Replicate OLS estimation using GMM command

[Tyler Ransom]

Hi Statalisters,

I have a question about using the -gmm- command to replicate OLS estimation. Things work fine up until I introduce a dummy variable, and I have no idea why that would be troublesome. Consider the following example:

sysuse auto
local rhs turn length headroom trunk
reg mpg `rhs', r
gmm (mpg -({xb:`rhs'}+{b0})), instruments(`rhs') winitial(identity) vce(robust) iterate(5)

The two commands give identical point estimates, but slightly different SEs (but that's to be expected). Now I add a dummy variable (and post output rather than source code):

. local rhs turn length headroom trunk foreign
. reg mpg `rhs', r

Linear regression                               Number of obs     =         74
                                                F(5, 68)          =      32.94
                                                Prob > F          =     0.0000
                                                R-squared         =     0.6473
                                                Root MSE          =     3.5602

------------------------------------------------------------------------------
             |               Robust
         mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        turn |  -.2573714   .1737776    -1.48   0.143    -.6041391    .0893963
      length |  -.1812296   .0578863    -3.13   0.003    -.2967399   -.0657193
    headroom |  -.0759515   .4046498    -0.19   0.852    -.8834176    .7315147
       trunk |    .004777   .1751617     0.03   0.978    -.3447527    .3543068
     foreign |  -1.632016   1.264629    -1.29   0.201    -4.155544    .8915119
       _cons |   66.20747   4.938808    13.41   0.000     56.35223     76.0627
------------------------------------------------------------------------------


. gmm (mpg -({xb:`rhs'}+{b0})), instruments(`rhs') winitial(identity) vce(robust) iterate(5)

Step 1
Iteration 0:   GMM criterion Q(b) =   15985229  (not concave)
Iteration 1:   GMM criterion Q(b) =    1253436  (not concave)
Iteration 2:   GMM criterion Q(b) =  98463.417  (not concave)
Iteration 3:   GMM criterion Q(b) =  7913.7578  (not concave)
Iteration 4:   GMM criterion Q(b) =  817.35425  (not concave)
Iteration 5:   GMM criterion Q(b) =  162.62732  (not concave)
convergence not achieved

note: model is exactly identified

GMM estimation

Number of parameters =   6
Number of moments    =   6
Initial weight matrix: Identity                   Number of obs   =         74
GMM weight matrix:     Robust

------------------------------------------------------------------------------
             |               Robust
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        turn |   .0861536   .3691139     0.23   0.815    -.6372964    .8096036
      length |   .0181301   .0977029     0.19   0.853    -.1733641    .2096244
    headroom |   1.134376   1.059623     1.07   0.284    -.9424463    3.211198
       trunk |   .2445109   .3016458     0.81   0.418     -.346704    .8357258
     foreign |   12.96847   3.387061     3.83   0.000     6.329955    19.60699
-------------+----------------------------------------------------------------
         /b0 |    3.45462   15.98317     0.22   0.829    -27.87182    34.78106
------------------------------------------------------------------------------
Instruments for equation 1: turn length headroom trunk foreign _cons
Warning: convergence not achieved

Does anyone have any idea what might be going on here?

[Sebastian Kripfganz]

Apparently, the weighting matrix winitial(identity) leads to convergence problems. When you use the default weighting matrix, everything works fine.

[Tyler Ransom]

Thank you Sebastian!