一、平稳性检验
由于数据是时间序列数据,所以在进行回归前用DF检验进行数据平稳性分析:
(1)LnQ0阶差分,有趋势和截距项,滞后1阶:
ADF Test Statistic -5.917774 1% Critical Value* -5.1152
5% Critical Value -3.9271
10% Critical Value -3.4104
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LNQ)
Method: Least Squares
Date: 06/14/05 Time: 11:00
Sample(adjusted): 1993 2003
Included observations: 11 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
LNQ(-1) -1.135721 0.191917 -5.917774 0.0006
D(LNQ(-1)) 0.027173 0.148432 0.183064 0.8599
C 7.377582 1.189240 6.203610 0.0004
@TREND(1991) 0.237208 0.044022 5.388422 0.0010
R-squared 0.847226 Mean dependent var 0.259087
Adjusted R-squared 0.781752 S.D. dependent var 0.197899
S.E. of regression 0.092453 Akaike info criterion -1.648951
Sum squared resid 0.059833 Schwarz criterion -1.504262
Log likelihood 13.06923 F-statistic 12.93980
Durbin-Watson stat 1.582204 Prob(F-statistic) 0.003046
属于I0情况,LnQ在0阶差分数据平稳。
(2)LnK0阶差分,有趋势和截距项,滞后2阶:
ADF Test Statistic -37.78220 1% Critical Value* -5.2735
5% Critical Value -3.9948
10% Critical Value -3.4455
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LNK)
Method: Least Squares
Date: 06/14/05 Time: 10:57
Sample(adjusted): 1994 2003
Included observations: 10 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
LNK(-1) -0.974837 0.025802 -37.78220 0.0000
D(LNK(-1)) 0.148143 0.025604 5.786014 0.0022
D(LNK(-2)) 0.086650 0.027483 3.152841 0.0253
C 6.654460 0.146776 45.33760 0.0000
@TREND(1991) 0.186118 0.011854 15.70117 0.0000
R-squared 0.997696 Mean dependent var 0.427755
Adjusted R-squared 0.995852 S.D. dependent var 0.774116
S.E. of regression 0.049856 Akaike info criterion -2.852505
Sum squared resid 0.012428 Schwarz criterion -2.701213
Log likelihood 19.26253 F-statistic 541.2017
Durbin-Watson stat 1.372784 Prob(F-statistic) 0.000001
(3)LnL1阶差分,有趋势和截距项,滞后0阶:
ADF Test Statistic -3.608727 1% Critical Value* -5.1152
5% Critical Value -3.9271
10% Critical Value -3.4104
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LNL,2)
Method: Least Squares
Date: 06/14/05 Time: 11:04
Sample(adjusted): 1993 2003
Included observations: 11 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(LNL(-1)) -1.237619 0.342952 -3.608727 0.0069
C 0.125454 0.086826 1.444899 0.1865
@TREND(1991) -0.004840 0.010253 -0.472084 0.6495
R-squared 0.619802 Mean dependent var -0.005157
Adjusted R-squared 0.524753 S.D. dependent var 0.153768
S.E. of regression 0.106005 Akaike info criterion -1.423660
Sum squared resid 0.089896 Schwarz criterion -1.315144
Log likelihood 10.83013 F-statistic 6.520836
Durbin-Watson stat 1.905856 Prob(F-statistic) 0.020895
属于I1情况,LnL在1阶差分10%的显著水平下,数据平稳。
由此可见,数据基本满足平稳性检验,可以进行回归分析。
二、因果性检验
为了检验解释变量能否解释因变量,对数据进行因果性检验。
(1)对于LnQ和LnK的因果关系:
Pairwise Granger Causality Tests
Date: 06/14/05 Time: 11:13
Sample: 1991 2003
Lags: 1
Null Hypothesis: Obs F-Statistic Probability
LNQ does not Granger Cause LNK 12 3.82570 0.08218
LNK does not Granger Cause LNQ 1.00981 0.34120
滞后1阶的情况下,接受原假设,LnQ和LnK没有因果关系。
Pairwise Granger Causality Tests
Date: 06/14/05 Time: 11:19
Sample: 1991 2003
Lags: 2
Null Hypothesis: Obs F-Statistic Probability
LNQ does not Granger Cause LNK 11 2.63312 0.15105
LNK does not Granger Cause LNQ 3.02876 0.12322
滞后2阶的情况,仍然接受原假设,LnQ和LnK没有因果关系。
Pairwise Granger Causality Tests
Date: 06/14/05 Time: 11:20
Sample: 1991 2003
Lags: 3
Null Hypothesis: Obs F-Statistic Probability
LNQ does not Granger Cause LNK 10 166.052 0.00078
LNK does not Granger Cause LNQ 2.09081 0.28008
滞后3阶时,拒绝LnQ不是LnK原因的原假设,说明滞后3阶后,LnQ对LnK有因果关系。
(2)对于LnQ和LnL的因果关系:
Pairwise Granger Causality Tests
Date: 06/14/05 Time: 11:23
Sample: 1991 2003
Lags: 1
Null Hypothesis: Obs F-Statistic Probability
LNL does not Granger Cause LNQ 12 0.02661 0.87402
LNQ does not Granger Cause LNL 3.23015 0.10585
滞后1阶,接受原假设,LnQ和LnL没有因果关系。
Pairwise Granger Causality Tests
Date: 06/14/05 Time: 11:24
Sample: 1991 2003
Lags: 2
Null Hypothesis: Obs F-Statistic Probability
LNL does not Granger Cause LNQ 11 0.40694 0.68277
LNQ does not Granger Cause LNL 1.33668 0.33105
滞后2阶,接受原假设,LnQ和LnL没有因果关系。
Pairwise Granger Causality Tests
Date: 06/14/05 Time: 11:25
Sample: 1991 2003
Lags: 3
Null Hypothesis: Obs F-Statistic Probability
LNL does not Granger Cause LNQ 10 221.439 0.00051
LNQ does not Granger Cause LNL 2.41803 0.24367
滞后3阶,拒绝LnL不是LnQ原因的原假设,说明滞后3阶后,LnL对LnQ有因果关系。
一、数据平稳性检验
(1)对于Ln(Q/K),0阶差分,有趋势和截距项,滞后3阶:
ADF Test Statistic -5.023192 1% Critical Value* -5.4776
5% Critical Value -4.0815
10% Critical Value -3.4901
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LNQK)
Method: Least Squares
Date: 06/14/05 Time: 11:28
Sample(adjusted): 1995 2003
Included observations: 9 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
LNQK(-1) -1.748682 0.348122 -5.023192 0.0152
D(LNQK(-1)) 0.063537 0.034240 1.855617 0.1605
D(LNQK(-2)) 0.112682 0.038210 2.948987 0.0601
D(LNQK(-3)) 0.056888 0.032926 1.727777 0.1825
C -0.979065 0.246751 -3.967826 0.0286
@TREND(1991) 0.068736 0.019780 3.474944 0.0402
R-squared 0.943674 Mean dependent var 0.030342
Adjusted R-squared 0.849796 S.D. dependent var 0.137464
S.E. of regression 0.053276 Akaike info criterion -2.791956
Sum squared resid 0.008515 Schwarz criterion -2.660473
Log likelihood 18.56380 F-statistic 10.05221
Durbin-Watson stat 2.113223 Prob(F-statistic) 0.043111
属于I0情况,说明Ln(Q/K)在0阶差分下数据平稳。
(2)对于Ln(Q/L),0阶差分,有趋势和截距项,滞后3阶:
ADF Test Statistic -3.787370 1% Critical Value* -5.4776
5% Critical Value -4.0815
10% Critical Value -3.4901
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LNLK)
Method: Least Squares
Date: 06/14/05 Time: 11:31
Sample(adjusted): 1995 2003
Included observations: 9 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
LNLK(-1) -0.793023 0.209386 -3.787370 0.0323
D(LNLK(-1)) 0.150163 0.029283 5.128009 0.0144
D(LNLK(-2)) 0.030352 0.025586 1.186263 0.3209
D(LNLK(-3)) 0.106169 0.021070 5.038785 0.0151
C -2.111536 0.652111 -3.238000 0.0479
@TREND(1991) -0.115221 0.020939 -5.502707 0.0118
R-squared 0.978247 Mean dependent var -0.130081
Adjusted R-squared 0.941993 S.D. dependent var 0.150261
S.E. of regression 0.036190 Akaike info criterion -3.565363
Sum squared resid 0.003929 Schwarz criterion -3.433880
Log likelihood 22.04414 F-statistic 26.98296
Durbin-Watson stat 2.948596 Prob(F-statistic) 0.010681
属于I0情况,说明Ln(Q/L)在0阶差分下数据平稳。
二、因果性检验
Pairwise Granger Causality Tests
Date: 06/15/05 Time: 11:34
Sample: 1991 2003
Lags: 1
Null Hypothesis: Obs F-Statistic Probability
LNLK does not Granger Cause LNQK 12 0.97904 0.34829
LNQK does not Granger Cause LNLK 2.51359 0.14733
滞后1阶,接受原假设,Ln(Q/K)和Ln(L/K)没有因果关系。
Pairwise Granger Causality Tests
Date: 06/15/05 Time: 11:36
Sample: 1991 2003
Lags: 2
Null Hypothesis: Obs F-Statistic Probability
LNLK does not Granger Cause LNQK 11 0.48686 0.63688
LNQK does not Granger Cause LNLK 1.19186 0.36656
滞后2阶,接受原假设,Ln(Q/K)和Ln(L/K)没有因果关系。
Pairwise Granger Causality Tests
Date: 06/15/05 Time: 11:36
Sample: 1991 2003
Lags: 3
Null Hypothesis: Obs F-Statistic Probability
LNLK does not Granger Cause LNQK 10 4.41945 0.12685
LNQK does not Granger Cause LNLK 4.18621 0.13511
滞后3阶,接受原假设,Ln(Q/K)和Ln(L/K)没有因果关系。
三、回归分析及模型检验
再一次回归得:
Dependent Variable: LNQK
Method: Least Squares
Date: 06/13/05 Time: 20:02
Sample: 1991 2003
Included observations: 13
Variable Coefficient Std. Error t-Statistic Prob.
C 2.153551 0.198552 10.84627 0.0000
LNLK 0.617948 0.058007 10.65308 0.0000
R-squared 0.911638 Mean dependent var 0.297182
Adjusted R-squared 0.903605 S.D. dependent var 1.105228
S.E. of regression 0.343146 Akaike info criterion 0.839316
Sum squared resid 1.295241 Schwarz criterion 0.926232
Log likelihood -3.455556 F-statistic 113.4880
Durbin-Watson stat 0.922328 Prob(F-statistic) 0.000000
经过模型修正后,t值得到了明显的改善,认为已经消除了多重共线性。
再对模型进行其它计量经济学检验。
再次进行异方差性检验,进行ARCH3阶检验得:
ARCH Test:
F-statistic 10.31765 Probability 0.008774
Obs*R-squared 8.376314 Probability 0.038842
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 06/13/05 Time: 20:20
Sample(adjusted): 1994 2003
Included observations: 10 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
C 0.057603 0.031785 1.812267 0.1199
RESID^2(-1) 1.176667 0.322186 3.652142 0.0107
RESID^2(-2) -0.665301 0.414758 -1.604070 0.1598
RESID^2(-3) -0.098451 0.322977 -0.304823 0.7708
R-squared 0.837631 Mean dependent var 0.109282
Adjusted R-squared 0.756447 S.D. dependent var 0.100440
S.E. of regression 0.049568 Akaike info criterion -2.881764
Sum squared resid 0.014742 Schwarz criterion -2.760730
Log likelihood 18.40882 F-statistic 10.31765
Durbin-Watson stat 2.275949 Prob(F-statistic) 0.008774
由此得出:P值小于5%,且有一项t值检验大于2,说明有异方差。
用加权最小二乘法进行修正,生成变量W=1/resid^2,得出:
Dependent Variable: LNQK
Method: Least Squares
Date: 06/13/05 Time: 20:18
Sample: 1991 2003
Included observations: 13
Weighting series: W
Variable Coefficient Std. Error t-Statistic Prob.
C 2.214774 0.057859 38.27888 0.0000
LNLK 0.639809 0.015322 41.75700 0.0000
Weighted Statistics
R-squared 0.998770 Mean dependent var -0.096224
Adjusted R-squared 0.998658 S.D. dependent var 0.703027
S.E. of regression 0.025755 Akaike info criterion -4.339761
Sum squared resid 0.007296 Schwarz criterion -4.252846
Log likelihood 30.20845 F-statistic 8930.541
Durbin-Watson stat 1.843561 Prob(F-statistic) 0.000000
Unweighted Statistics
R-squared 0.910480 Mean dependent var 0.297182
Adjusted R-squared 0.902341 S.D. dependent var 1.105228
S.E. of regression 0.345388 Sum squared resid 1.312223
Durbin-Watson stat 0.853115
此时再次进行ARCH3阶检验:
ARCH Test:
F-statistic 0.364515 Probability 0.781479
Obs*R-squared 1.541606 Probability 0.672702
Test Equation:
Dependent Variable: STD_RESID^2
Method: Least Squares
Date: 06/13/05 Time: 20:18
Sample(adjusted): 1994 2003
Included observations: 10 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
C 0.000533 0.000386 1.382173 0.2162
STD_RESID^2(-1) 0.079135 0.376152 0.210381 0.8403
STD_RESID^2(-2) 0.198006 0.380613 0.520229 0.6215
STD_RESID^2(-3) -0.278641 0.312680 -0.891138 0.4072
R-squared 0.154161 Mean dependent var 0.000499
Adjusted R-squared -0.268759 S.D. dependent var 0.000585
S.E. of regression 0.000659 Akaike info criterion -11.52386
Sum squared resid 2.60E-06 Schwarz criterion -11.40282
Log likelihood 61.61929 F-statistic 0.364515
Durbin-Watson stat 2.294740 Prob(F-statistic) 0.781479