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1、ApEc8212EconometricAnalysis--Lecture#7SystemEstimationbyInstrumentalVariables(Wooldridge,Chapter8)I.IntroductionInthepreviouslectureweassumedthattheerrorterminanygivenequation(ug)wasuncorrelatedwiththeexplanatoryvariables(xg’s)inthatequation(thiswasAs
2、sumptionSOLS.1).Thisisunlikelytobetrueinmanyapplications.ThislectureexplainshowthiscanbeovercomeusingIVestimation.Wooldridgegivestwoexamples.Thefirstisestimatingalaborsupply(hoursofwork)function:h=γ1w+z1δ1+u1wherehishoursofworksupplied,wisthewageratea
3、ndthez1variablesareotherthingsthatwethinkaffectlaborsupply,suchasage,education,maritalstatus,numberofchildrenandnonlaborincome.Whathappensifthewageratealsodependsonhoursworked?Inthiscasethewagefunctionis:w=γ2h+z2δ2+u21Inthissystemof2equationsitisveryl
4、ikelythatu1iscorrelatedwithhandthatu2iscorrelatedwithw,evenifweassumethatbothuvariablesarenotcorrelatedwithallthez1andz2variables.Toseewhy,assumearandomjumpinu1.Thisclearlyincreasesh,anditalsoincreaseswthroughhinthesecondequation.Thusu1willbecorrelate
5、dwithw.Thesameargumentcanbeusedtoshowthatu2iscorrelatedwithh.Wooldridge’ssecondexampleistheimpactoftheHeadStartprogram(apreschoolprogram)onstudentperformanceinschool.Inthissimpletwoequationsystem,correlationbetweenthetwoerrortermscausescorrelationbetw
6、eentheerrortermandthedummyvariablefortheHeadStartprogramintheequationforthedeterminantsoftestscores.Infact,weknowhowtouseIVestimationforasingleequation.WhataretheadvantagesofestimatingasystemofequationsusingIV?Thetwoadvantagesarethesameasinthelastlect
7、ure:1.Increasedefficiency(smallerstandarderrors)2.Testingofcross-equationrestrictions.2II.AGeneralLinearSystemofEquationsThesystemofGlinearequationstobeestimatedis:yi=Xiβ+uiwhereyiisaG×1columnvector,XiisaG×Kmatrix,βisaK×1columnvectoranduiisaG×1columnv
8、ector.Thisisthesamemodelasinthepreviouslecture,butnowweareworriedthatsomeoftheu’sandsomeofthex’smaybecorrelated.Inthecaseofpaneldata,wesaythethereareTtimeperiods,andreplaceGbyT.HerearetheassumptionsweneedregardingIV’stogetconsistentestimatesof
