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st: Estimating SEs for interacted IVs in a 2-stage Probit


From   "Sergiy Radyakin" <Radyakin@aoek.uni-hannover.de>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Estimating SEs for interacted IVs in a 2-stage Probit
Date   Tue, 20 Feb 2007 11:21:34 +0100

Dear Statalist readers,

the interacted endogenous variables have been already discussed
here several times.

E.g.:
http://www.stata.com/statalist/archive/2004-10/msg00417.html
http://www.stata.com/statalist/archive/2002-09/msg00478.html

The way to deal with them is to interact the exogenous variable (X3)
with the instrument (Z) and use this new variable (Z*X3) as an
instrument for the interaction term (X2*X3). Here X2 is endogenous
and Z is an instrument for it.

In my model the second stage is a Probit and the standard errors
will be estimated (by -ivprobit- and -mfx-) incorrectly in the model
with an interaction term (Ai & Norton (2003) "Interaction terms in
logit and probit models", http://www.unc.edu/~enorton/AiNorton.pdf ),
i.e. mfx fails in this case since X2*X3 is not independent from X2 and X3.

How do I adopt the standard solution (http://www.stata.com/support/faqs/stat/mfx_interact.html)
to get the correct standard errors in this case ?

Is there any standard command or user-written program for this purpose?

Thanks,
Sergiy
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