Long Memory in Inflation Expectations: Evidence from International Financial Markets

Boardof Governorsof theFederalReserveSystem InternationalFinanceDiscussionPapers Number538 February1996 LONGMEMORYIN INFLATIONEXPECTATIONS: EVIDENCEFROMINTERNATIONALFINANCIALMARKETS JosephE. Gagnon NOTE: InternationalFinance Discussion Papers are preliminary materials circulated to stimulate discussionandcriticalcomment. Referencesin publicationstoInternationalFinanceDiscussionPapers (otherthananacknowledgmentthatthewriterhashadaccesstounpublishedmaterial)shouldbecleared withtheauthoror authors.

ABSTRACT This study providesevidence that 10-year-aheadinflationexpectationsadapt very slowly to changesinrealizedinflation. Thisevidencederivesprimarilyfromyieldson 10-yeargovernmentbonds inasampleofOECDcountries,includinginflation-indexedbondswheretheyareavailable. Thestudy examinesboththecross-countryand time-seriesbehaviorof interestratesand inflationrates. Forthe UnitedStates,additionalevidenceis providedfroma surveyof 10-yearinflationexpectationsheldby marketparticipants.Thisstudydoesnotpresentatheoreticalmodelofexpectationsformation.However, longmemoryofthetypedocumentedinthisstudywouldbeimpliedbya modelof multipleinflationary regimes in which agents base their probabilitydistributionsof future regimes on past inflationary experience.

i JosephE. Gagnon] L InproductionandMotivation This study providesevidence that 10-year-aheadinflationexpectationsadapt very slowly to changesinrealizedinflation.Thisevidencederivesprimarilyfromyieldson 10-yeargovernmentbonds in a sampleofOECDcountries,includinginflation-indexedbondswheretheyareavailable. Thestudy examinesboththecross-count~ and time-seriesbehaviorof interestratesand inflationrates. For the UnitedStates,additionalevidenceis providedfroma surveyof 10-yearinflationexpectationsheldby marketparticipants. EversinceIrvingFisher’sThe o (1930),economistshave arguedthat, interestratesoughtto moveone-for-onewithexpectedinflation.2Therearetwodifficultiesin provingthishypothesis:First,inflationexpectationsarenotobserveddirectly. Second,intherealworld the assumptiondoes not hold, so that otherfactors mustbe taken into consideration. Fisherhimselffocusedon theformationof expectations. He believedthatthe primarydeterminantof expectedinflationislikelytobepastinflation. ByregressinginterestratesonpastinflationFisherfound *SeniorEconomistintheDivisionofInternationalFinance,BoardofGovernorsoftheFederalReserve System. Thispaperdevelopedoutofworkfora studybytheG-10Deputieson October1995.Ireceivedhelpfulcommentsfromfellowdraftersofthatstudy,aswell as DavidBowman,JonFaust,DaleHenderson,andAndrewLevin. Thispaperrepresentsthe viewsof the authorand shouldnotbe interpretedas reflectingthoseof the Boardof Governorsof the Federal ReserveSystemor othermembersof its staff. 2Darby(1975)andFeldstein(1976)showedthat in a theoreticalclosedeconomy,incometaxation causesagreaterthanone-for-oneresponseofinterestratestoexpectedinflation.Hartman(1979)showed thatinatheoreticalsmallopeneconomy,interestratesmoveone-for-onewithexpectedinflationevenin the presenceof residence-basedincometaxes. Tobin(1969)arguedthathigherinflationleadsto a less thanone-for-oneincreaseininterestratesbecauseit reducesthedemandforthemonetarybaserelative to productivecapital. However,giventhe smallsizeof themonetarybaserelativeto thecapitalstock, theTobineffectis likelytobe extremelysmallforanyreasonableestimateof theelasticityof demand for the monetarybase.

2 thatalongdistributedlagofpastinflationprovidedthebestfit,butthatthetotaleffectof laggedinflation ontheinterestratewasmuchlessthanone-for-one. ThisstudyconcurswithFisherthata longlagofpast inflationprovidesthebest fit, but in postwardata for the UnitedStatesthe totaleffect is shownto be almostexactlyone-for-one. ThediscrepancybetweenFisher’sresultsand thepostwarresultsisalmost certainlyduetothefactthatundertheGoldStandardthepricelevelhadnolong-rundrift,aslongperiods of inflationwerefollowedby longperiodsof deflation. TheFishereffecthasbeenthesubjectof numerousstudiesin thepast30years. Manyofthese studiesmodeltheexpectationsformationprocessexplicitly. Nearlyallempiricalstudieshaveconcluded thatinterestratesmovelessthanone-for-onewithinflationexpectations,Somestudies,suchasSummers (1983),havepointedtoirrationalityintheformationofinflationexpectationsasthesourceoftheapparent rejectionof the Fishereffect. Other studies,such as Mishkin(1984),haveconjecturedthatthereis a systematictendencyforhighinflationratesto beassociatedwithlowrealinterestrates.3 Thisviolation of the assumptionmay bedueto the effectsof monetarypolicy. A sustainedmonetary expansiontendstokeeptheshort-terminterestratelowevenastheinflationratebeginstorise. However, mosteconomistsbelievethat monetarypolicycannotlowerthereai interestrateindefinitely. Moststudiesof the Fishereffect in postwardata havefocusedon short-texminterestratesand allowedonlyshortlags(uptothreeyears)intheinflationexpectationsprocess. Inordertominimizethe influenceofmonetarypolicythisstudyfocusesonlong-terminterestrates. Manyeconomistsbelievethat long-terminterestratesaremoreimportantforconsumptionandinvestmentdecisionsthanshort-termrates. FollowingtheleadofIrvingFisher,thisstudyexaminestheroleoflonglagsintheformationofinflation expectations. 3Mishkin(1992)showsthatitispossibletoacceptthehypothesisofaone-for-oneFishereffectover certainsampleperiodsusingU.S.short-terminterestrates. Peng(1995)findssimilarevidenceforFrance and the UnitedKingdom,butnotfor Germanyand Japan.

3 Onecomplicationintroducedbythefocusonlong-terminterestratesisthepotentialforsignificant riskpremiaduetothelowerliquidityof long-termbondsin manycountriesandduetothesensitivityof bondpricestochangesininflationexpectationsandrealinterestrates. (Theseriskpremiaaremuchless likelyto be significantforshort-terminterestrates.) It is difficultto distinguishbetweenthe inflation expectation,the inflation-riskpremium,andotherrisk premiumcomponentsof thenominalbondyield. The primary focusof this studyis on the sum of these components,which is looselyreferred to as inflationary expectations, but some efforts are devoted to examining the inflation-risk premium independently. Theanalysispresentedhereispurelyempirical,butitdoeslendsupporttoaclassoftheoretical modelsofinflationcharacterizebdyoccasionalshiftsinpolicyregimes,EvansandLewis(1995)showthat a regime-switchingmodelof inflationcanexplaintheempiricalfailureof the Fisherrelation. In their paper,theregimesdifferbythevarianceandpersistenceofshockstoinflation. Theevidencepresented inthisstudysuggestsanalternativespecification,inwhichregimesdifferbytheaveragerateofinflation. If agents’beliefsabouttherelativeprobabilitiesoffutureinflationregimesarebasedonpastexperience, then the unobservedinflationexpectationsprocess will be correlatedwith past inflationover a long horizon. JI. cross-CountrvEviolence The cross-countryanalysisis basedon data for 16OECDcountries.4 The interestrate is the annualyieldon 10-yeargovernmentbondssuppliedby theOECDSecretariat. Theinflationrateis the percentageincrease in the CPI over the previous four quarters, taken from realexchangerateisa multilateralweightedaverageagainsttheother15countries ‘Australia(AL),Austria(AT),Belgium(BE),Canada(CA),Denmark(DE),France(FR),Germany (GE),Ireland(IR),Italy(IT),Japan(JA),theNetherlands(NE),NewZealand(NZ),Spain(SP),Sweden (SD),theUnitedKingdom(UK),andtheUnitedStates(US).

4 in thesampleusingCPISandweightsbasedoneachcountry’ssharein total worldtradein 1993, Each country’srealexchangerate isnormalizedby itsaveragevalueoverthe period 1975-94. Theexchange ratesandtradesharesaretakenfromIFS. Netpublicsectordebtistakenfrom (December1994).sTheaveragesandstandarddeviationsarecomputedwithquarterlydataoverfive-year periods. 7 IRLxy Ave. InterestRate,x-y rNFxy Ave. InflationRate,x-y I RERxy Ave.RealEx. Rate,x-y VEXxy Std.Dev.(RealEx.Rate) vPIxy I Std.Dev.(InflationRate) I DEBTx I Net Debt/GDPin x II Interestrateregressionsarerunoverthreedifferenttimeperiods:1980-84,1985-89,and1990-94. Thestudyemploysageneral-to-specificstrategy,but,duetolimiteddegreesoffreedom,theinitialgeneral specificationdoes not includeail possiblei;lclependentvariables. Theinitialspecificationis IRL909$,= a+~INFfM)9#+iylNF&S89,+6lNF8084i+0DEBZ391+ADEB~, +ei andsimilarlyfor the othertimeperiods. In everyperiod,therestrictionthatthe coefficientsoncurrent . . and laggedinflationsum to unitycould not be rejectedat the 10percent level, so this restrictionwas imposedbeforefutier analysis.Ifinflation-riskpremiawereimportantincountrieswithahistoryofhigh inflation,one wouldexpectto findthe sumof these coefficientsto be greaterthan unity. In fact,the unrestrictedestimatesalwayssummedto less than unity. This resultcastsdoubt on the importanceof inflation-riskpremiaincountrieswithhighinflation,atleastforinterestratesaveragedoverlongperiods of time. ‘AustriaandIrelandreportonlygrossdebt. NewZealanddebtis forcentraIgovernmentonly,from Thefindingswith respectto debtare notsensitiveto theexclusionof these countries.

5 Innocasewasacoefficientondebtindividuallysignificant,andineverycasethecoefficienton laggeddebtwasnegative. Thisresultsuggeststhatthechangeindebtmightbetherelevantvariable,so theregressionwasrespecifiedintermsof thedifferencebetweencurrentandpastdebt,andtheimplied restrictioncouidnotberejectedinanycase. However,eventhechangeindebtwasneversignificant-aithoughitalwayshadasmallpositivecoefficient--sothatitwasdroppedfromthepreferredregressions, whichare reportedin Table 1. Table 1 InterestRatesand InflationRates Dep.Var. Intercept INFxy INFxy-5 IN-Fxy-lo R2 std.err. IRL9094 4.03** 0.66** 0.11 0.23** .83 0.76 (.42) (.07) (.09) (.07) IRL8589 4.67** 0.80** 0.31** -0.11 .95 0.58 (.37) (,06) (.08) (.07) IRL8084 4.29** 0.87** -0.21 0.34* .67 1.92 (.64) (.25) (.24) (.16) *(**)slgmficantat5(1)percent Sampleof 16OECDcountries. Ineveryperiod,thecurrentinflationrateii thesinglemostimportantfactorbehindthelong-term interestrate. Laggedinflationis also importantin everyperiod,althoughthe natureof the lagpattern differsacrossperiods. The R*statisticsindicatethat currentand laggedinflationexplainmostof the differencesin interestratesacrosscountries. If currentand laggedinflationare proxyingforexpected futureinflation,theestimatedinterceptsindicatethatthereal interestrateliesbetween4 and5 percent overthepast 15years. Anumberofvariableswereaddedsequentiallytothepreferredspecificationtotestforadditional factorsinfluencinginterestrates. Thecurrentleveloftherealexchangerateisexpectedtobepositively correlatedwiththeinterestrateaccordingto standard modelsof theexchangeratewith

stickypricesandimperfectgoodssubstitutionacrosscountries. Inpractice,ithadasignificantlynegative coefficientin 1985-89,and it wasnotsignificantin the otherperiods. Thechangein the realexchange ratebetweenthecunent five-yearperiodandthepreviousperiodaisohadanegativecoefficientin 1985- 89and nosignificantcoefficientin theotherperiods. Variabilityof inflationor the real exchangerate is expectedto have a positiveeffect on the interestrateifitincreasestheriskpremiumdemandedbyinvestors. Thevariabilityoftherealexchange rate is measuredas the qumerly standarddeviationof the real exchangerate from 1975throughthe currentperiod. Thisvariablewasneversignificantlycomelatedwiththeinterestrate. Thevariabilityof inflationis measuredas the quarterlystandarddeviationof theannualinflationrate from 1970through thecurrentperiod. Thisvariablealwayshadastrongly coefficient,anditissignificantin 1990- 94 and 1985-89. Each percentagepointincreasein the standarddeviationof inflationis estimatedto reducetheinterestrateby around50basispoints. This resultis puzzling,butits statisticalsignificance is not robustto excluding one country--Japan--fromthe sample. However,even withoutJapan the coefficientis consistentlynegative. Chart1displayscross-countryscatterplotsofinterestratesandinflationrates. Eachplotcontains a 45 degreeline with an interceptof 4 upper left paneldisplaysthe current interestrates and inflationratesfor 1990-94. Theremainingthreepanelsdisplaythecumentinterestrateindifferentfiveyearperiodsagainstaweightedaverageofcurrentandpastinflation.dClearly,addinginflationratesfrom theearlierperiodshelps to explainthecross-countrydifferencesin nominalinterestrates. A common worldreal interestrate of 4 percent wouldimply that all countries lie on the 45 degree line, assumingthatthe weightedpast inflationis a goodproxyfor expectedfutureinflation.- % eachcasetheweightsare0.75oncurrentinflation,0.15oninflationfromthepreviousperiod,and 0.10on inflationfrom two periodsago.

7 Chart 2 displaysscatterplotsof nominalinterestrates in the 1990sand netdebt ratiosat the beginningandendofthisperiod(thetop twopanels). Verylittlecorrelationisapparent.Thebottomleft pane!plotsinterestratesagainstthechangeindebtratiosoverthisfive-yearperiod. Inthispanel,there is a weakpositiverelationship,whichis consistentwiththe regressionresultsdescribedabove. In the bottomrightpanelinterestratesareplottedagainstthehistoricalvariabilityof inflation. Thereappears to bea weakpositivecorrelation,withJapanasanoutlierneartie bottomof theplot. Thiscorrelation appearsto contradicttheregressionresultsdescribedabove,in whichthe coefficienton variabilitywas negative. These contradictoryresultsare due to the collinearityof the level and variabilityof past inflation.Oncethelevelofpastinflationiscontrolledfor,theeffectofvariabilityturnsnegative,although the significanceof thiseffectis dependentonthe inclusionof theJapaneseoutlier, ~ . Time-SeriesEvidence Thissectionexaminesthetime-seriesevidenceo theFishereffectinindividualcountries.Table 2presentsaugmentedDickey-Fullerstatisticsonquarterlyinterestratesandinflationrates. Thedataare thesameasthoseusedintheprevioussectionexceptfortheexclusionof Australia,Austria,andJapan duetomissingdatainthe 1960sandearly1970s.The2-yearinflationrateiscalculatedastheannualized growth rate of the CPI over the previous8 quarters. The 10-yearinflationrate is calculatedas the annualizedgrowthrate overtheprevious40 quarters. Table2showsthatboththeinterestrateandtheinflationrateappeartobenonstationarywiththe notableexceptionofGermany,wheretheinterestrateandthe2-yearinflationrateappeartobestationary.’ A standardpropertyof manytheoreticaleconomicmodelsis thatthe real rate of interestis’stationary. ‘TheaugmentedDickey-Fullertestsusefourlaggeddifferencesofthevariablebeingtested. F-tests againstregressionswithfiveandeightlaggeddifferencesrevealthatlongerlagsareoftensignificantin theinflationregressions,wheretheytendto reducethemagnitudeandsignificanceof theteststatistics for2-yearinflation. Longerlagsarealmostneversignificantfortheothervariables,andwheretheyare significanttheydo notchangetheresultspresentedin Table2.

8 Table 2. AugmentedDickey-FullerTests, 1961Q2-1994Q4 10-YearBondRateless 10-Year 2-Year IO-Year 2-Year 10-Year BondRate Inflation Inflation Inflation Inflation Belgium -1.90 -2.75* -1.79 -2.14 -2.85* Canada -I.90 -2.06 -1.86 -1.41 .3.70*** Denmark -1.44 -2.11 -1.58 -2.64* -1.99 France -1.63 -2.10 -1.31 -1.38 -2.36 Germany -3.43** .3,66*** -1.75 -3.13** -3.02** Ireland -1.70 -2.49 -1.98 -2.32 -2.24 Italy -1.54 -1.98 -1.98 -1.27 -1.86 Netherlands -2.54 -2.24 -1.63 -1.74 -1.98 New Zealand -1.36 -1.86 -1.41 -1.57 -2.72* Sweden -1.53 -2.66* -1.59 “1.71 .3.57*** UnitedKingdom -1.83 .-2.34 -2.16 -2.50 -2.06 UnitedStates -1.97 -2.54 -1.92 -2.32 -4.21*** l*”,l*,*denotesignificanceat 1,5,and10percentlevels,respectively. Alltestsuse4laggeddifferences. . . Table2alsopresentsstationaritytestsoftwomeasuresoftherealrateofinterest. Whentherealinterest rate is measuredusing the inflation rate from the previous2 years, one can reject the hypothesisof nonstationarityin onlytwocases. However,whenthe realinterestrate is measuredusingtheinflation

9 ratefromtheprevious10years,onecan rejectnonstationarityfor6 of the 12countries. Giventhelow powerof thetest,thisis a strongresult.8 Table 3 presents estimates of the cointegratingcoefficient between the long-term 3 EstimatedCointegrating Coefficients,1960Q1-1994Q4 bondrateandtheinflationrate. Onlyin thecase 10-Yr.BondRateand of Germany does the interest rate appear 2-Year 10-Year Inflation Inflation cointegrated with the 2-year inflation rate. Belgium 0.40 0.88 However,in 6 countriesthe interestrateappears Canada 0.60 0.93** cointegratedwiththe 10-yearinflationrate. AIso, Denmark 1.02 1.48 France 0.63 0.99 in every countryexceptGermany and Denmark Germany 0.54*** 0.53** the cointegratingcoefficientis closer to 1 when Ireland 0.51 0.72* 10-yearinflationisused,whichisconsistentwith Italy 0.56 0.82 Netherlands 0.35 0.62 a stationaryreal interestrate. NewZealand 0.47 0.89 Because high inflation tends to be Sweden 0.63 1.08** associatedwithmorevariableinflation,onemight u.K. 0.42 0.59* expecttheinflation-riskpremiumtoincreasewith. u. s. 0.60 1.03*** OLSregressionofbondrateoninflationrateand thelevelofinflation. Suchbehaviorwouldimply inkrcept. l**,**,l denotesignificanceat1,s,and 10percentlevels,respectively,usingtheEnglea cointegratingcoefficient greater than 1, In Grangcrtestontheresidualsofthecointegrating regression.Alltestsuse4 laggeddifferencesofthe residuals. practice,theestimatedcoefficientislessthan 1in 1 nearlyall countriesfor both proxiesof inflation expectations,thuscastingdoubtontheimportanceoftheinflation-riskpremium. Itshould& notedthat 8HorvathandWatson(1993)proposeamultivariatetestofaknowncointegratingvectorthatgenerally has a higherpowerthanthe univariatetest usedhere. Thehigherpowerderivesfrom themodelingof thedifferentdynamicpropertiesofthecomponentseries. Inthisexample,however,theHorvath-Watson test also rejects non-cointegrationin only 6 of the 12 countriesat the 10 percent level, and only 3 countriesat the 5 percentlevel.

10 sinceboth2-yearand 10-yearlaggedinflationareimperfectmeasuresof inflationaryexpectations,their estimatedcoefficientsare biaseddownwards. However,thefindingof a stationaryreal interestratein Table2 impliesthatthe inflation-riskpremium mustbe stationaryandthat it cannothavedriftedover time. Chart3plotsthemeasuredrealinterestrateusing2-yearinflation.Onecommonfeatureformany of thecountriesin Chart3 is thesharpdrop in themeasuredrealrateinthe 1970sandthesharprisein the 1980s. This patternreflectsthe rise and fall of inflationrates in these countries. Thereare two possibleexplanationsfor this commonpattern: First, 2-yearlaggedinflationdoes not proxywell for expectedfutureinflation. Second,expansionarymonetarypolicydrovethe real ratedownat the same time thatit increasedinflationaryexpectations. Whilethe secondexplanationsurelyplayedsomerole, it isdifficulttobelievethatmonetarypolicydrovethe 10-yearrealinterestratedownbyasmuchas 10 percentagepointsinsomecountries. Almostno economistbelievesthatmonetarynonneutralitiesareas largeandpersistent asthat. It is particularlyinterestingto note that Germany did not share this common pattern of the measuredreaiinterestrate. Germaninflationoverthisperiodwasmuchmorestablethaninflationinthe othercountries.Thus,itisreasonabletosupposethatthe2-yearproxyforinflationexpectationsdoesnot performasbadlyforGermanyasfortheothercountries. TherelativestabilityofthemeasuredGerman real interest rate providesfutier evidence against the argumentthat expansionarymonetarypolicy drasticallyIoweredthetruereallong-terminterestrateinmostofthesecountries. Iftherealinterestrate diddropprecipitouslyintherestoftheworldin the 1970s,Germanyshouldhaveexperiencedasimilar declineinitsrealinterestrateora massiverealappreciationof itsexchangerate.9 Ontheotherhand,if ~o fullyoffseta 5 percentagepointdecreaseintheworid10-yearrealinterestrate,a country’sreal exchangeratewouldhavetoappreciateby70percent. BetweenDecember1971andDecember1975the Deutschemarkappreciatedagainstthedoilarby 25percentinnominaltermsand 18percentinrealterms usingCPIS. .

11 2-yearinflationisnota goodproxyforexpectedfutureinflationinmostofthesecountries,therewould benoreasontoexpectadropinthemeasuredrealrateforcountrieswhereinflationhasbeenmorestable. Chart 4 shows that measuredreal interest rates are more similar across countries,and their movementsovertimearesmallerandlesspersistent,when10-yearlaggedinflationratesareusedtoproxy forinflationaryexpectations. (Therealinterestratesusing2-yearlaggedinflationare plottedasdotted lines.) TheonlyexceptionstothispatternareGermany,wheremeasuredrealratesareinsensitivetothe choiceofexpectationsproxy,imdDenmark,wheretherealrateappearsto undergoa structuralbreakin the early 1980swhen 10-yearlaggedinflationis used. Overall,the visualevidenceof Charts3 and4 confirmsthe statisticalevidenceprovidedby Tables2 and3. If a long lag of past inflationhelps to explainthe long-terminterestrate, it is naturalto ask whetheralonglagofpastinflationisabetterpredictoroffutureinflationoveralonghorizon. Somewhat surprisingly,the answer is no. However,in order to test whether10-yearlaggedinflationis a good predictorof 10-yearaheadinflation,onewouldliketo havemanyindependentobservationsof 10-year aheadinflation.Inthepostwarperiodweeffectivelyhave5suchobservations,oneofwhichmustbeused forinitialconditions.Thisissimplynotalongenoughsampletotestthepredictivepropertyoflong-term inflationmodels. .. Thesmallsampleproblemisevidentintheinflationexperienceofmanycountries,includingthe UnitedStates. Between1948and 1995,theyears 1974-82standoutas highinflationyears,whilethe remainingyearshavemuchlowerinflationrates. T’hus,intheearly andearly 1990s(sofar)along 1960S lagofinflationwasabetterpredictorof 10-yearaheadinflation,butinthemid 1970sandthelate1980s a shortlagof inflationwasa betterpredictorof 10-yearaheadinflation. Itispossiblethatthe 1974-82periodreflectsadifferentinflationregimethantheotheryears. In thepresenceofinfrequentregimeshifts,a longbackwardaverageofinflationmayprovidea reasonable proxyfortheformationofexpectations,especiallyasagentsthemselveslearnabouttheregime-switching

processovertime. Thus,inthemid-1970s,agentsmayhaveexpectedanearlyreturntothelowinflation of the previoustwodecades. Afterinflationremainedhighforseveralyears,agentsmayhaveupgraded their subjectiveprobabilitiesof remainingin a high-inflationregime. The conversemaybe truein the 1980s. SurvevExpectations The Federal Reserve Bank of Philadelphia conducts a quarterly survey of 10-year ahead inflationaryexpectationsheldbyfinancialmarketparticipantsintheUnitedStates,includinginvestment banksandconsultingfirms. Chart5 plotstheseIong-terminflationexpectationsas wellasaveragepast inflation rates over varioushorizons.io Althoughnoneof the past inflationseriesexactly matchesthe survey expectations,the 10-yearpastinflationmeasurecomesclosest. To confirmthisvisualimpressionmoreaccurately,the rootmeansquareddeviations(RMSDS) betweensurveyexpectationsandpastaverag; inflationwerecalculatedforbackwardhorizonsof 1to 15 years. The minimumRMSDof 1.04is obtainedwitha backwardhorizonof 9 years,themaximumof 2.35 is associatedwitha horizonof 1year. In orderto comparesurveyexpectationswithex futureinflation,the sampiewasshortened to 1978-85.RMSDSwerecalculatedforfiture inflationoverhorizonshorn 1to 10years. RMSDSwere also calculated for past inflationover horizons from 1 to 1S years. The closest proxy to survey expectations in this sampleis a backwardaverage of 14 years with an RMSI) of 1.09. All of the backwardaverageRMSDSexceptthe l-yearweresmailerthanthesmallestfutureaverageRMSD,which was the 8-yearat 2.75. ‘%e PhiladelphiaFedsurveybeginsin 1980. A similarsumeybyBarclay’sextendsbackto 1978, butitcontainsmanymissingobservations.Duringtheperiodsofoverlapthetwosurveysareessentially identical. Inordertoextendthesampleforcomparison,Chart5usestheBarclay’sdatafor 1978-79and interpolatessomemissingobservationsfor thesetwo years only.

V. Index-I.inkedBon& Forcountriesthathavebondslinkedto theconsumerpriceindex,therealinterestrateon these bondsprovidesadditionalevidenceonthebehaviorof inflationaryexpectationsin nominalbondyields. Twofactorsmustbetakenintoconsiderationwhencomparingindex-linkedyieldsto yieldsonnominal bonds. First,themarketsforindex-linkedbondsaremuchlessliquidthanthemarketsfornominalbonds, sothatindex-linkedyieldsmayincludea significantliquiditypremium. Second,index-linkedbondsare 1argelyfree of inflationrisk, so theiryieldsare lowerthannominalyieldsdue to the absenceof both expectedinflationand any inflation-riskpremium. Charts6-8plotthelong-termindex-linked bond yields for the three countries that have 4 RootMeanSquaredDeviation fromIndex-LinkedRate historicaldataon such bonds.’l In recentyears, NominaI Nominal yieldless yieldless thebestproxyfortherealindexedyieldhasbeen 2-year 10-year inflation inflation the nominalyield minusa longaverageof past Australia I 1.43 [ 0.89 inflation.12 In the early 1980s in the United Canada I 1.22 I 0.48 Kingdom, a short average of past inflation U.K. I 1.50 I 1.76 possiblybecauseoftheimproved. perform better, inflationcredibilityassociatedwiththechangeof governmentin 1979. Overtheentiresampleavailable,theRMSDbetweentherealindexedyieldandthenominalyield lesspast inflationis substantiallysmallerforAustraliaandCanadawhen10yearsof inflationare used 1lAconstant-maturity10-yearindex-linkedyield is availableoniy for the United Kingdom. For Australia,thechartusestheyieldonanindex-linkedbondmaturingin2005. ForCanada,thechartuses theyieldon anindex-linkedbondmaturingin 2021. 12Thevolatilityof the nominalbond yield relative to the real indexedbondyield providessome evidencein favor of a time-varyingrisk premium,as both surveyexpectationsof inflationand past averagesof inflationare quitesmooth.

1 thanwhen2yearsofinflationareused. (SeeTable4.) FortheUnitedKingdom,theRMSDissomewhat lowerwhen2-yearinflationis used. VI.Conclusion Thisstudyisanempincalexercisedemonstratingthatexpectationsaboutfutureinflationovera longhorizonappearto be betterexplainedby a longaverageof pastinfIationthanby a shortaverage. Thisconclusiondoesnotimplythatmarketexpectationsaboutfutureinflationareimational.Thisstudy has not presenteda theoreticalmodelof expectationsformation. However,long memoryof the type documentedin thisstudywouldbeimpliedby a modelof multipleinflationaryregimesin whichagents basetheirprobabilitydistributionsof futureregimeson past inflationaryexperience. This studyhasnotfocusedattentionontheissueof theinflation-riskpremiumin nominallongtermbonds. However,thelimitedevidencethatisexamineddoesnotsupportasignificantriskpremium thatis systematicallyreiatedto the Ieveior variabilityof inflation.

15 References Darby,Michael,1975,“TheFinancialandTaxEffectsofMonetaryPolicyonInterestRates,” 13,266-276. Evans,Martin,andKarenLewis,1995,“DOExpectedShiftsinInflationAffectEstimatesoftheLong-Run FisherRelation?” o Feldstein,Martin, 1976,“Inflation,IncomeTaxes, and the Rate of Interest:A TheoreticalAnalysis,” Fisher,Irving, 1930, o York:Macmillan). Hartman,David, 1979,“Taxationand the Effects of Inflationon the Real CapitalStock in an Open Economy,” Mishkin,Frederic,1984,“TheRealInterestRate:AMulti-CountryEmpiricalStudy,” 1992,“IStheFisherEffectfor Real?” o — Peng, Wensheng,1995,“TheFisher Hypothesisand InflationPersistence--Evidencefrom FiveMajor IndustrialCountries,”IMFWorkingPaperNo.95/118,November. Summers,Lawrence,1983,“TheNonadjustrnentofNominalInterestRates:AStudyoftheFisherEffect,” in Tobin,cd., i o (Washington:TheBrookingsInstitution). Tobin,James, 1969,“AGeneralEquilibriumApproachtoMonetaryTheory,” o 1

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International Finance Discussion Papers IFDP - 538 LongMemoryinInflationExpectations: Evidence JosephE.Gagnon from InternationalFinancialMarkets 537 UsingMeasuresof Expectationsto Identifi the AlIanD. Brunner Effectsof a MonetaryPolicyShock 536 RegimeSwitchingintheDynamicRelationship ChanHuh betweenthe FederalFundsRateand Innovationsin NonborrowedReserves 535 The Risksand Implicationsof ExternalFinancial EdwinM.Truman Shocks: LessonsfromMexico 534 CurrencyCrashesinEmergingMarkets: An JeffreyA. Frankel EmpiricalTreatment AndrewK. Rose 533 RegionalPatternsintheLawof One Price: CharlesEngel The Rolesof Geographyvs. Currencies John H. Rogers .1995 532 AggregateProductivityandtheProductivity SusantoBasu of Aggregates JohnG. Femald 531 A Centuryof TradeElasticitiesfor Canada,Japan, Jaime Marquez and the UnitedStates . 530 ModellingInflationinAustraiia Gordonde Brouwer Neil R. Ericsson 529 Hyperinflationand Stabilisation: Cagan MarcusMiller Revisited LeiZhang 528 On the Inverseof theCovarianceMatrix in GuyV.G. Stevens PortfolioAnalysis 527 InternationalComparisonsof the Levelsof Unit PeterFIooper LaborCosts in Manufacturing Elizabeth‘Vrankovich Pleaseaddressrequestsfor copiesto InternationalFinanceDiscussionPapers,Divisionof InternationalFinance,Stop24,Boardof Governorsof the FederaiReserveSystem, Washington,D.C. 20551.

25 International Finance Discussion Papers IFDP -r Utn@@ J995 526 Unce~inty, InstrumentChoice,andtheUniqueness DaleW. Henderson ofNash Equilibrium: Macroeconomicand Ning S.Zhu MacroeconomicExamples 525 TargetingInflationinthe 1990s: RecentChallenges RichardT. Freeman JonathanL. Willis 524 EconomicDevelopmentand Intergenerational MuratF. 1yigun EconomicMobility 523 HumanCapitalAccumulation,Fertilityand MuratF. Iyigun Growth: A Re-Analysis 522 ExcessReturnsand Riskat the LongEndof the AlianD. Brunner TreasuryMarket: An EGARCH-MApproach DavidP, Simon 521 TheMoneyTransmissionMechanismin Mexico MartinaCopelman AlejandroM. Werner 520 Whenis MonetaryPolicyEffective? JohnAmmer AlIanD. Brunner 519 CentralBankIndependence,Inflationand PrakashLoungani Growth in TransitionEconomies NathanSheets 518 AlternativeApproachesto RealExchangeRates HaliJ. Edison and RealInterestRates: ThreeUpandThreeDown WilliamR. Meiick 517 Productmarketcompetitionandthe impactof VivekGhosal priceuncertaintyon investment: someevidence PrakashLoungani fromU.S. manufacturingindustries 516 BlockDistributedMethodsfor Solving Jon Faust Multi-countryEconometricModels RalphTryon 515 Supply-sidesourcesof inflation: evidence PrakashLoungani fromOECDcountries PhillipSwagel 514 CapitalFlightfromtheCountriesinTransition: Nathan Sheets SomeTheoryand EmpiricalEvidence 513 BankLendingand EconomicActivityin Japan: AllanD. Brunner Did “FinancialFactors”Contributeto the Recent StevenB. Kamin Downturn?