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  • Specification System-GMM xtabond2

    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:
    Code:
      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:

    Code:
    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?
    Last edited by Fillipe Soares; 05 Oct 2018, 09:42.

  • #2
    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

    Comment


    • #3
      Thank you for the response and recommendations, Dr. Kripfganz.

      I really appreciate that.

      Comment

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