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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u X Y ++=21ββ中的未知参数1β和2β,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: 60Variable Coefficient Std. Error t-Statistic Prob. C 9.347522 3.638437 2.569104 0.0128 X 0.637069 0.019903 32.00881 0.0000 R-squared 0.946423 Mean dependent var 119.6667 Adjusted R-squared 0.945500 S.D. dependent var 38.68984 S.E. of regression 9.032255 Akaike info criterion 7.272246 Sum squared resid 4731.735 Schwarz criterion 7.342058 Log likelihood -216.1674 Hannan-Quinn criter. 7.299553 F-statistic 1024.564 Durbin-Watson stat 1.790431 Prob(F-statistic) 0.0000001β=9.35,2=0.64β,样本回归模型书写格式:01e=9.35+0.64XY X ββ=++(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1222n n ==。

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2122603.01482495.840e e==∑∑求F 统计量为22212495.844.1390603.0148e F e===∑∑给定0.05α=,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 =4.1390>0.05(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F-statistic6.301373 Probability 0.003370Test Equation:Dependent Variable: RESID^2 Method: Least SquaresDate: 06/08/15 Time: 12:25 Sample: 1 60C -10.03614 131.1424 -0.076529 0.9393 X 0.165977 1.619856 0.102464 0.9187 R-squared0.181067 Mean dependent var 78.86225 Adjusted R-squared 0.152332 S.D. dependent var 111.1375 S.E. of regression 102.3231 Akaike info criterion 12.14285 Sum squared resid 596790.5 Schwarz criterion 12.24757 Log likelihood -361.2856 F-statistic6.3013730.05α=,在自由度为2下查卡方分布表,得25.9915χ=。

比较临界值与卡方统计量值,即2210.8640 5.9915nR χ=>=,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: Y Method: Least SquaresDate: 06/08/15 Time: 13:10 Sample: 1 60Included observations: 60 C 10.37051 2.629716 3.943587 0.0002 R-squared0.211441 Mean dependent var 106.2101 Adjusted R-squared 0.197845 S.D. dependent var 8.685376 S.E. of regression 7.778892 Akaike info criterion 6.973470 Sum squared resid 3509.647 Schwarz criterion 7.043282 Log likelihood -207.2041 F-statistic1159.176 R-squared0.946335 Mean dependent var 119.6667 Adjusted R-squared 0.945410 S.D. dependent var 38.68984 S.E. of regression 9.039689 Sum squared resid 4739.526其估计的书写形式为2ˆ10.37050.63100.2114,..7.7789,1159.18YX R s e F =+===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t t t u X Y ++=21ββ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:Dependent Variable: Y Method: Least Squares Date: 06/09/15 Time: 20:20 Sample: 1970 1994 Included observations: 25Variable Coefficient Std. Error t-Statistic Prob.C -68.16026 15.26513 -4.465096 0.0002 X1.5297120.05097630.008460.0000R-squared0.975095 Mean dependent var 388.0000 Adjusted R-squared 0.974012 S.D. dependent var 43.33397 S.E. of regression 6.985763 Akaike info criterion 6.802244 Sum squared resid 1122.420 Schwarz criterion 6.899754 Log likelihood -83.02805 Hannan-Quinn criter. 6.829289 F-statistic 900.5078 Durbin-Watson stat 0.348288Prob(F-statistic)0.000000Y=-68.16+1.53X(1)220.975,0.974,900.5078,..0.348R R F DW ====(2)Dependent Variable: Y Method: Least Squares Date: 06/09/15 Time: 20:58 Sample: 1970 1994 Included observations: 25VariableCoefficientStd. Errort-StatisticProb.C 18.33144 29.51518 0.621085 0.5409 X 1.202239 0.109382 10.99121 0.0000 TIME^20.0505020.0155223.2536110.0036R-squared 0.983186 Mean dependent var 388.0000 Adjusted R-squared 0.981657 S.D. dependent var 43.33397 S.E. of regression 5.868976 Akaike info criterion 6.489404 Sum squared resid 757.7875 Schwarz criterion 6.635669 Log likelihood -78.11755 Hannan-Quinn criter. 6.529972 F-statistic 643.2046 Durbin-Watson stat 0.403640 Prob(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,L U d d ==,由于D.W.=0.35<L d ,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)22R 0.983,R 0.982,643.205,..0.404F DW ====,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:2t t-12e =50.81-0.19X+0.03T 0.75e 0.75R +=%%于是,LM=240.75⨯=18,该值大于显著性水平为5%,自由度为1的2χ分布的临界值20.05=3.84χ(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: Dependent Variable: A Method: Least Squares Date: 06/09/15 Time: 22:00 Sample: 1970 1994Included observations: 25Variable Coefficient Std. Error t-Statistic Prob.C -0.620166 19.49328 -0.031814 0.9749 X 0.001895 0.072225 0.026239 0.9793 TIME^2 0.001447 0.010240 0.141311 0.8890 RE 0.9176810.2108534.352228 0.0003 RE2-0.197403 0.213975-0.9225500.3672R-squared 0.604654 Mean dependent var 1.98E-14 Adjusted R-squared 0.525585 S.D. dependent var 5.619117 S.E. of regression 3.870322 Akaike info criterion 5.721409 Sum squared resid 299.5879Schwarz criterion5.965184 Log likelihood -66.51761 Hannan-Quinn criter. 5.789022 F-statistic7.647165 Durbin-Watson stat 1.826752 Prob(F-statistic)0.000657(RE2为2e t -%)2t t-1t-22e -0.620.00190.001440.924e -0.197e 0.605X time R =+++=%%%采用科克伦-奥克特两步法处理模型中的自相关问题 根据01111t t t Y X ββρμε-=+++,eviews 运行结果如下:112167.00 1.130.980.99t t Y X R μ-=++=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。

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