计量经济学报告

计量经济学报告计量经济学报告计量经济学报告课程名称计量经济学班级与班级代码专业国际经济与贸易任课教师学号：姓名：日期：年月日研究储蓄额与GDP之间的关系中国储蓄存款总额（Y，亿元）与GDP（亿元）数据如下表。表1年GDP储蓄(Y)年GDP储蓄(Y)19722518.1105.2198711962.53081.419732720.9121.2198814928.33822.219742789.9136.5198916909.25196.419752997.3149.6199018547.97119.819762943.7159.1199121617.89141.619773201.9181.6199226638.11175819783624.1210.6199334634.415203.519794038.2281199446759.421518.819804517.8399.5199558478.129662.319814862.4523.7199667884.638520.819825294.7675.4199774462.646279.819835934.5892.5199878345.253407.5198471711214.7199982067.4659621.819858964.41622.6200089442.264332.4198610202.22238.5200195933.373762.4第一步，散点图（图1）图1第二步，建立数学模型由经济理论知，中国储蓄存款总额受GDP的影响，当GDP增加时，中国储蓄存款总额也随着增加，它们之间具有正向的同步变动趋势。中国储蓄存款总额除受GDP的影响外，还受到其他一些变量的影响及随机因素的影响，将其他变量及随机变量的影响均归并到随机变量u中，根据GDP与Y的样本数据，作GDP与Y之间的散点图可以看出，它们的变化趋势是线性的，由此建立中国储蓄存款总额Y与GDP之间的一元线性回归模型：第三步，估计参数样本回归模型为：下面是Eviews的估计结果（表2）：表2DependentVariable:YMethod:LeastSquaresDate:12/13/11Time:12:27Sample:Includedobservations:30CoefficientStd.Errort-StatisticProb.

C-4366.305932.1408-4.0.0001GDP0.0.02291831.354660.0000R-squared0.

Meandependentvar15044.68AdjustedR-squared0.S.D.S.D.dependentvar22537.94S.E.ofregression3816.918

Akaikeinfocriterion19.39661Sumsquaredresid4.08E+08

Schwarzcriterion19.49003Loglikelihood-288.9492

Hannan-Quinncriter.19.42650F-statistic983.1150

Durbin-Watsonstat0.Prob(F-statistic)0.000000(-4.68)(31.35),R2=0.9723，DW=0.，T=30第四步，统计检验拟合优度样本可决系数为R-squared=0.修正样本可决系数为：AdjustedR-squared=0.即R2=0.，2=0.计算结果表明，估计的样本回归方程较好地拟合了样本观测值。回归系数估计值的显著性检验——t检验提出检验的原假设为：得t统计量为的t-Statistic=-4.的t-Statistic=31.35466对于给出显著性水平α=0.05，查自由度v=30-2=28的t分布表，得临界值t0.025（28）=2.05，|t0|=4.＞t0.025（28）=2.05，t1=31.35466＞t0.025（28）=2.05，故回归系数均显著不为零，回规模型中应包含常数项，GDP对Y有显著影响。从以上的评价可以看出，此模型是比较好的。F检验提出检验的原假设为：-=0对立假设为：至少有一个不等于零(i=1,2)F-statistic=983.1150对于给定的显著性水平α=0.05，查出分子自由度为2，分母自由度为27的F分布上侧分位数F0.05（2，27）=3.35因为F=983.1150＞3.35,所以否定H0，总体回归方程是显著的，即在中国储蓄存款总额Y与GDP之间存在显著的线性性。第五步，检验异方差(-4.68)(31.35),R2=0.9723，DW=0.，T=301．利用残差图判断。建立残差关于GDP的散点图，如图5.1，可以发现随着GDP增加，残差呈现不断增大的趋势，即存在递增性的异方差。图22．用White方法检验是否存在异方差，得表3HeteroskedasticityTest:WhiteF-statistic10.36874

Prob.F(2,27)0.0005Obs*R-squared13.03220

Prob.Chi-Square(2)0.0015ScaledexplainedSS13.06975

Prob.Chi-Square(2)0.0015TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:12/15/11Time:21:15Sample:Includedobservations:30CoefficientStd.Errort-StatisticProb.

C-57307.36.-0.0109730.9913GDP650.9958433.64191.0.1449GDP^2-0.0023760.004863-0.0.6291R-squared0.

MeandependentvarAdjustedR-squared0.S.D.S.D.dependentvarS.E.ofregression

Akaikeinfocriterion36.15282Sumsquaredresid7.22E+15

Schwarzcriterion36.29294Loglikelihood-539.2922

Hannan-Quinncriter.36.19764F-statistic10.36874

Durbin-Watsonstat1.029242Prob(F-statistic)0.000456因为只含有一个解释变量，所以White检验辅助回归式中应该包括两个解释变量。辅助回归式估计结果如下：(-0.011)(1.50)(-0.49)R2=0.4344,T=30TR2=30*0.4344=13.03220＞，所以结论是该回归模型中存在异方差。克服异方差异方差修正如下：表4DependentVariable:YMethod:LeastSquaresDate:12/14/11Time:16:27Sample:Includedobservations:30Weightingseries:1/GDPCoefficientStd.Errort-StatisticProb.

C-1584.144176.6377-8.0.0000GDP0.0.03388215.513990.0000WeightedStatisticsR-squared0.

Meandependentvar2121.702AdjustedR-squared0.S.D.S.D.dependentvar1703.101S.E.ofregression880.7714

Akaikeinfocriterion16.46381Sumsquaredresid

Schwarzcriterion16.55723Loglikelihood-244.9572

Hannan-Quinncriter.16.49370F-statistic240.6838

Durbin-Watsonstat0.082459Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.

Meandependentvar15044.68AdjustedR-squared0.S.D.S.D.dependentvar22537.94S.E.ofregression7600.750

Sumsquaredresid1.62E+09Durbin-Watsonstat0.075333再进行White检验：表5HeteroskedasticityTest:WhiteF-statistic2.

Prob.F(2,27)0.1050Obs*R-squared4.

Prob.Chi-Square(2)0.0996ScaledexplainedSS2.

Prob.Chi-Square(2)0.2972得=0.1050大于0.05，所以认为已经消除了回归模型的异方差性。得输出结果，整理后得到回归式为：t(-8.97)(15.51)R2=0.,DW=0.082459第六步，检验误差项ut是否存在自相关已知DW=0.082459，若给定α=0.05，查表可得DW检验临界值dL=1.35，dU=1.49。因为DW=0.082459＜1.35，依据判别规则，认为误差项ut存在严重的正自相关。图3残差分布图2.用LM检验判断是否存在自相关设定滞后期为一阶，得到LM检验结果表6Breusch-GodfreySerialCorrelationLMTest:F-statistic195.2096

Prob.F(1,27)0.0000Obs*R-squared26.35479

Prob.Chi-Square(1)0.0000TestEquation:DependentVariable:RESIDMethod:LeastSquaresDate:12/14/11Time:16:39Sample:Includedobservations:30Presamplemissingvaluelaggedresidualssettozero.Weightseries:1/GDPCoefficientStd.Errort-StatisticProb.

C-90.4259463.03508-1.0.1629GDP0.0175370.0120921.0.1585RESID(-1)1.0.08147113.971740.0000WeightedStatisticsR-squared0.

Meandependentvar-3.18E-13AdjustedR-squared0.S.D.S.D.dependentvar865.4524S.E.ofregression312.6517

Akaikeinfocriterion14.42270Sumsquaredresid.

Schwarzcriterion14.56282Loglikelihood-213.3404

Hannan-Quinncriter.14.46752F-statistic97.60479

Durbin-Watsonstat1.Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.

Meandependentvar2429.691AdjustedR-squared0.S.D.S.D.dependentvar7047.859S.E.ofregression1227.018

SumsquaredresidDurbin-Watsonstat0.089874然后，设定滞后期为二阶，得到LM检验结果表7Breusch-GodfreySerialCorrelationLMTest:F-statistic95.66349

Prob.F(2,26)0.0000Obs*R-squared26.41094

Prob.Chi-Square(2)0.0000TestEquation:DependentVariable:RESIDMethod:LeastSquaresDate:12/14/11Time:16Sample:Includedobservations:30Presamplemissingvaluelaggedresidualssettozero.Weightseries:1/GDPCoefficientStd.Errort-StatisticProb.

C-78.2202066.55056-1.0.2505GDP0.0152650.0127361.0.2415RESID(-1).0000RESID(-2)-0.0.-0.0.5292WeightedStatisticsR-squared0.

Meandependentvar-3.18E-13AdjustedR-squared0.S.D.S.D.dependentvar865.4524S.E.ofregression316.1443

Akaikeinfocriterion14.47384Sumsquaredresid.

Schwarzcriterion14.66067Loglikelihood-213.1076

Hannan-Quinncriter.14.53361F-statistic63.77566

Durbin-Watsonstat1.Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.

Meandependentvar2429.691AdjustedR-squared0.S.D.S.D.dependentvar7047.859S.E.ofregression1228.054

SumsquaredresidDurbin-Watsonstat0.据值判断拒绝原假设，所以BG（LM）检验结果也说明本式存在自相关。用广义最小乘数估计回归参数方法一：首先，估计自相关系数=1-DW/2=1-0.082459/2=0.9588对原变量做广义差分变换。令GDYt=Yt-0.9588Yt-1GDGDPt=GDPt-0.9588GDPt-1以GDYt、GDGDPt，（1972~2001）为样本再次回归，得图8DependentVariable:GDYMethod:LeastSquaresDate:12/14/11Time:17:05Sample(adjusted):Includedobservations:29afteradjustmentsCoefficientStd.Errort-StatisticProb.

C-268.1692444.0470-0.0.5509GDGDP0.0.07254810.882350.0000R-squared0.

Meandependentvar3076.325AdjustedR-squared0.S.D.S.D.dependentvar3933.489S.E.ofregression1725.983

Akaikeinfocriterion17.81145Sumsquaredresid

Schwarzcriterion17.90575Loglikelihood-256.2661

Hannan-Quinncriter.17.84099F-statistic118.4255

Durbin-Watsonstat0.Prob(F-statistic)0.000000得到回归式（-0.604）（10.88）R2=0.，DW=0.，T=30根据图7得，*=-268.17=*/(1-)=-268.17/(1-0.9588)=-6508.98则原模型的广义最小二乘估计结果是回归方程拟合得效果比较好，且DW=0.。通过查表，得dL=1.35，dU=1.49。因为DW=0.＞1.35，依据判别规则，误差项还没消除自相关，所以使用方法二消除自相关。图4残差图方法二1.首先，引进ar(1)，消除自相关，建立模型如下：表9DependentVariable:YMethod:LeastSquaresDate:12/15Sample(adjusted):Includedobservations:29afteradjustmentsConvergenceachievedafter32iterationsCoefficientStd.Errort-StatisticProb.

C-3399.4591818.546-1.0.0729GDP924090.0047AR(1)1.0.05195822.847450.0000R-squared0.

Meandependentvar15559.83AdjustedR-squared0.S.D.S.D.dependentvar22756.41S.E.ofregression1334.663

Akaikeinfocriterion17.32844Sumsquaredresid

Schwarzcriterion17.46989Loglikelihood-248.2624

Hannan-Quinncriter.17.37274F-statistic4056.981

Durbin-Watsonstat1.070551Prob(F-statistic)0.000000InvertedARRoots

1.19EstimatedARprocessisnonstationary得到回归式（-1.869）（3.092）R2=0.，DW=1.070551回归方程中的DW=1.070551，通过查表，得dL=1.35，dU=1.49。因为DW=1.070551＜1.35，依据判别规则，误差项还没有消除自相关，说明误差项存在二阶及以上的自相关。2.接着，引进ar(1)、ar(2)，消除自相关，得出模型表10DependentVariable:YMethod:LeastSquaresDate:12/15Sample(adjus