# st: selection bias with bivariate probit

 From Sam Lee To statalist@hsphsun2.harvard.edu Subject st: selection bias with bivariate probit Date Wed, 20 May 2009 16:15:05 -0500

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

University of Illinois (RM# 2302)
601 S. Morgan St, Chicago Il 60607

Ph:312.413.2131 Fax:312.996.4520

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