st: biprobit, interactions, and correct marginal effects

["Dimitriy V. Masterov" <dvmaster@gmail.com>]

I would like to calculate the correct marginal effect of an
interaction after a bivariate probit. It is the interaction of the
endogenous binary variable and a continuous exogenous variable.

Here's an example where the outcome is a child attending private
school. I am interested in whether voting for the property tax
increase and the property tax paid make private education more likely:

#delimit;
webuse school;
biprobit
(private = c.years c.logptax##i.vote)
(vote = year c.loginc c.logptax), robust;

I would like to get the AME of just vote#c.logptax. The index function
coefficient for that term is 0.72.

Is there a way to get margins to report this? I don't think this code

margins, dydx(logptax) predict(pmarg1) over(vote) force;

does it because it also included the non-interaction effect of
logptax. Tricking Stata by defining the interaction manually will not
produce the correct AME for reasons described in Ai and Norton (2003).

Any advice would be much appreciated.

Ai, C., and E. Norton. 2003. Interaction terms in logit and probit models.
Economics Letters, 80: 123–129

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/