计量经济学模型分析方法.docx

1、计量经济学模型分析方法计量经济学上机模型分析方法总结一、随机误差项的异方差问题的检验与修正模型一：Dependent Variable: LOG(Y)Method: Least SquaresDate: 07/29/12 Time: 09:03Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb.C1.6025280.8609781.8612880.0732LOG(X1)0.3254160.1037693.1359550.0040LOG(X2)0.5070780.04859910.43

2、3850.0000R-squared0.796506Mean dependent var7.448704Adjusted R-squared0.781971S.D. dependent var0.364648S.E. of regression0.170267Akaike info criterion-0.611128Sum squared resid0.811747Schwarz criterion-0.472355Log likelihood12.47249F-statistic54.79806Durbin-Watson stat1.964720Prob(F-statistic)0.000

3、000（一）异方差的检验1、GQ检验法模型二：Dependent Variable: LOG(Y)Method: Least SquaresDate: 07/29/12 Time: 09:19Sample: 1 12Included observations: 12VariableCoefficientStd. Errort-StatisticProb.C3.7446261.1911133.1438040.0119LOG(X1)0.3443690.0829994.1490770.0025LOG(X2)0.1689040.1188441.4212280.1890R-squared0.669065

4、Mean dependent var7.239161Adjusted R-squared0.595524S.D. dependent var0.133581S.E. of regression0.084955Akaike info criterion-1.881064Sum squared resid0.064957Schwarz criterion-1.759837Log likelihood14.28638F-statistic9.097834Durbin-Watson stat1.810822Prob(F-statistic)0.006900模型三：Dependent Variable:

5、 LOG(Y)Method: Least SquaresDate: 07/29/12 Time: 09:20Sample: 20 31Included observations: 12VariableCoefficientStd. Errort-StatisticProb.C-0.3533811.607461-0.2198380.8309LOG(X1)0.2108980.1582201.3329420.2153LOG(X2)0.8565220.1086017.8868560.0000R-squared0.878402Mean dependent var7.769851Adjusted R-sq

6、uared0.851381S.D. dependent var0.390363S.E. of regression0.150490Akaike info criterion-0.737527Sum squared resid0.203824Schwarz criterion-0.616301Log likelihood7.425163F-statistic32.50732Durbin-Watson stat2.123203Prob(F-statistic)0.000076进行模型二和模型三两次回归，目的仅是得到出去中间7个样本点以后前后各12个样本点的残差平方和RSS1和RSS2，然后用较大的

7、RSS除以较小的RSS即可求出F统计量值进行显著性检验。2、怀特检验法（White）模型一的怀特残差检验结果：White Heteroskedasticity Test:F-statistic4.920995Probability0.004339Obs*R-squared13.35705Probability0.009657Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 05/29/13 Time: 09:04Sample: 1 31Included observations: 31VariableCoeff

8、icientStd. Errort-StatisticProb.C3.9821372.8828511.3813190.1789LOG(X1)-0.5792890.916069-0.6323640.5327(LOG(X1)20.0418390.0668660.6257100.5370LOG(X2)-0.5636560.203228-2.7735140.0101(LOG(X2)20.0402800.0138792.9021730.0075R-squared0.430873Mean dependent var0.026185Adjusted R-squared0.343315S.D. depende

9、nt var0.038823S.E. of regression0.031460Akaike info criterion-3.933482Sum squared resid0.025734Schwarz criterion-3.702194Log likelihood65.96898F-statistic4.920995Durbin-Watson stat1.526222Prob(F-statistic)0.004339 一方面，根据上面的Obs*R2=31*0.430873=13.357052(4)，说明存在显著的异方差问题；另一方面，根据下面的辅助回归模型可以看出LOG(X2) 与(LO

10、G(X2)2均通过了t检验，说明异方差的形式可以用LOG(X2) 与(LOG(X2)2的线性组合表示，权变量可以简单确定为1/LOG(X2)。（二）加权最小二乘法（WLS）修正1、方法原理：具体参见教材。2、回归结果分析模型四：Dependent Variable: LOG(Y)Method: Least SquaresDate: 07/29/12 Time: 09:06Sample: 1 31Included observations: 31Weighting series: 1/LOG(X2)VariableCoefficientStd. Errort-StatisticProb.C1.4

11、780850.8176101.8078110.0814LOG(X1)0.3779150.0969253.8990440.0006LOG(X2)0.4734710.0483989.7828640.0000Weighted StatisticsR-squared0.872646Mean dependent var7.423264Adjusted R-squared0.863550S.D. dependent var0.436598S.E. of regression0.161276Akaike info criterion-0.719639Sum squared resid0.728274Schw

12、arz criterion-0.580866Log likelihood14.15440F-statistic49.27256Durbin-Watson stat2.036239Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.789709Mean dependent var7.448704Adjusted R-squared0.774688S.D. dependent var0.364648S.E. of regression0.173088Sum squared resid0.838862Durbin-Watson stat2

13、.028211加权修正以后的模型四怀特检验结果如下：White Heteroskedasticity Test:F-statistic6.555091Probability0.000870Obs*R-squared15.56541Probability0.003661可以看出并没有消除异方差性，加权修正无效。下面采用1/abs(e)权变量进行WLS回归，结果如下：模型五：Dependent Variable: LOG(Y)Method: Least SquaresDate: 07/29/12 Time: 09:10Sample: 1 31Included observations: 31Wei

14、ghting series: 1/ABS(E)VariableCoefficientStd. Errort-StatisticProb.C1.2279290.2972684.1307080.0003LOG(X1)0.3757480.0568306.6117340.0000LOG(X2)0.5101200.01778128.688470.0000Weighted StatisticsR-squared0.999990Mean dependent var7.558578Adjusted R-squared0.999989S.D. dependent var12.31758S.E. of regre

15、ssion0.041062Akaike info criterion-3.455703Sum squared resid0.047210Schwarz criterion-3.316930Log likelihood56.56339F-statistic1960.131Durbin-Watson stat2.487309Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.794514Mean dependent var7.448704Adjusted R-squared0.779836S.D. dependent var0.3646

16、48S.E. of regression0.171099Sum squared resid0.819694Durbin-Watson stat2.007122对加权以后的模型五进行怀特检验如下：White Heteroskedasticity Test:F-statistic0.199645Probability0.936266Obs*R-squared0.923778Probability0.921125可以看出，模型已经不再存在异方差问题，模型五可以作为修正以后的最终模型。二、随机误差项序列相关性问题的检验与修正 模型一：Dependent Variable: YMethod: Least

17、 SquaresDate: 07/29/12 Time: 09:48Sample: 1991 2011Included observations: 21VariableCoefficientStd. Errort-StatisticProb.C178.975555.064213.2503050.0042X0.0200020.00113417.641570.0000R-squared0.942463Mean dependent var922.9095Adjusted R-squared0.939435S.D. dependent var659.3491S.E. of regression162.

18、2653Akaike info criterion13.10673Sum squared resid500270.3Schwarz criterion13.20621Log likelihood-135.6207F-statistic311.2248Durbin-Watson stat0.658849Prob(F-statistic)0.000000 初始回归模型一经济意义合理，统计指标较为理想，但DW值偏低，模型可能存在序列相关性。（一）序列相关性的检验方法1、自回归模型检验法Dependent Variable: EMethod: Least SquaresDate: 07/29/12 T

19、ime: 09:49Sample (adjusted): 1992 2011Included observations: 20 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.E(-1)0.7170800.2018523.5524970.0021R-squared0.398929Mean dependent var2.801737Adjusted R-squared0.398929S.D. dependent var161.7297S.E. of regression125.3870Akaike info criter

20、ion12.54939Sum squared resid298716.2Schwarz criterion12.59918Log likelihood-124.4939Durbin-Watson stat1.080741说明模型一的随机误差项至少存在一阶正序列相关性，结合该自回归模型的DW值为1.08，怀疑存在更高阶的序列相关，继续引入e(-2)如下：Dependent Variable: EMethod: Least SquaresDate: 07/29/12 Time: 09:49Sample (adjusted): 1993 2011Included observations: 19 a

21、fter adjustmentsVariableCoefficientStd. Errort-StatisticProb.E(-1)1.0949740.1787686.1251080.0000E(-2)-0.8150100.199977-4.0755130.0008R-squared0.692885Mean dependent var7.790341Adjusted R-squared0.674819S.D. dependent var164.5730S.E. of regression93.84710Akaike info criterion12.02051Sum squared resid

22、149723.7Schwarz criterion12.11993Log likelihood-112.1949Durbin-Watson stat1.945979由于e(-2)的t检验显著，说明模型一的随机误差项确实存在二阶正序列相关性，结合该二阶自回归模型的DW值为1.95，基本确定不存在更高阶的序列相关。Breusch-Godfrey Serial Correlation LM Test:F-statistic0.888958Probability0.431668Obs*R-squared1.998924Probability0.368077可以看出二阶自回归模型的随机误差项不存在序列相

23、关性，论证了原模型仅存在二阶序列相关。2、DW检验法0DWdL 存在正自相关(趋近于0) DLDWdU 不能确定 DUDW4dU 无自相关（趋近于2）3、LM检验法原理：一方面，根据上面的假设检验结果判断是否存在序列相关性，即根据(n-p)*R2统计量值与卡方检验临界值2(P)进行比较，其中n为原模型样本容量，P为选择的滞后阶数，R2为下面辅助回归模型的可决系数。若(n-p)*R22(P)，则拒绝不序列相关的原假设，说明模型存在显著的序列相关性；另一方面，结合下面的辅助回归模型中残差滞后变量是否通过t检验及DW值判断序列相关的具体阶数，方法与上面的自回归模型检验法相同。选择滞后一阶检验：Breusch-Godfrey Serial Correlation LM Test:F-statistic13.15036Probability0.001931Obs*R-squared8.865308Probability0.002906Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 07/29/12