第七章练习题及参考解答(第四版)计量经济学

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:匀年消费支出(PCE)和城镇居民人均

可支配收入(PDI)数据。

表7.41981-2015年中国城镇居民消费支出(PCE)和可支配收入(PDI)数据(单位：元)

年度城镇居民人均城镇居民人均可支年度城镇居民人均城镇居民人均可支

消费支出PCE配收入PDI消费支出PCE配收入PDI

1981456.80500.4019991615.915854.02

1982471.00535.3020004998.006280.00

1983505.90564.6020015309.016859.60

1984559.40652.1020026029.887702.80

1985673.20739.1020036510.948472.20

1986799.00900.9020047182.109421.60

1987884.401002.1020057942.8810493.00

19881104.001180.2020068696.5511759.50

1989121LOO1373.9320079997.4713785.80

19901278.901510.20200811242.8515780.76

19911453.801700.60200912264.5517174.65

19921671.702026.60201013471.4519109.44

19932110.802577.40201115160.8921809.78

19942851.303496.20201216674.3224564.72

19953537.574283.00201318022.6426955.10

19963919.474838.90201419968.0829381.00

19974185.645160.30201521392.3631790.31

19984331.615425.10

估计卜列模型:

PCE,=4+A2PDI,+从

PCE,=B]+B2PDI,+B3PCE.1+ur

(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。

DependentVariable:PCE

Method:LeastSquares

Date:03/10/18Time:09:12

Sample;19812005

Includedobservations:25

VariableCoefficientStd.Errort-StatisticProb.

C149.097524,567346.0689330.0000

PDI0.7575270.005085148.98400.0000

R-squared0.998965Meandependentvar2983.768

AdjustedR-squared0.998920S.D.dependentvar2364.412

S.E.ofregression77.70773Akaikeinfocriterion11.62040

Sumsquaredresid138885.3Schwarzcriterion11.71791

Loglikelihood-143.2551F-statistic22196.24

Durbin-Watsonstat0.531721Prob(F-statistic)0.000000

——_-

收入跟消费间有显著关系。收入每增加1元，消费增加0.76元。

DependentVariable:PCE

Method:LeastSquares

Date:03/10/18Time:09:13

Sample(adjusted):19822005

Includedobservations:24afteradjustingendpoints

VariableCoefficientStd.Errort-StatisticProb.

C147.688626.735795.5240010.0000

PDI0.6791230.0699599.7073850.0000

PCE(-1)0.1110350.1001861.1082870.2803

R-squared0.999012Meandependentvar3089.059

AdjustedR-squared0.998918S.D.dependentvar2354.635

S.E.ofregression77.44504Akaikeinfocriterion11.65348

Sumsquaredresid-25952.4Schwarzcriterion11.80074

Loglikelihood-136.8418F-statistic10620.10

Durbin-Watsonstat_0.688430_Prob(F-statistic)0.000000

(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/(l-0.l11)=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：

DependentVariable:PCE

Method:LeastSquares

Date:03/10/18Time:09:25

Sample(adjusted):19862005

Includedobservations:20afteradjustingendpoints

VariableCoefficientStd.Errort-StatisticProb.

C167.959033.277935.0471580.0002

PDI0.7079330.1248785.6689810.0001

PDI(-1)0.2252720.2742930.8212830.4263

PDI(-2)-0.1789110.316743-0.5648470.5818

PDI(-3)-0.0695250.328725-0.2114980.8358

PDI(-4)0.2648740.3004700.8815320.3940

PDI(-5)-0.2269660.145557-1.5592920.1429

R-squared0.999382Meandependentvar3596.396

AdjustedR-squared0.999096S.D.dependentvar2254.922

S.E.ofregression67.79561Akaikeinfocriterion11.54009

Sumsquaredresid59751.18Schwarzcriterion11.88860

Loglikelihood-108.4009F-statistic3501.011

Durbin-Watsonstat1.471380Prob(F-statistic)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。库力克模型估计结果见上表，PCE(-1)

部分।可ri结果t检验不显著八

7.2表7.5中给出了中国1980-20I6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：

Y产a+0°X户优X-+p2X,_2+用X_+dXf+u,

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)

年份固定资产投资社会消费品零售总额年份固定资产投资社会消费品零售总

YXY额X

1980910.92140.0199929854.735647.9

1981961.02350.02(XM)32917.739105.7

19821230.42570.0200137213.543055.4

19831430.12849.4200243499.948135.9

19841832.93376.4200355566.652516.3

19852543.24305.0200470477.459501.0

19863120.64950.0200588773.667176.6

19873791.75820.02006109998.276410.0

19884753.87440.0200/137323.989210.0

19894410.48101.42008172828.4114830.1

19904517.08300.12009224598.8132678.4

19915594.59415.62010251683.8156998.4

19928080.110993.72011311485.1183918.6

199313072.314270.42012374694.7210307.0

199417042.118622.92013446294.1237809.9

199520019.323613.82014512020.7271896.1

199622913.528360.22015561999.8300930.8

199724941.131252.92016606465.7332316.3

199828406.233378.1

【练习题7.2参考解答】

直接估计结果如下：

DependentVariable:Y

Method:LeastSquares

Date:03/10/18Time:09:32

Sample(adjusted):19842016

Includedobservations:33afteradjustingendpoints

VariableCoefficientStd.Errort-StatisticProb.

C-23633.423701.825-6.3842600.0000

X0.4619270.9181980.5030800.6190

X(-1)2.0865661.6859581.2376140.2265

X(-2)-0.5432541.708205-0.3180260.7529

X(-3)1.1505771.8438080.6240220.5379

X(-4)-1.3173211.283331-1.0264860.3138

R-squared0.993755Meandependentvar128264.7

AdjustedR-squared0.992598S.D.dependentvar180131.0

S.E.ofregression■5497.23Akaikeinfocriterion22.29768

Sumsquaredresid6.48E+09Schwarzcriterion22.56977

Loglikelihood-361.9117F-statistic859.2660

Durbin-Watsonstat0.229807Prob(F-statistic)0.000000

使用阿尔蒙变换估计结果如下：

DependentVariable:Y

Method:LeastSquares

Date:03/10/18Time:09:37

Sample(adjusted):19842016

Includedobservations:33afteradjustingendpoints

VariableCoefficientStd.Errort-StatisticProb.

C-23683.133619.054-6.5440100.0000

ZO0.8016780.6237781.2851980.2089

Z10.4823171.3667070.3529050.7267

Z2-0.2333220.358793-0.6502980.5206

R-squared0.993572Meandependentvar128264.7

AdjustedR-squared0.992907S.D.dependentvar180131.0

S.E.ofregression15170.17Akaikeinfocriterion22.20526

Sumsquaredresid6.67E+09Schwarzcriterion22.38666

Loglikelihood-362.3868F-statistic1494.254

Durbin-Watsonstat0.287072Prob(F-statistic)0.000000

根据力++a1可计算出

Bo-4)-0.802

=a{}+a]+«2=1.051

=a()+2al+4a2=0.833

py=a()+3。]+9a2=0.149

8=%+4%+16a2=-1.002

直接使用软件结果：

DependentVariable:Y

Method:LeastSquares

Date:03/10/18Time:09:39

Sample(adjusted):19842016

Includedobservations:33afteradjustingendpoints

VariableCoefficientStd.Errort-StatisticProb.

C-23683.133619.054-6.5440100.0000

PDL010.8330240.7026451.1855550.2454

PDL02-0.4509710.144976-3.1106620.0042

PDL03-0.2333220.358793-0.6502980.5206

R-squared0.993572Meandependentvar128264.7

AdjustedR-squared0.992907S.D.dependentvar180131.0

S.E.ofregression15170.17Akaikeinfocriterion22.20526

Sumsquaredresid6.67E+09Schwarzcriterion22.38666

Loglikelihood-362.3868F-statistic1494.254

Durbin-Watsonstat0.287072Prob(F-statistic)0.000000

LagjCoefficienStd.ErrorT-Statistic

DistributionofXt

*|00.801680.623781.28520

*|11.050670.427232.45927

*|20.833020.702641.18555

.*|30.148730.311660.47722

A|4-1.002210.92567-1.08269

Sumof1.831900.185629.86901

Lags_一一

7.3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，并解称

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

Y；=a+flX,

其中匕'为预期最佳值。

2)设定模型

Y；=aX^e11'

其中匕•为预期最佳值。

3)设定模型

匕=a+外：+/

其中X；为预期最佳值。

【练习题7.3参考解答】

1)设定模型

y：=a+px,+wz

其中匕"为预期最佳值。

DependentVariable:Y

Method:LeastSquares

Date:03/10/18Time:10:09

Sample(adjusted):19812016

Includedobservations:36afteradjustingendpoints

VariableCoefficientStd.Errort-StatisticProb.

0-5669.5052498.919-2.2687830.0299

X0.6649820.1301835.1080430.0000

Y(-1)0.7335440.0778119.4272690.0000

R-squared0.997893Meandependentvar117676.6

AdjustedR-squared0.997765S.D.dependentvar175881.8

S.E.ofregression8314.081Akaikeinfocriterion20.96894

Sumsquaredresid2.28E+09Schwarzcriterion21.10090

Loglikelihood-374.4410F-statistic7815.118

Durbin-Watsonstat_0.925919_Prob(F-statistic)0.000000

根据回归结果，可算Hlh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5==1-0.734=0.266,这表示了局部调整的速度。

P=/V/5=0.665/0.266=2.5

2)设定模型

Y；=aXj}e

其中匕”为预期最佳值。

假设调整方程为：lnX-]n%=3(lnR-lnL),则转化为一阶自I可归模型后的I可归结果

为：

DependentVariable:LOG(Y)

Method:LeastSquares

Date:03/10/18Time:10:11

Sample(adjusted):19812016

Includedobservations:36afteradjustingendpoints

VariableCoefficientStd.Errort-StatisticProb.

C-0.5414920.692089-0.7824030.4396

LOG(X)0.2996850.2623221.1424340.2615

LOG(Y(-1))0.7649000.2006083.8129090.0006

R-squared0.997423Meandependentvar10.25491

AdjustedR-squared0.997267S.D.dependentvar1.956096

S.E.ofregression0.102265Akaikeinfocriterion-1.642847

Sumsquaredresid0.345117Schwarzcriterion-1.510887

Loglikelihood32.57124F-statistic6386.241

Durbin-Watsonstat0.873321Prob(F-statistic)0.000000

根据回归结果，计算h统广量时开方部分为负，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5=1-夕；=1-0.765=0.235,这表示了局部调整的速度。

P=/(^=0.2997/0.235=1.275

3)设定模型

Yt=a+0X：+ut

其中X；为预期最佳值。

DependentVariable:Y

Method:LeastSquares

Date:03/10/18Time:10:09

Sample(adjusted):19812016

Includedobservations:36afteradjustingendpoints

VariableCoefficientStd.Errort-StatisticProb.

C-5669.5052498.919-2.2687830.0299

X0.6649820.1301835.1080430.0000

Y(-1)0.7335440.0778119.4272690.0000

R-squared0.997893Meandependentvar117676.6

AdjustedR-squared0.997765S.D.dependentvar175881.8

S.E.ofregression8314.081Akaikeinfocriterion20.96894

Sumsquaredresid2.28E+09Schwarzcriterion21.10090

Loglikelihood-374.4410F-statistic7815.118

Durbin-Watsonstat0.925919Prob(F-statistic)0.000000

可算出调节系数为7=1-〃；=1-0.734=0.266,这表示了预期修正的速度。=/3；!y=

0.665/0.266=2.5

7.4表7.6给出中国各年末货币流通量Y,社会商品零售额XI、城乡居民储蓄余额X2

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社会消费品零售总颔XI城乡居民储蓄年底余额X2

19892344.08101.45184.50

19902644.48300.17119.60

19913177.89415.69244.90

19924336.010993.711757.30

19935864.714270.415203.50

19947288.618622.921518.80

19957885.323613.829662.30

19968802.028360.238520.80

199710177.631252.946279.80

199811204.233378.153407.47

199913455.535647.959621.83

200014652.739105.764332.38

200115688.843055.473762.43

200217278.048135.986910.65

200319746.052516.3103617.65

200421468.359501.0119555.39

200524031.767176.6141050.99

200627072.676410.0161587.30

200730334.389210.0172534.19

200834219.0114830.1217885.35

200938246.0132678.4260771.66

201044628.2156998.4303302.49

201150748.5183918.6343635.89

201254659.8210306.9399551.00

201358574.4237809.9447601.57

201460259.5271896.1485261.34

利用表中数据设定模型：Y；=a+/3】X1户员X?卢冉

Z"=aX””

其中，匕•为长期(或所需求的)货币流通最。成根据局部调整假设，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】

利用表中数据设定模型：Y：=a+°\Xz+dX?"内

Y：=aX^X^2eUl

其中，匕“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：乂一％=演匕"一%),对工*=。+片X“+AX〃+从，可转化为

回归方程：X=3a+(l—5)%+或QXk+p/Xz+K〃,，其回归结果如下：

DependentVariable:Y

Method:LeastSquares

Date:03/10/18Time:10:03

Sample(adjusted):19902014

Includedobservations:25afteradjustingendpoints

VariableCoefficientStd.Errort-StatisticProb.

C1618.034732.14892.2099790.0383

Y(-1)0.9810200.1493126.5702800.0000

X1-0.1304290.041464-3.1455900.0049

X20.0783990.0337062.3259720.0301

R-squared0.997519Meandependentvar23457.75

AdjustedR-squared0.997164S.D.dependentvar18266.54

S.E.ofregression972.7612Akaikeinfocriterion16.74380

Sumsquaredresid19871553Schwarzcriterion16.93882

Loglikelihood-205.2975F-statistic2813.916

Durbin-Watsonstat1.112498Prob(F-statistic)0.000000

各回归系数在5%显著水Y：下均显著。可算出调整系数为5=1-4=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：lnX-ln%=b(lnR-lni；J,对Y*=aX^X9小，可转化为【可

归方程：In%=(Slna+(l-5)lnL+/?QlnX|I+A31nX2,+S4，其回归结果如下:

DependentVariable:LOG(Y)

Method:LeastSquares

Date:03/10/18Time:10:04

Sample(adjusted):19902014

Includedobservations:25afteradjustingendpoints

VariableCoefficientStd.Errort-StatisticProb.

C0.6577880.2771622.3732960.0273

LOG(Y(-1))0.7419100.2306023.2172700.0041

LOG(X1)0.0533500.1027270.5193320.6090

LOG(X2)0.1211540.1785370.6785930.5048

R-squared0.996730Meandependentvar9.716778

AdjustedR-squared0.996263