第十讲 虚拟变量DUMMY VARIALBE

SIB-BFSU,ECONOMETRICSLECTURE101第十讲虚拟变量DUMMYVARIALBE•DUMMYVARIABLECLASSIFICATIONWITHTWOCATEGORIES•DUMMYCLASSIFICATIONWITHMORETHANTWOCATEGORIES•TWOSETSOFDUMMYVARIABLES•SLOPEDUMMYVARIABLESSIB-BFSU,ECONOMETRICSLECTURE102DUMMYVARIABLECLASSIFICATIONWITHTWOCATEGORIESThissequenceexplainshowyoucanincludequalitativeexplanatoryvariablesinyourregressionmodel.NCOSTOccupationalschoolsRegularschoolsSIB-BFSU,ECONOMETRICSLECTURE103DUMMYVARIABLECLASSIFICATIONWITHTWOCATEGORIESSupposethatyouhavedataontheannualrecurrentexpenditure,COST,andthenumberofstudentsenrolled,N,forasampleofsecondaryschools,ofwhichtherearetwotypes:regularandoccupational.NCOSTOccupationalschoolsRegularschoolsSIB-BFSU,ECONOMETRICSLECTURE104DUMMYVARIABLECLASSIFICATIONWITHTWOCATEGORIESTheoccupationalschoolsaimtoprovideskillsforspecificoccupationsandtheytendtoberelativelyexpensivetorunbecausetheyneedtomaintainspecializedworkshops.NCOSTOccupationalschoolsRegularschoolsSIB-BFSU,ECONOMETRICSLECTURE105DUMMYVARIABLECLASSIFICATIONWITHTWOCATEGORIESOnewayofdealingwiththedifferenceinthecostswouldbetorunseparateregressionsforthetwotypesofschool.NCOSTOccupationalschoolsRegularschoolsSIB-BFSU,ECONOMETRICSLECTURE106DUMMYVARIABLECLASSIFICATIONWITHTWOCATEGORIESHoweverthiswouldhavethedrawbackthatyouwouldberunningregressionswithtwosmallsamplesinsteadofonelargeone,withanadverseeffectontheprecisionoftheestimatesofthecoefficients.NCOSTOccupationalschoolsRegularschoolsSIB-BFSU,ECONOMETRICSLECTURE107OCC=0RegularschoolCOST=b1+b2N+uOCC=1OccupationalschoolCOST=b1'+b2N+uDUMMYVARIABLECLASSIFICATIONWITHTWOCATEGORIESAnotherwayofhandlingthedifferencewouldbetohypothesizethatthecostfunctionforoccupationalschoolshasaninterceptb1'thatisgreaterthanthatforregularschools.NCOSTOccupationalschoolsRegularschoolsb1b1'SIB-BFSU,ECONOMETRICSLECTURE108DUMMYVARIABLECLASSIFICATIONWITHTWOCATEGORIESEffectively,wearehypothesizingthattheannualoverheadcostisdifferentforthetwotypesofschool,butthemarginalcostisthesame.Themarginalcostassumptionisnotveryplausibleandwewillrelaxitinduecourse.NCOSTOccupationalschoolsRegularschoolsOCC=0RegularschoolCOST=b1+b2N+uOCC=1OccupationalschoolCOST=b1'+b2N+ub1b1'SIB-BFSU,ECONOMETRICSLECTURE109DUMMYVARIABLECLASSIFICATIONWITHTWOCATEGORIESdLetusdefinedtobethedifferenceintheintercepts:d=b1'-b1.NCOSTOccupationalschoolsRegularschoolsOCC=0RegularschoolCOST=b1+b2N+uOCC=1OccupationalschoolCOST=b1'+b2N+ub1b1'SIB-BFSU,ECONOMETRICSLECTURE1010DUMMYVARIABLECLASSIFICATIONWITHTWOCATEGORIESThenb1'=b1+dandwecanrewritethecostfunctionforoccupationalschoolsasshown.NCOSTOccupationalschoolsRegularschoolsb1+ddOCC=0RegularschoolCOST=b1+b2N+uOCC=1OccupationalschoolCOST=b1+d+b2N+ub1SIB-BFSU,ECONOMETRICSLECTURE1011CombinedequationCOST=b1+dOCC+b2N+uOCC=0RegularschoolCOST=b1+b2N+uOCC=1OccupationalschoolCOST=b1+d+b2N+uDUMMYVARIABLECLASSIFICATIONWITHTWOCATEGORIESWecannowcombinethetwocostfunctionsbydefiningadummyvariableOCCthathasvalue0forregularschoolsand1foroccupationalschools.NCOSTOccupationalschoolsRegularschoolsdb1b1+dSIB-BFSU,ECONOMETRICSLECTURE1012DUMMYVARIABLECLASSIFICATIONWITHTWOCATEGORIESDummyvariablesalwayshavetwovalues,0or1.IfOCCisequalto0,thecostfunctionbecomesthatforregularschools.IfOCCisequalto1,thecostfunctionbecomesthatforoccupationalschools.NCOSTOccupationalschoolsRegularschoolsdb1b1+dCombinedequationCOST=b1+dOCC+b2N+uOCC=0RegularschoolCOST=b1+b2N+uOCC=1OccupationalschoolCOST=b1+d+b2N+uSIB-BFSU,ECONOMETRICSLECTURE1013DUMMYVARIABLECLASSIFICATIONWITHTWOCATEGORIESWewillnowfitafunctionofthistypeusingactualdataforasampleof74secondaryschoolsinShanghai.01000002000003000004000005000006000007000000200400600800100012001400NCOSTOccupationalschoolsRegularschoolsSIB-BFSU,ECONOMETRICSLECTURE1014SchoolTypeCOSTNOCC1Occupational345,00062312Occupational537,00065313Regular170,00040004Occupational526.00066315Regular100,00056306Regular28,00023607Regular160,00030708Occupational45,00017319Occupational120,000146110Occupational61,000991DUMMYVARIABLECLASSIFICATIONWITHTWOCATEGORIESThetableshowsthedataforthefirst10schoolsinthesample.Theannualcostismeasuredinyuan,oneyuanbeingworthabout20centsU.S.atthetime.Nisthenumberofstudentsintheschool.SIB-BFSU,ECONOMETRICSLECTURE1015SchoolTypeCOSTNOCC1Occupational345,00062312Occupational537,00065313Regular170,00040004Occupational526.00066315Regular100,00056306Regular28,00023607Regular160,00030708Occupational45,00017319Occupational120,000146110Occupational61,000991DUMMYVARIABLECLASSIFICATIONWITHTWOCATEGORIESOCCisthedummyvariableforthetypeofschool.SIB-BFSU,ECONOMETRICSLECTURE1016.DependentVariable:COSTMethod:LeastSquaresDate:05/16/04Time:19:22Sample:174Includedobservations:74VariableCoefficientStd.Errort-StatisticProb.C-33612.5523573.47-1.4258640.1583N331.449339.758448.3365780.0000OCC133259.120827.596.3982010.0000R-squared0.615637Meandependentvar187418.0AdjustedR-squared0.604810S.D.dependentvar141969.9S.E.ofregression89248.09Akaikeinfocriterion25.67592Sumsquaredresid5.66E+11Schwarzcriterion25.76933Loglikelihood-947.0092F-statistic56.86072Durbin-Watsonstat2.422989Prob(F-statistic)0.00000