GMM vs OLS linear prediction values

[rizki taufik]

edit: i figured it out hehe.

I ran the example from the GMM documentation, specifically "example 1" about linear regression using GMM.

. gmm (mpg- {xb: weight length}- {b0}), instruments(weight length)
. regress mpg weight length, vce(robust)

and i got identical results.

. gmm (mpg- {xb: weight length}- {b0}), instruments(weight length)

Step 1
Iteration 0:   GMM criterion Q(b) =   475.4138  
Iteration 1:   GMM criterion Q(b) =  2.696e-20  
Iteration 2:   GMM criterion Q(b) =  2.622e-27  

Step 2
Iteration 0:   GMM criterion Q(b) =  4.001e-28  
Iteration 1:   GMM criterion Q(b) =  1.368e-31  

note: model is exactly identified.

GMM estimation

Number of parameters =   3
Number of moments    =   3
Initial weight matrix: Unadjusted                 Number of obs   =         74
GMM weight matrix:     Robust

------------------------------------------------------------------------------
             |               Robust
             | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
      weight |  -.0038515   .0019472    -1.98   0.048    -.0076679   -.0000351
      length |  -.0795935   .0677532    -1.17   0.240    -.2123873    .0532003
-------------+----------------------------------------------------------------
         /b0 |   47.88487   7.506024     6.38   0.000     33.17334    62.59641
------------------------------------------------------------------------------
Instruments for equation 1: weight length _cons

. regress mpg weight length, vce(robust)

Linear regression                               Number of obs     =         74
                                                F(2, 71)          =      55.38
                                                Prob > F          =     0.0000
                                                R-squared         =     0.6614
                                                Root MSE          =     3.4137

------------------------------------------------------------------------------
             |               Robust
         mpg | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      weight |  -.0038515   .0019879    -1.94   0.057    -.0078152    .0001122
      length |  -.0795935   .0691697    -1.15   0.254     -.217514    .0583271
       _cons |   47.88487   7.662958     6.25   0.000     32.60537    63.16438
------------------------------------------------------------------------------

I noticed that that the predicted values I got from `predict ... , xb` are different between the gmm one and the regress one. I further noticed that the GMM predicted values is the OLS one minus the constant. Here some example of the predicted values I got:
.

mpg	weight	length	gmm	ols
22	2,930	186	-26.08	21.79
17	3,350	173	-26.67	21.21

.
why are they different?

Thanks in advance.

[Maarten Buis]

In your GMM model the constant is its own equation, so if you ask for the linear predictor of the xb equation, you don't include the constant.