计量经济学第二版第五章答案

5.2(1)建立某地区消费额Y与收入X的回归模型12YXu估计模型参数，结果为DependentVariable:YMethod:LeastSquaresDate:05/16/12Time:20:21Sample:160Includedobservations:60VariableCoefficientStd.Errort-StatisticProb.C9.3475223.6384372.5691040.0128X0.6370690.01990332.008810.0000R-squared0.946423Meandependentvar119.6667AdjustedR-squared0.945500S.D.dependentvar38.68984S.E.ofregression9.032255Akaikeinfocriterion7.272246Sumsquaredresid4731.735Schwarzcriterion7.342058Loglikelihood-216.1674F-statistic1024.564Durbin-Watsonstat1.790431Prob(F-statistic)0.000000该模型样本回归估计式的书写格式为22ˆ9.347522+0.637069t=(2.569104)(32.00881)R=0.946423R=0.945500F=1024.564DW=1.790431iYX（2）用Goldfeld-Quandt法进行检验1）将样本X按递增顺序排序，去掉中间1/4的样本，再分为两个部分的样本，即1222nn在Sample菜单里，将区间定义为1—22，然后用OLS方法求的如下结果：DependentVariable:YMethod:LeastSquaresDate:05/16/12Time:20:26Sample:122Includedobservations:22VariableCoefficientStd.Errort-StatisticProb.C12.536957.0695781.7733650.0914X0.6059110.0639109.4807300.0000R-squared0.817990Meandependentvar78.63636AdjustedR-squared0.808890S.D.dependentvar12.56050S.E.ofregression5.490969Akaikeinfocriterion6.330594Sumsquaredresid603.0148Schwarzcriterion6.429780Loglikelihood-67.63654F-statistic89.88424Durbin-Watsonstat1.136382Prob(F-statistic)0.000000DependentVariable:YMethod:LeastSquaresDate:05/16/12Time:20:27Sample:3960Includedobservations:22VariableCoefficientStd.Errort-StatisticProb.C-39.5439327.08272-1.4601160.1598X0.8412150.1132667.4269270.0000R-squared0.733898Meandependentvar160.8182AdjustedR-squared0.720593S.D.dependentvar21.13367S.E.ofregression11.17103Akaikeinfocriterion7.751033Sumsquaredresid2495.840Schwarzcriterion7.850219Loglikelihood-83.26137F-statistic55.15924Durbin-Watsonstat0.610587Prob(F-statistic)0.000000由表可以得到两个部分的残差平方和，即2122603.01482495.840ee2）求F统计量为22212495.844.1390603.0148eFe3）给定0.05，查F分布表，得临界值为0.05(20,20)2.12F。比较临界值与F统计量值，有F=4.13900.05(20,20)2.12F，所以拒绝原假设，表明模型确实存在异方差。用White法进行检验。具体结果见下表WhiteHeteroskedasticityTest:F-statistic6.301373Probability0.003370Obs*R-squared10.86401Probability0.004374TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:05/16/12Time:20:35Sample:160Includedobservations:60VariableCoefficientStd.Errort-StatisticProb.C-10.03614131.1424-0.0765290.9393X0.1659771.6198560.1024640.9187X^20.0018000.0045870.3924690.6962R-squared0.181067Meandependentvar78.86225AdjustedR-squared0.152332S.D.dependentvar111.1375S.E.ofregression102.3231Akaikeinfocriterion12.14285Sumsquaredresid596790.5Schwarzcriterion12.24757Loglikelihood-361.2856F-statistic6.301373Durbin-Watsonstat0.937366Prob(F-statistic)0.003370给定0.05，在自由度为2下查卡方分布表，得25.9915。比较临界值与卡方统计量值，即2210.86405.9915nR，所以拒绝原假设，不拒绝备择假设，表明模型确实存在异方差。（3）用权数11WX，作加权最小二乘估计，得如下结果DependentVariable:YMethod:LeastSquaresDate:05/17/12Time:14:42Sample:160Includedobservations:60Weightingseries:W1VariableCoefficientStd.Errort-StatisticProb.C10.370512.6297163.9435870.0002X0.6309500.01853234.046670.0000WeightedStatisticsR-squared0.211441Meandependentvar106.2101AdjustedR-squared0.197845S.D.dependentvar8.685376S.E.ofregression7.778892Akaikeinfocriterion6.973470Sumsquaredresid3509.647Schwarzcriterion7.043282Loglikelihood-207.2041F-statistic1159.176Durbin-Watsonstat1.969805Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.946335Meandependentvar119.6667AdjustedR-squared0.945410S.D.dependentvar38.68984S.E.ofregression9.039689Sumsquaredresid4739.526Durbin-Watsonstat1.796748用White法进行检验得如下结果：WhiteHeteroskedasticityTest:F-statistic3.138491Probability0.050925Obs*R-squared5.951910Probability0.050999给定0.05，在自由度为2下查卡方分布表，得25.9915。比较临界值与卡方统计量值，即225.9519105.9915nR，说明加权后的模型中的随机误差项不存在异方差。其估计的书写格式为22ˆ10.37050.6309(3.943587)(34.04667)R0.211441R=0.197845DW=0.958467F=1159.176YXt5.3(1)建立家庭人均消费支出Y与家庭人均纯收入X的回归模型12YXu估计模型参数，结果为DependentVariable:YMethod:LeastSquaresDate:05/17/12Time:15:07Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.C179.1916221.57750.8087090.4253X0.7195000.04570015.744110.0000R-squared0.895260Meandependentvar3376.309AdjustedR-squared0.891649S.D.dependentvar1499.612S.E.ofregression493.6240Akaikeinfocriterion15.30377Sumsquaredresid7066274.Schwarzcriterion15.39628Loglikelihood-235.2084F-statistic247.8769Durbin-Watsonstat1.461684Prob(F-statistic)0.000000参数估计结果如下：ˆ179.1916+0.7195YX（0.808709）（15.74411）20.895260,F=247.8769R（2）利用White方法检验异方差，则White检验结果见下表：WhiteHeteroskedasticityTest:F-statistic7.194463Probability0.003011Obs*R-squared10.52295Probability0.005188TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:05/17/12Time:15:10Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.C69872.27641389.00.1089390.9140X-72.02221248.7240-0.2895670.7743X^20.0203370.0206270.9859720.3326R-squared0.339450Meandependentvar227944.3AdjustedR-squared0.292268S.D.dependentvar592250.3S.E.ofregression498241.3Akaikeinfocriterion29.16732Sumsquaredresid6.95E+12Schwarzcriterion29.30610Loglikelihood-449.0935F-statistic7.194463Durbin-Watsonstat2.390409Prob(F-statistic)0.003011由上述结果可知，给定0.05，在自由度为2下查卡方分布表，得25.9915。比较临界值与卡方统计量值，即2210.52