GMM estimation: Different estimation samples for moment conditions

[Manuel Montesinos]

Dear Statalisters,

I am interested in estimating a two-equation system by GMM, using two different estimation samples, one for each equation. In particular, to fit the first equation I can only use those observations for which one of my variables -let's call it select- is equal to 1, and to fit the second equation I can only use the observations for which select is equal to zero.

If I were interested in using the same estimation sample for both equations, my code would be like:

 gmm (eqa: y1 - ({xb1: year_*})*exp({xb2:`varlist1'})) ///
            (eqb: y2 - exp({xb3:`varlist1'})+exp({xb4:`varlist2'})) [pw=wt], ///
            instruments(eqa: year_* `varlist1') ///
            instruments(eqb: `varlist1' `varlist2')

where y1 is the dependent variable of the first equation, y2 is the dependent variable of the second equation, year_* is used to call a list of variables starting by "year_";`varlist1' and `varlist2' are two locals I am using to store two sets of regressors, and I am using the variable wt as probability weights.

I would like to know if there is a way to write the condition I mentioned above, so that the first equation is fitted with the observations for which select is equal to 1, and the second equation equation with those for which select is equal to zero. I have been trying to approach the problem using the moment-evaluator program version of gmm, but I am not getting it right. This is what I tried:

program jointgmm, eclass
        version 15.1
        syntax resideq(min=2 max=2) [if] [pweight/], at(name)
        quietly {
            local resideq1 : word 1 of `resideq'
            local resideq2 : word 2 of `resideq'
            local if1 : word 1 of `if'
            local if2 : word 2 of `if'
            replace `if1' = (select==1)
            replace `if2' = (select==0)
            gen double `xb1' = 0 `if1'
            local i=1
            foreach var of local allvars {
                replace `xb1'=`xb1'+`at'[1,`i']*`var' `if1'
                local `++i'
            }
            gen double `xb3' = 0 `if2'
            local i=`ly'-`fy'+2
            foreach var of local varlist1 {
                replace `xb2'=`xb2'+`at'[1,`i']*`var' `if2'
                local `++i'
            }
            gen double `xb4' = 0 `if2'
            local i=`ly'-`fy'+2
            foreach var of local varlist2 {
                replace `xb3'=`xb3'+`at'[1,`i']*`var' `if2'
                local `++i'
            }
            replace `resideq1' = y1- `xb1' `if1'
            replace `resideq2' = y2- exp(`xb3') + exp(`xb4') `if2'
        }
    end

local np=0
foreach v of local allvars {
        local ++np
}

gmm jointgmm [pw=wt], nequations(2) nparameters(`np') ///
    instruments(1: year_* `varlist1') instruments(2: `varlist1' `varlist2')

where `allvars' is a local containing the year_* variables I mentioned before and those in `varlist1', and `ly' and `fy' are two parameters I use to define the set of year_* variables (I generate `ly'-`fy'+1 variables, i.e., these variables are year_`fy', year_`fy+1',..., year_`ly').

[Manuel Montesinos]

Just in case someone finds it useful, I solved my problem by creating different sets of variables for the different subsamples I had to use for estimation. My problem consisted of estimating a system of two equations by GMM, where one of the equations was for workers in the first year of a working spell, and the other was for workers in the second or later years of a spell.

To solve my problem, I interacted the variables used in the first equation with a dummy for being in the first year of a spell. Similarly, for the second equation, I interacted the variables with a dummy for being in later years of a spell. Therefore, I wrote zeros in those observations that are not supposed to enter the first (or the second) equation.

It was easier for me to implement this solution by GMM interactive mode. Apart from that, using the “nocommonesample” option also helped.