计量虚拟变量讲解.ppt

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1、中级计量经济学INTERMEDIATEECONOMETRICS多元回归虚拟变量之二ChapterOutlineDescribingQualitativeInformationASingleDummyIndependentVariableUsingDummyVariableforMultipleCategoriesInteractionsInvolvingDummyVariablesABinaryDependentVariable:TheLinearProbabilityModel7/20/2021

2、2InteractionsAmongDummyVariablesInteractionsofdummyvariableswithotherdummyvariablesand/orotherexplanatoryvariablesmakestheregressionanalysismuchmorepowerful.Westartwiththeinteractionofadummywithanotherdummy.Interactionsofdummiesallowsanotherwaytoobser

3、veandtestgroupdifferenceamongdifferentgroups.7/20/20213InteractionsAmongDummyVariablesConsiderthewagemodelwithfemale-marriedinteractionwiththebasegroupstillbesinglemen:Thismodelalsoallowsustoobtaintheestimatedwagedifferentialamongallfourgroups,buthere

4、wemustbecarefultopluginthecorrectcombinationofzerosandones.Comment:norealadvantageoverusingmultipledummyvariables.Justanotherpossibleway.7/20/20214InteractingDummieswithOtherExplanatoryVariablesForwhat?Toallowdifferencesinslopes.Nowsupposethatwewishto

5、testwhetherthereturntoeducationisthesameformenandwomen,allowingforaconstantwagedifferentialbetweenmenandwomen.Weneedamodelthatallowsforaconstantwagedifferentialaswellasdifferentreturnstoeducation.7/20/20215InteractingDummieswithOtherExplanatoryVariabl

6、esTobemorespecific,wewishtomodeltobelog(wage)=β0+β1educ+uformale,log(wage)=β’0+β’1educ+uforfemale,whereβ0≠β’0aswehavealreadyfoundevidencethatthereexistswagedifferentialbetweenmaleandfemale.Letβ’0=β0+δ0,β’1=β1+δ1,thenwecancombinetheabovetwoequationsusi

7、ngadummyfemale:log(wage)=β0+δ0female+(β1+δ1female)educ+u,rearranging,log(wage)=β0+δ0female+β1educ+δ1female·educ+u,whereweobservethedummy,andtheinteractionofthedummywithotherexplanatoryvariables.7/20/20216InteractingDummieswithOtherExplanatoryVariables

8、Theequationlog(wage)=β0+δ0female+β1educ+δ1female·educ+u,showsthatδ0measuresthedifferenceininterceptsbetweenwomenandmen,andδ1measuresthedifferenceinthereturntoeducationbetweenwomenandmen.AfterweestimatetheaboveequationusingOLS,wecanperformhypot