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  • System-GMM without level equation

    I have a question regarding system-GMM. In this case, it seems that I have a two-step system GMM but I have not specified the instrument variables in the level equation. Is it correct to say that I am estimating a system-GMM, and not mention anything about the level equation?

    Code:
    . xtabond2 Y l.Y a b c ab ac coalition 
    > l.lngdp l.lngdppercapita l.gdpgrowth l.lninflation l.govtexp l.pop14 l.pop65, ///
    > gmm(l.Y , lag(1 2) collapse eq(diff)) ///
    > iv(a b c ab ac coalition l.lngdp l.lngdpperca
    > pita l.gdpgrowth l.lninflation l.govtexp l.pop14 l.pop65, eq(diff)) ///
    > nodiffsargan twostep robust
    Favoring space over speed. To switch, type or click on mata: mata set matafavor speed
    > , perm.
    
    Dynamic panel-data estimation, two-step system GMM
    ------------------------------------------------------------------------------
    Group variable: country                         Number of obs      =       486
    Time variable : year                            Number of groups   =        26
    Number of instruments = 16                      Obs per group: min =        15
    Wald chi2(14) =    146.89                                      avg =     18.69
    Prob > chi2   =     0.000                                      max =        20
    --------------------------------------------------------------------------------
                   |              Corrected
             Y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
    ---------------+----------------------------------------------------------------
             Y |
               L1. |   .7222813   .1701339     4.25   0.000      .388825    1.055738
                   |
         a |  -.2317608   .2530301    -0.92   0.360    -.7276908    .2641691
             b |  -.5301456   .5432221    -0.98   0.329    -1.594841    .5345502
              c |  -.0224109    .484336    -0.05   0.963    -.9716921    .9268703
    ab |  -.1367733   .3817006    -0.36   0.720    -.8848927     .611346
     ac |  -.0723654   .3836385    -0.19   0.850    -.8242831    .6795523
         coalition |   .2727919   .3676454     0.74   0.458    -.4477798    .9933636
                   |
             lngdp |
               L1. |  -11.97239   5.726428    -2.09   0.037    -23.19598   -.7487975
                   |
    lngdppercapita |
               L1. |   10.03662   5.629337     1.78   0.075    -.9966812    21.06991
                   |
         gdpgrowth |
               L1. |   -3.21324   4.289274    -0.75   0.454    -11.62006    5.193584
                   |
       lninflation |
               L1. |  -.0736836   .0800735    -0.92   0.357    -.2306248    .0832577
                   |
           govtexp |
               L1. |   4.048511   4.055335     1.00   0.318      -3.8998    11.99682
                   |
             pop14 |
               L1. |  -.1944994   .1995454    -0.97   0.330    -.5856012    .1966024
                   |
             pop65 |
               L1. |  -.2088385   .1905127    -1.10   0.273    -.5822365    .1645594
                   |
             _cons |   41.23084   18.69118     2.21   0.027     4.596788    77.86488
    --------------------------------------------------------------------------------
    Instruments for first differences equation
      Standard
        D.(a b c ab ac coalition L.lngdp
        L.lngdppercapita L.gdpgrowth L.lninflation L.govtexp L.pop14 L.pop65)
      GMM-type (missing=0, separate instruments for each period unless collapsed)
        L(1/2).L.Y collapsed
    Instruments for levels equation
      Standard
        _cons
    ------------------------------------------------------------------------------
    Arellano-Bond test for AR(1) in first differences: z =  -2.18  Pr > z =  0.029
    Arellano-Bond test for AR(2) in first differences: z =   0.61  Pr > z =  0.544
    ------------------------------------------------------------------------------
    Sargan test of overid. restrictions: chi2(1)    =   1.69  Prob > chi2 =  0.194
      (Not robust, but not weakened by many instruments.)
    Hansen test of overid. restrictions: chi2(1)    =   0.89  Prob > chi2 =  0.344
      (Robust, but weakened by many instruments.)
    
    
    . 
    end of do-file

  • #2
    The only reason why xtabond2 labels the estimates as "system GMM" is the regression constant (which has automatically applid a constant as an instrument for the level model). Ignoring that constant term, what you have done is essentially a difference GMM estimation.

    More on GMM estimation of dynamic panel models:
    https://twitter.com/Kripfganz

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