北大暑期课程《回归分析》(Linear Regression Analysis)讲义PKU6

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1、Class6,Page7Class6:Auxiliaryregressionandpartialregressionplots.Moreindependentvariables?I.ConsequencesofIncludingIrrelevantIndependentVariablesWhataretheconsequencesofincludingirrelevantindependentvariables?Inotherwords,shouldwealwaysincludeasmanyindependentvariablesaspossible?Theanswerisno.Yoush

2、ouldalwayshavegoodreasonsforincludingyourindependentvariables.Donotincludeirrelevantindependentvariables.Therearefourreasons:A.MissingTheoreticallyInterestingFindingsB.ViolatingtheParsimonyRule(Occom'sRazor)C.WastingDegreesofFreedomD.MakingEstimatesImprecise.(e.g.,throughcollinearity).Conclude:Inc

3、lusionofirrelevantvariablesreducestheprecisionofestimation.II.ConsequencesofOmittingRelevantIndependentVariablesSaythetruemodelisthefollowing:.Butforsomereasonweonlycollectorconsiderdataony,x1andx2.Therefore,weomitx3intheregression.Thatis,weomitx3inourmodel.Theshortstoryisthatwearelikelytohaveabia

4、sduetotheomissionofarelevantvariableinthemodel.Thisissoeventhoughourprimaryinterestistoestimatetheeffectofx1orx2ony.Giveyouanexample.ForagroupofChineseyouthsbetweenages20-30:y=earningsx1=educationx2=partymemberstatusx3=ageIfweignoreage,theeffectsofeducationandpartymemberstatusarelikelytobebiased(1

5、)becausepartymembersarelikelytobeolderthannon-partymembersandoldpeopleearnmorethantheyoung.(2)becauseolderpeoplearelikelytohavemoreeducationinthisageinterval,andolderpeopleonaverageearnmorethanyoungpeople.Butwhy?Wewillhaveaformalpresentationofthisproblem.Class6,Page7III:EmpiricalExampleofIncremen

6、talR-SquaresXieandWu’s(2008,ChinaQuarterly)studyofearningsinequalityinthreeChinesecities:Shanghai,Wuhan,andXi’anin1999.Seethefollowingtables:Table1:PercentVarianceExplainedinLoggedEarningsVariablesDFR2DR2(1)DR2(2)City217.47***18.11***19.12***EducationLevel57.82***5.49***4.46***Experience+Experienc

7、e220.230.170.05Gender14.78***4.84***3.05***CadreStatus13.08***2.27***0.63***Sector33.54***2.18***1.80***DanweiProfitability(linear)112.52***9.30***DanweiProfitability(dummies)412.89***N=1771Note:DFreferstodegrees