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1、JOIJRNALOFEconometricsELSEZVIEIRJournalofEconometrics71(1996)389-397SemiparametricestimationofpartiallylinearpaneldatamodelsQiLi,ThanasisStengosDepartmentofEconomics,UniversityofGuelph,Guelph,Ont.NIG2WI.Canada(ReceivedJune1992;finalversionreceivedOct
2、ober1994)AbstractInthispaperweconsiderestimatingageneralpartiallylinearsemiparametricpaneldatamodel,whereweallowforsomeoftheregressorstobecorrelatedwiththeerrors.WeassumetheusualempiricalcaseofNlargeandTsmallandasinRobinson(1988)theproposedinstrument
3、alvariableestimatorisshowntobe&-consistent.Keywords:Semiparametric;Paneldata;Instrumentalvariables;PartiallylinearmodelsJELclassijcation:C14;C23.1.IntroductionEconomicresearchhasbeenenrichedbytheavailabilityofpaneldatathatmeasureindividualcross-secti
4、onalbehaviourovertime.Hsiao(1986)reviewstheliteratureofestimationandinferenceinparametricpaneldatamodels.Inthispaper,weadoptasemiparametricapproachtomodellingageneralpartiallylinearpaneldatamodel.Weallowsomeoftheregressorstobecorrelatedwiththeerrorte
5、rm.Weproposetoestimatethemodelbyinstrumentalvariable(IV)estimationbyadaptingRobinsons(1988)framework.TheproposedIVestimatorisshowntobefl-consistent.*Correspondingauthor.Wewouldliketothankaneditor,anassociateeditor,andtworefereesforhelpfulcomments.Wew
6、ouldalsoliketoacknowledgethefinancialsupportfromtheSocialSciencesandHumanitiesResearchCouncilofCanada.0304-4076/96/$15.0001996ElsevierScienceS.A.AllrightsreservedSSDI0304407694017118390Q.Li,T.StengoslJournalofEconometrics71(1996)389-3972.ThemodelWeco
7、nsiderthefollowingsemiparametricpaneldatamodel:Yit=XitP+e(zit)+42,i=l,...,N,t=l,...,T,(I)wherexitandzilareofdimensionpandqrespectively,/Iisapx1unknownparametervector,andthefunctionalformof0(.)isunknowntotheresearcher.Someorallthecomponentsofxitmaybec
8、orrelatedwiththeerrornit.WeconsiderthecommonempiricalcaseofNlargeandTsmall.Inordertogetafi-consistentestimatorof/I,wehave,asinRobinson(1988),toeliminatetheunknownfunctional0(.).Takingconditionalexpectationof(1)yieldsE(~itIZit)=E(xitIzit)P+@(zit).(2)S
