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1、Thisfileandseveralaccompanyingfilescontainthesolutionstotheodd-numberedproblemsinthebookEconometricAnalysisofCrossSectionandPanelData,byJeffreyM.Wooldridge,MITPress,2002.TheempiricalexamplesaresolvedusingvariousversionsofStata,withsomedatingbacktoStata4.0.Partlyoutoflaziness,butalsobecauseitisusef
2、ulforstudentstoseecomputeroutput,IhaveincludedStataoutputinmostcasesratherthantypetables.Insomecases,IdomorehandcalculationsthanareneededincurrentversionsofStata.Currently,therearesomemissingsolutions.Iwillupdatethesolutionsoccasionallytofillinthemissingsolutions,andtomakecorrections.Forsomeproble
3、msIhavegivenanswersbeyondwhatIoriginallyasked.Pleasereportanymistakesordiscrepenciesyoumightcomeacrossbysendingmee-mailatwooldri1@msu.edu.CHAPTER2dE(y
4、x1,x2)dE(y
5、x1,x2)2.1.a.-----------------------------------------------------dx=b1+b42xand-----------------------------------------------------dx=b2
6、+2b32x+b41x.122b.Bydefinition,E(u
7、x1,x2)=0.Becausex2andxx12arejustfunctionsof(x1,x2),itdoesnotmatterwhetherwealsoconditiononthem:2E(u
8、x1,x2,x2,xx12)=0.c.AllwecansayaboutVar(u
9、x1,x2)isthatitisnonnegativeforallx1andx2:E(u
10、x1,x2)=0innowayrestrictsVar(u
11、x1,x2).2.3.a.y=b0+b11x+b22x+b312xx+u,whereuhasaz
12、eromeangivenx1andx2:E(u
13、x1,x2)=0.Wecansaynothingfurtheraboutu.b.dE(y
14、x1,x2)/dx1=b1+b32x.BecauseE(x2)=0,b1=1E[dE(y
15、x1,x2)/dx1].Similarly,b2=E[dE(y
16、x1,x2)/dx2].c.Ifx1andx2areindependentwithzeromeanthenE(xx12)=E(x1)E(x2)2=0.Further,thecovariancebetweenxx12andx1isE(xx12Wx1)=E(xx12)=2E(x1)E(x2)(byindep
17、endence)=0.Asimilarargumentshowsthatthecovariancebetweenxx12andx2iszero.Butthenthelinearprojectionofxx12onto(1,x1,x2)isidenticallyzero.Nowjustusethelawofiteratedprojections(PropertyLP.5inAppendix2A):L(y
18、1,x1,x2)=L(b0+b11x+b22x+b312xx
19、1,x1,x2)=b0+b11x+b22x+b3L(xx12
20、1,x1,x2)=b0+b11x+b22x.d.Equation(
21、2.47)ismoreusefulbecauseitallowsustocomputethepartialeffectsofx1andx2atanyvaluesofx1andx.2Undertheassumptionswehavemade,thelinearprojectionin(2.48)doeshaveasitsslopecoefficientsonx1andx2thepartialeffectsatthepopu
