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Re: st: Probit with endogenous interactions


From   "Dimitriy V. Masterov" <dvmaster@gmail.com>
To   Statalist <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Probit with endogenous interactions
Date   Mon, 17 Jun 2013 11:25:38 -0700

I believe this is surprisingly straight forward for the same reasons
that allow you to estimate a bivariate probit with endogenous
explanatory variables without any extra work.

Here's a quote from the adult Wooldridge:

We can use exactly the same routine to estimate a model with
interactions in the structural equation [...] with no more work than
defining the interactions and including them in the appropriate
command.

You can find this in Econometric Analysis Of Cross Section And Panel
Data, 2nd edition, p. 597.


On Mon, Jun 17, 2013 at 10:06 AM, Laura Crispin <lcrispin@sju.edu> wrote:
> 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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