计量经济学面板回归讲义

ECONOMETRICS:Cross-SectionalAnalysis4CREDITS,68HOURSJianhuaGangSchoolofFinanceRenminUniversityofChinaSeptember2015JIANHUAGANG(RUC)ECONOMETRICS:Cross-SectionalAnalysisSEPTEMBER20151/126OUTLINEOBJECTIVESOBJECTIVES1Theory2Econometricmodeling3EconomicexplanationJIANHUAGANG(RUC)ECONOMETRICS:Cross-SectionalAnalysisSEPTEMBER20152/126OUTLINEWORKLOADWORKLOAD68teachinghoursProblemsets,experiments,end-termevaluationRevisionclassesbeforeend-termexamBloombergtrainings.JIANHUAGANG(RUC)ECONOMETRICS:Cross-SectionalAnalysisSEPTEMBER20153/126OUTLINEREFERENCEREFERENCEThereisnotabookthatcoversalltheinformationNotesareimportantNotintendedtogivedetails,shouldresorttoreferencesJIANHUAGANG(RUC)ECONOMETRICS:Cross-SectionalAnalysisSEPTEMBER20154/126OUTLINEREADINGSREADINGSOtherthanthelecturenotes,manyintroductoryeconometrictextbooksareavailable.Twoverygoodtextbooksatamoderatelevelare:1DamodarN.Gujarati,BasicEconometrics,5th.edition.,McGraw-HillHigherEducation,2003;2J.M.Wooldridge,IntroductoryEconometrics:AModernApproach,4th.edition.CengageLearning;3WilliamH.Greene,EconometricAnalysis,6edition.,PearsonEducation.JIANHUAGANG(RUC)ECONOMETRICS:Cross-SectionalAnalysisSEPTEMBER20155/126OUTLINEASSIGNMENTSASSIGNMENTSThreeproblemsets.JIANHUAGANG(RUC)ECONOMETRICS:Cross-SectionalAnalysisSEPTEMBER20156/126OUTLINECOMPUTINGCOMPUTINGOxmetrics-PcGiveexperiments;Bloombergtrainings.JIANHUAGANG(RUC)ECONOMETRICS:Cross-SectionalAnalysisSEPTEMBER20157/126OUTLINEEXAMSEXAMSTheend-termevaluationconsistsof:1Closed-bookexam:60%2Assignments(includingexperiments):30%3Attendance:10%,(absenttwiceandyouwillloseall).Finalexam:willbeofsimilarformasassignments;should…nishallthequestions.JIANHUAGANG(RUC)ECONOMETRICS:Cross-SectionalAnalysisSEPTEMBER20158/126TOPIC1SIMPLEREGRESSIONMODELTOPIC1SIMPLEREGRESSIONMODELReadings:Wooldridge,Ch.2JIANHUAGANG(RUC)ECONOMETRICS:Cross-SectionalAnalysisSEPTEMBER20159/126TOPIC1SIMPLEREGRESSIONMODELREGRESSIONANALYSISREGRESSIONANALYSISRegressionanalysisinvolvestheestimationandevaluationoftherelationshipbetweenavariableofinterest(dependentvariable,explainedvariable,regressand)andoneormoreothervariables(independentvariables,explanatoryvariables,regressors).Whatisestimation,prediction(forecast),the…tting?JIANHUAGANG(RUC)ECONOMETRICS:Cross-SectionalAnalysisSEPTEMBER201510/126TOPIC1SIMPLEREGRESSIONMODELCLASSICALNORMALSIMPLEREGRESSIONMODELCLASSICALNORMALSIMPLEREGRESSIONMODELGeneralizedideaofarandomsampleofnindependentlyandidenticallydistributed(i.i.d.)observationsfromNm,s2
.Havesampleofnindependentobservationsy1,...,yn,eachofwhichisnormallydistributedwithvariances2,butconditionalmeangovernedbyE(yi)=a+bxi,i=1,...,n.where,1aandbaretermedregressionparameters/regressioncoe¢cients.2Thetermxivarieswithi,butisnotrandom(nonstochastic,…xedinrepeatedsampling).3Whatissampling?JIANHUAGANG(RUC)ECONOMETRICS:Cross-SectionalAnalysisSEPTEMBER201511/126TOPIC1SIMPLEREGRESSIONMODELCLASSICALNORMALSIMPLEREGRESSIONMODELCLASSICALNORMALSIMPLEREGRESSIONMODELIfweregardE(yi)=a+bxiastheequationofastraightlinethen,1theinterceptaisthemeanofyiwhenxiequalszero;2theslopebisthechangeinthemeanofyiwhenxiincreasesbyoneunit.(Thisinterpretationoftheinterceptisnotalwayssensibleineconomicapplications.)JIANHUAGANG(RUC)ECONOMETRICS:Cross-SectionalAnalysisSEPTEMBER201512/126TOPIC1SIMPLEREGRESSIONMODELCLASSICALNORMALSIMPLEREGRESSIONMODELCLASSICALNORMALSIMPLEREGRESSIONMODELNow,if#i=yi(a+bxi)denotestheerror(ordisturbanceterm),thenwritesimpleregressionmodelas:yi=a+bxi+#i,#iNID(0,s2),i=1,...,n.(1)where‘NID’standsforNormallyandIndependentlyDistributed(andwewillusethisdenotationalot).Theassumptionthattheregressorxiisnonstochasticisinappropriateinmanyapplicationsineconomicsanditisrelaxedlater.JIANHUAGANG(RUC)ECONOMETRICS:Cross-SectionalAnalysisSEPTEMBER201513/126TOPIC1SIMPLEREGRESSIONMODELCLASSICALNORMALSIMPLEREGRESSIONMODELCLASSICALNORMALSIMPLEREGRESSIONMODELForthemoment,itisprobablymoreusefultothinkoftheclassicalassumptionasbeingappropriatewhenweconditionalonthevaluesofx1,...,xn.Thus,conditionaluponthevaluesofx1,...,xn,theyiareindependentnormalvariableswithmeansa+bxiandcommonconstantvariances2fori=1,...,n.JIANHUAGANG(RUC)ECONOMETRICS:Cross-SectionalAnalysisSEPTEMBER201514/126TOPIC1SIMPLEREGRESSIONMODELESTIMATIONOFPARAMETERSESTIMATIONOFPARAMETERSThefollowinggeneralapproachestoestimatea,bands2areconsidered:methodofmoments(MM);ordinaryleastsquares(OLS);andmaximumlikelihoodestimation(MLE).Theseslidesdonotcontainfullmathematicaldetails.JIANHUAGANG(RUC)ECONOMETRICS:Cross-SectionalAnalysisSEPTEMBER201515/126TOPIC1SIMPLEREGRESSIONMODELMETHODOFMOMENTSESTIMATIONMETHODOFMOMENTSESTIMATIONPopulationmomentsconditions(assumptionsprovidedbeforeasin(1)):E(ui)=0,E(xiui)=0,E(u2is2)=0.LettheMMestimatorofaandbbebaandbb,withassociatedresidualsbui=yi(ba+bbxi),i=1,...,n.JIANHUAGANG(RUC)ECONOMETRICS:Cross-SectionalAnalysisSEPTEMBER201516/126TOPIC1SIMPLEREGRESSIONMODELMETHODOFMOMENTSESTIMATIONMETHODOFMOMENTSESTIMATIONObtainMM:solvingthederivedequations(replacingE(.)byn1åi(.),anduibybui),theequationsare:åibui=åi[yi(b