Hi guys!

I have a quick question regarding the CE results for VECM and performing Error Correction Equations manually (ie. reg ... ).

Running VEC on cointegrated time series USA GDP and Australia GDP.
Then running OLS Regression on Predicted Residuals of Reg USA, AUS.

Why are the red results not the same?
Why are the blue results not the same?


. vec aus usa, lag(1) rank(1)

Vector error-correction model

Sample: 1970q2 - 2000q4 Number of obs = 123
AIC = 3.162664
Log likelihood = -189.5039 HQIC = 3.209099
Det(Sigma_ml) = .0746914 SBIC = 3.276981

Equation Parms RMSE R-sq chi2 P>chi2
----------------------------------------------------------------
D_aus 2 .605562 0.4600 103.0638 0.0000
D_usa 2 .498621 0.5309 136.9459 0.0000
----------------------------------------------------------------

------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
D_aus |
_ce1 |
L1. | -.106621 .0242331 -4.40 0.000 -.1541171 -.059125
|
_cons | -.0947774 .1456994 -0.65 0.515 -.380343 .1907882
-------------+----------------------------------------------------------------
D_usa |
_ce1 |
L1. | -.0616202 .0199536 -3.09 0.002 -.1007285 -.0225119
|
_cons | .1639928 .1199691 1.37 0.172 -.0711424 .399128
------------------------------------------------------------------------------

Cointegrating equations

Equation Parms chi2 P>chi2
-------------------------------------------
_ce1 1 1566.539 0.0000
-------------------------------------------

Identification: beta is exactly identified

Johansen normalization restriction imposed
------------------------------------------------------------------------------
beta | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_ce1 |
aus | 1 . . . . .
usa | -1.111995 .0280952 -39.58 0.000 -1.167061 -1.056929
_cons | 2.538856 . . . . .
------------------------------------------------------------------------------

. reg aus usa

Source | SS df MS Number of obs = 124
-------------+---------------------------------- F(1, 122) = 26925.45
Model | 38151.1204 1 38151.1204 Prob > F = 0.0000
Residual | 172.863839 122 1.41691672 R-squared = 0.9955
-------------+---------------------------------- Adj R-squared = 0.9955
Total | 38323.9843 123 311.577108 Root MSE = 1.1903

------------------------------------------------------------------------------
aus | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
usa | 1.000993 .0061003 164.09 0.000 .9889166 1.013069
_cons | -1.072372 .4032246 -2.66 0.009 -1.870596 -.274149
------------------------------------------------------------------------------

. predict e_hat, resid

. reg D.aus L.e_hat, r

Linear regression Number of obs = 123
F(1, 121) = 9.12
Prob > F = 0.0031
R-squared = 0.0645
Root MSE = .63081

------------------------------------------------------------------------------
| Robust
D.aus | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
e_hat |
L1. | -.1386206 .0459061 -3.02 0.003 -.2295038 -.0477374
|
_cons | .499631 .0568723 8.79 0.000 .3870372 .6122248
------------------------------------------------------------------------------

. reg D.usa L.e_hat, r

Linear regression Number of obs = 123
F(1, 121) = 0.00
Prob > F = 0.9914
R-squared = 0.0000
Root MSE = .5179

------------------------------------------------------------------------------
| Robust
D.usa | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
e_hat |
L1. | .0004075 .0376054 0.01 0.991 -.0740422 .0748572
|
_cons | .5074786 .0466928 10.87 0.000 .4150379 .5999194
------------------------------------------------------------------------------

They should be the same and I am not sure whether it is some trend or constraint option that VEC introduces in the command but any comments on this would be greatly appreciated!!

Thanks

Sam