Difference-in-Hansen tests of exogeneity missing

[Drishta Tengur]

Hello, I have a dynamic panel data of 26 countries and 21 years. I am estimating my regression equation using the system-GMM command, however the Difference-in-Hansen tests of exogeneity of instrument subsets are missing. Can somebody please point out what is wrong with my command?

xtabond2 PATR1 l.PATR1 electpredright electpredleft electendright electendleft pit cor
> porate govtexp inflation gdp gdpgrowth unemployment dependencyold dependencyyoung popb
> elow14 pop65andabove, gmm(PATR1 pit corporate govtexp inflation gdp gdpgrowth unemploy
> ment, lag(2 2) collapse eq(diff)) iv(electpredright electpredleft electendright electe
> ndleft dependencyold dependencyyoung popbelow14 pop65andabove, eq(diff)) gmm(PATR1 pit
>  corporate govtexp inflation gdp gdpgrowth unemployment, lag(1 1) collapse eq(level)) 
> twostep robust
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, p
> erm.

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: country                         Number of obs      =       494
Time variable : year                            Number of groups   =        26
Number of instruments = 25                      Obs per group: min =        19
Wald chi2(16) =    871.47                                      avg =     19.00
Prob > chi2   =     0.000                                      max =        19
---------------------------------------------------------------------------------
                |              Corrected
          PATR1 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
          PATR1 |
            L1. |   .9698838    .142762     6.79   0.000     .6900754    1.249692
                |
 electpredright |  -.0105237   .0070724    -1.49   0.137    -.0243854    .0033379
  electpredleft |  -.0055908   .0028285    -1.98   0.048    -.0111346    -.000047
  electendright |   .0006971    .004853     0.14   0.886    -.0088145    .0102088
   electendleft |   .0014974   .0043417     0.34   0.730    -.0070121    .0100069
            pit |   .0553782   .2076029     0.27   0.790     -.351516    .4622724
      corporate |  -.0434264    .072638    -0.60   0.550    -.1857942    .0989415
        govtexp |  -.0301283    .125029    -0.24   0.810    -.2751806     .214924
      inflation |  -.0021349    .003167    -0.67   0.500    -.0083422    .0040724
            gdp |  -1.13e-15   4.08e-15    -0.28   0.781    -9.14e-15    6.87e-15
      gdpgrowth |  -.0063547   .0818767    -0.08   0.938    -.1668301    .1541207
   unemployment |   .0572732   .0772129     0.74   0.458    -.0940613    .2086077
  dependencyold |   .0882096   1.569993     0.06   0.955     -2.98892    3.165339
dependencyyoung |   2.169483   2.930996     0.74   0.459    -3.575164     7.91413
     popbelow14 |  -3.731681   5.153118    -0.72   0.469    -13.83161    6.368244
  pop65andabove |  -.9278412   2.825606    -0.33   0.743    -6.465927    4.610244
          _cons |   .2337575   .3122037     0.75   0.454    -.3781504    .8456655
---------------------------------------------------------------------------------
Instruments for first differences equation
  Standard
    D.(electpredright electpredleft electendright electendleft dependencyold
    dependencyyoung popbelow14 pop65andabove)
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L2.(PATR1 pit corporate govtexp inflation gdp gdpgrowth unemployment)
    collapsed
Instruments for levels equation
  Standard
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL.(PATR1 pit corporate govtexp inflation gdp gdpgrowth unemployment)
    collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -2.43  Pr > z =  0.015
Arellano-Bond test for AR(2) in first differences: z =   0.83  Pr > z =  0.407
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(8)    =  13.14  Prob > chi2 =  0.107
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(8)    =   9.32  Prob > chi2 =  0.316
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(0)    =   0.00  Prob > chi2 =      .
    Difference (null H = exogenous): chi2(8)    =   9.32  Prob > chi2 =  0.316
  gmm(PATR1 pit corporate govtexp inflation gdp gdpgrowth unemployment, collapse eq(diff
> ) lag(2 2))
    Hansen test excluding group:     chi2(0)    =   0.00  Prob > chi2 =      .
    Difference (null H = exogenous): chi2(8)    =   9.32  Prob > chi2 =  0.316
  gmm(PATR1 pit corporate govtexp inflation gdp gdpgrowth unemployment, collapse eq(leve
> l) lag(1 1))
    Hansen test excluding group:     chi2(0)    =   0.00  Prob > chi2 =      .
    Difference (null H = exogenous): chi2(8)    =   9.32  Prob > chi2 =  0.316
  iv(electpredright electpredleft electendright electendleft dependencyold dependencyyou
> ng popbelow14 pop65andabove, eq(diff))
    Hansen test excluding group:     chi2(0)    =   0.99  Prob > chi2 =      .
    Difference (null H = exogenous): chi2(8)    =   8.33  Prob > chi2 =  0.402

[Sebastian Kripfganz]

You have a total of 25 instruments and you are estimating 17 coefficients. Each subgroup of instruments considered in the Difference-in-Hansen tests contains 8 instruments. Excluding them, there are only 25 - 8 = 17 instruments left such that the model becomes just identified. This is also indicated by the 0 degrees of freedom for the Hansen tests excluding the respective group of instruments. The Hansen test is only useful in overidentified models.

Moreover, your sample is rather small but the Hansen test is justified based on asymptotic principles. I would recommend to be cautious with its interpretation in your case.

A further remark on a different issue with your estimation: The coefficient and standard error of your gdp variable are essentially zero. This is a strong indication that there is perfect multicolinearity among your variables.

[Sebastian Kripfganz]

You do not have to do anything about the Difference-in-Hansen tests because you do not need them. If you believe in the validity of the Hansen test for the full model despite your small sample, you are fine because it does not indicate a model misspecification, and hence your results would be "valid". (The p-value is well above 0.10.)

Regarding the gdp variable: You could check the pairwise correlations to find out whether it is highly correlated with another variable. But my conjecture could also have been wrong and the gdp just does not matter for your regression. In that case, simply remove the gdp variable.

[Sebastian Kripfganz]

Do you get a similarly tiny coefficient if you only look at a subsample (say, for a subset of the countries or a subset of the years)? Maybe the answer is just the simple one: Your gdp variable does not have any effect.