Specification System-GMM xtabond2

[Fillipe Soares]

I need to run a two-step System-GMM, but due to my lack of experience in using this kind of approach, I'm not sure if my model is correctly specified.

My dependent variable is I
My explanatory regressors are: P Arpc Etanol (endogenous)
I also want to include time dummies - 11 years (exogenous)

I'm considering the first two lags as instruments to the difference equation and the first lag as instrument to the level equation.

My code is specified as:

  xtabond2  L(0/1).I P Arpc Etanol  year3-year11, gmm(L.I, laglimits(1 2) collapse equation(diff)) gmm(P Arpc Etanol , laglimits(1 2) collapse equation(diff)) gmm(L.I, laglimits(0 1) collapse eq(level)) gmm(P Arpc Etanol , laglimits(1 1) collapse eq(level)) ivstyle(year3-year11 , eq(level)) twostep small robust

My output is reported above:

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: Ufs                             Number of obs      =       270
Time variable : years                        Number of groups   =        27
Number of instruments = 23                      Obs per group: min =        10
F(13, 26)     =   1421.07                                      avg =     10.00
Prob > F      =     0.000                                      max =        10
------------------------------------------------------------------------------
             |              Corrected
           I |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           I |
         L1. |   .8946351    .150555     5.94   0.000     .5851649    1.204105
             |
           P |   .1013345   .1491141     0.68   0.503    -.2051738    .4078429
        Arpc |   .0102151   .1137837     0.09   0.929    -.2236706    .2441008
      Etanol |   .0367713   .0355978     1.03   0.311     -.036401    .1099435
        year3 |   .1133744   .0309018     3.67   0.001     .0498548    .1768941
        year4 |   .0733699   .0272426     2.69   0.012      .017372    .1293678
        year5 |   .0001349   .0255086     0.01   0.996    -.0522989    .0525686
        year6 |   .0980599   .0411414     2.38   0.025     .0134926    .1826272
        year7 |   .0512383   .0323415     1.58   0.125    -.0152405    .1177172
        year8 |   .1682475   .0409207     4.11   0.000     .0841339    .2523611
        year9 |   .1223861   .0460504     2.66   0.013     .0277281    .2170441
       year10 |   .1339396   .0440615     3.04   0.005     .0433699    .2245092
       year11 |   -.000983   .0441197    -0.02   0.982    -.0916723    .0897064
       _cons |   -.160847   .3426776    -0.47   0.643    -.8652309    .5435369
------------------------------------------------------------------------------
Instruments for first differences equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(1/2).(P Arpc Etanol) collapsed
    L(1/2).L.I collapsed
Instruments for levels equation
  Standard
    year3 year4 year5 year6 year7 year8 year9 year10 year11
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL.(P Arpc Etanol) collapsed
    DL(0/1).L.I collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -2.83  Pr > z =  0.005
Arellano-Bond test for AR(2) in first differences: z =  -0.39  Pr > z =  0.694
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(9)    =   9.62  Prob > chi2 =  0.382
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(9)    =  12.31  Prob > chi2 =  0.196
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(4)    =   4.20  Prob > chi2 =  0.379
    Difference (null H = exogenous): chi2(5)    =   8.11  Prob > chi2 =  0.150
  gmm(L.I, collapse eq(diff) lag(1 2))
    Hansen test excluding group:     chi2(7)    =   8.70  Prob > chi2 =  0.275
    Difference (null H = exogenous): chi2(2)    =   3.61  Prob > chi2 =  0.165
  gmm(P Arpc Etanol, collapse eq(diff) lag(1 2))
    Hansen test excluding group:     chi2(3)    =   3.06  Prob > chi2 =  0.382
    Difference (null H = exogenous): chi2(6)    =   9.25  Prob > chi2 =  0.160
  gmm(L.I, collapse eq(level) lag(0 1))
    Hansen test excluding group:     chi2(7)    =  11.18  Prob > chi2 =  0.131
    Difference (null H = exogenous): chi2(2)    =   1.13  Prob > chi2 =  0.569
  gmm(P Arpc Etanol, collapse eq(level) lag(1 1))
    Hansen test excluding group:     chi2(6)    =   8.68  Prob > chi2 =  0.193
    Difference (null H = exogenous): chi2(3)    =   3.63  Prob > chi2 =  0.304
  iv(year3 year4 year5 year6 year7 year8 year9 year10 year11, eq(level))
    Hansen test excluding group:     chi2(0)    =   0.00  Prob > chi2 =      .
    Difference (null H = exogenous): chi2(9)    =  12.31  Prob > chi2 =  0.196

Can anyone indicate me whether my equation specification is right?

[Sebastian Kripfganz]

It is unusual to specify both the zeroth and first lag of the differenced lagged dependent variable for the model in levels. I would recommend to use gmm(L.I, laglimits(0 0) collapse eq(level)) instead of gmm(L.I, laglimits(0 1) collapse eq(level)).

Otherwise, your specification looks alright, although the number of groups is quite small and you might want to reduce the number of instruments even a litte more. With such a small sample size, I cannot really recommend to specify all variables as endogenous. You are asking too much from your data.

More on GMM estimation of dynamic panel models in Stata:
XTDPDGMM: new Stata command for efficient GMM estimation of linear (dynamic) panel models with nonlinear moment conditions

[Fillipe Soares]

Thank you for the response and recommendations, Dr. Kripfganz.

I really appreciate that.