Aspects-of-Maximum-Likelihood-EstimationPPT课件.ppt

Aspects of Maximum Likelihood EstimationApplied Econometrics 20.Aspects of Maximum Likelihood EstimationInvarianceReparameterizing the Log LikelihoodEstimating the Tobit ModelApplied EconometricsWilliam GreeneDepartment of EconomicsStern School of BusinessApplied Econometrics 21.Two Applications of Maximum Likelihood Estimation and a Two Step Estimation MethodModel for a Binary Dependent VariableoDescribe a binary outcome.nEvent occurs or doesnt(e.g.,the democrat wins,the person enters the labor force,nModel the probability of the eventoRequirementsn0 Probability 1nP(x)should be monotonic in x its a CDFTwo Standard ModelsoBased on the normal distribution:nProby=1|x=(x)=CDF of normal distributionnThe“probit”modeloBased on the logistic distributionnProby=1|x =exp(x)/1+exp(x)nThe“logit”modeloLog likelihoodnP(y|x)=(1-F)(1-y)Fy where F=the cdfnLog-L=i(1-yi)log(1-Fi)+yilogFi =i F(2yi-1)x since F(-t)=1-F(t)for both.Coefficients in the Binary Choice Models Ey|x=0*(1-Fi)+1*Fi =P(y=1|x)=F(x)The coefficients are not the slopes,as usual in a nonlinear modelEy|x/x=f(x)These will look similar for probit and logitApplication:Female Labor Supply1975 Survey Data:Mroz(Econometrica)Subsample of the 753 ObservationsDescriptive Statistics=Variable Mean Std.Dev.Minimum Maximum CasesLFP .600000000 .490880694 .000000000 1.00000000 250WHRS 799.840000 915.603480 .000000000 4950.00000 250KL6 .236000000 .511223432 .000000000 3.00000000 250K618 1.36400000 1.37077353 .000000000 8.00000000 250WA 42.9200000 8.42648340 30.0000000 60.0000000 250WE 12.3520000 2.16491186 5.00000000 17.0000000 250WW 2.27523000 2.59774974 .000000000 14.6310000 250HHRS 22.3483200 6.00670151 7.68000000 50.1000000 250HA 45.0240000 8.17132217 30.0000000 60.0000000 250HE 12.5360000 3.10600920 3.00000000 17.0000000 250HW 7.49443480 4.63619249 1.08980000 40.5090000 250FAMINC 23.0625400 12.9239815 3.30500000 91.0440000 250KIDS .684000000 .465845520 .000000000 1.00000000 250Marginal EffectsGARCH Models:A Model for Time Series with Latent Heteroscedasticity Bollerslev/Ghysel,1974ARCH ModelGARCH ModelEstimated GARCH Model