Hansen's J statistic and GMM Model Selection

[Jenner Kerr]

Hi all,

I'm running a Panel VAR model and am having a little trouble interpreting Hansen's J stat and ultimately which model to select.

I've used the command

pvarsoc $totlist, pvaro(instl(1/5))

, where $totlist is my list of endogenous variables. I've got 4 models so have done this 4 times which has generated the 4 model selection outputs:

 pvarsoc $totlist, pvaro(instl(1/5))
Running panel VAR lag order selection on estimation sample
....

 Selection order criteria
 Sample:  2011 - 2017                              No. of obs      =      2639
                                                   No. of panels   =       377
                                                   Ave. no. of T   =     7.000

  +--------------------------------------------------------------------------+
  |   lag |    CD          J      J pvalue     MBIC       MAIC       MQIC    |
  |-------+------------------------------------------------------------------|
  |     1 | -2.596933   65.13786   .0020818  -218.4757  -6.862139  -83.47689 |
  |     2 | -5.053263   31.64495   .2454891  -181.0652  -22.35505  -79.81612 |
  |     3 | -1.246003   23.18428   .1836075  -118.6225  -12.81572  -51.12309 |
  |     4 |  .3191439   10.48746   .3124811  -60.41594  -7.512539  -26.66623 |
  +--------------------------------------------------------------------------+

My interpretation would be that the 2nd lag above would be optimal as it doesn't reject Hansen's null that overidentifying restrictions are valid, whereas the 1st lag does. Then the 2nd lag has the lowest BIC, AIC and QIC of the remaining possible specifications.

pvarsoc $domlist, pvaro(instl(1/5))
Running panel VAR lag order selection on estimation sample
....

 Selection order criteria
 Sample:  2011 - 2017                              No. of obs      =      2639
                                                   No. of panels   =       377
                                                   Ave. no. of T   =     7.000

  +--------------------------------------------------------------------------+
  |   lag |    CD          J      J pvalue     MBIC       MAIC       MQIC    |
  |-------+------------------------------------------------------------------|
  |     1 | -.0752307   105.3864   9.96e-09  -178.2272   33.38636  -43.22839 |
  |     2 | -3.862367   50.55263   .0039265  -162.1576  -3.447369  -60.90843 |
  |     3 | -.0798814   28.17421   .0594531  -113.6326  -7.825792  -46.13317 |
  |     4 |  .7180911   18.62677   .0285602  -52.27663   .6267652  -18.52692 |
  +--------------------------------------------------------------------------+

Would I have to pick the 3rd lag model here as it's the specification which doesn't reject Hansen's null at 10%, despite it having a lower J statistic and higher IC scores than the 1st and 2nd lag specifications?

pvarsoc $tralist, pvaro(instl(1/5))
Running panel VAR lag order selection on estimation sample
....

 Selection order criteria
 Sample:  2011 - 2017                              No. of obs      =      2639
                                                   No. of panels   =       377
                                                   Ave. no. of T   =     7.000

  +--------------------------------------------------------------------------+
  |   lag |    CD          J      J pvalue     MBIC       MAIC       MQIC    |
  |-------+------------------------------------------------------------------|
  |     1 | -.6489056   73.37046    .000233  -210.2431   1.370459  -75.24429 |
  |     2 | -57.66134   28.93977   .3638259  -183.7704  -25.06023   -82.5213 |
  |     3 |  -.499046     18.289   .4367726  -123.5178    -17.711  -56.01838 |
  |     4 |  .4825675   8.501449   .4845053  -62.40195  -9.498551  -28.65224 |
  +--------------------------------------------------------------------------+

Here I assume one would pick the 2nd lag specification using the same logic as for the first model?

pvarsoc $comlist, pvaro(instl(1/5))
Running panel VAR lag order selection on estimation sample
....

 Selection order criteria
 Sample:  2011 - 2017                              No. of obs      =      2639
                                                   No. of panels   =       377
                                                   Ave. no. of T   =     7.000

  +--------------------------------------------------------------------------+
  |   lag |    CD          J      J pvalue     MBIC       MAIC       MQIC    |
  |-------+------------------------------------------------------------------|
  |     1 | -4.369977   66.75003    .001379  -216.8636  -5.249975  -81.86473 |
  |     2 | -2.193906   13.62676   .9846386  -199.0834  -40.37324  -97.83431 |
  |     3 |  .1746443   14.51639   .6948614  -127.2904  -21.48361  -59.79098 |
  |     4 |  .5633934   9.842786    .363362  -61.06061  -8.157214   -27.3109 |
  +--------------------------------------------------------------------------+

Here I'd also assume we'd pick the 2nd lag specification?

[Sebastian Kripfganz]

I would agree with your choices: Select the model with the lowest (most negative) value of the model selection criteria, provided the J-test does not reject the null hypothesis.