第七章练习题及参考答案

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7.101970-1987年美国个人消费支出(PCE)和个人可支配收入(PDI)数据年份PCEPDI年份PCEPDI年份PCEPDI19701492.01668.119711538.81728.419721621.91797.419731689.61916.319741674.01896.619751711.91931.719761803.92001.019771883.82066.619781961.02167.419792004.42212.619802000.42214.319812042.22248.619822050.72261.519832146.02331.919842249.32469.819852354.82542.819862455.22640.919872521.02686.3估计下列模型：tttttttPCEBPDIBBPCEPDIAAPCE132121(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，DependentVariable:PCEMethod:LeastSquaresDate:07/27/05Time:21:41Sample:19701987Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.C-216.426932.69425-6.6197230.0000PDI1.0081060.01503367.059200.0000R-squared0.996455Meandependentvar1955.606AdjustedR-squared0.996233S.D.dependentvar307.7170S.E.ofregression18.88628Akaikeinfocriterion8.819188Sumsquaredresid5707.065Schwarzcriterion8.918118Loglikelihood-77.37269F-statistic4496.936Durbin-Watsonstat1.366654Prob(F-statistic)0.000000回归方程：ˆ216.42691.008106ttPCEPDI=-+（32．69425）（0.015033）t=（-6.619723）（67.05920）2R=0.996455F=4496.936第二个模型回归的估计结果如下，DependentVariable:PCEMethod:LeastSquaresDate:07/27/05Time:21:51Sample(adjusted):19711987Includedobservations:17afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.C-233.273645.55736-5.1204360.0002PDI0.9823820.1409286.9708170.0000PCE(-1)0.0371580.1440260.2579970.8002R-squared0.996542Meandependentvar1982.876AdjustedR-squared0.996048S.D.dependentvar293.9125S.E.ofregression18.47783Akaikeinfocriterion8.829805Sumsquaredresid4780.022Schwarzcriterion8.976843Loglikelihood-72.05335F-statistic2017.064Durbin-Watsonstat1.570195Prob(F-statistic)0.000000回归方程：1ˆ233.27360.98240.0372tttPCEPDIPCE-=-+-（45.557）（0.1409）（0.1440）t=（-5.120）（6.9708）（0.258）2R=0.9965F=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：011223344tttttttYXXXXXu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YX198036.9952.8051991128.68168.129198133.6055.9061992123.97163.351198235.4263.0271993117.35172.547198342.3572.9311994139.61190.682198452.4884.7901995152.88194.538198553.6686.5891996137.95194.657198658.5398.7971997141.06206.326198767.48113.2011998163.45223.541198878.13126.9051999183.80232.724198995.13143.9362000192.61239.4591990112.60154.3912001182.81235.142【练习题7.2参考解答】分布滞后模型：01144...tttttYXXXus=4，取m=2。假设00，1012，201224，301239，4012416（*）则模型可变为：001122tttttYZZZu，其中：0123411234212342344916ttttttttttttttttZXXXXXZXXXXZXXXX估计的回归结果如下，DependentVariable:YMethod:LeastSquaresDate:25/02/10Time:23:19Sample(adjusted):19842001Includedobservations:18afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.C-35.492348.192884-4.3320930.0007Z00.8910120.1745635.1042480.0002Z1-0.6699040.254447-2.6327830.0197Z20.1043920.0623111.6753380.1160R-squared0.984670Meandependentvar121.2322AdjustedR-squared0.981385S.D.dependentvar45.63348S.E.ofregression6.226131Akaikeinfocriterion6.688517Sumsquaredresid542.7059Schwarzcriterion6.886378Loglikelihood-56.19666F-statistic299.7429Durbin-Watsonstat1.130400Prob(F-statistic)0.000000回归方程：^01235.492430.8910120.6699040.104392tttYZZZ01235.49124,0.89101,0.66990,0.10439由（*）式可得，012340.89101,0.32550,0.03123,0.17917,0.11833由阿尔蒙多项式变换可得如下估计结果：^1234-35.492340.891010.32550-0.03123-0.17917-0.11833ttttttYXXXXX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tttuXY*其中*tY为预期最佳值。2）设定模型tutteXY*其中*tY为预期最佳值。3）设定模型tttuXY*其中*tX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：****011ttttYXYu回归的估计结果如下，DependentVariable:YMethod:LeastSquaresDate:25/02/10Time:22:42Sample(adjusted):19812001Includedobservations:21afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.C-15.104034.729450-3.1936130.0050X0.6292730.0978196.4330310.0000Y(-1)0.2716760.1148582.3653150.0294R-squared0.987125Meandependentvar109.2167AdjustedR-squared0.985695S.D.dependentvar51.78550S.E.ofregression6.193728Akaikeinfocriterion6.616515Sumsquaredresid690.5208Schwarzcriterion6.765733Loglikelihood-66.47341F-statistic690.0561Durbin-Watsonstat1.518595Prob(F-statistic)0.000000回归方程：1ˆ15.104030.6292730.271676tttYXY（4.729450）（0.097819）（0.114858）t=（-3.193613）（6.433031）（2.365315）2R=0.987125F=690.0561DW=1.518595根据局部调整模型的参数关系，有****01,,1,ttuu将上述估计结果代入得到：*1110.2716760.728324*20.738064*00.864001故局部调整模型估计结果为：^*20.7380640.864001ttYX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：*21121(1)(11.518595)1.2972821()21-210.114858dnhnVar在显著性水平05.0上，查标准正态分布表得临界值21.96h，由于21.297281.96hh，则接收原假设0，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*lnlnlntttYXu在局部调整假定下，先估计一阶自回归模型：****011lnlnlnttttYXYu回归的估计结果如下，DependentVariable:LNYMethod:LeastSquaresDate:25/02/10Time:22:55Sample(adjusted):19812001Includedobservati