DummyVariablesDummyVariablesEarningsi=β1+β3MALEi+uiHowtointerpretthecoefficientsinthismodel?Weneedtofindmeanearningsforeachgenderbytakingconditionalexpectationofearnings:Meanearningsofmaleemployee:E(Earnings|MALE=1)=β1+β3.1+E(ui)=β1+β3Meanearningsoffemaleemployee:E(Earnings|MALE=0)=β1+β3.0+E(ui)=β1Earningsi=β1+β3MALEi+uiAverageearningsofmen:E(Earnings|MALE=1)=β1+β3Averageearningsofwomen:E(Earnings|MALE=0)=β1Thedifferenceinmeanearningsbetweenmaleandfemaleisgivenas:E(Earnings|MALE=1)–E(Earnings|MALE=0)=β3Consider,Earningsi=β1+β2Si+β3MALEi+uiAverageearningsofmale(forsamelevelofschooling):E(Earnings|MALE=1,S)=(β1+β3)+β2SiAverageearningsoffemale(forsamelevelofschooling):E(Earnings|MALE=0,S)=β1+β2SiThedifferenceinmeanearningsbetweenmaleandfemalewiththesamelevelofschooling:E(Earnings|MALE=1,S)–E(Earnings|MALE=0,S)=β3Thecoefficientβ3measuresthedifferentsalarylevelbetweenmenandwomen,holdingschoolingconstantDummyvariableMALEallowstheinterceptoftheearningsregressiontovaryacrossgenderGraphicalIllustration:Earningsi=β1+β2Si+β3MALE+u,β3>0Earningsi=b1+b2Si+b3MALEiFittedregressionformale:Earnings=(b1+b3)+b2SiFittedregressionforfemale:Earnings=b1+b2SiHowtotestwhetherthereisa‘genderdifferential’betweentwoemployeeswiththesameyearsofschooling?Needtocheckifb3issignificantornot:H0:β3=0H1:β3≠0orβ3>0Usingt-testcomputet-statisticandcomparewitht-criticalwithn–3d.fatαsignificancelevel…andrejectH0iftcomputed>tcriticalMicrofitregressionoutput:Earningsi=β1+β2Si+β3MALEi+uiAwordofcaution:DummyVariableTrapEarningsi=β1+β2Si+β3MALEi+uiObservethatMalehastwocategorieswhichismale&femaleQu.:Whydon’tIincludeanotherdummyvariableforfemale?Includingadummyfor‘female’wouldcreateperfectcollinearity(dummyvariabletrap)betweenthedummiesasthesingledummyvariableMALEalreadydefines‘female’asthebenchmarkgroupIntercepttermmeasurestheexcludedattribute,hereitgivesthebasicsalaryofafemaleworkerIfS=0,E(Earngs./Male=0)=β1,meaningthisissa