资源描述：
《ln12 Maximum Likelihood Estimation (MLE)》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、ApEc8212EconometricAnalysisII--Lecture#12MaximumLikelihoodEstimation(MLE)Reading:Wooldridge,Chapter13(Sections1-8)I.IntroductionMaximumlikelihoodestimation(MLE)methodsareonetypeofM-Estimationmethod.Inlinearmodels,itisraretouseMLEbecauseefficientestimatorscanbeobtained
2、withoutassumingthattheerrorterm(u)followsaparticularstatisticaldistribution.Innon-linearmodels,efficiencyishardertoshowwithoutmakingsometypeofassumptions.MLEmethodsareefficientinawidevarietyofcircumstancesifthedistributionalassumptionsarecorrect.Iftheassump-tionsareno
3、tcorrect,MLEmethodshavetheseriousdisadvantagethattheyare,ingeneral,inconsistent.Maximumlikelihoodmethodshavebecomelesspopularasothermethods(e.g.GMM,whichwillbediscussedinthenextlecture)havebeendeveloped,andasmorepowerfulcomputershavebeendeveloped(whichallowsforsemi-pa
4、rametricmethods).Buttheyarestillprettycommon,partlybecauseinsomecases(e.g.probitandlogit)itseemsthattheinconsistencyisnotveryserious.1II.PreliminariesandExamplesSupposethatwehaveGyvariables,denotedbyyiforobservationi,andKxvariables,denotedbyxi.Wewanttoestimatethecondi
5、tionaldistributionofyi,conditionalonxi.Wedon’treallycareaboutthedistributionofxinoreventhe(unconditional)distributionofyi.Sotechnicallyspeakingthislectureisonconditionalmaximumlikelihoodestimation(CMLE).Infact,unconditionalMLEisaspecialcaseofCMLE,inwhichwehavenoxvaria
6、bles.Toimplement(standard)(C)MLEweneedtospecifythedensity(distribution)ofyiconditionalonxi,whichinmostapplicationsisequivalenttospecifyingthedistributionoftheerrorterm(u).Wemustassumeaparametricdensity(onethathasafinitenumberofparameters)sowemustspecifyaparametricmode
7、lfortheconditionaldistributionofyi.Example1:SimpleProbitModelSupposethereissomeunobservedvariable,yi*,with:yi*=xi′θ+ei,Assumethateiisindependentofxi,thatxiandθeachhaveKelements,andei~N(0,1).Observedyiis:2yi=1ifyi*>0=0ifyi*≤0Itisconvenienttodefineanindicatorfunction,1[
8、z],thatequals1ifzis“true”andequalszeroifzis“nottrue”.Thisallowsusetodefineyias:yi=1[yi*>0].Considertheprobabilitythatyi=1,co
