《计量经济学导论》ch7.ppt

©2012CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.Chapter7MultipleRegressionAnalysiswithQualitativeInformationWooldridge:IntroductoryEconometrics:AModernApproach,5e©2012CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.QualitativeInformationExamples:gender,race,industry,region,ratinggrade,…AwaytoincorporatequalitativeinformationistousedummyvariablesTheymayappearasthedependentorasindependentvariablesAsingledummyindependentvariableDummyvariable:=1ifthepersonisawoman=0ifthepersonisman=thewagegain/lossifthepersonisawomanratherthanaman(holdingotherthingsfixed)MultipleRegressionAnalysis:QualitativeInformation©2012CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.GraphicalIllustrationAlternativeinterpretationofcoefficient:i.e.thedifferenceinmeanwagebetweenmenandwomenwiththesamelevelofeducation.InterceptshiftMultipleRegressionAnalysis:QualitativeInformation©2012CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.DummyvariabletrapThismodelcannotbeestimated(perfectcollinearity)Whenusingdummyvariables,onecategoryalwayshastobeomitted:Alternatively,onecouldomittheintercept:ThebasecategoryaremenThebasecategoryarewomenDisadvantages:1)Moredifficulttotestfordiffe-rencesbetweentheparameters2)R-squaredformulaonlyvalidifregressioncontainsinterceptMultipleRegressionAnalysis:QualitativeInformation©2012CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.EstimatedwageequationwithinterceptshiftDoesthatmeanthatwomenarediscriminatedagainst?Notnecessarily.Beingfemalemaybecorrelatedwithotherproduc-tivitycharacteristicsthathavenotbeencontrolledfor.Holdingeducation,experience,andtenurefixed,womenearn1.81$lessperhourthanmenMultipleRegressionAnalysis:QualitativeInformation©2012CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.ComparingmeansofsubpopulationsdescribedbydummiesDiscussionItcaneasilybetestedwhetherdifferenceinmeansissignificantThewagedifferencebetweenmenandwomenislargerifnootherthingsarecontrolledfor;i.e.partofthedifferenceisduetodiffer-encesineducation,experienceandtenurebetweenmenandwomenNotholdingotherfactorsconstant,womenearn2.51$perhourlessthanmen,i.e.thedifferencebetweenthemeanwageofmenandthatofwomenis2.51$.MultipleRegressionAnalysis:QualitativeInformation©2012CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.Furtherexample:EffectsoftraininggrantsonhoursoftrainingThisisanexampleofprogramevaluationTreatmentgroup(=grantreceivers)vs.controlgroup(=nogrant)Istheeffectoftreatmentontheoutcomeofinterestcausal?HourstrainingperemployeeDummyindicatingwhetherfirmreceivedtraininggrantMultipleRegressionAnalysis:QualitativeInformation©2012CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.Usingdummyexplanatoryvariablesinequationsforlog(y)DummyindicatingwhetherhouseisofcolonialstyleAsthedummyforcolonialstylechangesfrom0to1,thehousepriceincreasesby5.4percentagepointsMultipleRegressionAnalysis:QualitativeInformation©2012CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.Holdingotherthingsfixed,marriedwomenearn19.8%lessthansinglemen(=thebasecategory)Usingdummyvariablesformultiplecategories1)Definemembershipineachcategorybyadummyvariable2)Leaveoutonecategory(whichbecomesthebasecategory)MultipleRegressionAnalysis:QualitativeInformation©2012CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.IncorporatingordinalinformationusingdummyvariablesExample:CitycreditratingsandmunicipalbondinterestratesMunicipalbondrateCreditratingfrom0-4(0=worst,4=best)Thisspecificationwouldprobablynotbeappropriateasthecreditratingonlycontainsordinalinformation.Abetterwaytoincorporatethisinformationistodefinedummies:Dummiesindicatingwhethertheparticularratingapplies,e.g.CR1=1ifCR=1andCR1=0otherwise.Alleffectsaremeasuredincomparisontotheworstrating(=basecategory).MultipleRegressionAnalysis:QualitativeInformation©2012CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.InteractionsinvolvingdummyvariablesAllowingfordifferentslopesInterestinghypotheses=interceptmen=interceptwomen=slopemen=slopewomenInteractiontermThereturntoeducationisthesameformenandwomenThewholewageequationisthesameformenandwomenMultipleRegressionAnalysis:QualitativeInformation©2012CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.GraphicalillustrationInteracting