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EndogeneityinEconometrics:SimultaneousEquationsModels,MingLU,Simultaneity,Thisariseswhenoneormoreoftheexplanatoryvariablesisjointlydeterminedwiththedependentvariable,typicallythroughanequilibriummechanism.Themethodofinstrumentalvariables.Whydoweneedtoestimatestructuralmodelratherthanreduced-formmodel?,THENATUREOFSIMULTANEOUSEQUATIONSMODELS,Concepts,EndogenousvariablesExogenousvariablesStructuralerrorsEachequationshouldhaveabehavioral,ceterisparibusinterpretationonitsown.,SIMULTANEITYBIASINOLS,simultaneitybias,IDENTIFYINGANDESTIMATINGASTRUCTURALEQUATION,IdentificationinaTwo-EquationSystemThefirstissupplyequation.Thesecondisdemandequation.,Ageneraltwo-equationmodel,Exclusionrestrictions,Inotherwords,weassumethatcertainexogenousvariablesdonotappearinthefirstequationandothersareabsentfromthesecondequation.,RANKCONDITIONFORIDENTIFICATIONOFASTRUCTURALEQUATION,Thefirstequationinatwo-equationsimultaneousequationsmodelisidentifiedifandonlyifthesecondequationcontainsatleastoneexogenousvariable(withanonzerocoefficient)thatisexcludedfromthefirstequation.Theorderconditionisnecessaryfortherankcondition.Therankconditionrequiresmore:atleastoneoftheexogenousvariablesexcludedfromthefirstequationmusthaveanonzeropopulationcoefficientinthesecondequation.,Estimationby2SLS,Thisissimilarinthepreviouschapter.,SYSTEMSWITHMORETHANTWOEQUATIONS,ORDERCONDITIONFORIDENTIFICATION,AnequationinanySEMsatisfiestheorderconditionforidentificationifthenumberofexcludedexogenousvariablesfromtheequationisatleastaslargeasthenumberofright-handsideendogenousvariables.Overidentifiedequation,justidentifiedequation,andunidentifiedequation.,Estimation,2SLS3SLSMoreefficientusingtheresidualstodoGLSestimationatthethirdstage.Moresensitivetovariableselection.,SIMULTANEOUSEQUATIONSMODELSWITHPANELDATA,(1)eliminatetheunobservedeffectsfromtheequationsofinterestusingthefixedeffectstransformationorfirstdifferencing;(2)findinstrumentalvariablesfortheendogenousvariablesinthetransformedequation.Challenging,becauseforaconvincinganalysisweneedtofindinstrumentsthatchangeovertime.,Howtodoifyouwanttoidentifythefixed-effects?,Puttimedummiesandfixed-effectsdummiesinthestructuralmodel.,Theend.,
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