如何看NJohansen检验的结果表明三个变量之间存在一个协整关系得到的协整方程？

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收藏 2015-04-18

Date: 04/18/15 Time: 13:03
Sample (adjusted): 1982 2014
Included observations: 33 after adjustments
Trend assumption: Linear deterministic trend
Series: LGINI LGDP LM2_GDP
Lags interval (in first differences): 1 to 1

Unrestricted Cointegration Rank Test (Trace)

Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**

None *    0.525708    50.43720    29.79707    0.0001
At most 1 *    0.418877    25.82143    15.49471    0.0010
At most 2 *    0.213116    7.909260    3.841466    0.0049

Trace test indicates 3 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values

Unrestricted Cointegration Rank Test (Maximum Eigenvalue)

Hypothesized Max-Eigen 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**

None *    0.525708    24.61577    21.13162    0.0155
At most 1 *    0.418877    17.91217    14.26460    0.0127
At most 2 *    0.213116    7.909260    3.841466    0.0049

Max-eigenvalue test indicates 3 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values

Unrestricted Cointegrating Coefficients (normalized by b'*S11*b=I):

LGINI LGDP LM2_GDP
-8.507695    2.553396    6.253475
4.441308 -1.441260 -5.497460
-10.40806 -1.598748 -0.606222

Unrestricted Adjustment Coefficients (alpha):

D(LGINI)    0.019976    0.004535    0.014972
D(LGDP) -0.033448    0.019273    0.007184
D(LM2_GDP) -0.023112    0.056714 -0.007829

1 Cointegrating Equation(s): Log likelihood    160.1074

Normalized cointegrating coefficients (standard error in parentheses)
LGINI LGDP LM2_GDP
1.000000 -0.300128 -0.735038
   (0.06835)    (0.14047)

Adjustment coefficients (standard error in parentheses)
D(LGINI) -0.169950
   (0.06145)
D(LGDP)    0.284565
   (0.07435)
D(LM2_GDP)    0.196627
   (0.14778)

2 Cointegrating Equation(s): Log likelihood    169.0635

Normalized cointegrating coefficients (standard error in parentheses)
LGINI LGDP LM2_GDP
1.000000    0.000000    5.453005
   (1.21333)
0.000000    1.000000    20.61802
   (3.99220)

Adjustment coefficients (standard error in parentheses)
D(LGINI) -0.149810    0.044471
   (0.06883)    (0.02103)
D(LGDP)    0.370164 -0.113184
   (0.07624)    (0.02329)
D(LM2_GDP)    0.448513 -0.140753
   (0.13119)    (0.04008)