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Re: st: atypical (?) 2sls question


From   "Austin Nichols" <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: atypical (?) 2sls question
Date   Tue, 29 May 2007 15:57:48 -0400

Diego / Gio Reidi --
This is called the forbidden regression, and for good reason.  You
cannot plug in the fitted value. Instead, you have two endogenous
variables now, X and Ins*X, and you may need additional excluded
instruments.  You may want to consider interacting excluded
instruments... but be sure to check the diagnostic tests provided by
the newest copy of -ivreg2- (ssc install ivreg2, replace).

On 5/29/07, Gio Reidi <gioreidi@gmail.com> wrote:
Dear Statalisters,
sorry if this will reach you twice..

I hope you could give me an insight about this problem, concerning
econometrical theory and Stata commands for 2sls.

I am trying to run a sort of two stages least squares regressing the
impact of some institutions on how variable Y responds to variable X
(endogenous):

Y=a+B(X)+Z(Institution*X)+K
(exogenous variables, including main effect of the institution)

To do so I want to instrument X, for which I have my good
instrument(s). I do not have an instrument for the interactions
between
 X and the institution, but I was thinking (and  maybe I am completely
wrong) that I would not need one if I just plug the fitted values of X
from the first stage regression and construct with them the
interaction term.  At the end, this is  what I want to assess: the
impact on the "purified" X of the institutions. The goal is to obtain:

Y=a+B(fittedX)+Z(Institution
*fittedX)+K(exogenous variables).

I cannot do this using ivreg or ivreg2 because then they would
consider the interaction as an exogenous variable and insert it in the
first stage. So I was thinking to do two stage least squares by
hand,including all the exogenous regressors in the first stage plus
the additional instruments. and then plugging in the fitted X series
and the fitted X sinteracted with the institutions.
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