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st: how to include an interaction term with distance in a specification


From   joachim jarreau <joachim.jarreau@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: how to include an interaction term with distance in a specification
Date   Wed, 18 Nov 2009 13:24:03 +0100

Hi,

This is a proper econometrics question rather than a stata one. My
apologies in advance if this is not the proper place.

I am using a panel sample to estimate the impact of a variable x on an
outcome y; in my baseline estimate,  i find a positive estimate of the
elasticity, of about 0.16 (both variables are in log). Now, I would
like to test whether the impact of x on y is varying with the distance
between them, e.g. with a gap X-Y, or X/Y  - X,Y being the variables
in level, and X being bigger than Y most of the time. (In short, Id
like to test a catching up effect: X and Y both are measures of
performance of foreign and domestic firms, respectively - im testing
the hypothesis of a spillover effect).
I don't know how i should specify this. Should I include the "gap"
variable also in the spec., along with the interaction? when i do
this, the gap comes out with a big negative coefficient, while the x
and the interact coming out with positive coeffs; the resulting
estimate of the elasticity is much higher than what i obtained in the
linear spec. I think this is just because the LHS variable appears in
the gap with a negative sign - on the other hand, if I don't include
it, i get a positive coeff on x and a negative on y, but again, the
resulting estimate of the elasticity does not match at all with the
linear case.
I see there's something wrong with this specification, but i don't see
how to do this properly. Is there a way? Are there some references on
this type of problem?
Thanks in advance.

Joachim
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