計量經(jīng)濟學龐浩版習題5.3

1、 孫暉計星經(jīng)濟學習題5.3下表是2007年我國各地區(qū)農(nóng)村居民家庭人均純收入與家庭人均生活消費支出的數(shù)據(jù)。表5.9各地區(qū)農(nóng)村居民家庭人均純收入與家庭人均生活消費支出的數(shù)據(jù)（單位：元）土也區(qū)家庭人均純收入家庭生活消費支出地區(qū)家庭人均純收入家庭生活消費支出北京9439.636399.27湖北3997.483090天津7010.063538.31湖南3904.23377.38河北4293.432786.77廣東5624.044202.32山西3665.662682.57廣西3224.052747.47內(nèi)蒙古3953.13256.15海南3791.372556.56遼寧4773.433368.16重慶3

2、509.292526.7吉林4191.343065.44四川3546.692747.27黑龍江4132.293117.44貴州2373.991913.71I-.海10144.628844.88云南2634.092637.18江蘇6561.014786.15西a2788.22217.62浙江8265.156801.6陜西2644.692559.59安徽3556.272754.04甘肅2328.922017.21福建5467.084053.47W海2683.782446.5江西4044.72994.49寧夏3180.842528.76山東4985.343621.57新跚3182.972350.58

3、河南3851.62676.41（1）試根據(jù)上述數(shù)據(jù)建立2007年我國農(nóng)村居民家庭人均消費支出對人均純收入的線性回歸模型。（2）選用適當方法檢驗模型是否在異方差，并說明存在異方差的理由。（3）如果存在異方差，用適當方法加以修正。（1）新建一個MicrosoftExcel匸作表，并錄入全部數(shù)據(jù)。建立一元線性回歸模型：&=0o+0X+O打開Eviews軟件，進入主界面，點擊FileNe叭Workfile,彈出WorkfileCreate對話框。在WorkfileCreate對話框左側(cè)Workfilestructuretype欄中選擇UnstructuredUndated選項，在右側(cè)DataRange

4、中填入樣本個數(shù)31,點擊OKo定義解釋變量X:在Workfile窗口中，點擊0bjectsNewObjectseries,在Nameforobject中輸入X,點擊OK。以相同的方法定義被解釋變量Y。按住Ctrl鍵,同時選中X、Y,右擊0penasGroupEdit+/,復制Excel中的整列數(shù)據(jù)，右擊選擇Paste粘貼在Eviews中，將31組數(shù)據(jù)錄入。點擊主界面菜單QuickEstimateEquation選項，在彈出的對話框中輸入:“YCX”，點擊確定即可得到回歸結(jié)果。EViewsFileEditObjectViewProcQuickOptionsWindowHelp匡莎RasasNQa

5、|vieviewxjobedPrintNameFreezeIEstimateIForecastIStatsResids399DependentVariable:YMethod:LeastSquaresDate:05/19/13Time17:06Sample:131Includedobservations:31VariableCoetncientSid.Errort-StatlstlcProbC179.1916221.57750.8087090.4263X0719500004570015.7441100000R-squarod0.895260MoandopondGntvar3376.309Adj

6、ustedR-squard0891B49SDdependemyar1499.6123.E.cfregression4936240Akaikeinfocriterion1530377Sumsquaredresid7066274.ScnAarzcritorion15.39628Loglikelihood-2352084Hannan-Ouinnenter1533392F-statistic2478769Durbin-Watsonstat1.461684Prob(F-statistc)0.000000叵Equation:UNTITLEDWorkfile:UNTITLED:Untitled-axPath

7、=ulusers孫庫documents08=noneNF=untitled由此可知，居民人均消費支出與可支配收入的線性模型為Y=179.1916+0.7195X(221.58)(0.0457)t=(0.8087)(15.7441)R2=0.8953F二247.87D.W.=1.4617RSS=7066274異方差性檢驗圖示法檢驗生成殘差序列。在Workfile窗口中點擊ObjectGenerateSeries,在彈出的對話框中的Enterequation輸入e2二resid2”，得到殘差平方和序列e2。繪制e：對備的散點圖。按住Ctrl鍵，先選擇變量x,再選擇e2,點擊主界面菜單QuickGr

8、aph選項,彈出的對話框中Graphtype的Specific選項選擇Scatter,可得到散點圖。孫暉計星經(jīng)濟學習題 孫暉計星經(jīng)濟學習題EViewsFileEditObjectViewProcQuickOptionsWindowHelpRango1Sample1c2=：c5id2|(EnterequationFilter*excancelUnti(ledI、NewPege/園Workfile:UNTITLEDViw|ProcObject|PrintSaveDetails-,-1ShowFetchStoreloeietedsicfe3-GenerateSeriesbyEquation131Sa

9、irpie0EViewsFileEditObjectViewProcQjickOptonsWindowHelp國WorkfiLzJproqCGraphOptionsopaonPagesGraphTypePPath二c:sers孫眸idocumcntsDB二noneWF二untitledRange13Sample13(Ec0e2resid0 xUntitleBasictype3Fremc&Sizci-Axes&Scalng5Leocnd3-GraphEfementsffl-QuickFonts3Tcmoetcs&ObjectsUndo%兀EditsGraphtypeGGTGfal：Basicgr

10、aphSpecific:Line&Symbol5arSpkeAreaAreaBardMxedAithLinesDotPlotErrorEcrTd*；ow(Openlosc)ScatterXYUnexrqDstribuionQjantieQuartieBoxpbtGraphdata:RawdataFitlines:Artsherders:NonevoptionsNonevSngegraphCancelPath二c:serG孫documentsDB二noneWF二untitled孫暉計星經(jīng)濟學習題 孫暉計星經(jīng)濟學習題由散點圖可以看出，殘差平方和嶄對備大致存在遞增關系，即存在單調(diào)增型異方差。Gold

11、fe1d-Quanadt檢驗對變量取值排序。在Workfile窗口中點擊ProcSortCurrentPage，在彈出對話框中輸入x,點擊OKo本列選擇升序排列（默認項是Ascenging升序）,這時變量Y將以X按升序排列。孫暉計星經(jīng)濟學習題 孫暉計星經(jīng)濟學習題ViewProc(ObjectPrint!Save園Workfile:UNTITLEDRango:131-31obsSample!31一31ob3Filter*.000S.00010Path二c:u,crs孫臉documentsDB二noneWF二untitledD吉ailshowFetthstHwDeletQ|GrnsamplSort

12、WorkfileSeriesErteron亡ormoreseriesremesorseriesexpressionsSortorefer(SjAscerdngODescendngJUnMIedINgwPegE/2.0004.0006000Xp-ShadeRemoEViewsFileEditObjectViewProcQuickOptonsWindowHelp孫暉計星經(jīng)濟學習題 #孫暉計星經(jīng)濟學習題構(gòu)造子樣本區(qū)間，建立回歸模型。在本題中，樣本容量n二31,刪除中間1/4的觀測值，大約7個數(shù)據(jù)，余下部分平分得兩個樣本區(qū)間：112和2031,它們的樣本個數(shù)均是12個，即*=坯=12。雙擊V/orkf

13、ile中的Sample一欄，彈出Sample對話框，將Samplerangepairs中的改為“112”，這樣就把區(qū)間定義為112。然后用OLS方法求得子樣本區(qū)間的估計結(jié)果，即點擊主界面菜單QuickEstimateEquation選項，在彈出的對話框中輸入：“YCX”，彈出的DeleteUnt譏led對話框選擇Yes。孫暉計星經(jīng)濟學習題孫暉計雖經(jīng)濟學習題 Workfile:UNTITLED-(c:users?/Jdesktopuntitled.wf.-nxView|ftrocObject|PrintSaveDetails-/-show|Fetchstore|DeleteGenrjsampie

14、|Rango:13131obsFilterSample131一31obsBSEJUnMIedNewPwgE/Path二c;users孫陰idocumtntsDB二noneWF二untitled0EViewsFileEditObjectViewProcQuickOptonsWindowHelpfaWorkfile:UNTITLED-Cc:users?/Jdesktopuntitled.wf.-xUiewjfocObject|PrintSaveDetails-/-showjFetchJstorejDeleteGenrjsampieFiller*Range:131-31obsS3mple1-34ob

15、sBSEresicSample5amoierangepars(orsarntfeobjecttoccpv)l12-IFcondibon(opbonaQConedEViewsFileEditObjectViewProcQuickOptonsWindowHelp孫暉計星經(jīng)濟學習題孫暉計雖經(jīng)濟學習題 #孫暉計星經(jīng)濟學習題孫暉計雖經(jīng)濟學習題 #八UntitledI、NewPage/Path二c;uscrs孫陰idocumcntsDB二noneWF二untitled0EViewsFileEditObjectViewProcQuickOptonsWindowHelp(=Equation:UNTITLEDW

16、orkfile:UNTITLED:Untitled-cXIViewProcODject|Print|Name|Freeze|Estimate|ForecaststatiReadsDependentVanaDl:YMethod:LeastSquaresData：05/19/13Tima：17：18Sample:112incluaedooseivsticns:12VariableConicintStdErrorl-StatistlcProbC11112234095750271311200218X0.4519000.1364283.3123780.0078R-squarca0.523170Meand

17、opendentvar2463.886AdjustedR-squared0475487S.D.dependentvar280.7556S.E.ofregression203.3323AkaiKeinfocriterion13.61857Sumsquaredresid413440.3Schwarzcriterion13.59939LogHKGiinooa79.71143Hannan-Quinnenter.13.58865F-statstic10.97185Durbin-Watscnstat2.030396PrOD(F-Sl2tlSfiC)0007848Path二c;sers孫暉documcnts

18、DB二noneWF二untitled由此得到112的子樣本區(qū)間的模型估計結(jié)果為:Y=U11.22+0.4519X(409.58)(0.1364)t=(2.7131)(3.3124)R2=0.5232F=10.9719D.W=2.0304RSS】=413440.3同樣的，雙擊Sample-欄，將區(qū)間定義為2031,用OLS方法求得估計結(jié)果。孫暉計戢經(jīng)濟學習題 孫暉計雖經(jīng)濟學習題 #孫暉計戢經(jīng)濟學習題 孫暉計雖經(jīng)濟學習題 #EViewsFileEditObjectViewProcQuickOptonsWindowHelp-31obs一12obsrlliGCSamoierangeoars(orsam

19、deobjecttoccpy)2031X園Workfile:UNTITLED-Cc:users?KdesktopuntitledAvf.-x/lwlf0C|ObjectIPrintSaveDetaik*；-fshowlFetchlstorelDeleteGenrlsampie|Rango131Sample!SampleIFcondition(opbonai)2.97=I05(10,10),所以拒絕無異方差性假設,表明模型存在異方差性。White檢驗雙擊Workfile中的Sample一欄，將Samplerangepairs中的“2031”改為“all”或“131”,用0LS方法重新求得原模型的

20、估計結(jié)果，點擊Vie叭ResidualDiagnosticsHeteroskedasticityTests,彈出的對話框中Testtype選擇White,得到White檢驗的結(jié)果。孫暉計星經(jīng)濟學習題 孫暉計雖經(jīng)濟學習題 #孫暉計星經(jīng)濟學習題 孫暉計雖經(jīng)濟學習題 #0EViewsFileEdrtObjectViewProcQuickOptionsWindowHelpWorkfile:UNTITLED-(c:users?desktopuntilledAvf.-xUiewjProcObjectPrintSaveDerails/showFetthstowDeiwte|GwnrsamplwRange:1

21、:Sample:2C1一31OtS31-12obsFiller*IdSampleSamoierangeoars(orsamdeobjecttoccpv)LFconditon(opbona)UrUiNedNewPeg?/Path二c:us6眸idocumcntsDB二noneWF二untitledEViewsFileEditObjectVie內(nèi)ProcQuickOptonsWindowHelp國Workfile:UfSevjprgdo映aRange131一Sample:131一(=)Equation:UNTITLEDWoridile:UNTITLED:Untitled-cx(E0l30eCe2r

22、esiUntitledNRepresentationsEstimationOutputActuoljitted.Residue1ARMAStructure.GradientsandDeivativiCovarianceMatrixStd.Errort-StatisticProb.nfinP70QnICoefficientDiagncctcsJJ17!7004570015.7441100000ResidualDiagnosticsCcrrelogiamQ-statistics.StabilityDiagnosticsCorrelogramSquaredResiduals*.LabelHktogr

23、amNormalityTwstSerialCorrelationLMTest.F-statlsticPro0F-statistic)247876?0.00000(HetcroUredarticrtylest?.ViewjProc|OUjed|PrintjNome|FreezejEstimateForecastTaatsTRcsidsPath二documentsDB二noneWF二untitled孫暉計星經(jīng)濟學習題 孫暉計雖經(jīng)濟學習題 #EViewsFileEditObjectViewProcQuickOptonsWindowHelpUntitledb園Workfile:UlView|ProcO

24、bjectRango:131-Sample!31一孫暉計星經(jīng)濟學習題 #孫暉計雖經(jīng)濟學習題 #孫暉計星經(jīng)濟學習題 孫暉計雖經(jīng)濟學習題 #Path二c;u,g孫蔭idocumcntsDB二noneWF二untitledEViewsFileEditObjectViewProcQjickOptonsWindowHelp(=)Equation:UNTITLEDWorkfile:UNTITLED:Untitled-exviewProcjObjectJPrintjNomeFreezeEstimateForecast|StatsjResidsHeteroskedastlcltyTest:WhiteAF-st

25、atistic7194463Prob.F(228)00030ObsR-squarod10.52295Proo.Chi-Square(2)0.0052ScaledexplainedS330.03105Prob.Chi-SQuare(2)0.0000TestEquation:DependentVariable:RESIDEMethod:LeastSquaresData:05/19/13Timo17:24Sample:131indudsaooseRations:31variableCoetncientstdErrort-sratisticProb.CB98722764138900.108939091

26、40X72.02221248.7240-0.2896670.7743K200203370020627093597203326R-squared0.339450Meandependents227944.3A(j4u$tecR-squared0.292268s.D.oependentvar592250.3SEofregression498241.3Akaikeinfocriterion29.16732Sumsquaredresid695E+12Schwar2criterion2930510Loglikelihood449.0935HannarrQuinncriter2921256F-statist

27、ic7194463Durbin-Watsonstat2430258Pro0(F-statistic)0.003011V國Workfile:UrWevvJpnKObjectRange:131-Sample131ce2Untitled/hPath二c;u,g孫蔭idocumcntsDB二noneWF二untitled由White檢驗結(jié)果得到：R-=0.339450White統(tǒng)計量11R2=31x0.339450=10.52，該值大于5%顯著性水平下自由度為2的才分布的相應臨界值加“妙，（在估計模型中含有兩個解釋變量,所以自由度為2）,因此拒絕同方差性的原假設。（3）異方差性的修正加權(quán)最小二乘法在對

28、原模型進行OLS估計后，在Workfile窗口中點擊ObjectGenerateSeries,在彈出的對話框中的Enterequation輸入e二resid,得到新序列e。為了找到合適的權(quán)，作lne關于X的OLS回歸，即點擊主界面菜單QuickEstimateEquation選項，在彈出的對話框中輸入：aLOG（e2）CX”,彈出的DeleteUntitled對話框選擇Yes。EViewsFileEditObjectViewProcQuickOptonsWindowHelp孫暉計星經(jīng)濟學習題 孫暉計雖經(jīng)濟學習題 #iew|ProcObject)jPrintSaveDetails*；-)show

29、|Fetch|store|Delete|Genr|sample|Rango13Sample!3FilterGenerateSeriesbyEquationxWorkfile:UNTITLED-(c:users?ddesktopuntitled.wf.-nx120013EntercquotionCKcancelUntitled?Path二c;u5crsJ星documentsD6二noneWF二untitled孫暉計雖經(jīng)濟學習題 孫暉計雖經(jīng)濟學習題 #孫暉計雖經(jīng)濟學習題 孫暉計雖經(jīng)濟學習題 #EViewsFileEditObjectViewProcQuickOptonsWindowHelp園Wor

30、kfile:EquationEstimationRango:131一Sample131一UiwftrociObject-Equatorgpea令cationESEE92residLOG(“2)CXAVEstmationsertngsDependentvariablefollowedbylistofregressorsincludingandPDLterms,ORanexplicitequationlikeY=c(1)+c(2)*X.MethodLSLeastSquares(NLSandARMA)Sample:131EViewsFileEditObjectViewProcQuickOptonsW

31、indowHelpPath二c:u,bs妙蔭idocumcntsDB二noneWF二untitled(=Equation:UNTITLEDWorkfile:UNTITLED:UntitledViw|at1view!FroclObjectPrintINameFreezeEstimateForecastStatsReside園WoRangoSampleDependent也nsbl:LOG(已2)Method:LeastSquaresD3t9：05/19J13Time:17：26Sample:131includedooser/anons:31ESEE92resicvariableCoeffidenl

32、StdErrort-SiatisticProb.c76138771.040038732076800000X0.0005480.0002152.6536460.0162R-squarod0.183572Meandependentvar10.04780AdjustedR-squared0.155419SDdependentvar2.521154SE.ofregression2316967AKaikeintocriterion4.680736Sumsquaredresid155.5817Schwarzcriterion4.673251Loglikelihood69.00141Hannan-Quinn

33、enter4.610894F-statistic5.520590Durbin-Watsonstat1.377203Prob(F-statistic)0015183Path二c：u,b$.孫陰documentsDB二noneWF二untitled孫暉計雖經(jīng)濟學習題 孫暉計雖經(jīng)濟學習題 #OLSIhI歸結(jié)果表明，X前的參數(shù)在5%的顯著性水平下不為零，同時F檢驗也表明方程的線性關系在5%的顯著性水平下成立。于是生成權(quán)序列w,w=1/Jexp(7.6139+0.000548X)。在Workfile窗口中點擊ObjectGenerateSeries，在彈出的對話框中的Enterequation輸入“W二

34、l/sqrt(exp(7.6139+0.000548*X)生成權(quán)序列w。EViewsFileEditObjectViewProcQjickOptonsWindowHelp國Workfile:UNTITLED-(c:users?/jkdesktopuntitled.wf.-OXyew|ProcbjectlPrintSaveDetaHs-；-show|Fetch|storeDeiete|Genr|5dmpieRange:13*cee2rexYGenerateSeriesbyEquationEnterequationw=l/&：qrt(ep(Z6L39+0.000S8*X)Sarplc131CKCa

35、ncelUntitled、：Nev/PagejFiner*Path二guscts孫暉documentsDB二noneWF二untitled回到原模型的OLS估計結(jié)果窗口，點擊Estimate,出現(xiàn)EquationEstimation對話框,點擊Options按鈕,Coefficientcovariancematrix選項選擇White,Weights中的Type選項選擇Inversestd.dev.,Weightseries欄輸入“w”，點擊確定，得到估計結(jié)果。孫暉計雖經(jīng)濟學習題 孫暉計雖經(jīng)濟學習題 #92re$Path二cu5eriJJKdocumentsDB二noneWF二untitled

36、EViewsFileEditObjectViewProcQuickOptionsWindowHelp園WorkfihViewjproc01Rango:131Sample!31(=)Equation:UNTITLEDWorkfile:UNTITLED:Untitled-OXviewProcODject|pnnt|rJameFreeze|EstimateForecaststatiRecidsidcOJ92rewxYDependentVariable:YMethod:LeastSquaresDate：05H9/13Time:1730Sample:131includedobservations:31W

37、eightingseries:WWeighitype:Inversestandarddelation(EVIewsdefauliscaling)Whiteheteroskedastidt/-con3istentstandarderrors&covarianeevanabieCoGtliciGntStd.Errort-StatisticProD.C743.9217203.08213.6631570.0010X0.5722020.05531410344520.0000WeightedStatisticsR-scuared0.819539Meandeoendenivar2896711AdjustedR-squared0813317sddependentvar573.7370S.E.ofregression280.1456Akaiinfocriterion14.17084Sumsquaredresid2275966.Schwarzcriterion1426335Loglivelihood-217.6480Hannan-Quinncriter.14.20099F-statislic1316999Durbin-Watsonstat1800160Prob(F-statstic)0.000000Weightedmea