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st: selection bias with bivariate probit
Hello all,
I'm looking for a procedure to control selection bias, but a bit special
case that I don't know whether STATA supports this.
Outcome regression: dichotomous dependent variable (high earnings or not) y
= beta * x + gamma * z (college or not)
Selection regression: dichotomous choice dependent variable (college degree
or not) z = alpha * w
Classic Heckman procedure deals with the situation where a selection model
with a dummy dependent variable (work or not) and an outcome model with a
continuous dependent variable (wage) with truncated (only observed if chosen).
My challenges to use a Heckman procedure are two folds: (1) a dummy
variable (high wage or not instead of continuous wage) in an outcome model
(2) outcome observations not truncated (we observe earnings for both
college degree and non-college degree) - so this is more of a treatment
model instead of a selection model.
STATA has "heckprob" dealing with the first problem and "treatreg" dealing
with the second problem. But so far I couldn't find any stata function or
ado file dealing with both extensions.
As far as I know, we can include both mills ratio of selected and
not-selected in the outcome model from the selection model.
Then I'll have a consistent coefficient estimate for gamma. But I don't
know how to correct std dev of gamma in the outcome probit model (I guess
since it is difficult to deal with covariance matrix, I prefer a standard
procedure supporting this correction).
Your help will be greatly appreciated.
Sincerely,
Sam Lee
Sam Lee
Department of Accounting
College of Business Administration
University of Illinois (RM# 2302)
601 S. Morgan St, Chicago Il 60607
Ph:312.413.2131 Fax:312.996.4520
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