计量经济学计量经济学第五章异方差性作业.doc

本文档系作者精心整理编辑，实用价值高。作业 计量经济学第五章异方差性 5.1手写板已交5.2解(1)由题中数据由Eviews软件进行估计结果如下 Dependent Variable: YMethod: Least SquaresDate: 01/01/04 Time: 00:54Sample: 1901 1960Included observations: 60VariableCoefficientStd. Errort-StatisticProb. C9.3475223.6384372.5691040.0128X0.6370690.01990332.008810.0000R-squared0.946423 Mean dependent var119.6667Adjusted R-squared0.945500 S.D. dependent var38.68984S.E. of regression9.032255 Akaike info criterion7.272246Sum squared resid4731.735 Schwarz criterion7.342058Log likelihood-216.1674 F-statistic1024.564Durbin-Watson stat1.790431 Prob(F-statistic)0.000000样本回归模型为 (3.638437) (0.019903) t= (2.569104) (32.00881) F=1024.564(2) 解Goldfiele-Quandt法检验：1） 对变量取值排序2） 构造子样本区间，建立回归模型。其中n=60，删除1/4的观测值即大约14个观测值，余下部分评分得两个样本区间：123和3860，他们的样本个数均是8个，即在Sample菜单里，将区间定义为123，然后用OLS方法求得如下估计结果 Dependent Variable: YMethod: Least SquaresDate: 01/01/04 Time: 01:27Sample: 1901 1923Included observations: 23VariableCoefficientStd. Errort-StatisticProb. C9.5122386.7353501.4122860.1725X0.6362350.05995910.611110.0000R-squared0.842809 Mean dependent var79.91304Adjusted R-squared0.835324 S.D. dependent var13.71434S.E. of regression5.565315 Akaike info criterion6.353926Sum squared resid650.4275 Schwarz criterion6.452664Log likelihood-71.07014 F-statistic112.5958Durbin-Watson stat1.212347 Prob(F-statistic)0.000000在Sample菜单里，将区间定义为3860，再用OLS方法求得如下结果 Dependent Variable: YMethod: Least SquaresDate: 01/01/04 Time: 01:31Sample: 1938 1960Included observations: 23VariableCoefficientStd. Errort-StatisticProb. C-46.6786624.86518-1.8772700.0744X0.8697810.1046778.3091810.0000R-squared0.766777 Mean dependent var159.0435Adjusted R-squared0.755671 S.D. dependent var22.33318S.E. of regression11.03921 Akaike info criterion7.723726Sum squared resid2559.148 Schwarz criterion7.822464Log likelihood-86.82284 F-statistic69.04250Durbin-Watson stat0.692905 Prob(F-statistic)0.0000003)求F统计量由表中数据可知残差平方和 根据Golefield-Quanadt检验，F统计量 在,所以拒绝原假设，表明模型确实存在异方差。White法检验模型根据模型White检验结果如下 White Heteroskedasticity Test:F-statistic6.301373 Probability0.003370Obs*R-squared10.86401 Probability0.004374Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 01/01/04 Time: 01:42Sample: 1901 1960Included observations: 60VariableCoefficientStd. Errort-StatisticProb. C-10.03614131.1424-0.0765290.9393X0.1659771.6198560.1024640.9187X20.0018000.0045870.3924690.6962R-squared0.181067 Mean dependent var78.86225Adjusted R-squared0.152332 S.D. dependent var111.1375S.E. of regression102.3231 Akaike info criterion12.14285Sum squared resid596790.5 Schwarz criterion12.24757Log likelihood-361.2856 F-statistic6.301373Durbin-Watson stat0.937366 Prob(F-statistic)0.003370从表中可知，由White检验知，在,所以拒绝原假设，表明模型存在异方差。(3)修正异方差选用权数，运用加权最小二乘法（WLS）进行估计结果如下选取权数w1的结果Dependent Variable: YMethod: Least SquaresDate: 01/01/04 Time: 01:59Sample: 1901 1960Included observations: 60Weighting series: W1VariableCoefficientStd. Errort-StatisticProb. C10.370512.6297163.9435870.0002X0.6309500.01853234.046670.0000Weighted StatisticsR-squared0.211441 Mean dependent var106.2101Adjusted R-squared0.197845 S.D. dependent var8.685376S.E. of regression7.778892 Akaike info criterion6.973470Sum squared resid3509.647 Schwarz criterion7.043281Log likelihood-207.2041 F-statistic15.55188Durbin-Watson stat0.958467 Prob(F-statistic)0.000219Unweighted StatisticsR-squared0.946335 Mean dependent var119.6667Adjusted R-squared0.945410 S.D. dependent var38.68984S.E. of regression9.039689 Sum squared resid4739.526Durbin-Watson stat0.800564选取权重w2的结果Dependent Variable: YMethod: Least SquaresDate: 01/01/04 Time: 02:49Sample: 1901 1960Included observations: 60Weighting series: W2VariableCoefficientStd. Errort-StatisticProb. C10.123272.7557753.6734750.0005X0.6330290.02459025.743740.0000Weighted StatisticsR-squared0.961581 Mean dependent var94.01206Adjusted R-squared0.960918 S.D. dependent var41.02965S.E. of regression8.111184 Akaike info criterion7.057130Sum squared resid3815.896 Schwarz criterion7.126941Log likelihood-209.7139 F-statistic1451.660Durbin-Watson stat2.091305 Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.946381 Mean dependent var119.6667Adjusted R-squared0.945457 S.D. dependent var38.68984S.E. of regression9.035795 Sum squared resid4735.444Durbin-Watson stat1.795043选取权重w3的结果Dependent Variable: YMethod: Least SquaresDate: 01/01/04 Time: 02:50Sample: 1901 1960Included observations: 60Weighting series: W3VariableCoefficientStd. Errort-StatisticProb. C10.109082.9807893.3914090.0013X0.6326710.01837934.423410.0000Weighted StatisticsR-squared0.801827 Mean dependent var112.9123Adjusted R-squared0.798411 S.D. dependent var18.33568S.E. of regression8.232480 Akaike info criterion7.086817Sum squared resid3930.877 Schwarz criterion7.156628Log likelihood-210.6045 F-statistic234.6742Durbin-Watson stat1.874009 Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.946378 Mean dependent var119.6667Adjusted R-squared0.945454 S.D. dependent var38.68984S.E. of regression9.036056 Sum squared resid4735.718Durbin-Watson stat1.795491选取权重w4的结果Dependent Variable: YMethod: Least SquaresDate: 01/01/04 Time: 02:51Sample: 1901 1960Included observations: 60Weighting series: W4VariableCoefficientStd. Errort-StatisticProb. C-4.8193998.678108-0.5553510.5808X0.7019620.03725618.841780.0000Weighted StatisticsR-squared0.988973 Mean dependent var142.6838Adjusted R-squared0.988783 S.D. dependent var122.1399S.E. of regression12.93572 Akaike info criterion7.990626Sum squared resid9705.300 Schwarz criterion8.060438Log likelihood-237.7188 F-statistic5202.006Durbin-Watson stat1.720951 Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.930773 Mean dependent var119.6667Adjusted R-squared0.929579 S.D. dependent var38.68984S.E. of regression10.26711 Sum squared resid6113.985Durbin-Watson stat1.354364经估计检验w2的效果最好估计结果如下10.12327+0.633029 t= (3.673475) (25.74374) F=1451.6605.3解(1)建立模型 (Y表示农村居民家庭人均消费支出,X表示人均纯收入)通过eviews对数据进行估计 Dependent Variable: YMethod: Least SquaresDate: 01/01/04 Time: 02:19Sample: 1901 1931Included observations: 31VariableCoefficientStd. Errort-StatisticProb. C179.1916221.57750.8087090.4253X0.7195000.04570015.744110.0000R-squared0.895260 Mean dependent var3376.309Adjusted R-squared0.891649 S.D. dependent var1499.612S.E. of regression493.6240 Akaike info criterion15.30377Sum squared resid7066274. Schwarz criterion15.39628Log likelihood-235.2084 F-statistic247.8769Durbin-Watson stat1.461684 Prob(F-statistic)0.000000样本回归模型为Y=179.1916+0.719500X(221.5775) (0.045700) t=(0.808709) (15.74411) （2）对模型进行White检验根据模型White检验结果如下White Heteroskedasticity Test:F-statistic7.194463 Probability0.003011Obs*R-squared10.52295 Probability0.005188Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 01/01/04 Time: 02:26Sample: 1901 1931Included observations: 31VariableCoefficientStd. Errort-StatisticProb. C69872.27641389.00.1089390.9140X-72.02221248.7240-0.2895670.7743X20.0203370.0206270.9859720.3326R-squared0.339450 Mean dependent var227944.3Adjusted R-squared0.292268 S.D. dependent var592250.3S.E. of regression498241.3 Akaike info criterion29.16732Sum squared resid6.95E+12 Schwarz criterion29.30610Log likelihood-449.0935 F-statistic7.194463Durbin-Watson stat2.390409 Prob(F-statistic)0.003011由表知，由White检验知，在,所以拒绝原假设，表明模型存在异方差。理由：这样的两个变量属于截面数据，运用截面数据，研究消费和收入之间的关系时，如果采取不同家庭收入组的数据，低收入组的家庭用于购买生活必需品的比例相对较大，消费的分散成都不大，组内个家庭消费的差异也较小。高收入组的家庭有更多自由支配的收入，家庭消费有更广泛的选择范围，消费的分散程度较大，组内各家庭消费的差异也较大。这种家庭的消费偏离均值程度的差异，最终反映为随机误差项偏离其均值的程度有变化，而出现异方差。(3) 修正异方差选用权数，运用加权最小二乘法（WLS）进行估计结果如下选取权数w1的结果Dependent Variable: YMethod: Least SquaresDate: 01/01/04 Time: 02:30Sample: 1901 1931Included observations: 31Weighting series: W1VariableCoefficientStd. Errort-StatisticProb. C578.2963174.57163.3126600.0025X0.6233050.04768213.072260.0000Weighted StatisticsR-squared0.274523 Mean dependent var2983.378Adjusted R-squared0.249507 S.D. dependent var373.3588S.E. of regression323.4445 Akaike info criterion14.45827Sum squared resid3033875. Schwarz criterion14.55079Log likelihood-222.1032 F-statistic10.97372Durbin-Watson stat1.836477 Prob(F-statistic)0.002484Unweighted StatisticsR-squared0.878889 Mean dependent var3376.309Adjusted R-squared0.874712 S.D. dependent var1499.612S.E. of regression530.8026 Sum squared resid8170791.Durbin-Watson stat1.746914选取权重w2的结果Dependent Variable: YMethod: Least SquaresDate: 01/01/04 Time: 02:31Sample: 1901 1931Included observations: 31Weighting series: W2VariableCoefficientStd. Errort-StatisticProb. C787.2847173.69644.5325340.0001X0.5614720.05573110.074680.0000Weighted StatisticsR-squared0.946060 Mean dependent var2743.600Adjusted R-squared0.944200 S.D. dependent var1165.059S.E. of regression275.2095 Akaike info criterion14.13528Sum squared resid2196468. Schwarz criterion14.22780Log likelihood-217.0969 F-statistic508.6387Durbin-Watson stat2.482750 Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.848003 Mean dependent var3376.309Adjusted