st: estimating treatment effect of a binary endogenous regressor on binary outcome

[Erkan Duman <erduman@sabanciuniv.edu>]

Hello.
I am working on the impacts of having a migrant at home on the school
attendance of children. My regressor is an endogenous binary variable
and the outcome is also binary. I have searched a lot to find an
estimator which will consistently estimate the treatment effect.
Chiburis et al. (2012) paper recommends bivariate probit or IV2SLS.
However, bivariate probit requires strong assumptions (bivariate
normal errors) and my specification does not satisfy this assumption
which results in severly biased estimates. IV2SLS gives a treatment
effect over 1 (actually around 10). In my study, the treatment
receivers only constitute around 2 percent of the sample. I believe
this low treatment probability causes problems in estimating the
treatment effects because when I reduce the size of the control group
and come up with a treatment group of 16% of the sample, the treatment
estimate fits in (0,1) range ; still it is too high around 0.80. I
have encountered a similar thing to my problem as "rare events" in the
literature, but doesn't seem to solve my problem or maybe I am wrong.
Also in http://www.stata.com/meeting/chicago11/materials/chi11_nichols.pdf
some semi-parametric estimators are suggested by  Austin Nichols which
do not require bivariate normal errors but weaker assumptions.
However, I am not familiar with semi-parametric or nonparametric
estimators. Can anyone help me with an appropriate semiparametric
estimator and its stata command?
I believe there is a solution to this estimation problem and I hope
someone will help me.
Thanks.
Best regards.

-- 
Erkan Duman
Graduate student - PhD
Faculty of Art and Social Sciences
Sabancı University

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