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Inflation Forecasts and Monetary Policy Author(s): Ben S. Bernanke and Michael Woodford Source: Journal of Money, Credit and Banking, Vol. 29, No. 4, Part 2: Dynamic Effects of Monetary Policy (Nov., 1997), pp. 653-684 Published by: Blackwell Publishing Stable URL: http://www.jstor.org/stable/2953656 Accessed: 05/05/2010 16:07 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=black. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].

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BEN S. BERNANKE MICHAEL WOODFORD

InflationForecastsandMonetaryPolicy Proposals for "inflationtargeting"as a strategy for monetarypolicy leave open the importantquestion of how to determinewhethercurrentpolicies are consistent with the long-mn inflationtarget. An interestingpossibility is that the central bank might targetcurrentprivate-sectorforecastsof inflation,either those made explicitly by professional forecastersor those implicit in asset prices. We address the issue of existence and 1miquenessof rationalexpectations equilibriawhen the central bank uses private-sectorforecasts as a guide to policy actions. In a dynamic model which incorporatesboth sluggish price adjusttnentand shocks to aggregatedemandand aggregate supply, we show that strict targeting of inflation forecasts is typically inconsistent with the existence of rationalexpectationsequilibrium,and that policies approximating strictinflation-forecasttargetibgare likely to liave undesirableproperties.We also show that economies with more general forecast-basedpolicy rules are particularly susceptibleto indeterminacyof rationalexpectationsequilibria.We conclude that, although private-sectorforecasts may contain informationuseful to the central bank, ultimately the monetaryauthoritiesmust rely on an explicit structuralmodel of the economy to guide their policy decisions.

IN RECENT YEARSa number of major central banks have adopted, or at least actively considered, some form of "inflationtargeting'+as a frameworkfor monetarypolicy.1 In an inflation-targetingregime, the central bank (usually in conjunctionwith the government)establishesexplicit goals for the inflation rate at medium-termand long-term horizons. Although pursuitof an inflation targetdoes not precludeother objectives, such as short-runoutputor exchange-rate The authorsthank V. V. Chari, LarryChristiano,MarvinGoodfriend, Ed Nelson, Julio Rotemberg Lars Svensson, Alberto Trejos, and an anonymousreferee for helpful comments. Both authorsreceived financial supportfrom the NationalScience Foundation. 1. Central banks recently making highly publicized switches to an inflation-targetingapproachinclude New Zealand, Canada, the United Kingdom, Sweden, and Australia,many other countries have moved towardmakingprice stabilitythe primaryobjective of the centralbank, often in conjunctionwith institutionalreforms to increase central bank independence (Goodhartand Vinals 1994, Debelle and Fischer 1994; Leidermanand Svensson 1995; Haldane 1995- Bernankeand Mishkin, forthcoming). A few countries, notablyGermanyand Switzerland,have long used medium-terminflationobjectives as an importantcomponent of their monetary policy making (Bernanke and Mishkin 1992, Bernanke and Mihov, forthcoming).In the United States, the Fed has so far resisted the adoption of explicit inflation targets, althoughthe perceptionis that the relative importanceof price stability among the Fed's objectives has increased. Formallegislation introducedin the U.S. Senate by SenatorMack would amend the Humphrey-Hawkinsbill and requirethe Fed to pursuean inflationtarget.

BENS. BERNANKE and MICHAEL WOODFORD are bothprofessors of economics at Princeton Universityand research associates at the National Bureau of Economic Research. Journal of Money, Credit, and Banking, Vol. 29, No. 4 (November 1997, Part2) Copyright 1997 by The Ohio State University Press

654

: MONEY, CREDIT,AND BANKING

stabilization,it is understoodthattheseobjectivesare subsidiaryto achievingthe targetlevel of inflation. As a strategyfor conductingmonetarypolicy,inflationtargetinghasbothadvantages and disadvantages.One potentialadvantageis increased"transparency" of monetarypolicy,thatis, bettercommunication of policymakers' objectivesandintentionsto the publicandthe financialmarkets;see BernankeandMishkin(forthcoming).A seconddesirablefeatureis that,by settingtargetsfor its goal variable ratherthanfor an intermediate indicator(suchas moneygrowthor the exchange rate),the inflation-targeting centralbankmayavoidthe "velocityinstability" problem, whichariseswhenthereareunexpectedchangesin the relationship between the intermediate targetandtheultimateobjective. The maindisadvantages of the inflation-targeting approachfollow fromthe empiricalobservation thatinflationrespondsto changesin monetarypolicyonlywitha substantial lag, fromoneto twoyearsor more.Thelackof quickfeedbackfromthe economyto policyimpliestwo relatedproblems:First,the information the central bankrequiresin orderto implementinflationtargetingmay be muchgreaterthan thatneededto targetanintermediate variable,whoseresponseto policychangescan be observedwithless delay.Second,as it is difficultforthe inflation-targeting centralbankto tell whetherit is "ontrack,"it is equallydifficultforthepublicandthe financialmarketsto make thatjudgment,which has potentiallyadverseconsequencesforthecentralbank'saccountability andcredibility. Is theresomewayto overcometheproblemsassociatedwiththelonglag between changesin policyandchangesin the inflationrate?An interestingpossibilityis for the centralbankto targetcurrentforecasts of medium-term inflation,ratherthan inflationitself. Thecurrentforecastof inflation,unlikeactualfutureinflation,is (at leastin principle)a contemporaneously observablevariable;thus, in a regimethat targetsinflationforecasts, boththe centralbankandthe publicwouldbe able to monitorpolicycontinuously. Further,therationallyformedforecastof inflationincorporates,by definition,all information currentlyavailableaboutfutureinflation, so thattherecanneverbe anyconflictbetweenthe objectivesof targetingthe inflationforecastandtargetinginflationitself. Forbothof thesereasons,it hasbeenargued that the forecastof inflationis the "ideal"intermediatevariablefor an inflation-targeting regime(Svensson,forthcoming and1997). In practice,how couldthe centralbankgo abouttargetingthe forecastof inflation?At leastthreetypesof approaches havebeenproposed.First,thecentralbank couldtry to "target"the predictionsof private-sector forecasters,for example,by raisinginterestrateswhentheconsensusprivate-sector forecasthas inflationabove thecentralbank'sannounced targetandloweringrateswhentheinflationforecastis belowthetarget.HallandMankiw(1994)proposea strategyof thistype.2Second, the centralbankmightattemptto targetthe forecastof inflationimplicitin various assetprices;for example,as we discussin section4, therehavebeenproposalsto 2. Actually, Hall and Mankiw suggest that the centralbank target forecasts of nominal GDP growth ratherthaninflation;however, many of the criticismsmade here are independentof the particularvariable whose forecast is to be targeted.

BEN S. BERNANKEAND MICHAELWOODFORD : 655

adjustmonetarypolicy automaticallyin responseto movementsin commodity prices,to changesin long-termbondyieldsor in interest-rate spreads,to CPIfuture prices, and to changesin the spreadbetweennominaland indexedgovernment bonds,amongothers.Finally,the centralbankmighttryto targetits own internal forecastsof inflation(Svensson,forthcoming), in the senseof adjustingits instrumentto eliminateany discrepancybetweenits staff'sforecastof inflationandthe target.Examplesapproximating each of these proposalsmay be foundin central bankpractice:Forexample,in its quarterly InflationReport, the Bankof England reportsextensivelyon bothprivate-sector andits owninternalforecastsof inflation; and,thoughtheBankdoesnotfollowa mechanical rule,thereis a presumption that if a preponderance of forecastsareabovetheBank'sinflationtarget,a tighteningof policywill be recommended [seeBowen(1995)andKing(1994)fordiscussionsof the Bankof England'sstrategy].A similarapproachhas beenfollowedby the ReserveBankof New Zealand(MayesandRiches1996).Virtuallyall centralbanks pay close attentionto financial-market indicatorsof inflation,such as long-term bondyieldsandyieldspreads. Theobjectiveof thispaperis to studythebehaviorof theeconomywhenthecentralbankattemptsto "targettheforecast"of inflation,settingits instrument to eliminatedeviationsof some explicitor implicitinflationforecastfrom a prespecified target.Forconcreteness,formostof thepaperwe considerthecasein which(1) the inflationforecastbeingtargetedis theconsensusprivate-sector forecast,and(2) the privatesectorhas someinformation aboutthe economythatthe centralbankdoes nothave.3However,as we discussin thefinalsectionof thepaper,thoroughanalysis of thiscaseallowsus to drawconclusionsaboutothertypesof forecasttargeting, andaboutthe cases in whichthe centralbankhas equalor superiorinformation to theprivatesector. Unfortunately, we findthattargetingthe forecastof inflation,in the senseof allowingmonetarypolicyto respondstronglyto deviationsbetweentheinflationforecast andthe target,is not likelyto be a usefultacticfor monetarypolicy,for two broadsetsof reasons:First,somewhatparadoxically, to theextentthattargetingthe forecastis successful,the signal-to-noise ratioin the inflationforecastis likely to become(endogenously) small.In the limit, as perfectstabilization of the inflation forecastis approached, thereis no incentivefortheprivatesectorto gatherinformation, andthe inflationforecastbecomesuninformative. We showfurtherthatpolicies approximating stabilizationof the inflationforecast-arealso likely to have undesirable properties.Thesefindingsconfirmandextendthe analysisof Woodford (1994a);see alsoWest(1994). Second, we find that attemptsto targetthe inflationforecastlead, for broad classesof policies, to indeterminacy of the rationalexpectationsequilibrium.An implicationis thateven successfulattemptsto targetthe inflationforecastmaybe 3. Romer and Romer (1996) have presentedevidence that Fed forecasts are superiorto those of the privatesector. Even if this finding is correct, however, it does not lule out the possibility that the private sector has informationthat the Fed would like to infer (the reversemay also be true, of course). It is well known, for example, that the Fed attemptsto use private-sectorinformationimplicit in asset prices.

656


associatedwitharbitrary volatilityin inflationitself, as well as in outputandother goal variables.Thus, directtargetingof private-sector inflationforecastsis not a panaceafor the problemsraisedby the long lag betweenmonetarypolicy actions andtheresponseof inflation. Ona somewhatmorepositivenote,ouranalysisshowsthat,despitetheproblems withstrictforecasttargeting,a moresubtleapproachin whichforecastsaresimply usedas one of severalsourcesof information canbe helpful.In particular, the centralbankmaywell be ableto inferusefulinformation fromprivate-sector forecasts of macroeconomic variablesotherthaninyS!ation, suchas outputor interestrates.4 However,againcautionmustbe urged,as we show thatthe problemof indeterminacyof equilibrium canapplyto monetarypolicyrulesbasedon forecastsof outputandinterestrates,just as it can to policiesbasedon forecastsof inflation.The mostgeneralconclusionof ourpaperis thatcentralbanksshouldbe carefulnot to tie monetarypolicytoo closelyto anyvariablethatis too sensitiveto the expectationsof thepublic. Toavoidmisunderstanding, we shouldemphasizethatourresultshavelittleto say aboutthe desirability or feasibilityof inflationtargetingperse, as opposedto inflation-forecast targeting; indeed,thispolicystrategyhasmanyattractiveaspects.Our claim is only that, for successfulimplementation of inflationtargeting,thereappearsto be no substituteforexplicitstructural modelingof the economyandextensive informationgatheringby the centralbank. Private-sectorforecasts, and forecastsinferredfromfinancialmarkets,shouldbe partof theinformation gathered by the bank,buttheyshouldbe combinedwithotherinformation in the makingof policy. The rest of the paperproceedsas follows. Section 1 analyzesthe effects of inflation-forecast targetingin a simple, reduced-formmodel due to Woodford (1994a).WeconfirmWoodford's earlierresultthat,whenthe centralbankattempts to targetthe inflationforecastpreciselyat the target,no rationalexpectationsequilibriumexists.Moregenerally,we findthatattemptsby thecentralbankto keepthe inflationforecastclose to the target,whiletechnicallyfeasible,mayleadto excessive volatilityin actualinflationoutcomes. The modelof section1 is staticandthushas no role for private-sector expectationsaboutfuturepolicies.Toremedythis shortcoming,in section2 we analyzea dynamicmacroeconomicmodel which incorporatesprice stickinessand disturbancesto bothaggregatedemandandaggregatesupply.Wefindthattheresultsfrom thestaticmodelgeneralizeto thedynamiccase. Insection3 we showfurtherthat,in thedynamicmodel,forecast-based policyrulesin manycasesleadtypicallyto nonuniquenessof rationalexpectationsequilibrium; in particular, undersuchrulesthe economymaybe subjectto "sunspot" equilibriaandrelatedpathologies. As notedabove,ouranalysisfocusseson the case in whichthe centralbankattemptsto targetprivate-sector inflationforecasts,andin whichtheprivatesectorhas 4. More generally, our point is that the most useful informationvariable will not be the target variable. Thus inflationforecastsmight be useful to a centralbankthat seeks to stabilize nominalGDP rather than inflation.


someinformation abouttheeconomythatthecentralbankdoesnothave.Section4 discussestheapplication of ourresultsto alternative formsof forecasttargeting,and to alternative assumptions aboutinformation. Thebasicmessageof thispaper-that thereis no alternativeto structuralmodelingof the economyfor implementing forward-looking monetarypolicies- survivesthesegeneralizations. SectionS is a briefconclusion.

1. MACROECONOMICEQUILIBRIUMWHEN MONETARYPOLICYDEPENDS ON PRIVATE-SECTORFORECASTS:A SIMPLEMODEL

In this sectionwe extendthe exampleoriginallydue to Woodford(1994a),who used it to illustratethe potentialincompatibility of inflation-forecast targetingand the revelationof private-sector informationin rationalexpectationsequilibrium. Supposethatnextperiod'sinflationis givenby st+l

=

St +

Ut +

Et+l

(l)

wherest+ 1 iS realizedinflationin periodt + 1, St iS a statevariableindicatingunderlyinginflationpressures,utis the instrument of the centralbank(which,as the subscriptindicates,mustbe chosenone periodpriorto the realizationof the inflation rate),and Et+l iS an unforecastable disturbance thatalso affectsthe realized inflationrate.TherandomvariablesSt andEt+ l areassumedto be independent of the policyactionut;thedifferencebetweenthemis thatSt iS realizedpriorto thechoice of policyactionandEt+ 1 iS realizedsubsequent to thepolicyaction.Withoutloss of generalitywe mayalsoassumethatSt andEt+ l aremutuallyindependent. Wedenote thevariancesof s andE by cr2 andcr2, respectively,andwe normalizetheirmeansto zero. Finally, below we drop the time subscriptswhen there is no potential ambiguity. Fornow,assumethattheobjectiveof thecentralbankis to minimizeuncertainty aboutinflation,as measured by theconditional variance.(Implicitly,we assumethat thetargetedinflationlevel is zero;thisassumption is easilymodified.)If thecentral bankobservesthe underlyingstates, thenits taskis simple;it needonly set its instrumentu = -s. In thiscase, var(1r)= cr2, whichis evidentlythelowerboundthat canbe achieved. However,supposeinsteadthattheunderlyingstates is observedby privateforecastersbut not by the centralbank.The authoritymay thenseek to inferthe true statefromtheprivate-sector forecasts.If thecentralbanktakesthisapproach,will it be ableto achievethe sameminimalvarianceof inflationattainable whenit has directinformation of thestate?Clearlytheansweris no;if thecentralbankcouldinfer thestates fromtheprivate-sector forecasts,thenit wouldset u = -s, so thatir = e. Butthenthe rationalprivate-sector forecastsof inflationwouldhaveto be independentof s, so that(contrary to hypothesis)thecentralbankwouldnotbe ableto infer therealizationof s fromtheforecasts.

658


Moreformally,supposethattheloss functionof eachforecasteris givenby Lf =

Et{(rf-st+l)

(2)

}

whereTrfis theindividual's (publiclyannounced) forecastof inflation.Minimization of thisloss requiresthe announcement wf = Et{st+1|

St}

(3)

*

(Forthe momentwe assumethatforecastershavethe sameinformationandthus makethesameforecast.)Now supposethatthecentralbankobservesthe(common) forecastandchooses u = +rf.

(4)

Equations(1), (3), and(4) jointlyimplya uniquerationalexpectations equilibrium, so long as + 7&1, in which trf= ps,

with

(S)

1

+

(6)

1- +

Now as long as + 7&O,the valueof s canbe recoveredfromthe forecast[by using (5)]. So it mightseemthatthe centralbankcan achievethe minimumvariancefor inflationby usinga ruleof the form(4) forwhich (>

_ 1

(7)

However,it can be readilyseen thatthereexists no joint solutionfor (6) and(7): From(7), minimization of thevarianceof inflationrequires++ =-1, whichin turn implies,from(6), thatforecasters will rationallychoose+ = O.Butthen(7) hasno solution. Somemightarguethatthisexampleis of littlepracticalimport,sincethereexist well-behavedrationalexpectationsequilibriain whichthe centralbankachievesa level of inflationvariabilityarbitrarilyclose to the theoreticalminimum.Note that equations(1), (3), and(4) implya uniquesolutionforanyfinitechoiceof thepolicy reactioncoefficient+, so longas + 7&1. Intheassociatedequilibria,thevarianceof inflationis givenby (

)

(+

_

1)2

E

(8)


Thusit is possibleto makethevarianceof inflationarbitrarily close to its minimum valuecr£2 by choosinga sufficientlylargepositiveor negativevalueof + (although the lowerboundis attainedonly in the limitas + is madeunboundedly large,with eithersign). But the equilibriaof this simplemodelassociatedwith very large(in absolute value)+ areunappealing as a basisfor a policyrecommendation, eventhoughthey aretechnicallywell behaved.Oneproblemis thatthe modelassumesthatforecasterswill maketheeffortto observethetruestates precisely,eventhoughin equilibrium the forecaster'sloss will barelydependon whethershe knowss or not. To be specific,supposethatobservationof the realizedvalueof s costs the forecasteran amountc > 0, wherethiscostis measuredin thesameunitsas theloss in (2). Since eachforecastercan achievea loss of E{1r2}simplyby choosingtrf = O, thatis, by forecastinginflationto be at its unconditional mean,it will be worthwhilefor the forecasterto gatherinformation abouttherealizationof s if andonly if E{(rrf(s)--

X)2} + C < E{Tr2}

(9)

wherevrf(s)is theoptimalforecastconditional on knowledgeof thestates. Equation (9) represents anadditional constraint on theproblemof thecentralbank.Using(1), (3), and(4), one canshowthat(9) requiresvarfTr)2 CT£2+ C, or equivalently 2 (+_

1)2 C

s *

(10)

Equation(10) showsthatthereis a limitto howlarge+ canbe set, andthereforeto the degreeto whichthe variabilityof inflationcanbe reduced,withouteliminating the incentiveof the forecastersto gatherinformation. On the otherhand,it should be noted,as longas c < crS2, theconstraint (10) doespermitvaluesof + thatimplya varianceof inflationlowerthanthe centralbankcouldachievewithoutusingthe information in theprivate-sector forecasts(thatis, lowerthan(rS2 + (r2e).5 So thereis a sensein whichthecentralbankcanuse outsideforecaststo improveits policy,as we notedin the introduction. Butthisis not, strictlyspeaking,an inflation-forecast targetingpolicy,sincein equilibrium forecastsdiiTerent fromtheinflationtargetcan occurwithoutimplyingthatthe centralbank'spolicyis too "tight"or too "loose." Anotherpracticalconcernaboutrecommending a "large-+"policyto the central bank(thatis, one in whichthecentralbank'sactionsarehighlysensitiveto privatesectorforecasts)is that-even if thereis sufficientincentiveforforecasters to gather information-someforecastersmaybe "incompetent" at usingtheirinformation to produceoptimalforecasts.Toillustrate,supposethereis a randomcomponentin the averageforecastmadeby theprivatesector,conditionalon theunderlyingstate.For example,we mightreplace(3) with 1rf=

E{sls}

+ v

(11)

5. In this case, one can show that there are two constrained-optimalsolutions to the central bank's problem, correspondingto the two values of + one negative and one greater than 2 that satisfy (10) with equality.Under either of these policies, var(Tr)= (J2 + C < (J2 + (J2.

660


wherev is a randomvariablethatwe assume(forsimplicity)to be independent of s andE andto havemeanzeroandvarianceC2. Therearevariousinterpretations that maybe givento the noise termv in (11): As alreadysuggested,one possibilityis "incompetence"-thatis, systematicerrorsin thecomputation orcommunication of the forecast- or, perhaps,"herdbehavior," eventhoughovermanytrialsthe forecastersmakethecorrectinferenceon average.An alternative possibilityis strategic randomization by the forecasters,whichmayoccurif in fact theirloss functionis notgivenby (2). Forexample,Laster,Bennett,andGeoum(1996)showthatif forecastersobtainbenefitnot only fromthe accuracyof theirforecastsin an absolute sense,butalsofrombeingobservedto havemadetherelativelymostaccurateforecast, thenin equilibriumthey will distributetheirforecastsratherthanannounce theirconditionalexpectations,evenif all forecasters haveidenticalinformation.6 If we supposethattherearethreeor moreforecasters andtheforecastsareannounced simultaneously, thenthisgamecanhavea mixed-strategy equilibrium in whichthe averageforecastis random,evenconditionalon thetruestate5.7 In suchanequilibrium(11) will hold, whereXf refersnow to the averageprivate-sector forecast. If thecentralbankfollowsa ruleof theform(4), andtheaverageforecastis given by (11) ratherthan(3), thenequation(5) is replacedby Sf = +5 + V, where+ is determinedby (6). The analogueto equation(8), whichdescribesthe varianceof inflationattainable by the centralbank,is Val*(7r)

=

(+

1)2

+

+

¢V

+

¢E

'

(12)

Equation(12) showsthatthe varianceof inflationis now boundedaboveits minimumvalueunderperfectinformation (equalto C2), regardlessof the valueof the centralbank'sreactioncoefficient+. Furthermore, the varianceof inflationis no longerminimizedby choosing+ as largeas possible(eitherpositiveor negative); indeed,"targeting the forecast"by choosing+ largemayleadto a veryhighvarianceof inflationbecauseof thepresenceof thesecondtermon therightsideof (12). Analysisof (12) showsthatthe globalminimumfor the varianceof inflationis attainedfor a finitevalue+* < O, thoughthereis also a local minimumat a value +** > 1.8

Likethe problemof inducingforecastersto bearthe costsof gatheringinformation, the problemof eitherpotential"incompetence" or strategicbehaviordoes not imply thatthe centralbankcannotbenefitfromusing private-sector forecaswts in 6. For a related analysis of strategy regarding incentives for scattering of forecasts, see Lamont (1996). 7. Note that the strategicdispersionof forecastsrequiresthat the forecastersbe uncertainabout what the realized value of inflationwill be, which in this model is guaranteedby the presence of the shock e. 8. The proof proceeds as follows: Differentiationof (12) indicatesthat two local minimaexist, correspondingto the roots of the equationk = (+ - 1)-3, where k 8 2/ff2. The two roots are as described in the text. Furthermore,defining g 8 1/+, this equationmay equivalentlybe writtenk(l - ()3 = (4. Letting (* = 1/+*, (** - 1/+**, one observes that O < 1 - (** < 1 < 1 - (*, implying that |g* | > | (** | and hence | +* | < | +** 1. Finally, since at either of the local minima | + - 1 |-3 = k|+ |, one must have |+* - 1 > |+** - 1|. Thus each of the first two terms on the right side of (12) takes a smaller value at + = c)* than at + = +**, so that +* is the global minimum.

BEN S. BERNANKE AND MICHAELWOODFORD : 661

makingits policy:Afterall, the varianceof inflationis still lowerfor + = +* than for+ = O.However,againit is alsotruethatit is dangerous to literallytryto "target the forecast";althoughmonetarypolicyshouldreactto deviationsof privateforecastsfromthe inflationtarget,a policyof completelyeliminatingdeviationsof privateforecastsfromtheofficialinflationtargetis generallynotoptimal,andcanlead to an extremelyhighvarianceof inflation. "Targeting the forecast"is a misleadingdescriptionof the properuse of privatesectorforecastsin anothersenseas well:Thestrategyof targetingtheforecastseems to implythatthe private-sector forecastof thegoalvariable(forexample,inflation) is a sufficientstatisticfor the information thatthe centralbankcan usefullyobtain fromoutsideforecasters.In fact, in general,the centralbankmayfindit usefulto observeprivate-sector forecastsof variablesotherthanthegoalvariable,evenin the extremecase whenits objectivefunctiondependsonly on the stabilizationof the single goal variable.To illustratethis pointin the contextof our simpleredu.cedformmodel, supposethat,priorto the centralbank'schoiceof policy,it observes private-sector forecastsof bothinflationandalso the centralbank'spolicyvariable u. (Thinkof u as the short-term interestrate,for example;the choiceof u as the particular additionalvariableto be forecastis inessential,as we showlater.)With this assumption,we can now considerthe consequencesof monetarypolicyrule$ thatdependon the averageprivate-sector forecastuf of the centralbank'spolicy action,as well as on the forecastwrrf of subsequent inflation. Wewill wantto assumethattheprivate-sector forecasters careabouttheaccuracy of boththeirinflationforecastsandtheirforecastsof centralbankactions;forexample, theirclientsmay be interestedin the likely pathof short-terminterestrates. Generalizing (2), let us supposethatforecasters minimizea loss functionof theform Lf = E{(rrf-Orr)2}

+ alE{(uf-u)2}

(13)

wherea > Ois therelativeweightforecasters puton accuratepredictionof thecentralbank'spolicy variable.Becausethe loss functionis quadratic,the forecasters optimallychoose to announcethe conditionalexpectationsof Trand u as their forecasts: rrf= E{s js},

uf = E{UIs}*

(14)

Now supposethatthemonetarypolicyruleis of the form a

= +wsf ,+ U"S *

( 15)

Thecombination of (1), (14), and(15) impliesa uniquerationalexpectationsequilibrium,as long as + + u 7&1, in which orrf= +5,

+

- 1-

+

-

+

662


uf = 05, Tr = s+

0

-1 - +w- u

E

u = Os.

(16)

It may be observedthat,if in additionwe imposeu 7&1, the equilibriumdescribedby (16) is equivalentto the one resultingfromthe simplerpolicyrule (4), with+ = +w/(1 - a). Thusat firstglanceit mightappearthatimposingu = Oin (15) is innocuous,andthatthe inflationforecastof the privatesectoris all thatthe centralbankneedsto know.However,this conclusionis incorrect.Indeed,as we shownext, allowingfor u 7&0 canmitigatethe problemsassociatedwithrulesof theform(4) withverylargevaluesof +. First,we observedabovethatno ruleof theform(4) cancompletelyeliminatethe effectsof the statevariables on inflation,andtherebyreducethe varianceof inflationto its full-information lowerbound.Moreprecisely,we showedthatthereis no equilibrium in which(1) inflationis independent of thestatevariablein equilibrium and(2) the centralbankis ableto inferthe valueof the statevariablefromprivatesectorforecasts.However,this problemdisappearswhenthe centralbankuses a rule of the form(15), thatis, it respondsto forecastsbothof inflationandof an additionalvariable(in thisexample,the centralbank'spolicyvariable).In particular,if thecentralbanksetsu = 1, + 7&O,thenin equilibrium + = Oando = - 1, with the consequencesthatTris independent of s andvar(Tr)= cr£2, its theoretical minimum.It is interestingto note that,whenthe centralbankuses this rule, the private-sector inflationforecastneverdeviatesfromthe targetrateof inflationin equilibrium. (If it did, thecentralbankwouldchoosea valueof u differentfromits forecastedvalue, butin a rationalexpectationsequilibrium sucha deviationcould not predictablyoccur.)But the centralbankdoes not achievethis resultby the heavy-handed meansof movingthepolicyinstrument violentlyin responseto deviations of the forecastfromthe target;instead,it inducesthe privateforecastersto revealtheirinformation throughtheirforecastof the policyinstrument. Second,a ruleof the form(15) caneliminate,or at leastameliorate,the forceof the incentiveconstraintthatariseswhenforecastershavea cost of collectinginformation.In particular, if the forecasters' loss functionis givenby (13), plusthe cost c > Owhichis incurredif thetruestateis observed,thentheincentiveconstraint(9) becomes E{(sf(s)-s)2

+

al(uf(s)-u)2}+ c ' E{Tr2 + au2}.

(17)

Thatis, the improvement in forecastaccuracyfromobservingthe truestatemust exceedthe cost of gatheringthe information. Note that,if c < acrS2, thenthe constraint(17) is satisfiedin theequilibrium resultingfromthe (unconstrained) optimal policyrule,u = 1, + 7&O.Thusif information-gathering costs, thoughpositive,


arenot too large,it maystill be possibleto reducethe varianceof inflationaround its targetto thetheoreticalminimum. Finally,a ruleof the form(15) thateliminates(ornearlyso) the influenceof the statevariables on inflation(withu closeto 1) will in generalbe muchmorerobust to randomnoise in private-sector forecasts even thoughpolicynow respondsto two distinctforecasts,eachof whichmaybe noisy.Toillustrate,supposethat( 14)is replacedby Trf =E{s|S}+V,

Uf =

E{u|s}+ (1)

(18)

wherev andX aremean-zerorandomvariables,independent of s, , andeachother, andwithvariancesC2 andC2, respectively.If the policyruleis againof the form (15),in equilibrium theprivateforecastswillbe givenby Trf= s + v, uf = 05 + @, where+ ando areas definedin (16). Theresultinginflationrateis s

= +5 + +oV

+ uX

+ E

(19)

andthe varianceof inflationis ( 1

+

_

+

)

C s + + U2

+ + 2C 2 + a 2

(20)

In the benchmark case u = 1, + 7&0, whicheliminatesthe effectsof the state variableon inflation(butwhichis notnecessarilythe optimumin thisclassof policies), (20) implies var(s) =

d)cr2 + a2 + a2

(21)

Forecastnoisedoescauseadditional inflationvolatility,butoverallthispolicydominatespoliciesthatdo notconditionon theforecastof thepolicyinstrument (thatis, for whichu = 0) as long as the idiosyncratic noise in the forecastof the policy instrumentis not too large(specifically,we need crX,< crS2/(+* - 1)2 + +*2crV, where+* < 0 is theoptimalpolicyreactioncoefficientdescribedabove).Moregenerally,one can writethe first-order conditionsdefiningthe optimalreactioncoefficients+ andu for the case of noisyforecasts,verifyingthatu = 0 cannotbe a solution;hence,in generalit canneverbe optimalto ignorethe information in the forecastof thepolicyinstrument. The desirablepropertiesof the rule(15) withu = 1, + 7&0 showthatuse of private-sector forecasts,includingforecastsof inflation,can improvethe performance of monetarypolicy. We reiterate,however,that the ideal rules are not usefullydescribedas "targetingthe inflationforecast":First,the best policy rule doesnotusuallyinvolveresponding to forecastsonlyof inflation(eventhoughstabilizing inflationmaybe the centralbank'sonly objective);andsecond,the optimal policyrulewill typicallynotinvolvea highdegreeof sensitivityof thepolicyinstrumentto deviationsof private-sector inflationforecastsfromthe inflationtarget.

664


2. MONETARYPOLICYAND PRIVATE-SECTOR FORECASTSIN A DYNAMIC MODEL

The modelof section1 is staticandratherstylized.Wenow presenta moredetailedandexplicitlydynamicmodelwhichallowsforbothmonetaryandnonmonetarysollrcesof inflation.In thismorerealisticmodelthe inflationratedependsnot solelyupona monetarypolicyactiontakenata singlepointin timebutalsouponthe rule (orreactionfunction)thatis expectedto dictatemonetary policyin the future. Thismodification introduces important complications, in particular, thepossibleindeterminacy of rationalexpectations equilibrium undercertaintypesof rules.As we showin section3, thispotentialindeterminacy is a furtherproblemwithsimpleproposalsto "targetthe forecast." In section1 we werenot specificaboutthe centralbank'spolicyinstrument.In line withthe actualpracticeof mostof the world'scentralbanks,we now assume thatthe policyinstrument is the short-term nominalinterestrate,Rt, andask how private-sector forecastsmightbe usedin settingthisparticular instrument. Apartfromthe monetarypolicyruleitself, to be discussedbelow,ourdynamic modelconsistsof two structural equations,an"expectational IS equation" (Kerrand King 1996;Woodford1996;McCallumandNelson 1997)andan aggregatesupply or price determination equation.The expectationalIS equation,which relates spendingdecisionsto the interestrate,is givenby Yt-EtYt+l-cr[Rt-Etst+l-Pt]

(22)

whereYtis the log of realoutputin periodt, Trt+ 1 is the rateof inflationbetween periodst andt + 1, andPtis an exogenousdisturbance. Equation(22) is derivable as a log-linearapproximation foroptimalconsumption on thepartof therepresentative household,intowhichhasbeensubstituted the equilibrium conditionthatconsumptiondemandequalstheeconomy'soutput(thereis no investment,government spending,or netforeigndemandin themodel).In thisinterpretation, theparameter C > Ois the intertemporal elasticityof substitution of coonsumption, andthe exogenousdisturbance term{Pt}representsrandom(percentage) variationsin the intertemporalmarginalrateof substitution, arising,for example,fromvariationsin the rateof timepreferenceandevaluatedat a planinvolvingconstantconsumption over time.9 Theaggregatesupplyrelationship is assumedto be st-Et-

1st+1 + KEt-1(Yt-Ot)

(23)

whereOtis an exogenousstochasticprocessinterpretable as the log of the "natural rate"level of outputin periodt. Equation(23) can be obtainedas a log-linearapproximation to a first-order conditionforoptimalpricesettingin a discrete-time ver9. Otherinterpretationsof the randomdisturbanceterm p, are possible. For example, in a model with governmentspending, exogenous shifts in the share of resources consumed by the governmentwould give rise (by changing the relationshipbetween private consumptionand total output)to a disturbance term of the same form, in the log-linear approximation.


sion of the modelof staggeredpricechangesintroducedby Calvo(1983). Alternatively,(23)canbe derivedfroma modelwitha convexcostof changingprices,as in Cochrane(1995).The parameter ,B,O< ,B< 1, maybe interpreted as the discountfactorof the price-setterswhile K > O iS a measureof the speedof price adjustment. The modelunderlyingequation(23) is one in whichonly somesuppliersareallowedto choosea newpricefortheiroutputin anygivenperiod,these"lucky"suppliersbeing randomlyselectedin an independent drawingeach period.It is also assumedthatanypricechangechosenat datet takeseffectonlyoneperiodlater,in t + 1;hence,(23) differsfromtheformof theaggregatesupplyfunctionobtainedin severalrecentpapers(for example,Roberts1995;Yun 1996;King and Watson 1996;Woodford1996)whichassumethatpricechangestakeeffectwithinthe same period.In particular, whereasthe citedpapersobtaina first-order conditionof the formst = EtXt+l, we hereobtaininsteada relationship of theformxrt= Et_lXt+1* Thus,in ourspecification,theperiod-tinflationratedependsonlyon period-(t- 1) information, becauseall pricesin effectin periodt werechosenin t - 1 or earlier. Wechoosethisspecification to capturethenotionthatinflationis "inertial," in particular,thatit is affectedby monetarypolicyactionsonly witha lag.10 Forconcreteness,assumethe shocksto theIS equationandthe aggregatesupply equationarefirst-order autoregressive: Pt= Ap,_l + vt ot= 80t-l + Nt

(24)

whereAand8 haveabsolutevaluesless thanoneandtheinnovationsseries{Vt}, {Nt} areseriallyuncorrelated, mean-zerodisturbances, also mutuallyuncorrelated at all leadsandlags. Equations(22)-(24), togetherwiththemonetarypolicyrule,constitute a completemodelof the inflationprocess.In this model,bothaggregatedemandandaggregatesupplyshocks,if not offsetby monetarypolicy,may lead to changesin the inflationrate. Weturnnowto theanalysisof monetarypolicyin thismodel.Letus supposethat thecentralbank'sobjectiveis notonlyto stabilizetheinflationratebutalsoto minimize deviationsof outputYtfromthe naturalratelevel of output,Ot.Stabilizing outputis not only consistentwith the pursuitof stableinflationin this modelbut actuallyimpliesit, sincein anystationary equilibrium (23) implies 00

st=

K E

SEt_l(Yt+j- ot+j)*

(25)

j=o

10. For furtherdiscussion of aggregatesupply specificationswith time lags in price setting of the kind assumed here, see Rotembergand Woodford(forthcoming).

666

: MONEY, CRED1T,AND BANKING

In any case, as a practicalmatter,not even the most hawkishinflationtargeters among-centralbankshavenot demonstrated thatthey arewillingto ignoreoutput fluctuations entirely. It is easilyseenhowinterestratesmustvaryif theobjectivesof inflationstabilizationandoutputatthenaturalrateareto be fullyachieved.If we assumewithoutloss of generalitythatthe inflationtargetis zero, substitution of Trt= OandYt= Ot(for all t) into(22) yields Rt = Pt +

ff

(EtOt+l-Ot) = Pt-

ff

(26)

wherewe haveused (24) to substitutefor EtOt+l.Equation(26) showsthat,if the centralbankdirectlyobservesthecurrentrealizations of thetwo shocks,PtandOt,it will be ableto set the nominalinterestrateRtto stabilizebothinflationandoutput perfectly. Whatif the centralbankdoes not directlyobservethe two shocks,butonly the historyof outputandinflation?To be precise(andto makethe mostgenerousassumptionaboutthe timingof information receipt),supposethatat the time thatit mustchooseRtthe centralbankcanobserveYt-jand Trtjfor allj 2 0.ll Is it possiblein thiscase for the centralbankto implementthe first-bestoutcome?The answeris plainlyno: Equation(26) requiresthatRtrespondto the innovationsvt and at, or morespecifically- to thelinearcombination vt - (1 - b)t/cr. It is thereforenecessarythatthe centralbankbe ableto inferthisquantity.ButYtis the only variablein the centralbank'sinformation set thatis not determined at datet - 1 or earlier;andsinceYt= Otin the first-bestcase, observingoutputin periodt would permitthecentralbank(underthehypothetical first-bestpolicy)to inferonly,, the innovationto Ot.Thusif the centralbankobservesonly currentandpastvaluesof outputandinflation,it caMotimplementthe first-best. 12 Whatif, besidesobservingthe historiesof outputandinflation,the centralbank can also observea private-sector inflationforecast?To give privateforecastersan informationadvantageover the centralbank,let us assumethat(perhapsat some cost),theforecasters canmakedirectobservations in periodt of theshocksPtandOt, as wellas thehistoriesof outputandinflation (equivalently, thehistoriesof theshocks), uponwhichtheybasetheirforecastof inflationbetweenperiodst andt + 1. Let rrf denotetheforecastof Trt+ 1 announced by theprivateforecasters in periodt. Wecontinueto assumethatforecastersseekto minimizethe varianceof theirforecasterrorandhenceannouncerrf = E{Trt+ 1 |It}, wheretheinformation setIt consists 11. Strictlyspeaking, we have in mind thatthe centralbankcan conditionthe nominalinterestrate on the currentvalue of output, so that the interestrate and output are simultaneouslydetermined.It is not necessary to think of y, as being determinedstrictlybefore R, is chosen. 12. Nor is it possible, we may add, to approximatethis outcome arbitrarilyclosely. An informalargument is as follows: In any equilibrium, under the informationassumptionsof the last paragraph,the centralbank can infer only the linear combinationof v, and 1l, that is revealed by the observationof y For any equilibriumthat is near-optimal,innovationsin y, will be almost perfectly correlatedwith 1l, and so not a close approximationto the variablethatthe centralbankneeds to know. Thus the assumptionthat prices are determinedat least one period in advance implies that observing the history of output and inflation alone does not provide the centralbank enough informationto achieve complete stabilization.


of {Pt) [

1

A + cr(+lr-l)]bl

1. (Thisturnsoutto be the case of greatest relevance,sinceit corresponds to a policyof attempting to "targettheinflationforecast"by choosinga largevalue for +1r;see below.)Then, letting(es, e") be the corresponding righteigenvectorsand(vs, v")the corresponding left eigenvectors, normalizedso thatvseS = vueU= 1, we knowthatanyprocessof the form xt= steU+ wteS

(37a)

is a boundedsolutionto (35), where(1) the scalarprocess{st}is definedby 00

st=-

2

j=o

A"-j-lvtEtzt+j;

(37b)

and(2) the scalarprocess{wt}evolvesaccordingto wt+l = ASWt + Et+lt

(37c)

where{et+1}is anyboundedrandomvariablesuchthatEtet+1 = ° The conditions(37a-c) admita wide varietyof solutions,dependingon the choiceof the unforecastable randomvariable{et+l}. One solutionarisesfromsettingwt = 0 for all t, so thatxt = ste";it is easilyverifiedthatthis solutionis of the form(28), so thatthisis thesolutioncharacterized in section2. However,if instead 15. We consider only bounded solutions because these solutions to our log-linear approximationsto the exact equilibriumconditions constitute approximatesolutions to the exact (nonlinear) conditions. Even in the case that there is a unique bounded solution to the log-linear equilibriumconditions, there may exist a multiplicityof solutions to the exact conditions;but one cannotdeterminethis from the form of the log-linearizedconditions alone. Further,even when the exact conditions have multiple solutions the bounded solution representsan approximatecharacterizationof a rationalexpectations equilibrium that is at least locally unique, in an appropriatetopology (Woodford1996). In the "indeterminate"case analyzed here, by contrast,the REE is not even locally unique-thus it is less plausible that the economy can be relied to settle into the particularstationaryequilibriumof the forrn(28), ratherthaninto one of the large multiplicityof nearbyequilibria.

while n oo. Then |+yn|/|+1nr| the quantity O Butinneither squarecondition bracketsin (39) thenor first condition equation (40) of (31) allows must |+n|become to grow unboundedly withoutbound large

672


we let {Et+ 1} be whitenoiseindependent of themodel'sstructural disturbances, then (37) describesa "sunspot" equilibrium. Foryet anotherdisturbingpossibility,suppose that{Et+l} dependson the innovationsto the model'sstructural disturbances, for example, Et+ 1 = Ntt+

1 + tant+

(38)

1 *

In this case it canbe shownthat,althoughoutputandinflationrespondonly to the structural disturbances of the model,in equilibrium the responsesof bothendogenousvariablesto the structural shocksareindeterminate. Evidently,the robustnessof rules thatrelatethe policy instrumentto privatesectorforecastsdependscriticallyon the magnitudesof the eigenvaluesof M. It turnsoutthatwhetherthe unique-or multiple-equilibrium case obtainsdependson the parameters of thepolicyrule,(27), itself. OnecanshowthatM hasbotheigenvaluesoutsidetheunitcircleif andonly if either py > - ( 1 - )(r

and - ( 1 - )+y
K(+s

-

1 ) > ( 1 + )(+y

+

2ff)

(40)

or y < - ( 1 - )(r

and - ( 1 - )+y

Clearly,thereexistpolicyrulesthatsatisfyeither(39) or (40) andso leadto a determinateequilibrium of the form(28). However,the requirement thatpolicy satisfy one of these conditionsrepresentsa furtherrestrictionon what can be achieved throughpolicyrulesof the form(27), in whichthe nominalinterestrateis allowed to dependon outputandthe inflationforecast. In particular, it is notpossibleto approximate closelythefirst-bestoutcomebl = b2 = 0 by usinga policyruleof theform(27), withoutleavingtherangeof parameter valuesfor whichthereexistsa determinate equilibrium. 16 Thusthe concernto maintainthe determinacyof equilibriumlimitsthe degreeto whicha rule of the form(27) can be usedto stabilizeinflation,even supposingthereis no problemof inducingforecastersto collectinformation andno noise in the forecasts.Furthermore,thereis no ruleof theform(27) thatcanguarantee that,in a rationalexpectations equilibrium,fluctuationsin the inflationrate will be small. In particular, vigorous"targeting" of theinflationforecast(|+1r| large)canneverensurethatinflationwill be stable:Tosee why,notethatif |+ylis alsomadelarge,so as to preserve determinacy of equilibrium, theninflationvariabilityin theuniqueequilibrium with boundedfluctuations is not small,becauseof the excessiveresponseof monetary 16. Proof: Suppose instead that there exists a sequence of policies {(g)n, (g)yn}, and an associated sequence of equilibria{bl, b2n}satisfying (31) for each n, with the propertythat bnl- > O and bn2- > O as as n grows, while the quantity(1 - 8 + aXyn)must not grow at the same rate, and indeed must eventually become an arbitrarilysmall fractionof the quantityin the squarebrackets.This can occur only if lXn| > °° unless |+yn|grows at the same rate, so that 1+1rl/|+yn| remainsboundedand |+y|/|+1r|remainsboundedaway from zero. Thus one obtains a contradiction.


policyto the fluctuations in outputcausedby supplyshocks.Butif |+ylis chosento be small,so thatb2is smallin theuniquesolutionof theform(28), thenthisequilibriumis no longerthe only one; andthe set of possiblerationalexpectationsequilibriain this case includesequilibriawitharbitrarily largefluctuations in inflation. In thelastsectionwe sawthattheproblemswithusinga ruleof theform(27), in whichonlythe inflationforecastwas considered,couldbe ameliorated by a ruleof the form(32), whichallowspolicyto respondto forecastsof the policyinstrument itself as well as to forecastsof inflation.Unfortunately, problemsof indeterminacy afflictrulesof the form(32) as well. To analyzepolicyrulesof this formwe may restrictattentionto the case R = 1, sinceonly this case is not coveredby the discussionabove. A rule of the form(32) with pR = 1 impliesthatin any rational expectationsequilibrium +1rst+1 =-yYt

(41)

Let us assume+1r7&o.l7 Then(41) impliesthatqTt+l= YYt,wherey---+v/+1r. Combiningthiswith(23) yields YYu (ay + K)EtYt+ X - KEtot+ l

(42)

Equation(42) hasa uniqueboundedsolutionif andonly if y 7&0 and -(1 + ) < - < 1 -

&

.

(43)

Thissolutionis givenby

Yt

w .=1 (

w)

8 ( 8 + K)

(44a)

Substitution of (44a)into(41) yieldsthe uniquesolutionfor inflation: st+ 1

(44b)

K

1 - 8(8

+ w)

Ontheotherhand,if y = Oor if eitherinequalityin (43) failsto hold,equilibrium is indeterminate undera ruleof theform(32). In particular, anyprocessof theform

( 7

+ K ) (Yt

7

t)

e,+l

(45)

17. It is easy to show that a rule of form (32) with + + Odoes not stabilize inflation, unless there is no stochastic disturbanceto the aggregatesupply equation(23).

674


where{et+l} is any boundedrandomvariablesuchthatEtet+l = O, representsa boundedsolutionto (42). Thecorresponding solutionfor inflationis thengivenby qTt+l= YYtAs discussedabove,thesesolutionsadmitarbitrary responsesof inflationandoutputto fundamental shocksor responsesto "sunspot" events.In particular,solutionsof theform(45) includeequilibriawitharbitrarily largefluctuations in output(bothin absolutetermsandrelativeto the"natural rate")and,exceptwheny = O,arbitrarily largefluctuations in inflationas well. Condition(43) showsthatdeterminacy of equilibrium requires,in the case of a ruleof the form(32) withR = 1, that1w1be sufficientlylarge.l8However,(44b) indicatesthatthe responseof inflationto supplyshockscanbe madesmallonly by makingI^YIsufficientlysmall.(Recallthatperfectstabilization was achieved,at the endof thelastsection,by a policycorresponding to y = O.) Thustherequirement of determinacy notonlyexcludescompletestabilization of inflationandoutput(around the naturalrate)throughthistypeof policy,butit also does not allowthe first-best equilibrium to be approximated. Indeed,condition(43) substituted intoconditions (44a,b) impliesthat, in any locally uniqueequilibrium,var(w)> (K8/(1 + a))2 var(o)andvar(y- 0) > ((1 - 8)/(1 + b))2var(o). Anypolicyimplyinganequilibriuminvolvingmorestabilization of inflationor outputthanthisresultsin indeterminacy.In particular, the policyR = 1, y = O, +s + O discussedat the end of section2 resultsin indeterminacy. l9 Wehaveexaminedtheproperties of relativelysimplepolicyrules,in the formof (27) or (32), thatlinkthe monetaryauthority's policyinstrument to forecastsof inflationand othervariables;andwe haveshownthat, if we imposethe additional restrictionthattheserulesdo not openthe economyto possibleindeterminacy of equilibrium, theserulescannotbe usedto perfectlystabilizetheeconomy.Now,as a theoreticalmatter,it is nottruethattherequirement of determinacy rulesoutperfect stabilizationby policy rules of any form:To displaya counterexample, let Rtlf denotetheforecastatthebeginningof periodt of Rt+1,Rt2ftheforecastatthebeginningof datet of Rt+2,andYfttheforecastatthebeginningof datet of Yt+l . Then[as provedin BernankeandWoodford (1997)]a policyrulethatresultsin a determinate rationalexpectationsequilibrium with completestabilizationof bothinflationand output(aroundits naturalrate)is givenby20 Rt = R,f l + A-l(R,lf-R2f l) +

+ g

+ (8

I-1)(1-8)

(

f

where+1ris anynonzeroquantity.Further, (46) canbe shownto be a specificexample of a muchwiderclass of ruleswiththeseproperties.Nevertheless,becauseof 18. In the case in which all prices are fixed one period in advance, which correspondsto the limiting case of the model of section 2 with K infinitelylarge, no finite |0YI is large enough, that is, any rule of the form discussed in the text results in indeterminacy. 19. Actually,in this case, because Py= 0, complete stabilizationof inflationis guaranteedin equilibrium; however, equilibriumoutputis indeterminateand the fluctuationsof outputaroundthe "naturalrate" can be unboundedlylarge. 20. We assume here that A 7&0, 8 7&0, and 8 7&1 + A. In the special case that 8 = 1 + A exactly, a more complicatedvariantof this rule will still work.


thecomplexityof (46), andits sensitivityto someelementsof themodel'sstructure, we do not wishto offerthisparticular ruleas a practicalpolicyproposal. The mainconclusionof this sectionis thatthe requirement of determinacy puts important restrictions on thecentralbank'schoiceof policyrules,particularly policy rulesthatrelatethecentralbank'sinstrument to explicitorimplicitprivate-sector forecasts.We reiteratethatthis resultby no meansprecludesthe use of privatesectorforecastsby the centralbankas sourcesof information not easily attainable by othermeans.But the information contentof private-sector forecastsshouldbe evaluatedin the contextof an explicitstructural modelof the economy;andthis is especiallycrucialin the case of policyrulesthatrespondin a highlysensitivemannerto changesin private-sector forecasts,whetherof inflationor of othermacroeconomicvariables.Such policies must be adoptedwith care. Finally,because conclusionsregarding thedeterminacy of rationalexpectations equilibrium areoften sensitiveto thedynamicspecification of one'smodel,it wouldbe prudentto analyze the predictedperformance of a contemplated ruleunderalternativespecifications. Withthesecaveatsas background, it is alsointeresting to notethattherulegiven in (46), whichdoes achieveperfectstabilizationwithinthe requirement of determinacy,ties policyto forecastsof interestratesandoutputbutnotof inflation.Thus the fact thata centralbank'smainobjectiveis to hit an inflationtargetdoes not imply that forecastsof inflationare moreuseful thanforecastsof othermacroeconomicvariables.Indeed,inflationforecastsareproblematic as a sourceof informationfor the centralbank,for the reasonstressedby Woodford(1994a)and in sections1 and2: If completestabilization of inflationis possible,private-sector inflationforecastscease to containany informationaboutexogenousshocksto the economy.Ontheotherhand,evenwithcompletestabilization, outputforecastswill revealthe conditionalexpectationof futurevaluesof the aggregatesupplyshock0 (andhence,if 8 + 0, thecurrent0); andinterestrateforecasts(or,perhaps,theterm structure)will revealthe conditionalexpectationof futurevaluesof the IS disturbancep (andhence, if A + 0, currentp). Thus,as a generalrule, it makesmore sense for the centralbankto makeuse of the information revealedby theseother forecasts,ratherthanforecastsof the goalvariable. 4. DISCUSSION OF RELATEDPROPOSALS

Althoughwe havefocussedfor concretenesson the effectsof targetingprivatesectorforecasts,thereareseveralproposalsformanagingmonetarypolicythatraise closelyrelatedissues. In this sectionwe brieflyconsidersomeof theseproposals. 4.1 AssetPricesas lndicatorsof lnflationExpectations It is sometimesarguedthatmonetarypolicyshouldrespondto the changesin inflationexpectations thatmaybe inferredfromvariousassetprices,as opposedto the explicit forecastsmadeby individualforecasters.Well-knownexamplesinclude proposalsto adjustmonetarypolicyin responseto movementsin a commodityprice index(forexample,Reynolds1982),to movementsin long-termbondyieldsor in

676 : MONEY,CRED1T, ANDBANKING

interestratespreads(forexample,Goodfriend1993),to CPIfuturesprices(forexample,Dowd 1994;Sumner1995),or in responseto the yield spreadbetweenindexed and nonindexedgovernmentbonds (for example,Hetzel 1990, 1992).21 Reasonsformakinguse of assetpricesas indicators insteadof (oratleastin addition to) explicitforecastsmightincludethe belief that financialmarketsaggregatea greateramountof informationthanis po-ssessedby any smallnumberof market participants alone;a beliefthatpeoplemayrevealtheirbeliefsmoretruthfullyin the waythattheyrisktheirownmoneythanin theirpublicstatements; or a concernthat forecasterscouldbe subjectto politicalmanipulation. Proposalsof thiskind,however,arepotentiallysubjectto all of thedrawbacks of "forecasttargeting" discussedabove.Toillustrate,considera ruleof the form

Rt= 4)7r(Rt-Rtr) + 4)yYt

( )

whereRtrdenotesthe realinterestratepaidon a one-periodindexedbond.Suppose furthermore thatin a rationalexpectationsequilibrium, the yieldson the two types of bondsarelinkedby Rtr= Rt-Etqrt+l

(48)

Thenequilibriumis determinedby relations(33)-(34) and (47)-(48). But, using (48) to eliminateRtr,oneobtainsthesamesystemof threeequationsas in thecaseof policyrule(27), whenqrf= Etqrt+ 1is usedto eliminateEtqrt+ 1 Thusall conclusions withregardto rlllesof the form(27) areobtainedin thiscase as well. Becauseour criticismof "forecasttargeting" rulesof thatkinddidnotdependuponanyassumed inadequacy of the forecasters'inform-ation or difficultyin elicitinghonestreportsof theirconditionalexpectations,theuse of assetpricesto infer"market expectations" doesnot solve anyof the problemspreviouslydiscussed. It is truethatourdiscussionof strategicrandomization by forecastersas a source of forecast"noise"wouldnot applyto the "marketexpectations" impliedby asset prices.However,asset-pricemeasuresof inflationexpectationsarelikelyto be contaminated by othersourcesof noise.Forexample,CampbellandShiller(1996)discuss the possibleuse the spreadbetweenindexedandnonindexedbondyieldsas a measureof inflationexpectations,andpointoutthatsucha measurecouldeasilybe contaminated by changesin expectationsregardingthe futuretax treatmentof the two kindsof bonds,or by changesin the inflationriskpremium.The presenceof theseextraneoussourcesof variationin the yield spreadmakesa policyruleof the form(47) wiffia large| + | as unappealing as a policyruleof the form(27) witha large|+ |. Furtherproblemswith using the inflationexpectationsimplicitin asset prices arisewhentheconnectionbetweenassetpricesandexpectedinflationis notreasonablystraightforward (as it is in the indexedbondcase)butinsteadmaybe sensitive 21. Proposalsof this kind were given particulatattentionwithin the FederalReserve System following the endorsementof an approachof this general type by Vice ChairmanManuel H. Johnson(1988).

BENS. BERNANKE ANDMICHAEL WOODFORD: 677

to the policyregime.Considerfor exampleGoodfriend's (1993) proposalthatthe fundsratebe raisedwheneverlongratesrise(anincreasein longratesbeingtakento indicateanincreasein expectedinflation).Tosimplifytheanalysis,supposethatthe centralbankobservesthe nominalyieldRt on a consol.In accordancewiththe expectationstheoryof thetermstructure, supposethatthisyieldis determined in equilibriumby therelation 00

Rt=(l-)

E

T=t

T-tEtRT+tt

(49)

wherethetermpremium(t iS assumedto be anexogenousstochasticprocess.Then it is easyto describepolicyregimesunderwhichequilibrium fluctuations in thelong rateRltcorrespond largelyto variationsin expectedinflation.Supposefor simplicity thatA - 8 = Oin (24). Conditions(22)-(24) thenimplythat EtRT = EtqrT+ 1 + ((rs)-l(Et5sT+l-Et5flT+2)

-

Substitution of thisinto(49) yields 00

Rlt= (1-ORt + (1-)

E

T-tEtflt+l

+

(1-)+(ffK)

lEt5flt+2 + (t

T=t+ 1

If e is nearone (becauseperiodsareshort),thenthe returnon the consolis essentiallya weightedaverageof theexpectedrateof inflationovervariousfutureperiods (plusthe termpremium,if any). Nonetheless,in this settinga policyruleof the kindthatGoodfriendappearsto advocatewouldnot help to guaranteestableprices.Considera policy rule of the form Rt=

XRt

for sorne+ > O. The completesystemof equilibrium conditionsis thengiven by (22)-(23) and (49)-(50). Note thatthe subsystem(49)-(50) determinesthe processes{Rt,R:, withto referenceto theevolutionof pricesor output,whilethe subsystem (22)-(23) then determinesthe processes{stt, Yt}, given the equilibrium processfor nominalinterestrates. Subsystem(49)-(50) may or may not uniquelydeterminerationalexpectations equilibrium processesfor shortandlong nominalrates.If 1