计量经济学作业 (6)(共5页)

1、2、设模型(mxng)（C/CP）=1+2YCP+ut，（t=1，2，,n）模型(mxng)中各变量的解释参见式（369）。（1）利用(lyng)表3-1给出的数据，运用广义最小二乘法，对上述模型进行估计。做变换时，用1-DW2代替未知参数，其中DW为对模型进行最小二乘估计时给出的DW值。（2）对比最小二乘法、广义最小二乘法和CO方法给出的各个估计方程，计算各个方程给出的被解释变量的估计值，并对结果进行解释。城镇家庭实际人均消费性支出与世纪人均可支配收入年度C/CPY/CP19801634.561892.9819811766.431935.0319821785.442029.191983188

2、0.672098.8819842024.612360.1219852229.142447.3519862484.452801.3119872562.742903.819882692.682878.5419892503.12839.8119902563.933027.5919912819.083297.6519923046.663693.4619933353.674095.0119943650.36447619953867.464682.3519963956.694884.8219974110.385067.5619984287.865370.3219994634.445877.51200049

3、986279.9820015272.116811.9220026036.567711.2820036440.748380.8520046837.498969.5420057428.119812.9620068013.0410835.2520078789.7612120.4520089333.9913101.43200910390.0214549.65解：(1)根据(gnj)以上(yshng)数据，应用(yngyng)最小二乘法，得到基于以上数据的回归方程（Y=CCP , X=YCPt）最小二乘法Dependent Variable: YMethod: Least SquaresDate: 11

4、/11/14 Time: 23:23Sample: 1980 2009Included observations: 30VariableCoefficientStd. Errort-StatisticProb.C541.176438.8279713.937800.0000X0.6886150.005886116.98470.0000R-squared0.997958Mean dependent var4379.806Adjusted R-squared0.997885S.D. dependent var2472.456S.E. of regression113.6985Akaike info

5、criterion12.36932Sum squared resid361965.8Schwarz criterion12.46273Log likelihood-183.5398Hannan-Quinn criter.12.39920F-statistic13685.41Durbin-Watson stat0.541618Prob(F-statistic)0.000000故回归方程为：CCP=541.2+0.6886YCPtt （13.9） （117）R2=0.998 R2=0.998 S=114 DW=0.54取显著性水平为0.05，k=2,，n=30，查DW表得到临界值为L=1.35 U

6、=1.49，在模型中DW=0.54，即DWL，表明存在序列正相关。由=1-DW2，得=0.729191先对数据进行广义差分变换，然后运用最小二乘法得到以下估计模型：Dependent Variable: YSTARMethod: Least SquaresDate: 11/16/14 Time: 12:42Sample: 1980 2009Included observations: 30VariableCoefficientStd. Errort-StatisticProb.CSTAR541.943682.808026.5445790.0000XSTAR0.6836440.01106461.

7、791250.0000R-squared0.990869Mean dependent var1421.397Adjusted R-squared0.990543S.D. dependent var825.5422S.E. of regression80.28320Akaike info criterion11.67334Sum squared resid180471.0Schwarz criterion11.76675Log likelihood-173.1001Hannan-Quinn criter.11.70322Durbin-Watson stat2.166851得到(d do)模型(m

8、xng)为：Y*=541.9436+0.6836X* （6.54） （61.79）R2=0.9908 R2=0.9905 S=80.28 DW=2.166取显著性水平(shupng)为0.05，k=2,，n=29，时L=1.34 U=1.48， UDW4-1.34，所以已不存在自相关性。(2)最小二乘法：CCP=541.2+0.6886YCPtt,广义最小二乘法：Y*=594.6372+0.6812X*CO法：CCP=650.2+0.674YCPtt由上边的计算结果可以，边际消费倾向在0.68，基本消费在550元。3、设20个家庭的消费与收入有如下数据，其中Y表示消费，X表示收入20家庭的消费

9、与收入Y消费X收入19.922.331.232.331.836.612.112.140.742.36.16.238.644.725.526.110.310.338.840.288.133.134.533.53813.114.114.816.421.624.129.330.12528.317.918.219.820.1（1）设模型Yt=+Xt+ut （t=1，2，20）运用最小二乘法，对上述模型进行估计。以X轴为横轴，残差为纵轴，画出残差的散点图，利用图形讨论异方差性的存在性，并对出现的结果进行解释。（2）对变量Xt，Yt取对数后，运用最小二乘法，对模型进行估计。以lnX为横轴，残差为纵轴，画出

10、残差的散点图，讨论异方差的存在性，并对出现的结果进行解释。解：有上述数据计算得：Dependent Variable: YMethod: Least SquaresDate: 11/15/14 Time: 14:37Sample: 1 20Included observations: 20VariableCoefficientStd. Errort-StatisticProb.C0.8470520.7033551.2043020.2441X0.8993250.02530935.533600.0000R-squared0.985944Mean dependent var23.55500Adjus

11、ted R-squared0.985164S.D. dependent var10.78691S.E. of regression1.313895Akaike info criterion3.478509Sum squared resid31.07377Schwarz criterion3.578082Log likelihood-32.78509Hannan-Quinn criter.3.497947F-statistic1262.637Durbin-Watson stat2.582686Prob(F-statistic)0.000000故回归方程为：Yt=0.8471+0.8993Xt (

12、1.204) (35.5336)R=0.9859 R2=0.9853 S=1.31 DW=2.5826以X为横轴，残差为纵轴，得到(d do)残差的散点图：对图形进行(jnxng)分析，可以看到随着收入(shur)X的变大，残差的绝对值有变大的趋势，故模型的误差项之间存在异方差性。对变量X,Y取对数之后，运用最小二乘法，得到以下估计模型：Dependent Variable: LNYMethod: Least SquaresDate: 11/15/14 Time: 16:29Sample: 1 20Included observations: 20VariableCoefficientStd.

13、 Errort-StatisticProb.C0.0756720.0573931.3184960.2039LNX0.9561860.01825552.380220.0000R-squared0.993482Mean dependent var3.033911Adjusted R-squared0.993120S.D. dependent var0.550836S.E. of regression0.045689Akaike info criterion-3.239278Sum squared resid0.037575Schwarz criterion-3.139705Log likelihood34.39278Hannan-Quinn criter.-3.219840F-statistic2743.688Durbin-Watson stat2.166013Prob(F-statistic)0.000000故回归方程为：ln（Y)=0.0757+0.9562ln（X） (1.3184) (52.3802)R2=0.9935 R2=0.9931 S=0.0457 DW= 2.1660以ln（X）为横轴，残差为纵轴，得到