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  • No Cointegration with Johansen but VECM shows significant coefficient.

    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
    -----------------------------------------------------------------------------------
    Oh and I ran the VECM anyway because the variables in difference have a cointegration ecuation according to stationary residuals in OLS.
    Last edited by John Riveros; 17 Dec 2018, 18:57.

  • #2
    I don't understand your last sentence (at the end of your post)
    But think of it this way: there is no cointegration between your variables. Therefore, _ce1 is I(1). If _ce1 is I(1) then your residuals must be I(1) since your dependent variable is I(0). Therefore, _ce1 combines with the residuals to give you an I(0) variable. This has to be the case, since you have an I(0) variable on the left hand side of the equation. Therefore, _ce1 is significant.

    Comment


    • #3
      Both variables are I(1), VECM doesn't show autocorrelation, also residuals are stationary. and model is stable. No inverse roots bigger than 1. The last sentence was because the first difference variables with OLS estimation had stationary residuals. I still can't figure out why VECM shows cointegration but johansen test cannot find it.

      Comment

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