Sergiy Radyakin --
It is not that the standard errors are estimated incorrectly--note
that the Cov matrix \Sigma in Ai & Norton's eq 5 is the one saved by
Stata in e(V)--just that you cannot use the reported SEs directly to
measure the statistical significance of the marginal effect, since the
marginal effect is somewhat more complicated in a nonlinear model
(given by Eq 2 in Ai & Norton for your probit case). I guess this is
primarily a matter of terminology, where you want to measure the size
and significance of a marginal effect but refer to the problem as one
of measuring the std error on coefficients, including an interaction
term. Personally, I would bootstrap (see link below), but you could
also use the Delta method referred to in Ai & Norton. Just a little
more complicated to work out with the added wrinkle of IV, I guess.
http://www.stata.com/statalist/archive/2006-12/msg00471.html
On 3/5/07, Sergiy Radyakin <Radyakin@aoek.uni-hannover.de> wrote:
Hello Statalisters,
May I repost my question from Febr. 20 this year?
I still haven't received any replies :(
In short:
I can estimate SEs for interacted variables in a regular probit model.
How do I do this if one of them is an IV (in an IV-probit)?
Thank you, Sergiy
----- Original Message -----
From: "Sergiy Radyakin" <Radyakin@aoek.uni-hannover.de>
To: <statalist@hsphsun2.harvard.edu>
Sent: Tuesday, February 20, 2007 11:21 AM
Subject: st: Estimating SEs for interacted IVs in a 2-stage Probit
> 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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