[经济学]第六章习题讲解计量经济学.docVIP

第六章自相关习题参考答案练习题6.1参考解答:（）建立回归模型，回归结果如下：Dependent Variable: YMethod: Least SquaresDate: 05/06/10 Time: 22:58Sample: 1960 1995Included observations: 36CoefficientStd. Errort-StatisticProb.X0.9358660.007467125.34110.0000C-9.4287452.504347-3.7649510.0006R-squared0.997841Mean dependent var289.9444Adjusted R-squared0.997777S.D. dependent var95.82125S.E. of regression4.517862Akaike info criterion5.907908Sum squared resid693.9767Schwarz criterion5.995881Log likelihood-104.3423Hannan-Quinn criter.5.938613F-statistic15710.39Durbin-Watson stat0.523428Prob(F-statistic)0.000000估计结果如下Se = (2.5043) (0.0075)t = (-3.7650)(125.3411)R2 = 0.9978，F = 15710.39，d f = 34，DW = 0.5234（）对样本量为36、一个解释变量的模型、5%显著水平，查DW统计表可知，dL=1.411，dU= 1.525，模型中DW dU，说明广义差分模型中已无自相关。同时，判定系数R2、t、F统计量均达到理想水平。由差分方程式可以得出：所以最终的消费模型为：由上述模型可知，美国个人实际可支配收入每增加1元，个人实际消费支出平均增加0.9484元。练习题6.2参考解答：（1） 模型1中存在自相关，模型2中不存在自相关。（2） 通过DW检验可以判定自相关的存在；在模型1中，DW=0.8252，查5%显著水平的DW统计表可知，因此模型1存在正自相关；而在模型2中，DW=1.82, 查5%显著水平的DW统计表可知，因此模型2不存在自相关。（3） 虚假自相关是由模型设定失误所造成的自相关，主要包括遗漏某些重要的解释变量或者模型函数形式不正确，因此在区分虚假自相关和真正自相关是主要从这两个方面来判断，即根据经济意义检查解释变量是否遗漏了重要的变量，或者根据数据的数字特征检验模型形式的设定是否恰当。练习题6.3参考解答：（）先对数据进行处理，收入-消费模型（个人实际收入与个人实际消费支出）个人实际消费支出=人均生活消费支出/商品零售物价指数*100建立回归模型，回归结果如下：Dependent Variable: YMethod: Least SquaresDate: 05/06/10 Time: 23:20Sample: 2001 2019Included observations: 19CoefficientStd. Errort-StatisticProb.X0.6904880.01287753.620680.0000C79.9300412.399196.4463900.0000R-squared0.994122Mean dependent var700.2747Adjusted R-squared0.993776S.D. dependent var246.4491S.E. of regression19.44245Akaike info criterion8.872095Sum squared resid6426.149Schwarz criterion8.971510Log likelihood-82.28490Hannan-Quinn criter.8.888920F-statistic2875.178Durbin-Watson stat0.574663Prob(F-statistic)0.000000估计结果如下（）DW0.575，对样本量为36、一个解释变量的模型、5%显著水平的DW统计表可知，说明误差项存在正自相关。（）采用广义差分法使用普通最小二乘法估计的估计值，得 由上式可知=0.657352，对原模型进行广义差分，得到广义差分方程：回归结果如下：Dependent Variable: Y-0.657352*Y(-1)Method: Least SquaresDate: 05/06/10 Time: 23:25Sample (adjusted): 2002 2019Included observations: 18 after adjustmentsCoefficientStd. Errort-StatisticProb.C35.977618.1035464.4397370.0004X-0.657352*X(-1)0.6686950.02064232.395120.0000R-squared0.984983Mean dependent var278.1002Adjusted R-squared0.984044S.D. dependent var105.1781S.E. of regression13.28570Akaike info criterion8.115693Sum squared resid2824.158Schwarz criterion8.214623Log likelihood-71.04124Hannan-Quinn criter.8.129334F-statistic1049.444Durbin-Watson stat1.830746Prob(F-statistic)0.000000估计结果如下DW=1.830，已知，模型中因此，在广义差分模型中已无自相关。由差分方程式可以得出：（错误）（正确）因此，修正后的回归模型应为由上述模型可知，个人实际收入每增加1元，个人实际支出平均增加0.668695元。6.4参考答案1原题（1）建立回归模型，回归结果如下：Dependent Variable: YMethod: Least SquaresDate: 11/26/10 Time: 19:47Sample: 1970 1994Included observations: 25CoefficientStd. Errort-StatisticProb.X1.5297120.05097630.008460.0000C-68.1602615.26513-4.4650960.0002R-squared0.975095Mean dependent var388.0000Adjusted R-squared0.974012S.D. dependent var43.33397S.E. of regression6.985763Akaike info criterion6.802244Sum squared resid1122.420Schwarz criterion6.899754Log likelihood-83.02805Hannan-Quinn criter.6.829289F-statistic900.5078Durbin-Watson stat0.348288Prob(F-statistic)0.000000 给定n=25，,在的显著水平下，查DW统计表可知，。模型中，所以可以判断模型中存在正自相关。（2）对模型的修正1）采广义差分法修正自相关：使用普通最小二乘法估计的估计值，得由上式可知=0.873772，对原模型进行广义差分，得到广义差分方程：回归结果如下：Dependent Variable: Y-0.873772*Y(-1)Method: Least SquaresDate: 11/26/10 Time: 20:04Sample (adjusted): 1971 1994Included observations: 24 after adjustmentsCoefficientStd. Errort-StatisticProb.X-0.873772*X(-1)1.2520330.1877946.6670590.0000C3.1980657.7907390.4104960.6854R-squared0.668922Mean dependent var54.86397Adjusted R-squared0.653873S.D. dependent var6.671848S.E. of regression3.925217Akaike info criterion5.652375Sum squared resid338.9612Schwarz criterion5.750547Log likelihood-65.82850Hannan-Quinn criter.5.678420F-statistic44.44968Durbin-Watson stat1.322343Prob(F-statistic)0.000001给定n=24，,在的显著水平下，查DW统计表可知，。模型中，DW值落在了无法判断的区域。 所以修正后的模型为：2）一阶差分法对模型进行一阶差分，回归结果如下：Dependent Variable: Y-Y(-1)Method: Least SquaresDate: 11/26/10 Time: 20:37Sample (adjusted): 1971 1994Included observations: 24 after adjustmentsCoefficientStd. Errort-StatisticProb.X-X(-1)1.3333330.13142210.145430.0000R-squared0.652682Mean dependent var6.208333Adjusted R-squared0.652682S.D. dependent var6.678839S.E. of regression3.936084Akaike info criterion5.619023Sum squared resid356.3333Schwarz criterion5.668109Log likelihood-66.42828Hannan-Quinn criter.5.632046Durbin-Watson stat1.591830给定n=24，,在的显著水平下，查DW统计表可知，。模型中，因此模型已不存在自相关。3）德宾两步法 建立辅助回归方程，回归结果如下：Dependent Variable: YMethod: Least SquaresDate: 11/26/10 Time: 20:43Sample (adjusted): 1971 1994Included observations: 24 after adjustmentsCoefficientStd. Errort-StatisticProb.C-7.63364112.84334-0.5943660.5589X1.1726220.1885276.2199190.0000X(-1)-1.0062720.254581-3.9526660.0008Y(-1)0.8962550.1239097.2331720.0000R-squared0.992083Mean dependent var391.6667Adjusted R-squared0.990896S.D. dependent var40.10927S.E. of regression3.827019Akaike info criterion5.673061Sum squared resid292.9215Schwarz criterion5.869403Log likelihood-64.07673Hannan-Quinn criter.5.725151F-statistic835.4552Durbin-Watson stat1.369050Prob(F-statistic)0.000000 把的回归系数看做的一个估计值，之后进行广义差分，回归模型为：回归结果如下：Dependent Variable: Y-0.896255*Y(-1)Method: Least SquaresDate: 11/26/10 Time: 20:47Sample (adjusted): 1971 1994Included observations: 24 after adjustmentsCoefficientStd. Errort-StatisticProb.X-0.896255*X(-1)1.2010310.1893056.3444250.0000C4.6528996.5955020.7054660.4879R-squared0.646596Mean dependent var46.19771Adjusted R-squared0.630532S.D. dependent var6.352384S.E. of regression3.861224Akaike info criterion5.619501Sum squared resid327.9990Schwarz criterion5.717672Log likelihood-65.43401Hannan-Quinn criter.5.645545F-statistic40.25173Durbin-Watson stat1.305817Prob(F-statistic)0.000002给定n=24，,在的显著水平下，查DW统计表可知，。模型中，DW值落在了无法判断的区域。2调换X和Y之后（1）建立回归模型，回归结果如下：Dependent Variable: YMethod: Least SquaresDate: 12/04/10 Time: 11:21Sample: 1970 1994Included observations: 25CoefficientStd. Errort-StatisticProb.X0.6374370.02124230.008460.0000C50.874548.2910586.1360730.0000R-squared0.975095Mean dependent var298.2000Adjusted R-squared0.974012S.D. dependent var27.97320S.E. of regression4.509491Akaike info criterion5.926864Sum squared resid467.7167Schwarz criterion6.024374Log likelihood-72.08580Hannan-Quinn criter.5.953909F-statistic900.5078Durbin-Watson stat0.352762Prob(F-statistic)0.000000 给定n=25，,在的显著水平下，查DW统计表可知，。模型中，所以可以判断模型中存在正自相关。（2）对模型的修正1）采广义差分法修正自相关：使用普通最小二乘法估计的估计值，得由上式可知=0.850961，对原模型进行广义差分，得到广义差分方程：回归结果如下：Dependent Variable: Y-0.850961*Y(-1)Method: Least SquaresDate: 12/04/10 Time: 11:17Sample (adjusted): 1971 1994Included observations: 24 after adjustmentsCoefficientStd. Errort-StatisticProb.X-0.850961*X(-1)0.5351250.0747937.1547960.0000C13.973344.7894362.9175330.0080R-squared0.699417Mean dependent var48.03762Adjusted R-squared0.685754S.D. dependent var4.550930S.E. of regression2.551144Akaike info criterion4.790616Sum squared resid143.1833Schwarz criterion4.888787Log likelihood-55.48739Hannan-Quinn criter.4.816661F-statistic51.19110Durbin-Watson stat2.377660Prob(F-statistic)0.000000给定n=24，,在的显著水平下，查DW统计表可知，。模型中，因此可以判断模型不存在自相关。 所以修正后的模型为：6.5参考解答：（1）建立回归模型，回归结果如下：Dependent Variable: LOG(Y)Method: Least SquaresDate: 05/07/10 Time: 00:17Sample: 1980 2000Included observations: 21CoefficientStd. Errort-StatisticProb.C2.1710410.2410259.0075290.0000LOG(X)0.9510900.03889724.451230.0000R-squared0.969199Mean dependent var8.039307Adjusted R-squared0.967578S.D. dependent var0.565486S.E. of regression0.101822Akaike info criterion-1.640785Sum squared resid0.196987Schwarz criterion-1.541307Log likelihood19.22825Hannan-Quinn criter.-1.619196F-statistic597.8626Durbin-Watson stat1.159788Prob(F-statistic)0.000000给定n=21，,在的显著水平下，查DW统计表可知，。模型中，所以可以判断模型中存在正自相关。（2）采用广义差分法修正自相关：使用普通最小二乘法估计的估计值，得由上式可知=0.400234，对原模型进行广义差分，得到广义差分方程：回归结果如下：Dependent Variable: LOG(Y)-0.400234*LOG(Y(-1)Method: Least SquaresDate: 05/07/10 Time: 00:21Sample (adjusted): 1981 2000Included observations: 20 after adjustmentsCoefficientStd. Errort-StatisticProb.C1.4770950.2256366.5463720.0000LOG(X)-0.400234*LOG(X(-1)0.9059890.05976715.158710.0000R-squared0.927357Mean dependent var4.882162Adjusted R-squared0.923321S.D. dependent var0.344052S.E. of regression0.095271Akaike inf