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1、FoundationsandTrendsRinEconometricsVol.1,No1(2005)1–111c2007P.K.TrivediandD.M.ZimmerDOI:10.1561/0800000005CopulaModeling:*AnIntroductionforPractitionersPravinK.Trivedi1andDavidM.Zimmer21DepartmentofEconomics,IndianaUniversity,WylieHall105,Bloomington,IN47405,trivedi@indiana.edu
2、2WesternKentuckyUniversity,DepartmentofEconomics,1906CollegeHeightsBlvd.,BowlingGreen,KY42101.,dmzimmer@gmail.com,formerlyatU.S.FederalTradeCommissionAbstractThisarticleexploresthecopulaapproachforeconometricmodelingofjointparametricdistributions.Althoughtheoreticalfoundationsofc
3、op-ulasarecomplex,thispaperdemonstratesthatpracticalimplementa-tionandestimationarerelativelystraightforward.Anattractivefeatureofparametricallyspecifiedcopulasisthatestimationandinferencearebasedonstandardmaximumlikelihoodprocedures,andthuscopulascanbeestimatedusingdesktopeconome
4、tricsoftware.Thisrepresentsasubstantialadvantageofcopulasoverrecentlyproposedsimulation-basedapproachestojointmodeling.*TheauthorsaregratefultotheEditorBillGreeneandananonymousreviewerforhelpfulcommentsandsuggestionsforimprovement,butretainresponsibilityforthecontentsofthepresent
5、paper.1IntroductionThisarticleexploresthecopulaapproachforeconometricmodelingofjointparametricdistributions.Econometricestimationandinferencefordatathatareassumedtobemultivariatenormaldistributedarehighlydeveloped,butgeneralapproachesforjointnonlinearmodel-ingofnonnormaldataareno
6、twelldeveloped,andthereisafrequenttendencytoconsidermodelingissuesonacase-by-casebasis.Inecono-metrics,nonnormalandnonlinearmodelsarisefrequentlyinmodelsofdiscretechoice,modelsofeventcounts,modelsbasedontruncatedand/orcensoreddata,andjointmodelswithbothcontinuousanddis-creteoutco
7、mes.Existingtechniquesforestimatingjointdistributionsofnonlinearoutcomesoftenrequirecomputationallydemandingsimulation-basedestimationprocedures.Althoughtheoreticalfoundationsofcopulasarecomplex,thispaperdemonstratesthatpracticalimplementationandestimationisrelativelystraightforw
8、ard.Anattractivefeatureofpara-metrically
