JOHANN WOLFGANG GOETHE- UNIVERSITÄT FRANKFURT

JOHANN WOLFGANG GOETHE- UNIVERSITÄT FRANKFURT FACHBEREICH WIRTSCHAFTSWISSENSCHAFTEN Gradualism vs Cold Turky How o sablish crdibiliy for h ECB by Grhard Illing Arbispapir Nr. 9 Frankfurr Volkswirschaflich Diskussionsbiräg hp://www.wiwi.uni-anankfur.d/profssorn/spahn/fvd/

Gradualism vs Cold Turky How o sablish crdibiliy for h ECB Grhard Illing * Univrsiy of Frankfur Jun 998 Absrac Th papr analyzs h incniv for h ECB o sablish rpuaion by pursuing a rsriciv policy righ a h sar of is opraion. Th bank is modlld as risk avrs wih rspc o dviaions of boh inflaion and oupu from hr arg. Th public, bing imprfcly informd abou h bank s prfrncs uss obsrvd inflaion as imprfc) signal for h unknown prfrncs. Undr linar larning ruls - which ar commonly usd in h liraur - a gradual build up of rpuaion is h opimal rspons. Th papr shows ha such a linar larning rul is no consisn wih fficin signaling. I is shown ha in a gam wih fficin signaling, a cold urky approach - allowing for dflaion - is opimal for a srong bank - accping high currn oupu losss a h bginning in ordr o dmonsra is oughnss. Zusammnfassung Di Arbi unrsuch di Anriz dr Europäischn Znralbank, in dr Sarphas durch rsrikiv Poliik Rpuaion aufzubaun. Di Öffnlichki knn di Präfrnzn dr Znralbank nich; si vrwnd di bobach Inflaionsra als imprfks) Signal. Wird in linar Lrnrgl unrsll - dr Sandardfall in dr Liraur - rwis s sich als opimal, hoh Inflaionsrwarungn zuminds ilwis zu akkommodirn und so Rpuaion nur schriwis aufzubaun. Di Arbi zig abr, daß in solch linar Lrnrgl mi ffizinm Signalvrhaln nich konsisn is. Bi ffizinm Signalisirn kann s für in har Znralbank opimal sin, in dr Sarphas durch in shr rsrikiv, dflaionär Poliik ihr Präfrnzn zu offnbarn. Kywords: cnral bank policy, crdibiliy, signaling, im consisncy JEL classificaion: D 8, E 58 * I would lik o hank Ebrhard Fss and Frank Hinmann for hlpful commns. hp://www.wiwi.uni-anankfur.d/profssorn/spahn/fvd/

) Inroducion Whn h Europan Cnral Bank sars is opraions January 999, a nw ra bgins. Righ from h sar, h bank has o fac many challngs. Carful and dailld prparaions hav bn don by h EMI, h forrunnr of h ECB, o provid a smooh ransiion of monary policy from h naional cnral banks o a Europan agncy. Bu dspi all his imprssiv work, h ECB has o ravl in up o now unknown Europan rriory. Sinc i has no rack rcord on which i can build, hr is considrabl uncrainy abou is policy. Of cours, h ray of Maasrich rid o sablish a numbr of dvics o mak sur ha h ECB will car for pric sabiliy. In many ways, hs ruls follow h xampl of h succss sory of h Dusch Bundsbank. Evn hough his dsign is man o as a difficul sar by ransfrring a las par of h lgndary rpuaion h Bundsbank has acquird during h pas 50 yars, h ECB crainly canno inhri is rpuaion righ from h bginning. To ovrcom h difficulis causd by h lack of rack rcord, som vn propos h ECB should xacly copy h sragy of h Bundsbank. Omar Issing for insanc, h chif conomis of h Bundsbank, suggsd ha h bs way o gain rpuaion would b o adop h Bundsbank s monary arging procdur rahr han following h las fashion of inflaion arging. Evn if such a sragy urnd ou o b succssful in h nd, i is qui unlikly ha a mr imiaion of h Bundsbank modl can b sufficin o prsuad public opinion abou h ECB s drminaion o figh inflaion. Crainly, copying lgal ruls and procdurs ar no sufficin for succss. Thy canno crdibly guaran how acual monary policy will b carrid ou. In Grmany, for a long im, far prvails in public ha h hard Grman mark will b sacrificd for a much wakr Euro. Lacking h public suppor h sabiliy culur ) on which h Bundsbank could build on, so h argumn, h Europan Cnral Bank is doomd o giv in o prssurs from a In fac, i is qui doubful ha adoping monary arging would b of much hlp, givn ha in is acual monary policy h Bundsbank bhavd in a vry pragmaic way. As svral sudis show s Brnank/Mihov 996, Clarida/Grlr 996), monary aggrgas play a rahr limid rol in is sragy; insad, h Bundsbank follows mor a policy of disciplind discrion s Laubach/Posn 997). Whras h Bundsbank wih is immacula rpuaion obviously can afford o miss h slf imposd monary args whnvr i sms appropria, h ECB would hav a much oughr im in jusifying dviaions from hos args, dspi h fac ha monary aggrgas on h Europan lvl ar bound o b rahr volail righ a h bginning. hp://www.wiwi.uni-anankfur.d/profssorn/spahn/fvd/

coaliion of wak counris - h infamous so calld Lain counris Franc, Ialy, Spain and Porugal) - gaining by a laxr policy. Public dbas abou sric nforcmn of h Maasrich budg ruls did no hlp much o dampn hos fars, spcially whn h ambiguiy of h saisics bcam vidn and vn h Grman govrnmn rid o manipula h saisics in is rush for rvaluaing gold rsrvs. Th quarrl abou who and for how long) should b appoind as h firs prsidn of h ECB has bn inrprd as vidnc for such a ndncy. Basd on such fars, som conomiss vn rid o go o cour in ordr o prvn h sar of a wak Euro. On h ohr hand, as h sar of h Euro coms closr, fars poining in h opposi dircion now domina h public dba. Mor and mor fars aris ha, a las righ a h bginning, h ECB may bhav as an inflaion nur in ordr o gain crdibiliy. Sinc a h sam im, h sabiliy pac also svrly limis h scop of fiscal policy for sabilizing h conomy, massiv unmploymn as h rsul of an unforuna mix bwn sric monary and fiscal policy all ovr Europ appars o b a no unlikly scnario. Of cours, such a sric policy migh hardly b susainabl, a las whn h unmployd, unid from all counris, bgin o march o h Euro owr in Frankfur. So h ECB is no only facing h complx ask of dsigning a singl monary policy in dark and as y no wll known Europan rriory, which should fi h divrging nds of all hos counris joining. In addiion, i has o avoid h Scylla of an ovrkill of h conomy arising from h oo ambiious zal for pric sabiliy and h Charybdis of an accommodaing, sof inflaionary policy. Thr has bn a lo of inrs in h problm whhr a singl monary policy migh b suiabl for all prospciv EMU mmbrs. Iniially, h main focus has bn on h qusion of whhr hos counris form som sor of common currncy ara, which would jusify a common sabilizaion policy. Rcnly, anion shifd o h issu ha vn if all counris wr hi by h sam shocks, diffrncs in h naional ransmission mchanism imply ha a common policy may affc diffrn counris in a qui diffrn way s Dornbusch/ Favro/ Giavazzi 998), Ramaswamy/Slok 997)). In h prsn papr, w focus on a qui diffrn aspc of sabilizaion policy: Wha impac will h lack of rack rcord hav on h policy of h ECB? Sinc h public is uncrain abou h policy sanc of h ECB, addiional risk is inroducd in h marks. Obviously, h prior hp://www.wiwi.uni-anankfur.d/profssorn/spahn/fvd/

crdibiliy will b lowr compard o som sablishd insiuions i is supposd o rplac. So, hr is a srong incniv for h ECB o sablish a rpuaion for oughnss by pursuing a rsriciv policy righ a h sar. In paricular, w ar inrsd in h impac on sabilizaion policy. Could h zal for gaining rcogniion rsul in an ovrkill of h conomy or will h bank a las parly accommoda highr inflaionary xpcaions and prfr o build up crdibiliy a a smooh, gradual pac? Whn analyzing his issu, w will absrac from h problm of dsigning a common policy fi for all counris. Tha is, w nglc complicaions arising ou of asymmric dmand and supply shocks. Signaling modls provid h naural saring poin o analyz h issu of rpuaion. In h conx of dynamic inconsisncy, i has long bn rcognizd ha currn monary policy may b disciplind by rpuaional ffcs, whn h public is uncrain abou h cnral bank prfrncs. Basd on h Barro/Gordon 983) modl, rpuaional ffcs hav bn sudid - among ohrs - by Backus/Driffill 985), Cukirman/Mlzr 986), Vickrs 986), Mino/Tsusui 990) and mos rcnly by Faus/Svnsson 997). Following sandard gam horic liraur, mos of h iniial work confind h analysis o h cas of a limid numbr of cnral bank yps wih linar prfrncs w.r.. oupu, choosing among prfcly rliabl signals in a mixd sragy quilibrium. This s up givs a far oo simplifid picur of monary policy, disrgarding h coninuous naur of uncrainy abou cnral bank bhavior and h problm of imprfc conrol. A noicabl xcpion is h highly original papr by Cukirman/Mlzr 986). Evn in ha papr, howvr, cnral bank prfrncs ar assumd o b linar in oupu for compuaional rasons. Such prfrncs imply risk nuraliy w.r.. oupu flucuaions, so all shocks can b absorbd by oupu flucuaions wihou any wlfar losss. Givn his assumpion, h issu of sabilizaion policy bcoms rivial and rahr uninrsing. Faus/Svnsson 997) modify h s up of Cukirman/Mlzr 986) by allowing for quadraic prfrncs for oupu in ordr o sudy h impac of risk avrsion for oupu flucuaions on sabilizaion policy. Following Cukirman/Mlzr 986), hy us a saionary, infini horizon scnario in which cnral banks prfrncs ar priva informaion and chang coninuously across im. As in Cukirman/Mlzr, h public uss a linar larning rul o upda is blifs afr obsrving h cnral bank s policy h inflaion ra). Nois, howvr, maks h cnral banks s acions no complly ransparn o h public, so h signals can rval currn prfrncs only parially. hp://www.wiwi.uni-anankfur.d/profssorn/spahn/fvd/

Bcaus of h complxiy arising from h quadraic loss funcion, Faus/Svnsson do no solv dircly h larning procss and h bank s opimizaion problm. Insad, xploiing h saionary srucur of hir modl, hy us Kalman filr and dynamic programming chniqu o find a saionary soluion. Thy show ha rpuaion will b build up gradually: A cnral bank wih low crdibiliy will parly accommoda highr inflaionary xpcaions. So h lowr is crdibiliy, h mor xpansionary h policy of a bank wih givn prfrncs will b. Bu sinc xpcaions will b accommodad only parly, oupu will, on avrag, b lss han xpcd. Evn hough inflaion is blow h xpcd ra, h gradual build up of rpuaion will rsul boh in lss mploymn and highr inflaion. In conras, low crdibiliy dos no affc h bank s flxibiliy o rspond opimally o supply shocks. Th inuiion bhind Faus/Svnssons rsul, a firs sigh, appars o b fairly sraighforward: Th lowr h iniial rpuaion, h highr inflaionary xpcaions. Taking hs ino accoun, h bank will accommoda xpcaions o som xn, sinc an ovrly rsriciv policy would involv vn highr oupu losss. So i sms no o b opimal o gain crdibiliy a a fasr pac - implying ha a gradual build up of rpuaion should b h opimal rspons. This inuiion, howvr, urns ou no o b robus. As h currn papr shows, h fac ha gradualism is h opimal sragy is a consqunc of h implausibl linar larning rul imposd on priva agns. W argu ha linar larning ruls do no capur h sragic naur of h asymmric informaion gam a issu: Using sandard rsuls from h signaling liraur, i is shown ha such ruls ar no robus agains sragic xprimnaion. In a gam wih fficin signaling, a srong cnral bank may vry wll hav an incniv o signal is innions in a drasic way, rahr han o accommoda high inflaionary xpcaions a las parially. Th modl is closly rlad o Faus/Svnsson xcp ha w us a wo priod modl. 3 This s up capurs h non saionariy naur of problm facd by inroducing h Euro. Th sar of h ECB implying a drasic chang of h ruls of h gam) can hardly b inrprd as h oucom of a saionary procss. Th main advanag of h currn s up, howvr, is ha i allows o driv h xplici soluion of h crdibiliy gam vn in a modl wih quadraic Mino/Tusui 99) analyzd rpuaional consrains in a wo priod vrsion of h Barro/Gordon modl. Again, howvr, hy limi hir analysis o h cas of prfrncs bing linar w.r.. o oupu and o linar larning ruls. 3 In conras o Backus/Driffill 985), h rpuaion ffcs of h modl ar robus o an xnsion o infini horizon, hy ar no drivn by som srang ffcs of an nd gam scnario. hp://www.wiwi.uni-anankfur.d/profssorn/spahn/fvd/

prfrncs. Characrizing his soluion may b of inrs in is own. Bu h main conomic payoff coms from sing h robusnss of h rsuls drivd in Faus/Svnsson. Th nx scion prsns h wo priod modl oulining h signaling problm: Inflaion oday srvs as a noisy) signal abou h bank s prfrncs. Thn, scion 3 characrizs quilibrium undr linar larning ruls. Boh h Baysian larning problm h priva agns ar facing and h opimal cnral bank sragy ar analyzd in dail. Th sup allows o driv cnral rsuls in a sraighforward way: If h public is abl o obsrv oupu shocks whn updaing simas abou h bank s prfrncs, h bank s sabilizaion rspons will b indpndn of hr crdibiliy. Concrn for rpuaion dampns hr mpaion o pursu a discrionary policy. Rpuaional concrns ar srongr h highr h discoun facor and h mor ransparn h policy h mor rliabl h signal is for h public). Undr linar larning ruls, parial accommodaion of inflaionary xpcaions implying a gradual rspons) is always opimal. Linar larning ruls, howvr, vn hough vry popular in macroconomics, ar no robus agains sragic xprimnaion. Scion 4 analyzs h fficin signaling sragy for h cas of a complly rvaling signal. W show ha hir rsuls do no hold in an fficin signaling gam. I is shown ha in ha cas, a srong bank is willing o incur high currn oupu losss in ordr o dmonsra is oughnss o h public. ) Th signaling problm ). Rpuaion undr imprfc conrol W analyz h following wo priod modl. Th cnral bank has h quadraic loss funcion: E L = E L, ) + δ E L, ) + + + + wih L L > 0, and < 0 ) = Throughou h papr, w assum h quadraic loss funcion: y + ) + δ { } + + y+ ) Th shor run aggrga supply curv is givn by: hp://www.wiwi.uni-anankfur.d/profssorn/spahn/fvd/

y = ) + ε ε is a supply shock wih E ε ) = 0 ; Var ε ) = σ ε. Sinc h cnral bank can obsrv ε, i can, in principl, sabiliz oupu flucuaions. Priva agns ar uncrain abou cnral bank s ru prfrncs. As in Faus/Svnsson 997), his uncrainy is modld by incompl informaion abou h oupu arg : Th opimal policy dpnds on h oupu arg, bu is assumd o b priva informaion of h cnral bank. For h public, is a random variabl wih E ) > 0 ; Var ) = σ. A h bginning of priod, h public knows only E ). E ) characrizs iniial rpuaion h highr E ), h lowr h rpuaion). Th conduc of monary policy provids a signal abou h undrlying prfrncs: Th lowr, h mor rsriciv policy will b. Th cnral bank may b willing o incur currn oupu losss in ordr o signal a low oupu arg and so gain highr rpuaion in h nx priod. In gnral, howvr, h signal will b noisy h acions of h cnral bank canno rval complly h undrlying prfrncs. Following Cukirman/Mlzr 986), his nois is modld as imprfc conrol of h cnral bank abou h inflaion ra capurd conrol rrors inroduc addiiv nois in h signal: = i + 3 i ar h unobsrvabl) innions of h cnral bank, is a conrol rror wih E ) = 0 ; Var ) = σ. Th public canno obsrv h innions i i crainly has mor or lss daild informaion abou h acual monary policy insrumns h inrs ra s by h cnral bank is dircly obsrvabl), bu i dos no hav sufficin knowldg abou informaion moivad a chang rsp. no chang) in h monary policy insrumns. Th mor ransparn h policy, h mor prcis h cnral bank s innions can b dducd by h public. So highr ransparncy such as publishing daild rpors rvaling innions bhind h policy acions) is quivaln o rducing h varianc σ. This has h somwha implausibl implicaion ha highr ransparncy a h sam im also rducs h conrol rror of monary policy. As in Faus/Svnsson 997), w could disinguish bwn ransparncy and conrol rror wih somwha mor complx noaion, bu no addiional insighs will b gaind by doing so. hp://www.wiwi.uni-anankfur.d/profssorn/spahn/fvd/

Afr obsrving, agns upda hir blifs abou cnral bank and rvis inflaionary xpcaions. Th highr h inflaion ra, h mor damagd, in gnral, h rpuaion will b. Thr ar, howvr, wo cavas. Firs, high inflaion may b h rsul of a ngaiv supply shock. If h cnral bank ris o sabiliz h conomy and if priva agns can obsrv ha x pos, onc monary policy has bn carrid ou, bu bfor nx priods inflaionary xpcaions hav bn formd), hn h public will ak ha informaion ino accoun and may absolv h cnral bank for is acion. Furhrmor, h high inflaion may simply b du o conrol rrors. Whn updaing rpuaion, h public will ak ino accoun his nois. Of cours, srongr yps will ry o signal hir policy sanc via pursuing a sric policy. So obsrving a low inflaion ra having adjusd for h ffcs of supply sid shocks), raiss h posrior for a sric cnral bank. Th probabiliy disribuion will b shifd. Th smallr and/or h largr σ, h mor valuabl informaion abou h signal provids and hus h srongr xpcaions will b updad. If hr wr no nois σ =0), a complly sparaing quilibrium will occur in ha cas, acions rval h ru yp). Th concrn for rpuaion works as a disciplinary dvic, limiing h mpaion for surpris inflaion. Thrfor, firs priod inflaion will b lowr han in h discrionary quilibrium - xcp for h cas ha fuur payoffs ar irrlvan δ = 0 ) or ha hr is no uncrainy abou h prfrncs σ =0). ). Th cnral bank s sragy In a wo priod sing, obviously, rpuaional ffcs ar of no concrn in h las priod. So h opimal policy a + simply dpnds on prfrncs and xpcd inflaion: i f, ). In conras, whn formulaing is policy in priod, h cnral bank will ak + = + ino accoun ha an incras in h inflaion arg a highr i ) will affc nx priod s rpuaion E i )) ). Policy oday is disciplind by h impac on rpuaion nx priod, as long as objciv is: + srvs as a noisy) signal abou. In gnral rms, h cnral bank s σ + + + + 4 Min EL i ) = EL i, i ) + δ EL i, i )) Using, h cnral bank s quadraic loss funcion can b wrin as: 5 EL ) = + + ε ) + δ { + + + + ) + ε + ) } hp://www.wiwi.uni-anankfur.d/profssorn/spahn/fvd/

In rms of h insrumn, h objciv is: EL i ) = E i ) + E i + ε ) + { E i + ) + E i + + ε + + ) ) } σ + δ σ + δ + Th firs ordr condiion for h opimal sragy is: 6 E L EL + + ) = i + i + + + ε ) δ i + i =0 Th firs rm characrizs h marginal loss in priod arising ou of highr xpcd inflaion, whras h scond rm capurs h bnfi from inflaion a via incrasd oupu). Th final rm rprsns h discound fuur loss arising from a laxr policy a. For δ > 0, inflaion will, in gnral, b lowr han in h absnc of rpuaional ffcs sinc L + + ) + > 0; = and > 0 xcp for h limi cas ha h signal has no + i informaional conn). Following backward inducion, h opimal policy in + can b solvd for givn + as: 7 i + ε ). + = + + From 7 follows ha h raional forcas for inflaion is jus h forcas for h unknown paramr : 8 + ) = E ) This is bcaus E ) = E i ) raional xpcaions + + and, according o 7, E i ) = + E ). Thus, wih = E ), w g + ) = E ). + + + + Equaion 6 characrizs h opimal policy. Obviously, h bank s sragy dpnds on how h public inrprs h oucom. In h following scion, w discuss h public s larning problm. W considr h spcial cas ha h updaing can b dscribd by a linar larning rul. In his cas, i urns ou ha h raional xpcaions quilibrium is indd characrizd by a linar rul. hp://www.wiwi.uni-anankfur.d/profssorn/spahn/fvd/

3) Linar larning ruls 3). Th larning problm A h nd of priod, priva agns obsrv h inflaion ra and h supply shock ε. Suppos ha priva agns bliv h bank s policy rul 6 can b dscribd by h following linar quaion: 9 i = α + β + γ ε Bcaus of 3 and 9, hn = +. Using all availabl informaion, h i + = α + β + γ ε public ris o infr h cnral bank s prfrncs rsp. i ) in ordr o minimiz xpcaional rrors abou nx priods inflaion ra: = F ) +. Assum ~ N E ); σ ) and ~ N 0; ). Furhrmor, and ar assumd o b uncorrlad. Thn σ ~ N α β E ) + γ ε ; β σ + + σ ) Whn h shock ε can b obsrvd prfcly x pos, priva agns can dduc h impac of ε on, as long as h sabilizaion rspons is indpndn of h yp. This will b ru if h policy indd can b characrizd by a linar rul such as in 9. Knowing h opimal racion γ ε, priva agns can sor ou 4 h ffc of ε on. Using Baysian updaing, h bs simas for and i, basd on h signals h cnral bank s sragy 9, ar: and ε and 4 This argumn implis ha sabilizaion policy will b indpndn of crdibiliy- ha is h opimal rspons o shocks ε will b γ = s quaion 9 blow). Th indpndnc bwn sabilizaion impac and rpuaion holds as long as w can spara h ffc of ε on whn making infrnc abou h yp. Obviously, his rsul dos no longr hold whn hr is uncrainy w. r.. o h wigh h cnral bank aachs o oupu sabilizaion as is wll known, h lowr his wigh, h lss dampnd will b oupu flucuaions). Dpnding on h cnral banks wigh rlaiv o h sociy s wigh, bias in sabilizaion policy may b posiiv or ngaiv s Bsma/Jnsn 998). This, howvr, dos no imply ha a givn yp will no b abl o implmn h policy which is fficin from hr poin of viw. Th prsn s up allows o work ou h impac of rpuaion on h sabilizaion rspons in h clars way. hp://www.wiwi.uni-anankfur.d/profssorn/spahn/fvd/

α ρ 0 E, ε ) = E ) ρ ρ) + γ ε ) β β and corrspondingly: Cov i, ) = + ) = α + β E ) + γ ε ) ρ + ρ) Var ) E i, ε ) E i ) [ E ] wih σ β σ ρ = ; ρ = β σ + σ β σ + σ Cov i, ) = Var ) Givn h blif 9, priva agns mak a linar forcas: 3 + = λ0 + λ + λε + Th impac of a chang in h ra of inflaion a on nx priod s xpcaion is = λ Obviously, λ 0 will dpnd on. rsp. on h prior knowldg E ) ). To solv for h quilibrium, h cnral bank aks λ 0 ; λ; λ as givn. This dfins hr opimal rul spcifying quaion 9), givn h assumd updaing bhavior of priva agns. In a REE, h sima + = λ0 + λ + λ ε mus corrspond o h acual opimal bhavior of h cnral bank. Thus, in REE, updaing mus corrspond o h acual bhavior his drmins h soluion. 3). Equilibrium undr linar larning ruls Th opimal forcas for E ) is dfind by quaion 0 and h inflaion forcas ) + by quaion 3. Bcaus + ) = E ), in REE h paramrs in 0 and 3 mus b idnical: α 4 λ0 = E ) ρ ρ) β 5 λ ρ = β 6 λ = γ λ hp://www.wiwi.uni-anankfur.d/profssorn/spahn/fvd/

As shown in h appndix A, using h rsricions abov h opimal linar sragy of h cnral bank is characrizd by: δ λ 7 α = ) δ λ ρ + δ λ E = E ) [ δ λ ρ] β 8 β δ = + δ λ λ 9 γ = δ λ 0 δ λ i E ) δ λ ρ + ε δ λ + + δ λ δ λ E ε + ) + δ λ = = [ ] δ λ wih = E ) δλ ρ + δ λ According o 9, h cnral bank rsponds fficinly o oupu shocks, indpndn of is crdibiliy. Th rason is similar o h sandard Barro/Gordon modl: Thr, lack of crdibiliy rsuls jus in an inflaion bias, laving h sabilizaion rspons and hus ral oupu unchangd. Hr, howvr, h impac on sabilizaion policy is mor subl du o h lack of informaion abou cnral bank s prfrncs. Sinc a srong bank wih < E ) ) pursus a policy rsuling on avrag in lss inflaion han xpcd, i will caus a rcssion on avrag in ordr o gain rpuaion for h fuur. Th opposi is ru for a wak bank > E ) ). A srongr concrn for rpuaion du o a highr δ ) will caus a mor sabl policy for all yps and hus rduc inflaionary xpcaions: δ < 0 wih < E) for δ > 0 and ρ <. Th indpndnc bwn sabilizaion rspons and rpuaion holds as long as h ffc of ε on can b sparad whn priva agns mak infrnc abou h yp. This is also ru for nonlinar.g. muliplicaiv) conrol rrors. Tak h cas of muliplicaiv uncrainy: = i wih E ) = = and σ = E ) E )) Thn, h FOC has o b modifid o hp://www.wiwi.uni-anankfur.d/profssorn/spahn/fvd/

E ) EL + + ) + i E ) + ε ) + δ + i or EL + + ) + i = + ε ) δ + σ ) + i Now, h bank will ac mor cauiously in gnral, and so as is wll known from Brainard 967) i will sabiliz shocks o a lssr xn. Bu as long as h impac of ε on i can b infrrd prcisly, h sabilizaion policy dos no affc updaing by priva agns, and so crdibiliy has no impac on h sabilizaion rspons. 5 Wha is h impac of damagd rpuaion as a rsul of changing from a wll sablishd insiuion as h Bundsbank o an insiuion lacking any rack rcord? In ordr o valua h impac of rpuaion, assum ha h nw insiuion has idnical prfrncs h sam ). Th public, howvr, bing unsur abou, raiss is xpcaion E ). Tha is, h loss of rpuaion for h nw insiuion is capurd by an incras in E ) of cours, in gnral his gos hand in hand wih an incras in varianc σ, bu h ffcs ar similar). Obviously, yp will also parly accommoda h highr inflaionary xpcaions, bu only o som xn: According o quaion 0, h rspons will b lss han ½ for δ > 0 and ρ <. Thus, givn h linar larning rul, a gradual rspons is opimal whn rpuaion drioras. As a rsul, on avrag oupu and mploymn will b lowr and inflaion highr whn rpuaion drioras. Th ndogniy of h signal o nois raio ρ complicas calculaion of h xplici soluion: Th srongr h cnral bank rsponds o is own prfrncs h highr β ), h srongr h public will upda is priors whn obsrving a high ra of inflaion, hus dampning h bank s incniv o rais β. Th wo priod s up allows o calcula xplicily h cnral bank s racion as a funcion of im prfrnc and h varianc of h shocks. As shown in appndix B, comparaiv saic rsuls show ha, in gnral, h cnral bank rsponds mor cauiously o is own prfrncs, h mor valuabl fuur rpuaion h highr h discoun facor δ ) and h mor rliabl h informaional conn of h signal h mor prcis h informaion, ha is, h smallr h raio σ σ ): / 5 This argumn no longr holds if insad ε can only b obsrvd wih som nois. Thn, whn hy upda hir priors, priva agns can no longr spara h impac of supply shocks on h inflaion ra, and his may affc h cnral bank s incnivs o sabiliz fficinly. Th impac of noisy obsrvaion is lf for fuur rsarch. hp://www.wiwi.uni-anankfur.d/profssorn/spahn/fvd/

β δ < 0 β and > 0 σ / σ 4) Efficin Signaling Equilibrium Up o now, following sandard procdur in h macro liraur Cukirman/Mlzr 986), Mino/Tsusui 990) and Faus/Svnsson 997)), a linar larning rul was imposd on h updaing bhavior of h public. Such a rul prsrvs h linar srucur of h modl and maks calculaion of xpcd valus fairly sraighforward. As is wll known from signaling modls, hr can b an infini numbr of quilibria dpnding on h blifs imposd on h uninformd playrs. Mos of hs blifs, howvr, ar rahr implausibl. For h discr yp analysis, gam horic ools provids a mnu of rfinmns o narrow down h s of quilibria. Rfinmns ar ndd bcaus, in h discr yp cas, in quilibrium mos of h signals ar no usd, and so arbirary rsricions can b imposd on ou of quilibrium bhavior. In a coninuous yp sing, a coninuous s of signals will b sn in quilibrium, and so h problm of indrminacy bcoms lss srious. As shown blow, imposing a linar larning curv is no jusifid in his conx. Following h sandard signaling liraur s Rily 979), h fficin signaling quilibrium will b analyzd. I urns ou ha undr fficin signaling, i is qui likly ha a ough bank has incnivs o nforc a vry rsriciv cold urky policy vn risking an ovrkill ) in ordr o prov is oughnss. Sinc h quilibrium oucom is highly nonlinar, updaing ruls undr noisy signals bcom fairly mssy and unsolvabl. W illusra h argumn for h cas of prfc ransparncy a complly rvaling signal ρ = 0 ) and a fini suppor of h random variabl. Th fini suppor allows o characriz h sragy of h wors cnral bankr in a sraighforward way. To wha xn h argumn blow can b xndd o h cas of disribuions wih infini suppor is lf for fuur rsarch. So from now on assum ha = i Furhrmor, is assumd o b disribud coninuously wih fini suppor [ ], min max. Firs, w show ha sragis implid by a linar larning rul canno b h opimal sragy for h waks yp. L hp://www.wiwi.uni-anankfur.d/profssorn/spahn/fvd/ ˆ = b h yp wih h highs prfrnc for oupu max

simulaion. Undr a linar larning rul as imposd in 3, h public assums ha sh will always choos som ˆ ) = θ ˆ < ˆ. Obviously, his choic will rval hr yp in h scond priod anyway + ˆ )) = ˆ. Bu hn, wha should prvn yp ˆ from pursuing h shor run opimal policy ˆ ) = ˆ which clarly would giv hr a highr payoff? Th problm wih h linar rul is ha i implis for any ~ ˆ ) inflaionary xpcaions will b vn highr + ~ ) > ˆ + ), bcaus = λ > 0 s figur ). This, howvr, ˆ ) dos no mak sns, sinc in a rvaling quilibrium, h highs possibl ra a + is = ˆ. So, h larning curv should bcom fla for ˆ ) all ohr larning + sragis ar sricly dominad). Givn a fla updaing, howvr, h bs yp ˆ can do is o choos ˆ ) = ˆ. Th waks yp has no rason o signal a all. Tha mans ha any rfind > > larning curv mus b fla a ˆ ha is + + ˆ ) = ˆ wih 0 ˆ = - s figur ). Figur In conras, all lowr yps hav an incniv o signal. Th fficin signaling is pinnd down by incniv condiions: I mus no b in h inrs of high yps o disguis as low yps wak yps mus no b abl o gain by rducing inflaion and so sablishing a hp://www.wiwi.uni-anankfur.d/profssorn/spahn/fvd/

rpuaion as bing srong). Givn som larning curv ) of h public, ach yp will + choos hr opimal sragy according o h FOC. In a raional xpcaions quilibrium, h opimal rspons of yp mus confirm o h blif hld by h public. Th cnral banks problm is o minimiz h loss: EL ) = + + ε ) [ ] + δ ) + ) + + ) + wih + ). Indiffrnc curvs in h, + ) spac ar slopd according o: Figur 4 + )) d + δ + + ) d + = 0 So givn any larning rul ), h opimal choic for ach is characrizd by h + condiion compar quaion 4 and figur ): 3 + = + ) 4 δ + ) + + 0 for + ) which always holds) hp://www.wiwi.uni-anankfur.d/profssorn/spahn/fvd/

3 pins down h signaling choic for any yp. If h larning rul + ) is coninuous, i should corrspond for ach yp o hr acual bhavior, which is characrizd by his condiion. Ingraing 3 givs h opimal larning rul: + + + = 4 δ ) δ + ) + A In a rvaling quilibrium, h following addiional condiions mus hold: ) Givn ha is a rvaling signal for, in quilibrium, xpcaions mus conform o acual bhavior. 5 ), = + ) ) Th waks yp canno gain by disoring his shor run opimal choic: 6 ) = + ) for = max Using 5 and 6, h consan A is drmind by: 7 A = 3 ) δ + Th opimal policy for yp is characrizd by h quaion: + ) 3 4 δ ) + 4 + ) = 0 which yilds h soluion: 8 ) = ) )[3δ ) ) ] + + According o 8, is incrasing in. Th highr h discoun facor δ, h mor currn policy is disciplind by h impac on fuur rpuaion. Rpuaion works as disciplinary dvic only for δ > δˆ = + 3 3. δˆ is dcrasing in. For δ δˆ, rpuaional ffcs do + no consrain monary policy, so w g h unconsraind opimum as a cornr soluion: ) = + ) hp://www.wiwi.uni-anankfur.d/profssorn/spahn/fvd/

Compard o h quilibrium undr linar larning ruls quaion 0), obviously is highr for wak yps high ). In conras o 0, howvr, a policy of gradualism accommodaing high inflaionary xpcaions o som xn), is no opimal for srong yps. For low nough, i pays o caus dflaion in h firs priod in ordr o dmonsra oughnss. Equaion 8 shows ha <0 for. < + ) 3 δ Thus, in conras o h oucom undr linar larning rul, undr fficin signaling a cold urky approach is qui likly for srong cnral bank yps. 5) Conclusions and furhr rsarch Th papr analyzs h signaling problm a cnral bank is facing in a wo-priod modl whn h bank is risk avrs wih rspc o dviaions of boh inflaion and oupu from hr arg and h public is imprfcly informd abou h bank s prfrncs rprsnd by a coninuous random variabl). Sinc h public updas h priors afr obsrving h policy oucom, concrn for rpuaion dampns h bank s mpaion o pursu a discrionary policy. Whn h public uss a linar larning rul, h raional xpcaions quilibrium can b characrizd xplicily. As long as h public obsrvs boh ε and bfor updaing h prior and so is abl o spara h impac of supply shocks on h inflaion ra, h cnral bank will rspond fficinly o oupu shocks, indpndn of hr crdibiliy. Undr a linar larning rul, inflaionary xpcaions will always b parly accommodad - i will nvr b opimal o pursu a dflaionary policy in ordr o prov hr oughnss. This rsul, howvr, is no robus agains mor sophisicad larning ruls. Undr fficin signaling, i is shown for h cas of prfc ransparncy, ha a ough bank has srong incnivs o nforc a vry rsriciv cold urky policy, in ordr o prov is oughnss. Thus imposing linar larning ruls, as is sandard in h macroconomic liraur, givs mislading rsuls. Th papr can b xndd in svral ways. Firs, i sms rahr implausibl o assum ha h public is abl o obsrv supply shocks prfcly. If hs shocks can b obsrvd only wih som nois, priva agns can no longr spara h impac of supply shocks on h inflaion ra, whn updaing hir priors. This may affc h cnral bank s incnivs o sabiliz fficinly, and so h sparaion bwn fficin sabilizaion rspons and crdibiliy may no longr hold. Th impac of noisy obsrvaion is lf for fuur rsarch. Efficin signaling quilibria rsul in highly nonlinar oucoms. Consqunly, updaing ruls undr noisy signals bcom fairly mssy and unsolvabl. For ha rason, h analysis in ha par was rsricd o h cas of prfc ransparncy. Fuur work will show whhr h rsuls can b xndd o signaling quilibria vn in h cas of noisy signals. hp://www.wiwi.uni-anankfur.d/profssorn/spahn/fvd/

6) Appndix 6). Appndix A According o 7, EL + + ) = + ) + + + ) and hus EL 9 + + ) = + +. + Givn ha priva agns mak a linar forcas + = λ0 + λ + λε, implying + = λ ), w can rformula h FOC condiion 4 as: = i + ε ) δ λ + ) or: + 30 i = ) 0 ) ) + δ λ δ λ λ + δ λ λ ε + δ λ 30 dfins h opimal sragy dpnding on priva forcass and hus drmins h cofficins in i = α + β + γ ε Subsiuing λ 0 and λ givs 30 as a funcion of and λ and hus characrizs oghr wih 5 and h xplici soluion. Firs, solv for : [ ) δ λ ) δ λ λ ] = 0 + δλ E = = [ E ) δ λ + ρ)) + δ α λ ] + δλ α, β, γ This givs: 3 = [ E ) δ λ + ρ)) + α δ λ )] i + [ E ) ] + δ λ δ λ + δ λ γ δ λ + ε + δ λ δ λ + ρ) δ λ So α = E ) + α δ λ δ λ δ λ. From his quaion, w can + + + δ λ immdialy solv for α o g 7. 6). Appndix B From 8, β is dfind implicily using 5 and ) as: hp://www.wiwi.uni-anankfur.d/profssorn/spahn/fvd/

g β ): = 4 4 β σ β σ β + δ + = 0 ) β β σ + σ β σ + σ g β ) characrizs h soluion for β as a funcion of δ and of h variancs of h shocks. For σ > 0 g β = 0) = < 0 and g β = ) > 0. Sinc g is coninuous in β, hr xiss a las) on soluion β 0, ) monoon incrasing in β, ha is if:. Uniqunsss of h soluion can b sablishd whn g is 3 dg dβ δ β σ + σ β σ σ σ β σ ) + ) 4 = + 3 β σ + σ ) 4 4 6 > 0 4 6 4 4 6 β δ ) β σ + 6β + 3δ ) β σ σ + 3β + δ ) σ σ + σ > 0 6 4 4 4 4 4 6 6 β + β 3σ / σ δ ) + 3β δσ / σ + σ / σ ) + δσ / σ + σ / σ > 0 Sufficin condiions for 3 o hold ar 33: ihr: β δ orδ < 3σ / σ. If 33 is fulfilld, h cnral bank rsponds mor cauiously o is own prfrncs, h mor valuabl fuur rpuaion h highr h discoun facor δ ) and h mor rliabl h informaional conn of h signal h mor prcis h informaion, ha is, h smallr h raio σ σ ). / β δ < 0 g sinc > 0 δ β for β > 0, < 0 δ g whnvr > 0 β β For h sam rason, > 0 σ / σ sinc < 0 σ gσ / α If 33 holds, w also g boh < 0 δ and δ ρ) ρ < 0, sinc α = E ) β and δ β = E ) β δ ρ) ρ β. Thus, according o 0, xpcd inflaion dcrass wih hp://www.wiwi.uni-anankfur.d/profssorn/spahn/fvd/

incrasing discoun facor. In conras, h impac of h qualiy of h signal on xpcd inflaion is indrmind: α 0 ρ Whn σ = 0, β = / 4 ± 6δ ) W can rul ou h ngaiv roo for h following rason: for h limi cas δ = 0 and/or ρ = bcaus σ = 0 or σ ), h wo soluions for β ar β = 0 and β =. Sinc only β = maks sns in his cas, w migh xclud h soluion β = 0. If w rquir h soluion o b coninuous for small changs in δ, only h posiiv soluion for h squar roo maks conomic sns: 6).3 Spcial cass: a) ρ = or σ = 0 no uncrainy abou ). Thn β = λ 0 = ; λ = 0. Obviously, hr canno b any rpuaional ffcs; so i = + ) wih = b) δ = 0 no rpuaional ffc) Thn again β = ; i ) E + Updaing givs: λ 0 ρ = = ρ ) E ); λ = ), so E ) = λ + λ = E )ρ ) + ρ) E ) + ) : = ρ + ρ) 0 c) ρ = 0 or σ = 0 Limi rgim wihou nois. Whn is a prfc signal, h a priori informaion E ) will no b usd o sima. Tha is, λ = E ); λ. Sinc β 0 = now α = β and so = i = βe ) + β, w g E ) = λ + λ = E ) + ) + ) = 0 E = E) β wih β + 6 δ = dcrasing in δ for δ < 6. 4 hp://www.wiwi.uni-anankfur.d/profssorn/spahn/fvd/

7) Rfrncs: Backus, David/Driffil, John 985), Inflaion and Rpuaion, Amrican Economic Rviw 75, 530-538 Barro, Robr J. / David B. Gordn 983), Ruls, Discrion, and Rpuaion in a Modl of Monary Policy 983), in: Journal of Monary Economics,, 0-0. Bsma, Rol/ Hnrik Jnsn 997), Inflaion Targs and Conracs wih Uncrain Cnral Bankr Prfrncs, CEPR discussion papr 56 o appar in Journal of Mony, Crdi and Banking Brnank, Bn / Ilian Mihov 996), Wha dos h Bundsbank Targ?: Europan Economic Rviw, 997 Brainard, William 967), Uncrainy and h Effcivnss of Policy Amrican Economic Rviw 57 Clarida, Richard / Mark Grlr 997), How h Bundsbank Conducs Monary Policy, in: Romr, Chrisina D. and David H. Romr ds.) Rducing Inflaion:Moivaion and Sragy, Th Univrsiy of Chicago Prss Cukirmann, Alx /Mlzr, Allan 986), A Thory of Ambiguiy, Crdibiliy and Inflaion undr Discrion and Asymmric Informaion, Economrica 54, 099-8 Dornbusch, Rüdigr/Favro, Carlo/Giavazzi, Francsco 998), Th Immdia Challngs for h Europan Cnral Bank, NBER Working Papr Sris 6369 Eijfingr, S./Hobrichs, M./Schaling E. 997) Why Mony alks and Walh whisprs: Monary Uncrainy and Mysiqu, CnER Tilburg Faus, Jon/Svnsson, Lars 997), Transparncy and Crdibiliy: Monary Policy wih Unobsrvabl Goals, NBER Working Papr 645 Mino,-Kazuo; Tsusui,-Shunichi, Rpuaional Consrain and Signaling Effcs in a Monary Policy Gam, Oxford-Economic-Paprs,-N.-S.;43), July 990,pags 603-9. Laubach, Thomas/ Posn, Adam 997), Disciplind Discrion: Monary Targing in Grmany and Swizrland, Essays in Inrnaional Financ 06, Princon Univrsiy Ramaswamy, Ramana; Slok, Torsn 997) Th Ral Effcs of Monary Policy in h Europan Union: Wha Ar h Diffrncs?, IMF Working Papr 97/60 Rily, John 979) Informaional Equilibrium, Economrica 47, 33-359 Vickrs, John 986), Signaling in a Modl of Monary Policy wih Incompl Informaion, Oxford Economic Paprs, 383), 443-55. hp://www.wiwi.uni-anankfur.d/profssorn/spahn/fvd/