计量经济学

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

0.826210 S.D. dependent var 127.6320 Akaike info criterion 162899.2 Schwarz criterion -74.12314 F-statistic 1.055825 Prob(F-statistic)

306.1590 12.68719 12.76801 53.29478 0.000026

⑶利用样本2建立回归模型2（回归结果如图4），其残差平方和为63769.67。

SMPL 19 31 LS Y C X

Dependent Variable: Y Method: Least Squares Date: 05/14/15 Time: 09:16 Sample: 19 31

Included observations: 13

Variable C X

R-squared

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

Coefficient 650.1853 0.043657

Std. Error 694.6909 0.021797

t-Statistic 0.935935 2.002851

Prob. 0.3694 0.0705 2031.615 334.1358 14.37771 14.46462 4.011411 0.070459

0.267224 Mean dependent var 0.200608 S.D. dependent var 298.7466 Akaike info criterion 981744.6 Schwarz criterion -91.45509 F-statistic 1.409224 Prob(F-statistic)

⑷计算F统计量：F?RSS2/RSS1＝981744.6/162899.2=6.086，RSS1和RSS2分别是模型1和模型2的残差平方和。

⒊White检验

⑴建立回归模型：LS Y C X，回归结果如图5

Dependent Variable: Y Method: Least Squares Date: 05/14/15 Time: 09:23 Sample: 1 31

Included observations: 31

Variable C X R-squared

Adjusted R-squared S.E. of regression Sum squared resid

Coefficient -648.1236 0.084665 Std. Error 118.1625 0.004882 t-Statistic -5.485018 17.34164 Prob. 0.0000 0.0000 820.9407 13.92404 14.01655

0.912050 Mean dependent var 1250.323 0.909017 S.D. dependent var 247.6234 Akaike info criterion 1778203. Schwarz criterion

Log likelihood Durbin-Watson stat

-213.8226 F-statistic 0.911579 Prob(F-statistic)

300.7324 0.000000

收入储蓄模型

White Heteroskedasticity Test: F-statistic Obs*R-squared

Test Equation:

Dependent Variable: RESID^2 Method: Least Squares Date: 05/14/15 Time: 09:24 Sample: 1 31

Included observations: 31

Variable C X X^2 R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Coefficient 11957.49 -1.085004 0.000119 Std. Error 69304.55 6.784670 0.000147 t-Statistic 0.172535 -0.159920 0.808623 Prob. 0.8643 0.8741 0.4255 68305.92 24.81742 24.95619 7.840687 0.001977 7.840687 Probability 11.12883 Probability

0.001977 0.003832

0.358995 Mean dependent var 57361.38 0.313208 S.D. dependent var 56607.09 Akaike info criterion 8.97E+10 Schwarz criterion -381.6700 F-statistic 1.842409 Prob(F-statistic)

图6 White检验结果

因为本例为一元函数，没有交叉乘积项，则辅助函数为 ?t=?0+?1xt+?2xt+?t

22从上表可以看出，nR=11.12889 ，有White检验知，在?=0,05下，查?2分布表，得临界值?20.05（2）=5.99147。比较计算的?2统计量与临界值，因为nR= 11.12889> ?20.05（2）=5.99147 ，所以拒绝原假设，不拒绝备择假设，这表明模型存在异方差。 ⒋Park检验

⑴建立回归模型（结果同图5所示）。

⑵生成新变量序列：GENR LNE2=log(RESID^2)

GENR LNX=log(x)

Lne2 = log (resid^2)

22

一、调整异方差性 ⒈确定权数变量

根据Park检验生成权数变量：GENR W1=1/X

根据Gleiser检验生成权数变量：GENR W2=1/sqr(x) 另外生成：GENR W3=1/ABS(RESID）

GENR W4=1/ RESID ^2

⒉利用加权最小二乘法估计模型

在Eviews命令窗口中依次键入命令：

LS(W=Wi) Y C x

Dependent Variable: Y Method: Least Squares Date: 05/14/15 Time: 08:58 Sample: 1 31

Included observations: 31 Weighting series: W1

Variable C X

Weighted Statistics R-squared

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

Coefficient -722.5037 0.088139

Std. Error 72.36495 0.004372 t-Statistic -9.984166 20.15822 Prob. 0.0000 0.0000 399.3095 13.42353 13.51605 99.68358

0.774641 Mean dependent var 894.6561 0.766870 S.D. dependent var 192.8008 Akaike info criterion 1077992. Schwarz criterion -206.0648 F-statistic

Durbin-Watson stat Unweighted Statistics R-squared

Adjusted R-squared S.E. of regression Durbin-Watson stat Dependent Variable: Y Method: Least Squares

0.994618 Prob(F-statistic)

0.000000 820.9407 1809626.

0.910496 Mean dependent var 1250.323 0.907409 S.D. dependent var 249.8017 Sum squared resid 0.882555

表一

Date: 05/14/15 Time: 09:02 Sample: 1 31

Included observations: 31 Weighting series: W2

Variable C X Weighted Statistics R-squared

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

Adjusted R-squared S.E. of regression Durbin-Watson stat Dependent Variable: Y Method: Least Squares Date: 05/14/15 Time: 09:10 Sample: 1 31

Included observations: 31 Weighting series: W3 Variable C X Weighted Statistics R-squared

Adjusted R-squared S.E. of regression

Coefficient -33.92583 0.061347 Std. Error 246.1740 0.008093 t-Statistic -0.137812 7.579815 Prob. 0.8913 0.0000 1656.803 14.95203

Coefficient -706.6985 0.087277

Std. Error 87.89896 0.004334

t-Statistic -8.039896 20.13992

Prob. 0.0000 0.0000 592.3382 13.63491 13.72742 200.2157 0.000000 820.9407 1795757.

0.873482 Mean dependent var 1071.763 0.869119 S.D. dependent var 214.2931 Akaike info criterion 1331725. Schwarz criterion -209.3411 F-statistic 0.955188 Prob(F-statistic) 0.911182 Mean dependent var 1250.323 0.908119 S.D. dependent var 248.8427 Sum squared resid 0.892586 表二

0.939637 Mean dependent var 1594.726 0.937555 S.D. dependent var 414.0173 Akaike info criterion