在计量经济学的Endogeneity ： 同时等式模型(1)

EndogeneityinEconometrics:SimultaneousEquationsModelsMingLUSimultaneity•Thisariseswhenoneormoreoftheexplanatoryvariablesisjointlydeterminedwiththedependentvariable,typicallythroughanequilibriummechanism.•Themethodofinstrumentalvariables.•Whydoweneedtoestimatestructuralmodelratherthanreduced-formmodel?THENATUREOFSIMULTANEOUSEQUATIONSMODELSConcepts•Endogenousvariables•Exogenousvariables•Structuralerrors•Eachequationshouldhaveabehavioral,ceterisparibusinterpretationonitsown.SIMULTANEITYBIASINOLSsimultaneitybiasIDENTIFYINGANDESTIMATINGASTRUCTURALEQUATION•IdentificationinaTwo-EquationSystem•Thefirstissupplyequation.Thesecondisdemandequation.Ageneraltwo-equationmodelExclusionrestrictions•Inotherwords,weassumethatcertainexogenousvariablesdonotappearinthefirstequationandothersareabsentfromthesecondequation.RANKCONDITIONFORIDENTIFICATIONOFASTRUCTURALEQUATION•Thefirstequationinatwo-equationsimultaneousequationsmodelisidentifiedifandonlyifthesecondequationcontainsatleastoneexogenousvariable(withanonzerocoefficient)thatisexcludedfromthefirstequation.•Theorderconditionisnecessaryfortherankcondition.•Therankconditionrequiresmore:atleastoneoftheexogenousvariablesexcludedfromthefirstequationmusthaveanonzeropopulationcoefficientinthesecondequation.Estimationby2SLS•Thisissimilarinthepreviouschapter.SYSTEMSWITHMORETHANTWOEQUATIONSORDERCONDITIONFORIDENTIFICATION•AnequationinanySEMsatisfiestheorderconditionforidentificationifthenumberofexcludedexogenousvariablesfromtheequationisatleastaslargeasthenumberofright-handsideendogenousvariables.•Overidentifiedequation,justidentifiedequation,andunidentifiedequation.Estimation•2SLS•3SLS–MoreefficientusingtheresidualstodoGLSestimationatthethirdstage.Moresensitivetovariableselection.SIMULTANEOUSEQUATIONSMODELSWITHPANELDATA•(1)eliminatetheunobservedeffectsfromtheequationsofinterestusingthefixedeffectstransformationorfirstdifferencing;•(2)findinstrumentalvariablesfortheendogenousvariablesinthetransformedequation.•Challenging,becauseforaconvincinganalysisweneedtofindinstrumentsthatchangeovertime.Howtodoifyouwanttoidentifythefixed-effects?•Puttimedummiesandfixed-effectsdummiesinthestructuralmodel.•Theend.