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1、TestingforCommonBreaksinaMultipleEquationsSystemTatsushiOkayPierrePerronzNationalUniversityofSingaporeBostonUniversityApril19,2009;Revised:July8,2011AbstractTheissueaddressedinthispaperisthatoftestingforcommonbreaksacrossorwithinequations.Ourframeworkisverygeneralandallowsintegratedregressorsandtr
2、endsaswellasstationaryregressors.Thenullhypothesisisthatsomesubsetsoftheparameters(eitherregressioncoecientsorelementsofthecovariancematrixoftheerrors)shareoneormorecommonbreakdates,withthebreakdatesinthesystemasymptoticallydistinctsothateachregimeisseparatedbysomepositivefractionofthesamplesize.U
3、nderthealternativehypothesis,thebreakdatesarenotthesameandalsoneednotbeseparatedbyapositivefractionofthesamplesize.Thetestcon-sideredisthequasi-likelihoodratiotestassumingnormalerrors,thoughasusualthelimitdistributionofthetestremainsvalidwithnon-normalerrors.Alsoofindepen-dentinterest,weprovideresu
4、ltsabouttheconsistencyandrateofconvergencewhensearchingoverallpossiblepartitionssubjectonlytotherequirementthateachregimecontainsatleastasmanyobservationsasthenumberofparametersinthemodel.Sim-ulationresultsshowthatthetesthasgood nitesampleproperties.Wealsoprovideanapplicationtovariousmeasuresofin
a
5、tiontoillustrateitsusefulness.Keywords:change-point,segmentedregressions,breakdates,hypothesistesting,modelselection,systemofregressions.Perronacknowledges nancialsupportforthisworkfromtheNationalScienceFoundationunderGrantSES-0649350.WearegratefultoDouglasSondakforadvicesonthecomputations.yDepart
6、mentofEconomics,NationalUniversityofSingapore,AS2Level6,Singapore117570(oka@nus.edu.sg).zDepartmentofEconomics,BostonUniversity,270BayStateRd.,Boston,MA,02215(perron@bu.edu).1IntroductionIssuesrelatedtostructuralchangehavereceivedaconsiderableamountofattentioninthestatisticsandeconometricsliteratur
7、e(seePerron,2006,forasurvey).Inthelast fteenyearsorso,substantialadvanceshavebeenmadeintheeconometricsliteraturetocovermodelsatalevelofgeneralitythatallowsahostofinterestingpracticalapplicationsinthecontext
