而β矩阵的估计为：
------------------------------------------------------------------------------
beta | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- _ce1 |
y | 1 . . . . . x | -.764085 .0261479 -29.22 0.000 -.8153339 -.7128362 _cons | 146.9988 . . . . . ------------------------------------------------------------------------------ 即146.9988+y-0.764085 x=0
而αβ’即为π，即α’=（0.0418615 0.0256414），β’=（1 -0.764085）， π的第一行即为第一个方程中的π的估计值（0.0418615 -0.0319857） 其中，0.0418615*（-0.764085）= -0.0319857
π的第二行即为第二个方程中的π的估计值（0.0256414 -0.0195922） ------------------------------------------------------------------------------
Pi | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- D_y | y |
L1. | .0418615 .0069215 6.05 0.000 .0282956 .0554273 x |
L1. | -.0319857 .0052886 -6.05 0.000 -.0423512 -.0216203 -------------+---------------------------------------------------------------- D_x | y |
L1. | .0256414 .0094143 2.72 0.006 .0071897 .044093 x |
L1. | -.0195922 .0071933 -2.72 0.006 -.0336908 -.0054935
此时虽然β矩阵的估计中有截距项，但在π的显示结果中没有截距项，此时截距项被放在误差修正模型中了。
如果用t(rc)命令，则截距项出现在π中，而误差修正模型中没有截距项。 vec y x, t(rc) pi al
Vector error-correction model
Sample: 3 - 204 No. of obs = 202 AIC = 18.30856 Log likelihood = -1841.164 HQIC = 18.36157 Det(Sigma_ml) = 283111.1 SBIC = 18.43958
Equation Parms RMSE R-sq chi2 P>chi2 ----------------------------------------------------------------
D_y 3 20.9329 0.6666 395.9259 0.0000 D_x 3 28.5972 0.5280 221.5231 0.0000 ----------------------------------------------------------------
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- D_y | _ce1 |
L1. | .041464 .0045894 9.03 0.000 .0324688 .0504591 y |
LD. | .1128688 .0801805 1.41 0.159 -.044282 .2700196 x |
LD. | .0765203 .054746 1.40 0.162 -.0307799 .1838205 -------------+---------------------------------------------------------------- D_x | _ce1 |
L1. | .0386104 .0062698 6.16 0.000 .0263218 .050899 y |
LD. | .4012721 .1095377 3.66 0.000 .1865822 .6159621 x |
LD. | -.1705861 .0747907 -2.28 0.023 -.3171732 -.0239991 ------------------------------------------------------------------------------
Cointegrating equations
Equation Parms chi2 P>chi2 -------------------------------------------
_ce1 1 924.1123 0.0000 -------------------------------------------
Identification: beta is exactly identified
Johansen normalization restriction imposed ------------------------------------------------------------------------------
beta | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- _ce1 |
y | 1 . . . . . x | -.773902 .025458 -30.40 0.000 -.8237986 -.7240053 _cons | 105.6838 81.37255 1.30 0.194 -53.8035 265.171 ------------------------------------------------------------------------------
Adjustment parameters
Equation Parms chi2 P>chi2 -------------------------------------------
D_y 1 81.62498 0.0000 D_x 1 37.92271 0.0000
------------------------------------------------------------------------------
alpha | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- D_y | _ce1 |
L1. | .041464 .0045894 9.03 0.000 .0324688 .0504591 -------------+---------------------------------------------------------------- D_x | _ce1 |
L1. | .0386104 .0062698 6.16 0.000 .0263218 .050899 ------------------------------------------------------------------------------
Impact parameters
Equation Parms chi2 P>chi2 -------------------------------------------
D_y 1 81.62498 0.0000 D_x 1 37.92271 0.0000 -------------------------------------------
------------------------------------------------------------------------------
Pi | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- D_y | y |
L1. | .041464 .0045894 9.03 0.000 .0324688 .0504591 x |
L1. | -.032089 .0035518 -9.03 0.000 -.0390504 -.0251277 _cons | 4.382067 .4850288 9.03 0.000 3.431428 5.332706
-------------+---------------------------------------------------------------- D_x | y |
L1. | .0386104 .0062698 6.16 0.000 .0263218 .050899 x |
L1. | -.0298806 .0048522 -6.16 0.000 -.0393908 -.0203705 _cons | 4.080489 .6626169 6.16 0.000 2.781784 5.379194 ------------------------------------------------------------------------------
此时在π的矩阵估计中，有截距项，但是在误差修正模型中没有截距项。
如果用t(rt)命令，在协整向量β中有趋势项的估计（即对时间t的系数的估计），而在整个误差修正模型中没有趋势项，但是有截距项的估计。在π的估计中，只有趋势项，没有截距项，因为截距项的估计已经包含在误差修正模型中了。 vec y x, t(rt) pi al
Vector error-correction model
Sample: 3 - 204 No. of obs = 202 AIC = 18.2926 Log likelihood = -1837.553 HQIC = 18.35887 Det(Sigma_ml) = 273167.6 SBIC = 18.45638
Equation Parms RMSE R-sq chi2 P>chi2 ----------------------------------------------------------------
D_y 4 20.8735 0.6702 400.296 0.0000 D_x 4 28.0435 0.5484 239.2424 0.0000 ----------------------------------------------------------------
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- D_y | _ce1 |
L1. | .0769485 .01239 6.21 0.000 .0526645 .1012325 y |
LD. | .0861433 .0819685 1.05 0.293 -.0745121 .2467986 x |
LD. | .0989288 .0554018 1.79 0.074 -.0096569 .2075144 _cons | -2.443936 3.5442 -0.69 0.490 -9.390441 4.502569 -------------+---------------------------------------------------------------- D_x | _ce1 |
L1. | .0632409 .016646 3.80 0.000 .0306153 .0958664 y |
LD. | .3552693 .1101247 3.23 0.001 .1394288 .5711098 x |
LD. | -.1724981 .0744324 -2.32 0.020 -.3183828 -.0266133 _cons | 2.973666 4.761634 0.62 0.532 -6.358965 12.3063 ------------------------------------------------------------------------------
Cointegrating equations
Equation Parms chi2 P>chi2 -------------------------------------------
_ce1 1 143.3685 0.0000 -------------------------------------------