st: Probit with endogenous interactions

[Laura Crispin <lcrispin@sju.edu>]

Dear Statalist Users, 
Does anyone have suggestions on how to estimate a bivariate probit model with an interaction between an endogenous and exogenous indicator variable? 

Here's my basic setup: 
I am trying to estimate the effect of participating in an activity (P = 0 or 1) on the decision to drop out of school (HSD = 1 if drop out, = 0 if stay in ). I am controlling for a number of exogenous variables, plus an indicator for being at-risk (AR = 0 or 1). Since it is likely that participation effects may differ by at-risk status, I am trying to estimate the following model: 

PR(HSD = 1) = a + B_1*P + B_2* AR + B_3*P*AR + B_4*X + error (all with subscript_i to denote individual level observations) 

Since P is endogenous, without an interaction term, I would just estimate a bivariate probit model with instruments Z. However, with the interaction term, it isn't so simple. If all were continuous, 2SLS would work. But with the discrete nature of the data, I'm not convinced that this is the correct approach. I was looking into two-step methods as well, but can't seem to find an appropriate reference to this situation. 

If anyone has suggestions on how to estimate a bivariate probit model with an interaction between an endogenous and exogenous indicator variable, I'd love any advice or references to current methods. 

Thanks, 
Laura 

Laura M. Crispin 
Assistant Professor 
Department of Economics 
Saint Joseph's University 

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