Expectations and Exchange Rate Policy

Transcription

1 Expecaons and Exchange Rae Polcy Mchael B. Devereux UBC Charles Engel Wsconsn Aprl 24, 2006 Absrac Boh emprcal evdence and heorecal dscusson have long emphaszed he mpac of `news on exchange raes. In mos exchange rae models, he exchange rae acs as an asse prce, and as such responds o news abou fuure reurns on asses. Bu he exchange rae also plays a role n deermnng he relave prce of non-durable goods when nomnal goods prces are scky. In hs paper we argue ha hese wo roles may conflc wh one anoher. If news abou fuure asse reurns causes movemens n curren exchange raes, hen when nomnal prces are slow o adjus, hs may cause changes n curren relave goods prces ha have no effcency raonale. In hs sense, ancpaons of fuure shocks o fundamenals can cause curren exchange rae msalgnmens. Fredman s (953) case for unfeered flexble exchange raes s overurned when exchange raes are asse prces. We oulne a seres of models n whch an opmal polcy elmnaes he effecs of news on exchange raes. We hank parcpans n semnars a he European Cenral Bank and he Inernaonal Moneary Fund. We hank Joong-Shk Kang for research asssance. Engel receved suppor for hs research from a gran from he Naonal Scence Foundaon, Award No. SES

2 Much of analyss of open economy macroeconomcs n he pas 30 years has been bul on he foundaon ha exchange raes are asse prces and ha some goods prces adjus more slowly han asse prces. If hs s rue, means ha exchange raes wear wo has: They are asse prces ha deermne he relave prce of wo mones, bu hey also are mporan n deermnng he relave prces of goods n nernaonal markes n he shor run. For example, f expor prces are scky n he exporng currency, hen nomnal exchange rae movemens drecly change he erms of rade. Whle of course he leraure has recognzed hs dual role for exchange rae movemens, has no recognzed he mplcaon for exchange-rae or moneary polcy. Asse prces move prmarly n response o news ha alers expecaons of he fuure. Mos exchange rae movemens n he shor run reflec changes n expecaons abou fuure moneary or real condons. Bu fuure expecaons should no be he prmary deermnan of he relave prce of nondurable goods. Those relave prces ough o reflec curren levels of demand and supply. So, news ha causes nomnal exchange raes o jump may have undesrable allocaonal effecs as he news leads o neffcen changes n he relave prces of goods. I may be ha conrollng exchange raes dampenng her response o news s an mporan objecve for moneary polcy. The asse marke approach o exchange raes has long recognzed ha exchange rae movemens are prmarly drven by news ha changes expecaons. For example, he survey of he feld by Frenkel and Mussa (985, p. 726) n he Handbook of Inernaonal Economcs saes: These facs sugges ha exchange raes should be vewed as prces of durable asses deermned n organzed markes (lke sock and commody exchanges) n whch curren prces reflec he marke s expecaon concernng presen and fuure economc condons relevan for deermnng he approprae values of hese durable asses, and n whch prce changes are largely unpredcable and reflec prmarly new nformaon ha alers expecaons concernng hese presen and fuure economc condons. In her monograph, Foundaons of Inernaonal Macroeconomcs, Obsfeld and Rogoff (996, p. 529) sae One very mporan and que robus nsgh s ha he nomnal exchange rae mus be vewed as an asse prce. Lke oher asses, he exchange rae depends on expecaons of fuure varables. A he same me, a broad par of he leraure has acceped, as Dornbusch (976, p. 6-62) pus, he fac of dfferenal adjusmen speeds n goods and asse markes. Indeed, was hs dfference n he speed of adjusmen ha led Mlon Fredman (953, p. 65) o advocae for flexble exchange raes: If nernal prces were as flexble as exchange raes, would make lle economc dfference wheher adjusmens were brough abou by changes n exchange raes or equvalen changes n nernal prces. Bu hs condon s clearly no fulflled A leas n he modern world, nernal prces are hghly nflexble. Fredman s case for flexble exchange raes was derved, however, n a world n whch capal flows were absen. In hs world, he exchange rae would deermne he erms of rade, bu was no

3 forward lookng and dd no reflec expecaons of he fuure as would an asse prce. Bu when he exchange rae changes are prmarly drven by news, he erms of rade or oher nernaonal prces may be badly msalgned n he shor run. The msalgnmen of relave prces s a he hear of he moneary polcy analyss n modern macroeconomc models of nflaon argeng. Woodford (2003, p. 2-3) explans: when prces are no consanly adjused, nsably of he general level of prces creaes dscrepances beween relave prces owng o he absence of perfec synchronzaon n he adjusmen of he prces of dfferen goods. These relave-prce dsorons lead n urn o an neffcen secoral allocaon of resources, even when he aggregae level of oupu s correc. Here, we are focusng on possbly severe msalgnmens n relave prces when large changes n exchange raes are caused by changes n expecaons. Ths dsoron would no be presen f all goods prces changed flexbly. Then relave prces would no be forced o ncorporae hese expecaons effecs, and nomnal goods prces would reac (effcenly) o news abou he fuure. To help focus he cenral dea of hs paper, s useful o make a ls of hngs we are no sayng:. We are no sayng ha oher models of moneary polcy n open economes have no modeled exchange raes as asse prces. They have. Our cenral nsgh s ha moneary polcy mus reac o news ha moves exchange raes. In exsng models, he only news ha hs he marke s shocks o curren economc varables. By argeng curren economc varables n hose models, moneary polcy does effecvely arge he news. Bu n a realsc model, agens have many oher sources of nformaon han smply shocks o curren macro aggregaes. Targeng he aggregaes does no acheve he goal of offseng he nfluence of news on relave prces. Our model explcly allows agens o have nformaon abou he fuure ha s dfferen han shocks o he curren level of macro varables. 2. We are no lookng a dfferences n he nformaon se of he marke and polcy makers. Whle ha may be an neresng area for sudy, s no our prmary concern. To make hs clear, we model he marke and polcy makers as havng he same nformaon. 3. The problem we have pnponed s no one of excess volaly n asse prces. We do no consruc a model n whch here s nose or bubbles n asse prces. Insead, we model he exchange rae as he no-bubble soluon o a forward-lookng dfference equaon, so s modeled as an effcen, raonal expecaons, presen dscouned value of expeced fuure fundamenals. Indeed, as Wes (988) has demonsraed, he more news he marke has, he smaller he varance of nnovaons n he exchange rae. Noneheless, s he nfluence of ha news on exchange raes ha concerns us. Our nuon s ha movemens n nomnal exchange raes caused by nose or bubbles would also be neffcen, bu we purposely pu asde ha ssue for ohers o sudy. 4. We are no sayng ha moneary polcy should arge all asse prces, such as equy prces. Our 2

4 nuon s ha exchange raes are dfferen. Exchange raes are he only asse prce whose movemen drecly causes a change n he relave prce of wo non-durables ha have fxed nomnal prces. Tha happens because nomnal prces of dfferen goods (or he same good sold n dfferen locaons) can be scky n dfferen currences. Flucuaons n oher asse prces cause a change n he prce of a durable (e.g., equy prces are he prce of capal) relave o he prce of a non-durable. A leas n some crcumsances, ha flucuaon s no a concern of moneary polcy. As Woodford (2003, p. 3) explans, Large movemens n frequenly adjused prces and sock prces are among he mos flexble can nsead be allowed whou rasng such concerns, and f allowng hem o move makes possble greaer sably of he scky prces, such nsably of flexble prces s desrable. 5. Our concerns abou how news nfluences exchange raes and affecs relave goods prces do no depend on wheher nernaonally raded goods prces are se n he producers currences (PCP) or he consumers currences (LCP). Some of our earler work (Devereux and Engel, 2003, 2004) has focused on ha ssue, n models where news was no mporan. Bu we se asde ha dspue here. If here s PCP, hen nomnal exchange rae changes (arsng from news of he fuure) can lead o neffcen changes n he erms of rade. If here s LCP, hese nomnal exchange rae changes lead o neffcen devaons from he law of one prce. 6. We are no sayng ha a polcy of fxed nomnal exchange raes s opmal. Frs of all, n response o radonal conemporaneous dsurbances (non-news shocks), exchange rae adjusmen may be desrable. Bu even wh news shocks alone, our resuls do no necessarly say ha exchange raes should be fxed, bu ha unancpaed movemens n exchange raes should be elmnaed. In fac, ancpaed movemens n exchange raes may play a role n faclang relave prce movemens afer a news shock. In general, our pon s ha news shocks can lead o relave prce dsorons ha are ranslaed hrough exchange rae changes, and hese shocks should be a arge of polcy. Techncally, our model s smple. The cenral dea s based on he propery ha effcen relave prces of non-durable goods depend only on curren fundamenals, and should no be drecly lnked o news abou fuure fundamenals. Ths propery s sasfed n mos recen general equlbrum exchange rae models. In fac, he cleares saemen of ndependence of curren allocaons on fuure fundamenals s n Barro and Kng (984). They show ha n general equlbrum models wh me-addve uly and absenng nvesmen, curren (effcen) equlbrum allocaons are ndependen of expecaons abou fuure fundamenals. Ths resul exends o an open economy where markes are suffcenly complee o suppor a me-nvaran rsk sharng rule. Bu, n he presence of scky nomnal prces, hs dchoomy beween curren allocaons and fuure fundamenals no longer necessarly holds. When prces canno adjus, any news shocks ha affec he curren exchange rae auomacally affec relave prces. In general hs s neffcen, and he moneary auhory should ake acon o dampen or elmnae he 3

5 mpac of news shocks on curren allocaons. Secon presens some emprcal evdence on he mporance of news n movng exchange raes. Secon 2 hen explans n a general conex why prces of nondurables should no ac lke asse prces and reflec expecaons of fuure fundamenals. The res of he paper demonsraes he logc of argeng shocks o exchange raes caused by news n wo dfferen models. Secon 3 descrbes he frs model, n whch prces are pre-se one perod n advance, and can fully adjus afer one perod. In hs model, we fnd ha an opmal moneary polcy n face of news shocks s o manan a fxed exchange rae. Secon 4 hen exends he model o allow gradual prce adjusmen. The exended model no longer calls for a fxed exchange rae, bu mples ha an opmal moneary rule elmnaes he mpac of news shocks on he exchange rae. In secon 5, we buld a more realsc model wh nvesmen. Opmal nvesmen decsons are forward lookng, so n hs model s no longer srcly rue ha curren relave goods prces should no depend on fuure producvy shocks. Noneheless, under sandard parameerzaons, our conclusons are no alered opmal moneary polcy should no only arge nflaon bu also ry o elmnae he effec of news on exchange raes. Secon. Emprcal Evdence on he Effec of Expecaons on Exchange-Rae Volaly Several recen emprcal papers have emphaszed he role of news n drvng exchange raes. Engel and Wes (2005) demonsrae ha sandard exchange rae models do no n fac mply ha exchange rae changes should be predcable usng curren values of fundamenal varables, or even necessarly srongly correlaed wh conemporaneous changes n fundamenals. Insead, hey show ha a esable hypohess of he models s ha he news ha s ncorporaed n exchange raes should help he exchange rae forecas fuure macroeconomc varables. They fnd emprcal evdence o suppor ha poson. Andersen, e. al. (2003) use sx years ( ) of real-me quoaons from he foregn exchange marke o assess he mpac of macroeconomc news on exchange raes. They measure news as he dfference beween announced values of macro varables (payroll employmen, rade balance, real sales, ec.) and a survey measure of he marke s expecaon of hese announcemens. They fnd ha exchange raes reac sgnfcanly o hese announcemens, and over 5-mnue wndows, a smple OLS regresson of he exchange rae on he news yelds hgh R 2 values: ofen around 0.3 and somemes approachng 0.6. Whle he emphass n Andersen, e. al. s on he shor-run nfluence of news on exchange raes, Faus, e. al. (2005) use real-me daa and nformaon from he erm srucure of neres raes o examne how news announcemens affec expecaons of long-run exchange rae changes. They fnd ha news announcemens abou U.S. real or nomnal acvy move exchange raes and also nfluence longer-erm neres raes, wh he maxmum effec a 2 years. They argue ha he effec on long-erm 4

6 raes mgh reflec he response of long-run changes n expeced currency deprecaon. Here we provde some alernave evdence on he effec of changes n expecaons on exchange raes. In parcular, we consder models n whch he exchange rae can be expressed as a presen dscouned value of curren and fuure fundamenals: (.) j I + j j= 0 x ( b) b E( f I ), 0< b <. Here, facor s b. f measures he economc fundamenals ha drve he log of he exchange rae. The dscoun I represens he nformaon se of agens. I s helpful o rewre hs as: (.2) j I = + + j j= x f ( b) b E( f f I ). Our models sugges ha moneary polcy should have as one objecve he sablzaon of nnovaons (unexpeced changes) n he second erm on he rgh-hand-sde of equaon (.2). Tha s, moneary polcy should work o offse he effecs of news shocks on exchange raes ha work hrough unexpeced changes n fuure fundamenals relave o he curren fundamenal. How mporan s hs second erm n drvng exchange rae nnovaons relave o he effec of nnovaons n he curren fundamenal? We would lke o know how much of he varance of unexpeced changes n x I can be arbued o nnovaons n he curren fundamenals, f. Tha s, we would lke o calculae (.3) var( f E( f I )) η. var( x E( x I )) I I Our premse s ha nnovaons n curren fundamenals do no conrbue much o he varance of nnovaons n x I. We beleve ha s mosly news abou fuure fundamenals ha causes varaon n x I. If our hypohess s correc, hen η should be small. However, seems hopeless o measure he varances n he numeraor and denomnaor of equaon (.3), because we do no have he nformaon he marke uses n formng s expecaons. We can calculae a measure of he expeced dscouned sum of curren and fuure fundamenals based on he nformaon se avalable o he economercan, H. Defne (.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 varances n equaon (.3). Tha s, from Wes, we have var( f E( f I )) < var( f E( f H )), and var( x E( x I )) < var( x E( x H )). I I H H 5

7 Havng an upper bound on boh he numeraor and he denomnaor does no help us esablsh even an upper bound on η. We could follow he mehod of Campbell and Shller (987), and mpose ha he log of he exchange rae exacly equals x I. Ther mehods hen allow one o exrac he relevan nformaon n because ha nformaon s refleced n exchange rae movemens. Bu as Engel and Wes (2005) argue, ha approach requres ha we have measures of all he relevan fundamenals ha drve he exchange rae. Whle one mgh plausbly argue ha he fundamenals for some asse prces such as eques are compleely observable ex pos (ha s, dvdends are observable), s much less plausble o asser ha we can observe all he fundamenals ha drve exchange raes, whch nclude such varables as money demand shocks, producvy shocks, ec. If he fundamenals are no ex pos observable, we canno apply he procedures of Campbell and Shller (987). of We can, however, rely on a resul of Engel and Wes (2004) o ge a measure of he denomnaor η from equaon (.3). They show ha as he dscoun facor ges large ( b ), he economercan s measure of he varance of nnovaons n he presen value s approxmaely equal o he varance based on he marke s nformaon se: var( x E( x I )) var( x E( x H )). I I H H Even hough he economercan canno replcae he nformaon se of he marke, he can accuraely measure he varance of he nnovaon n he dscouned sum when he dscoun facor s large. Engel and Wes show ha n pracce he dscoun facors mpled by common emprcal models are large enough ha he approxmaon s a good one. Engel and Wes (2004) proceed o show ha he volaly of nnovaons n he acual exchange rae s approxmaely wce he sze of var( xi E( xi H )) for U.S. exchange raes relave o oher G7 counres usng wo famlar models of exchange raes. observed fundamenal s measured as ( ) The frs s a moneary model, n whch he f = m y m y, he log of he money/oupu rao n he U.S. relave o anoher counry. The fundamenals n hs model correspond approxmaely o hose n our model n secon 3. The second s a model based on a Taylor rule for moneary polcy, n whch he fundamenal can be wren as eher prces, or f = p p, he dfference n he log of U.S. versus foregn-counry f = p p + ( ), he sum of he log of he prce level and he neres rae n he U.S. relave o anoher counry. Engel and Wes (2005) demonsrae how hese fundamenals are derved from he underlyng model. These fundamenals correspond o he ones n our model n secons 4 and 5. The I Engel and Wes (2004) rely on a resul of Engel and Wes (2005) o show ha nnovaons n he log of he exchange rae can be measured approxmaely by change n he log of he exchange rae when he dscoun facor s near one. 6

8 fac ha exchange rae nnovaons are more volale han nnovaons n he dscouned sum of curren and expeced fuure fundamenals ndcaes eher ha here are fundamenals ha are no ncluded, or ha exchange raes may be drven by non-fundamenal sources. Our objecve here s no o ask wheher economc fundamenals from radonal models can accoun for exchange rae volaly. Insead, we ake he se of observed fundamenals as gven, and smply ry o measure η. Usng he Engel-Wes heorem, we can approxmaely calculae he varance n he denomnaor of equaon (.3). As we have noed, we can calculae an upper bound on he varance n he numeraor, and hence can calculae an upper bound for η. Table repors our measure of η for he fundamenals consdered by Engel and Wes (2004), for varous values of he dscoun facor, b. In calculang hese sascs, we ake he economercan s nformaon se o be only curren and lagged values of he fundamenals, f. We esmae an auoregresson wh four lags (n all cases) on each measure of he fundamenals. From hese, we calculae our esmaes of var( f E( f H )) and xi E xi H var( ( )). We use he same daa used n Engel and Wes (2004, 2005). I s quarerly daa, 973:-2003:. 2 The US s he home counry, and we measure he fundamenals relave o he oher G7 counres. The money supples are seasonally adjused M (excep for he UK, for whch we use M4) from he OECD Man Economc Indcaors. The US money supply daa s correced for sweeps, as descrbed n Engel and Wes (2004), usng daa from he Federal Reserve Bank of S. Lous. We use seasonally adjused GDP from he same source (excep for Germany, whch combnes daa from he IMF s Inernaonal Fnancal Sascs (IFS) wh he OECD daa.) The neres raes are 3-monh Eurocurrency reurns aken from Daasream. The consumer prces are from he IFS. Whle he esmaed value of η vares from counry o counry, ypcally we fnd ha s around More precsely, he average across all counres and all measures of he fundamenals, n he case of b = 0.99 s The average s slghly hgher for lower values of b and lower for hgher values of b. Tha s, mos of he surprse movemen n he dscouned sum ha s supposed o deermne exchange raes comes from nnovaons n expeced fuure values of fundamenals raher han unexpeced changes n curren values. I s mporan o noe ha he upper bounds for η repored n Table mgh be crude upper bounds. Tha s, nnovaons n he curren fundamenals mgh conrbue much less o nnovaons n x I han he numbers repored n hs Table. For example, durng 2005, he Federal Reserve rased he Fed Funds rae by 25 bass pons each me ha he FOMC me. Fed Funds fuures ndcaed before each 2 In a few cases, he me span dffers because of daa avalably. See Engel and Wes (2005) for daa spans. 7

9 meeng ha here was vrual cerany ha he Fed would rase raes. Tha s, here was essenally no nnovaon n he curren fundamenal he neres rae on he FOMC meeng days. Bu clearly he Fed s polcy decsons are mporan for exchange raes, and ha s refleced n exchange rae movemens on hose FOMC days. The exchange rae, however, was no changng because of any surprse n he curren fundamenal. The news ha h he marke came n he announcemens of he Fed s assessmen of marke condons, whch n urn mpared news abou fuure neres rae changes. Our measure of he varance n he nnovaons n he curren fundamenal, var( f E( f H )), s a crude one because he marke uses much more nformaon han four quarerly lags of he fundamenals o form s expecaons. For example, our measure does no even use he Fed funds fuure raes o help capure he marke s nformaon abou fuure neres raes, and so we end o overesmae he varance of nnovaons n curren fundamenals. Secon 2. A General Resul The echncal resul of he paper ress on an nsgh no dynamc general equlbrum models frs dscussed by Barro and Kng (984). In a closed economy model wh me-addve uly and whou endogenous nvesmen, hey show ha all real allocaons and relave prces are deermned solely by conemporaneous fundamenals. Tha s, here are no nrnsc ner-emporal lnks beween perods, and no perssence n he effecs of shocks, apar from ha due o perssence n he shocks hemselves. An equlbrum allocaon n her model s Pareo effcen, snce here s a represenave ndvdual and all prces are fully flexble. I follows ha, n an economy wh scky prces, f an opmal moneary polcy s desgned o replcae he flexble prce equlbrum, should nsulae curren allocaons and relave prces agans shocks ha come n he form of announcemens abou fuure fundamenals. We develop hs basc nuon whn he sandard wo-counry envronmen of recen open economy macroeconomc models. We frs se ou a general verson of he model, o llusrae he logc of Barro and Kng whn our framework. We hen apply hs model o wo parcular ypes of prce seng envronmens one where prces are pre-se one perod ahead for jus one perod, and hen o an envronmen of Calvo-ype saggered prcng. In each case, we denfy one or more opmal moneary polcy rules o deal wh news shocks. Alhough he analycal resuls rely on he src separaon across perods, we do no argue ha be aken lerally. There are a number of facors ha gve rse o effcen lnks beween curren allocaons or relave prces and fuure fundamenals shocks. One obvous channel s nvesmen. Bu we argue ha even once we allow for hs lnkage, our cenral resul, ha he curren exchange rae response o announcemens abou fuure fundamenals should be dampened, wll sll hold n a quanave sense. An exenson of he model o allow for endogenous nvesmen esablshes hs pon. 8

10 The Basc Model Take a general example of an open economy macro model. Say ha here are wo equally szed counres: home and foregn, where n each counry he measure of households s normalzed o one. In each counry, households maxmze expeced lfeme uly akng prces and wages as gven. Households consume raded goods, consung a mx of home and foregn goods, and a non-raded good, produced and consumed only n he domesc counry. Frms are monopolsc and maxmze uly for her owners. Say ha consumer preferences are: 0 β υ = 0 ϒ= E, 0< β <, where υ = UC (, L) + VM ( / P ), wh U > 0, U2 < 0, U < 0, U22 < 0. Here C represens aggregae consumpon, L s labor supply, and M / P are real money balances. Aggregae consumpon C s a funcon of non-raded consumpon and raded consumpon; C = C( C, C ). Traded consumpon s also a funcon of home and foregn raded goods consumpon; C = C ( C, C ). Each funcon s N T T T H F homogenous of degree, and each argumen of hese funcons s a homogenous of degree funcon of a connuum of dfferenaed ndvdual goods, wh consan elascy of subsuon λ across varees. The prce ndex P reflecs he weghs mpled by he consumpon aggregaor, and P = P( P, P ) = P( P, P ( P, P )), where agan each funcon s homogenous of degree. N T N T H F Frms are monopolsc compeors, and se prces as a markup over margnal cos. Assume frs ha all prces are fully flexble. In addon, le he producon echnologes of ypcal frms n he nonraded and raded secors of he home counry economy be (gnorng frm specfc noaon): YN = θ LN, YH = θ L H. Thus, here s a common echnology shock o boh secors, and he only npu o producon s labor. Fnally, we assume ha here exss a full se of sae conngen asses for sharng consumpon rsk across counres. There s only one ype of fundamenal shock n hs model, a shock o he counry specfc echnologes. Bu he argumen may be easly generalzed o oher shocks. I s sraghforward o show ha he equlbrum of hs economy, where all households whn a counry and all frms whn a secor are dencal, may be represened by he followng condons (leng foregn varables be denoed wh an asersk). (2.) P λ U ( C, L ) =, θ H 2 P λ U( C, L ) (2.2) θ L = P (, ) P P C, N N T (2.3) 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 9

11 (2.4) SP U( C, L) =Λ U( C, L). P Equaon (2.) relaes he equlbrum real prce for home goods o he prce-cos markup mes he frm s margnal cos, represened by he rao of he real wage o he echnology varable. Snce non-raded and raded goods share he same echnology, and labor s moble across secors, hs condon s he same for boh secors (so ha P N = P ). Equaons (2.2) and (2.3) represen marke clearng n he home nonraded and raded goods markes, respecvely, where he noaon represens he frs dervave of he prce ndex wh respec o he frs argumen, ec. Fnally, equaon (2.4) represens he rsk-sharng condon across counres, relang margnal ules o he real exchange rae (where he nomnal exchange rae), for a me-nvaran consan H Λ. P (, ) PN PT Equaons (2.)-(2.3), her analogues for he foregn economy, and equaon (2.4) represen a general equlbrum n seven equaons ha deermne he endogenous varables (where ldes denoe equlbrum values); C, C, L N, L H, L N, L SP H, and τ = P shocks F H, he erms of rade. The key feaure of hs soluon s ha represens a mappng from conemporaneous echnology θ and θ o he equlbrum values of endogenous varables. More parcularly, fuure echnology shocks have no mpac on allocaons or he erms of rade. In fac, he sysem (2.)-(2.4) conans no pas or fuure varables a all (excep Λ, whch reflecs nal wealh based on nal expecaons, and whch s no me-varyng.) The followng resul hen mmedaely follows. If nomnal prces P H and P F are scky, and he moneary auhory follows a rule amed o susan he flexble prce equlbrum of he model descrbed by (2.2)-(2.4), hen mus necessarly choose a value of he nomnal exchange rae ha s ndependen of unancpaed curren announcemens abou fuure echnology shocks (or news shocks). If hs were no he case, hen news shocks would affec he curren erms of rade, and allocaons would be pushed away from he flexble prce equlbrum of he model. We now explore he mplcaon of hs resul n a number of sengs where prces are scky. S s Secon 3. A Model wh One-perod Prce Seng. We now apply hs resul o a model where prces are pre-se for one perod. The model s a smple exenson of Devereux and Engel (2003) (henceforh DE) and s based also on Duare and Obsfeld (2005). We le: υ ρ = C + ρ ε P ε χ M ηl, ρ > 0, ε > 0, 0

12 γ CC T N where C = γ γ ( γ) γ ( γ ) and C T.5.5 = 2C CF. The parameer γ represens he share of raded goods n H consumpon. The prce ndces P are defned by P= P γ P γ, and P = P 0.5 P 0.5. T N T H F Followng Beaudry and Porer (2003), we assume ha echnology shocks have a componen ha s known one perod n advance of he shock. Thus, for he home counry, we assume ha he echnology shock s θ = θθ, θ = exp( v ), θ = exp( u ), 2 2 where v and u are normally dsrbued, wh mean zero, and varance 2 σ v and 2 σ u respecvely. The crcal feaure of he echnology process s ha he nnovaon n θ becomes known one perod n advance,.e. a me -. On he oher hand, he componen θ 2, s realzed a he same me as becomes known. 3 The mplcaon of hs assumpon s ha households and frms wll know par of fuure echnology nnovaons one perod n advance. Hence, snce n hs verson of he model prces are pre-se for only one perod, prces for fuure perods can fully adjus o a forecas n he echnology shock. Bu prces for he curren perod, based on perod - nformaon, canno adjus o he shock. The soluon o he model follows closely ha of DE. An approxmaon o he money marke equlbrum may be wren as: ρ (3.) m ( ) p = c Ep+ + ρec + p ρc +Γ m, ε ε where Γ m s a consan, s he seady-sae nomnal neres rae, and lower-case leers refer o logs of he respecve varables. An analogous condon may be derved for he foregn counry. The opmal rade-off beween consumpon and lesure mples: W (3.2) = η. ρ PC The rsk sharng condon mples: (3.3) where Γ 0 SP C =Γ 0 P C depends on nal condons and s no me-varyng. ρ, Prce Seng Prces for perod are se one perod n advance, based on perod - nformaon ses. Frms 3 Beaudry and Porer (2003) assume ha he forecasable componen of echnology s permanen. Here we assume ha s ransory. Ths makes lle dfference o he resuls of hs secon. In secon 4, some of deals of he resuls are alered n he presence of a permanen forecasable echnology shock, alhough he cenral resul (elmnang surprse exchange rae changes) s unchanged.

13 choose prces o maxmze profs usng he sochasc dscoun facor of her owners. We allow for expored goods prces o be se eher n he frm s own currency (producer currency prcng, or PCP) or n foregn currency (local currency prcng, or LCP). Equlbrum The goods marke equlbrum condon n he home counry non-raded goods secor s: PC (3.4) θ ( ) LN = γ, P N where L N represens employmen n he non-raded goods secor. In he raded goods secor, for he PCP prcng envronmen, he equlbrum condon s ( s employmen n he home raded goods secor): (3.5) (3.6) θ L H L H PC S P C = γ + 2 PH PH Wh LCP he goods-marke equlbrum condon n he home raded goods secor s wren as: θ L H PC P C = γ + 2 P H PH The dfference beween (3.5) and (3.6) s due o he fac ha n he laer case here are separae pre-se prces of home goods n domesc currency (for domesc sales) and foregn currency (for expor). Flexble-Prce Soluon Wh flexble prces, we may apply he condons (2.)-(2.4) o solve for consumpon and he erms of rade as: λη = λ ρ ( /2) ( /2) (3.7) C ( θ θ ) (3.8) γ θ 0 θ τ =Γ... γ γ ρ Whou non-raded goods, consumpon would be equalzed across counres. Generally however, wh γ <, home consumpon s more sensve o a home echnology shock han o a foregn echnology shock. Moneary Polcy Rules Money supply of each counry s gven by: (3.9) m = m + µ + δ, (3.0) m = m + µ + δ. Moneary polcy rules are desgned o respond o unancpaed shocks, so E ( µ ) = E ( µ ) = 0, and E ( δ ) = E ( δ ) = 0 wll hold. Here µ ( µ ) s an addon o he me nformaon se, whle δ 2 2 2

14 ( δ ) s an addon o he me - nformaon se. Noe ha hs assumpon means ha condonally (on me nformaon) expeced money growh wll vary over me, alhough he uncondonal expecaon of money growh s zero. Ths moneary rule s desgned so ha he µ componen reacs o curren u shocks, whle he δ componen reacs o fuure Exchange Rae and Consumpon under PCP (3.) v shocks, whch are announced oday. Wh PCP prcng, he law of one prce holds for raded goods. Hence, from (2.4): ( γ ) ( c E c) = ( c E c ) + ( s E s). ρ Unancpaed changes n he exchange rae wll affec he real exchange rae, and herefore relave consumpon levels, o he exen ha hey aler he nernaonal relave prce of non-raded goods, whch n hs model, s also equal o he erms of rade. Snce prces fully adjus afer one perod, he expeced real allocaons from nex perod on wll be governed by (3.7) and (3.8). Therefore: (3.2) Ec+ E c+ = ( 0.5 γ ) v+ 0.5 γv ρ. There are no expeced changes n nomnal neres raes from me perod + 2 onwards, snce he news shock s hen dsspaed, and n expecaon, he money sock s consan. We can hen use hs propery and he perod + verson of (3.), o oban: (3.3) ρ Ep+ E p+ = Em + E m+ ( Ec + E c+ ) ε. ρ( + ) = δ + Em E m ( Ec + E c+ ) ( + ε) Equaons (3.), (3.2), and (3.3) ogeher wh (3.), and he analogous equaons for he foregn counry, lead o he exchange rae: (3.4) ( ε ) ( γ )( v v ) + δ δ ( + ε ) ( m E m) ( m E m ) ( + ε ) s E s = + + ( γ( ε)) + ( γ( ε)) The exchange rae s he sum of wo elemens. Frs, here are revsons o curren fundamenals,.e. unancpaed movemens n relave money growh across he home and foregn counry. The second elemen s fuure fundamenals, capured by he second erm n (3.4). Ths s explaned as follows. When v > v, here s a shock o fuure home producvy ha exceeds ha o fuure foregn producvy. If n addon γ <, hs mus ncrease ancpaed consumpon a home more han n he foregn counry, snce home resdens consumpon s more sensve o home producvy n he presence of a non-raded goods secor. From (3.), holdng he curren moneary nnovaon consan, a rse n expeced fuure 3

15 home relave consumpon wll ncrease he home nomnal neres rae, relave o he foregn nomnal neres rae, when ε >. Ths wll reduce demand for money a home relave o he foregn counry, and as a resul here s an unancpaed home currency deprecaon. Fnally, fuure fundamenals also ncorporae fuure changes n he relave money supples, announcemens of fuure relave echnology growh raes. δ δ, whch can be forecased based on The key feaure of hs mechansm s ha he exchange rae responds o fuure fundamenals raher han curren fundamenals. Tha s, he me + producvy shock becomes known a me, and generaes news, whch leads he curren exchange rae o move, and he resulng changes n he expeced fuure money supply have a smlar effec. There are no changes n curren supply or demand varables, however. How do home and foregn consumpon raes respond o fuure producvy shocks? Agan from he money marke clearng condon (3.), we can derve he expresson for he unexpeced response of home and foregn consumpon, respecvely, as: γ ( ε ) δ = 2 + +, ( + ) ( + ε ) ρ (3.5) c E c φ ( m E m ) ( s E s ) ( Ec E c ) + + γ ( ε ) δ = ( + ) ( + ε ) ρ (3.6) c E c φ ( m E m ) ( s E s) ( Ec + E c+ ) + ε where φ ρ +. We may explan hese expressons as follows. Take equaon (3.5), and magne ha here s an ancpaed posve home counry producvy shock. Then here s a rse n expeced fuure home consumpon, whch wll end o rase nomnal neres raes when ε >. Ths causes an excess supply of home money, and would lead o an unancpaed rse n curren home consumpon. Agans hs, however, s he fac ha he ancpaed home producvy shock causes an exchange rae deprecaon, when ε >. Ths reduces real money supply, and ends o reduce home consumpon. The ne effec on curren perod home consumpon may be posve or negave. When ε < he reasonng goes he oher way. The mpac of fuure money supply changes are sraghforward a posve δ represens an expeced fuure moneary expanson, whch rases nomnal neres raes and rases curren consumpon. Local-Currency Prcng (LCP) Under local-currency prcng, he law of one prce wll no generally hold. Snce wh LCP all domesc and foregn nomnal goods prces are pre-deermned, he CPIs of each counry are also 4

16 predeermned. Then, from (3.3), we ge: (3.7) ( c E c ) ( c E c ) ( s E s ρ = + ). The behavor of expeced perod + consumpon s he same as n (3.7), snce LCP and PCP are equvalen o one anoher afer prces have fully adjused. For he same reason, equaon (3.3) s he same as before. Then, equaons (3.7), (3.7), (3.3), and he money marke equlbrum condons (3.) for each counry, gve: (3.8) + ε ( ε ) s E s = ( m E m) ( m E m ) + ( γ )( v v ) + δ δ + ( + ) ( + ε ). Ths dffers from expresson (3.4) due o he fac ha prce levels are predeermned under LCP. Bu qualavely, we ge a smlar message. The exchange rae s a funcon of curren and fuure fundamenals. A fuure producvy shock, whch becomes known oday, represens `news, whch mpacs on he curren exchange rae. The sze of hs effec depends on he sze of he non-raded goods secor, as well as he sze of ε. The mpac of fuure producvy shocks on consumpon s gven by: ( ε ) δ = + +, ( + ) ( + ε ) ρ (3.9) c E c φ( m E m ) ( Ec E c ) + + ( ε ) δ = + + ( + ) ( + ε ) ρ (3.20) c E c φ( m E m ) ( Ec + E c+ ) These effecs are equvalen o he PCP case, save for he absence of he exchange rae from (3.9) and (3.20), snce movemens n he exchange rae no longer drecly mpac on CPI values. Bu agan, as n he PCP case, we have announcemens effecs of fuure producvy shocks nfluencng curren consumpon. Ths case also allows us o be more precse regardng he mpac of fuure producvy shocks. Whenever ε >, a rse n fuure home or foregn producvy wll lead o a rse n curren consumpon. Ths happens because here s no secondary channel of he nal neres rae ncrease arsng from he fuure producvy shock, as exss n he PCP case. Opmal Moneary Polcy wh News Shocks So far we have no been specfc abou he moneary polcy response o curren or ancpaed fuure producvy shocks. Implc n he analyss above s ha curren producvy shocks (.e. shocks o θ 2 ) have no mpac on eher he exchange rae or consumpon, ndependen of he endogenous response of moneary polcy. Bu, followng he analyss of DE, here are clear welfare reasons why moneary polcy should be desgned o ensure he effcen response of he real economy o curren 5

17 producvy shocks n he presence of scky prces. The opmal values for he moneary polcy response o curren producvy shocks are smlar o hose analyzed n DE and Duare and Obsfeld (2005). For he PCP model, he moneary polcy responses n he home and foregn currency can perfecly replcae he flexble prce equlbrum. For he LCP model, gven he absence of exchange rae pass-hrough, he flexble prce equlbrum canno be susaned. The opmal moneary polcy response ensures ha consumpon responds o curren producvy shocks as n he flexble prce equlbrum, bu he exchange rae responds by less han n he flexble prce equlbrum. In face of ancpaed fuure producvy shocks however, he raonale for an opmal polcy response becomes less clear. When here s a shock o θ +, whch by assumpon s observed a me, hen prces have he chance o respond fully before he shock akes effec. In ha case, here s no reason for moneary polcy o be used n order o ensure he effcen adjusmen of he perod + allocaons o he producvy shock. Bu he key feaure of our examples above, and he cenral message of he paper, s ha hese ancpaed fuure shocks wll affec he economy n he presen. Tha s, by mpacng on neres raes and exchange raes, curren consumpon wll be moved away from s flexble prce equlbrum, gven by (3.7). The reason s ha, whle fuure prces have me o adjus o he shock ha occurs n perod +, curren prces canno reac o he announcemen. To he exen ha he announcemen effecs shf curren allocaons away from her flexble prce equlbrum, hey are undesrable, and an opmal moneary polcy can be devsed o deal wh hs. The naure of he opmal moneary polcy for fuure producvy shocks urns ou o be he same, for boh ypes of prcng. Thus, we can sae: Resul : Le he moneary polcy rules be defned as δ = av 0 + av δ = av + av 0 Then for boh LCP and PCP, he opmal moneary rule s descrbed by Proof: a ( ε ) γ = a = ( ) ( + ε ) 2 0 ( ε ) γ a = a0 =. ( + ε ) 2 These rules elmnae he mpac of fuure producvy shocks on curren consumpon n boh counres. Therefore, employmen s also unchanged. Therefore he rules susan he flexble prce equlbrum, n face of announced fuure producvy shocks. Resul 2: The opmal moneary rules from Resul preven he exchange rae from respondng o fuure producvy shocks. Proof: By nspecon.. 6

18 Resul 2 s n a sense he more neresng one. Sandard Opmal Currency Area (OCA) reasonng suggess ha s effcen o allow he exchange rae o respond o counry specfc producvy shocks. We fnd, n he absence of a moneary response, ha ndeed he exchange rae wll respond o announcemens of counry specfc producvy shocks. The drecon of movemen depends on he sze of ε. For ε >, he exchange rae wll deprecae n response o an announced fuure home producvy expanson. I s empng o nerpre hs movemen along effcency (or OCA) lnes he fuure home producvy expanson should cause a home counry erms of rade deeroraon. Hence, he response of agens n fnancal markes, forecasng hs, leads o an mmedae nomnal exchange rae deprecaon. Bu he problem wh hs reasonng s ha he mmedae response of he curren nomnal exchange rae causes a change n he curren real exchange rae (by dfferen degrees n he PCP and LCP envronmens), because curren nomnal prces canno respond o he announced fuure shock. In he absence of a curren (as opposed o fuure) producvy shock, however, here s no effcency reason for he real exchange rae o move a all. In fac, movemens n he real exchange rae are assocaed wh welfare losses snce hey push consumpon and employmen away from her effcen levels. Thus, n a scky prce envronmen, when he exchange rae responds o `news, here s no guaranee ha wll do so n an effcen manner. Indeed, n our model, he opmal moneary rule should preven he exchange rae from respondng o news shocks a all. The crcal requremen s ha here no be any unancpaed movemens n he exchange rae. Tha s, he me exchange rae wll be known n me -. Gven he form of he moneary rules defned here, we can acually go beyond hs, and esablsh ha under hese rules he exchange rae s fxed over me (when all shocks are observed n advance). To see hs, noe ha ρε ( ) + = ρ( + + ) = ( + + ) s c c p p c c m m ( + ε ) ρε ( ) ( ε ) ( γ) = ( + ε) ( + ε) ( c c ) m m ( v v ) δ δ ρε ( ) = ( c c ) + m m = s ( + ε ) The frs equaly comes drecly from he rsk sharng condon (2.5). The second comes from he soluons for perod + prces dscussed before equaon (3.3). The hrd equaly comes from a decomposon of money growh and consumpon growh, whle he fourh uses he opmal money rule of Resul. Hence, he moneary auhory follows a rule n whch nex perod s money supply responds o fuure producvy shocks, leng nomnal prce levels ake he full burden of adjusng he fuure real exchange rae o he producvy shocks, and keepng he exchange rae fxed over me. From a welfare 7

19 perspecve however, hs s no necessary. The effcen allocaon could jus as easly be aaned by a polcy whch prevens he curren exchange rae from reacng o news shocks, bu allowng par of he real exchange rae adjusmen o occur va movemens n he fuure nomnal exchange rae. Thus, here could be expeced changes n he exchange rae over me. These changes would no be cosly, because prces can adjus over he same me frame. The crcal ngreden n he analyss s ha fuure producvy shocks do no generae surprse movemens n he curren nomnal exchange rae. Of course he model s que sylzed, snce we have assumed ha all prces can adjus before he news akes effec. Bu hs s no necessarly unrealsc. A an anecdoal level, we see he exchange rae respondng o all ypes of poenal evens (e.g. effecs of Socal Secury changes ha may affec he budge defc n 5 or more years me) ha may occur much furher n he fuure han would be relevan for busness cycle frequences. These exchange rae movemens are no necessarly desrable, because we have o recognze ha he response o fuure shocks may no be conssen wh he currenly desred srucure of relave prces. Neverheless, we now urn o an exended verson of he model, whch assumes ha nomnal prces mus be adjused gradually raher han all a once. Secon 4. Exenson o Gradual Prce Adjusmen We now exend he model o allow gradual prce adjusmen usng he Calvo specfcaon where only a gven fracon of frms may adjus her prces whn a perod, and ex ane, all frms have an equal chance of prce adjusmen. The specfcaon for households and frms s unchanged excep for he prce seng rule. For smplcy, we focus only on he PCP prcng case. In addon, o make he analyss comparable o he prevous model, we follow Roemberg and Woodford (997) n assumng ha a frm ha has an opporuny o change s prce mus se s prce for perod wh nformaon based on perod -. Tha s, prces ha are adjused are se one perod n advance, as n he prevous model. Unlke he prevous model however, no all prces are adjused n every perod. Assume ha all frms n boh counres have a probably κ of recevng an opporuny o change her prce n any perod. Then he newly se prce for any home counry frm n he non-raded goods secor ha can change s prce for perod s gven by (4.) P N W E P Y λ = λ C ρ + λ + ( βκ) N+ N+ = 0 θ + P+ ρ λ C+ E ( βκ) PN+ YN+ = 0 P+. Usng sandard properes of he Calvo prce seng scheme, we may wre he non-raded goods prce ndex as (4.2) P λ N = κp λ N ( κ) P λ + N. 8

20 Now, akng a lnear approxmaon of (4.) and (4.2) around a zero-nflaon seady sae, and pung he wo condons ogeher, we may oban he convenonal forward lookng nflaon equaon, gven by (4.3) π N = ϕe ( w pn u v ) + βe πn +. Snce he margnal cos facng frms n he home counry raded goods secor s dencal o ha of he non-raded goods frm, o a lnear approxmaon he prce nflaon equaon for raded goods wll be dencal o (4.3). We hen follow he convenon of referrng o nflaon n he home goods prce (eher raded or non-raded) as π. To conform o he sandard n he leraure, we assume now ha he moneary auhores follow an neres rae rule raher han a rule for he money supply. The gross nomnal neres rae n he home economy may be read off he Euler equaon as: ρ ρ C C + (4.4) R = E β P P+ Agan, akng a lnear approxmaon around a seady sae: γ (4.5) r = r + ρe( c+ c) + Eπ+ + E( τ+ τ), 2 where τ = p + s p f an neres rae rule gven by: (4.6) r = r + σπ + δ, h s he home counry erms of rade. Assume ha he moneary auhory follows where E δ = 0. 4 Dfferen assumpons regardng δ wll be examned below. Table 2 descrbes he full model. u = 0. 5 For smplcy, we deal for now only wh he case where all shocks are `news shocks, so ha Noe ha he flexble prce soluon o he model s dencal o (3.7) and (3.8) above, so ha γ γ γ γ c v v c v ρ 2 2 ρ 2 2 = ( ) +, = ( ) + v, and τ v v he erms of rade are ndependen of ancpaed fuure producvy shocks. =. Effcen consumpon and The objecve of moneary polcy, as n he prevous secon, should be o replcae he response of he flexble prce economy. Bu n conras o he prevous secon, here s an ndependen welfare cos of nflaon, even f s perfecly ancpaed. Ths s because n an envronmen of gradual prce adjusmen, nflaon generaes prce dsperson, snce no all frms may change her prces 4 Under he Taylor rule gven by equaon (4.3), nflaon s ancpaed one perod n advance. So argeng acual nflaon or one-perod ahead ancpaed nflaon s equvalen. Svensson and Woodford (2005) have advocaed nflaon forecas argeng. 5 Snce he nflaon rae s predeermned, an opmal polcy response o a curren producvy dsurbance wll requre an neres rae adjusmen: δ wll need o fall n response o a posve u shock. 9

21 smulaneously. By seng nflaon o zero, frms wll never wsh o adjus her prces, and hus prce dsperson wll be elmnaed. As n Woodford (2003), an opmal moneary polcy should herefore replcae he response of he flexble prce economy, whle achevng a zero rae of prce change. Table 2 The model wh gradual prce adjusmen Home nflaon γ π = ϕe ( ρc + τ u v ) + βe π + 2 Foregn nflaon γ π = ϕe ( ρc τ u v ) + βe π + 2 Rsk sharng ρ( c c ) = ( γτ ) Home neres rae γ 2 σπ + δ = ρe( c+ c) + Eπ+ + E( τ+ τ ) Foregn neres rae γ σπ + δ = ρe( c+ c ) + Eπ+ E( τ+ τ) 2 Noe ha so long as he moneary auhory follows a rule n whch σ >, he sysem n Table 2 s saddle pah sable, and here s a unque soluon for bounded shock processes. Case. Smple Inflaon Targeng Assume ha he moneary auhores follow a smple nflaon argeng polcy, seng σ >, bu no adjusng neres raes o ex-pos nformaon, so ha δ = 0. We may wre he general soluons for he erms of rade as τ = av 0 + av 0 + av + av. Noe ha, snce all prces are pre-se, he unancpaed componen of he erms of rade; τ E τ = av + av, s equvalen o he movemen n he nomnal exchange rae. I s easy o verfy ha: (4.7) The soluon for home counry nflaon s wren as: a a σϕ ( ) 0 0, a a σ ϕ = = = =. + σϕ + σϕ ϕ (4.8) π = v. + σϕ The consumpon responses may be wren as: 20

22 (4.9) ϕσ γ γ ϕ( σ -) γ γ c = - v v - ( σϕ+) ρ ( σϕ+) ρ v + v 2 2, ϕσ γ γ ϕ( σ -) γ γ (4.0) c = - v v - ( σϕ+) ρ ( σϕ+) ρ v + v 2 2 As we ncrease he `ghness of he moneary polcy rule (.e. seng σ ), he varance of nflaon falls o zero. Ths also ensures ha he ancpaed componen of he erms of rade and consumpon responds as n he flexble prce equlbrum. Bu hs fals o suppor he full flexble prce equlbrum, because does no generae he approprae response of he erms of rade o conemporaneous news shocks. In fac, a gh money rule exacerbaes he neffcency of news shocks. As σ ncreases, he response of he nomnal exchange rae movemen o news shocks s ncreased, generang a larger (neffcen) erms of rade and consumpon movemen. 6 The nuve explanaon for he relaonshp beween he sance of moneary polcy (as descrbed by he parameer σ ) and he response o news shocks can be undersood as follows. Snce a posve news shock wll rase fuure consumpon, wll end o rase real neres raes n boh counres. Bu wh advance prce seng and he neres rae rule (4.6), he nomnal neres rae s pre-deermned wh respec o curren news shocks. Moreover, he hgher s σ, he smaller s he mpac of news shocks on ancpaed nflaon. Gven ha boh he nomnal neres rae and ancpaed nflaon are smoohed, he upsho s ha he equlbrum real neres rae s prevened from respondng he news shock, and more so, he hgher s σ. Ths makes he news shock more expansonary n he curren perod, rasng consumpon n boh counres. A smlar explanaon les behnd he erms of rade response o he news shock. Combnng he wo neres rae equaons n Table 2, we have an equaon n he erms of rade and nflaon dfferenals, gven by: (4.) σ π = Eτ+ τ + E π+, where π π π. Agan, a news shock wll end o ncrease he ancpaed fuure erms of rade, as ncreases home relave o foregn producvy. Wh perfecly flexble prces, he mpac would be offse by a fall n ancpaed fuure relave nflaon. Bu when nflaon argeng sablzes expeced nflaon, he change n he ancpaed fuure erms of rade splls over no he curren erms of rade. 6 There s no separae role n he Taylor rule for he oupu gap. Bu, as n Clarda, Gal, and Gerler (2002), we can nroduce mark-up shocks ha lead oupu o devae from effcen levels. When ha shock has a common elemen across counres, he oupu gap (a home and n he foregn counry) should ener he Taylor rule. Bu even wh he oupu gap n he Taylor rule o deal wh hs dsoron, here remans he dsoron when he erms of rade reac o news. Terms of rade shocks mus ener as a separae erm, as n Case 3 below. 2

23 Case 2. Targeng news shocks. δ = cv + cv Now exend he neres rae rule so ha δ = cv 0 + cv for he home auhores, and for he foregn moneary auhores. Seng c = and 0 0 nflaon s zero (for any value of c = jonly ensures ha σ > ) and he erms of rade (and consumpon) respond as n he fully flexble prce equlbrum. Noe ha hs mples ha he nomnal exchange rae s nsulaed agans news shocks. Bu does no mean ha he exchange rae s fxed over me. The effcen moneary rule ensures ha he nflaon rae of domesc goods prces s zero n each counry. Hence all erms of rade movemen mus nvolve exchange rae changes. Bu he key feaure of hs rule s ha elmnaes any unancpaed exchange rae changes. The exchange rae wll change n response o conemporaneous producvy shocks. Bu hs change s ancpaed one perod n advance. Case 3. Targeng exchange raes. Snce he opmal moneary polcy elmnaes exchange rae surprses, s here a case for ncludng he exchange rae drecly n he neres rae rule? Say now ha he sae-conngen componen of neres rae rules for he home and foregn counry are gven by ω ω (4.2) δ = ( τ E τ), δ = ( τ E τ). 2 2 We may solve he model under hs specfcaon. The soluon for he erms of rade s gven by: σϕ ( σ ) ϕ (4.3) τ = ( v v ) + ( v v ). + σϕ + ω + σϕ Ths dffers from case only due o he presence of he ω expresson. Bu hs dfference s crucal, for allows he polcy maker o jonly ensure ha he erms of rade responds appropraely o conemporaneous producvy shocks hrough an ex-ane `gh money rule (.e. seng σ very hgh) rasng neres raes n response o ancpaed nflaon shocks, whle a he same me elmnang he effecs of news shocks on he erms of rade hrough an ex-pos neres rae rule whch rases neres raes n response o an unancpaed nomnal exchange rae deprecaon (seng ω very hgh). Hence, n he presence of news shocks, he sandard nflaon argeng prescrpon for an opmal moneary rule s no adequae. I can be mproved by an explc ncluson of he exchange rae n he neres rae rule. More precsely, he polcy-maker should arge a low expeced rae of nflaon, and dampen any unexpeced movemens n he nomnal exchange rae. Of course, hs analyss perans only o he response o news shocks. As poned ou n foonoe 3 above, o he exen ha here are unancpaed curren producvy shocks, he opmal moneary polcy should allow he exchange rae o respond mmedaely. Then, he exen o whch moneary polcy 22