Inflation-Adjusted Potential Output

Board of Governors of the Federal Reserve System International Finance DiscussionPapers Number 561 August 1996 INFLATION-ADJUSTED POTENTIAL OUTPUT Jane T. Haltmaier NOTE: Intematioml Finance Discussion Papers are prelimi.narymaterials circulated to stimulate discussionand critical comment. References in publicationsto International Finance DiscussionPapers (other than an acknowledgmentthat the writer has had access to unpublishedmaterial) should be cleared with the author or authors.

paperestimatespotentialoutputfor sevencountriesusinga multivariateversion of theHodrick-l?rescotftilterin whichobservationson inflationare usedto helpseparate trendfromcyclicalmovementsinoutput. Thepotentialseriesare estimatedfwstonan aggregatebasis,andthenby disaggregatingoutputintothreemajorcomponents:labor productivity,theemployment-populationratio, andpopulation. Potentiallevelsof productivityandtheemployment-populationratiosare calculatedusingthemultivariatefilter andcombinedwithactualpopulationto derivean alternative,“disaggregated”estimateof potential. ThemethodisthenappIiedto forecastingpotentialgrowth.

Inflation-AdjustedPotentiaIOutput Jane Haltmaier~ I. Introduction Measuresof potentialoutput, both Ieve{sandgrow&rates, are quite importantas guides for macroeconomicpolicymakers. This is especiallythe case for monetaryauthorities tryingto determinetheappropriatestance of monetarypolicy. At Ieastin theory, inflation shoulddeceleratewhenoutputis belowpotentialandviceversa. Thus, expansionary monetarypolicyshouIdnot mn the risk of resultingin an increasein inflationas Iongas outputis belowpotential. Similariy, a centraibankthatis tryingto engineera reductionin the inflationratewillneedto pursue a contractiomrypolicyif outputis at or abovepotential. Thus, knowledgeof thecumentoutputgap is critical, Giventhesizablelagswith whichmonetarypolicyaffectsthe economy,it is also importantto havean estimateof the rate at whichpotentialoutputis growing. For instance, the BritishChancellorrecentlysuggestedthatmonetarypolicycouldafford to be a little looserbecauseof his beliefthat the rate of potentialoutputgrowthhad increased,suggesting that a higherrate of growthof actualoutputthan inthe recentpastwouldnot be infiatiomry. Estimatedpotentialoutputgrowthis also a keyeIementinthedeterminationof monetary ‘Theauthorisan Economistin theDivisionofInternationalFinance,Boardof Governorsofthe FederalReserveSystem. Thispaperrepresentstheviewsoftheauthorandshouldnotbe interpreted as reflectingtheviewsoftheBoardof GovernorsoftheFederalResene Systemor othermembersof itsstaff.

-2targetsin thosecountriesin whichmonetaryaggregatesare usedas principalpolicyguides. IIIa monetaryruIeregime,a constantrate of inflationcan theoreticallybe achievedby setting the rate of moneysupplygrowthequalto the targetedinflationrate, plusthe rate ofpotential outputgrowth,minusthe expectedrate of changeof veiocity. This is in factthe methodused by the GermanBundesbankin settingits moneygrowthtargets. In other countrieswhere moneysupplyrulesare not theprimaryguidetopolicy, the rate of growthof potentialoutput is still takenintoconsiderationh determiningthe non-inflationaryrate of actualoutput grOVAL However,despiteits importance,potentialoutputisprobablyevenmore difilcuitto estimateaccuratelythanthe relatedconceptof theNAIRLJ. Thereare basicallytSVOtypesof approachesto estimatingpotentialoutput.2 Oneist. usesometypeof filterto separatetrend tiom cyclicalcomponentsin theaggregateoutput data. An ahernativemethodis theso-caIIed“production-tictionwapproach,which decomposespotentialoutputintoitstechnology,labor, andcapitalcomponents,andestimates MI-employmentlevelsof each. Eachapproachhasbothadvantagesanddisadvantages. A commonly-usedfilteringtechniqueis thatintroducedby Hodrickand Prescott (1980). The Hodrick-Prescott(HP)filter smoothsactualoutputso thatpotentialoutputis a weightedaverageof pastand futureactualvalues. Althoughthistechniquecan be very usefid, it alsohasseveraldrawbacks. For instance,it suffershorn an “endpoint”problem thatoccursbecause,althoughthe smoothedseriesiscalculatedasa centeredweighted averageof actualobservationstioughout mostof theperiodanalyzed,it dependsoniyon 2Laxtona T ( p a comprehensivseummrayofmuchoftheliteratureint area.

-3past valuesat the end(andon fi~re vaiuesat the beginning). In addition,this methodwill u p a p OUtpUtsefies hat a t a l of actualoutput over time, that is, theestfiated outputg w g h a v c to zero. T t thUSdoes not allow f t p t o m a potentialmoreoftenthanit is belowor vice versa. In addition,outputgapsderivedfromthe W filter will not necessarilybe consistentwiththe concurrentbehaviorof inflation. Kuttner(1994)addressesthe latter problemby usinga Kahnanfilterto derive estimatesof potentiaIoutputfor the UnitedStatesthat are consistentwithobservedinflation rates. However, thisapproachassumesthat the potentialoutputgrowthrate followsa randomwalk, whichmaybe true for the UnitedStates,butdoesnotappearto be thecasefor mostof the foreignindustrialcountries. An alternativemethod,developedby Laxtonand Tetlow(1992)usesanexpandedversionof the HP filter, whichdoesallowmeangrowth rates to vary over time, toadjustgaps for inflation. Thistechniqueis termeda muItivariate ( filter. The productionfimctionmethodshould in theoryproducean estimateof potential output that is relatedto theactualbehavior of inflation,sinceemployment,a k component, can be adjustedto itsfill-employmentlevel usingestimatesof theNAIRUthat are compatible with inflationdata. ThismethodgeneralIyalsorequiresinformationon capitalstockand labor force participation,as wellas some techniquefor adjustingthe latterto its ‘Memployment”leveL (Thecapitalstock is generaiIyassumedto beeitherfiJIIyutilizedor utilizedat its “average”levelat p ) Totai factorproductivitymustalsobe adjusted f cyclicalvariation. TheOECDp p o estimatesfor mostof its member

countriesusinga productionfinc~im approachin whichtheHP filter is used to adjusttotal factorproductivity,withtie s~e advantagesanddisadvantagesthatapplyto adjustingtotal output. However,oneadv~~ge to tie productionfinction approachis tit, beca~e it hasa structuralas wellas a timeserieseiement,it is somewhatmoreusefhlfor extrapolating potentialgrowthratesthanthe aggregatefilteringtechniques. In fact, theabilityto projectpotentialoutputgrowth,at leastover a forecasthorizon of a coupleof years, wouldappearto be critical for suchmeasuresto reallybe usefulfor poiicymakers. Althoughit maybe importantfor somepurposesto lmowthe sizeofhistorical outputgaps, it is clearlymuchmore importantto how thesizeof the currentgapas weilas howit is Iikelyto changeover the relevantforecastperiod. Simplyadjustingthe outputgap so that it is consistentwiththe currentbehaviorof inflationdoesnot reallygiveus much more informationthansimp~ylookingat inflationitself. o if our estimatesof potentialoutputcangiveus someinsightintohowthegap is Iikeiyto changegiventhe currentandprojectedbehaviorof actualoutputthat h r gainedanything. Thispapercombineselementsof the MVfilterandtheproductionfhnctionmethodsin an attemptto produceestimatesof potentiaioutputfor theG-7countriesthat are both adjustedfor inflationandable to be extrapolated.3Themethodis f~st appliedto aggregate GDP, andthento a decompositionof GDP intoits laborproductivityand laborcomponents (a pafiialproduction%mctionapproach). The latteris representedby the employmentpopulationratio, as working-agepopulationis assumednotto havea cyclicalcomponent. 3 W Germany was used in placeofunifiedGermanybecauseofthelackofunifieddata b 1

-5- Potentialoutpulgrowthcanthenbe extrapolatedby usingactualprojectionsof working-age population(one variablefor whichwe do havefairlyaccurateforecasts),as wellas assumptionsabouttrendproductivitygrowth and the fhI1+mpIoymenIteveIof the employment-populationratio. The disaggrega~d methodthusallowsus to makeuseof a muchlarger informationset in forecastingthandoestheaggregateapproach SectionII describesthetechniquein more detail,SectionIII presentst estimation resul~, and Section~ usestheestimatesto projectpotentialoutputgrowthoverthe nexttwo years. SectionV concludeswithsomesuggestionsfor fkther analysis. IL TheMuitivariateFilter The Hodrick-Prescott(HP)filter calculatesa smoothedseriesby minimizingthe expression: (1) [(q where Y is actualoutputandY is the smoothedoutputseries. The smoothedseriesisthus calculatedby tradingoffdeviationsbetweenthe actualandsmoothedseries(thefrostterm) for variationsin the growthmte of the smoothedseriesfkomoneperiodto the next(the secondterm). The parameterk determineshowcloselythesmoothedseriesfollowsthe actual; a higher valueof Z willproducea smootherseries,whilea lowervaluewillproduce one that is closer to the actual. The choiceof A,althoughimportantto the fmI result, is somewhatarbitrary, althoughit hasbeen suggestedthatit shouIdrepresentthe ratioof the varianceof the cycIeto the varianceof the trend. The valuemostofienusedfor quarterly data is 1600,as doneby the originalresearchers, andthisvaluewasalsousedhere.

-6- Themultivariatefilteraugmentsthe aboveexpressionwithan output-inflation equation,andthencalculatesa Dotentialoutputseriesthatminimizestheentireexpression. In theequationusedhere, thecurrentinflationrate dependsprimarilyonpast inflationandthe laggedoutputgap. Changesinthe exchangerate and, whereapplicable,the value-addedtax, are includedas additionalexplanatoryvariablesfor inflation. The inflationequationis: . ‘yt-l)+~t ( I =A + B + C(L)(Yt-l whereH is the quarterlychangeinthe logof the price level,andZ representsthe vectorof othervariablesthataffectthe currentinflationrate. The weightsinA(L)are assumedto sum to 1. Theexpressionto be minimizedis: ( x= pi f-z t+z wherea is the weightingfactorfor the inflationexpression. Rearranging(2)and substituting into(3), theexpressionto be minimizedbecomes: r-l T T (4) l where~ is the accelerationin Mation relativeto its pastvaluesthat is notdue to changesin othervariablessuchas the exchangerate or taxes. The resultingpotentialoutputserieswill thusdifferfrom thatob~ined fromm applicationof thesimpleHP filterto the extentthat it explainsmoreof the changein inflation. It will, however,stillbe subjectto a smoothness

con,straint,meaningthatsuddenchangeshorn accelerationto decelerationh inflationwillnot be allowedtoproduceoverlysharpswingsin the rate of growthofpotentialoutput. Thereare twoproblemswiththis techniquethatneedto be addressedbeforeit canbe appiiedempirically. Th fust k thatestimatesof theparametersof (2)are requiredto calcuiatethepotentiaioutputseries,but estimatesof thepotentiaioutputseries are also neededto calculatetheparameters. In theory, theycouldail be estimatedjointly, butin practice, this is verydifficult.4 Thesolutionusedhere wasa two-stepprocedure. First, an initialpotentialoutputserieswasobtainedusingthe traditionalHP filter, and thisserieswas used to estimateequation(2). Theresultingparameterswerethenusedto minimize(4). AS a check, the newestimateswerethenusedto reestimatedthe inflationequation,butthe changeswereso trivialthatno fimher iterationswere done. The secondproblemis thechoiceof a, the weightpiacedon the inflationcomponent. Intuitively,it shouldbe apparentwhysucha weightis needed. The inflationacceleration texm,measuredas theunexplainedpart of the quarteriy changein the logof the pricelevel, is of an order of magnitudesimilarto the changein the trend, whichis weightedbya factor of 1600. Unweighed, the inflationterm willhave no impacton the minimizationproblem. H t e lesstheoryto guidethe choiceof a than thereis in choosingL S differentvalueswere tried, rangingfkom200 to 800. Altiough the resulting differenceswerenot large, 400 seemedto producethe mostsensibleresults, and so thatwas the valueusedfor the mainresults. Somefurtherdiscussionof this issue,alongwithresults obtainedusinga’s of 2 and 800are containedin the Appendix. 4I w h t s t i i im b i i c b thescopeo t paper.

- The disaggregate Mation equationdecomposesthedifferencebetweenactualand potentialoutputintoW components:thegapbetweenactualandtrendlaborproductivityand thegapbetweentheactualandtrendemployment-to-working-agpeopulationratio. (Working-agepopulationis assumedto be invariantto thecycle.) Variationsin the unemploymenrtateandtheparticipationrate, bothof whichare cyclical,are thus consolidatedintotheemployment-populatiornatio. Whileit wouldprobablybe more satisfactoryto treattheseW elementsseparately,thatwouldproduceanexpressionthat wouldbetoounwieldy. Thedisaggregate inflationequation,&en, is: ( I =A + B + D + E + E whereP is laborproductivityandR istheemployment-populatiornatio. Theexpressionto be minimizedis: T-1 (6) t=2 r + @- -E t III. Empirical Results TheHP filterwasusedto calculatepotentialoutputseriesfor westernGermany, France,Italy,theUnitedKingdom,Camda, Japan,andthe UnitedStates,fortheperiod 1968through1995. Theresultingserieswereusedtoestimateinflationequationsfkom1

through1993, periodsfor whichtheestimatesof potentialoutputarethe t e t mostuncertain.s ASindicatedabove,in additionto the “gap”terms,theestimatedinflationequations includepastlagsof inflation,withtheweightsconstrainedto sumto one, as wellascurrent and/orIaggedchangesin t ( o the exchangerateandoilprices, andchangesinthe value-addedtax.6 TheGermanequationalsoincludeda d-y for theperiodofunification. Thepreciselagsusedvarytiom oneequationto another,sincethet ofthe i of exchangerate andoilp c a differacrossc T e a includedoneandtwol of thegapterms. Theresultsfkomtheestimationof theaggregateinflationequationsare summarizedin th followingtable. Sevenof thefourteenGAPvariablesweresignificantat leastat the5 p l andseveralotherswereclose. GeneraIlythecoefficientonthefwstlagwas positiveandthaton thesecondwassmallerandnegative,suggestinga “speedeffect”horn changesinthe outputgap. h fact,thespeedeffect,measuredasthecoefficienton the secondgapterm (signreversed),isgenerallylargerthantheleveleffect(thesumofthetwo coefficients). The mainexceptionisFrance,wherebothcoefficientsare positiveandneither are significant. ST o e w t J e w w e o t n 1 T r t t 1 p c e v h i a w a v h o g T p e l g c t d n s r t r t s 6T V c s w p C B a D L

E R f A O G E Germany F I U C J Us. I-I., . O J . . . . l5 ( ( ( ( ( ( ( H . . . l2 . . - ( ( ( ( ( ( ( • - . - . . . ( ( ( ( “ n n l . . . . . n n n n n n n A . • . l~ n l n ( ( ( ( ( A - . - . - . - ( ( ( ( ( ( ( A n - n - - - - ( ( ( ( ( A n n n - - n n ( ( . . . n - . . ( ( ( ( ( ( 4 n . n n . . n ( ( ( G . . . . .1 . . ( ( ( ( ( ( ( S - . - - - - - ( ( ( ( ( ( ( . . . . . . . * ‘S t 1%l ! t 5 70ievei. n = n a Charts1through7 showO g obtainedwithboththeHP filterandthe multivariatefalter. Alsoi t “ a t c t p t current-periodi r t n e byeitherp i c t VAT, e r o p m ( t inflationaccelerationandgap termsare plottedas fourquarter movingaveragesto showthetrendmoreclearly.) As

-11expected,the MV fiker outputgapsfollowthe patternof inflationmuchmorecloselythan the HP filtergaps. For example,the longperiodof disinflationin WesternGermanyinthe 1980’ssuggeststhat the outputgap wasmore negativethanthe HP filter shows,whilethe period of inflationaccelerationthatfo~lowedsuggeststhat the outputgapwasmuchnarrower thanthe HP filtergap. ~ tie currentperiod, thedownwardtrend in inflationsuggeststhat the outputgap is widerw the w filter shows. Similaradjustmentsoccurfor the 1980’s for the other Europeancountries. For Cana&, thedifferencesbetweenthe twogapseries tendto be somewhatsmaller, althoughthepatternof inflationcurrentiysuggeststhatthe outputgap is closeto zero rather thanin thepositiverangeas the HP falterseriesimplies. TheJapaneseMVoutputgap seriesis currentlycloserto zero nowthanthe simpleHP filter series. For the UnitedStat.M,the MVfilterseriessuggeststhatthe outputgap is closeto zero, rather than in the positiverangeas indicatedby the HP filter series. ed&rod Oneadvantageto disaggregation,apartfkompossibledifferentialimpactsof inflation on the productivityand laborcomponents,is simplythat it ailowsincorporationof trendsin working-agepopulationgrowth~d 1aborforceparticipation,whichmayshiftover time. The resuhs fkomthe estimationof theequationsthatbreakoutputinto itsproductivityand laborcomponentsare shownin the followingtable. The coe!llcientson laggedinflation,the VAT, the oil price term, and the exchangerate are similarto thoseobtainedusingaggregate GDP. The coefficientson the gaptermsin theseequationsare lessoftensignificantthan those in the aggregateequations. Thismaybe dueto multicollinearity,sincetheproductivity and employmentgaps are generallycorrelatedwithoneanother. It is interestingthatthe

-12- II EstimationResultsfor DkaggregaOtuetpdutGap Equations II Germany France Italy U.K. Canada Japan Us. r ml .484** .656** .66*1* .654** .599** lj43** .506** (.097) (.096) (.104) (.107) (.101) (.116) (.090) rI* .107 .173 .116 .203* .156 .138 .019 (.104) (.112) (.130) (.124) (.116) (.133) (.105) I l’?, .227* -.115 .133 -.068 .069 .219 .475 (.100) (.118) (.124) (.121) (.118) n.a. n.a. I-r. .182 .286 .090 .211 .176 n.a. n.a. n.a. n.a. n.a. n.a. n.a. AVAT .002 .)03** .Ooo .~2* n.a. lW* n.a. (.002) (.001) (0006) (.OO1) (.002) AEx -.032** .009 .o~* .002 -.004 -.002 -.008 (.O1l) (.018) (.027) (.029) (.014) (.015) (.011) , Aix., n.a. -.020 n.a. -.024 -.021 n.a. -.005 (.017) (.029) (.015) (.011) r AEX.2 n.a. n.a. n.a. -.026 -.029* n.a. -.015 (.029) (.013) (.010) APo .Q(j5** .013** .012* n.a. -.002 .(XI5 .0I1* (.002) (.003) (.006) (.003) (.006) (.003) I APo., n.a. n.a. .018** n.a. .O1l** .009 n.a. (.006) (.003) (.006) I GAPE.,‘ l~3* .107 .X()* .142 .124 .411 .440** (.162) (.093) (.152) (.306) (.085) (.277) (.095) GAPE.Z -.192 -.039 .e~()* -.042 -.062 -.236 .0401** (.158) (.084) n.a. (.300) (.080) (.261) (.091) GAPP.,2 .073* .Ooo .158* .145 J~* .271* .049 (.040) (.070) (.092) (.104) (.063) (.116) (.046) GAPP.Z .a)(j7* -.000 -.158* .010 -.100 ..~4* -.049 (.036) (.070) n.a. (.105) (.070) (.124) (.046) , R2 .86 .93 .90 .81 .89 .82 .91 , ~mpioyment gap. 2. prductlvl~ Gap **Sigmhcantatthe1% level. *Signihcantatthe5% level.

“productivitygap”tCXTkXsIignificantmore oftenthanthe “employmentgap” t suggesting thatonlyadjustinglabormarketdatato reflecttiation, as in the productionfilnction approach,maynotbe sufficient. Charts8 throughM showthe inflation-adjustedgapsfor both the aggregateand disaggregate series. Althoughmostof the differencesare fairly minor, there are some rather large discrepancies. Probablythe mostnotableis for Germanyin the late 1980’s, whenthe aggregateseriesshowsa slightlynegativeoutputgap, whilethe disaggregated showsa fairly substantialpositivegap. As chart 15shows,the differenceis in largepart due to the sizableswingsin working-agepopulationgrowthexperiencedby westernGexmany over this period. In particular, the very lowrate ofpopulationgrowth in the late 1980’s leadsthe disaggregatedapproachto showmuchslowerpotentiaigrowththanthe aggregate method. As shownin charts 16through21, suchswingsin populationgrowthhavealso occurredin mostothercountries,suggestingthatan aggregateapproachmay wellmisssome importantchangesin potentialgrowth. Onenoteworthyexampleis the projecteddrop in Japaneseworking-agepopulationfor 1996and 1997,whichmay IimitJapanesepotentiai growthover thatperiod. IV. ForecastingPotentiaiGrowth As notedearlier, estimationof the currentandnear-termrate of potentialgrowthis probablyat leastas importantfor policyas estimationof the current gap. Estimatedpotential growth is an explicitcomponentof the Bundesbank’smoneysupplygrowthtarget, andis takeninto account,at leastixnpiicitly,in manyothercountries. In addition, if speede exist, which theyappearto do for severalcountries,changesin the gap (the difference

-14betweenactualandpotentialgrowth)maybe as importantasthe levelinthedeteminationof inflation. Thefollowingtableshowsforecastsfor potentialoutputusingboththeaggregateand disaggregatedmethods,basedontheinflation-adjustedseries. Thesameseriesareshownfor thepreviousfive-yearperiodforcomparison. Theforecastsfor aggregateGDPandfor productivityare derivedhorn simpletime-seriesmodelsthatrelatecurrenttopastgrowth. Theemployment-populatiornatiosare assumedto remainconstantovertheforecastperiod. Thiswasdonebecausetheseratios,whichare composedof theparticipationrateandthe NMRU, are notwell-suitedto simpletime-seriesmodelling. For instance,theNAIRUis assumedhere, as isgenerallythecase,to be a structuralparameterthatchangesonlydueto unforeseenshocks. Theparticipationratemaybe somewhatmorepredictable,to theextent thatit is relatedto shifi intheagedistributionof thepopulation,for example. However, lesspredictableshiftsinpreferencesmayalsoplaya role. It is somewhatdangerousto simplyextenda pasttrendina variableof thistype,sincethereare obviouslimitsto the extentthateitheranupwardor downwardtrendcancontinue. Althoughit maybepossibleto useothertypesof informationto refinetheforecastsofboththeparticipationrateandthe NAIRU(for instance,a modelthatincorporateshysteresiseffects),sucheffortsarebeyond thescopeof thispaper.

-15- G i P O a C ( a r o c 1 1 1 1 Canada W G Ag 1 1 A 2 2 Di 1 2 D 2 2 Pr 1 1 P 1 1 Em - . E -.3 Po . . P 1 1 F J Ag 1 1 Aggregate 1 Di 1 2 D . pr 1 1 P . Em - 5 . E . Po . . P . -2 I U S Aggregate 1 2 A 2 2 Di 1 2 D 2 1 Pr 2 2 P . . Em - E . Po - 1 1 P 1.0 1 U K Ag 2 2 Di 2 2 Pr 2 2 Em - 6 Po .

-16- For the continentalEuropeancountries(westernGermany,France and Italy),the disaggregatedmethodproducesa higherestimateof potentialgrowththanthe aggregate. This is primarilydueto thefactthatpan of the recent Iowrate of potentialoutputgrowth (whichis essentiallyprojectedtocontinueby the time-seriesmodel)appearsto be attributable to a sharpdrop in theemployment-populationratio, andthisdrop is notprojectedto continue. For the UnitedKingdomandCanadathere is littledifferencebetweenthetwo methods. For bothJapanandthe UnitedStates,the disaggregate methodproducesa lower estimateof potentialgrowththantheaggregatemethod. The mainreasonis the converseof the explamtion for thedifferencesfor the Europeancountries. Employment-populationratios have risen in bothof thesecountriesin recentyears; unlessthistrendcontinuesor productivitygrowthaccelerates,potentialoutputgrow is likelyto SIOW.Anotherfactor~ the Japaneseforecastis thatthe rateof working-agepopulationgrowthis projectedto turn horn slightIypositiveto sIightlynegative,furtherdepressingpotentialgrowth. V. Conclusion This paper hasappliedan augmentedHodrick-Prescottfilter, developedby Laxtonand Tetlow for estimatinginflation-adjustedpotentialoutput, to bothaggregateGDPanda disaggregationintolaborproductivityandemploymentcomponents. The techniqueis generallysuccessfidinthatreasonableestimatesof sensitivityof inflationto outputgapsare calculated, althoughtheyare notalwayssignificant,duemostlikelyto multicollineari~and the limitedsizeof thedataset. The resultingestimatesof inflation-adjustedoutputgaps appear to at leastmovetheestfiates of potentialoutputin the rightdirectionfor themost part. Forecastsof potentialoutputgrowthwerederivedusingthe inflation-adjustedseries.

- T resultingdifferencesbetweentheaggregateanddisaggregate versionssuggestthat takingaccountof the majorcomponentsof growthis importantinestimatingtrendsin potentialoutput. Probablythe mostimportantdifficultywiththeapplicationof thistechnique,as with applicationsof the simpleHP falter,isthe indeterminacyof the “best”weightsin the optimizationproblem. Theresultspresentedinthispaperusethetraditionalweightof 1600 forthetrend, or smoothness,parameter,anda weightof400forthe inflationparameter. Eitheror bothof thesecouldk adjusted. Inparticular,forthedisaggregate method,it couldbe arguedthatunderlyingproductivitygrowthshouldbetreatedas beingmuch smootherthana weightof 1600wouIdimply. Becausetheemployment-populatiornatiois generallymorecyclicalrelativeto trendthanoutput,it couldalsobe arguedthat a weight largerthan 1600shouldbe usedforthatseries. Similariy,the morecloselyonewantsto tiepotentialoutputto inflation,the greater theweighton inflationshouldbe. Thelatterpointis particularlyimportantbecausepotential outputis akr aHa constructedseriesthatbydeftition is supposedto be theamountthatthe economycanproducewithoutcausinginflationto accelerate. Theonlyreasonwegiveany weightto theother components(theactuallevelanda smoothtrend)mustbe thatwe think thatthe inflationserieshasenoughnoisein it thatweshouldnottakeit literallyperiod-byperiod. Futureresearchmightprofitablybe directedat determiningmorepreciselyhowwe shouldbalancethesevariousobjectivesin constructingpotentialoutput.

-18- Chart 1 Output Gaps a I A WesternG . 3 I . . A \ f )~\ \ 1’ ‘ 1, \ I I , .n\l 1 ,\ /~ \ 2 ~- ‘,--------------- , -------------------- -------i /) J\ --+--+ --------/ I , Uu i 1 1 L - -, I -+ \ -- --- - -- -- - - - - - -- I ------- m ./ - - - i \ , i I 1I 7 0 I I \ / - - ‘“I I I I \ , t $ -\-/v-- n - J -- --i I -. -.----- ----- I \ c -. .--.-- ----- -\- - ‘-?- - - - - - - - - - - - - - - : - - ~- - - - - - - - - - - - - - - - - - - - - - - - - - - ‘- + - - - - ( i 1’ I \ /’ ,4. , i # ~ / \) I -3 ---.-- ----- -+;: -------------------- -------------------- --------------, 1 1i , , 1II 1 1974 “’(’197“8 ‘1982‘“ “1986‘‘ I ““ i’ I 99 1 0 1 ‘ 1 1 i F - F _ I A I

- I -. t C 2 Output Gaps and InflationA F 4 I I I 1 I -I I– -- 3 I I 2 m- - - - - - - - - - - - - - -- - - - - - —– , , I I I I 1 -ift . I I1 I I u - - - -- -- -- - -- -- -, >- -- -- - - - - -b I I 1 I I 4 I j 1 1 -2 L-- - - . -- I ‘/ 1 */ -3 ----------------------------------- --------- I 4 [ 1 1 1 r , ‘‘‘‘ I ‘ ‘ 1 ! T 1 1‘“ 1 ! “‘‘1‘ ‘ F - F m Inf.A I —

-2 L 3 Output Gaps and I A I 6 I 1 I I . 4 I --------------------------------------------------------- ------------- YI r I I \ 2 ---- ------------------------------------------- \ I t I I I I / II I f , I --------- \ t ! --- t: - - - - -- --- -- - - -- - - W- - - - - .---- 1 ! I \ L I 1 4 -- -- -- -- ---- ------- -’. / -- --- -- -------- -----. , II 1I I II 1 I I II’ I II I II I 1 1 ‘ 1974 ‘ “1978 ‘1982 ‘““ 1’986“’ “’1990 ‘ ‘1’994 HP F - F m I A I # -—

-21- C 4 1 O G a I A I I U K - 6 , I I I ( I I I I 4 I I / 2 --- -------------. I > I \ \ , 0 I I I I l - -- I +.. - ------------- 1 -----------------------------------i I I -6 ---- .---------_--_--- ----------------------------------- .---.-.------ I -8 1 ‘ 1 II ‘‘‘ r I ‘ I 1 I ‘‘ I I ‘ I ‘ ‘‘ T11 ‘ 1 ‘‘‘ 11 , “‘‘ I n r I 1 HP Filter ---- MVFilter hf. Ace. I -

-22- ( O G a I A Canada . I 4 I I I I I 1 I i I 2 T I - -A - - 1 A .\ - ------------------- - /7-’ - ” ---- J ------------ -- I I u I E I 0 2 ,~ \ -~ \J ,1 $ / \ - - ! , - - - -- -- 4 /: I 1 I \/ :I --------------------------------- ---------------------------------- - \J ,1 ) 1, \/ I I -6 II II 1!I 1 ‘ ‘1974“ ‘ ‘ I 1 [ 978 1I ‘ I “ I I 1982 ‘ II I I 1 I 990 !I ‘“ 1 ‘ l i’994 II ‘ F - F = I A l— ———

-23- C 6 O G a I A J 8 I I I 1I I I i 6 +---------- --------------------------- ----------------------------- ---i I / I “ 4 - --------------- - ----------- ---- - -------------------------- -- ---- , I 2 &----.------ !I I 4 +--.-------- I -6 ------------ I I \ -8 I Ili 1II ,, III ” ” 1 ,7 ~ 1974 I1 ‘ I ‘ i , 1 I I 9 I 7 r , 8 ! 1 ‘ r1111 “ I ! 11 “ 1 I F - F = h A I L

- C 7 O G a I A I I U S I 4 1-------- I h\ I /1 2 “,----------wL I I I 1 I 0 ~ I I I 1’ \ ,. / -- \ -- ---/----------------. I \ \ v Iv\ ,’ I \ I 1, I /’ ~ + - - - - - & - u- - - - - - -- - - -- - - --- - -- -- -6 ~. I II II, I 1 ~1982 1II~~ [ 1 ‘ i I 917 1, 8 ! I 1[ga6i i (i [II I 1~[ ~!, ,,,,,,, W , ~ ‘ ‘ ‘‘ ‘ n F - F i A i

-25- Chart8 Output G a I A Western Germany . 4 I l 1A 1 I 1, \ At / ’ 1’ 2 ~ h~t A ! ‘ -- I 1 \ I ,-- ; I _ I I, ------------------ --------- -------- 1 lull 0 I I “v I \ I I t I ! I \ ---- \ I \ t ‘ I I \,, ,} I I I I iI II I 1111111I11 r illII I , 1970 ‘ ‘ 1974 ““ ‘1978 19821‘I““’l’’b8I6T ’ [ 1 I I ‘‘‘ lIb9I r 4I I “ I ,— A - D m I A

-26- Chart9 Output G a I A F 4 - - - - --1 I ! 3 ‘1‘:~1- _- ,---_------- - --- ------------------------------ -- ~ -------- I I 1I I 2 -------- ~I- .--__------- -------------------------------- J 1 I , -. t II /’ U I 1 .E- 1 -- + I - - / 1I - -- -- -t / - - - - - - - - - - - - - - - - 2 ‘- t I 1 I I I i ----------- I < I i I u I Jb ---------------- \ v - - 1 ---W- -T-- ‘ ‘ - - - -‘-‘- - - ---- -t ---------------- ----------\-t------------------------- - - I - - - -- ,4 . I 4 I I III1IIIIII111’111’i I 1970 ‘ “ 1974 “II “1978 I I [‘ ‘19812 “i‘“II 1II QT- ”8’TIII6IIII III1’990 1994 1 “ ‘ “ — A ---- Di = h A

-27- C 1 O G a I A I I 6 I , ,, I I , ,( 4 1 ----------------------- - -- -------------- ---- _____ - ------ -, ( I I 1 i I 1 I 1 r 2 A -- Ll- - -- —.-- - - - - -- - -- ------------------------------ \ - 1 I i ~ \ 4 I -------------- 1- -- /’- 4--------- ------- -- -/+-- I I I I ! - . \ / “\ If ! I I 4 t------ ------ .- - -s- - - - - - - - - - - - - - -,W. \ —- - - - 7/ - - - - - - - - - - - - - - - - - - - - - - - - - - - - I ------ , i 1 1 I -6 !. I 111I11I 1970 “ ‘ 19 1 I I I ‘ II I ‘ I 1 7 I ‘ 1 T ‘‘“““ 1“ “ ‘‘ I I 1 I I ,— A - D _ I A I -

-28- 1 I OutputGapsa I A U K 6 I I i I I ~ 4 --- -------------------- [ 1 I I i I I 2 --- 1 0 &#45;&#45;&#45; 1 I I ----------.------ - 1 - - --------------------------------- 1 ( , 4 ----------------- -- - .------------------ _-------------, -a- , I1 I I rII111’1111I1IIIIIIIIII I 1I I I 1970 ‘ ‘“ 1974 “’’’’1978 ‘ I l“” “’1I I9T812 “[[’” 119’‘86 ‘ 1$90 ‘‘1’994 I 1 I ( I n — A - D I A I

-29- 1 [ C I O G a I A i I Canada .- I 4 I 1 i I A ,\ I ,’ \ . I 2 + ----------- r /’ - \ b- -’/- t ---- ! - I _I-------- ----------------------i I I I ! I I f \ I I I ! I I 0 I I 1 —v I w 1 - ---- \/ v I& I ------------- - -v I ! /’ Ii I I I i 4 ----------------------------------- ~! I I t -\L -‘ - . - - - - - -- _ . _ - -- --------- _ ---- - -- - ; I \! u~//t I I I1 / I I 1I I I 1 I 1 ‘ 1 “ ‘ 1 ‘‘“‘‘‘ ‘ ‘ ‘1 1 1 T ‘ I 1 I — A - D = I A

-30- 1 Chart Output G a I A I Japan . I I 8 1 1 I , I I 6 — I ---------- ------------------------------------------------------------ I I 4 —1 -------- i ----------------------------------------------------------- I I I I 1 -- - -- 2 t I 1 I !’ I , / I - ! ------------- I 1 / I / I -------------- -,- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ------------ -------------------------------------------------------- I I 1 ,*II 1970 1974 ‘ “197 I 8’ I i 1 “ I ‘ I 1 I 982 ‘ I ill 1 l ’19I I8I 61I ‘ Ii Ii I1I 9 1I9I0 r ’ Iii I I I I19 r 9 1 4 I n ( 1 A ---- D h A ,— I I

-31i C I Output Gaps and Inflation Acceleration I I U S I 4 , I \ I \ I I 1 I t ! 1 Y I .. \ I / ; 2 —.--- ._---------r -- - - -- -- / t (“ I I 1 \ I , I I I1 0 h \ $.#$ t’ I 1 I I )’ I -- - L - ,-+- -- -- - -- -- - ) / P ’ ------------------- - - ‘ - I1 I I I I I I I i 4 ---------- - .. 1., --------- ~-------------------- ---- ---------- --------- \f -6 I 1II I rI 1 1 1 “‘“ “ ‘ ‘( “ ‘i~ ‘‘“ I “ r ‘ — A - D _ I A

-32- 1 C ! 1 W P G I I W G 1 2 I 1 I f I I I m I I I 1. I I I I I I I - I 1 ._--- ----- ---------- --- 1 I 1 I I J I 0. 0 I - I ( ). 1 1 1 ‘ , 1 i 1 f“ I 1I I 1 i 1 r I I I i I

- 33 11 C- hart 1. 1 I W P G I France - 1 I 1. I I I - -- - I I / 1. A - - - - --- - - -_ - - - - - - I -- I I I I 1. - - ------------ --_---- _--- _ _l I , I I I 1 + ------------------------- --------------------------------- I I I 0. ------------- --------------------------------- I I I 0. ----- -- - --- - - - - - - . - - -- - - - - --- ~ I 0. ---------. 4 Ml 0. 0 1970 ‘1974 ‘ ‘1978 ‘ 1982 ‘ ‘1986 ‘ ‘1590 ‘ ‘1994 ‘ ‘

-34- Ch 1 1 1 Working-AgeP Growth I 2 I I I 1 9 1. - - - - - - -- -- --- - - -- -- --- --- -_ --- ---- - ---- I I I I I I 1 - -- -- -- - - - -------- 1 - -- 0. ~. 0 - ----------------------------------- 0. ---------- -*- -------------------- -1 ,, 1970 1974 1978 1982 ‘ 1986 ‘ ‘ 1990 ‘ 1994 ‘ ‘ I 1 I I

-35- 1 —. .- 1 C 18 I Working-AgeP G 1 I United Kingdom “ I 1 i i 0.8 —------------------------------------ I ---------------------------------- I I 0. —------------------- ----- 1 ---------------------------------- I I 0. ------------------- ---------------------------------- Ii ~ w- I 0. ---------------- I 0 I I - 0. I 1970 1974 1978 1982 ‘ 1986 ‘ 1990 ‘ ‘ 1994 ‘ ‘ II —

-36- Chart19 Working-AgePopulation Growth C 3 2. —------- ------ --- --- .---------- ------------- --------- --- .-----_------ 2 ,_- --- ---------- ------------- .--_----- --- ------------ 1. --- ------------- -------- --------- 1 0. o t , 1970 ~ 1974 ‘ ‘ 1978 ‘ ,982 T 1 1986 ‘ ‘ 1990 ‘ 1994 ‘ ‘

-37- 1 C 2 Working-AgeP G Japan 2 I I I I 1. + - ----- ------ ------------------- - - -- - .-..---------- .-_. I 1 ----- ----- -- -- ----- -------_-_----- --- 0. ------------_-- --- 0 m mI I I I I I I 4. I I I I 4I 1970 1974 1978 ‘ 1982 ‘ 1986 1990 1994 I ‘

-38- 1 C ! Working-AgeP G I UnitedStates . t 2 I I I ~ I I I 1. --- --- --- ------_--- --- .---_-------------- --- --i 1 --- --- ----- ----- --- -- 0. 0 1 1974 ‘ ‘1978 ‘ ‘1982 ‘ I 1 r 1990 ‘ ‘1994 ‘ I

- A ChartsAl throughA7comparethe outputgapsobtainedusingweightsof 200,400, and800onthe inflationterm. earlier, 400wasusedfor themainset of results.) (As noted Thedifferencesare fairly formosttimeperiods,butcanbe substantial,particularlyfor small FranceandItalyinthemid-1980’s.Onewayto viewthechoiceof a isas depending primarilyonhowmuchmoreof theresidualintheinflationequationonewishesto explain byalteringthe outputgap. Asshownin the toppartof thefollowingtable,thepercentageof the inflationaccelerationtermexplainedby the outputgapincreasessubstantially,although u amongcountries,as a increases. However,as showninthe lowerpanel, the standarddeviationoftheoutputgapalsoincreasesa fair amount,particularlyfor Italye (The variationamongcountriesmaysuggestthatthechoiceof a shouldaisovaryby country.7) Theresultsshowninthetablesuggestthat the improvementinthe “fit”of the inflation equationis krger relativetothe increasein the standarddeviationof thegapas a increases fkomOto 400thanit isasa increasesfrom400to 800. Thisprovidessomejustificationfor thechoiceof a usedhere,althoughcertainlya morewell-groundedcriteriawouldbe preferable. 7 T s i a t f t c a i p 1 c t b m co u

-40f Percentof InflationAccelerationExplainedand StandardDeviationof OutputGap ForDifferentvalues of a a=(l a=200 a–=lOO a=800 4 Percentof InflationAccelerationExplained W.Germany 12 15 18 21 France 4 9 12 16 Italy 7 10 12 15 UnitedKingdom 8 13 16 18 Canada 10 13 14 16 I Japan 19 15 18 22 I UnitedStates 18 21 22 25 I StandardDeviationoftheOutputGap(percent) W.Germany 1.6 1.7 1.8 2.0 France 1.1 1.1 1.2 1.4 Italy 1.6 1.8 2.0 2.4 , UnitedKingdom 1.7 1.8 1.9 2.1 Canada 1.7 1.7 1.7 1.8 Japan 1.4 1.5 1.7 1.9 united States 1.8 1.8 1.9 1.9 l

-4 Chart Al I , I Output Gaps(MVFiiter) I WesternGermany . 1 4 I I I I 1 2 , 1 0 I I t II i I -2 I I 4 ,1 I / 1 I I 1 1 I -6- I11” I r 4 1970 1974 ‘197 1 8‘ (“’1’982 ‘‘j986“’1’1’’1’9901’9’“9”‘4‘‘“‘““‘ I ‘‘ —— Alpha= 200 — Alpha = 400 ---- Alpha= 800

-42- I AZ Chart Output Gaps (MV Filter) France 3 --,.--,-----------------------------_---_------_ 2 -.----- ;/ n / f,s I -+--- ------------ {7 l A \ 14It 1/ f\ . 1 L ----,.- ,$ I ------------- ---------- -/- ~-- i --- A--- I I 0 I 1 t- -- ---- 1 -2 -. --- -- -- ---- I ! I -3 I , I I 1 4 II111~~( I 1970 ‘ ‘‘1974 ‘I““’i’97I 8I 1 i1g821 *~Ih[!i,~1 g61 TTii1I(il[gg~l 1i 1 il 91194 ‘“ ‘“ I I – Alpha=200 — Alpha=400 ---- Alpha= 800 l–

-43t I I i Italy 6 I ! 1 I ,A“ . ‘\ It , 4 ---------- - ----------------------------------------------------------- {4 -1--------1/\------------------ 2 1 I ~\ \ ‘ ---------- ‘ ---------- ‘ ----------- --------- E d I -2 .,h’ 1 , L‘ j 1’ I ‘,\r t ‘-,i “ \ i I --------------- - - ,1 Yv \\f . / I $1 ,./ -J I I 1, ,! I ‘1 ,1, 4 I ~/ ,-, I -6 II 111I1’’1 I T I I I I i“ I“” [1’ 1970 1974 ‘‘ “1978’ ‘ ‘1’982’‘“‘‘1“9‘86’‘‘“’’’1’9‘9‘‘0‘‘‘19g~’“‘‘ I , I I ,—— Alpha = 200 — Alpha= 400 ---- Alpha= 800 I I L

-44t I UnitedKingdom 6 -I ---?h ------------- / -----,------------------------------ I I ---------- 4 2 E 8 0 G CL -2 4 -----_.-------- 1 I , ( I -6 1970 1974 1 1[’11 1 1 ’ 1 9 1 7 ” r 8 ” ‘I ’ ‘ Ifl-l 1 I 982 I ‘“ I ‘ 1 ‘ l 1 l 6 r 8 ” 6 ~IrIIl1 “ “ ‘1 1T ’ i 9 II 9 I 0 IIIII 1 I ’994‘‘‘‘ I Alpha = 200 — Alpha= 400 ---- Alpha= 800 II ——

-45- I I I Canada . 4 I I I I 2 I I I I -- Ii I I ( */ ( I 4 —----- -- -- -- -- -- -- -_-------- -- --\ -- -- ---- ----- ----- ------ --- - -i -- --1 I -{ I i I I ! \ I .--------------------------- v ,---------------------- ------ .- - ----- ---- - - -1 1 I ! I I I I 1 ! 1970 1974 I1 I II 1 1’ 978 , T rII ‘ I[ ‘1982’11‘1 ! I98 I 6I r~[ I 1 1 1 9 1 ’ ! 1 9[ I 0 III II 1I ‘ I 1 I 99 I 4 I ( “ 1 I I ! —— Alpha = 200 — Alpha= 400 ---- Alpha = 800 I I

-46t ChartA6 I , Japan . 8 I I I -1 1 II 6 - . . ----- 4-- I- - : ------------------------- -------------------------------- --- I I ‘1’ 0 \L 4 -------- --I r - ---- -------------------- -------------------- --------------- ! r --j *-1-------------------------------------------------------------- # I 9. I ----- 1, iy~ / I ,\! ‘ ~\ ’~’\ I v I I \ f I -2 --- ---- 4 ---- -- \ --- --- ----------------------------- --------- I I I N 4 +-- ----- ----- :yL-- --- v ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- - -- ,1 II f I -6 i’1[11[[1’”’ 1 1970 ‘ 1974‘ “ I 1 ( 9 , 78 1982 IIl”rlll’’rl[llll 1986 Ilrllr ‘ ’’’’[lrli 1 llll 990 1.1 ‘ ’ 1994( “ Alpha = 200 — Alpha= 400 ---- Alpha = 800 I l—— I

-47- UnitedStates 4 I ! I I I 4 I , I II 1 VI I I 2 -------- /\-- ----------- - ------ ---- - - - - - - -_t I ~ I 1 h I I I o d I \ “2 +- \, - ------ - - )/)/ \ \ I II N i I ! I ,! /t I ! -4 -------------- I ----------------- ,1 ‘,I‘ Ii 1 I-I ‘ I \ I i \ 4 I I I 4 i I iI I 1970 1974 f 1 ‘ II I “ 1 1’ 1T 9 T 7 1 8IIII(I“1982‘“‘T‘19T86 , ‘“i“’I1’191I9“0’’’1’9’9’4”I Ir ‘ I Alpha = 200 — Alpha= 400 ---- Alpha = 800 I !——

-48- References Adams, Charlesand DavidT. Coe. “A SystemsApproachto Estimatingthe NaturalRateof Unemploymentand Potential Output for the United States.” LW SfaffPapers37 (June 1990):232-93. Beveridge,Stephenand Charles R. Nelson. “ANew Approachto Decompositionof Economic Time Seriesinto Permanentand TransitoryComponentswith ParticularAttentionto Measurementof the Business Cycle.’”JournaZofMonefa~ Economics7 (March 1981):151-74. Blanchard,Olivierand Danny DynamicEffectsof AggregateDemandand Supply Disturbances.” AmericanEconomicReview79 (September 1989):655-73. Hodrick RobertJ. and EdwardC. Prescott. Post-WarU.S. BusinessCycles:An Empirical Investigation. DiscussionPaper 451. Evanston,11:Centerfor MathematicalStudiesin EconomicsandManagementScience,NorthwesternUniversity,1980. Kuttner, “EstimatingPotentialOutput as a Latent Variable.” JournalofBusinessand EconomicStatistics12:3 (July1994). Laxton, Douglasand RobertTetlow. “A SimpleMuitivariateFilter for the Measurementof PotentialOutput.” Bankof Canada TechnicalReportNo. 59 (1992). Laxton, Douglas,Kevin Shoom,and Robert Tetlow. “Shouldthe change in the gap appearin the Phillips Cume?: Some Consequencesof MismeasuringPotentialOutput.” WorkingPaper 92-I. Ottawa: Bankof Canada (January 1992). OECD EconomicOutlook,“EstimatingPotential Output,OutputGaps,and StructuralBudget Balances,”56, December1994:31-37.

-49- InternationaI Finance Discussion Papers IFDP Number Titles Author(s] 1996 561 Inflation-AdjustedPotentialOutput JaneT. Haltmaier 560 TheManagementofFinancialRisksat German Allen B. Frankel NonfinancialFirms: Thecaseof Metallgesellschafl DavidE. Palmer 559 Broad MoneyDemandandFinancialLiberalization Neii R. Ericsson inGreece SunilSharma 558 StockholdingBehaviorofU.S.Households:Evidence CarolC. Bertaut bm the 1983-89SumeyofConsumerFinances 557 Finn SizeandtheImpactofProfit-MarginUncertainty VivekGhosal onInvestment:DO FinancingConstraintsPlaya Role? PrakashLoungani 556 RegulationandtheCostofCapitalinJapan: A Case JohnAmmer Study MichaelS. Gibson 555 TheSovereigntyOption: TheQuebecReferendumand MichaelP. Leahy MarketViewson the CanadianDollar CharlesP. Thomas 554 RealExchangeR and Inflation inExchange-Rate StevenB. Kamin BasedStabilizations: An EmpiricalExamination 553 MacroeconomicStateVariablesas Determinants JohnAmmer of Asset Price Covariances 552 The Tequila Effect: Theoryand Evidencefrom MartinUribe Argentina 551 The Accumulationof HumanCapital: Alternative MuratF. Iyigun Methodsand W T Matter Ann L. Owen 550 Alternatives in Human CapitalAccumulation: MuratF. Iyigun Implicationsfor EconomicGroti Ann L. Owen 549 More Evidenceon theLink be~een Bank MichaelS. Gibson Health and Investment inJapan 548 TheSyndromeofExchange-Rate-Based EnriqueG. Mendoza Stabilizationand the UnceminDurationof MartinUribe Currency Pegs Pleaseaddressrequests for copiesto InternationalFinanceDiscussionPapers, Divisionof InternationalFinance, Stop 24, Bored of Governorsof the Federal Reserve System, Washington,D.C. 20551.

-50- International Finance Discussion Papers IFDP Number Titles Author(s) 1996 547 GemmnUnification: what Have We Learned JosephE. Gagnon horn Multi-CountryModels? PaulR. Masson WarwickJ. McKibbin 546 Returnsto ScaieinU.S.Production:Estimates SusantoBasu andImplications JohnG. Femaid 545 Mexico’sBalance-of-paymentCsrisis: A Chronicle GuillermoA. Calvo of Death Foretold 544 The Twin Crises: The C of Bankingand GracielaL. Kaminsky Balance-of-PaymentsProblems CarmenM. Reinhart 543 HighRealInterestR in the Afierrnathof GracielaL. Kaminsky Disinflation: Is it a bck of Credibility? LeonardoLeiderman 542 PrecautionaryPotioiio Behaviortim a Life-Cycle CarolC. Bertaut Perspective MichaelHaliassos 541 UsingOptionsPricesto Infer PDF’s for AssetPrices: WilliamR. Meiick An Applicationto Oil Prices During the Gulf Crisis ChariesP. Thomas 540 MonetaryPolicyin the End-Gameto Exchange-Rate StevenB. Kamin Based!Nabili=tions: The Caseof Mexico John H. Rogers 539 ComparingtheWelfw Costsand the InitialDynamics MartinUribe of AlternativeTempomy StabilizationPolicies 538 Long Memo~ in Inflation Expectations: Evidence JosephE. Gagnon horn InternationalFin~ciai Markets 537 UsingMeasuresof Expectationsto Identifi the Allan D. Bmnner Effectsof a MonetaryPolicy Shock 536 RegimeSwitchingin t DynamicRelationship ChanHuh behveenthe FedemiFundsRateand Innovationsin NonborrowedReserves 535 The RisksandImplicationsofExternalFinancial EdwinM.Truman Shocks: Lessonsfrom Mexico 534 CurnmcyCrashesin EmergingMarkets: h Jeffrey A. Frankei EmpiricalTreatment AndrewK. Rose