计量经济学第二 答案

1、5.2(1) 建立某地区消费额Y与收入X的回归模型 估计模型参数，结果为Dependent Variable: YMethod: Least SquaresDate: 05/16/12 Time: 20:21Sample: 1 60Included observations: 60VariableCoefficientStd. Errort-StatisticProb. C9.3475223.6384372.5691040.0128X0.6370690.01990332.008810.0000R-squared0.946423 Mean dependent var119.6667Adjuste

2、d 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该模型样本回归估计式的书写格式为 （2）用Goldfeld-Quandt法进行检验1） 将样本X按递增顺

3、序排序，去掉中间1/4的样本，再分为两个部分的样本，即在Sample菜单里，将区间定义为122，然后用OLS方法求的如下结果：Dependent Variable: YMethod: Least SquaresDate: 05/16/12 Time: 20:26Sample: 1 22Included observations: 22VariableCoefficientStd. Errort-StatisticProb. C12.536957.0695781.7733650.0914X0.6059110.0639109.4807300.0000R-squared0.817990 Mean d

4、ependent var78.63636Adjusted R-squared0.808890 S.D. dependent var12.56050S.E. of regression5.490969 Akaike info criterion6.330594Sum squared resid603.0148 Schwarz criterion6.429780Log likelihood-67.63654 F-statistic89.88424Durbin-Watson stat1.136382 Prob(F-statistic)0.000000Dependent Variable: YMeth

5、od: Least SquaresDate: 05/16/12 Time: 20:27Sample: 39 60Included observations: 22VariableCoefficientStd. Errort-StatisticProb. C-39.5439327.08272-1.4601160.1598X0.8412150.1132667.4269270.0000R-squared0.733898 Mean dependent var160.8182Adjusted R-squared0.720593 S.D. dependent var21.13367S.E. of regr

6、ession11.17103 Akaike info criterion7.751033Sum squared resid2495.840 Schwarz criterion7.850219Log likelihood-83.26137 F-statistic55.15924Durbin-Watson stat0.610587 Prob(F-statistic)0.000000由表可以得到两个部分的残差平方和，即2）求F统计量为3）给定，查F分布表，得临界值为。比较临界值与F统计量值，有=4.1390>，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Whi

7、te Heteroskedasticity Test:F-statistic6.301373 Probability0.003370Obs*R-squared10.86401 Probability0.004374Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 05/16/12 Time: 20:35Sample: 1 60Included observations: 60VariableCoefficientStd. Errort-StatisticProb. C-10.03614131.1424-0.07

8、65290.9393X0.1659771.6198560.1024640.9187X20.0018000.0045870.3924690.6962R-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

9、 F-statistic6.301373Durbin-Watson stat0.937366 Prob(F-statistic)0.003370给定，在自由度为2下查卡方分布表，得。比较临界值与卡方统计量值，即，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，作加权最小二乘估计，得如下结果Dependent Variable: YMethod: Least SquaresDate: 05/17/12 Time: 14:42Sample: 1 60Included observations: 60Weighting series: W1VariableCoefficient

10、Std. 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 crite

11、rion7.043282Log likelihood-207.2041 F-statistic1159.176Durbin-Watson stat1.969805 Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.946335 Mean dependent var119.6667Adjusted R-squared0.945410 S.D. dependent var38.68984S.E. of regression9.039689 Sum squared resid4739.526Durbin-Watson stat1.796

12、748用White法进行检验得如下结果：White Heteroskedasticity Test:F-statistic3.138491Probability0.050925Obs*R-squared5.951910Probability0.050999给定，在自由度为2下查卡方分布表，得。比较临界值与卡方统计量值，即，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 估计模型参数，结果为Dependent Variable: YMethod: Least SquaresDate: 05/17/12 Time: 15

13、:07Sample: 1 31Included 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 criterion15.3037

14、7Sum squared resid7066274. Schwarz criterion15.39628Log likelihood-235.2084 F-statistic247.8769Durbin-Watson stat1.461684 Prob(F-statistic)0.000000参数估计结果如下：（0.808709）（15.74411）（2）利用White方法检验异方差，则White检验结果见下表：White Heteroskedasticity Test:F-statistic7.194463 Probability0.003011Obs*R-squared10.52295 P

15、robability0.005188Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 05/17/12 Time: 15:10Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb. C69872.27641389.00.1089390.9140X-72.02221248.7240-0.2895670.7743X20.0203370.0206270.9859720.3326R-squared0.33945

16、0 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由上述结果可知，给定，在自由度为2

17、下查卡方分布表，得。比较临界值与卡方统计量值，即，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。该模型存在异方差的理由是，从数据可以看出，一是截面数据；二是各省市经济发展不平衡，使得一些省市农村居民收入高出其它省市很多，如上海市、北京市、天津市和浙江省等。而有的省就很低，如甘肃省、贵州省、云南省和陕西省等。（3）用权数分别作加权最小二乘估计，得如下结果：用权数W1的结果：Dependent Variable: YMethod: Least SquaresDate: 05/17/12 Time: 15:32Sample: 1 31Included observations: 31Wei

18、ghting 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

19、 squared resid3033875. Schwarz criterion14.55079Log likelihood-222.1032 F-statistic170.8839Durbin-Watson stat1.836477 Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.878889 Mean dependent var3376.309Adjusted R-squared0.874712 S.D. dependent var1499.612S.E. of regression530.8026 Sum squared

20、resid8170791.Durbin-Watson stat1.746914用权数W2的结果：Dependent Variable: YMethod: Least SquaresDate: 05/17/12 Time: 15:37Sample: 1 31Included observations: 31Weighting series: W2VariableCoefficientStd. Errort-StatisticProb. C787.2847173.69644.5325340.0001X0.5614720.05573110.074680.0000Weighted Statistics

21、R-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-statistic101.4992Durbin-Watson stat2.482750 Prob(F-statistic)0.000000U

22、nweighted StatisticsR-squared0.848003 Mean dependent var3376.309Adjusted R-squared0.842762 S.D. dependent var1499.612S.E. of regression594.6448 Sum squared resid10254472Durbin-Watson stat1.741955用权数W3的结果：Dependent Variable: YMethod: Least SquaresDate: 05/17/12 Time: 15:38Sample: 1 31Included observa

23、tions: 31Weighting series: W3VariableCoefficientStd. Errort-StatisticProb. C391.3489190.69752.0521970.0493X0.6717550.04605414.586260.0000Weighted StatisticsR-squared0.650056 Mean dependent var3155.918Adjusted R-squared0.637989 S.D. dependent var650.0776S.E. of regression391.1345 Akaike info criterio

24、n14.83832Sum squared resid4436601. Schwarz criterion14.93084Log likelihood-227.9940 F-statistic212.7591Durbin-Watson stat1.622416 Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.891318 Mean dependent var3376.309Adjusted R-squared0.887570 S.D. dependent var1499.612S.E. of regression502.8279

25、Sum squared resid7332241.Durbin-Watson stat1.641703经估计检验发现用权数W2的效果最好，书写结果为5.6（1）设表示人均生活费支出，表示农村人均纯收入，建立人均生活费支出Y与农村人均纯收入X的回归模型 估计模型参数，结果为Dependent Variable: YMethod: Least SquaresDate: 05/17/12 Time: 15:45Sample: 1978 2008Included observations: 31VariableCoefficientStd. Errort-StatisticProb. C70.9557718.077293.9251330.0005X0.7609490.01081970.336170.0000R-squared0.994172 Mean dependent var1030.669Adjusted R-squared0.993971 S.D. dependent var850.3132S.E. of regression66.02245 Akaike info criterion11.28021Sum squared resid126410.0 Schwarz criterion11.37272Log lik