上海财经大学研究生试题命题纸

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1、上海财经大学研究生试题命题纸（20--20学年第学期）课程名称：计量经济学（I）（经济学院各专业）（B）命题教师：周亚虹1．Supposethatinthelinearmodely=+xuβ,Exu(')0=(wherexcontainunity).2Varux()=σ,butEux()≠Eu().22(a)IsittruethatEux()=σ?(b)Whatrelevancedoespart(a)haveforOLSestimation?2.Considerthesimpleregressionmodely=β++βxuand

2、letzbeabinaryinstrumentalvariable01n∑()zzyyii−(−)forx.Useβˆ=i=1toshowthattheIVestimatorβˆcanbewrittenas:1n1∑()zzxxii−(−)i=1βˆ=(y–y)/(x–x)11010Whereyandxarethesampleaveragesofyiandxioverthepartofthesamplewithz=0and00iwhereyandxarethesampleaveragesofyiandxioverthepartof

3、thesamplewithz=1.11i3.FortheclassicalnormalregressionmodelYX=β+εwithnoconstanttermandK2RK/regressors,whatispFlim[,KnKp−=]lim,assumingthatthetruevalueof2(1−−R)/(nK)βiszero?4.Inthediscussionoftheinstrumentalvariablesestimatorweshowedthattheleastsquaresestimatorbisbiased

4、andinconsistent.Nonetheless,bdoesestimatesomething:−1pblim==+θβQγ.Derivetheasymptoticcovariancematrixofb,andshowthatbisasymptoticallynormallydistributed.5.ProvethatunderthehypothesisthatRβ=q,theestimator2()YX−−bYX'(b)s=nKJ−+2WhereJisthenumberofrestrictions,isunbiasedf

5、orσ6．Thefollowingequationdescribesthemedianhousingpriceinacommunityintermsofamountofpollution(noxfornitrousoxide)andtheaveragenumberofroomsinhousesinthecommunity(rooms):log(price)=β+log(nox)+rooms+uββ012(a)Whataretheprobablesignsofβandβ?Whatistheinterpretationofβ?Expl

6、ain.121(b)Whymightnox[ormoreprecisely,log(nox)]androomsbenegativelycorrelated?Ifthisisthecase,doesthesimpleregressionoflog(price)onlog(nox)produceanupwardoradownwardbiasedestimatorofβ?1(c)UsingthedatainHPRICE2.RAW,thefollowingequationswereestimated:log(priceˆ)11.711.0

7、43log(nox)=−2nR==506,0.264log(priceˆ)=−9.230.718log(nox)+0.306rooms2nR==506,0.264Istherelationshipbetweenthesimpleandmultipleregressionestimatesoftheelasticityofpricewithrespecttonoxwhatyouwouldhavepredicted,givenyouranswerinpart(b)?Doesthismeanthat-.718isdefinitelycl

8、osertothetrueelasticitythan-1.043?Solution1:（a）Notingeneral.Theconditionalvariancecanalwaysbewrittenas22var()uxEuxEux=−()[()