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1、JournalofEconomicPerspectivesÐVolume15,Number4ÐFall2001ÐPages87±100ApplicationsofGeneralizedMethodofMomentsEstimationJeffreyM.Wooldridgehemethodofmomentsapproachtoparameterestimationdatesbackmorethan100years(Stigler,1986).Thenotionofamomentisfunda-Tmentalfordescribing
2、featuresofapopulation.Forexample,thepopula-tionmean(orpopulationaverage),usuallydenotedm,isthemomentthatmea-surescentraltendency.Ifyisarandomvariabledescribingthepopulationofinterest,wealsowritethepopulationmeanasE(y),theexpectedvalueormeanofy.(Themeanofyisalsocalledt
3、he®rstmomentofy.)Thepopulationvariance,2usuallydenotedsorVar(y),isde®nedasthesecondmomentofycenteredabout2itsmean:Var(y)5E[(y2m)].Thevariance,alsocalledthesecondcentralmoment,iswidelyusedasameasureofspreadinadistribution.Sincewecanrarelyobtaininformationonanentirepopu
4、lation,weuseasamplefromthepopulationtoestimatepopulationmoments.If{yi:i51,...,n}isasamplefromapopulationwithmeanm,themethodofmomentsestimatorofmisjustthesampleaverage:y#5(y11y21...1yn)/n.Underrandomsampling,y#isunbiasedandconsistentformregardlessofotherfeaturesoftheun
5、derlyingpopulation.Further,aslongasthepopulationvarianceis®nite,y#isthebestlinear2unbiasedestimatorofm.Anunbiasedandconsistentestimatorofsalsoexistsand21iscalledthesamplevariance,usuallydenoteds.Methodofmomentsestimationappliesinmorecomplicatedsituations.Forexample,su
6、pposethatinapopulationwithm.0,weknowthatthevarianceis2threetimesthemean:s53m.Thesampleaverage,y#,isunbiasedandconsistent1SeeWooldridge(2000,appendixC)formorediscussionofthesamplemeanandsamplevarianceasmethodofmomentsestimators.yJeffreyM.WooldridgeisUniversityDistingui
7、shedProfessorofEconomics,MichiganStateUniversity,EastLansing,Michigan.Hise-mailaddressis^wooldri1@msu.edu&.88JournalofEconomicPerspectives2form,butsoisadifferentestimator,namely,s/3.Theexistenceoftwounbiased,consistentmethodofmomentsestimatorsraisesanobviousquestion:W
8、hichshouldweuse?Onepossibleansweristochoosetheestimatorwiththesmallestsamplingvariance,sothatweobtainthemostpreciseestimator
