Hansen test of over identifying restrictions problem

[Labib Choudhry]

Hello all,

I am using the system gmm estimator / xtabond2 command:

 xtabond2 d.ly l.ly lpop lk m ic ec coc ge ps cocinter geinter psinter i.year, gmm (m l.ly cocinter geinter psinter, lag (2 3) collapse) iv(lpop lk ic ec coc ge ps) iv(i.year, eq(level)) small twostep cluster(country_id) artests(3)

Where cocinter, geinter and psinter are all interaction terms of the form (c.m#c.coc).

After running the code my output is:

 Favoring speed over space. To switch, type or click on mata: mata set matafavor space, perm.
Warning: Two-step estimated covariance matrix of moments is singular.
  Using a generalized inverse to calculate optimal weighting matrix for two-step estimation.
  Difference-in-Sargan/Hansen statistics may be negative.

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: country_id                      Number of obs      =      1666
Time variable : year                            Number of groups   =       131
Number of instruments = 37                      Obs per group: min =         9
F(28, 130)    =    192.86                                      avg =     12.72
Prob > F      =     0.000                                      max =        15
                             (Std. Err. adjusted for clustering on country_id)
------------------------------------------------------------------------------
             |              Corrected
        D.ly |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          ly |
         L1. |  -1.147309    .046074   -24.90   0.000    -1.238461   -1.056157
             |
        lpop |  -.1852715   .0713066    -2.60   0.010    -.3263431   -.0441999
          lk |  -.0194833     .11117    -0.18   0.861    -.2394199    .2004533
           m |   .7779683   .1944361     4.00   0.000     .3932997    1.162637
          ic |  -.1029847   .0334933    -3.07   0.003    -.1692472   -.0367223
          ec |  -.0391848   .0491677    -0.80   0.427    -.1364571    .0580876
         coc |  -1.051792   .4942712    -2.13   0.035    -2.029649   -.0739356
          ge |   1.468222   .4284199     3.43   0.001      .620644    2.315799
          ps |   .8128296   .3973314     2.05   0.043     .0267569    1.598902
    cocinter |   .3480291   .2157807     1.61   0.109    -.0788671    .7749253
     geinter |  -.2542672   .2046206    -1.24   0.216    -.6590846    .1505503
     psinter |  -.2713972   .1339949    -2.03   0.045    -.5364901   -.0063044
             |
        year |
       1999  |          0  (empty)
       2000  |  -.0471537   .1624147    -0.29   0.772    -.3684718    .2741644
       2001  |  -.0264524    .152251    -0.17   0.862    -.3276628     .274758
       2002  |  -.0593186   .1635109    -0.36   0.717    -.3828054    .2641682
       2003  |  -.1311803   .1565015    -0.84   0.403    -.4407998    .1784391
       2004  |  -.0304291   .1639134    -0.19   0.853    -.3547122     .293854
       2005  |  -.1496382   .1663039    -0.90   0.370    -.4786506    .1793741
       2006  |  -.1541005   .1759981    -0.88   0.383    -.5022917    .1940907
       2007  |  -.0991207   .1839558    -0.54   0.591    -.4630553     .264814
       2008  |  -.0818435   .1366794    -0.60   0.550    -.3522474    .1885604
       2009  |  -.1026197   .1459502    -0.70   0.483    -.3913647    .1861253
       2010  |          0  (omitted)
       2011  |  -.1124625   .1576818    -0.71   0.477    -.4244172    .1994921
       2012  |  -.1500997   .1730024    -0.87   0.387    -.4923642    .1921649
       2013  |  -.0168417   .1658905    -0.10   0.919    -.3450363    .3113529
       2014  |  -.1325509   .1610889    -0.82   0.412    -.4512461    .1861442
             |
       _cons |   7.170602   .8361954     8.58   0.000      5.51629    8.824915
------------------------------------------------------------------------------
Instruments for first differences equation
  Standard
    D.(lpop lk ic ec coc ge ps)
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(2/3).(m L.ly cocinter geinter psinter) collapsed
Instruments for levels equation
  Standard
    1999b.year 2000.year 2001.year 2002.year 2003.year 2004.year 2005.year
    2006.year 2007.year 2008.year 2009.year 2010.year 2011.year 2012.year
    2013.year 2014.year
    lpop lk ic ec coc ge ps
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL.(m L.ly cocinter geinter psinter) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -5.88  Pr > z =  0.000
Arellano-Bond test for AR(2) in first differences: z =  -1.00  Pr > z =  0.316
Arellano-Bond test for AR(3) in first differences: z =  -1.03  Pr > z =  0.302
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(8)    =  33.78  Prob > chi2 =  0.000
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(8)    =  39.23  Prob > chi2 =  0.000
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(3)    =  28.27  Prob > chi2 =  0.000
    Difference (null H = exogenous): chi2(5)    =  10.96  Prob > chi2 =  0.052
  iv(lpop lk ic ec coc ge ps)
    Hansen test excluding group:     chi2(1)    =   8.55  Prob > chi2 =  0.003
    Difference (null H = exogenous): chi2(7)    =  30.68  Prob > chi2 =  0.000

I have tried reducing the number of lags, from (2 3) to (1 1), and also adding more lags of the dependent variable to the model. However the Hansen test of overid. restrictions is still significant, why could this be?

[Sebastian Kripfganz]

First of all, notice that xtabond2 has a severe bug when you specify time dummies with Stata's factor variable notation. It computes the degrees of freedom and hence the p-value for the Hansen test incorrectly. In your case, the degrees of freedom should be 10 instead of 8. See my comment in a previous Statalist topic: xtabond2

Second, I do not recommend to use the iv() option without explicitly specifying the equation as a suboption. See my comments in another Statalist topic: xtabond2 ivstyle vs compound ivstyle

Third, it might be that some of your variables that you have put in the iv() option do not satisfy the strong exogeneity requirements. This could be a reason why the Hansen test rejects the null hypothesis of correct model specification (even if you correct for the above-mentioned bug).

[Tobias Wendler]

Hey,

I am wondering about the notes on the output of the Sargan/Hansen Test. I thought that both have as null hypothesis that the instruments are exogenous.
Why does although the p-value is below 0.05 the Hansen test state "Robust...").

I have the same output where although my p-value of the Sargan is 0.084, STATA states "Not robust..." which seems wrong to me.

Am I overlooking something ?

Thanks and best wioshes
Tobi

[Sebastian Kripfganz]

In this context, "robust" means robust to nonstandard error-covariance structures (such as a robust variance-covariance matrix in the conventional sense). This note is displayed irrespective of the obtained p-value.

[Tobias Wendler]

Great, thank you so much for this information.