计量经济学 - 庞皓 - 第三版课后答案

6.1

(1)建立居民收入-消费模型，用Eviews分析结果如下： Dependent Variable: Y Method: Least Squares Date: 12/20/14 Time: 14:22 Sample: 1 19 Included observations: 19

Variable Coefficient Std. Error t-Statistic X 0.690488 0.012877 53.62068 C 79.93004 12.39919 6.446390 R-squared 0.994122 Mean dependent var

Adjusted R-squared 0.993776 S.D. dependent var S.E. of regression 19.44245 Akaike info criterion Sum squared resid 6426.149 Schwarz criterion Log likelihood -82.28490 Hannan-Quinn criter. F-statistic 2875.178 Durbin-Watson stat Prob(F-statistic) 0.000000

所得模型为： Y=0.690488X+79.93004 Se=(0.012877)(12.39919) t=(53.62068)(6.446390) R2=0.994122 F=2875.178 DW=0.574663 （2） 1）检验模型中存在的问题 ①做出残差图如下： 50403020100-10-20-30-4024681012141618 Prob. 0.0000 0.0000 700.2747 246.4491 8.872095 8.971510 8.888920 0.574663

Y Residuals 残差的变动有系统模式，连续为正和连续为负，表明残差项存在一阶自相关。

②该回归方程可决系数较高，回归系数均显著。对样本量为19，一个解释变量的模型，5%的显著水平，查DW统计表可知，dL=1.180，dU=1.401，模型中DW=0.574663,< dL,显然模型中有自相关。

③对模型进行BG检验，用Eviews分析结果如下： Breusch-Godfrey Serial Correlation LM Test:

F-statistic 4.811108 Prob. F(2,15) 0.0243

Obs*R-squared 7.425088 Prob. Chi-Square(2) 0.0244

Test Equation: Dependent Variable: RESID Method: Least Squares Date: 12/20/14 Time: 15:03 Sample: 1 19 Included observations: 19 Presample missing value lagged residuals set to zero.

Variable Coefficient Std. Error t-Statistic Prob. X -0.003275 0.010787 -0.303586 0.7656 C 1.929546 10.35593 0.186323 0.8547 RESID(-1) 0.608886 0.292707 2.080189 0.0551 RESID(-2) 0.089988 0.291120 0.309110 0.7615

R-squared 0.390794 Mean dependent var -1.65E-13

Adjusted R-squared 0.268953 S.D. dependent var 18.89466 S.E. of regression 16.15518 Akaike info criterion 8.587023 Sum squared resid 3914.848 Schwarz criterion 8.785852 Log likelihood -77.57671 Hannan-Quinn criter. 8.620672 F-statistic 3.207406 Durbin-Watson stat 1.570723 Prob(F-statistic) 0.053468

如上表显示，LM=TR2=7.425088，其p值为0.0244，表明存在自相关。

2）对模型进行处理： ①采取广义差分法

a)为估计自相关系数ρ。对et进行滞后一期的自回归，用EViews分析结果如下： Dependent Variable: E Method: Least Squares Date: 12/20/14 Time: 15:04 Sample (adjusted): 2 19