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st: Issue with GMM moment conditions


From   Jason Turkiela <turkiela@uoregon.edu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: Issue with GMM moment conditions
Date   Tue, 14 May 2013 19:58:59 +0000

Dear Stata listers-

I was wondering if someone may be able to make sense of an issue I am having running -gmm- in Stata 12.1-SE. Consider the code below which estimates a probit model using -gmm-:

**********************************************************************
#delimit;

*Bringing data in;
use http://fmwww.bc.edu/ec-p/data/wooldridge/mroz, clear;

*Macros;
local xb ({h0} + {h1}*educ + {h2}*kidslt6 +{h3}*age);
local phi normalden(`xb');
local Phi normal(`xb');

*Probit in GMM - Example 1;
gmm (eq1: (inlf - `Phi')*((`phi')/(`Phi')*(1-`Phi'))),
        instruments(eq1: educ kidslt6 age);

*Probit in GMM - Example 2;
gmm ((inlf - `Phi')*((`phi')/(`Phi')*(1-`Phi')))
         ((inlf - `Phi')*((`phi')/(`Phi')*(1-`Phi'))*educ)
         ((inlf - `Phi')*((`phi')/(`Phi')*(1-`Phi'))*kidslt6)
         ((inlf - `Phi')*((`phi')/(`Phi')*(1-`Phi'))*age),
         winitial(identity);
**********************************************************************

When I run Examples 1 and 2 above, the models yield identical results (i.e. coefficients and standard errors) which makes sense given that Example 1 is merely a more condensed version of Example 2. However, when I attempt a similar set up to estimate an OLS model, a problem emerges. Consider the following code:

**********************************************************************
#delimit;

*Bringing data in;
use http://fmwww.bc.edu/ec-p/data/wooldridge/mroz, clear;

*OLS in GMM - Example 3;
gmm (lwage - {b1}*educ - {b2}*hours - {b3}*faminc - {b0}),
        instruments(educ hours faminc);

*OLS in GMM - Example 4;
gmm (eq1: ((lwage - {b1}*educ - {b2}*hours - {b3}*faminc - {b0})))
        (eq2: ((lwage - {b1}*educ - {b2}*hours - {b3}*faminc - {b0})*educ))
        (eq3: ((lwage - {b1}*educ - {b2}*hours - {b3}*faminc - {b0})*hours))
        (eq4: ((lwage - {b1}*educ - {b2}*hours - {b3}*faminc - {b0})*faminc)),
        winitial(identity);
**********************************************************************

In this case, Example 3 runs fine, but Example 4 states that the GMM criterion is not concave and fails to estimate the model. Thus, I am puzzled why Example 4 is not able to be estimated given that Example 2 is. If at all possible, I would prefer to be able to list the moment conditions explicitly as in Examples 2 and 4 above. Is there something obvious I am missing? I am aware that the error is likely on my part, but if so, I genuinely do not know where it is.

Thank you for any insight you can provide,

Jason

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