the robustness of GMM estimation

[yahya laasri]

Hello, I am just starting panel data estimation, I am working on the impact of economic complexity on growth and productivity.
And I am trying to get robust results to support the theoretical findings when I run my regression i get these results:

. xtabond2 TxCroiss l(1/2).TxCroiss l(0/2).ICE l(0/2).ICE2 Crise demc log_FBCF log_TermEchg,gmm(l.TxCroiss, lag(1 4)
> ) iv(ICE ICE2, equation(level)) twostep robust noconstant
Favoring speed over space. To switch, type or click on mata: mata set matafavor space, perm.
Warning: Number of instruments may be large relative to number of observations.
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: Identifiant                     Number of obs      =      1634
Time variable : Année                           Number of groups   =        84
Number of instruments = 95                      Obs per group: min =        10
Wald chi2(0)  =         .                                      avg =     19.45
Prob > chi2   =         .                                      max =        21
------------------------------------------------------------------------------
             |              Corrected
    TxCroiss | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    TxCroiss |
         L1. |   .2462095   .0416867     5.91   0.000     .1645051     .327914
         L2. |  -.0886464   .0359049    -2.47   0.014    -.1590187   -.0182741
             |
         ICE |
         --. |   .0442683   .0228675     1.94   0.053    -.0005513    .0890878
         L1. |    -.00271   .0286292    -0.09   0.925    -.0588223    .0534022
         L2. |  -.0424254   .0290039    -1.46   0.144    -.0992721    .0144213
             |
        ICE2 |
         --. |   .0230861   .0171097     1.35   0.177    -.0104483    .0566205
         L1. |  -.0280227   .0179891    -1.56   0.119    -.0632807    .0072352
         L2. |   .0032116   .0162239     0.20   0.843    -.0285866    .0350098
             |
       Crise |  -.0190959   .0022202    -8.60   0.000    -.0234475   -.0147444
        demc |  -.0104433   .0099849    -1.05   0.296    -.0300133    .0091267
    log_FBCF |   .0017105   .0002071     8.26   0.000     .0013046    .0021164
log_TermEchg |  -2.337807   3.151097    -0.74   0.458    -8.513845     3.83823
------------------------------------------------------------------------------
Instruments for first differences equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(1/4).L.TxCroiss
Instruments for levels equation
  Standard
    ICE ICE2
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    D.L.TxCroiss
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -4.21  Pr > z =  0.000
Arellano-Bond test for AR(2) in first differences: z =  -0.72  Pr > z =  0.474
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(83)   = 538.71  Prob > chi2 =  0.000
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(83)   =  82.85  Prob > chi2 =  0.484
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(62)   =  81.43  Prob > chi2 =  0.050
    Difference (null H = exogenous): chi2(21)   =   1.42  Prob > chi2 =  1.000
  iv(ICE ICE2, eq(level))
    Hansen test excluding group:     chi2(81)   =  82.12  Prob > chi2 =  0.444
    Difference (null H = exogenous): chi2(2)    =   0.73  Prob > chi2 =  0.694


. 

So as you are seeing I am struggling with

xtabond2

command but I found another way through

xtdpdsys

xtdpdsys TxCroiss l(1/2).TxCroiss l(0/2).ICE l(0/2).ICE2 Crise demc log_FBCF log_TermEchg,twostep vce(robust) noconstant

I wanted to try to get p-values of both the Hansen and Sargan test above 5% (as you can see the Sargan is 0) and the difference in Hansen tests is always above 5% no matter what I try.
PS:

TxCroiss: Is the variable representing growth ( dependant variable)
ICE : economic complexity index
Crise: dummy variable for financial crises
demc: variable for democracy
log_FBCF: natural logarithm of gross fixed capital formation
log_TermEchg: is the inverse of Terms of trade

[Sebastian Kripfganz]

In your xtabond2 command line, you have not specified any instruments for demc log_FBCF log_TermEchg (and for the second lag of ICE ICE2). Effectively, you are instrumenting them with the lagged dependent variable, which might lead to a weak-instruments problem. Also, it is advisable to collapse the instruments to avoid a too-many-instruments problem.

For two-step system GMM estimation, the Sargan test is irrelevant; only the Hausman test is asymptotically valid.

More on dynamic GMM panel data estimation:

• Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.

[yahya laasri]

Thank you for your response, the fact that I didn't specify instruments for other control variables is because I was trying to not weaken the Hansen J test by the big number of instruments. Thank you for your feedback.