Greetings Stata Users.

I have one simple question. It exist cointegration betwen variables when the VECM model displays a significant long run coefficient, but Johansen Test showed 0 ecuations of cointegration?.

This is Johansen output test with ideal lags (3) from varsoc command:

Code:
vecrank log_pib_real log_gasto_publico, trend(rconstant) lag(3)

                       Johansen tests for cointegration                        
Trend: rconstant                                        Number of obs =      62
Sample:  1953 - 2014                                             Lags =       3
-------------------------------------------------------------------------------
                                                         5%
maximum                                      trace    critical
  rank    parms       LL       eigenvalue  statistic    value
    0      8       223.27711           .     15.0767*   19.96
    1      12      228.95815     0.16745      3.7146     9.42
    2      14      230.81546     0.05815
-------------------------------------------------------------------------------

I've used the ideal lag from varsoc command (which is 3) and i estimated anyway the VECM model since variables are I(1). But i thought VECM would confirm Johansen test... however it didn't happen. Here it is the VECM out put model.

Code:
vec log_pib_real log_gasto_publico, trend(rconstant) lag(3)

Vector error-correction model

Sample:  1953 - 2014                            Number of obs     =         62
                                                AIC               =   -6.99865
Log likelihood =  228.9581                      HQIC              =  -6.837005
Det(Sigma_ml)  =  2.13e-06                      SBIC              =  -6.586946

Equation           Parms      RMSE     R-sq      chi2     P>chi2
----------------------------------------------------------------
D_log_pib_real        5     .027681   0.7742   191.9551   0.0000
D_log_gasto_pu~o      5     .062084   0.5260   62.14303   0.0000
----------------------------------------------------------------

-------------------------------------------------------------------------------------
                    |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------------+----------------------------------------------------------------
D_log_pib_real      |
               _ce1 |
                L1. |  -.0761765   .0253495    -3.01   0.003    -.1258605   -.0264925
                    |
       log_pib_real |
                LD. |   .4663022   .1264797     3.69   0.000     .2184064    .7141979
               L2D. |   .1955121   .1214004     1.61   0.107    -.0424284    .4334525
                    |
  log_gasto_publico |
                LD. |   .1191235   .0638254     1.87   0.062    -.0059721     .244219
               L2D. |  -.1618306   .0646488    -2.50   0.012      -.28854   -.0351212
--------------------+----------------------------------------------------------------
D_log_gasto_publico |
               _ce1 |
                L1. |   .0125409   .0568538     0.22   0.825    -.0988906    .1239724
                    |
       log_pib_real |
                LD. |    .603882   .2836692     2.13   0.033     .0479006    1.159863
               L2D. |    .218229   .2722772     0.80   0.423    -.3154246    .7518826
                    |
  log_gasto_publico |
                LD. |    .202472   .1431479     1.41   0.157    -.0780928    .4830367
               L2D. |   .0906771   .1449946     0.63   0.532    -.1935072    .3748614
-------------------------------------------------------------------------------------

Cointegrating equations

Equation           Parms    chi2     P>chi2
-------------------------------------------
_ce1                  1   278.1473   0.0000
-------------------------------------------

Identification:  beta is exactly identified

                 Johansen normalization restriction imposed
-----------------------------------------------------------------------------------
             beta |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
_ce1              |
     log_pib_real |          1          .        .       .            .           .
log_gasto_publico |  -.7668141   .0459783   -16.68   0.000    -.8569299   -.6766983
            _cons |  -4.778057   .4516397   -10.58   0.000    -5.663255    -3.89286
-----------------------------------------------------------------------------------