Two-step system GMM estimations

[Justin Zhang]

Hi all,

I am trying to do a simulation of Canh, Binh, Thanh, &Schinckus (2020): https://www.sciencedirect.com/scienc...1070171930040X

I collected part of the data from sources listed in the paper and try to run two-step system GMM estimations, however, some of the results are not significant as expected.

I use FDI inwards as the dependent variable and have 8 independent variables.

This is what I did:

. xtabond2 FDII L.FDII lnEPU GDPg Inf Cap REER Trade CO2 hc, gmm (lnEPU GDPg Inf Cap REER Trade CO2 h
> c, lag(2 2)) iv(i.year, equation(level)) twostep robust noconstant small orthogonal
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: countryid                       Number of obs      =       294
Time variable : year                            Number of groups   =        18
Number of instruments = 272                     Obs per group: min =        11
F(0, 18)      =         .                                      avg =     16.33
Prob > F      =         .                                      max =        17
------------------------------------------------------------------------------
             |              Corrected
        FDII |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        FDII |
         L1. |   .5967331   .0756997     7.88   0.000     .4376939    .7557722
             |
       lnEPU |    .109172   .8895851     0.12   0.904    -1.759777    1.978121
        GDPg |   .2959404   .1470744     2.01   0.059    -.0130515    .6049324
         Inf |  -.1722542   .1901387    -0.91   0.377    -.5717208    .2272123
         Cap |   .2089427   .4025101     0.52   0.610    -.6366996    1.054585
        REER |   -.026296   .1010408    -0.26   0.798    -.2385749    .1859829
       Trade |   .0215861   .0151573     1.42   0.172    -.0102583    .0534305
         CO2 |  -.1006967   .3959977    -0.25   0.802     -.932657    .7312637
          hc |  -3.601994   5.743118    -0.63   0.538    -15.66784    8.463849
------------------------------------------------------------------------------
Instruments for orthogonal deviations equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L2.(lnEPU GDPg Inf Cap REER Trade CO2 hc)
Instruments for levels equation
  Standard
    1996b.year 1997.year 1998.year 1999.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
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL.(lnEPU GDPg Inf Cap REER Trade CO2 hc)
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -1.74  Pr > z =  0.083
Arellano-Bond test for AR(2) in first differences: z =  -1.68  Pr > z =  0.092
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(263)  = 280.20  Prob > chi2 =  0.223
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(263)  =   8.72  Prob > chi2 =  1.000
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(135)  =   8.72  Prob > chi2 =  1.000
    Difference (null H = exogenous): chi2(128)  =  -0.00  Prob > chi2 =  1.000
  gmm(lnEPU GDPg Inf Cap REER Trade CO2 hc, lag(2 2))
    Hansen test excluding group:     chi2(7)    =  11.35  Prob > chi2 =  0.124
    Difference (null H = exogenous): chi2(256)  =  -2.63  Prob > chi2 =  1.000
  iv(1996b.year 1997.year 1998.year 1999.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, eq(level))
    Hansen test excluding group:     chi2(247)  =   8.72  Prob > chi2 =  1.000
    Difference (null H = exogenous): chi2(16)   =  -0.00  Prob > chi2 =  1.000

I have compared my descriptive statistics with Canh(2020) and believe we are using a similar database.

How should I do this correctly?
Thank you all in advance.

[Sebastian Kripfganz]

You are using almost as many instruments as observations. That leads to severe overfitting problems. You need to use strategies to substantially reduce the number of instruments (in particular collapsing), as I discussed for example in my 2019 London Stata Conference presentation:

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

Also, it is almost always not a good idea to omit the constant when you do a system GMM estimation.