1、第七章练习题及参考答案7.1 表7.10中给出了1970-1987年期间美国的个人消费支出(PCE)和个人可支配收入(PDI)数据,所有数字的单位都是10亿美元(1982年的美元价)。表7.10 1970-1987年美国个人消费支出(PCE)和个人可支配收入(PDI)数据年份 PCE PDI年份 PCE PDI年份 PCE PDI1970 1492.0 1668.1 1971 1538.8 1728.41972 1621.9 1797.41973 1689.6 1916.31974 1674.0 1896.61975 1711.9 1931.71976 1803.9 2001.0 1977 1
2、883.8 2066.61978 1961.0 2167.41979 2004.4 2212.61980 2000.4 2214.31981 2042.2 2248.61982 2050.7 2261.51983 2146.0 2331.9 1984 2249.3 2469.81985 2354.8 2542.81986 2455.2 2640.91987 2521.0 2686.3估计下列模型: (1) 解释这两个回归模型的结果。(2) 短期和长期边际消费倾向(MPC)是多少?【练习题7.1参考解答】1)第一个模型回归的估计结果如下,Dependent Variable: PCEMethod
3、: Least SquaresDate: 07/27/05 Time: 21:41Sample: 1970 1987Included observations: 18VariableCoefficientStd. Errort-StatisticProb.C-216.426932.69425-6.6197230.0000PDI1.0081060.01503367.059200.0000R-squared0.996455Mean dependent var1955.606Adjusted R-squared0.996233S.D. dependent var307.7170S.E. of reg
4、ression18.88628Akaike info criterion8.819188Sum squared resid5707.065Schwarz criterion8.918118Log likelihood-77.37269F-statistic4496.936Durbin-Watson stat1.366654Prob(F-statistic)0.000000回归方程: (3269425) (0.015033) t =(-6.619723) (67.05920) =0.996455 F=4496.936第二个模型回归的估计结果如下,Dependent Variable: PCEMe
5、thod: Least SquaresDate: 07/27/05 Time: 21:51Sample (adjusted): 1971 1987Included observations: 17 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C-233.273645.55736-5.1204360.0002PDI0.9823820.1409286.9708170.0000PCE(-1)0.0371580.1440260.2579970.8002R-squared0.996542Mean dependent var1
6、982.876Adjusted R-squared0.996048S.D. dependent var293.9125S.E. of regression18.47783Akaike info criterion8.829805Sum squared resid4780.022Schwarz criterion8.976843Log likelihood-72.05335F-statistic2017.064Durbin-Watson stat1.570195Prob(F-statistic)0.000000回归方程: (45.557) (0.1409) (0.1440) t = (-5.12
7、0) (6.9708) (0.258) =0.9965 F=2017.0642)从模型一得到MPC=1.008;从模型二得到,短期MPC=0.9824,由于模型二为自回归模型,要先转换为分布滞后模型才能得到长期边际消费倾向,我们可以从库伊克变换倒推得到长期MPC=0.9824/(1+0.0372)=0.9472。7.2 表7.11中给出了某地区1980-2001年固定资产投资Y与销售额X的资料。取阿尔蒙多项式的次数m=2,运用阿尔蒙多项式变换法估计分布滞后模型: 表7.11 某地区1980-2001年固定资产投资Y与销售额X的资料(单位:亿元) 年份YX年份YX198036.9952.8051
8、991128.68168.129198133.6055.9061992123.97163.351198235.4263.0271993117.35172.547198342.3572.9311994139.61190.682198452.4884.7901995152.88194.538198553.6686.5891996137.95194.657198658.5398.7971997141.06206.326198767.48113.2011998163.45223.541198878.13126.9051999183.80232.724198995.13143.9362000192.61
9、239.4591990112.60154.3912001182.81235.142【练习题7.2参考解答】分布滞后模型: s=4,取m=2。假设, (*)则模型可变为:,其中:估计的回归结果如下,Dependent Variable: YMethod: Least SquaresDate: 25/02/10 Time: 23:19Sample (adjusted): 1984 2001Included observations: 18 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C-35.492348.192884
10、-4.3320930.0007Z00.8910120.1745635.1042480.0002Z1-0.6699040.254447-2.6327830.0197Z20.1043920.0623111.6753380.1160R-squared0.984670Mean dependent var121.2322Adjusted R-squared0.981385S.D. dependent var45.63348S.E. of regression6.226131Akaike info criterion6.688517Sum squared resid542.7059Schwarz crit
11、erion6.886378Log likelihood-56.19666F-statistic299.7429Durbin-Watson stat1.130400Prob(F-statistic)0.000000回归方程:由(*)式可得,由阿尔蒙多项式变换可得如下估计结果:7.3利用表7.11的数据,运用局部调整假定或自适应预期假定估计以下模型参数,并解释模型的经济意义,探测模型扰动项的一阶自相关性:1)设定模型 其中为预期最佳值。 2)设定模型 其中为预期最佳值。3)设定模型 其中为预期最佳值。【练习题7.3参考解答】1)在局部调整假定下,先估计一阶自回归模型:回归的估计结果如下,Depen
12、dent Variable: YMethod: Least SquaresDate: 25/02/10 Time: 22:42Sample (adjusted): 1981 2001Included observations: 21 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C-15.104034.729450-3.1936130.0050X0.6292730.0978196.4330310.0000Y(-1)0.2716760.1148582.3653150.0294R-squared0.987125Mean
13、dependent var109.2167Adjusted R-squared0.985695S.D. dependent var51.78550S.E. of regression6.193728Akaike info criterion6.616515Sum squared resid690.5208Schwarz criterion6.765733Log likelihood-66.47341F-statistic690.0561Durbin-Watson stat1.518595Prob(F-statistic)0.000000回归方程: (4.729450) (0.097819) (
14、0.114858) t = (-3.193613) (6.433031) (2.365315) =0.987125 F=690.0561 DW=1.518595根据局部调整模型的参数关系,有将上述估计结果代入得到: 故局部调整模型估计结果为:经济意义:该地区销售额每增加1亿元,未来预期最佳新增固定资产投资为0.864001亿元。运用德宾h检验一阶自相关:在显著性水平上,查标准正态分布表得临界值,由于,则接收原假设,说明自回归模型不存在一阶自相关问题。 2)先对数变换模型,有在局部调整假定下,先估计一阶自回归模型:回归的估计结果如下,Dependent Variable: LNYMethod:
15、Least SquaresDate: 25/02/10 Time: 22:55Sample (adjusted): 1981 2001Included observations: 21 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C-1.0780460.184144-5.8543660.0000LNX0.9045220.1112438.1310390.0000LNY(-1)0.2600330.0877992.9616840.0084R-squared0.993725Mean dependent var4.55982
16、3Adjusted R-squared0.993028S.D. dependent var0.562953S.E. of regression0.047007Akaike info criterion-3.145469Sum squared resid0.039774Schwarz criterion-2.996251Log likelihood36.02742F-statistic1425.219Durbin-Watson stat1.479333Prob(F-statistic)0.000000回归方程: (0.184144) (0.111243) (0.087799) t = (-5.8
17、54366) (8.131039) (2.961684) =0.993725 F=1425.219 DW1=1.479333根据局部调整模型的参数关系,有,将上述估计结果代入得到: 故局部调整模型估计结果为:,也即经济意义:该地区销售额每增加1%,未来预期最佳新增固定资产投资为1.22238%。运用德宾h检验一阶自相关:在显著性水平上,查标准正态分布表得临界值,由于,则接收原假设,说明自回归模型不存在一阶自相关。3)在自适应预期假定下,先估计一阶自回归模型:回归的估计结果如下,Dependent Variable: YMethod: Least SquaresDate: 25/02/10 Ti
18、me: 22:42Sample (adjusted): 1981 2001Included observations: 21 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C-15.104034.729450-3.1936130.0050X0.6292730.0978196.4330310.0000Y(-1)0.2716760.1148582.3653150.0294R-squared0.987125Mean dependent var109.2167Adjusted R-squared0.985695S.D. de
19、pendent var51.78550S.E. of regression6.193728Akaike info criterion6.616515Sum squared resid690.5208Schwarz criterion6.765733Log likelihood-66.47341F-statistic690.0561Durbin-Watson stat1.518595Prob(F-statistic)0.000000回归方程: (4.729450) (0.097819) (0.114858) t = (-3.193613) (6.433031) (2.365315) =0.987
20、125 F=690.0561 DW=1.518595根据局部调整模型的参数关系,有将上述估计结果代入得到: 故局部调整模型估计结果为:经济意义:该地区销售额每增加1亿元,未来预期最佳新增固定资产投资为0.864001亿元。运用德宾h检验一阶自相关:在显著性水平上,查标准正态分布表得临界值,由于,则接收原假设,说明自回归模型不存在一阶自相关。7.4 表7.12给出某地区各年末货币流通量Y,社会商品零售额X1、城乡居民储蓄余额X 2的数据。表7.12 某地区年末货币流通量、社会商品零售额、城乡居民储蓄余额数据(单位:亿元)年份年末货币流通量Y社会商品零售额X1城乡居民储蓄余额X2年份年末货币流通量
21、Y社会商品零售额X1城乡居民储蓄余额X21953105187867641631970385002403322615619541408810143348881971471002745343094419551337510398956891972572002991973596119561835412452574061973600003140063966719571686712646791561974625003189544332019581851513444610193197564500336015461841959225581549611393919766800035292448311196029
22、036170370154951977630003781155331319614147214918212553197866000415830612901962348261545641008019797600045203270033196330000142548116021980850005125439280019642430014341515031198190000547956109707196529300156998171081982101000591088133799196633900176387193011983100000646427164314196736100178162204851
23、984160000733162201199196839600167074225721985192000919045277185利用表中数据设定模型: 其中,为长期(或所需求的)货币流通量。试根据局部调整假设,作模型变换,估计并检验参数,对参数经济意义做出解释。【练习题7.4参考解答】1)在局部调整假定下,先估计一阶自回归模型:回归的估计结果如下:Dependent Variable: YMethod: Least SquaresDate: 26/02/10 Time: 15:56Sample (adjusted): 1954 1985Included observations: 32 afte
24、r adjustmentsVariableCoefficientStd. Errort-StatisticProb.C6596.2284344.0781.5184420.1401X10.0474510.0396101.1979400.2410X20.2748380.0905343.0357360.0051Y(-1)0.4052750.1872202.1646990.0391R-squared0.967247Mean dependent var55355.97Adjusted R-squared0.963738S.D. dependent var40464.90S.E. of regression7705.604Akaike info criterion20.85375Sum squared resid1.66E+09Schwarz criterion21.03697Log likel