格兰杰因果检验（正式版）

一．北京的存款增长对北京的人均GDP增长的格兰杰因果检验 （一）单根检验

1. A1（北京的存款增长）的单根检验

Null Hypothesis: A1 has a unit root Exogenous: Constant

Lag Length: 0 (Automatic based on SIC, MAXLAG=6)

t-Statistic -4.218621 -3.699871 -2.976263 -2.627420

Std. Error 0.198131 5.072943

t-Statistic -4.218621 3.811324

Prob.* 0.0029

Prob. 0.0003 0.0008 0.105185 14.84304 7.805761 7.901749 17.79676 0.000282

Augmented Dickey-Fuller test statistic Test critical values:

1% level 5% level 10% level

*MacKinnon (1996) one-sided p-values.

Dependent Variable: D(A1) Method: Least Squares Date: 10/25/11 Time: 10:04 Sample (adjusted): 1983 2009

Augmented Dickey-Fuller Test Equation

Included observations: 27 after adjustments

Variable A1(-1) C

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

Coefficient -0.835841 19.33463

0.415844 Mean dependent var 0.392477 S.D. dependent var 11.56922 Akaike info criterion 3346.172 Schwarz criterion -103.3778 F-statistic 2.021836 Prob(F-statistic)

2.A2（北京人均GDP增长）的单根检验 （1）未滞后

Null Hypothesis: A2 has a unit root Exogenous: Constant

Lag Length: 0 (Automatic based on SIC, MAXLAG=6)

t-Statistic

Prob.*

Augmented Dickey-Fuller test statistic Test critical values:

1% level 5% level 10% level

-2.648793 -3.699871 -2.976263 -2.627420

0.0960

Prob. 0.0138 0.0210 -0.148148 5.045590 5.937951 6.033939 7.016106 0.013795

*MacKinnon (1996) one-sided p-values.

Dependent Variable: D(A2) Method: Least Squares Date: 10/25/11 Time: 10:08 Sample (adjusted): 1983 2009

Augmented Dickey-Fuller Test Equation

Included observations: 27 after adjustments

Variable A2(-1) C

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

Null Hypothesis: A2(-1) has a unit root Exogenous: Constant

Lag Length: 0 (Automatic based on SIC, MAXLAG=6)

t-Statistic -2.962731 -3.711457 -2.981038 -2.629906

Coefficient -0.479685 6.910332

Std. Error 0.181096 2.804785

t-Statistic -2.648793 2.463765

0.219143 Mean dependent var 0.187909 S.D. dependent var 4.546889 Akaike info criterion 516.8550 Schwarz criterion -78.16234 F-statistic 1.735513 Prob(F-statistic)

（2）.A2(-1)单根检验

Prob.* 0.0519

Augmented Dickey-Fuller test statistic Test critical values:

1% level 5% level 10% level

*MacKinnon (1996) one-sided p-values.

Augmented Dickey-Fuller Test Equation

Dependent Variable: D(A2(-1)) Method: Least Squares Date: 10/25/11 Time: 10:11 Sample (adjusted): 1984 2009

Included observations: 26 after adjustments

Variable A2(-2) C

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

Null Hypothesis: A2(-2) has a unit root Exogenous: Constant

Lag Length: 0 (Automatic based on SIC, MAXLAG=5)

t-Statistic -2.862298 -3.724070 -2.986225 -2.632604

Coefficient -0.540309 8.050071

Std. Error 0.182368 2.860246

t-Statistic -2.962731 2.814468

Prob. 0.0068 0.0096 -0.019231 5.099962 5.899272 5.996049 8.777775 0.006779

0.267797 Mean dependent var 0.237288 S.D. dependent var 4.453969 Akaike info criterion 476.1083 Schwarz criterion -74.69054 F-statistic 1.776754 Prob(F-statistic)

（3）.A2(-2)单根检验（效果不好）

Prob.* 0.0642

Std. Error 0.176498 2.752981

t-Statistic -2.862298 2.839440

Prob. 0.0088 0.0093

Augmented Dickey-Fuller test statistic Test critical values:

1% level 5% level 10% level

*MacKinnon (1996) one-sided p-values.

Augmented Dickey-Fuller Test Equation Dependent Variable: D(A2(-2)) Method: Least Squares Date: 10/25/11 Time: 10:13 Sample (adjusted): 1985 2009

Included observations: 25 after adjustments

Variable A2(-3) C

Coefficient -0.505189 7.816925

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

0.262649 Mean dependent var 0.230590 S.D. dependent var 4.281757 Akaike info criterion 421.6692 Schwarz criterion -70.79028 F-statistic 1.790508 Prob(F-statistic)

0.328000 4.881386 5.823222 5.920732 8.192747 0.008809

3.A3(A2的对数化)单根检验 （1）未滞后

Null Hypothesis: A3 has a unit root Exogenous: Constant

Lag Length: 0 (Automatic based on SIC, MAXLAG=6)

t-Statistic -2.611346 -3.699871 -2.976263 -2.627420

Std. Error 0.204326 0.542896

t-Statistic -2.611346 2.555371

Prob.* 0.1031

Prob. 0.0150 0.0171 -0.020242 0.372695 0.733104 0.829092 6.819130 0.015031

Augmented Dickey-Fuller test statistic Test critical values:

1% level 5% level 10% level

*MacKinnon (1996) one-sided p-values.

Dependent Variable: D(A3) Method: Least Squares Date: 10/25/11 Time: 10:16 Sample (adjusted): 1983 2009

Augmented Dickey-Fuller Test Equation

Included observations: 27 after adjustments

Variable A3(-1) C

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

Coefficient -0.533566 1.387300

0.214309 Mean dependent var 0.182882 S.D. dependent var 0.336896 Akaike info criterion 2.837478 Schwarz criterion -7.896903 F-statistic 1.623005 Prob(F-statistic)

（2）A3(-1)单根检验

Null Hypothesis: A3(-1) has a unit root Exogenous: Constant

Lag Length: 0 (Automatic based on SIC, MAXLAG=6)

t-Statistic -3.411417 -3.711457 -2.981038 -2.629906

Prob.* 0.0198

Std. Error 0.194118 0.518899

t-Statistic -3.411417 3.384223

Prob. 0.0023 0.0025 -0.002080 0.367688 0.556109 0.652886 11.63777 0.002292

Augmented Dickey-Fuller test statistic Test critical values:

1% level 5% level 10% level

*MacKinnon (1996) one-sided p-values.

Augmented Dickey-Fuller Test Equation Dependent Variable: D(A3(-1)) Method: Least Squares Date: 10/25/11 Time: 10:17 Sample (adjusted): 1984 2009

Included observations: 26 after adjustments

Variable A3(-2) C

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

Coefficient -0.662217 1.756069

0.326557 Mean dependent var 0.298497 S.D. dependent var 0.307960 Akaike info criterion 2.276143 Schwarz criterion -5.229419 F-statistic 1.773706 Prob(F-statistic)

（二）格兰杰因果检验

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