Difference GMM: Hansen test 0.000 despite N>T, collapse doesn't fix

[Max Brauer]

Hello all,

I am running difference GMM to eliminate known reverse causality between my dependent variable (ihsdti) and my main independent variable of interest (happy1). I have 5088 groups and only 59 instruments, but my Hansen test still came back 0.000. I also flunked AR[2].

I collapsed instruments (which worked in a previous specification with a slightly different calculation for my dependent variable), and increased the lag dependent variable to L2. This corrected my AR[2] issue, but my Hansen test is still 0.000.

Any help on my Hansen test problem is much appreciated.

Here are the results:

. xtabond2 ihsdti L2.ihsdti L(1/1)happy1 L(1/1)age L(1/1)age2 L(1/1)child L(1/1)race L(1/1)married L(1/1)widow L(1/1)divse
> p L(1/1)employd L(1/1)unemploy L(1/1)edu1 L(1/1)lnrinc15 L(1/1)numfam year13 year15 year17 year19, iv(year13 year15 year
> 17 year19) gmm(L.lndti L.happy1 L.age L.age2 L.child L.race L.married L.widow L.divsep L.employd L.unemploy L.edu1 L.lnr
> inc15 L.numfam, collapse) noleveleq robust
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
year17 dropped due to collinearity
Warning: Two-step estimated covariance matrix of moments is singular.
  Using a generalized inverse to calculate robust weighting matrix for Hansen test.
  Difference-in-Sargan/Hansen statistics may be negative.

Dynamic panel-data estimation, one-step difference GMM
------------------------------------------------------------------------------
Group variable: id                              Number of obs      =     11268
Time variable : year                            Number of groups   =      5088
Number of instruments = 59                      Obs per group: min =         0
Wald chi2(0)  =         .                                      avg =      2.21
Prob > chi2   =         .                                      max =         3
------------------------------------------------------------------------------
             |               Robust
      ihsdti |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      ihsdti |
         L2. |  -.0050029   .0210653    -0.24   0.812    -.0462901    .0362844
             |
      happy1 |
         L1. |   .0000441   .0132605     0.00   0.997     -.025946    .0260342
             |
         age |
         L1. |   .0080277   .0482873     0.17   0.868    -.0866136     .102669
             |
        age2 |
         L1. |   .0000109   .0001968     0.06   0.956    -.0003747    .0003966
             |
       child |
         L1. |   .0028104    .047455     0.06   0.953    -.0901996    .0958205
             |
        race |
         L1. |   23.59687   14.92014     1.58   0.114    -5.646055     52.8398
             |
     married |
         L1. |   .6248527    .248282     2.52   0.012     .1382288    1.111477
             |
       widow |
         L1. |  -1.450568   1.060808    -1.37   0.171    -3.529713     .628577
             |
      divsep |
         L1. |   .6696009   .3496698     1.91   0.055    -.0157393    1.354941
             |
     employd |
         L1. |   -.125849    .046303    -2.72   0.007    -.2166013   -.0350968
             |
    unemploy |
         L1. |  -.0541125   .0439053    -1.23   0.218    -.1401654    .0319404
             |
        edu1 |
         L1. |    .501768   .2192204     2.29   0.022     .0721038    .9314322
             |
    lnrinc15 |
         L1. |  -.0095542   .0186659    -0.51   0.609    -.0461387    .0270302
             |
      numfam |
         L1. |   .0594206   .0500564     1.19   0.235    -.0386881    .1575293
             |
      year13 |   .1096201   .1721624     0.64   0.524    -.2278119    .4470522
      year15 |   .0634726   .0856652     0.74   0.459     -.104428    .2313733
      year19 |  -.0411584   .0851321    -0.48   0.629    -.2080143    .1256974
------------------------------------------------------------------------------
Instruments for first differences equation
  Standard
    D.(year13 year15 year17 year19)
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(1/5).(L.lndti L.happy1 L.age L.age2 L.child L.race L.married L.widow
    L.divsep L.employd L.unemploy L.edu1 L.lnrinc15 L.numfam) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -4.33  Pr > z =  0.000
Arellano-Bond test for AR(2) in first differences: z =   0.19  Pr > z =  0.853
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(42)   = 139.84  Prob > chi2 =  0.000
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(42)   = 143.47  Prob > chi2 =  0.000
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  iv(year13 year15 year17 year19)
    Hansen test excluding group:     chi2(39)   = 133.51  Prob > chi2 =  0.000
    Difference (null H = exogenous): chi2(3)    =   9.96  Prob > chi2 =  0.019

[Max Brauer]

just to add additional info, I have an unbalanced panel

[Max Brauer]

It occured to me that perhaps I should be using system GMM if Y follows a random walk. I failed to check for this. Is it possible that Y following a random walk could be causing my troubles -- that I shouldn't be using difference GMM in the first place?

Also, I have no idea how to test for if Y follows a random walk. help here is also appreciated. I posted that question in a separate thread a few hours ago, but now am wondering if random walk could result in flunking Hansen. https://www.statalist.org/forums/for...ws-random-walk