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st: MLE of Heckman model with endogeneity


From   Nina Parfinenko <nparfin@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: MLE of Heckman model with endogeneity
Date   Wed, 12 Feb 2014 00:17:32 +1100

Dear Statalist,

I need to estimate a two-equation sample selection model for wage (y1)
and hours (y2). y2 is not observed, only whether y2>0 or y2=0. Wage y1
is observed only if y2>0. Also y1 is endogenous in the y2 equation.
More precisely, the two equations are

y1=betaX+e1
y2*=alpha*y1+gammaZ+e2

and (e1, e2) are jointly normal.

This model could be estimated with ivprobit if y1 were always
observed. On the other hand, it would be a candidate for heckman
command if not for the endogeneity of y1 in the y2 equation. I seems
that Stata ml commands do not take endogenous variables either.

Is it possible to estimate the above model with maximum likelihood
(the 2 equations simultaneously) in Stata using built-in commands? I
have already estimated the system with a two-step procedure and now
need to estimate it jointly and simulatenously with Maximum
Likelihood.
Many thanks,
Nina
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