. Differen assumpions regarding δ will be examined below. Table 2 describes he full model. Table 2 The model wih gradual price adjusmen Home inflaion γ π = ϕe ( ρc + τ u v ) + βe π + 2 Foreign inflaion γ π = ϕe ( ρc τ u v ) + βe π+ 2 Risk sharing ρ( c c ) = ( γτ ) Home ineres rae γ σπ + δ = ρe( c+ c) + Eπ+ + E ( τ+ τ) 2 Foreign ineres rae γ σπ + δ = ρe( c+ c ) + Eπ+ E ( τ+ τ) 2 For simpliciy, we deal for now only wih he case where all shocks are `news shocks, so 30

32 ha u = 0. 4 Noe ha he flexible price soluion o he model is idenical o (3.7) and (3.8) above, so ha γ γ γ γ c = ( ) v v, c ( ) v ρ = + ρ v 2 2, and τ = v v. Efficien consumpion and he erms of rade are independen of anicipaed fuure produciviy shocks. The objecive of moneary policy, as in he previous secion, should be o replicae he response of he flexible price economy. Bu in conras o he previous secion, here is an independen welfare cos of inflaion, even if i is perfecly anicipaed. This is because in an environmen of gradual price adjusmen, inflaion generaes price dispersion, since no all firms may change heir prices simulaneously. By seing inflaion o zero, firms will never wish o adjus heir prices, and hus price dispersion will be eliminaed. As in Woodford (2003), an opimal moneary policy should herefore replicae he response of he flexible price economy, while achieving a zero rae of price change. Noe ha so long as he moneary auhoriy follows a rule in which σ >, he sysem in Table 2 is saddle pah sable, and here is a unique soluion for bounded shock processes. Case. Simple Inflaion Targeing Assume ha he moneary auhoriies follow a simple inflaion argeing policy, seing σ >, bu no adjusing ineres raes o ex-pos informaion, so ha δ = 0. We may wrie he general soluions for he erms of rade as = av 0 + av 0 + av + av. Noe ha, since all τ prices are pre-se, he unanicipaed componen of he erms of rade; τ E τ = av + av, is equivalen o he movemen in he nominal exchange rae. I is easy o verify ha: 4 Since he inflaion rae is predeermined, an opimal policy response o a curren produciviy disurbance will require an ineres rae adjusmen - δ will need o fall in response o a posiive u shock. 3

33 a a σϕ ( ) 0 0, a a σ (4.7) = = = = ϕ. + σϕ + σϕ The soluion for home counry inflaion is wrien as: ϕ (4.8) π = v. +σϕ The consumpion responses may be wrien as: ϕσ γ γ ( -) c - v v ϕ σ - γ v γ (4.9) = v ( σϕ+) ρ ( σϕ+) ρ 2 2 (4.0) ϕσ γ γ ϕ( σ -) γ γ c = - v v - ( σϕ+) ρ ( σϕ+) ρ v + v 2 2 As we increase he `ighness of he moneary policy rule (i.e. seing σ ), he variance of inflaion falls o zero. This also ensures ha he anicipaed componen of he erms of rade and consumpion responds as in he flexible price equilibrium. Bu his fails o suppor he full flexible price equilibrium, because i does no generae he appropriae response of he erms of rade o conemporaneous news shocks. In fac, a igh money rule exacerbaes he inefficiency of news shocks. As σ increases, he response of he nominal exchange rae movemen o news shocks is increased, generaing a larger (inefficien) erms of rade and consumpion movemen. The inuiive explanaion for he relaionship beween he sance of moneary policy (as described by he parameer σ ) and he response o news shocks can be undersood as follows. Since a posiive news shock will raise fuure consumpion, i will end o raise real ineres raes in boh counries. Bu wih advance price seing and he ineres rae rule (6.6), he nominal ineres rae is pre-deermined wih respec o curren news shocks. Moreover, he higher is σ, he smaller is he impac of news shocks on anicipaed inflaion. Given ha boh he nominal ineres rae and anicipaed inflaion are smoohed, he upsho is ha he equilibrium real ineres 32