mean deviation vs. dummy variable in fixed effects with GMM estimation

[alicewong]

I have a panel data (unbalance, not dynamic data), and I want to use fixed effect to control within individual effects.

The model have simultaneous equations and I want to use GMM to estimate (PROC MODEL with GMM option)

Since there are way more individuals (100+) than periods (several), dummy variable means sacrifice a lot of degree of freedom.  I wonder if mean deviation method would give the same results for GMM, compared with the dummy variable method? I am asking because OLS estimates with fixed effects dummy variables will give the same estimates as the mean deviation method. But for comparison of the two methods for GMM estimation method, I am not sure. Since with GMM estimation method, the instruments used will affect the parameter estimates, hence the comparison may be more complicated.

What I mean by  mean deviation method is that for each person and for each time-varying variable, I compute the means over time for that person.  Then I subtract the person-specific means from the observed values of each variable. Would this mean deviation give the same estimation results as using dummy variables? I want to use the PROC MODEL with GMM and simultaneous equations in SAS to estimate.

Thanks very much,

Alice