在计量经济学的Endogeneity : 同时等式模型(1)EndogeneityinEconometrics:SimultaneousEquationsModelsMingLUSimultaneityThisariseswhenoneormoreoftheexplanatoryvariablesisjointlydeterminedwiththedependentvariable,typicallythroughanequilibriummechanism.Themethodofinstrumentalvariables.Whydoweneedtoestimatestru...
EndogeneityinEconometrics:SimultaneousEquationsModelsMingLUSimultaneityThisariseswhenoneormoreoftheexplanatoryvariablesisjointlydeterminedwiththedependentvariable,typicallythroughanequilibriummechanism.Themethodofinstrumentalvariables.Whydoweneedtoestimatestructuralmodelratherthanreduced-formmodel?THENATUREOFSIMULTANEOUSEQUATIONSMODELSConceptsEndogenousvariablesExogenousvariablesStructuralerrorsEachequationshouldhaveabehavioral,ceterisparibusinterpretationonitsown.SIMULTANEITYBIASINOLSsimultaneitybiasIDENTIFYINGANDESTIMATINGASTRUCTURALEQUATIONIdentificationinaTwo-EquationSystemThefirstissupplyequation.Thesecondisdemandequation.Ageneraltwo-equationmodelExclusionrestrictionsInotherwords,weassumethatcertainexogenousvariablesdonotappearinthefirstequationandothersareabsentfromthesecondequation.RANKCONDITIONFORIDENTIFICATIONOFASTRUCTURALEQUATIONThefirstequationinatwo-equationsimultaneousequationsmodelisidentifiedifandonlyifthesecondequationcontainsatleastoneexogenousvariable(withanonzerocoefficient)thatisexcludedfromthefirstequation.Theorderconditionisnecessaryfortherankcondition.Therankconditionrequiresmore:atleastoneoftheexogenousvariablesexcludedfromthefirstequationmusthaveanonzeropopulationcoefficientinthesecondequation.Estimationby2SLSThisissimilarinthepreviouschapter.SYSTEMSWITHMORETHANTWOEQUATIONSORDERCONDITIONFORIDENTIFICATIONAnequationinanySEMsatisfiestheorderconditionforidentificationifthenumberofexcludedexogenousvariablesfromtheequationisatleastaslargeasthenumberofright-handsideendogenousvariables.Overidentifiedequation,justidentifiedequation,andunidentifiedequation.Estimation2SLS3SLS–MoreefficientusingtheresidualstodoGLSestimationatthethirdstage.Moresensitivetovariableselection.SIMULTANEOUSEQUATIONSMODELSWITHPANELDATA(1)eliminatetheunobservedeffectsfromtheequationsofinterestusingthefixedeffectstransformationorfirstdifferencing;(2)findinstrumentalvariablesfortheendogenousvariablesinthetransformedequation.Challenging,becauseforaconvincinganalysisweneedtofindinstrumentsthatchangeovertime.Howtodoifyouwanttoidentifythefixed-effects?Puttimedummiesandfixed-effectsdummiesinthestructuralmodel.Theend.
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