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st: 2-stage estimation of probit with first-stage oprobit


From   Klaus Brösamle <broesamle@hertie-school.org>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: 2-stage estimation of probit with first-stage oprobit
Date   Fri, 27 Jul 2012 11:51:08 +0200

Hi Stata-List,

I have what I think is a neat little problem. I'm want to estimate a probit (the choice whether to work in the private or public sector) and use various (ordered) education levels in X. Moreover, I want to instrument these educational levels with father's education and background. So formally, I think I want to estimate an ordered probit (edu level) as first stage, and then a probit (sector choice) as second stage. 

After some reading, esp Wooldridge (2002: 621-25) I think I should estimate an ordered probit with EduLevel = FatherEduLevel etc., then obtain fitted values/probabilities, and use these as an instrument for my sector choice equation. (Rather than just use the fitted probabilities (in W. called G^hat) as a coefficient in my sector choice probit.)

My questions are now, a) is this presumption correct up to here, and b) if so, which IV command can I use to do this latter IVestimation? ivreg won't work because my main outcome (sector choice) is binary. ivprobit won't work because it requires a continuous endogenous variable, but my endogenous variable is "ordered categorical" (i.e. I have a fitted probability for each education level).

Thanks for any hints on this.
Klaus


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