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1、第七章 多元回归分析异方差问题的处理1contentsWhat’sheteroskedasticity?Whyworryaboutheteroskedasticity?Howtotesttheheteroskedasticity?Correctionsforheteroskedasticity?2What’sheteroskedasticity?3WhatisHeteroskedasticityRecalltheassumptionofhomoskedasticityimpliedthatcondition
2、alontheexplanatoryvariables,thevarianceoftheunobservederror,u,wasconstantvar(u
3、x)=s2(homoskedasticity)Ifthisisnottrue,thatisifthevarianceofuisdifferentfordifferentvaluesofthex’s,thentheerrorsareheteroskedasticvar(ui
4、xi)=si2(heteroskedasticity)Example:ifwee
5、xamineacrosssectionoffirmsinoneindustry,errortermsassociatedwithverylargefirmsmighthavelargervariancesthanthoseerrortermsassociatedwithsmallerfirms;salesoflargerfirmsmightbemorevolatilethansalesofsmallerfirms.Consideracross-sectionstudyoffamilyincomeandexp
6、enditures.Itseemsplausibletoexpectthatlowincomeindividualswouldspendatarathersteadyrate,whilethespendingpatternsofhighincomefamilieswouldberelativelyvolatile.4.xx1x2yf(y
7、x)ExampleofHeteroskedasticityx3..E(y
8、x)=b0+b1x5Patternsofheteroskedasticity6WhyWorryAb
9、outHeteroskedasticity?7WhyWorryAboutHeteroskedasticity?OLSisstillunbiasedandconsistent,evenifwedonotassumehomoskedasticityTheR2andadj-R2areunaffectedbyheteroskedasticity.ThestandarderrorsoftheestimatesarebiasedifwehaveheteroskedasticityTheOLSestimatesaren’
10、tefficient,that’sthevariancesoftheestimatesarenotthesmallestvariances.Ifthestandarderrorsarebiased,wecannotusetheusualtstatisticsorFstatisticsorLMstatisticsfordrawinginferences8Howtotesttheheteroskedasticity?9TestingforHeteroskedasticityGolfeld-QuandtTest1
11、0TestingforHeteroskedasticityGolfeld-QuandtTestEssentiallywanttotestH0:Var(u
12、x1,x2,…,xk)=s2,whichisequivalenttoH0:E(u2
13、x1,x2,…,xk)=E(u2)=s2H1:si2=cxi2.Goldfeld-Quandttestprocedure:Orderthedatabythemagnitudeoftheindependentvariablex,whichisthoughttoberelate
14、dtotheerrorvariance.Omitthemiddledobservations.dmightbechosen,forexample,tobeapproximately1/5ofthetotalsamplesize.Fitthetwoseparateregressions,thefirstfortheportionofthedataassociatedwithlowvaluesofxandthesec
