Panel Data Unit Root Tests with an Application

*Theworkforthispaperwasundertakeninthesecondhalfof2000whileIwasvisitingtheDepartmentofEconomicsoftheCentralEuropeanUniversity,Budapest.IwouldliketothankLászlóMátyásforhissupportandhelp.Ofcourse,theusualcaveatappliesforresponsibility.Commentsarefullyappreciated.Email:[e-mail]thanApplication*LászlóKónyaSchoolofAppliedEconomicsVictoriaUniversity,MelbourneAbstractUsingseveraldifferentunitroot/stationaritytestsonsingletimeseriesKónya(2000)foundthelogarithmofrealGDPofmostOECDcountriesbehavingasarandomwalkduringthelastfourdecades.Thisoutcome,however,mightbeduetothegenerallylowpowerofthesetests.Theaimofthispaperistoreconsiderthisissuebyexploitingtheextrainformationprovidedbythecombinationofthetime-seriesandcross-sectionaldataandthesubsequentpoweradvantagesofpaneldataunitroottests.WeapplythetestsadvocatedbyLevinandLin(1993),Im,PesaranandShin(1997)andMaddalaandWu(1999).Thejointunit-rootnullhypothesiscannotberejectedforthewholepanel,however,afterhavingdroppedtheleastlikelystationaryseriesfromthepanel,theIm,PesaranandShin(1997)andMaddalaandWu(1999)testscanrejectthenullfortheremainingsub-panels.Sincethesetestsarenotvalidundercross-correlatederrorterms,werepeatthemwithdataspecificbootstrapcriticalvaluestakingcontemporaneouscross-correlationintoaccount.Thisway,bothtestscanrejecttheunit-rootnullhypothesisevenforthewholepanel.Yet,theycannotsuggesthowmanyandwhichparticularpanelmembersarestationary,sotheseresultsarenotreallyinformative.Forthisreason,finallyweapplytheunit-roottestofBreuer,McNownandWallace(1999)withbootstrapcriticalvalues.Thisproceduremakesuseofthepaneldatasettingandseeminglyunrelatedregressions,butperformsseparateunit-roottestsoneachpanelmember.TheresultsaremarkedlydifferentfromtheconventionalunivariateDickey-Fullertestresults,andtheysupporttrendstationarityinthecaseoffourcountries:Australia,Japan,theNetherlandsandSwitzerland.February2001JELclassification:C12,C15,C22,C23,O57Keywords:unitroot,paneldata,GDP,OECDcountries.1Forareviewofthisissueseeeg.MaddalaandKim(1998),Chapter4.2I.IntroductionKónya(2000)studiedGrangercausalitybetweenthelogarithmsofrealexportsandGDPintheOECDcountriesduringthelastfourdecades.Inordertore-enforcetheresultstwocomplementarystrategieswereused.First,dependingonthepropertiesofthedata,causalitywastestedwithWaldtestswithinfinite-ordervectorautoregressive(VAR)modelsinlevelsand/orinfirst-differences.Then,amodifiedWaldprocedure,whichisvalidevenunderuncertaintyaboutintegrationandcointegration,wasappliedonlevelVARsystems.Thecleardisadvantageofthefirststrategyisitsdependenceonpreliminaryunit-rootandcointegrationtestoutcomeswhichthemselvesareoftenuncertainandmisleading.Forexample,theunitroottestsonthelogarithmsofrealGDPproducedambiguousorcontradictingresultsforabouttwothirdsofthecountriesconsidered.Thisissueisinthefocusofthispaper.Itiswell-documentedintheeconometricliteraturethatthemostpopularunitroottests,suchasthe(augmented)Dickey-Fuller(DF)andPhillips-Perron(PP)tests,havelowpoweragainstthestationaryalternative.1Consequently,theytendnottorejecttheunit-rootnull,evenifitisfalse.Thisproblemisparticularlysevereforthesamplesizesgenerallyusedinpractice(n#50).Therearebasicallytwopossiblesolutions.Ontheonehand,wecanturntoalternativeprocedures,likethemorepowerfulmodificationsoftheDFandPPtestsdevelopedbyElliott,RothenbergandStock(1996),PerronandNg(1996),theParkandFuller(1995)testbasedonaweightedsymmetricestimator,theLeybourne(1995)testbasedonreverseandforwardregressions,orthetestofKwiatkowski,Phillips,SchmidtandShin(1992)whichtakesstationarityasthenullhypothesis.Ontheotherhand,sincethepowerofanytestdependsontheavailableinformation,theoreticallytheperformanceofaunitroottestmaybeimprovedbyincreasingthesamplesize.Thiscanbeachievedbylongerdataspan,thougharelativelylongtimeseriesislikelytogothroughsomestructuralchangepotentiallycausingnewproblems.Alternatively,extrainformationcanbegainedbyusingpaneldata,i.e.bycombiningtime-seriesandcross-sectionalobservations.Thispaperfollowsthislatterrouteand,analysingthelogarithmsoftherealGDPseriesfromKónya(2000),comparesunivariateDFtestswithpaneldataunitroottests.First,weapplyconventionalunivariateDickeyandFuller(1979)Jtestsontheindividualseriesandrejecttheunit-rootnullhypothesisonlyfortwocountries,DenmarkandtheUSA..Then,weusethepaneldataunitroottestsadvocatedbyLevinandLin(1993),Im,PesaranandShin(1997)andMaddalaandWu(1999).Thejointunit-rootnullhypothesiscannotberejectedforthewholepanel.However,afterhavingdroppedtheleastlikelystationaryseriesfromthepanel,fortheremainingsub-panelstheIm,PesaranandShin(1997)andMaddalaandWu(1999)testsfindevidenceinfavourofthealternativehypothesisthatthereisatleastonestationaryseries.Sincethesetestsarenotvalidundercross-correlatederrorterms,werepeatthemwithdataspecificbootstrapcriticalvaluestakingcontemporaneouscross-correlationintoaccount.Thisway,bothtestscanrejecttheunit-rootnullhypothesisevenforthewholepanel.Yet,theycannotsuggesthowmanyandwhichparticularpanelmembersarestationary,sotheseresultsarenotreallyi