第七章练习题及参考解答(第四版)计量经济学

1、精选文档第七章练习题及参考解答7.1 表7.4中给出了1981-2015年中国城镇居民人均年消费支出(PCE)和城镇居民人均可支配收入(PDI)数据。表7.4 1981-2015年中国城镇居民消费支出(PCE)和可支配收入(PDI)数据 （单位：元）年度城镇居民人均消费支出PCE城镇居民人均可支配收入PDI年度城镇居民人均消费支出PCE城镇居民人均可支配收入PDI1981456.80500.4019994615.915854.021982471.00535.3020004998.006280.001983505.90564.6020015309.016859.601984559.40652.1

2、020026029.887702.801985673.20739.1020036510.948472.201986799.00900.9020047182.109421.601987884.401002.1020057942.8810493.0019881104.001180.2020068696.5511759.5019891211.001373.9320079997.4713785.8019901278.901510.20200811242.8515780.7619911453.801700.60200912264.5517174.6519921671.702026.60201013471

3、.4519109.4419932110.802577.40201115160.8921809.7819942851.303496.20201216674.3224564.7219953537.574283.00201318022.6426955.1019963919.474838.90201419968.0829381.0019974185.645160.30201521392.3631790.3119984331.615425.10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？分析该地区消费同收入的关系。(3) 建立适当的分布滞后模型，用库伊

4、克变换转换为库伊克模型后进行估计，并对估计结果进行分析判断。【练习题7.1参考解答】(1) 解释这两个回归模型的结果。Dependent Variable: PCEMethod: Least SquaresDate: 03/10/18 Time: 09:12Sample: 1981 2005Included observations: 25VariableCoefficientStd. Errort-StatisticProb. C149.097524.567346.0689330.0000PDI0.7575270.005085148.98400.0000R-squared0.998965 M

5、ean dependent var2983.768Adjusted R-squared0.998920 S.D. dependent var2364.412S.E. of regression77.70773 Akaike info criterion11.62040Sum squared resid138885.3 Schwarz criterion11.71791Log likelihood-143.2551 F-statistic22196.24Durbin-Watson stat0.531721 Prob(F-statistic)0.000000收入跟消费间有显著关系。收入每增加1元，

6、消费增加0.76元。Dependent Variable: PCEMethod: Least SquaresDate: 03/10/18 Time: 09:13Sample(adjusted): 1982 2005Included observations: 24 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C147.688626.735795.5240010.0000PDI0.6791230.0699599.7073850.0000PCE(-1)0.1110350.1001861.1082870

7、.2803R-squared0.999012 Mean dependent var3089.059Adjusted R-squared0.998918 S.D. dependent var2354.635S.E. of regression77.44504 Akaike info criterion11.65348Sum squared resid125952.4 Schwarz criterion11.80074Log likelihood-136.8418 F-statistic10620.10Durbin-Watson stat0.688430 Prob(F-statistic)0.00

8、0000(2) 短期和长期边际消费倾向（MPC）是多少？分析该地区消费同收入的关系。短期MPC=0.68，长期MPC=0.679/(1-0.111)=0.764(3) 建立适当的分布滞后模型，用库伊克变换转换为库伊克模型后进行估计，并对估计结果进行分析判断。在滞后1-5期内，根据AIC最小，选择滞后5期，其回归结果如下:Dependent Variable: PCEMethod: Least SquaresDate: 03/10/18 Time: 09:25Sample(adjusted): 1986 2005Included observations: 20 after adjusting

9、endpointsVariableCoefficientStd. Errort-StatisticProb. C167.959033.277935.0471580.0002PDI0.7079330.1248785.6689810.0001PDI(-1)0.2252720.2742930.8212830.4263PDI(-2)-0.1789110.316743-0.5648470.5818PDI(-3)-0.0695250.328725-0.2114980.8358PDI(-4)0.2648740.3004700.8815320.3940PDI(-5)-0.2269660.145557-1.55

10、92920.1429R-squared0.999382 Mean dependent var3596.396Adjusted R-squared0.999096 S.D. dependent var2254.922S.E. of regression67.79561 Akaike info criterion11.54009Sum squared resid59751.18 Schwarz criterion11.88860Log likelihood-108.4009 F-statistic3501.011Durbin-Watson stat1.471380 Prob(F-statistic

11、)0.000000当期收入对消费有显著影响，但各滞后期影响并不显著。不显著可能是分布滞后模型直接估计时共线性造成的，也可能是真没显著影响。库伊克模型估计结果见上表，PCE(-1)部分回归结果t检验不显著。7.2 表7.5中给出了中国1980-2016年固定资产投资Y与社会消费品零售总额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以下分布滞后模型：表7.5中国1980-2016年固定资产投资Y与社会零售总额X数据 （单位：亿元）年份固定资产投资Y社会消费品零售总额X年份固定资产投资Y社会消费品零售总额X1980910.92140.0199929854.735647.91981

12、961.02350.0200032917.739105.719821230.42570.0200137213.543055.419831430.12849.4200243499.948135.919841832.93376.4200355566.652516.319852543.24305.0200470477.459501.019863120.64950.0200588773.667176.619873791.75820.02006109998.276410.019884753.87440.02007137323.989210.019894410.48101.42008172828.4114

13、830.119904517.08300.12009224598.8132678.419915594.59415.62010251683.8156998.419928080.110993.72011311485.1183918.6199313072.314270.42012374694.7210307.0199417042.118622.92013446294.1237809.9199520019.323613.82014512020.7271896.1199622913.528360.22015561999.8300930.8199724941.131252.92016606465.73323

14、16.3199828406.233378.1【练习题7.2参考解答】直接估计结果如下：Dependent Variable: YMethod: Least SquaresDate: 03/10/18 Time: 09:32Sample(adjusted): 1984 2016Included observations: 33 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C-23633.423701.825-6.3842600.0000X0.4619270.9181980.5030800.6190X

15、(-1)2.0865661.6859581.2376140.2265X(-2)-0.5432541.708205-0.3180260.7529X(-3)1.1505771.8438080.6240220.5379X(-4)-1.3173211.283331-1.0264860.3138R-squared0.993755 Mean dependent var128264.7Adjusted R-squared0.992598 S.D. dependent var180131.0S.E. of regression15497.23 Akaike info criterion22.29768Sum

16、squared resid6.48E+09 Schwarz criterion22.56977Log likelihood-361.9117 F-statistic859.2660Durbin-Watson stat0.229807 Prob(F-statistic)0.000000使用阿尔蒙变换估计结果如下：Dependent Variable: YMethod: Least SquaresDate: 03/10/18 Time: 09:37Sample(adjusted): 1984 2016Included observations: 33 after adjusting endpoin

17、tsVariableCoefficientStd. Errort-StatisticProb. C-23683.133619.054-6.5440100.0000Z00.8016780.6237781.2851980.2089Z10.4823171.3667070.3529050.7267Z2-0.2333220.358793-0.6502980.5206R-squared0.993572 Mean dependent var128264.7Adjusted R-squared0.992907 S.D. dependent var180131.0S.E. of regression15170.

18、17 Akaike info criterion22.20526Sum squared resid6.67E+09 Schwarz criterion22.38666Log likelihood-362.3868 F-statistic1494.254Durbin-Watson stat0.287072 Prob(F-statistic)0.000000根据可计算出0.802=1.051=0.833=0.149=-1.002直接使用软件结果：Dependent Variable: YMethod: Least SquaresDate: 03/10/18 Time: 09:39Sample(ad

19、justed): 1984 2016Included observations: 33 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C-23683.133619.054-6.5440100.0000PDL010.8330240.7026451.1855550.2454PDL02-0.4509710.144976-3.1106620.0042PDL03-0.2333220.358793-0.6502980.5206R-squared0.993572Mean dependent var128264.7

20、Adjusted R-squared0.992907S.D. dependent var180131.0S.E. of regression15170.17Akaike info criterion22.20526Sum squared resid6.67E+09Schwarz criterion22.38666Log likelihood-362.3868F-statistic1494.254Durbin-Watson stat0.287072Prob(F-statistic)0.000000 Lag Distribution of XiCoefficientStd. ErrorT-Stat

21、istic . * |0 0.80168 0.62378 1.28520 . *|1 1.05067 0.42723 2.45927 . * |2 0.83302 0.70264 1.18555 .* |3 0.14873 0.31166 0.47722 * . |4-1.00221 0.92567-1.08269Sum of Lags 1.83190 0.18562 9.869017.3利用表7.5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

22、佳值。【练习题7.3参考解答】1）设定模型 其中为预期最佳值。Dependent Variable: YMethod: Least SquaresDate: 03/10/18 Time: 10:09Sample(adjusted): 1981 2016Included observations: 36 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C-5669.5052498.919-2.2687830.0299X0.6649820.1301835.1080430.0000Y(-1)0.733544

23、0.0778119.4272690.0000R-squared0.997893 Mean dependent var117676.6Adjusted R-squared0.997765 S.D. dependent var175881.8S.E. of regression8314.081 Akaike info criterion20.96894Sum squared resid2.28E+09 Schwarz criterion21.10090Log likelihood-374.4410 F-statistic7815.118Durbin-Watson stat0.925919 Prob

24、(F-statistic)0.000000根据回归结果，可算出h统计量为3.64，明显大于2，表明5%显著水平下存在相关性。根据回归数据，可算出调整系数为1-0.734=0.266，这表示了局部调整的速度。0.665/0.266=2.5 2）设定模型 其中为预期最佳值。假设调整方程为：，则转化为一阶自回归模型后的回归结果为:Dependent Variable: LOG(Y)Method: Least SquaresDate: 03/10/18 Time: 10:11Sample(adjusted): 1981 2016Included observations: 36 after adjus

25、ting endpointsVariableCoefficientStd. Errort-StatisticProb. C-0.5414920.692089-0.7824030.4396LOG(X)0.2996850.2623221.1424340.2615LOG(Y(-1)0.7649000.2006083.8129090.0006R-squared0.997423 Mean dependent var10.25491Adjusted R-squared0.997267 S.D. dependent var1.956096S.E. of regression0.102265 Akaike i

26、nfo criterion-1.642847Sum squared resid0.345117 Schwarz criterion-1.510887Log likelihood32.57124 F-statistic6386.241Durbin-Watson stat0.873321 Prob(F-statistic)0.000000根据回归结果，计算h统计量时开方部分为负，没法计算。故没法根据h统计量判断相关性。根据回归数据，可算出调整系数为1-0.765=0.235，这表示了局部调整的速度。0.2997/0.235=1.2753）设定模型 其中为预期最佳值。Dependent Variab

27、le: YMethod: Least SquaresDate: 03/10/18 Time: 10:09Sample(adjusted): 1981 2016Included observations: 36 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C-5669.5052498.919-2.2687830.0299X0.6649820.1301835.1080430.0000Y(-1)0.7335440.0778119.4272690.0000R-squared0.997893 Mean de

28、pendent var117676.6Adjusted R-squared0.997765 S.D. dependent var175881.8S.E. of regression8314.081 Akaike info criterion20.96894Sum squared resid2.28E+09 Schwarz criterion21.10090Log likelihood-374.4410 F-statistic7815.118Durbin-Watson stat0.925919 Prob(F-statistic)0.000000可算出调节系数为1-0.734=0.266，这表示了

29、预期修正的速度。0.665/0.266=2.57.4表7.6给出中国各年末货币流通量Y，社会商品零售额X1、城乡居民储蓄余额X 2的数据。表7.6中国年末货币流通量、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社会消费品零售总额X1城乡居民储蓄年底余额X219892344.08101.45184.5019902644.48300.17119.6019913177.89415.69244.9019924336.010993.711757.3019935864.714270.415203.5019947288.618622.921518.8019957885.32361

30、3.829662.3019968802.028360.238520.80199710177.631252.946279.80199811204.233378.153407.47199913455.535647.959621.83200014652.739105.764332.38200115688.843055.473762.43200217278.048135.986910.65200319746.052516.3103617.65200421468.359501.0119555.39200524031.767176.6141050.99200627072.676410.0161587.30

31、200730334.389210.0172534.19200834219.0114830.1217885.35200938246.0132678.4260771.66201044628.2156998.4303302.49201150748.5183918.6343635.89201254659.8210306.9399551.00201358574.4237809.9447601.57201460259.5271896.1485261.34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

32、】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。假设局部调整方程为：，对，可转化为回归方程：，其回归结果如下：Dependent Variable: YMethod: Least SquaresDate: 03/10/18 Time: 10:03Sample(adjusted): 1990 2014Included observations: 25 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C1618.034

33、732.14892.2099790.0383Y(-1)0.9810200.1493126.5702800.0000X1-0.1304290.041464-3.1455900.0049X20.0783990.0337062.3259720.0301R-squared0.997519 Mean dependent var23457.75Adjusted R-squared0.997164 S.D. dependent var18266.54S.E. of regression972.7612 Akaike info criterion16.74380Sum squared resid1987155

34、3 Schwarz criterion16.93882Log likelihood-205.2975 F-statistic2813.916Durbin-Watson stat1.112498 Prob(F-statistic)0.000000各回归系数在5%显著水平下均显著。可算出调整系数为1-0.981=0.019，这表示了局部调整的速度。假设局部调整方程为：，对，可转化为回归方程：，其回归结果如下：Dependent Variable: LOG(Y)Method: Least SquaresDate: 03/10/18 Time: 10:04Sample(adjusted): 1990 2014Included observations: 25 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C0.6577880.2771622.3732960.0273LOG(Y(-1