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1、本文档系作者精心整理编辑，实用价值高。CHAPTER5SOLUTIONSTOPROBLEMS5.1Writey=+x1+u,andtaketheexpectedvalue:E(y) = +E(x1) +E(u),orµy = +µxsinceE(u)=0,whereµy=E(y)andµx =E(x1).Wecanrewritethisas =µy -µx.Now, = -.Takingtheplimofthiswehaveplim() =plim( -) =plim() –plim()plim()
2、 =µy -µx,whereweusethefactthatplim() =µy andplim() =µxbythelawoflargenumbers,andplim() =.WehavealsousedthepartsofPropertyPLIM.2fromAppendixC.5.2Ahighertoleranceofriskmeansmorewillingnesstoinvestinthestockmarket,so >0.Byassumption,fundsandrisktolareposi
3、tivelycorrelated.Nowweuseequation(5.5),whered1 >0:plim() = +d1 >,sohasapositiveinconsistency(asymptoticbias).Thismakessense:ifweomitrisktolfromtheregressionanditispositivelycorrelatedwithfunds,someoftheestimatedeffectoffundsisactuallyduetotheeffectofri
4、sktol.5.3Thevariablecigshasnothingclosetoanormaldistributioninthepopulation.Mostpeopledonotsmoke,socigs =0foroverhalfofthepopulation.Anormallydistributedrandomvariabletakesonnoparticularvaluewithpositiveprobability.Further,thedistributionofcigsisskewed
5、,whereasanormalrandomvariablemustbesymmetricaboutitsmean.5.4Writey=+x +u,andtaketheexpectedvalue:E(y) = +E(x) +E(u),orµy = +µx,sinceE(u) =0,where µy =E(y)andµx =E(x).Wecanrewritethisas =µy -µx.Now, = -.Takingtheplimofthiswehaveplim() =plim( -) =plim()
6、–plim()×plim() =µy -µx,whereweusethefactthatplim() =µyandplim() =µxbythelawoflargenumbers,andplim() =.WehavealsousedthepartsofthePropertyPLIM.2fromAppendixC.CHAPTER6SOLUTIONSTOPROBLEMS6.1Thegeneralityisnotnecessary.Thetstatisticonroe2isonlyabout-.30,wh
7、ichshowsthatroe2isverystatisticallyinsignificant.Plus,havingthesquaredtermhasonlyaminoreffectontheslopeevenforlargevaluesofroe.(Theapproximateslopeis.0215 -.00016roe,andevenwhenroe =25 –aboutonestandarddeviationabovetheaverageroeinthesample–theslopeis.
8、211,ascomparedwith.215atroe =0.)6.2BydefinitionoftheOLSregressionofc0yionc1xi1,,ckxik,i =2,,n,thesolve本文档系作者精心整理编辑，如有需要，可查看作者文库其他文档。本文档系作者精心整理编辑，实用价值高。[Weobtainthesefromequations(3.13),wherewepluginthescaleddependentandindependentvariab
