计量经济学案例作业

1、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）估计回归模型中的未知参数和，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: Least SquaresDate: 06/08/15 Time: 10:20Sample: 1 60Included observations: 60VariableCoefficientStd. Errort-StatisticProb.

2、0; 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 squa

3、red resid4731.735    Schwarz criterion7.342058Log likelihood-216.1674    Hannan-Quinn criter.7.299553F-statistic1024.564    Durbin-Watson stat1.790431Prob(F-statistic)0.000000，样本回归模型书写格式： （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

4、个部分的样本，即。2 / 11 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，即求F统计量为给定，查F分布表，得临界值为。c.比较临界值与F统计量值，有=4.1390>，说明该模型的随机误差项存在异方差。用White法进行检验White Heteroskedasticity Test:F-statistic6.301373 Probability0.003370Obs*R-squared10.86401 Probability0.004374Test Equation:Dependent Variable: RESID2Method: Least SquaresDat

5、e: 06/08/15 Time: 12:25Sample: 1 60Included 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

6、.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，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 Dependent Variable: YMethod: L

7、east SquaresDate: 06/08/15 Time: 13:10Sample: 1 60Included 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. de

8、pendent var8.685376S.E. of regression7.778892 Akaike info criterion6.973470Sum squared resid3509.647 Schwarz criterion7.043282Log likelihood-207.2041 F-statistic1159.176Durbin-Watson stat0.958467 Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.946335 Mean dependent var119.6667Adjusted R-squ

9、ared0.945410 S.D. dependent var38.68984S.E. of regression9.039689 Sum squared resid4739.526Durbin-Watson stat0.800564其估计的书写形式为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Y197019711972197323924825827230031132935119831984198519863043083103123843924

10、0040319741975197619771978197919801981198226828027928228529329129430235436436036637037837437138119871988198919901991199219931994314324326332334336334330411428434441449451449449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

11、一元线性回归结果可得：Dependent Variable: YMethod: Least SquaresDate: 06/09/15 Time: 20:20Sample: 1970 1994Included observations: 25VariableCoefficientStd. Errort-StatisticProb.  C-68.1602615.26513-4.4650960.0002X1.5297120.05097630.008460.0000R-squared0.975095    Mean dependent va

12、r388.0000Adjusted R-squared0.974012    S.D. dependent var43.33397S.E. of regression6.985763    Akaike info criterion6.802244Sum squared resid1122.420    Schwarz criterion6.899754Log likelihood-83.02805    Hannan-Quinn cr

13、iter.6.829289F-statistic900.5078    Durbin-Watson stat0.348288Prob(F-statistic)0.000000Y=-68.16+1.53X （1）（2）Dependent Variable: YMethod: Least SquaresDate: 06/09/15 Time: 20:58Sample: 1970 1994Included observations: 25VariableCoefficientStd. Errort-StatisticProb.  C18.3

14、314429.515180.6210850.5409X1.2022390.10938210.991210.0000TIME20.0505020.0155223.2536110.0036R-squared0.983186    Mean dependent var388.0000Adjusted R-squared0.981657    S.D. dependent var43.33397S.E. of regression5.868976    Akaike info cri

15、terion6.489404Sum squared resid757.7875    Schwarz criterion6.635669Log likelihood-78.11755    Hannan-Quinn criter.6.529972F-statistic643.2046    Durbin-Watson stat0.403640Prob(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，由于

16、D.W.=0.35<,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：（2），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：于是，LM=24=18，该值大于显著性水平为5%，自由度为1的分布的临界值，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：Dependent Variable: AMethod: Least SquaresDate: 06/09/15 Time: 22:00Sample: 1

17、970 1994Included observations: 25VariableCoefficientStd. Errort-StatisticProb.  C-0.62016619.49328-0.0318140.9749X0.0018950.0722250.0262390.9793TIME20.0014470.0102400.1413110.8890RE0.9176810.2108534.3522280.0003RE2-0.1974030.213975-0.9225500.3672R-squared0.604654    Mea

18、n dependent var1.98E-14Adjusted R-squared0.525585    S.D. dependent var5.619117S.E. of regression3.870322    Akaike info criterion5.721409Sum squared resid299.5879    Schwarz criterion5.965184Log likelihood-66.51761    H

19、annan-Quinn criter.5.789022F-statistic7.647165    Durbin-Watson stat1.826752Prob(F-statistic)0.000657（RE2为）采用科克伦奥克特两步法处理模型中的自相关问题根据，eviews运行结果如下：最终的消费模型为 Y t = 93.7518+0.5351 X t （3）模型说明日本工薪居民的边际消费倾向为0.5351，即收入每增加1元，平均说来消费增加0.54元。3. 下表给出了中国商品进口额Y、国内生产总值GDP、居民消费价格指数CPI。中国商品进口额、国内生

20、产总值、居民消费价格指数年份商品进口额(亿元)国内生产总值(亿元)居民消费价格指数(1985=100)19851257.89016.0100.019861498.310275.2106.519871614.212058.6114.319882055.115042.8135.819892199.916992.3160.219902574.318667.8165.219913398.721781.5170.819924443.326923.5181.719935986.235333.9208.419949960.148197.9258.6199511048.160793.7302.81996115

21、57.471176.6327.9199711806.578973.0337.1199811626.184402.3334.4199913736.489677.1329.7200018638.899214.6331.0200120159.2109655.2333.3200224430.3120332.7330.6200334195.6135822.8334.6200446435.8159878.3347.7200554273.7183084.8353.9200663376.9 211923.5359.2200773284.6 249529.9376.5请考虑下列模型：1)利用表中数据估计此模型的

22、参数。2)根据所学知识判断数据中有多重共线性吗？ 3)若存在多重共线性，利用逐步回归克服多重共线性。解：（1) Dependent Variable: LOG(Y)Method: Least SquaresDate: 06/10/15 Time: 14:34Sample: 1985 2007Included observations: 23VariableCoefficientStd. Errort-StatisticProb.  C-3.0601490.337427-9.0690590.0000LOG(X1)1.6566740.09220617.967030.0000LOG(X2)-1.0570530.214647-4.9246180.0001R-squared0.992218    Mean dependent var9.155303Adjusted R-squared0.