計量經濟學習題詳解

第四章習題4.1沒有進行t檢驗，并且調整的可決系數也沒有寫出來，也就是沒有考慮自由度的影響，會使結果存在誤差。4.3中國商品進口額、國內生產總值、居民消費價格指數年份商品進口額/億元國內生產總值/億元居民消費價格指數（以1985年為100）19851257.89016.0100.019861498.310275.2106.519871614.212058.6114.319882055.115042.8135.819892199.916992.3160.219902574.318667.8165.219913398.721781.5170.819924443.326923.5181.719935986.235333.9208.419949960.148197.9258.6199511048.160793.7302.8199611557.471176.6327.9199711806.578973.0337.1199811626.184402.3334.4199913736.489677.1329.7200018638.899214.6331.0200120159.2109655.2333.3200224430.3120332.7330.6200334195.6135822.8334.6200446435.8159878.3l347.7200554273.7183084.8353.9200663376.9211923.5359.2200773284.6249529.9376.5200879526.5314045.4398.7200968618.4340902.8395.9201094699.3401512.8408.92011113161.4472881.6431.0一研究的目的和要求我們知道，商品進口額與很多因素有關，了解其變化對進出口產品有很大幫助。為了探究和預測商品進口額的變化，需要定量地分析影響商品進口額變化的主要因素。二、模型的設定及其估計經分析，商品進口額可能與國內生產總值、居民消費價格指數有關。為此，考慮國內生產總值GDP、居民消費價格指數CPI為主要因素。各影響變量與商品進口額呈正相關。為此，設定如下形式的計量經濟模型：叫M侑+SJnGDPt+SJnCP/t

式中，Z為第t年中國商品進口額(億元)；InGDP為第t年國內生產總值(億元)；InCPI為居民消費價格指數(以1985年為100)。各解釋變量前的回歸系數預期都大于零。為估計模型，根據上表的數據，利用EViews軟件，生成Y、InGDP、InCPI等數據，采用OLS方法估計模型參數，得到的回歸結果如下圖所示：DependentVariable:LNYMethod:LeastSquar&sDate:04y15/17Time:19:54Sample:19352011Includedobservations:27VariableCoefficientStd.Errort-StatisticProbC-3.1114860.46J010 -6.7201260.0000LMGDP1.33S53-30.03S610 15.105820.0000LNCPI-0.4217910.2^295 -1.S079750.0832R-squared0.98805-1Meandependentvar9.4S4710AdjustedR-squared0.987055S.D.dependentyar1.455517S.E.口仃町曰33口門0.162189Akaikeinfocriterion-0.695670Sumsquared「e§id0.631326Schwarzcriterion-0.551689Loglikelihood12.3915-5Hannan-Quinncriter.-0.652857F-statisiic992.2532Durbin-Watsonstat0-522613Prob(F-statistic)O.OOQQOO模型方程為：lnY=-3.111486+1.338533lnGDP-0.421791lnCPI(0.463010)(0.088610) (0.233295)t=(-6.720126)(15.10582) (-1.807975)^2=0.988051R2=0.987055F=992.2582該模型氏2=0.988051，R2=0.987055，可決系數很高，F檢驗值為992.2582，明顯顯著。但是當a=0.05時，J(n-k)=%.O25(27-3)=2.064，不僅lnCPI的系數不顯著，而且，lnCPI的符號與預期相反，這表明可能存在2嚴重的多重共線性。計算各解釋變量的相關系數，選擇lnGDRlnCPI數據，“view/correlation”得相關系數矩陣。CorrelationLMCPILNGDFLNCPILNGDPLNCPI1.0000000.9&37400&537401.0000001由相關系數矩陣可以看出，各解釋變量相互之間的相關系數較高，證實確實存在一定的多重共線性。為了進一步了解多重共線性的性質，我們做輔助回歸，即每個解釋變量分別作為被解釋變量都對剩余的解釋變量進行回歸。□epenoentvariaUte:lngdfMetnod:LeastsquaresDale04/15717TitHe：21：&9sample.13352011includedobservations:27DependentVariatIe:LNCPIMethod:LeastSquaresDate:04^15/17Time:21:10Sample.19852011incluclecJonser/allons27VariableCoefficient31dErrort-SlatisticProb.variablecoeffidemstd.Errort-siatisticProb.C-2.7963010.062790 -3.1B76340.0040c工5154020.256313 5.912301O.OODDLNOFI25110220.156302 15.B6227O.OODOLMGDP0.3B22510.022837 15.BB227O.OODOR-squared0.909621Fdeandependentvar11.16214R-squared0.9D9621Meandependentvar5.55B900AdjustedR-squared0.906005S.D.dependentvar1.194029.AdjustedR-squa.red0.9D6005S.D.dependentvar0.453513B.E.DfregressionO.J66072AkaikeinfocriterionQ.099213S.E.ofregression0.139042Akaikeinfocriterion-1.05BB94Sumsquaredresid3-350216Schwarzcriterion0.935201SumsquaredresiU0.463317Schwarzcriterion-0.94D907Loglikelihood-10.13933Hannan-Quinncriter.Q.92775&lccineiinood15.99SD8Hannan-ouinnenter-1WB352F-statistic251.6117Durbin-Watsonstat0.089623F-Etatstc251.6117Durtsin-Watsonslat□.114568ProKF-statiGtic]0.000000Proti(F-￡tati￡tic)O.DDOOOOInGDP與InCPI的相關系數很高，證明存在多重共線性。三、其他分析1.進行下面的回歸①In%=4+4聯嗎+?DependentVariable:LNYMethod:LeastSquaresDate:04y27/17Time:09:10Sample:19852011Includedobservations:27VariableQoefTiGientStd.Errort-StatisticProbC-3,7&06700.312255-12.011560.0000LNGDP1.1357390.027S2242,615330.0000R-squared0.986423Meandependentvar9.484710Adjusi&fiR-squaretl0.98S3SOS.D.dependsntvar1.425517&.E.ofregression0.1&33S9Akaikeinfocriterion-0.642056Suinsquaredresid0.717312Schwarzcriterion-0.546068Loglikelihood10.66776Hannan-Quinncriter.-0.613514F-statistic1S16.407□urbin-Watsonstat0471111ProbfF-statistic）0.000000模型的估計結果為：叫=-3.750670+1.185739InGDPt（0.312255） （0.027822）t=（-12.01156） （42.61933）^2=0.986423 丘2=0.985880 F=1816.407②叫②1+斷叫+%DependentVariable:LNYMethod:LeastSquares□ate:04722/17Time:09:12Sample:19852011Includedobsenations:27VariableCoefficientStd.Errort-3tatisticProb.G-6.8545351.242243-5.517871a.ooaoLNCPI2.9392950.22275613,19511a.ooooR-squared0.874-442Meandependentvar3.434710AdjustedR-squared0.869419S.D.dependsntwar1425517S.E.ofregression0.&1&124Akaikeinfocriterion1.5S2363Sumsquaredresid6.633S10Schwarzcriterion1.673356Lo-glikelihood-1936196Hannan-Quinncriter.1.610910F-statistic174.1108□urbin-Watsonstat0.137042Prob[F-statistic）0.000000模型的估計結果為：叫=-6.854535+2.939295lnCPZt（1.242243） （0.222756）t=（-5.517871） （13.19511）

^2=0.874442 R2=0.869419F=174.1108③lnGDf+qlnCP"」DependentVariable:LNGDPMethod:LeastSquares□ate:04J22/17Tim-e:09:14Sample:19852011Includedobservations:27VariableCaefficientStdErrort-StatisticProb.C-2.7963S-10.8S2793 -5.167634O.QO+OLNCPI25110220.1&B302 15.862270.0000R-squared0.909621Meandependentvar11,16214AdjustedR-squared0.906005S.D.dependentvar1194029S.E.ofregression0366072Akaikeinfocriterion0899213Sumsquaredresid33&0216Schwarzcriterion0.995201Loglikelihood-10.13938Hannan-Quinncriter.0.927755F-statistic251.6117□urbin-Watsonstat0.099623-Prob(F-statistic)0.000000模型的估計結果為：[1]lnGDPt=-2.796381+2.511022lnCP，t(0.882798) (0.158302)t=(-3.167634) (15.86227)R2=0.909621 R2=0.906005 F=251.6117由此對多重共線性的認識：由上面的幾組擬合效果可知，單方程擬合效果都很好，可決系數分別為：0.986423和0.874442,可決系數較高，說明GDP和CPI單個對商品進口額有顯著的影響。但是，當這兩個變量同時引進模型時，影響方向發(fā)生了改變，這只有通過相關系數的檢驗才能發(fā)現，第三個回歸結果也說明了，它們間有很強的線性相關關系。建議：如果僅僅是做預測，可以不用在意這些多重共線性，如果是進行結構分析，就需要注意了4.41985~2011年財政收入及其影響因素數據年份財政收入CZSR/億元財政支出CZZC/億元國內生產總值GDP(現價)/億元稅收總額SSZE/億元19852004.802004.259016.042040.7919862122.002204.9110275.182090.7319872199.402262.1812058.622140.3619882357.202491.2115042.822390.4719892664.902823.7816992.322727.4019902937.103083.5918667.822821.8619913149.483386.6221781.502990.1719923483.373742.2026923.483296.9119934348.954642.3035333.924255.3019945218.105792.6248197.865126.88

19956242.206823.7260793.736038.0419967407.997937.5571176.596909.8219978651.149233.5678973.038234.0419989875.9510798.1884402.289262.80199911444.0813187.6789677.0510682.58200013395.2315886.5099214.5512581.51200116386.0418902.58109655.1715301.38200218903.6422053.15120332.6917636.45200321715.2524649.95135822.7620017.31200426396.4728486.89159878.3424165.68200531649.2933930.28184937.3728778.54200638760.2040422.73216314.4334804.35200751321.7849781.35265810.3145621.97200861330.3562592.66314045.4354223.79200968518.3076299.93340902.8159521.59201083101.5189874.16401512.8073210.792011103874.43109247.79472881.5689738.39、研究的目的和要求國家財政收入的高低是政府有效實施其各項職能的重要保障。國家財政收入主要來源于各項稅收收入，只有經濟持續(xù)而健康地增長，才能提供持續(xù)的稅收來源，因而經濟增長是其重要的影響因素；另外，財政收入需要滿足日益增長的財政支出的需要。為此，需要定量地分析影響國家財政收入的主要因素。二、模型設定及其估計為了分析各主要因素對國家財政收入的影響，建立財政收入（億元）（CZSR）為被解釋變量，財政支出（億元）（CZZC）、國內生產總值（億元）（GDP）、稅收總額（億元）（SSZE）等為解釋變量的計量模型。為此，設定如下形式的計量經濟模型：CZSRi=B0+B1cZZCi+B2GDPi+B3sSZEi+i式中，CZSRi為第i年財政收入（億元）；CZZCi為第i年財政支出（億元;；GD4為第i年國內生產總值GDP（現價）（億元）；SSZEi為第i年稅收總額（億元）。各解釋變量的系數預期都大于零。利用EViews軟件，生成CZSR、CZZC、GDP、SSZE等數據，采用OLS方法估計模型參數，得到回歸結果如下圖所示：DependentVariable:CZSRMethod:Leas.tSquaresDate:04/16J17Time:14:21Sample:1985.2011includedobsedations:27VariableCoefficientStd.Errort-StatisticProb.“修-221.8540130.6522-1.69803^80.1030pZZQ0.0901140.0443672.03'11<290.0540;GDP-0.02^340005069-4.9980360.0000SSZE1.176S940.062162.18.93-2710.0000R-squared0.999857Meandependentvar22572.56AdjustedR-squared0.999838S.D.dependentvar27739.498：.E.ofregregion353.0540Akaikeinfocriterion1470707Sumsquaredre.sid■2866884.Schwarzcriterion14,89905Loglikelihood-194.5455Hannan-Quinncriter.1476416F-statistic...53493.93Durbin-Watsonw怕t1.45S128PmbFstating'0.000000回歸方程可寫為： - i(130.6532)i(130.6532)t=(-1.698038)R2=0.999857(0.044367)(2.031129)(0.044367)(2.031129)R2=0.999838(-4.998036) (18.93271)F=53493.93—該模型區(qū)2=0.999857,R2=0.999838,可決系數很高，F檢驗值為53493.93,明顯顯著。但是當a=0.05時，td(n-k)=時，td(n-k)=t0.02K27-4)=2.069，不僅CZZC的系數不顯著，并且，GDP的系數與預期相反，這表明可能存在嚴2重的多重共線性。計算各解釋變量的相關系數，選擇CZZC、GDP、SSZE數據，點“view/correlation〃得相關系數矩陣，如下圖所示：由各相關系數矩陣可知，各解釋變量之間的相關系數較高，證實確實存在一定的多重共線性。為了進一步了解多重共線性的性質，我們做輔助回歸，即將每個解釋變量分別作為被解釋變量都對其余的解釋變量進行回歸。DependentVariable:CZZtMethod:LeastSquaresDate:04/16/17Time:14:49Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.C-285.2687598.2876-0.4768090.6378GDP-0.0084360.023257-0.36275107200SSZE1.2600840.12479110.102390.0000R-squared0.997168Meandependentvar24168.23AdjustedR-squared0.996932S.D.dependentvar29327.97S.E.ofregression1624.346Akaikeinfocriterion1772804Sumsquaredresid63323999Schwarzcriterion17,87202Loglikelihood-236.3286Harnan-Quiriricriter.1777086F-statistic4225.S95Durbin-Watsonstat1.379907Prob(F-statistic)0.000000Dependentvariable:GDPMethod:LeastSquaresDate:04n6>17Time:14:51Sample:19S52011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.C18385.223687.876 4.9853Ua.oooaCZZC-0.64636217B1835 -0.362751a.72oaSSZE6.1213642.169215 2.E219200.0094R-squared0.988633Meandependentfar126659.6AdjustedR-squared0.987902S.D.dependentvar129265.4S.E.ofregression14218.02Akaikeinfocriterion22,06685Sumsquaredresid4.85E40QSchwarzcriterion22,21083Loglikelihood-294.9024Hannan-Quinncriter.22,10966F-statistic1062.558Durbin-Watsonstat0.180550Prob(F-statiStic)0.000000DependentVariable:SSZEMeihod:LeastSquaresDate:04>16J17Time:14:52Sample:19852011Includedabsen/ations:27VariableCoefficientStdErrort-StallSticProb.C-432.2846419.8597-1.0295930.3135CZZC0.6422010.06356910,10239a.oooaGDP0.0407000.0144232.821920a.0094R-squared0.997862Meandependentvar20244.81AdjustedR-squared0.997684S.D.dependentvar24oga.5BS.E.ofregression1159.340Akaikeinfocriterion17,05353Sumsquaredresid32257673Schwarzcriterion17,19751Loglikelihood-237.2236Hannan-Quinncriter.17,09634F-statistic5601.263Durbin-Watsonstat1.262S11Prob(F-statiStic)0.000000下表是所得到的可決系數和方差擴大因子的數值，如下表所示:被解釋變量可決系數R2的值方差擴大因子VIF.=j1-Rj2CZZC0.997168353GDP0.98883390SSZE0.997862468由上表可知，輔助回歸的可決系數很高，經驗表明，方差擴大因子VIFj210時，通常說明該解釋變量與其余解釋變量之間有嚴重的多重共線性。三、對多重共線性的處理運用逐步回歸法，逐步選擇和剔除引起多重共線性的變量，具體步驟如下：.先用被解釋變量對每一個所考慮的解釋變量作簡單回歸，結果如下所示：aCZSR與CZZC的一元回歸結果DependentVariable:CZSRMethod:LeastSquares口日怡：口4門印Time:15:16Sample:19852011Includedobservations:27VariableCoefTicientStd.Errort-StatisticProb.c-257.5992350.3645-0.7100190.4709CZZC0.944635a.00953699,063660.0000R-squared0.997459Meandependentvar22572.56AdjustedR-sqjared0.997357S.D.dependentvar27739.49S.E.ofregression1425.996Akaikeinfocriterion17,43432Sumsquaredresid50B36616Schwarzcriterion17.53Q30Loglikelihood-233.3633Hannan-Quinncriter.17,46236F-staiistic9013.609Durbin-Watsonstat1.259741Prob(F-statistic}0.000000R2=0.997459R2=0.997357F=9813.609bCZSR與GDP的一元回歸的結果DependentVariable:CZSRMethod:LeastSquaresDate:04；16/17Time:15:17Sample:19852011Includedobsetvaiions:27VariableCoefficientStd.Errort-StatisticProb.C-4419.476919.2456-4.8077200.0001□DP0.2130560.00512741,552030.0000R-squared0.985727Meandependentvar22572.56AdjustedR-squared0.985156S.D.dependentvar27739.49S.E.ofregression3379.646Akaikeinfocriterion19,16012Sumsquaredresid2,%E+口NSchwarzcriterion19,2561CLoglikelihood-25G,eG1GHannan-Quinncriter.19,1086CF-statistic1726.571Durbin-Watsonstat0.178877Prob(F-statistic)0.000000R2=0.985727R2=0.985156F=1726.571c.CZSR與SSZE的一元回歸結果DependentVariable:CZSRMethod:LeastSquaresDate:04/16/17Time:15:18Sample:19852011Includedotiservations:27VariableCoefficientStd.Errort-StatisticProb.C-734.7667131.1949-5.6005590.0000SSZE1.1512740.004215273.1237a.ooaoR-squared0.999665Mearidependertvar22572.56AdjustedR-squared0.999652S.D.dependentvar27739.49S.E.ofregression517.7892Akaikeinfocriterion15,40820Sumsquaredresid6703642.Schwa(2criterion15,50419Loglikelihood-206.0107Hannan-Quinncriter.15,43674F-statistic74596.56Durbin-Watsonstat0.899852Prob(F-statistic)0.000000R2=0.999665R2=0.999652F=74596.56.對以被解釋變量貢獻最大的解釋變量所對應的回歸方程為基礎，518D逐個引入其余的解釋變量。由上面的回歸結果可知，SSZE對CZSR的回歸結果可決系數最大，再此基礎上，逐個引入剩下的解釋變量CZZC和GDP在c的基礎上引入解釋變量CZZC,得到如下的回歸結果：

DependentVariable:CZSRMethod:LeastSquaresDate:04/16/17Time:15:41Sample:19852011Includedobservations:27VariableCoefficientSid.Error t-StatisticProb.C-687.6167129.4806 -5.3105790.