Are Real Interest Rates Equal Across Countries An ...

1 THE JOURNAL OF FINANCE VOL. XXXIX, 1984 AreRealInterestRatesEqualAcrossCountries ?AnEmpiricalInvestigationofInternational ParityConditionsFREDERIC S. MISHKIN*ABSTRACTThis paperconductsempiricaltests oftheequalityof realinterest real rateequalityand the jointhypothesesofuncoveredinterest parity and ex anterelativePPP, or theunbiasednessofforwardrateforecastsand ex anterelativePPP. Theevidencesuggeststhat it isworthstudyingopeneconomymacroeconomicm odelswhichallow:1)domesticrealrates todifferfromworldrates,2)timevaryingrisk premiumsin theforwardmarket,or3)deviationsfromex , , ,Frenkel[11]andBilson[2].Ontheotherhand, financetheoryindicatesthatriskpremiamayw elldifferforcomparablesecuritiesdenomina tedindifferentcurrencies(Solnick[27],Rol landSolnick[26],Stulz[28],FamaandFarber[ 7],HansenandHodrick[17],andDornbusch[6]) ,andmorerecenttheoreticalmodelsintheexch angerateliterature,suchasDornbusch[5],Fr ankel[10],andMussa[24], ,thendomesticmonetaryauthoritieshavenoco ntrolovertheirrealraterelativetotheworld rate, ,asFeldstein[8]haspointedout,unlessrealr atescandifferacrosscountries, *GraduateSchoolofBusiness, thank thefollowingfor theirhelpfulcomments.

2 RobertCumby,ThomasDoan,RobertGordon,Fumi oHayashi,CraigHakkio,MarjorieMcElroy,Mic haelMussa,MichaelParkin, and the participants inworkshopsat theUniversityofLiverpoolSeminar in OpenEconomyMacroeconomics,The Board ofGovernorsof theFederalReserve,theUniversityofIllinoi s,Champaign-Urbana,NorthwesternUniversit y,Universityof WesternOntario,ColumbiaUniversity,Tulane University,and part of theNationalBureauofEconomicResearch' the Journal of Financeisintimatelylinkedtoandprovidesin formationonthebasicparityconditionsfeatu redsoprominentlyin open economy macro realratesacrosscountries,an exanteversionofpurchasingpowerparity,unc overedinterestparity,andtheunbiasednesso f forwardrateforecastsofexchangeratesovert he1967-11to isthenfollowed by 'srealrateofinterestforone-periodbondsis definedfromtheFisher[9]equationas(1)wher eif=thenominalinterestrateearnedon aone-periodbonddenominatedincountryj'scu rrencythatmaturesattimet, , it isthenominalreturnfromholdingtheone-peri odbondfromt-1 tot,7r?

3 =thecountry'srateofinflationfromt-1 totexpectedattimet-1,rr{=theone-periodre alrateofinterest.'Therealratedefinedabov e,whichis morepreciselyreferredto astheexanterealrate,is unobservableincontrasttotheexpostrealrat e,whichis definedas(2)whereeprr]=theone-periodexpo strealrateforthebondmaturingattimet,7r{= theactualinflationratefromt-1 tot, {=7rt-7r?= istheration-ality ofexpectationsinthebondmarket,which yieldstheconditionthattheforecasterrorof inflation, {,is unforecastableandhencerr{=E(eprr{I4>t-d( 3)IAllreturns,inflation,andinterestrates in theempiricalwork here arecontinuouslycompoundedsothatthe usualsecond-ordertermis notnecessaryin theFisherequation(1).)}}}}}}

4 Notethatif holdingperiodreturnsare used in theempiricalwork hereratherthancontinuouslycompoundedretu rns,thereis almostnochangein alsothatthisdefinitionof acountry'srealratematchesup the eurosecuritydenominatedin itscurrencywith itsinflationrate. Clearly, adomesticresidentmight beinterestedin the realrateobtainedbypurchasinga eurosecuritydenominatedin a , giventhatuncoveredinterestparityholds, inthiscase he willearnthesame will become obviousshortly,uncoveredinterestparityis intimatelyrelatedto theequalityof realratesacrosscountriesandthusit is onlynecessarytotesttheequalityof {-rd=E(eprr{-eprdIcPt-d=0(4)for unforecastablegivenanyinformationthatisa vailable at ,therearem(m-1)/2equationsofthetype above,butonlym - 1 ,thetestofthenullhypothesisof realrateequalityfor allcountriesisobtainedbyjointlytestingOl i=0 inthem - 1ordinaryleastsquares(OLS))}}

5 Regressionseprr{-eprr~=x.; +ui,j=2,..,m(5)whereXt-l=anyvariablesint heavailableinformationsetcPt-I,ui=E~-dun derthenullhypothesis,sothatE(uiIcPt-d=0 underrationalexpectations,andhenceuiwill beseriallyuncorrelatedunderthenull."Ther eare twoimportantpointsto (4) makes clear,thetestprocedureis valid foranyset of variables inXt-laslongastheyarecontainedin informationrelevanttothedeterminationof realratesindifferentcountriesis excluded fromXt-l,thetestproceduredescribedhere is valid;thatis, arejectionofthenullhypothesisis indeed arejectionoftheequalityof valid even whenrelevantinformationisignoredis acommonfeatureofrationalexpectationstest s(see AbelandMishkin[1]).)}

6 Onepitfallto beware isthatthesejointtestscannotbeconductedby estimatingeachcountry'sOLSconstrainedand unconstrainedregressionsseparately,addin guptheirsum ofsquares, be oftheparameterestimatesmustbe allowed for byusinggeneralizedleastsquares(GLS) whenconstructingtheteststatistics."As we have seen,thetestprocedureis validregardlessofthevariablesincludedinX t-las long , astheconditioninEquation(4) makes clear,theinformationsetXt-lmustbechosen2 Theparametersandtheirvariance-covarancem atrixwill beestimatedconsistentlywith OLSunderthe null, sothatteststatisticswill have , ifthe null is false, theujcould be seriallycorrelatedandthenthe power of thetestmight not be ,if thereis a failure to reject the null, we wouldwantto be surethatthisis not theresultof serialcorrelationin theEquation(5)regressionusingWPIdata(Dur bin-Watsonstatisticsof to )

7 ,butfirst-orderserialcorrelationis notpresentwhen CPIdataare used. In any case,strongrejectionsof the nullhypothesisarise ,theunbiasednessof the forward rate, and exantepurchasingpowerparity,no evidenceoffirst-orderserialcorrelationis proved more formally in a workingpaperversion ofthisarticle,Mishkin[22]. Notethattheparameterestimatesfrom the GLSprocedurewill beidenticaltothe OLSparameterestimatesbecause in thetestshere theexplanatoryvariablesin eachcountry'sregression are Financesothatithassignificantexplanatory powerintheexpostrealrateregressionsforth esecountriesifthestatisticaltestis ofEquation(5) as afourth-orderpolynomialintime.

8 Thatis,theXt-1variablesare aconstanttermandthefourvariablesTIME,TIM E2,TIME3,andTIME4 Thesetimevariablesareusedinthestatistica ltestsherebecauseinpreviousresearch(Mish kin[23]),theyhavebeenfoundtohavesignific antexplanatorypower,whileusingup fewdegreesoffreedom,"Clearly, , it ,wecanthinkofthetimevariablesas aproxyforthesmoothlymoving(lowfrequency) componentofeconomicvariablesthatarerelat edtorealrates,"Usingtheminthetestshereha stheadvantagethatthetestswillonlypickupd eviationsin , [25]hasnotedthat1)interestparity,2)anexa nteversionofpurchasingpowerparity(PPP),a nd3)theunbiasednessoftheforwardratesas ofthespotexchangerateandone-periodaheadf orwardrateforcountryjrelativetocountryig ivenattimet-1 asS{-landt-Ii{,respectively,theinterestp aritycondition(IP)isi{-ii=t-Iii-S{-lThee xanteversionofrelativePPPis7E(1r{-1r.}}} }}

9 -(s{-s{-dI t-d=0andtheunbiasednessofforwardratefore castsist-Ii{=E(s{I t-d(6)(7)(8)5 InMishkin[23], four lags ofinflation,the lagged money growth rate,andthenominaleuroratefor eachcountryhave been found to besignificantexplanatoryvariablesintheex post realrateregressionsfor includedthemintheX'-linformationset whenthenumberofcountries,m,is 7,thentherewould be 42variablesin each betestedwouldthenbe a very largenumber,252, and we wouldexpectthistestto have ,ontheotherhand, only involves5variablesper regression, for atotalof 30constraintsto be tested. Becausethesetimevariableshave been foundto havesignificantexplanatorypower inregressionsfor allthesecountries,we wouldexpectthistestto have muchgreaterpower because isdiscussedmoreextensivelyinMishkin[22]. ))}}}}

10 7 Thisis a weakerconditionthantheusualrelativePPPco nditionbecause it will besatisfiedevenif the log of the realexchangeratefollows ,findings such asFrenkel's[12]rejectingPPPbutfindingtha tthedeviationsfollow arandomwalk would beconsistentwithEquation(7). However, evidencediscussedlatersuggeststhateven exanterelativePPPis (6)and(8), weobtaintheuncoveredinterestparitycondit ion(VIP),which is alsoknownastheFisher-openhypothesis, ,E(i{-i:-(s{-s{-dItPt-d=0 Subtracting(7) from (9) we haveE(eprd-eprriItPt-d=0=rd- rd(9)(10)which , abreakdowninanyoftheconditionsin(6)-(9)c anleadto arejectionoftheequalityofrealrates,"Fren kelandLevich[13,14]andMcCormick[20] ,sinceinterestrateparityis apurearbitrageconditionfor eurorates,thereis somesuspicionthatmanyofthedeviationsmayb etheresultofdataproblems.)))}}}