计量经济学报告evjk.docx

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1、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)19722518.1105.2198711962.53081.419732720.9121.2198814928.33822.219742789.9136.5198916909.25196.419752997.3149.6199018547.97119.819762943.7159.1199121617.89141.61977320

2、1.9181.6199226638.11175819783624.1210.6199334634.415203.519794038.2281199446759.421518.819804517.8399.5199558478.129662.319814862.4523.7199667884.638520.819825294.7675.4199774462.646279.819835934.5892.5199878345.253407.5198471711214.7199982067.4659621.819858964.41622.6200089442.264332.4198610202.222

3、38.5200195933.373762.4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2Dependent Variable: YMe

4、thod: Least SquaresDate: 12/13/11 Time: 12:27Sample: 1972 2001Included observations: 30CoefficientStd. Errort-StatisticProb.C-4366.305932.1408-4.6841690.0001GDP0.7185770.02291831.354660.0000R-squared0.972308Mean dependent var15044.68Adjusted R-squared0.971319S.D. dependent var22537.94S.E. of regress

5、ion3816.918Akaike info criterion19.39661Sum squared resid4.08E+08Schwarz criterion19.49003Log likelihood-288.9492Hannan-Quinn criter.19.42650F-statistic983.1150Durbin-Watson stat0.206704Prob(F-statistic)0.000000 (-4.68) (31.35), R2 =0.9723，DW=0.206704，T=30第四步，统计检验1. 拟合优度样本可决系数为R-squared=0.972308修正样本

6、可决系数为：Adjusted R-squared=0.971319即R2=0.972308，2 =0.971319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。2. 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=-4.684169的t-Statistic=31.35466对于给出显著性水平=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|=4.684169t0.025（28）=2.05，t1=31.35466t0.025（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

7、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。3. 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=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=983.11503.35,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=0.206704，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GD

8、P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3Heteroskedasticity Test: WhiteF-statistic10.36874Prob. F(2,27)0.0005Obs*R-squared13.03220Prob. Chi-Square(2)0.0015Scaled explained SS13.06975Prob. Chi-Square(2)0.0015Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/15/11 Time:

9、21:15Sample: 1972 2001Included observations: 30CoefficientStd. Errort-StatisticProb.C-57307.365222451.-0.0109730.9913GDP650.9958433.64191.5012290.1449GDP2-0.0023760.004863-0.4885350.6291R-squared0.434407Mean dependent var13597608Adjusted R-squared0.392511S.D. dependent var20985874S.E. of regression1

10、6356723Akaike info criterion36.15282Sum squared resid7.22E+15Schwarz criterion36.29294Log likelihood-539.2922Hannan-Quinn criter.36.19764F-statistic10.36874Durbin-Watson stat1.029242Prob(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

11、=30*0.4344=13.03220，所以结论是该回归模型中存在异方差。3. 克服异方差异方差修正如下：表4Dependent Variable: YMethod: Least SquaresDate: 12/14/11 Time: 16:27Sample: 1972 2001Included observations: 30Weighting series: 1/GDPCoefficientStd. Errort-StatisticProb.C-1584.144176.6377-8.9683210.0000GDP0.5256390.03388215.513990.0000Weighted

12、StatisticsR-squared0.895788Mean dependent var2121.702Adjusted R-squared0.892066S.D. dependent var1703.101S.E. of regression880.7714Akaike info criterion16.46381Sum squared resid21721230Schwarz criterion16.55723Log likelihood-244.9572Hannan-Quinn criter.16.49370F-statistic240.6838Durbin-Watson stat0.

13、082459Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.890189Mean dependent var15044.68Adjusted R-squared0.886267S.D. dependent var22537.94S.E. of regression7600.750Sum squared resid1.62E+09Durbin-Watson stat0.075333再进行White检验：表5Heteroskedasticity Test: WhiteF-statistic2.453316Prob. F(2,27)0

14、.1050Obs*R-squared4.613428Prob. Chi-Square(2)0.0996Scaled explained SS2.426664Prob. 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 = 0.895788, DW=0.082459 第六步，检验误差项ut是否存在自相关1. 已知DW=0.082459，若给定=0.05，查表可得DW检验临界值dL=1.35，dU=1.49。因为DW=0.0824591.35，依据判别规则，认为误差

15、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-Godfrey Serial Correlation LM Test:F-statistic195.2096Prob. F(1,27)0.0000Obs*R-squared26.35479Prob. Chi-Square(1)0.0000Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 12/14/11 Time: 16:39Sample: 1972 2001Included obse

16、rvations: 30Presample missing value lagged residuals set to zero.Weight series: 1/GDPCoefficientStd. Errort-StatisticProb.C-90.4259463.03508-1.4345340.1629GDP0.0175370.0120921.4502230.1585RESID(-1)1.1382960.08147113.971740.0000Weighted StatisticsR-squared0.878493Mean dependent var-3.18E-13Adjusted R

17、-squared0.869493S.D. dependent var865.4524S.E. of regression312.6517Akaike info criterion14.42270Sum squared resid2639280.Schwarz criterion14.56282Log likelihood-213.3404Hannan-Quinn criter.14.46752F-statistic97.60479Durbin-Watson stat1.384248Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.

18、971780Mean dependent var2429.691Adjusted R-squared0.969690S.D. dependent var7047.859S.E. of regression1227.018Sum squared resid40650455Durbin-Watson stat0.089874然后，设定滞后期为二阶，得到LM检验结果表7Breusch-Godfrey Serial Correlation LM Test:F-statistic95.66349Prob. F(2,26)0.0000Obs*R-squared26.41094Prob. Chi-Squar

19、e(2)0.0000Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 12/14/11 Time: 16:49Sample: 1972 2001Included observations: 30Presample missing value lagged residuals set to zero.Weight series: 1/GDPCoefficientStd. Errort-StatisticProb.C-78.2202066.55056-1.1753500.2505GDP0.0152650.012736

20、1.1986450.2415RESID(-1)1.2639890.2136115.9172470.0000RESID(-2)-0.1649420.258630-0.6377550.5292Weighted StatisticsR-squared0.880365Mean dependent var-3.18E-13Adjusted R-squared0.866561S.D. dependent var865.4524S.E. of regression316.1443Akaike info criterion14.47384Sum squared resid2598628.Schwarz cri

21、terion14.66067Log likelihood-213.1076Hannan-Quinn criter.14.53361F-statistic63.77566Durbin-Watson stat1.610521Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.972780Mean dependent var2429.691Adjusted R-squared0.969639S.D. dependent var7047.859S.E. of regression1228.054Sum squared resid392110

22、44Durbin-Watson stat0.106734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。3. 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，（19722001）为样本再次回归，得图8Dependent Variable: GDYMethod: Least SquaresDate: 12/14/11 Time: 17:05Sample (adjusted): 197

23、3 2001Included observations: 29 after adjustmentsCoefficientStd. Errort-StatisticProb.C-268.1692444.0470-0.6039210.5509GDGDP0.7894960.07254810.882350.0000R-squared0.814338Mean dependent var3076.325Adjusted R-squared0.807462S.D. dependent var3933.489S.E. of regression1725.983Akaike info criterion17.8

24、1145Sum squared resid80433503Schwarz criterion17.90575Log likelihood-256.2661Hannan-Quinn criter.17.84099F-statistic118.4255Durbin-Watson stat0.879545Prob(F-statistic)0.000000得到回归式 （-0.604） （10.88） R2 =0.814338，DW=0.879545，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

25、效果比较好，且DW=0.879545。通过查表，得dL=1.35，dU=1.49。因为DW=0.8795451.35，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9Dependent Variable: YMethod: Least SquaresDate: 12/15/11 Time: 14:25Sample (adjusted): 1973 2001Included observations: 29 after adjustmentsConvergence achieved after 32 iter

26、ationsCoefficientStd. Errort-StatisticProb.C-3399.4591818.546-1.8693280.0729GDP0.3833810.1239753.0924090.0047AR(1)1.1871060.05195822.847450.0000R-squared0.996806Mean dependent var15559.83Adjusted R-squared0.996560S.D. dependent var22756.41S.E. of regression1334.663Akaike info criterion17.32844Sum sq

27、uared resid46314443Schwarz criterion17.46989Log likelihood-248.2624Hannan-Quinn criter.17.37274F-statistic4056.981Durbin-Watson stat1.070551Prob(F-statistic)0.000000Inverted AR Roots1.19Estimated AR process is nonstationary得到回归式（-1.869） （3.092） R2 =0.996806，DW=1.070551回归方程中的DW=1.070551，通过查表，得dL=1.35

28、，dU=1.49。因为DW=1.0705511.35，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10Dependent Variable: YMethod: Least SquaresDate: 12/15/11 Time: 14:37Sample (adjusted): 1974 2001Included observations: 28 after adjustmentsConvergence achieved after 38 iterationsCoefficientStd. Errort-St

29、atisticProb.C-4514.5103957.539-1.1407370.2652GDP0.7596560.0933658.1364450.0000AR(1)1.5414610.1989147.7493740.0000AR(2)-0.6496500.214026-3.0353800.0057R-squared0.996138Mean dependent var16111.21Adjusted R-squared0.995655S.D. dependent var22975.87S.E. of regression1514.528Akaike info criterion17.61516

30、Sum squared resid55051085Schwarz criterion17.80547Log likelihood-242.6122Hannan-Quinn criter.17.67334F-statistic2063.247Durbin-Watson stat1.699565Prob(F-statistic)0.000000Inverted AR Roots.77-.24i.77+.24i回归方程中的DW=1.699565，通过查表，得dL=1.35，dU=1.49。因为DW=1.699565（4-1.49）=2.51，依据判别规则，误差项已经消除自相关。得到原模型的广义最小二乘估计结果是（-1.14） （8.136） R2 =0.996138，DW=1.699565经济含义是GDP占中国储蓄存款总额的75.97%。第七步，预测假如2002年、2003年的GDP分别为110000亿元、125000亿元，求2002、2003年的储蓄存款总额预测值。图5从图中可以看出，在样本区间里，中国储蓄存款总额Y样本值及其估计值非常接近，2002年、2003年预测值的变化趋势也符合样本区间的变化趋势。即假如2002年、2003年的GDP分别为110000亿元、125000亿元，则YF2002=74677.22亿元,YF2003=85455.88亿元。15