计量经济学模型分析方法

1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：DependentVariable:LOG(Y)Method:LeastSquaresDate:07/29/12Time:09:03Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.C1.6025280.8609781.8612880.0732LOG(X1)0.3254160.1037693.1359550.0040LOG(X2)0.5070780.04859910.433850.0000R-squared0.796506Meandependentvar7.448704AdjustedR-squared0.781971S.D.dependentvar0.364648S.E.ofregression0.170267Akaikeinfocriterion-0.611128Sumsquaredresid0.811747Schwarzcriterion-0.472355Loglikelihood12.47249F-statistic54.79806Durbin-Watsonstat1.964720Prob(F-statistic)0.000000（一）异方差的检验1、GQ检验法模型二：DependentVariable:LOG(Y)Method:LeastSquaresDate:07/29/12Time:09:19Sample:112Includedobservations:12VariableCoefficientStd.Errort-StatisticProb.C3.7446261.1911133.1438040.0119LOG(X1)0.3443690.0829994.1490770.0025LOG(X2)0.1689040.1188441.4212280.1890R-squared0.669065Meandependentvar7.239161AdjustedR-squared0.595524S.D.dependentvar0.133581S.E.ofregression0.084955Akaikeinfocriterion-1.881064Sumsquaredresid0.064957Schwarzcriterion-1.759837Loglikelihood14.28638F-statistic9.097834Durbin-Watsonstat1.810822Prob(F-statistic)0.0069002模型三：DependentVariable:LOG(Y)Method:LeastSquaresDate:07/29/12Time:09:20Sample:2031Includedobservations:12VariableCoefficientStd.Errort-StatisticProb.C-0.3533811.607461-0.2198380.8309LOG(X1)0.2108980.1582201.3329420.2153LOG(X2)0.8565220.1086017.8868560.0000R-squared0.878402Meandependentvar7.769851AdjustedR-squared0.851381S.D.dependentvar0.390363S.E.ofregression0.150490Akaikeinfocriterion-0.737527Sumsquaredresid0.203824Schwarzcriterion-0.616301Loglikelihood7.425163F-statistic32.50732Durbin-Watsonstat2.123203Prob(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：WhiteHeteroskedasticityTest:F-statistic4.920995Probability0.004339Obs*R-squared13.35705Probability0.009657TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:05/29/13Time:09:04Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.C3.9821372.8828511.3813190.1789LOG(X1)-0.5792890.916069-0.6323640.5327(LOG(X1))^20.0418390.0668660.6257100.53703LOG(X2)-0.5636560.203228-2.7735140.0101(LOG(X2))^20.0402800.0138792.9021730.0075R-squared0.430873Meandependentvar0.026185AdjustedR-squared0.343315S.D.dependentvar0.038823S.E.ofregression0.031460Akaikeinfocriterion-3.933482Sumsquaredresid0.025734Schwarzcriterion-3.702194Loglikelihood65.96898F-statistic4.920995Durbin-Watsonstat1.526222Prob(F-statistic)0.004339一方面，根据上面的Obs*R2=31*0.430873=13.35705＞χ2(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(LOG(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：DependentVariable:LOG(Y)Method:LeastSquaresDate:07/29/12Time:09:06Sample:131Includedobservations:31Weightingseries:1/LOG(X2)VariableCoefficientStd.Errort-StatisticProb.C1.4780850.8176101.8078110.0814LOG(X1)0.3779150.0969253.8990440.0006LOG(X2)0.4734710.0483989.7828640.0000WeightedStatisticsR-squared0.872646Meandependentvar7.423264AdjustedR-squared0.863550S.D.dependentvar0.436598S.E.ofregression0.161276Akaikeinfocriterion-0.719639Sumsquaredresid0.728274Schwarzcriterion-0.580866Loglikelihood14.15440F-statistic49.27256Durbin-Watsonstat2.036239Prob(F-statistic)0.000000UnweightedStatistics4R-squared0.789709Meandependentvar7.448704AdjustedR-squared0.774688S.D.dependentvar0.364648S.E.ofregression0.173088Sumsquaredresid0.838862Durbin-Watsonstat2.028211加权修正以后的模型四怀特检验结果如下：WhiteHeteroskedasticityTest: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：DependentVariable:LOG(Y)Method:LeastSquaresDate:07/29/12Time:09:10Sample:131Includedobservations:31Weightingseries:1/ABS(E)VariableCoefficientStd.Errort-StatisticProb.C1.2279290.2972684.1307080.0003LOG(X1)0.3757480.0568306.6117340.0000LOG(X2)0.5101200.01778128.688470.0000WeightedStatisticsR-squared0.999990Meandependentvar7.558578AdjustedR-squared0.999989S.D.dependentvar12.31758S.E.ofregression0.041062Akaikeinfocriterion-3.455703Sumsquaredresid0.047210Schwarzcriterion-3.316930Loglikelihood56.56339F-statistic1960.131Durbin-Watsonstat2.487309Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.794514Meandependentvar7.448704AdjustedR-squared0.779836S.D.dependentvar0.364648S.E.ofregression0.171099Sumsquaredresid0.8196945Durbin-Watsonstat2.007122对加权以后的模型五进行怀特检验如下：WhiteHeteroskedasticityTest: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：DependentVariable:YMethod:LeastSquaresDate:07/29/12Time:09:48Sample:19912011Includedobservations:21VariableCoefficientStd.Errort-StatisticProb.C178.975555.064213.2503050.0042X0.0200020.00113417.641570.0000R-squared0.942463Meandependentvar922.9095AdjustedR-squared0.939435S.D.dependentvar659.3491S.E.ofregression162.2653Akaikeinfocriterion13.10673Sumsquaredresid500270.3Schwarzcriterion13.20621Loglikelihood-135.6207F-statist