计量经济学案例作业

2013级统计学专业《计量经济学》案例作业学号：130702060姓名：叶豪特1.下表是消费Y与收入X的数据，试根据所给数据资料完成以下问题：（1）估计回归模型uXY21中的未知参数1和2，并写出样本回归模型的书写格式；（2）试用Goldfeld-Quandt法和White法检验模型的异方差性；（3）选用合适的方法修正异方差。（1）eview结果Method:LeastSquaresDate:06/08/15Time:10:20Sample: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-216.1674Hannan-Quinncriter.7.299553F-statistic1024.564Durbin-Watsonstat1.790431Prob(F-statistic)0.0000001=9.35，2=0.64，样本回归模型书写格式：01e=9.35+0.64XYX（2）首先，用Goldfeld-Quandt法进行检验。a.将样本按递增顺序排序，去掉1/4，再分为两个部分的样本，即1222nn。b.分别对两个部分的样本求最小二乘估计，得到两个部分的残差平方和，即2122603.01482495.840ee求F统计量为22212495.844.1390603.0148eFe给定0.05，查F分布表，得临界值为0.05(20,20)2.12F。c.比较临界值与F统计量值，有F=4.13900.05(20,20)2.12F，说明该模型的随机误差项存在异方差。用White法进行检验WhiteHeteroskedasticityTest:F-statistic6.301373Probability0.003370Obs*R-squared10.86401Probability0.004374TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:06/08/15Time:12:25Sample: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)0.0033700.05，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，说明模型中的随机误差项存在异方差。（2）用加权最小二乘估计，得如下结果DependentVariable:YMethod:LeastSquaresDate:06/08/15Time:13:10Sample: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-Watsonstat0.958467Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.946335Meandependentvar119.6667AdjustedR-squared0.945410S.D.dependentvar38.68984S.E.ofregression9.039689Sumsquaredresid4739.526Durbin-Watsonstat0.800564其估计的书写形式为2ˆ10.37050.63100.2114,..7.7789,1159.18YXRseF2.下表给出了日本工薪家庭实际消费支出与可支配收入数据日本工薪家庭实际消费支出与实际可支配收入单位：1000日元年份个人实际可支配收入X个人实际消费支出Y年份个人实际可支配收入X个人实际消费支出Y1970197119721973197419751976197723924825827226828027928230031132935135436436036619831984198519861987198819891990304308310312314324326332384392400403411428434441197819791980198119822852932912943023703783743713811991199219931994334336334330449451449449要求：（1）建立日本工薪家庭的收入—消费函数；（2）检验模型中存在的问题，并采取适当的补救措施预以处理；（3）对模型结果进行经济解释。要求：（1）检测进口需求模型tttuXY21的自相关性；（2）采用科克伦－奥克特迭代法处理模型中的自相关问题。（1）由eviews一元线性回归结果可得：DependentVariable:YMethod:LeastSquaresDate:06/09/15Time:20:20Sample:19701994Includedobservations:25VariableCoefficientStd.Errort-StatisticProb.C-68.1602615.26513-4.4650960.0002X1.5297120.05097630.008460.0000R-squared0.975095Meandependentvar388.0000AdjustedR-squared0.974012S.D.dependentvar43.33397S.E.ofregression6.985763Akaikeinfocriterion6.802244Sumsquaredresid1122.420Schwarzcriterion6.899754Loglikelihood-83.02805Hannan-Quinncriter.6.829289F-statistic900.5078Durbin-Watsonstat0.348288Prob(F-statistic)0.000000Y=-68.16+1.53X（1）220.975,0.974,900.5078,..0.348RRFDW（2）DependentVariable:YMethod:LeastSquaresDate:06/09/15Time:20:58Sample:19701994Includedobservations:25VariableCoefficientStd.Errort-StatisticProb.C18.3314429.515180.6210850.5409X1.2022390.10938210.991210.0000TIME^20.0505020.0155223.2536110.0036R-squared0.983186Meandependentvar388.0000AdjustedR-squared0.981657S.D.dependentvar43.33397S.E.ofregression5.868976Akaikeinfocriterion6.489404Sumsquaredresid757.7875Schwarzcriterion6.635669Loglikelihood-78.11755Hannan-Quinncriter.6.529972F-statistic643.2046Durbin-Watsonstat0.403640Prob(F-statistic)0.000000D.W.检验结果表明，在5%显著性水平下，n=25，k=2（包含常数项），查表得1.29,1.45,LUdd，由于D.W.=0.35Ld,故（1）存在正自相关。引入时间变量T（T=1，2，……，25）以平方的形式出现，回归函数变化为：2ˆY=18.33+1.20X+0.05T（2）22R0.983,R0.982,643.205,..0.404FDW，这里，D.W.值仍然比较低，没有通过5%显著性水平下的D.W.检验，因此判断（2）式仍然存在正自相关性。再对（2）式进行序列相关性的拉格朗日乘数检验。含一阶滞后残差项的辅助回归为：2tt-12e=50.81-0.19X+0.03T0.75e0.75R于是，LM=240.75=18，该值大于显著性水平为5%，自由度为1的2分布的临界值20.05=3.84（1），由此判断原模型存在1阶序列相关性。含2阶滞后残差项的辅助回归为：DependentVariable:AMethod:LeastSquaresDate:06/09/15Time:22:00Sample:19701994Includedobservations:25VariableCoefficientStd.Errort-StatisticProb.C-0.62016619.49328-0.0318140.9749X0.0018950.0722250.0262390.9793TIME^20.0014470.0102400.1413110.8890RE0.9176810.2108534.3522280.0003RE2-0.1974030.213975-0.9225500.3672R-squared0.604654Meandependentvar1.98E-14AdjustedR-squared0.525585S.D.dependentvar5.619117S.E.ofregression3.870322Akaikeinfocriterion5.721409Sumsquaredresid299.5879Schwarzcriterion5.9651