关于GDP与其他经济因素关系的计量分
析
关于GDP与其他经济因素关系的计量分析 GDP是指本国在一年内所生产创造的劳动产品及劳务的总价值。GDP 的增长对于一个国家有着十分重要的意义。他是衡量一国在过去的一年里所创造的劳动成果的重要指标，而研究它的影响因素不仅可以很好的了解GDP的经济内涵，而且还有利于我们根据这些因素对GDP影响大小来制定工作的重点以更好的促进国民经济的发展，因此我们组以GDP与其他经济因素关系建立模型，想通过计量经济学的研究手段来阐述它们之间的关系，但因水平有限，中间不乏缺陷，望大家见谅。 我们把GDP的影响因素分为以下四个因素：x2 能源消费总量 x3 进出口贸易总额 x4 固定资产投资 x5 货币供应量 随机扰动项。 数据如下： obs Y X2 X3 X4 X5
1991 21662.50 103783.0 7225.800 5594.500 19349.90 1992 26651.90 109170.0 9119.600 8080.100 25402.20 1993 34560.50 115993.0 11271.00 13072.30 34879.80 1994 46670.00 122737.0 20381.90 17042.10 46923.50 1995 57494.90 131176.0 23499.90 20019.30 60750.50 1996 66850.50 138948.0 24133.80 22913.50 76094.90 1997 73142.70 137798.0 26967.20 24941.10 90995.30 1998 76967.20 132214.0 26849.70 28406.20 104498.5 1999 80579.40 130779.0 29896.20 29854.70 119897.9 2000 88254.00 130297.0 39273.20 32917.70 134610.3 2001 95727.90 134914.8 42183.60 37213.49 158301.9
2002 103553.6 148000.0 51378.20 43499.91 185007.0 一、建立模型： 根据GDP的定义,GDP=消费+投资+净出口，而x2，x3 ，x4，x5与消费，投资及净出口有着一定的线性相关关系，基于数据的有限和操作的方便，我们把模型设成以下形式： 参数估计： Dependent Variable: Y Method: Least Squares Date: 05/08/04 Time: 18:17 Sample: 1991 2002 Included observations: 12 Variable Coefficient Std. Error t-Statistic Prob. X5 0.096079 0.224342 0.428270 0.6813
X4 1.972191 1.257707 1.568085 0.1608 X3 -0.346822 0.530434 -0.653845 0.5341 X2 0.318439 0.295800 1.076533 0.3174 C -22452.30 27984.60 -0.802309 0.4488 R-squared 0.985639 Mean dependent var 64342.93 Adjusted R-squared 0.977432 S.D. dependent var 27118.27 S.E. of regression 4073.867 Akaike info criterion 19.75691 Sum squared resid 1.16E+08 Schwarz criterion 19.95895 Log likelihood -113.5415 F-statistic 120.1049 Durbin-Watson stat 1.264884 Prob(F-statistic) 0.000002 将上述回归结果整理
如下： 0.985639 0.977432 F=120.1049 从回归结果看，可决系数很高，F值很大，但在显著性水平下，各项的回归系数都不显著，因此回归方程不能投入使用；该模型很可能存在多重共线性。和F值大反映了模型中各解释变量联合对Y的影响力显著，而t值小于临界值恰好反映了由于解释变量共线性的作用，使得不能分解出各个解释变量对Y独立影响。 二、多重共线性的检验 用Eviews计算解释变量之间的简单相关系数： Y X5 X4 X3 X2
Y 1.000000 0.973852 0.990785 0.968615 0.897252 X5 0.973852 1.000000 0.987899 0.979698 0.814824 X4 0.990785 0.987899 1.000000 0.983539 0.879404 X3 0.968615 0.979698 0.983539 1.000000 0.853171
X2 0.897252 0.814824 0.879404 0.853171 1.000000 由上表可以看出，解释变量之间存在高度的线性相关，同时也证明了，虽然整体上拟合较好，但不能分解出各个解释变量对Y独立影响。 三、模型修正 运用OLS方法逐一求Y对各个解释变量的回归，结合经济意义和统计检验选出拟合效果最好的一元线性回归方程。Eviews过程如下： Dependent Variable: Y Method: Least Squares Date: 05/07/04 Time: 20:48 Sample: 1991 2002 Included observations: 12 Variable Coefficient Std. Error t-Statistic Prob. X2 1.892978 0.294565 6.426347 0.0001 C -177928.3 37873.57 -4.697954 0.0008 R-squared 0.805060 Mean dependent var 64342.93 Adjusted R-squared 0.785566 S.D. dependent var 27118.27 S.E. of regression 12557.65 Akaike info criterion 21.86506 Sum squared resid 1.58E+09 Schwarz criterion 21.94588 Log likelihood -129.1904 F-statistic 41.29793 Durbin-Watson stat 0.500518 Prob(F-statistic) 0.000076 Dependent Variable: Y Method: Least Squares Date: 05/07/04 Time: 20:50 Sample: 1991 2002 Included observations: 12 Variable Coefficient Std. Error t-Statistic Prob. X3 1.950644 0.158296 12.32279 0.0000 C 13596.91 4596.028 2.958406 0.0143 R-squared 0.938215 Mean dependent var 64342.93 Adjusted R-squared 0.932036 S.D. dependent var 27118.27 S.E. of regression 7069.689 Akaike info criterion 20.71603 Sum squared resid 5.00E+08 Schwarz criterion 20.79685 Log likelihood -122.2962 F-statistic 151.8512 Durbin-Watson stat 0.753355 Prob(F-statistic) 0.000000 Dependent Variable: Y Method: Least Squares Date:
05/07/04 Time: 20:50 Sample: 1991 2002 Included observations: 12 Variable Coefficient Std. Error t-Statistic Prob. X4 2.328702 0.100669 23.13220 0.0000 C 9316.680 2625.880 3.548022 0.0053 R-squared 0.981655 Mean dependent var 64342.93 Adjusted R-squared 0.979820 S.D. dependent var 27118.27 S.E. of
regression 3852.305 Akaike info criterion 19.50174 Sum squared resid 1.48E+08 Schwarz criterion 19.58256 Log likelihood -115.0105 F-statistic 535.0988 Durbin-Watson stat 0.797211 Prob(F-statistic) 0.000000 Dependent Variable: Y Method: Least Squares Date: 05/07/04 Time: 20:50 Sample: 1991 2002 Included observations: 12 Variable Coefficient Std. Error t-Statistic Prob. X5 0.490803 0.036207 13.55559 0.0000 C 21123.16 3693.877 5.718426 0.0002 R-squared 0.948388 Mean dependent var 64342.93 Adjusted R-squared 0.943227 S.D. dependent var 27118.27 S.E. of regression 6461.494 Akaike info criterion 20.53612 Sum squared resid 4.18E+08 Schwarz criterion 20.61694 Log likelihood -121.2167 F-statistic 183.7540 Durbin-Watson stat 0.341465 Prob(F-statistic) 0.000000 从上述结果可以看出Y对X4的线性关系强，拟合程度好，即 逐步回归，将其余解释变量逐一代入上式 Dependent Variable: Y Method: Least Squares Date:
05/07/04 Time: 20:59 Sample: 1991 2002 Included observations: 12 Variable Coefficient Std. Error t-Statistic Prob. X2 0.241568 0.183157 1.318910 0.2198
X4 2.092039 0.204046 10.25279 0.0000 C -16007.96 19367.66 -0.826531 0.4299 R-squared 0.984626 Mean dependent
var 64342.93 Adjusted R-squared 0.981210 S.D. dependent var 27118.27 S.E. of regression 3717.305 Akaike info criterion 19.49170 Sum squared resid 1.24E+08 Schwarz criterion 19.61293 Log likelihood -113.9502 F-statistic 288.2051 Durbin-Watson stat 1.001296 Prob(F-statistic) 0.000000 Dependent Variable: Y Method: Least Squares Date: 05/07/04 Time: 21:08 Sample: 1991 2002 Included observations: 12 Variable Coefficient Std. Error t-Statistic Prob. X3 -0.361505 0.488539 -0.739972 0.4782 X4 2.743670 0.570174 4.811989 0.0010 C 8915.734 2741.457 3.252188 0.0100 R-squared 0.982707 Mean dependent var 64342.93 Adjusted R-squared 0.978864 S.D. dependent var 27118.27 S.E. of regression 3942.525 Akaike info criterion 19.60935 Sum squared resid 1.40E+08 Schwarz criterion 19.73058 Log likelihood -114.6561 F-statistic 255.7182 Durbin-Watson stat 1.108596 Prob(F-statistic) 0.000000 Dependent Variable: Y Method: Least Squares Date:
05/07/04 Time: 21:08 Sample: 1991 2002 Included observations: 12 Variable Coefficient Std. Error t-Statistic Prob. X4 2.805894 0.664973 4.219560 0.0022 X5 -0.103576 0.142588 -0.726401 0.4861