计量经济学庞浩版习题5.3

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1、5.3下表是2007年我国各地区农村居民家庭人均纯收入与家庭人均生活消费支出的数据。表5.9各地区农村居民家庭人均纯收入与家庭人均生活消费支出的数据（单位：元）土也区家庭人均纯收入家庭生活消费支出地区家庭人均纯收入家庭生活消费支出北京9439.636399.27湖北3997.483090天津7010.063538.31湖南3904.23377.38河北4293.432786.77广东5624.044202.32山西3665.662682.57广西3224.052747.47内蒙古3953.13256.15海南3791.372556.56辽宁4773.433368.16重庆3509.292526

2、.7吉林4191.343065.44四川3546.692747.27黑龙江4132.293117.44贵州2373.991913.71I-.海10144.628844.88云南2634.092637.18江苏6561.014786.15西a2788.22217.62浙江8265.156801.6陕西2644.692559.59安徽3556.272754.04甘肃2328.922017.21福建5467.084053.47W海2683.782446.5江西4044.72994.49宁夏3180.842528.76山东4985.343621.57新跚3182.972350.58河南3851.626

3、76.41（1）试根据上述数据建立2007年我国农村居民家庭人均消费支出对人均纯收入的线性回归模型。（2）选用适当方法检验模型是否在异方差，并说明存在异方差的理由。（3）如果存在异方差，用适当方法加以修正。（1）新建一个MicrosoftExcel匸作表，并录入全部数据。建立一元线性回归模型：&=0o+0X+O打开Eviews软件，进入主界面，点击FileNe叭Workfile,弹出WorkfileCreate对话框。在WorkfileCreate对话框左侧Workfilestructuretype栏中选择UnstructuredUndated选项，在右侧DataRange中填入样本个数31,

4、点击OKo定义解释变量X:在Workfile窗口中，点击0bjectsNewObjectseries,在Nameforobject中输入X,点击OK。以相同的方法定义被解释变量Y。按住Ctrl键,同时选中X、Y,右击0penasGroupEdit+/,复制Excel中的整列数据，右击选择Paste粘贴在Eviews中，将31组数据录入。点击主界面菜单QuickEstimateEquation选项，在弹出的对话框中输入:“YCX”，点击确定即可得到回归结果。EViewsFileEditObjectViewProcQuickOptionsWindowHelp匡莎RasasNQa|vieviewxj

5、obedPrintNameFreezeIEstimateIForecastIStatsResids399DependentVariable:YMethod:LeastSquaresDate:05/19/13Time17:06Sample:131Includedobservations:31VariableCoetncientSid.Errort-StatlstlcProbC179.1916221.57750.8087090.4263X0719500004570015.7441100000R-squarod0.895260MoandopondGntvar3376.309AdjustedR-squ

6、ard0891B49SDdependemyar1499.6123.E.cfregression4936240Akaikeinfocriterion1530377Sumsquaredresid7066274.ScnAarzcritorion15.39628Loglikelihood-2352084Hannan-Ouinnenter1533392F-statistic2478769Durbin-Watsonstat1.461684Prob(F-statistc)0.000000叵Equation:UNTITLEDWorkfile:UNTITLED:Untitled-axPath=ulusers孙库

7、documents08=noneNF=untitled由此可知，居民人均消费支出与可支配收入的线性模型为Y=179.1916+0.7195X(221.58)(0.0457)t=(0.8087)(15.7441)R2=0.8953F二247.87D.W.=1.4617RSS=7066274(2) 异方差性检验图示法检验生成残差序列。在Workfile窗口中点击ObjectGenerateSeries,在弹出的对话框中的Enterequation输入e2二resid2”，得到残差平方和序列e2。绘制e：对备的散点图。按住Ctrl键，先选择变量x,再选择e2,点击主界面菜单QuickGraph选项,

8、弹出的对话框中Graphtype的Specific选项选择Scatter,可得到散点图。3孙晖计星经济学习题EViewsFileEditObjectViewProcQuickOptionsWindowHelpRango1Sample1c2=：c5id2|(EnterequationFilter*excancelUnti(ledI、NewPege/园Workfile:UNTITLEDViw|ProcObject|PrintSaveDetails-,-1ShowFetchStoreloeietedsicfe3-GenerateSeriesbyEquation131Sairpie0EViewsFil

9、eEditObjectViewProcQjickOptonsWindowHelp国WorkfiLzJproqCGraphOptionsopaonPagesGraphTypePPath二c:sers孙眸idocumcntsDB二noneWF二untitledRange13Sample13(Ec0e2resid0xUntitleBasictype3Fremc&Sizci-Axes&Scalng5Leocnd3-GraphEfementsffl-QuickFonts3Tcmoetcs&ObjectsUndo%兀EditsGraphtypeGGTGfal：BasicgraphSpecific:Line

10、&Symbol5arSpkeAreaAreaBardMxedAithLinesDotPlotErrorEcrTd*；ow(Openlosc)ScatterXYUnexrqDstribuionQjantieQuartieBoxpbtGraphdata:RawdataFitlines:Artsherders:NonevoptionsNonevSngegraphCancelPath二c:serG孙documentsDB二noneWF二untitled4孙晖计星经济学习题由散点图可以看出，残差平方和崭对备大致存在递增关系，即存在单调增型异方差。Goldfe1d-Quanadt检验对变量取值排序。在Wo

11、rkfile窗口中点击ProcSortCurrentPage，在弹出对话框中输入x,点击OKo本列选择升序排列（默认项是Ascenging升序）,这时变量Y将以X按升序排列。5孙晖计星经济学习题ViewProc(ObjectPrint!Save园Workfile:UNTITLEDRango:131-31obsSample!31一31ob3Filter*.000S.00010Path二c:u,crs孙脸documentsDB二noneWF二untitledD吉ailshowFetthstHwDeletQ|GrnsamplSortWorkfileSeriesErteron亡ormoreseries

12、remesorseriesexpressionsSortorefer(SjAscerdngODescendngJUnMIedINgwPegE/2.0004.0006000Xp-ShadeRemoEViewsFileEditObjectViewProcQuickOptonsWindowHelp6孙晖计星经济学习题构造子样本区间，建立回归模型。在本题中，样本容量n二31,删除中间1/4的观测值，大约7个数据，余下部分平分得两个样本区间：112和2031,它们的样本个数均是12个，即*=坯=12。双击V/orkfile中的Sample一栏，弹出Sample对话框，将Samplerangepairs中

13、的改为“112”，这样就把区间定义为112。然后用OLS方法求得子样本区间的估计结果，即点击主界面菜单QuickEstimateEquation选项，在弹出的对话框中输入：“YCX”，弹出的DeleteUnt讥led对话框选择Yes。#孙晖计星经济学习题Workfile:UNTITLED-(c:users?/Jdesktopuntitled.wf.-nxView|ftrocObject|PrintSaveDetails-/-show|Fetchstore|DeleteGenrjsampie|Rango:13131obsFilterSample131一31obsBSEJUnMIedNewPwgE

14、/Path二c;users孙陰idocumtntsDB二noneWF二untitled0EViewsFileEditObjectViewProcQuickOptonsWindowHelpfaWorkfile:UNTITLED-Cc:users?/Jdesktopuntitled.wf.-xUiewjfocObject|PrintSaveDetails-/-showjFetchJstorejDeleteGenrjsampieFiller*Range:131-31obsS3mple1-34obsBSEresicSample5amoierangepars(orsarntfeobjecttoccpv)

15、l12-IFcondibon(opbonaQConedEViewsFileEditObjectViewProcQuickOptonsWindowHelp孙晖计星经济学习题孙晖计星经济学习题八UntitledI、NewPage/Path二c;uscrs孙陰idocumcntsDB二noneWF二untitled0EViewsFileEditObjectViewProcQuickOptonsWindowHelp(=Equation:UNTITLEDWorkfile:UNTITLED:Untitled-cXIViewProcODject|Print|Name|Freeze|Estimate|Fore

16、caststatiReadsDependentVanaDl:YMethod:LeastSquaresData：05/19/13Tima：17：18Sample:112incluaedooseivsticns:12VariableConicintStdErrorl-StatistlcProbC11112234095750271311200218X0.4519000.1364283.3123780.0078R-squarca0.523170Meandopendentvar2463.886AdjustedR-squared0475487S.D.dependentvar280.7556S.E.ofre

17、gression203.3323AkaiKeinfocriterion13.61857Sumsquaredresid413440.3Schwarzcriterion13.59939LogHKGiinooa79.71143Hannan-Quinnenter.13.58865F-statstic10.97185Durbin-Watscnstat2.030396PrOD(F-Sl2tlSfiC)0007848Path二c;sers孙晖documcntsDB二noneWF二untitled由此得到112的子样本区间的模型估计结果为:Y=U11.22+0.4519X(409.58)(0.1364)t=(

18、2.7131)(3.3124)R2=0.5232F=10.9719D.W=2.0304RSS】=413440.3同样的，双击Sample-栏，将区间定义为2031,用OLS方法求得估计结果。孙晖计戢经济学习题9孙晖计戢经济学习题EViewsFileEditObjectViewProcQuickOptonsWindowHelp-31obs一12obsrlliGCSamoierangeoars(orsamdeobjecttoccpy)2031X园Workfile:UNTITLED-Cc:users?KdesktopuntitledAvf.-x/lwlf0C|ObjectIPrintSaveDeta

19、ik*；-fshowlFetchlstorelDeleteGenrlsampie|Rango131Sample!SampleIFcondition(opbonai)2.97=I05(10,10),所以拒绝无异方差性假设,表明模型存在异方差性。White检验双击Workfile中的Sample一栏，将Samplerangepairs中的“2031”改为“all”或“131”,用0LS方法重新求得原模型的估计结果，点击Vie叭ResidualDiagnosticsHeteroskedasticityTests,弹出的对话框中Testtype选择White,得到White检验的结果。10孙晖计星经济

20、学习题11孙晖计星经济学习题0EViewsFileEdrtObjectViewProcQuickOptionsWindowHelpWorkfile:UNTITLED-(c:users?desktopuntilledAvf.-xUiewjProcObjectPrintSaveDerails/showFetthstowDeiwte|GwnrsamplwRange:1:Sample:2C1一31OtS31-12obsFiller*IdSampleSamoierangeoars(orsamdeobjecttoccpv)LFconditon(opbona)UrUiNedNewPeg?/Path二c:us

21、6眸idocumcntsDB二noneWF二untitledEViewsFileEditObjectVie內ProcQuickOptonsWindowHelp国Workfile:UfSevjprgdo映aRange131一Sample:131一(=)Equation:UNTITLEDWoridile:UNTITLED:Untitled-cx(E0l30eCe2resiUntitledNRepresentationsEstimationOutputActuoljitted.Residue1ARMAStructure.GradientsandDeivativiCovarianceMatrixStd

22、.Errort-StatisticProb.nfinP70QnICoefficientDiagncctcsJJ17!7004570015.7441100000ResidualDiagnosticsCcrrelogiamQ-statistics.StabilityDiagnosticsCorrelogramSquaredResiduals*.LabelHktogramNormalityTwstSerialCorrelationLMTest.F-statlsticPro0F-statistic)247876?0.00000(HetcroUredarticrtylest?.ViewjProc|OUj

23、ed|PrintjNome|FreezejEstimateForecastTaatsTRcsidsPath二documentsDB二noneWF二untitled#孙晖计星经济学习题EViewsFileEditObjectViewProcQuickOptonsWindowHelpUntitledb园Workfile:UlView|ProcObjectRango:131-Sample!31一12孙晖计星经济学习题#孙晖计星经济学习题Path二c;u,g孙蔭idocumcntsDB二noneWF二untitledEViewsFileEditObjectViewProcQjickOptonsWind

24、owHelp(=)Equation:UNTITLEDWorkfile:UNTITLED:Untitled-exviewProcjObjectJPrintjNomeFreezeEstimateForecast|StatsjResidsHeteroskedastlcltyTest:WhiteAF-statistic7194463Prob.F(228)00030ObsR-squarod10.52295Proo.Chi-Square(2)0.0052ScaledexplainedS330.03105Prob.Chi-SQuare(2)0.0000TestEquation:DependentVariab

25、le:RESIDEMethod:LeastSquaresData:05/19/13Timo17:24Sample:131indudsaooseRations:31variableCoetncientstdErrort-sratisticProb.CB98722764138900.10893909140X72.02221248.7240-0.2896670.7743K200203370020627093597203326R-squared0.339450Meandependents227944.3A(j4u$tecR-squared0.292268s.D.oependentvar592250.3

26、SEofregression498241.3Akaikeinfocriterion29.16732Sumsquaredresid695E+12Schwar2criterion2930510Loglikelihood449.0935HannarrQuinncriter2921256F-statistic7194463Durbin-Watsonstat2430258Pro0(F-statistic)0.003011V国Workfile:UrWevvJpnKObjectRange:131-Sample131ce2Untitled/hPath二c;u,g孙蔭idocumcntsDB二noneWF二un

27、titled由White检验结果得到：R-=0.339450White统计量11R2=31x0.339450=10.52，该值大于5%显著性水平下自由度为2的才分布的相应临界值加“妙，（在估计模型中含有两个解释变量,所以自由度为2）,因此拒绝同方差性的原假设。（3）异方差性的修正加权最小二乘法在对原模型进行OLS估计后，在Workfile窗口中点击ObjectGenerateSeries,在弹出的对话框中的Enterequation输入e二resid,得到新序列e。为了找到合适的权，作lne关于X的OLS回归，即点击主界面菜单QuickEstimateEquation选项，在弹出的对话框中输入

28、：aLOG（e2）CX”,弹出的DeleteUntitled对话框选择Yes。EViewsFileEditObjectViewProcQuickOptonsWindowHelp13孙晖计星经济学习题iew|ProcObject)jPrintSaveDetails*；-)show|Fetch|store|Delete|Genr|sample|Rango13Sample!3FilterGenerateSeriesbyEquationxWorkfile:UNTITLED-(c:users?ddesktopuntitled.wf.-nx120013EntercquotionCKcancelUntitl

29、ed?Path二c;u5crsJ星documentsD6二noneWF二untitled#孙晖计虽经济学习题14孙晖计虽经济学习题EViewsFileEditObjectViewProcQuickOptonsWindowHelp园Workfile:EquationEstimationRango:131一Sample131一UiwftrociObject-Equatorgpea令cationESEE92residLOG(“2)CXAVEstmationsertngsDependentvariablefollowedbylistofregressorsincludingandPDLterms,OR

30、anexplicitequationlikeY=c(1)+c(2)*X.MethodLSLeastSquares(NLSandARMA)Sample:131EViewsFileEditObjectViewProcQuickOptonsWindowHelpPath二c:u,bs妙蔭idocumcntsDB二noneWF二untitled(=Equation:UNTITLEDWorkfile:UNTITLED:UntitledViw|at1view!FroclObjectPrintINameFreezeEstimateForecastStatsReside园WoRangoSampleDepende

31、nt也nsbl:LOG(已2)Method:LeastSquaresD3t9：05/19J13Time:17：26Sample:131includedooser/anons:31ESEE92resicvariableCoeffidenlStdErrort-SiatisticProb.c76138771.040038732076800000X0.0005480.0002152.6536460.0162R-squarod0.183572Meandependentvar10.04780AdjustedR-squared0.155419SDdependentvar2.521154SE.ofregres

32、sion2316967AKaikeintocriterion4.680736Sumsquaredresid155.5817Schwarzcriterion4.673251Loglikelihood69.00141Hannan-Quinnenter4.610894F-statistic5.520590Durbin-Watsonstat1.377203Prob(F-statistic)0015183Path二c：u,b$.孙陰documentsDB二noneWF二untitled#孙晖计虽经济学习题OLSIhI归结果表明，X前的参数在5%的显著性水平下不为零，同时F检验也表明方程的线性关系在5%的

33、显著性水平下成立。于是生成权序列w,w=1/Jexp(7.6139+0.000548X)。在Workfile窗口中点击ObjectGenerateSeries，在弹出的对话框中的Enterequation输入“W二l/sqrt(exp(7.6139+0.000548*X)生成权序列w。EViewsFileEditObjectViewProcQjickOptonsWindowHelp国Workfile:UNTITLED-(c:users?/jkdesktopuntitled.wf.-OXyew|ProcbjectlPrintSaveDetaHs-；-show|Fetch|storeDeiete|

34、Genr|5dmpieRange:13*cee2rexYGenerateSeriesbyEquationEnterequationw=l/&：qrt(ep(Z6L39+0.000S8*X)Sarplc131CKCancelUntitled、：Nev/PagejFiner*Path二guscts孙晖documentsDB二noneWF二untitled回到原模型的OLS估计结果窗口，点击Estimate,出现EquationEstimation对话框,点击Options按钮,Coefficientcovariancematrix选项选择White,Weights中的Type选项选择Inverse

35、std.dev.,Weightseries栏输入“w”，点击确定，得到估计结果。15孙晖计虽经济学习题92re$Path二cu5eriJJKdocumentsDB二noneWF二untitledEViewsFileEditObjectViewProcQuickOptionsWindowHelp园WorkfihViewjproc01Rango:131Sample!31(=)Equation:UNTITLEDWorkfile:UNTITLED:Untitled-OXviewProcODject|pnnt|rJameFreeze|EstimateForecaststatiRecidsidcOJ92r

36、ewxYDependentVariable:YMethod:LeastSquaresDate：05H9/13Time:1730Sample:131includedobservations:31Weightingseries:WWeighitype:Inversestandarddelation(EVIewsdefauliscaling)Whiteheteroskedastidt/-con3istentstandarderrors&covarianeevanabieCoGtliciGntStd.Errort-StatisticProD.C743.9217203.08213.6631570.001

37、0X0.5722020.05531410344520.0000WeightedStatisticsR-scuared0.819539Meandeoendenivar2896711AdjustedR-squared0813317sddependentvar573.7370S.E.ofregression280.1456Akaiinfocriterion14.17084Sumsquaredresid2275966.Schwarzcriterion1426335Loglivelihood-217.6480Hannan-Quinncriter.14.20099F-statislic1316999Dur

38、bin-Watsonstat1800160Prob(F-statstic)0.000000Weightedmeandep.2696.063UntitlecUnwQigntcdStatisticsR-squarod0.854034Meandepenconr/ar3376.309wPath二cu5eriJJKdocumentsDB二noneWF二untitledEViewsFileEditObjectViewProcQuickOptionsWindowHelp16孙晖计虽经济学习题与不加权的OLS结果对比可以看出，加权最小二乘估计使得X前的参数估计值略有下降，但标准差却增大了，表明OLS估计低估了

39、X对应参数的标准差。异方差稳健标准误法回到原模型的OLS估计结果窗口，点击Estimate,出现EquationEstimation对话框,点击Options按钮,Coefficientcovariancematrix选项选择White,Weights中的Type选项选择None，点击确定，得到估计结果。17孙晖计星经济学习题18孙晖计星经济学习题EViewsFileEditObjectViewProcQuickOptionsWindowHelpEquation:UNTITLEDWorkfile:UNTITLED:Untrtled-X|ViewProcObjert|Print|Name|Fre

40、eze|Estimate|Forecan|Stats|ReadsDependentVariaDle:YMethod:LeastSquaresData：05/19/13Time：1732Sample:131incluaedooseivticns:31Whiteheteroskedasticitf-consistentstand3rderrors&covarianceVariableCoefficientStdError1-StatisticProb.C179.1916325.96780.5497220.5867X0.71950000872108.2501850.0000R-squared0.89

41、5260Meandependentvar3376309.AdjustedR-squared0.891649S.D.dependentvar1499.6123.E.ofregression493.6240Akaikeinfocriterion15.30377sumsquaredresia7066274.senwarzcriterion15.39628Loolikelihood-235.2084Hannan-Quinncriter.15.33392F-siafisuc247.8769Durbin-waiscnstat2.119816Prob(F-statistc)0.000000Path二uu6孙晖documentsDB二noneWF二untitled从估计结果仍然可以看出，变量X对应参数修正后的标准差比OLS估计结果有所增大，表明原模型OLS估计结果低估了X的标准差。#