计量经济学实验报告 (2)

2 1978-2011年的数据搜集

城市化率

17.92

18.96

19.39

20.16

21.13

21.62

23.01

23.71

24.52

25.32

25.81

26.21

26.41

26.94

27.46

27.99

28.51

29.04

30.48

31.91

33.35

34.78

36.22

37.66

39.09

40.53

41.76

42.99

43.9

44.94

45.68

46.59

年份

1978

1979

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

人均GDP

381

419

463

492

528

583

695

858

963

1112

1366

1519

1644

1893

2311

2998

4044

5046

5846

6420

6796

7159

7858

8622

9398

10542

12336

14185

16500

20169

23708

25575

城镇居民家庭人均可支配收入

343.4

405

477.6

500.4

535.3

564.6

652.1

739.1

900.9

1002.1

1180.2

1373.9

1510.2

1700.6

2026.6

2577.4

3496.2

4283

4838.9

5160.3

5425.1

5854

6280

6859.6

7702.8

8472.2

9421.6

10493

11759.5

13785.8

15780.8

17174.7

政府支出

1122.09

1281.79

1228.83

1138.41

1229.98

1409.52

1701.02

2004.25

2204.91

2262.18

2491.21

2823.78

3083.59

3386.62

3742.2

4642.3

5792.62

6823.72

7937.55

9233.56

10798.18

13187.67

15886.5

18902.58

22053.15

24649.95

28486.89

33930.28

40422.73

49781.35

62592.66

76299.93

城镇居民消费水平

405

425

489

521

536

558

618

765

872

998

1311

1466

1596

1840

2262

2924

3852

4931

5532

5823

6109

6405

6850

7113

7387

7901

8679

9410

10423

11904

13526

15025

3 REVIEWS模型建立及检验

3.1

散点图变化分析

3.1.1 GDPP（人均GDP）和CSH（城市化）的关系

30,00025,00020,000GDPP15,00010,0005,32CSH36404448

3.1.2

GDPP（人均GDP）和JMKZPSR（城镇居民家庭人均可支配收入）的关系

30,00025,00020,000GDPP15,00010,0005,000005,00010,000JMKZPSR15,00020,000

3.1.3

GDPP（人均GDP）和ZFZC（政府支出）的关系

30,00025,00020,000GDPP15,00010,0005,0000020,00040,000ZFZC60,00080,000

3.1.4

GDPP(人均GDP)和GMXFSP（城镇居民消费水平）

30,00025,00020,000GDPP15,00010,0005,000004,0008,000GMXFSP12,00016,000

3.2 Ganger检验

3.2.1首先，我们研究GDPP和CSH的因果检验。

Pairwise Granger Causality Tests

Date: 06/03/12 Time: 10:42

Sample: 1978 2009

Lags: 1

Null Hypothesis:

Obs F-Statistic Prob.

31

0.78247

0.57193

0.3839

0.4558

CSH does not Granger Cause GDPPP

GDPPP does not Granger Cause CSH

由表可知，CSH影响GDPP的概率较大，故可以将CSH作为自变量，GDPP为因变量。

3.2.2其次，我们研究GDPP和JMKZPSR的因果检验。

Pairwise Granger Causality Tests

Date: 06/03/12 Time: 10:44

Sample: 1978 2009

Lags: 1

Null Hypothesis:

Obs F-Statistic Prob.

31

0.24821

0.19484

0.6222

0.6623

JMKZPSR does not Granger Cause GDPP

GDPP does not Granger Cause JMKZPSR

由表可知， JMKZPSR影响GDPP的概率高，故可以将JMKZPSR作为自变量，GDPP作为因变量。

3.2.3紧接着，我们研究GDPP和ZFZC之间的因果关系。

Pairwise Granger Causality Tests

Date: 06/03/12 Time: 10:45

Sample: 1978 2009

Lags: 1

Null Hypothesis:

Obs F-Statistic Prob.

31

0.02024

0.33720

0.8879

0.5661

ZFZC does not Granger Cause GDPP

GDPP does not Granger Cause ZFZC

由表可知，GDPP和ZFZC相互影响，概率都比较大，所以可以将ZFZC作为自变

量。

3.2.4最后，我们研究GDPP和GMXFSP的因果关系。

Pairwise Granger Causality Tests

Date: 06/03/12 Time: 10:44

Sample: 1978 2009

Lags: 1

Null Hypothesis:

Obs F-Statistic Prob.

30

16.0251

7.44216

0.0004

0.0111

JMXFSP does not Granger Cause GDPP

GDPP does not Granger Cause JMXFSP

由表可知，GDPP和 JMXFSP的相关可能性都非常低，顾将JMXFSP作为自变量剔除。

3.3选择模型形式，做回归,描绘模型

估计模型：GDPCCSH2JMKZPRSZFZC

Dependent Variable: GDPP

Method: Least Squares

Date: 06/07/12 Time: 16:47

Sample: 1978 2011

Included observations: 34

Variable

C

CSH^2

ZFZC

JMKZPSR

R-squared

Coefficient

472.7725

-1.589601

0.096333

1.269763

Std. Error

178.0388

0.416496

0.011037

0.086591

t-Statistic

2.655446

-3.816604

8.728460

14.66399

Prob.

0.0126

0.0006

0.0000

0.0000

7863.882

9292.254

13.99865

14.17822

14.05989

1.179488

0.999337 Mean dependent var

0.999271 S.D. dependent var

250.9664 Akaike info criterion

1889524. Schwarz criterion

-233.9770 Hannan-Quinn criter.

15070.08 Durbin-Watson stat

0.000000

Adjusted R-squared

S.E. of regression

Sum squared resid

Log likelihood

F-statistic

Prob(F-statistic)

令YGDP

X1 CSH2

X2 JMKZPSR

X3 ZFZC

Y472.7725-1.589601x^1^0.096333x21.269763x3

178.0388

0.4164

0.011037

0.086591

R20.999337

R20.999271

DW1.179488

SE250.9664

F0.00

n33

3.4随机误差项的正态性检验（JB检验）

876543210-600-400-2Series: RESIDSample 1978 2009Observations 32Mean

Median

Maximum

Minimum

Std. Dev.

Skewness

Kurtosis

Jarque-BeraProbability-1.56e-13 25.89469 606.3765-601.0734 246.4424-0.256965 4.277828 2.529290 0.282340

通过JB检验发现，估计模型随机误差项可能为正太分布的可能性P>5%,所以通过检验。

3.5 Ramsey reset test检验

Ramsey RESET Test:

F-statistic

Log likelihood ratio

Test Equation:

Dependent Variable: GDPP

Method: Least Squares

Date: 06/03/12 Time: 13:59

Sample: 1978 2009

4.085866 Prob. F(1,27)

4.509325 Prob. Chi-Square(1)

0.0533

0.0337

Included observations: 32

Variable

C

CSH^2

JMKZPSR

ZFZC

FITTED^2

R-squared

Adjusted R-squared

S.E. of regression

Sum squared resid

Log likelihood

F-statistic

Prob(F-statistic)

Coefficient

-44.45361

-0.208129

1.226143

-0.004762

8.81E-06

Std. Error t-Statistic Prob.

313.7799

0.798441

0.088068

0.051507

4.36E-06

-0.141671

-0.260669

13.92275

-0.092447

2.021353

0.8884

0.7963

0.0000

0.9270

0.0533

6325.906

7066.021

13.99197

14.22099

14.06788

1.060922

0.998943 Mean dependent var

0.998787 S.D. dependent var

Akaike info

246.1018 criterion

1635285. Schwarz criterion

Hannan-Quinn

-218.8715 criter.

6382.086 Durbin-Watson stat

0.000000

Prob.F值为0.533>5%,所以模型被误设可能性较小。

3.6 T、F检验，拟合优度检验

t-Statistic

2.288009

-3.385601

13.98170

7.726581

T值的绝对值>2，通过检验，说明此模型拟合优度较好。

Prob(F-statistic)

0.000000

F值为0，远远小于5%，说明此模型拟合优度较好。

R-squared 0.998784

R2=0.99，说明改模型可行性很大，拟合度好。

3.7 Wald Test检验，若 Prob. F>5%，接受约束条件

Wald Test:

Equation: Untitled

Test Statistic

F-statistic

Chi-square

Value

3.421460

3.421460

Value

2.792085

df Probability

(1, 28)

1

0.0749

0.0644

Std. Err.

1.509465

Null Hypothesis Summary:

Normalized Restriction (= 0)

-1 + C(2)^2 - 3*C(3) + C(4)

Delta method computed using analytic derivatives.

3.8邹氏突变检验：若 Prob. F<5%，认为该点很可能是突变点

通过观察整体数据较为平稳，未发现明显突变点，其中对1995年、2004年进行随机检测，如下图：

Chow Breakpoint Test: 1994

Null Hypothesis: No breaks at specified breakpoints

Varying regressors: All equation variables

Equation Sample: 1978 2009

F-statistic

10.66037

32.68074

42.64146

Prob. F(4,24)

Prob. Chi-Square(4)

Prob. Chi-Square(4)

0.0000

0.0000

0.0000

Prob. F(4,24)

Prob. Chi-Square(4)

Prob. Chi-Square(4)

0.0000

0.0000

0.0000

Log likelihood ratio

Wald Statistic

Chow Breakpoint Test: 2004

Null Hypothesis: No breaks at specified breakpoints

Varying regressors: All equation variables

Equation Sample: 1978 2009

F-statistic

51.32985

72.22598

205.3194

Log likelihood ratio

Wald Statistic

所以通过邹氏检验，发现无突变点。

3.9模型的比较：观察AIC和SC值的变化，若有下降的现象，该模型可能更好些。

Dependent Variable: GDPP

Method: Least Squares

Date: 06/07/12 Time: 19:12

Sample: 1978 2009

Included observations: 32

Variable

C

CSH^2

ZFZC

JMKZPSR

JMKZPSR^2

R-squared

Adjusted R-squared

S.E. of regression

Sum squared resid

Log likelihood

F-statistic

Prob(F-statistic)

Coefficient

-355.7275

1.175857

-0.157097

1.056712

5.91E-05

Std. Error

157.9942

0.448006

0.034252

0.058971

7.81E-06

t-Statistic

-2.251522

2.624645

-4.586449

17.91905

7.574526

Prob.

0.0327

0.0141

0.0001

0.0000

0.0000

6325.906

7066.021

12.99347

13.22249

13.06938

1.124435

0.999611 Mean dependent var

0.999553 S.D. dependent var

149.3804 Akaike info criterion

602491.2 Schwarz criterion

-202.8955 Hannan-Quinn criter.

17333.87 Durbin-Watson stat

0.000000

此时AIC12.99347 SC13.22249

原模型AIC13.99865 SC14.17822

通过比较发现 增加一个变量后的模型更适合

4 REVIEWS异方差检验及克服

4.1异方差检验

4.1.1图形法

400,000350,000300,000250,000RESID^2200,000150,000100,00050,32CSH

36404448

400,000350,000300,000250,000RESID^2200,000150,000100,00050,000005,00010,000JMKZPSR15,00020,000400,000350,000300,000250,000RESID^2200,000150,000100,00050,0000020,00040,000ZFZC

60,00080,0004.1.2 WHITE检验

Heteroskedasticity Test: White

F-statistic

Obs*R-squared

Scaled explained SS

4.375318 Prob. F(9,22)

20.53007 Prob. Chi-Square(9)

25.76099 Prob. Chi-Square(9)

0.0023

0.0149

0.0022

Test Equation:

Dependent Variable: RESID^2

Method: Least Squares

Date: 06/03/12 Time: 14:01

Sample: 1978 2009

Included observations: 32

Variable

C

CSH^2

(CSH^2)^2

(CSH^2)*JMKZPSR

(CSH^2)*ZFZC

JMKZPSR

JMKZPSR^2

JMKZPSR*ZFZC

ZFZC

ZFZC^2

R-squared

Adjusted R-squared

S.E. of regression

Sum squared resid

Log likelihood

F-statistic

Prob(F-statistic)

Coefficient

8464.488

-201.3539

0.390429

-0.209972

0.006477

-13.46487

0.028131

-0.005733

46.12346

0.000277

Std. Error t-Statistic Prob.

329747.7

1601.322

1.982626

0.662189

0.073271

270.5561

0.065792

0.017857

50.20082

0.001399

0.025670

-0.125742

0.196925

-0.317087

0.088393

-0.049767

0.427570

-0.321084

0.918779

0.198082

0.9798

0.9011

0.8457

0.7542

0.9304

0.9608

0.6731

0.7512

0.3682

0.8448

58835.95

108225.6

25.58907

26.04711

25.74090

2.022294

0.641565 Mean dependent var

0.494932 S.D. dependent var

Akaike info

76913.92 criterion

1.30E+11 Schwarz criterion

Hannan-Quinn

-399.4251 criter.

4.375318 Durbin-Watson stat

0.002261

nR220.53007，由white检验知，在0.05，查2分布表，得临界值20.0537.81473，所以拒绝原假设，接受备择假设，表明模型存在异方差。

4.2异方差的修正

Dependent Variable: GDPP

Method: Least Squares

Date: 06/03/12 Time: 14:34

Sample: 1978 2009

Included observations: 32

Weighting series: 1/RESID^2

Variable

C

CSH

ZFZC

JMKZPSR

R-squared

Coefficient

849.1712

-48.90755

0.086467

1.185499

Std. Error t-Statistic Prob.

171.2264

8.460355

0.004839

0.028887

4.959347

-5.780791

17.86810

41.03955

0.0000

0.0000

0.0000

0.0000

633.4496

3246.371

3.209302

3.392519

3.270033

1.364803

6325.906

7066.021

2681534.

Weighted Statistics

0.999925 Mean dependent var

0.999917 S.D. dependent var

Akaike info

1.135960 criterion

36.13133 Schwarz criterion

Hannan-Quinn

-47.34883 criter.

124296.8 Durbin-Watson stat

0.000000

Unweighted Statistics

Adjusted R-squared

S.E. of regression

Sum squared resid

Log likelihood

F-statistic

Prob(F-statistic)

R-squared

Adjusted R-squared

S.E. of regression

Durbin-Watson stat

0.998268 Mean dependent var

0.998082 S.D. dependent var

309.4658 Sum squared resid

0.658206

4.3再次对修正后的模型做white检验

Heteroskedasticity Test: White

F-statistic

Obs*R-squared

Scaled explained SS

Test Equation:

Dependent Variable: WGT_RESID^2

Method: Least Squares

Date: 06/03/12 Time: 14:41

Sample: 1978 2009

Included observations: 32

Collinear test regressors dropped from specification

Variable

Coefficient

Std. Error t-Statistic Prob.

1.09E+22 Prob. F(1,30)

32.00000 Prob. Chi-Square(1)

3.01E-10 Prob. Chi-Square(1)

0.0000

0.0000

1.0000

C

WGT^2

R-squared

2.45E-16

3.14E-08

5.44E-17

3.00E-19

4.498128

1.05E+11

0.0001

0.0000

1.00E-06

5.68E-06

2.75E-30

1.800809

1.000000 Mean dependent var

1.000000 S.D. dependent var

3.03E-16 Sum squared resid

1.09E+22 Durbin-Watson stat

0.000000

Adjusted R-squared

S.E. of regression

F-statistic

Prob(F-statistic)

nR23.01E1020.0537.81473,所以修正后的模型通过WHITE检验得到无异方差。

此时模型为：

Y849.1712-48.90755x^10.086467x21.185499x3

171.2264

8.460355

0.004839

0.028887

R20.999925

R20.999917

DW1.364803

SE1.135960

F0.00

n33

5 REVIEWS自相关检验及克服

5.1 自相关检验

5.1.1 DW检验法

Dependent Variable: GDPP

Method: Least Squares

Date: 06/07/12 Time: 17:28

Sample: 1978 2009

Included observations: 32

Variable

C

CSH^2

ZFZC

JMKZPSR

R-squared

Coefficient

459.4286

-1.558879

0.096554

1.265428

Std. Error

200.7984

0.460444

0.012496

0.090506

t-Statistic

2.288009

-3.385601

7.726581

13.98170

Prob.

0.0299

0.0021

0.0000

0.0000

6325.906

7066.021

14.07039

14.25360

0.998784 Mean dependent var

0.998653 S.D. dependent var

259.3089 Akaike info criterion

1882750. Schwarz criterion

Adjusted R-squared

S.E. of regression

Sum squared resid

Log likelihood

F-statistic

Prob(F-statistic)

-221.1262 Hannan-Quinn criter.

7663.496 Durbin-Watson stat

0.000000

14.13112

1.020692

DW1.020692 dl

说明在滞后一期时 该模型存在一阶自相关

5.1.2 LM检验法

Breusch-Godfrey Serial Correlation LM Test:

F-statistic

11.63691 Prob. F(1,27)

0.0021

0.0019

Prob.

0.3615

0.4776

0.1990

0.8403

0.0021

-4.19E-13

246.4424

13.77451

14.00354

13.85043

1.197067

Obs*R-squared

Test Equation:

Dependent Variable: RESID

Method: Least Squares

9.637960 Prob. Chi-Square(1)

Coefficient

-164.8782

0.288769

-0.015185

0.015708

0.772596

Std. Error

177.6396

0.401008

0.011532

0.077184

0.226482

t-Statistic

-0.928161

0.720107

-1.316774

0.203514

3.411291

Date: 06/07/12 Time: 18:03

Sample: 1978 2009

Included observations: 32

Presample missing value lagged residuals set to zero.

Variable

C

CSH^2

ZFZC

JMKZPSR

RESID(-1)

R-squared

0.301186 Mean dependent var

0.197658 S.D. dependent var

220.7472 Akaike info criterion

1315692. Schwarz criterion

-215.3922 Hannan-Quinn criter.

2.909226 Durbin-Watson stat

0.040137

Adjusted R-squared

S.E. of regression

Sum squared resid

Log likelihood

F-statistic

Prob(F-statistic)

nR29.6379600.0539.637960 LM检验也说明该模型在滞后一期时存在一阶自相关。

5.2 广义差分法克服自相关

ˆDW/20.510346

滞后一期时，

Yx101(x11)2x213x31

两边同时乘以 并将原模型与所得模型相减

得到差方后模型：

ˆ*389.849323.95x*0.04233x*0.9083x*

YX123

6 REVIEWS多重共线检验及克服

6.1多重共线检验

GDPP

CSH^2

ZFZC

JMKZPSR

GDPP

1

0.9661

18101

73518

1

08908

06614

0.986401731220.921508556861

96026

0.996187219120.976948210580.972093851591

CSH^2

47061

ZFZC

18101

08908

JMKZPSR

73518

06614

0.9726

0.96.986401731220.996187219120.921508556860.97694821058

6.1.1

去掉CSH2后 对模型R2重新进行计算

Dependent Variable: GDPP

Method: Least Squares

Date: 06/07/12 Time: 19:02

Sample: 1978 2009

Included observations: 32

Variable

C

ZFZC

JMKZPSR

R-squared

Adjusted R-squared

S.E. of regression

Sum squared resid

Log likelihood

F-statistic

Prob(F-statistic)

Coefficient

-167.6252

0.120358

0.992477

Std. Error

90.48260

0.012051

0.047977

t-Statistic

-1.852568

9.987319

20.68630

Prob.

0.0741

0.0000

0.0000

6325.906

7066.021

14.35103

14.48844

14.39657

0.869511

0.998286 Mean dependent var

0.998167 S.D. dependent var

302.4890 Akaike info criterion

2653487. Schwarz criterion

-226.6164 Hannan-Quinn criter.

8443.399 Durbin-Watson stat

0.000000

此时R20.9982860.999337 所以CSH2不应该被剔除

6.1.2

去掉ZFZC后 对模型R重新进行计算

Dependent Variable: GDPP

Method: Least Squares

Date: 06/07/12 Time: 19:05

Sample: 1978 2009

Included observations: 32

Variable

C

CSH^2

JMKZPSR

R-squared

Adjusted R-squared

S.E. of regression

Sum squared resid

Log likelihood

F-statistic

Prob(F-statistic)

Coefficient

995.1454

-3.560546

1.871291

Std. Error

327.7126

0.661954

0.078598

t-Statistic

3.036641

-5.378842

23.80846

Prob.

0.0050

0.0000

0.0000

6325.906

7066.021

15.14960

15.28702

15.19515

0.256818

2

0.996190 Mean dependent var

0.995927 S.D. dependent var

450.9395 Akaike info criterion

5897047. Schwarz criterion

-239.3937 Hannan-Quinn criter.

3791.291 Durbin-Watson stat

0.000000

此时R20.9961900.999337 所以ZFZC不应该被剔除

6.1.3

去掉JMKZPSR后 对模型R重新进行计算

Dependent Variable: GDPP

Method: Least Squares

Date: 06/07/12 Time: 19:11

Sample: 1978 2009

Included observations: 32

Variable

C

CSH^2

ZFZC

R-squared

Adjusted R-squared

S.E. of regression

Sum squared resid

Log likelihood

F-statistic

Coefficient

-1517.897

4.175785

0.247928

Std. Error

395.7188

0.580862

0.017324

t-Statistic

-3.835797

7.188952

14.31145

Prob.

0.0006

0.0000

0.0000

6325.906

7066.021

16.08504

16.22245

16.13059

0.469288

2

0.990291 Mean dependent var

0.989621 S.D. dependent var

719.8556 Akaike info criterion

15027571 Schwarz criterion

-254.3606 Hannan-Quinn criter.

1478.950 Durbin-Watson stat

Prob(F-statistic)

0.000000

此时R20.9902910.999337 所以JMKZPSR不应该被剔除

结果表明，虽然模型存在多重共线，但是并不影响本模型的分析效果，所以不必要进行处理。

7

结论

从对于1979—2009年的数据的计量分析中，我们发现了以下结论：

（1）城镇居民消费水平与人均GDP显著相关，但没有不显著影响人均GDP，不能构成影响人均GDP的自变量。故我们踢出了该自变量，初步估计是由于当前中国居民收入的不均衡，抑制了他更进一步发挥对经济增长的拉动作用。做出仅含三个自变量的回归模型。

（2）城镇居民家庭人均可支配收入、城市化率及城市政府支出对GDP的具有较大的影响，随着这三个自变量的增加，人均GDP显著增加，构成影响人均GDP的关键影响因素。

（3）为了GDP的更快更健康的增长，应加大城镇居民家庭人均可支配收入、城市化率及城市政府支出，另外要均衡居民收入，减小贫富差距。