《计量经济学》李子奈第三版课后习题Eviews实验报告

开始检验异方差 图示法：

在工作文件窗口按Genr,在主窗口键入命令e2=resid^2，依次单击Quick→Graph→Scatter可得散点图：

200000160000120000E280000400000400060008000X1000012000 显然，散点不在一条水平直线上，即说明存在异方差性。

White检验法:

依次单击View→Residual Tests→White Heteroskedasticity因为本题为一元函数，故无交叉乘积项，选no cross terms。经估计出现white检验结果，如下图： White Heteroskedasticity Test: F-statistic Obs*R-squared Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 12/11/11 Time: 11:16 Sample: 1 20 Included observations: 20 Variable C X X^2 Coefficient -180998.9 49.42846 -0.002115 Std. Error 103318.2 28.93929 0.001847 14.63595 Probability 12.65213 Probability t-Statistic -1.751858 1.708006 -1.144742 0.000201 0.001789 Prob. 0.0978 0.1058 0.2682 weibo.com/kouqintang

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat 0.632606 Mean dependent var 0.589384 S.D. dependent var 29014.92 Akaike info criterion 1.43E+10 Schwarz criterion -232.2649 F-statistic 2.081758 Prob(F-statistic) 42337.15 45279.67 23.52649 23.67585 14.63595 0.000201 2nR?12.65?5%置信水平下的卡方值5.99

所以拒绝原假设，表明模型存在异方差。

Goldfeld-Quanadt检验法：

在命令栏中直接输入：sort x，得到按照升序排列的x。 开始取样本，依次单击quick→sample，填入“1 8”，回归模型ls y c x； 得到如下结果：

Dependent Variable: Y Method: Least Squares Date: 12/11/11 Time: 11:26 Sample: 1 8

Included observations: 8

Variable C X

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

Coefficient 1277.161 0.554126

Std. Error 1540.604 0.311432

t-Statistic 0.829000 1.779287

Prob. 0.4388 0.1255 4016.814 166.1712 13.00666 13.02652 3.165861 0.125501

0.345397 Mean dependent var 0.236296 S.D. dependent var 145.2172 Akaike info criterion 126528.3 Schwarz criterion -50.02663 F-statistic 3.004532 Prob(F-statistic)

继续取样本，依次单击quick→sample，填入“13 20”，回归模型ls y c x； 得到如下结果：

Dependent Variable: Y Method: Least Squares Date: 12/11/11 Time: 11:28 Sample: 13 20

Included observations: 8

Variable C

Coefficient 212.2118

Std. Error 530.8892

t-Statistic 0.399729

Prob. 0.7032

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X

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

0.761893 0.060348 12.62505 0.0000 6760.477 1556.814 14.58858 14.60844 159.3919 0.000015

0.963723 Mean dependent var 0.957676 S.D. dependent var 320.2790 Akaike info criterion 615472.0 Schwarz criterion -56.35432 F-statistic 1.722960 Prob(F-statistic)

计算F

=4.28，拒绝原假设，表明模型确实存在异方差性。

统计量：F=RSS2/RSS1=615472.0/126528.3=4.864；F=4.864> F0.05（6,6）

异方差的修正：

在对原模型进行OLS后，单击Quick→Generate Series,在弹出的对话框内输w1=1/e,w2=1/e^2。再选择Quick→Estimate Equation,在弹出的对话框中选择Options按钮，在出现的画面中，选中Weight Ls/TLS复选框，在 Weight内分别输入“w1”，“w2”，分别得下图： Dependent Variable: Y Method: Least Squares Date: 12/11/11 Time: 11:33 Sample: 1 20 Included observations: 20 Weighting series: W1 Variable C X R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat R-squared Adjusted R-squared S.E. of regression Durbin-Watson stat Coefficient 415.6603 0.729026 Std. Error 116.9791 0.022429 t-Statistic 3.553288 32.50349 Prob. 0.0023 0.0000 4471.606 7313.160 11.62138 11.72096 1056.477 0.000000 5199.515 1625.275 920263.9 Weighted Statistics 0.999895 Mean dependent var 0.999889 S.D. dependent var 77.04831 Akaike info criterion 106856.0 Schwarz criterion -114.2138 F-statistic 2.367808 Prob(F-statistic) Unweighted Statistics 0.981664 Mean dependent var 0.980645 S.D. dependent var 226.1101 Sum squared resid 1.886959 weibo.com/kouqintang

Dependent Variable: Y Method: Least Squares Date: 12/11/11 Time: 11:34 Sample: 1 20 Included observations: 20 Weighting series: W2 Variable C X R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat R-squared Adjusted R-squared S.E. of regression Durbin-Watson stat Coefficient 117.0597 0.786976 Std. Error 134.7186 0.026058 t-Statistic 0.868920 30.20073 Prob. 0.3963 0.0000 4207.516 15774.21 8.396039 8.495613 912.0839 0.000000

Weighted Statistics 0.999999 Mean dependent var 0.999999 S.D. dependent var 15.35992 Akaike info criterion 4246.688 Schwarz criterion -81.96039 F-statistic 2.113659 Prob(F-statistic) Unweighted Statistics 5199.515 1625.275 989692.9 0.980281 Mean dependent var 0.979185 S.D. dependent var 234.4844 Sum squared resid 1.836717

经估计发现用w2=1/e^2作为合适的权。 再检验：

单击Quick→Generate Series，分别输入x1=x*w2,y1=y*w2,按住ctrl,依次点击x1,y1，右键选择Open as group，依次单击Quick→Graph可得下图：

504030Y1201000102030X1405060 由该图可知，加权后X和Y的散点图在同一直线上，所以是同方差性。

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