Standard models used for monetary policy analysis typically assume that households and

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1 Cenennial Issue Annuncemens and he Rle f Plicy Guidance Carl E. Walsh By prviding guidance abu fuure ecnmic develpmens, cenral banks can affec privae secr expecains and decisins. This can imprve welfare by reducing privae secr frecas errrs, bu i can als magnify he impac f nise in cenral bank frecass. I emply a mdel f heergeneus infrmain cmpare ucmes under paque and ransparen mneary plicies. While beer cenral bank infrmain is always welfare imprving, mre cenral bank infrmain may n be. (JEL E5, E58) This aricle firs appeared in he July/Augus 008 issue f Review. Federal Reserve Bank f S. Luis Review, Nvember/December 03, 95(6), pp Sandard mdels used fr mneary plicy analysis ypically assume ha husehlds and firms and he cenral bank share a cmmn infrmain se and ecnmic mdel, ye acual plicy decisins are aken in an envirnmen in which heergeneus infrmain is he nrm and many alernaive mdels cexis. The resuling heergeneiy in views can play an impran rle in affecing bh plicy chices and he mneary ransmissin prcess. Transparency in he cnduc f plicy can help reduce heergeneus infrmain. Inflainargeing cenral banks, fr example, make significan aemps reduce uncerainy abu plicy bjecives, such as hrugh he release f deailed inflain and upu prjecins, ensure he public shares cenral bank infrmain abu fuure ecnmy develpmens. By being ransparen abu is bjecives and is ulk fr he ecnmy, cenral banks help prvide he public wih guidance abu he fuure. Bu prviding guidance carries risks. As Ple (005, p. 6) has expressed i, [F]r me he issue is wheher under nrmal and ruine circumsances frward guidance will cnvey infrmain r wheher i will creae addiinal uncerainy. Because any frecas released by he cenral bank is subjec errr, being mre ransparen may simply lead he privae secr reac wha was, in rerspec, nise in he frecas. The pssibiliy ha he privae secr may verreac cenral bank annuncemens des capure a A he ime his aricle was wrien, Carl E. Walsh was a prfessr f ecnmics a he Universiy f Califrnia, Sana Cruz, and a visiing schlar a he Federal Reserve Bank f San Francisc. This aricle has been refrmaed since is riginal publicain in Review: Walsh, Carl E. Annuncemens and he Rle f Plicy Guidance. Federal Reserve Bank f S. Luis Review, July/Augus 008, 90(4), pp. 4-4; hp://research.sluisfed.rg/publicains/review/08/07/walsh.pdf. 03, The Federal Reserve Bank f S. Luis. The views expressed in his aricle are hse f he auhr(s) and d n necessarily reflec he views f he Federal Reserve Sysem, he Bard f Gvernrs, r he reginal Federal Reserve Banks. Aricles may be reprined, reprduced, published, disribued, displayed, and ransmied in heir enirey if cpyrigh nice, auhr name(s), and full ciain are included. Absracs, synpses, and her derivaive wrks may be made nly wih prir wrien permissin f he Federal Reserve Bank f S. Luis. Federal Reserve Bank f S. Luis REVIEW Nvember/December

2 Walsh cncern expressed by sme plicymakers. Fr example, in discussing he release f Federal Open Marke Cmmiee (FOMC) minues, Jane Yellen expressed he view ha Financial markes culd misinerpre and verreac he minues (Yellen, 005, p. ). In his paper, I explre he rle f ecnmic ransparency specifically, ransparency abu he cenral bank s assessmen f fuure ecnmic cndiins in alering he effeciveness f mneary plicy. I d s in a framewrk in which cenral bank prjecins may cnvey useful infrmain bu may als inrduce inefficien flucuains in he ecnmy. A fcus n ecnmic ransparency seems apprpriae fr undersanding he issues facing many cenral banks. The recen cncerns abu he implicains f he subprime mrgage marke reflec, in par, privae secr uncerainy abu he Fed s view f he ecnmic ulk and he way he ulk fr inflain and real ecnmic aciviy may be affeced by financial marke cndiins. Thrughu 007, fr example, many financial marke paricipans appeared hld mre pessimisic views han he Federal Reserve abu fuure ecnmic develpmens ; and in recen mnhs, marke paricipans have fen expeced significan ineres rae cus, while sme members f he FOMC have emphasized cncerns abu he ulk fr inflain, suggesing hey saw less need fr rae reducins. News reprs speculaing n pssible ineres rae cus by he Fed r he Eurpean Cenral Bank fcused very lile n uncerainy abu cenral bank preferences bu a grea deal n he uncerainy abu he ulk fr he ecnmy. These reprs reveal heergeneiy amng privae frecasers and uncerainy abu he Fed s (r he Eurpean Cenral Bank s) ulk fr he ecnmy. And public saemens by cenral bankers were designed cmmunicae heir views n fuure ecnmic develpmens. Jean-Claude Triche s saemen ha he markes have gne prgressively back nrmal (Akins, Mackenzie, and Davies, 007, p. ) and Ben Bernanke s (007) cmmen ha husing remains a significan drag n he ecnmy, bh exemplify hw cenral bankers signal heir assessmen f ecnmic cndiins, and his assessmen is ne facr ha influences he (heergeneus) ulks amng members f he privae secr. The uncerainy in financial markes in recen mnhs illusraes clearly he significan differences ha can arise beween he cenral bank and privae marke paricipans. This is a classic example f heergeneus infrmain abu he ecnmy. Much f he debae has been fcused n he quesin f fuure ineres rae cus, bu he underlying issues appear be relaed differing views amng privae frecasers and beween privae frecasers and he Fed ver he likely impac f financial marke disurbances n he real ecnmy and he likelihd f a fuure recessin. The nex secin discusses he w gals f ransparency Bill Ple (005) has sressed accunabiliy and plicy effeciveness. The hird secin develps a mdel f asymmeric and heergeneus ecnmic infrmain ha can be used mdel he implicains f ransparency. Tw plicy regimes are cnsidered. In he firs, he public bserves he plicy insrumen f he cenral bank bu he cenral bank prvides n furher infrmain he public. In he secnd, he cenral bank prvides infrmain n is ulk fr fuure ecnmic develpmens. The welfare implicains f hese regimes are discussed in he furh secin. Wihin each regime, beer qualiy cenral bank infrmain is always welfare imprving (he pr-ransparency aspec f Mrris and Shin, 00, emphasized by Svenssn, 006). Hwever, acrss regimes, mre cenral bank infrmain has ambiguus effecs. 576 Nvember/December 03 Federal Reserve Bank f S. Luis REVIEW

3 THE GOALS OF TRANSPARENCY Transparency requires asymmeric infrmain, bu he naure f his asymmery can ake many frms. In fac, Geraas (00) has classified five ypes f ransparency pliical, prcedural, ecnmic, plicy, and perainal. Briefly, hese crrespnd cenral bank ransparency abu bjecives, he inernal decisinmaking prcess, frecass and mdels, plicy acins, and insrumen seing and cnrl errrs. Each f hese dimensins f ransparency is impran and has been sudied exensively (see Geraas, 00, fr a survey). In recen years, cenral banks have becme mre ransparen alng all hese dimensins, and levels f ransparency ha wuld have been viewed as excepinal 0 years ag are day acceped as bes pracice amng mdern cenral banks. The rend ward independen cenral banks wih explici mandaes assigned hem and he widespread adpin f inflain argeing has cnribued grealy pliical ransparency. The Bank f England is amng he ms prcedurally ransparen cenral banks, publishing minues and individual ves f is Mneary Plicy Cmmiee discussins. Cenral banks, such as he Federal Reserve, ha were frmerly relucan cmmunicae plicy acins direcly nw d s clearly, imely, and direcly. The ms ransparen cenral banks, such as he Reserve Bank f New Zealand and he Bank f Nrway, publish heir prjecins fr he plicy ineres rae. The use f a shr-erm ineres rae as he plicy insrumen has grealy enhanced perainal ransparency. Bu alhugh ms cenral banks day are ransparen abu heir plicy sance and perainal prcedures smehing hard avid when he plicy insrumen is a shr-erm marke ineres rae here is much greaer variain in he exen which cenral banks are ransparen abu heir decisinmaking prcess, heir inernal frecass, and heir plicy bjecives. Bu wha is he pin f being ransparen? As ned earlier, Ple (006) has ariculaed w gals f ransparency: mee he Fed s respnsibiliy be pliically accunable and make mneary plicy mre effecive. The nex w subsecins discuss each f hese gals. Transparency and Accunabiliy The rle ransparency plays in suppring accunabiliy can differ depending n wheher he ulimae bjecives f mneary plicy are bservable r unbservable. Cnsider firs he case in which he bjecives f mneary plicy are, ex ps, clearly measurable and bservable. Fr cncreeness, assume inflain is he nly bjecive f he cenral bank and here is agreemen n he apprpriae measure f inflain ha he cenral bank shuld cnrl. In his envirnmen, i is in principle sraighfrward ensure accunabiliy. Observing he ex ps rae f inflain wuld seem prvide a simple means fr judging he perfrmance f he cenral bank. Hwever, even under he cndiins specified (a single measurable bjecive), he ex ps realizain f inflain is n a sufficien perfrmance measure. The reasn is ha inflain is n direcly cnrllable even under an pimal plicy (where he cenral bank is ding exacly wha i shuld be ding), he realized inflain rae can differ frm he desired value. This difference may be small, bu as lng as here is any randm variain ha is beynd he abiliy f he cenral bank eliminae, public accunabiliy based slely n inflain ucmes will punish sme gd cenral bankers and reward sme lucky nes. Cenennial Issue Federal Reserve Bank f S. Luis REVIEW Nvember/December

4 Walsh Transparency can help prme accunabiliy by allwing he public base is evaluain f he cenral bank n jus n bserved inflain bu n he infrmain ha was available he cenral bank when i had make is plicy decisin. Having access inernal bank frecass, fr example, allws usiders evaluae he decisins made by he cenral bank. This can miigae sme f he prblems assciaed wih evaluains based slely n realized inflain. Having access he infrmain n which decisins were based helps remve he influence f randm uncnrllable evens ha affec inflain and herefre supprs a beer sysem f accunabiliy. 3 In general, hwever, plicy bjecives are n direcly bservable, and hey may even be inherenly unmeasurable. Cerainly, recen hereical mdels, which have emphasized he use f he welfare f he represenaive agen as he apprpriae bjecive f plicy, have defined pimal plicy in erms f unmeasurable bjecives. I is n clear ha we culd reach agreemen n he crrec way measure welfare, as ha depends n he specific mdel we believe characerizes he ecnmy, even if we culd agree n hw define welfare. I cerainly is n bservable. Transparency can be especially criical when bjecives are unbserved. Assessing, r hlding accunable, an ecnmic agen when bjecives are unbservable is n a siuain unique mneary plicy and cenral banks. Educain is perhaps he ms prminen field in which public plicy mus deal wih his siuain; he bjecives are high-qualiy educain and eaching bu here exiss wide disagreemen ver hw define and measure hese qualiies. Because scial welfare des depend n inflain and inflain can be bserved, ne migh use inflain as a ype f perfrmance measure, hlding he cenral bank accunable fr achieving a lw and sable inflain rae. Inflain argeing can be hugh f as defining a perfrmance measure fr he cenral bank. The criical issue in chsing any perfrmance measure, hwever, is hw pwerful ne wans make he incenives. If accunabiliy is based sricly n realized inflain and he cnsequences f missing he arge are large, hen he cenral bank will naurally fcus n achieving he arge, even if his means sacrificing her, mre difficul measure, aspecs f scial welfare. The cncern ha inflain-argeing prduces much f a fcus n inflain cnrl is a he hear f ms criicisms f inflain argeing in he Unied Saes. Bu his is where ransparency becmes paricularly impran. Greaer ransparency can lessen he need rely n a single easily measured perfrmance indicar. When here is greaer ransparency, and he public is able assess he same infrmain he cenral bank has used se plicy, i is n lnger necessary base cenral bank accunabiliy n inflain ucmes nly (Walsh, 999). Transparency and he Effeciveness f Mneary Plicy Ple s secnd gal f ransparency, prming plicy effeciveness, requires ha privae secr decisins be influenced, and influenced sysemaically, by he infrmain cenral banks prvide. Wih he develpmen f New Keynesian mdels and heir emphasis n he imprance f frward-lking behavir, managing expecains imprve plicy effeciveness has aken n a new imprance. Wdfrd (005) has gne s far as sae ha n nly d expecains abu plicy maer, bu, a leas under curren cndiins, very lile else maers Nvember/December 03 Federal Reserve Bank f S. Luis REVIEW

5 The inuiin fr Wdfrd s saemen is sraighfrward. Plicymakers cnrl direcly nly a shr-erm ineres rae. Ye rainal agens are frward lking and s base heir spending and pricing decisins n heir assessmen f fuure ineres raes, n jus curren raes. The recgniin ha expecains maer is n cnfined academics; a recen aricle in he Financial Times (Guha, 007) saes ha Wha really maers, bh fr he markes and he ecnmy, is n he curren plicy rae bu he expeced pah f fuure raes. Transparency and is relainship plicy effeciveness played a key rle in he large lieraure ha fcused n he average inflain rae bias ha culd arise under pimal discreinary plicy. By and large, his lieraure emphasized pliical and perainal ransparency, and i emplyed mdels in which plicy surprises were he surce f he real effecs f mneary plicy. Geraas (00) prvides an excellen survey f he lieraure. In hese mdels, he cenral bank preferences were generally reaed as schasic and unknwn. The plicy insrumen was als aken be bserved wih errr r subjec a cnrl errr. Fr example, he cenral bank migh cnrl nnbrrwed reserves, bu his allwed nly imperfec cnrl f he mney supply. 5 Observing mney grwh wuld n prvide enugh infrmain fr he public disenangle he effecs f cnrl errrs frm shifs in cenral bank preferences. Thus, here was paqueness abu pliical bjecives and perainal implemenain. Trans par ency was ypically mdeled as a reducin in he nise in he signal n he plicy insrumen. The pimal degree f ransparency ensured he public wuld learn quickly when he cenral bank preferences shifed, bu sill lef pen he pssibiliy ha he bank culd creae a surprise if ne was needed aid sabiliy. Cukierman and Melzer (986) shwed ha he cenral bank may prefer adp a less efficien peraing prcedure han is echnically feasible (i.e., n reduce he cnrl errr variance is minimum pssible level). 6 As emphasized in recen discussins f ransparency, hwever, New Keynesian mdels imply ha i is predicable mneary plicies, n surprises, ha are ms effecive in achieving plicy gals. In such an envirnmen, ranspar ency, raher han reducing he efficacy f plicy can acually increase i. Cenral bank annuncemens abu fuure plicy acins, r abu fuure ecnmic develpmens, can affec privae secr expecains f fuure ineres raes, inflain, and ecnmic aciviy. Wih spending and pricing decisins dependen n hese expecains, using annuncemens influence expecains gives he cenral bank an addiinal plicy insrumen. As such, i serves make plicy mre effecive. The argumen ha ransparency can increase he effeciveness f mneary plicy is cerainly mre cnsisen wih he mdern pracice f cenral banks, which has been unifrmly mve in he direcin f greaer ransparency. Bu prviding infrmain he public may have penial css. These css are assciaed wih he cndiinal naure f any frecas. Sme ecnmiss have wrried ha he public will n undersand he disincin beween a cndiinal and an uncndiinal frecas. 7 Paricu larly because repuain is impran, deviaing frm a previusly annunced plicy pah may be inerpreed as a deviain frm a cmmimen equilibrium raher han as an apprpriae respnse based n new infrmain. If a cenral bank fails raise ineres raes afer signaling ha i planned, he privae secr may believe he bank has becme less cncerned abu inflain, causing inflain expecains rise. Financial marke paricipans may underesimae he cndiinaliy f he annunced rae pah and s view deviains as inrducing unwarraned Cenennial Issue Federal Reserve Bank f S. Luis REVIEW Nvember/December

6 Walsh uncerainy in financial markes. These facrs may make he cenral bank relucan adjus raes, prducing a lck-in effec ha wuld reduce flexibiliy and limi plicy effeciveness. Even when he public undersands he cndiinal naure f he guidance prvided by he cenral bank, annuncemens may inrduce new surces f vlailiy. The influenial paper by Mrris and Shin (00) has highlighed ne channel hrugh which cenral bank annuncemens may have a derimenal effec. Unlike sandard mdels ha assume all privae agens share he same infrmain, Mrris and Shin fcus n he mre realisic case in which privae agens have individual, heergeneus surces f infrmain and mus aemp frecas wha hers are expecing. 8 Mrris and Shin have argued ha here can be a cs prviding mre-accurae public infrmain; agens may verreac public infrmain, making he ecnmy mre sensiive any frecas errrs in he public infrmain. Subsequen research (e.g., Hellwig, 004, and Svenssn, 006) has suggesed ha he Mrris- Shin resul is n a general ne and ha beer, mre accurae, cenral bank infrmain is welfare imprving. Hwever, jus as he earlier lieraure n ransparency emplyed mdels a dds wih curren plicy framewrks (nly surprises maered, he mney supply was he insrumen), he Mrris-Shin analysis is cnduced wihin a framewrk ha fails capure impran aspecs f acual mneary plicy. Fr example, he issue facing ms cenral banks is n wheher prvide mre-accurae frecass. Insead, he issue is wheher r n prvide mre infrmain by, fr example, annuncing frecass. And even in he absence f explici annuncemens r guidance, cenral banks already prvide infrmain hrugh he seing f he plicy insrumen. The impac f a change in he plicy insrumen will depend, in par, n he infrmain ha i cnveys abu he cenral bank s view f he ecnmy. The wrk by Mrris and Shin has been exended by Ama and Shin (003), wh cas he Mrris-Shin analysis in a mre sandard macr mdel. In heir mdel, he cenral bank has perfec infrmain abu he underlying shcks. This ignres he uncerainy plicymakers hemselves face in assessing he sae f he ecnmy. Nr d Ama and Shin allw he privae secr use bservains n he plicy insrumen draw inferences abu cenral bank infrmain. They als assume ne-perid price seing and represen mneary plicy by a price level argeing rule. In Hellwig (004), prices are flexible and plicy is given by an exgenus schasic supply f mney; privae and public infrmain cnsiss f signals n he nminal quaniy f mney. The penial css and benefis f releasing cenral bank frecass have als been analyzed by Geraas (005). Hwever, Geraas assumes agens d n bserve he bank s plicy insrumen prir frming expecains and emplys a radiinal Lucas supply funcin. Her fcus is n repuainal equilibria in a w-perid mdel wih a schasic inflain arge. Thus, he mdel and he issues addressed differ frm he fcus n he rle f infrmain in a Mrris-Shin-like envirnmen. Rudebusch and Williams (006) and Gsselin, Lz, and Wyplsz (frhcming) fcus specifically n he prvisin f fuure ineres rae prjecins. Rudebusch and Williams explre he rle f ineres rae prjecins in a mdel f pliical ransparency he asymmery f infrmain perains plicy preferences and he cenral bank inflain arge. Transparency is mdeled as reducing nise in cenral bank prjecins. In cnras he mdel I develp in he nex secin, Rudebusch and William incrprae learning and find ha he public s abiliy learn and welfare increase when ineres rae prjecins are prvided. 580 Nvember/December 03 Federal Reserve Bank f S. Luis REVIEW

7 Gsselin, Lz, and Wyplsz (frhcming) adp a quie differen apprach and fcus n wha hey characerize as creaive paciy. In heir mdel, he privae secr learns frm he infrmain released by he cenral bank, bu he cenral bank als learns abu privae secr infrmain by bserving lng-erm ineres raes. By prviding is prjecin fr he shr-erm ineres rae, he cenral bank is able recver privae secr infrmain frm he lng-erm rae. This aligns expecains bu may require he cenral bank disr is curren ineres rae seing achieve he desired lng-erm rae. If cenral bank infrmain is pr, i may be beer remain paque. Alhugh he rle f cenral bank learning is a criical ne, I ignre i in he mdel in he nex secin in rder fcus n he way inflain and upu are affeced by cenral bank annuncemens. Thus, several quesins remain unreslved cncerning he rle f ransparency in an envirnmen in which agens have heergeneus infrmain and cenral bank acins and annuncemens are cmmnly available. Specifically, hw des he infrmain cnveyed by he cenral bank insrumen affec he cenral bank s incenives and aler he effeciveness f plicy? 9 Wha is he effec f mre infrmain as ppsed beer infrmain? And are cncerns abu he added uncerainy f greaer ransparency warraned? These quesins are addressed in he mdel in he nex secin. Cenennial Issue WELFARE EFFECTS OF OPAQUENESS AND TRANSPARENCY T invesigae he rle f ecnmic ranspar ency, I emply a simple mdel mivaed by New Keynesian mdels based n Calv-ype pricing adjusmen by mnplisic firms and by Mrris and Shin s (00) demnsrain f he rle heer genus infrmain can play. 0 Like Gsselin, Lz, and Wyplsz (frhcming), I assume he cenral bank s preferences are knwn. Unlike heir mdel, hwever, I incrprae he cmmn-knwledge effec cenral he Mrris and Shin mdel. Hw ever, I fcus n hw he privae secr learns frm infrmain prvided by he cenral bank and ignre he reverse inference, where he cenral bank learns frm privae secr infrmain, which is key in he Gsselin, Lz, and Wyplsz mdel. The basic mdel is similar he ne emplyed in Walsh (007a,b). In hese earlier papers, hwever, nly demand and cs shcks were presen, s i was necessary make jus a single prjecin (f inflain r he upu gap) fully reveal he cenral bank infrmain (because he public als bserved he plicy insrumen). The primary fcus was als n parial ransparency in he sense f Crnand and Heinmann (004). The chief cnribuins f he presen paper are enrich he infrmain srucure, accun fully fr he welfare css f relaive price dispersin creaed by heergeneus infrmain, and assess ransparency in erms f bh quaniy (he rle f prviding mre infrmain) and qualiy (he effec f beer infrmain). Firms receive privae signals n he fundamenal shcks affecing he ecnmy. Each perid, a fracin f firms adjus heir prices. In ding s, hey are cncerned wih heir relaive price and s mus aemp frecas wha her price-adjusing firms are ding. Bu his requires he individual firm predic wha her firms are predicing abu he shcks hiing he ecnmy. Hence, higher-rder expecains will maer, as in Mrris and Shin (00). Federal Reserve Bank f S. Luis REVIEW Nvember/December 03 58

8 Walsh The cenral bank, like individual firms, is assumed pssess penially nisy infrmain n he ecnmic ulk. I cnsider w plicy regimes. In he firs, he paque regime, dened by superscrip, he cenral bank makes n annuncemens. Hwever, even in his regime, he cenral bank reveals smehing abu is ulk fr he ecnmy when i ses is plicy insrumen. In he absence f her infrmain, he privae secr frms expecains by cmbining he bservain n he insrumen wih heir wn privae infrmain. A rise in he plicy ineres rae, fr example, will be inerpreed parially as a cenral bank aemp ffse a prjeced psiive demand shck and parially as an aemp cnrac real upu ffse a psiive cs shck. When deciding n is plicy, he cenral bank needs ake in accun hw he public will inerpre is acins because he insrumen cnveys infrmain. The secnd regime, dened by superscrip f, crrespnds full ransparency. In his regime, he cenral bank releases is prjecins n fuure ecnmic develpmens. Because i is n his infrmain ha he cenral bank bases is plicy decisin, he acual seing f he insrumen cnveys n addiinal infrmain. The benefis f his regime are ha privae secr frecass are imprved and, because here is mre cmmn infrmain acrss firms, relaive price dispersin is reduced. The penial cs is ha privae expecains reac wha may urn u ex ps be cenral bank frecas errrs. While I assume he cenral bank peraes in a discreinary manner in seing is plicy insrumen, I als assume i can cmmi a plicy regime (paque r ransparen). The Basic Mdel The underlying mdel f price adjusmen is based n Calv, cmbined wih he iming assumpins f Chrisian, Eichenbaum, and Evans (005) and he addiin f firm-specific infrmain. The Chrisian, Eichenbaum, and Evans iming implies ha firms wh adjus heir price fr perid d s based n infrmain. Expressed alernaively, firms in perid make decisins abu heir prices fr perid +. Because infrmain differs acrss firms, price-seing firms will n all se he same price as in he sandard cmmn-infrmain framewrk ha is emplyed in ms mdels. In addiin, because firms care abu heir relaive price, hey mus frecas he aggregae + price level when hey se heir individual price fr ha perid. This als differs frm sandard specificains in which firms are assumed knw he aggregae equilibrium price level when hey se heir price level. Three ypes f shcks are cnsidered: (i) css shcks ha are assumed represen inefficien vlailiy in real marginal css; (ii) aggregae demand shcks; and (iii) shcks he gap beween he ecnmy s flexible-price equilibrium level f upu and is efficien level f upu. The las ne will be referred as a welfare-gap shck. The mdel differs frm sandard New Keynesian mdels in ha he same infrmain is n cmmnly available all firms and firms mus se prices befre bserving he curren realizains f shcks. The basic iming is as fllws: (i) A he end f perid, he cenral bank frms prjecins abu + ecnmic cndiins and ses is plicy insrumen, q. (ii)firms bserve p, x, and q as well as individual specific signals abu + shcks. Firms may als bserve annuncemens made by he cenral bank. 58 Nvember/December 03 Federal Reserve Bank f S. Luis REVIEW

9 Cenennial Issue (iii)thse firms ha can adjus heir price se prices fr +. (iv) Perid + shcks ccur and p + and x + are realized. A randmly chsen fracin w f firms pimally se heir price fr perid +. If b is he discun facr (see Walsh, 007b), ne can shw ha j j j s j () π = ωβ j, ( ω) E π + ( ωβ) κe x + ( ωβ) E e E π, + ω where p j,+ is he lg price firm j ses fr perid + relaive he perid average lg price level (i.e., p j,+ p ); E jp + is firm j s expecain abu he average p i,+ being se by her adjusing firms; E jx + is firm j s expecain abu he upu gap in +; es + is he aggregae, cmmn cs shck; and E jp + is firm j s expecain abu fuure inflain. Fr simpliciy, I assume () is linearized arund a zer-inflain seady sae. T keep he mdel simple, I represen he demand side f he mdel in a very sylized, reduced-frm manner. Mneary plicy is represened by he cenral bank s chice f q and by any annuncemens he cenral bank migh make. I assume q is bserved a he sar f he perid s ha any firm ha ses is price in perid can cndiin is chice n he cenral bank s plicy acin. The upu gap is hen equal () x v = θ + e, + + where e v + is a demand shck. Alhugh I will call q he cenral bank insrumen, i essenially represens he cenral bank s inended upu gap. Infrmain. As ned, here are hree fundamenal disurbances in he mdel: e s represens cs facrs ha, fr a given upu gap and expecains f fuure inflain, generae inefficien inflain flucuains; e v he aggregae demand disurbance; and e u a shck he gap beween he flexible-price upu gap and he efficien upu gap. I assume each is serially and muually uncrrelaed. Firms mus se heir prices and he cenral bank mus se is plicy insrumen befre learning he acual realizains f he aggregae shcks. Firm j s idisyncraic infrmain, ej,+ i fr i = s, v, u, is relaed he aggregae shck accrding i i i ej, = e + φ,, i= s, v, u The f j,+ i erms are idenically and independenly disribued acrss firms and ime. These signals are privae in ha hey are unbserved by her agens. Fr cnvenience, each f j,+ i will be referred as a nise erm, even hugh fj,+ s is acually he idisyncraic cmpnen f he firm s cs shck. All schasic variables are assumed be nrmally disribued. Define he signal-nise rai, gj i = s i /(s i + s j,i ), where s i is he variance f ei and s j,i is he variance f f j i. Le W j,+ dene he vecr f privae signals received by firm j, and le W + = W j,+ be he infrmain aggregaed acrss firms. The cenral bank cmbines is infrmain, mdels, and judgmen bain frecass f fuure ecnmic disurbances. I will be cnvenien represen his infrmain, in parallel wih he reamen f firm infrmain, as signals n he hree aggregae disurbances: j Federal Reserve Bank f S. Luis REVIEW Nvember/December

10 Walsh i i i e = e + φ, i= s, v, u., +, The nise erms f i are assumed be indepen denly disribued and be independen f fi j fr all i, j, and. Define g i = s i /(s i + s i, ), where s i, is he variance f fi. Le W,+ dene he innvain he cenral bank infrmain se. Le Z = [e s e v e u ]. Then E Z + = G W,+, where E denes expecains cndiinal n cenral bank infrmain and The cenral bank s bjecive is minimize, under discrein, a sandard quadraic lss funcin ha depends n inflain variabiliy and upu-gap variabiliy. Specifically, lss is given by (3) where e u is equal schasic variain in he gap beween he flexible-price upu gap (x) and he welfare-maximizing upu gap. Wih saggered price adjusmen, New Keynesian mdels imply ha he welfare css f inflain variabiliy arise frm he dispersin f relaive prices i generaes (Remberg and Wdfrd, 997, Wdfrd, 003a). Relaive price dispersin can arise frm inflain (because f saggered price adjusmen) and because f heergeneus infrmain acrss firms. I can be shwn (see he appendix) ha he variance f relaive prices acrss firms depends n p and n he nise in he signals received by individual firms. Thus, scial lss is given by (4) Γ = s γ v γ γ where z is relaive price dispersin arising frm heergenus infrmain acrss individual firms, wih he apprpriae weigh n his surce f lss relaive p given by The lss assciaed wih heergeneus infrmain can be reduced if he cenral bank prvides mre infrmain. Hwever, his lss is n affeced by he perid-by-perid plicy chice he cenral bank makes in seing is insrumen (cndiinal n he plicy regime ha defines he ype f annuncemens he cenral bank makes). Thus, under discrein, he cenral bank akes as given he erm z in (4), which is due heergeneus infrmain, and minimizes (3). We can nw evaluae equilibrium under each plicy regime. u. u β π λ + i x( + i + i) i= 0 L = i E + x e s L = i E + z + x e, u β π λ λ + i I + i x( + i + i) i= 0 ( ω) λi =. ω, 584 Nvember/December 03 Federal Reserve Bank f S. Luis REVIEW

11 Cenennial Issue Equilibrium Under he Opaque Regime In regime, firms bserve heir wn privae signals and he cenral bank insrumen. In regime f, he cenral bank prvides is frecass (equivalenly, is signals) direcly he public. In he absence f cenral bank annuncemens, firm j s new infrmain is given by is privae signals and he plicy insrumen. The new infrmain available firm j cnsiss f W j,+ and q. Assume beliefs abu mneary plicy are θ = δ E ψ = δ Γ Ω +, +, where d 0 is 3. These beliefs are cnsisen wih a rainal expecains equilibrium under discreinary mneary plicy. Define Q = [Q Q ] such ha Q is 3 3 and Q is 3, where he ijh elemen f Q gives he effec f he firm s jh signal n is frecas f he ih shck. Similarly, he ih elemen f Q is he effec f q n he firm s frecas f he ih shck. Firm j s expecain f Z + is j EZ j, θ. + =Θ Ω + +Θ Because he firm s signals n he differen shcks are uncrrelaed, Q wuld, in he absence f he bservain f q, cnsis f a diagnal marix wih signal--nise rais alng he diagnal. The ff-diagnal elemens f Q can be nnzer when he firm cmbines is wn infrmain wih q frecas he shcks. Fr example, suppse q > 0. This migh indicae a respnse by he cenral bank a negaive demand shck, a negaive cs shck, r a psiive welfare-gap shck. If he firm s signal n he demand shck is psiive, hen given q, his makes i less likely he cenral bank is reacing a negaive demand shck. The firm will herefre aler is frecas f cs and arge shcks. As shwn in he appendix, he equilibrium sraegy fr firm j will ake he frm (5) π j b j b,, + = Ω, + + θ where b is 3. Under bh regimes, he expressin fr he cefficiens n W j,+ in he firm s equilibrium sraegy akes he same frm. The appendix shws als ha he impac f he insrumen n an individual firm s pricing decisin is ωβ (6) b = κ + ( ω) b ( ωβ)( ι κι ) ω ω + + Θ, where i i is a 3 vecr f zers wih a in he ih place. Equain (6) illusraes he channels hrugh which a plicy acin affecs he pricing decisins f firms. The firs erm, ( wb)k/w is he sandard effec peraing hrugh he upu gap. Because inflain is ( w) imes he pricing decisin f he individual firm in a sandard New Keynesian mdel, he effec n aggregae inflain peraing hrugh his erms wuld be ( w) ( wb)k/w, which is he nrmal cefficien n he upu gap in a New Keynesian mdel based n Calv pricing. Federal Reserve Bank f S. Luis REVIEW Nvember/December

12 Walsh Figure Elasiciy f Inflain wih Respec he Plicy Insrumen in he Opaque Regime as a Funcin f he Qualiy f Privae Infrmain ( ω)b Signal--Nise Rai fr Privae Infrmain NOTE: Slid line, g i = 0.5; ded line, g i = 0.9. The remaining erms n he righ side in (6) represen he infrmainal effecs f plicy acins. Fr example, bserving q affecs he firm s expecains abu cs, given by he erm ( wb)i i Q, and demand shcks, given by he erm ( wb)ki i Q. Observing q als affecs individual pricing decisins hrugh he firm s expecains f wha her firms are expecing, he ( w)b erm. Equilibrium inflain is given by (7) The infrmain channel can significanly affec he exen which he cenral bank insrumen impacs inflain. I calibrae he mdel by seing w = 0.65 (as a cmprmise beween micr evidence suggesing w n he rder f 0.5 and ime-series esimaes ypically n he rder f 0.8), b = 0.99, and k =.8. These values imply ( w) ( wb)k/w = The sandard deviains f all shcks are se equal. Figure shws hw ( w)b varies wih he qualiy f privae secr infrmain, as measured by he signal--nise rai, gj i. When firms have perfec infr- π = ω π = ω b Ω + b θ and π θ + = ω b. 586 Nvember/December 03 Federal Reserve Bank f S. Luis REVIEW

13 main n he shcks (gj i = ), he plicy insrumen, q, cnveys n infrmain and is effec n inflain equals , which is shwn by he hriznal line in Figure. Hwever, when q cnveys infrmain (i.e., when gj i < ), is impac n inflain is significanly reduced. Mvemens in q are parially aribued he cenral bank s respnse he varius shcks. A rise in q, fr example, lwers firms frecass f demand shcks. Because he ne effec n he expeced upu gap is q + E i j e+ v, he effec n price-seing behavir and inflain is less han he change in q. A rise in q als leads firms reduce heir frecas f cs shcks, parially ffseing he psiive impac f a rise in q n inflain. Fr a given qualiy f privae secr infrmain, he infrmain channel becmes mre impran as cenral bank infrmain imprves and privae firms place mre weigh n he infrmain cnveyed by plicy acins. The infrmainal effecs are larger, herefre, when he cenral bank has beer qualiy infrmain (in Figure, cmpare he slid line fr g i = 0.5 wih he dashed line fr g i = 0.9). Operaing in a discreinary regime, he cenral bank ses plicy pimally in each perid based n is curren frecass abu he fuure sae f he ecnmy. The firs-rder cndiin fr minimizing he expeced value f he cenral bank s lss funcin (3) subjec () and (7) is given in he appendix. This firs-rder cndiin can be slved fr he pimal plicy respnses, and heir values are als given in he appendix. The sluin he mdel is bained numerically by beginning wih iniial values fr he plicy cefficiens, using hese bain Q, b, and b, and hen baining new values fr he plicy cefficiens. This prcess cninues unil cnvergence. Once he equilibrium values f b and b and he plicy cefficiens are bained, aggregae inflain is given by whereas he welfare gap is given by + Equilibrium Under a Transparen Regime π b + bδ Γ ψ + = ( ω), + b δ Γφ, + u v u x e = θ + e e = δ Γ Ω + ι ι Z = δ Γ + ι ι Z + δ Γ φ , , +. I inerpre full ransparency as a regime in which he cenral bank shares is infrmain n he ecnmy. Wihin he cnex f he mdel, his wuld mean ha he cenral bank publishes is signals n he varius disurbances s ha W,+ becmes knwn all firms. Equivalenly, he cenral bank culd publish is frecass fr inflain and he upu gap. In a ransparen regime, he insrumen is n lnger a surce f infrmain he privae secr. This alers he impac f q n inflain and affecs he cenral bank s incenives fr seing plicy. When he cenral bank prvides is infrmain he public, he cenral bank infrmain se is a subse f he public infrmain se. In his cnex, Svenssn and Wdfrd (003) have shwn ha cerainy equivalence hlds and he plicy decisin f he cenral bank depends nly n he expeced values f he shcks. In paricular, his implies ha he pimal plicy will be independen f he qualiy f eiher cenral bank infrmain r privae secr infrmain. Cenennial Issue Federal Reserve Bank f S. Luis REVIEW Nvember/December

14 Walsh Le Q f = [Q f Q f ] be he apprpriae 3 6 cefficien marix such ha The appendix shws ha he equilibrium sraegy fr price-seing firms is where b f akes he same frm as b (excep when Q f replaces Q in he expressin fr b f ). Alhugh he frmula b f is he same as fr b, heir values will differ as Q f Q. The effecs f he cenral bank insrumen and infrmain are given by and EZ j Inflain will equal ( w)p +, s b π f f + =Θ Ω j, + +Θ Ω, +. f f f j, + = b Ω j, + + bθ + b3 Ω, +, ( ωβ) b f = κ ω = ( ω) b ( ωβ)( ι κι ) + + ω Θ. f f f 3 π θ + f ω ωβ κ = ( ω) b = ω and is independen f any infrmainal effecs. The exac expressins fr he pimal plicy respnse each ype f signal are given in he appendix. THE VALUE OF RELEASING INFORMATION We can nw cmpare he effecs f prviding infrmain by cmparing ucmes under he paque regime and he ransparen regime. T assess ucmes under he w regimes, he mdel is slved using he same calibraed parameers as emplyed earlier (i.e., w = 0.65, b = 0.99, k =.8). I iniially se he variances f all shcks equal. Fr he lss funcin, I se l x = /6, reflecing he use f quarerly inflain raes. Table shws he lss under each regime fr differen cmbinains f he signal--nise rais fr bh he privae secr and he cenral bank. The firs hing ne is he lss is increasing in he qualiy f privae secr infrmain (mving acrss rws frm lef righ) and decreasing in he qualiy f cenral bank infrmain (cmparing he p panel he bm panel). Beer privae infrmain makes expecains mre sensiive signals and s increases he vlailiy f expecains. Greaer vlailiy f expecains prduces mre inflain vlailiy. This is welfare decreasing. Beer cenral bank infrmain is welfare imprving because i allws he cenral bank engage in mre effecive sabilizain plicies ha reduce he vlailiy f inflain and he upu welfare gap. Alhugh Mrris and Shin (00) sugges ha imprved cmmnly available infrmain culd reduce welfare, he resuls in Table are cnsisen wih 588 Nvember/December 03 Federal Reserve Bank f S. Luis REVIEW

15 Cenennial Issue Table Lss Under Alernaive Regimes (s s = s v = s u = ) g j i g i = 0.5 Opaque regime Transparen regime p Equivalen g i = 0.9 Opaque regime Transparen regime p Equivalen NOTE: Bld indicaes he regime wih he leas lss. Hellwig (004) and Svenssn (006), wh argue ha beer qualiy cenral bank infrmain generally imprves welfare. When g i j =, firms bserve he rue shcks perfecly. In his case, he release f infrmain r prjecins by he cenral bank is irrelevan and he lss is he same under bh regimes, as shwn in he las clumn f Table. When privae infrmain is imperfec, lss differs under he w regimes (he regime wih he leas lss is indicaed in bld). The rws labeled p equivalen express he reducin in lss under he pimal regime in erms f he reducin in average inflain (expressed a annual raes) ha wuld yield a similar reducin in lss. Fr example, if g i j = 0.8 and g i = 0.5, he imprvemen f mving frm an paque regime a ransparen ne is equivalen a reducin in inflain f.66 percenage pins. The general resuls are similar in bh he p panel, when cenral bank infrmain is relaively pr (he signal and he nise have equal variances s ha g i = 0.5), and he bm panel, when cenral bank infrmain is relaively gd (g i = 0.9). Wha maers is he qualiy f privae infrmain. If his is lw, hen he expecains f firms (and wha individual firms expec ha her firms are expecing) are sensiive any cmmnly available infrmain released by he cenral bank. The resuls in Table are rbus differen values fr he variances f he underlying shcks. 3 The finding ha ransparency can lwer welfare when privae infrmain is pr is suggesive f he Mrris and Shin (00) argumen ha nisy public infrmain can decrease welfare. T invesigae wheher his is he effec ha accuns fr he relaive perfrmance f he w regimes, ne can calculae he surces f lss under each regime. Frm (4), lss arises frm inflain variabiliy, welfare-gap variabiliy, and relaive price dispersin caused by heergeneus infrmain. Table shws each f hese cmpnens fr he case g i = 0.9, which crrespnds he lwer panel f Table (resuls are similar fr g i = 0.5). Table reveals hree differences beween he equilibria fr he paque and ransparen regimes ha are independen f he qualiy f privae infrmain. Firs, inflain is less vlaile Federal Reserve Bank f S. Luis REVIEW Nvember/December

16 Walsh Table Cmpnens f Lss (s s = s v = s u = ) Opaque regime i g = 0.9 g i j L s p l x sx e u l I s z Transparen regime L s p l x sx e u l I s z when plicy is ransparen. Secnd, he cnribuin f welfare-gap vlailiy he verall lss is much larger when plicy is ransparen. And hird, he welfare cs f relaive price dispersin is much smaller when plicy is ransparen. When g i j is very lw, paciy is he preferred regime because he welfare gap is much mre sable. As will be discussed furher belw, he infrmainal effecs f plicy acins are larger when he qualiy f privae infrmain is pr and hus hese effecs disr he incenive f he cenral bank such ha plicy reacs lile cs shcks. This makes inflain mre vlaile bu leaves he welfare gap mre sable. Bh inflain and upu-gap vlailiy in he paque regime increase as g i j rises, s ha he ransparen regime becmes preferred when privae secr infrmain is gd. 4 Table 3 shws he pimal plicy respnses hree cenral bank signals fr g i j equal 0.4 and 0.8 and fr g i equal 0.5 and 0.9. Respnse cefficiens in he ransparen regime are independen f he qualiy f bh privae secr and he cenral bank infrmain. This resul fllws frm he demnsrain by Svenssn and Wdfrd (003) ha he cenral bank s decisin prblem saisfies he cndiins fr cerainy equivalence if he privae secr has mre infrmain han he cenral bank. This is he case in he ransparen regime because he privae secr knws bh he cenral bank signals and heir wn privae signals. The way infrmainal effecs in he paque regime disr sabilizain plicy is clear frm he mued respnse (in abslue value) signals n he cs shck and amplified respnse signals n he welfare-gap shck. The rade-ff beween inflain and welfare-gap vlailiy is clearly presen plicy under he ransparen regime respnds mre sabilize inflain and, as a resul, he welfare gap is mre vlaile, as was shwn in Table. In addiin, ransparency allws he cenral bank mre efficienly neuralize he effecs f expeced demand shcks. This can be seen by cmparing he plicy reacin cefficiens under he w regimes. Under he ransparen regime, expeced demand shcks are cmpleely 590 Nvember/December 03 Federal Reserve Bank f S. Luis REVIEW

17 Cenennial Issue Table 3 Opimal Plicy Cefficiens (s s = s v = s u = ) g ji = 0.4 g ji = 0.8 d s d v d u d s d v d u g i = 0.5 Opaque regime Transparen regime g i = 0.9 Opaque regime Transparen regime ffse (i.e., d v = ) regardless f he qualiy f privae secr r cenral bank infrmain. Under he paque regime, d v = nly when he public secr has perfec infrmain n he shcks. Oher wise, d v is less han in abslue value and demand shcks are n fully ffse. Under he paque regime, when he plicy insrumen is mved, he public will cnfuse mvemens designed ffse frecased demand shcks wih mvemens designed ffse eiher cs r welfare-gap shcks. As a cnsequence, mvemens aimed a ffseing demand shcks can affec inflain expecains and cause acual inflain flucuae as he public aribues par f he insrumen change he her shcks. This makes i pimal n ffse demand shcks cmpleely. Once he public can infer he cenral bank esimae f demand shcks, as i can under ransparency, here is n lnger any reasn n fully reac insulae he upu gap and inflain frm prjeced demand shcks, s d v =. In New Keynesian mdels, he welfare css f inflain are he resul f he relaive price dispersin ha arises wih saggered price adjusmen. Heergeneus infrmain amng firms will als creae relaive price dispersin. Because infrmain prvided by he cenral bank is cmmn all firms, i can help reduce relaive price dispersin. Figure shws he measure f relaive prices dispersin ha resuls frm heergeneus infrmain amng firms. The slid line wih aserisks crrespnds he case f pr-qualiy cenral bank infrmain (g i = 0.5) under he paque regime, and he uncnneced aserisks crrespnd he paque regime wih high-qualiy cenral bank infrmain (g = 0.9). The diamnds indicae he ucmes under he ransparen regime wih pr-qualiy cenral bank infrmain (he slid line) and highqualiy cenral bank infrmain (he uncnneced diamnds). When g j i =, all firms share he same infrmain, s dispersin due heergeneus infrmain ges zer under eiher plicy regime. When firms have very pr-qualiy infrmain (i.e., fr lw iniial values f g j i ) he heergeneiy f he infrmain is high, bu because he infrmain is f pr qualiy, firms d n respnd srngly i. As infrmain qualiy imprves, firms reac mre srngly heir wn privae infrmain and his increases price dispersin. Hence, relaive price dispersin is iniially increasing in g j i. Nw cnsider he rle f qualiy cenral bank infrmain under he paque regime. Relaive price dispersin is lwer when cenral bank infrmain is gd han when i is pr, hugh Federal Reserve Bank f S. Luis REVIEW Nvember/December 03 59

18 Walsh Figure Relaive Price Dispersin Due Heergeneus Infrmain σ z Opaque Regime, γ Lw Opaque Regime, γ High Transparen Regime, γ Lw Transparen Regime, γ High Qualiy f Privae Infrmain he lss frm relaive price dispersin acually cnsiues a larger fracin f al scial lss when cenral bank infrmain is gd. This is he resul f he beer sabilizain he cenral bank can achieve when i has high-qualiy infrmain n he ecnmy. N surprisingly, relaive price dispersin is always lwer under he ransparen regime. Fr he same reasn, high-qualiy cenral bank infrmain reduces relaive price dispersin under he ransparen regime. CONCLUSIONS Under an paque plicy regime, where he privae secr and he cenral bank d n share he same infrmain, plicy acins becme a surce f infrmain he public. And hese plicy acins have bh direc effecs n he upu gap and indirec infrmainal effecs. Under an paque regime, hwever, cerainy equivalence des n hld and infrmain channels affec he cenral bank s incenives. Opimal plicy will depend n he qualiy f bh cenral bank infrmain and public infrmain. In an paque regime, he cenral bank sabilizes inflain less and he welfare gap mre han i wuld in a ransparen regime. Under a cmpleely ransparen regime, he public secr has access he cenral bank assessmen f he ecnmy. In his case, plicy acins n lnger prvide any addiinal infrmain. Opimal plicy is independen f he qualiy f cenral bank infrmain. Cnsisen wih he wrk f Svenssn (006) and Hellwig (004), beer cenral bank infrmain was fund imprve welfare. Wih beer infrmain, he cenral bank can implemen mre effecive sabilizain plicies. The effec f prviding mre infrmain by making annuncemens abu prjeced inflain and he upu gap is mre ambiguus. Transparency always acs lwer relaive price dispersin acrss firms by expanding he se f cmmnly 59 Nvember/December 03 Federal Reserve Bank f S. Luis REVIEW

19 available infrmain, bu cenral bank annuncemens can make expecains mre vlaile, paricularly if firms have relaively pr infrmain. Transparency dminaes paciy when he privae secr has relaively gd infrmain because in his case firms d n verreac he infrmain cnained in cenral bank annuncemens. Hwever, if privae secr infrmain is pr, cenral bank annuncemens can reduce welfare. S alhugh beer cenral bank infrmain is desirable, mre cenral bank infrmain may n be. Cenennial Issue APPENDIX Welfare Weigh n Infrmain Dispersin The welfare lss in New Keynesian mdels arises frm inefficien price dispersin acrss firms. Le p j, dene firm j s price and le P be he aggregae price level. Then varj( lgpj, P ) = E lgp P E lgp P Using he assumpins f he Calv mdel, he firs erm n he righ can be wrien as Nw where he firs erm n he righ is zer in he sandard New Keynesian mdel wih cmmn infrmain acrss firms. Hence, because he idisyncraic nise is independen f he fundamenal shcks. Frm he definiin f inflain, s ( j, ) ( j, ) ( j, ) ( ) = E lg p P P P. ( j, ) ( j, ) ( j, ) lg + ω lg lg = ω + E p P E p P ω E lg p P. lg p P = lg p lg p + lg p P, j, j, E( lg pj, P ) = E( lg pj, lg p ) + ( lg p P ) π ( ω )( ) = lg p P, E( p j P ) = E( p j p ) + ω π lg, lg, lg. Federal Reserve Bank f S. Luis REVIEW Nvember/December

20 Walsh Cmbining hese resuls, ω ω lg, lg ω π π = + ( ) E( pj p ) + ω = ω + ( ω) ( lg, lg ) +. ω π E pj p I fllws ha i ω i E β i= E β π i λ I( pj i p i) ω ωβ lg, + lg +, i= 0 i= 0 where The Opaque Regime λi = ω / ω. Le Σ = σ s σ v σ u, and Σ Σ j = = σ s s + σ σ + σ j, s v σ + σ 0 0 0, s v j, v, v σ u + σ σ + σ σ u + σ j, u, u,. In he absence f cenral bank annuncemens, firm j s new infrmain is given by e e e + φ s s + j, + + φ v v + j, + + φ θ u u + j, + = Ω θ j,+, where θ = δ ΓΩ, Nvember/December 03 Federal Reserve Bank f S. Luis REVIEW

21 Cenennial Issue Define Σ Σ Γ δ j Θ= Σ Σ Γ δ δ ΓΣ δ ΓΣ Γ δ where Q is 3 3 and Q is 3. Thus, firm j s expecain f Z + is = Θ Θ, j EZ. + =Θ Ω j, + +Θ θ =Θ Ω j, + +Θ δ ΓΩ, + The aggregae infrmain (i.e., aggregaed acrss all firms) is + Defining i i as a 3 vecr wih a in he ih place and zers elsewhere, we can wrie (), a firm s price adjusmen, as An equilibrium sraegy fr firm j will ake he frm Ω θ s e+ v e u = + e+ θ = j j ωβ j π j, + = ( ω) E π+ + ( ωβ) κθ+ ( ωβ) ( ι+ κι) EZ+ + Eπ + ω j ωβ j = ( ω) E π + ( ωβ) κθ + ( ωβ) ( ι + κι )( Θ Ω j +Θ θ) + Eπ ω where b is 3. In frming expecains abu he pricing behavir f her firms adjusing in he curren perid, firm j s expecain f p + is given by Z + θ +, + + π + = b Ω j+ + b θ, j,,.. Because i fllws ha j j E π = b E Ω + b θ j = be Z + bθ + + = Θ Ω +Θ θ + b j,+ bθ = bθ Ω j, + ( bθ + b)θ π j j E π = ω E π = ( ω) π, + + j = ( ω) E b Θ Ω j, + b Θ + b θ = Federal Reserve Bank f S. Luis REVIEW Nvember/December