Hi Statalisters,


I'm running a VECM on data coming from a dataset with 87 obs regarding two variables over some years observed on a unique statistical unit (quarterly data). More specifically the variables being used are variable1 and variable2. Now, running the code to fit the VECM I get this:

Code:
vec variable1 variable2, lag(1) trend(rt)

Vector error-correction model

Sample:  1998q2 - 2019q3                        Number of obs     =         86
                                                AIC               =   2.098512
Log likelihood = -84.23601                      HQIC              =   2.167425
Det(Sigma_ml)  =  .0243122                      SBIC              =   2.269745

Equation           Parms      RMSE     R-sq      chi2     P>chi2
----------------------------------------------------------------
D_variable1           2      .46599   0.1386   13.35213   0.0013
D_variable2           2      .37733   0.2107   22.15087   0.0000
----------------------------------------------------------------

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
D_variable1  |
        _ce1 |
         L1. |  -.1296324   .0584052    -2.22   0.026    -.2441045   -.0151603
             |
       _cons |   .1331069   .0509223     2.61   0.009      .033301    .2329129
-------------+----------------------------------------------------------------
D_variable2  |
        _ce1 |
         L1. |  -.2118148   .0472929    -4.48   0.000    -.3045071   -.1191224
             |
       _cons |  -.0814626   .0412337    -1.98   0.048    -.1622792   -.0006459
------------------------------------------------------------------------------

Cointegrating equations

Equation           Parms    chi2     P>chi2
-------------------------------------------
_ce1                  1   9.250962   0.0024
-------------------------------------------

Identification:  beta is exactly identified

                 Johansen normalization restriction imposed
------------------------------------------------------------------------------
        beta |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
_ce1         |
   variable1 |          1          .        .       .            .           .
   variable2 |    .261243   .0858917     3.04   0.002     .0928984    .4295877
      _trend |  -.1412712    .007956   -17.76   0.000    -.1568647   -.1256777
       _cons |  -48.29221          .        .       .            .           .
------------------------------------------------------------------------------
According to these results all works fine. Now it does not seem unreasonable that there could be some endogeneity bias. In fact, it is not straighforward that the cointegrated vector is explaining adjustments of variable1 to variable2. Due to this, I proceed to impose restrictions on adjustment coefficients (alpha). Before doing this I run the following code to see better alpha coefficients:

Code:
vec, alpha nobtable noetable
Vector error-correction model

Sample:  1998q2 - 2019q3                        Number of obs     =         86
                                                AIC               =   2.098512
Log likelihood = -84.23601                      HQIC              =   2.167425
Det(Sigma_ml)  =  .0243122                      SBIC              =   2.269745

Adjustment parameters

Equation           Parms    chi2     P>chi2
-------------------------------------------
D_variable1           1   4.926337   0.0265
D_variable2           1   20.05953   0.0000
-------------------------------------------
------------------------------------------------------------------------------
       alpha |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
D_variable1  |
        _ce1 |
         L1. |  -.1296324   .0584052    -2.22   0.026    -.2441045   -.0151603
-------------+----------------------------------------------------------------
D_variable2  |
        _ce1 |
         L1. |  -.2118148   .0472929    -4.48   0.000    -.3045071   -.1191224
------------------------------------------------------------------------------
The first restriction I test would be alpha=(alpha1, 0) and the second restriction would be alpha=(0,alpha2). The first restriction would imply that variable2 does not error-correct whereas variable1 does. Viceversa in the second restriction (variable1 does error-correct and variable2 does not). I want to test these restrictions for my VECM using likelihood ratio tests. Now, I put the first restriction and I get this error:

Code:
constraint define 1 [D_variable2]L1._ce1=0

. vec variable1 variable2, lag(1) trend(rt) aconstraint(1)

Iteration 1:     log likelihood = -88.811238
Iteration 2:     log likelihood = -88.810546
Iteration 3:     log likelihood = -88.81052
Iteration 4:     log likelihood = -88.810519
Iteration 5:     log likelihood = -88.810518
Iteration 6:     log likelihood = -88.810518
Iteration 7:     log likelihood = -88.810518
Iteration 8:     log likelihood = -88.810518
Iteration 9:     log likelihood = -88.810518
Iteration 10:    log likelihood = -88.810518

lags() invalid -- invalid numlist has elements outside of allowed range
r(125);
Why do I get this error? Are the commands correctly specified?


Many thanks for your helpful suggestions in advance.


Best.


Francesco