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st: VECM model using vec command


From   Talal <talalesm@yahoo.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: VECM model using vec command
Date   Sat, 25 Sep 2010 17:17:00 -0700 (PDT)

Hi all

For whom using vec model regularily


1. I am trying to estimate a VECM model for demand (ln_qt) as dependent variable; and (ln_VKM , lnincome , Lnf ] as three independent variables.

2- After testing the number of cointegrating relation using "vecrank" 
the results shows that I have multiple cointegrating vectors (2).

3.  the number of lags decided using VAR and lag length criteria before doing the cointegration test for my VECM model (Lag no.=3)

4- based on above 

I belive my VECM model specification should be:

Δyt = λ1 + λ2 Δxt − γ1 (yt−1 − xt−1) + γ2 (yt−1 − xt−1)+ πxt−1 + ηt 

where y is the dependent variable and  X is a vector of Independent variables 



I have used a "vec" comand as follws:

vec ln_qt ln_VKM  lnincome  Lnf , lag(3) rank (2)





My question are:

A- did I specified the VECM equation and vec command correctl?

B- the vec outputs is very confusing (it seems specified 4 models where each variable i have used was specified as dependend variable in one of the four models).

I am only intersted to estimate a demand (ln_qt) model. 

Also the outputs in STATA are not well organised and I find it dificult to
interpret th paramaters. Any help in the interpretation will be appreciated.

Rgards
Talal

Vector error-correction model

Sample:  1983 - 2008                               No. of obs      =        26
                                                   AIC             = -18.18355
Log likelihood =  284.3861                         HQIC            = -17.51471
Det(Sigma_ml)  =  3.71e-15                         SBIC            = -15.86091

Equation           Parms      RMSE     R-sq      chi2     P>chi2
----------------------------------------------------------------
D_ln_qt              11     .031182   0.6703   28.46039   0.0028
D_lnvkm              11     .020371   0.7712   47.19024   0.0000
D_lnincome           11     .011182   0.9033   130.7283   0.0000
D_lnf                11     .039259   0.7739   47.90836   0.0000
----------------------------------------------------------------

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
D_ln_qt      |
        _ce1 |
         L1. |   .2503267   .7070148     0.35   0.723    -1.135397     1.63605
             |
        _ce2 |
         L1. |  -.0519306   .2854071    -0.18   0.856    -.6113183     .507457
             |
       ln_qt |
         LD. |  -.3892408   .5782202    -0.67   0.501    -1.522532      .74405
        L2D. |   -.210528   .3547468    -0.59   0.553    -.9058189     .484763
             |
       lnvkm |
         LD. |   .0952668   .3173674     0.30   0.764     -.526762    .7172955
        L2D. |  -.1789577   .3448023    -0.52   0.604    -.8547577    .4968424
             |
    lnincome |
         LD. |    1.39124   .6996217     1.99   0.047     .0200066    2.762473
        L2D. |   .0910786   1.043868     0.09   0.930    -1.954865    2.137022
             |
         lnf |
         LD. |  -.4656339   .4380534    -1.06   0.288    -1.324203    .3929351
        L2D. |  -.1438649   .2447154    -0.59   0.557    -.6234983    .3357685
             |
       _cons |   .0007162   .0172881     0.04   0.967    -.0331677    .0346002
-------------+----------------------------------------------------------------
D_lnvkm      |
        _ce1 |
         L1. |  -1.285009   .4618835    -2.78   0.005    -2.190284   -.3797342
             |
        _ce2 |
         L1. |  -.5471533   .1864527    -2.93   0.003    -.9125939   -.1817128
             |
       ln_qt |
         LD. |   .1844832   .3777436     0.49   0.625    -.5558807    .9248472
        L2D. |   .3597803   .2317514     1.55   0.121    -.0944441    .8140047
             |
       lnvkm |
         LD. |   .5725982    .207332     2.76   0.006      .166235    .9789614
        L2D. |   .2093582   .2252548     0.93   0.353    -.2321331    .6508495
             |
    lnincome |
         LD. |   .9908236   .4570537     2.17   0.030     .0950149    1.886632
        L2D. |   .0802654    .681945     0.12   0.906    -1.256322    1.416853
             |
         lnf |
         LD. |   .4226623   .2861745     1.48   0.140    -.1382295    .9835541
        L2D. |   .2055419   .1598694     1.29   0.199    -.1077963    .5188801
             |
       _cons |  -.0008924   .0112941    -0.08   0.937    -.0230283    .0212436
-------------+----------------------------------------------------------------
D_lnincome   |
        _ce1 |
         L1. |  -.2725985   .2535389    -1.08   0.282    -.7695257    .2243286
             |
        _ce2 |
         L1. |  -.0681478   .1023484    -0.67   0.506    -.2687469    .1324513
             |
       ln_qt |
         LD. |   .2758531   .2073526     1.33   0.183    -.1305504    .6822567
        L2D. |  -.1959344   .1272139    -1.54   0.124    -.4452691    .0534003
             |
       lnvkm |
         LD. |   .0957609   .1138095     0.84   0.400    -.1273016    .3188234
        L2D. |   .0480082   .1236478     0.39   0.698     -.194337    .2903534
             |
    lnincome |
         LD. |   .0166749   .2508877     0.07   0.947    -.4750561    .5084058
        L2D. |  -.0643503    .374336    -0.17   0.864    -.7980354    .6693348
             |
         lnf |
         LD. |   .1221691   .1570881     0.78   0.437    -.1857179    .4300561
        L2D. |  -.0698057   .0877561    -0.80   0.426    -.2418046    .1021932
             |
       _cons |   .0096477   .0061996     1.56   0.120    -.0025032    .0217987
-------------+----------------------------------------------------------------
D_lnf        |
        _ce1 |
         L1. |  -1.398677   .8901514    -1.57   0.116    -3.143341     .345988
             |
        _ce2 |
         L1. |  -.2213953   .3593355    -0.62   0.538      -.92568    .4828894
             |
       ln_qt |
         LD. |   .5618666   .7279954     0.77   0.440    -.8649782    1.988711
        L2D. |   .6363211   .4466361     1.42   0.154    -.2390697    1.511712
             |
       lnvkm |
         LD. |   .0969903   .3995745     0.24   0.808    -.6861613    .8801418
        L2D. |  -.2930602   .4341157    -0.68   0.500    -1.143911     .557791
             |
    lnincome |
         LD. |  -2.956396   .8808433    -3.36   0.001    -4.682817   -1.229975
        L2D. |  -1.461442   1.314259    -1.11   0.266    -4.037342    1.114458
             |
         lnf |
         LD. |    .813693   .5515215     1.48   0.140    -.2672694    1.894655
        L2D. |    .426378   .3081035     1.38   0.166    -.1774939     1.03025
             |
       _cons |  -.0009323   .0217661    -0.04   0.966    -.0435931    .0417286
------------------------------------------------------------------------------

Cointegrating equations

Equation           Parms    chi2     P>chi2
-------------------------------------------
_ce1                  2   414.1233   0.0000
_ce2                  2   21.02513   0.0000
-------------------------------------------

Identification:  beta is exactly identified

                 Johansen normalization restrictions imposed
------------------------------------------------------------------------------
        beta |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
_ce1         |
       ln_qt |          1          .        .       .            .           .
       lnvkm |   5.55e-17          .        .       .            .           .
    lnincome |  -.8126088   .2787991    -2.91   0.004    -1.359045   -.2661725
         lnf |   2.232979   .3353644     6.66   0.000     1.575677    2.890281
       _cons |   4.198856          .        .       .            .           .
-------------+----------------------------------------------------------------
_ce2         |
       ln_qt |  (omitted)
       lnvkm |          1          .        .       .            .           .
    lnincome |   3.087591   .7286725     4.24   0.000     1.659419    4.515763
         lnf |  -3.936948    .876512    -4.49   0.000     -5.65488   -2.219016
       _cons |  -35.40865          .        .       .            .           .
------------------------------------------------------------------------------




      

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