Do I need to compare the results of a standard GMM regression with those of a pooled OLS regression?

[Lucas Yeu]

Dear Statalist society,

I have carried out a standard GMM regression with two instruments that I chose by assuming that they were suitable (I did not use other methods because of their complexity). I then evaluated the validity of my instruments by using a Hansen J-test for overidentifying restrictions and results show that my instruments are uncorrelated with the error terms of my equation.
However, I was told that I need to compare the results of my OLS regression with the results of my GMM regression to show the reliance and consistency of my results.


These are the results of the OLS regression

 reg $ylist $xlist

      Source |       SS       df       MS              Number of obs =     720
-------------+------------------------------           F( 13,   706) =   86.39
       Model |    1218.138    13   93.702923           Prob > F      =  0.0000
    Residual |  765.768173   706  1.08465747           R-squared     =  0.6140
-------------+------------------------------           Adj R-squared =  0.6069
       Total |  1983.90617   719  2.75925754           Root MSE      =  1.0415

------------------------------------------------------------------------------
       lnFDI |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    lnAPA_ex |   1.061668   .2655766     4.00   0.000     .5402537    1.583083
    lngdp_ex |   2.218972   .2239381     9.91   0.000     1.779307    2.658636
    lngdp_im |   .1755009   .0566503     3.10   0.002     .0642776    .2867241
    lnCPI_ex |   3.746099   .9763996     3.84   0.000     1.829105    5.663094
    lnCPI_im |   .1393702   .0525016     2.65   0.008     .0362922    .2424481
   lndif_GDP |  -.0319451   .0067189    -4.75   0.000    -.0451366   -.0187536
   lndif_pop |  -.0463713   .0089667    -5.17   0.000    -.0639759   -.0287668
  lnfreed_im |   4.783194   .4739892    10.09   0.000     3.852597    5.713791
      lndist |   -.338742   .0528176    -6.41   0.000    -.4424404   -.2350437
      border |  -.1600089   .2449025    -0.65   0.514    -.6408334    .3208155
        open |  -.4679075   .1699626    -2.75   0.006       -.8016   -.1342149
        polc |   4.982644   .9516921     5.24   0.000     3.114159     6.8511
       _cons |   -41.7668   3.068047   -13.61   0.000    -47.79039   -35.74321

And these are the results of my GMM estimation

ivregress gmm  lnFDI lngdp_ex lngdp_im lnCPI_ex lnCPI_im lndif_GDP lndif_pop lnfreed_im
> lndist border open polc (lnAPA_ex = lnGAPA_l1 lnAPA_im)

Instrumental variables (GMM) regression                Number of obs =     720
                                                       Wald chi2(13) = 1529.99
                                                       Prob > chi2   =  0.0000
                                                       R-squared     =  0.5716
GMM weight matrix: Robust                              Root MSE      =  1.0865

------------------------------------------------------------------------------
             |               Robust
       lnFDI |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    lnAPA_ex |   3.393222   .6411406     5.29   0.000      2.13661    4.649835
    lngdp_ex |   1.776358   .2145395     8.28   0.000     1.355868    2.196847
    lngdp_im |   .1900265   .0604584     3.14   0.002     .0715302    .3085228
    lnCPI_ex |   11.52501   2.196498     5.25   0.000     7.219956    15.83007
    lnCPI_im |   .2067215   .0682706     3.03   0.002     .0729135    .3405295
   lndif_GDP |  -.0338982   .0072998    -4.64   0.000    -.0482056   -.0195909
   lndif_pop |   -.044247   .0089408    -4.95   0.000    -.0617707   -.0267233
  lnfreed_im |   4.827352   .4997397     9.66   0.000      3.84788    5.806824
      lndist |  -.3231212   .0494157    -6.54   0.000    -.4199742   -.2262681
      border |  -.0571234    .137437    -0.42   0.678     -.326495    .2122481
        open |  -.6323952   .2426697    -2.61   0.009    -1.108019   -.1567714
        polc |   3.084821   1.022805     3.02   0.003     1.080161    5.089482
       _cons |  -48.58023   4.029627   -12.06   0.000    -56.47815    -40.6823
------------------------------------------------------------------------------
Instrumented:  lnAPA_ex
Instruments:   lngdp_ex lngdp_im lnCPI_ex lnCPI_im lndif_GDP  lndif_pop
               lnfreed_im lndist border open polc lnGAPA_l1 lnAPA_im
               

I haven't found much information about this comparison on Google. So, I unfortunately don't know what to compare between the OLS and GMM and what the differences would imply.
I am eagerly requesting the help of an expert in this forum. Thank you very much in advance.

[Phil Bromiley]

No one responded quickly to your question. You'll increase your chances of a helpful answer if you follow the FAQ on asking questions - provide Stata code in code delimiters, Stata output, and sample data. Also, try to simplify your code to what is necessary to demonstrate the problem.

Look at hausman in the documentation. A difference between GMM (or any model that controls for endogeneity) and a model that doesn't is testing whether the constraints added in the OLS (essentially constraints on the parameters of the instrumental variable model) are appropriate.