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1、SimultaneousEquationsModelsPhDEconometricsWeiTanHanqingAdvancedInstituteofEconomicsandFinanceRenminUniversityofChinaWeiTan(RUC)SimultaneousEquationsModels1/60TopicsIntroductionofSimultaneousEquationModelIdenti…cationofSEMEstimationofSEMExampleWeiTan(RUC
2、)SimultaneousEquationsModels2/60IntroductionofSEMModelsFore¤ectiveapplicationofSEMs,wemustunderstandthekindsofsituationssuitableforSEManalysis.We…rstconsideranexample.Example(LaborSupplyandWageO¤erEquations):Considerthefollowinglaborsupplyfunctionrepres
3、entingthehoursoflaborsupply,hs,atanywage,w,facedbyanindividual.Asusual,weexpressthispopulationformhs(w)=w+z+u(1)11111isthemaincoe¢cientofinterest.z1isavectorofobservedlaborsupplyshifters,suchaseducation,pastexperience,age,maritalstatus,numberofchildren
4、,andnonlaborincome,andu1containsunobservablesa¤ectinglaborsupply.WeiTan(RUC)SimultaneousEquationsModels3/60IntroductionofSEMModelsThelaborsupplyfunctioncanbederivedfromindividualutilitymaximizingbehavior,andthenotationinequation(1)isintendedtoemphasizet
5、hat,forgivenz1andu1,alaborsupplyfunctiongivesthedesiredhoursworkedatanypossiblewage(w)facingtheworker.Asapracticalmatter,wecanonlyobserveequilibriumvaluesofhoursworkedandhourlywage.Butthecounterfactualreasoningunderlyingequation(1)istheproperwaytoviewla
6、borsupply.WeiTan(RUC)SimultaneousEquationsModels4/60IntroductionofSEMModelsAwageo¤erfunctiongivesthehourlywagethatthemarketwillo¤erasafunctionofhoursworked.Forobservedproductivityattributesz2andunobservedattributesu2,wewritethewageo¤erfunctionaswo(h)=h+
7、z+u(2)22222isthemaincoe¢cientofinterest.z2isavectorofobservedlabordemandshifters,suchaslocalunemploymentrate,localgdpgrowthrate,andlocalindustryactivityindex.u2containsunobservablesa¤ectinglabordemandThelabordemandfunctioncanbederivedfrom…rmpro…tmaximi
8、zingbehavior.Foranygivenz2andu2,alabordemandfunctiontellsthewageo¤eredbytheemployeratanypossiblelaborinput.WeiTan(RUC)SimultaneousEquationsModels5/60IntroductionofSEMModelsTheabovelaborsupplyanddemandexampleisalegitimateSEMapplic
