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st: conceptual doubt about IV regressions: I have to exclude some exogenous regressors from first-stage!


From   margherita Comola <margherita.comola@gmail.com>
To   statalist <statalist@hsphsun2.harvard.edu>
Subject   st: conceptual doubt about IV regressions: I have to exclude some exogenous regressors from first-stage!
Date   Mon, 8 Feb 2010 16:37:31 +0100

Dear Statalisters,

I have a conceptual doubt about IV regressions. My problem is a bit
more complicate (i.e. I have a multinomial selection rule) but I'll
try to make the example simple.

I am in the framework of the Heckman selection model: I have
information on a population where only some individuals work, and two
equations (binomial selection and wage equation). I have a group of
regressors (X) that are common to both selection and wage equation,
and "years of education" is one of them. Then I impose exclusion
restrictions, so that I have some regressors specific to the selection
equation (Z_1). Finally I have some regressors (Z_2) specific to the
wage equation only: in particular the sector of activity of the
respondent.

So now the problem comes as "years of education" is endogenous in both
equations. Since I have good instruments for that I use an IV
strategy, and I write down my model as a system of three equations
(selection, wage, "years of education") using the command cmp. That
is, "years of education" is the dependent variable in one of the
equations, and appears as a regressors in the other two equations.

Which regressors should I include in the equation for "years of
education", apart from the common variables (X) and the instruments?
My intuition would suggest to put both Z_1 and Z_2 (all the other
variables in the system) but I cannot put Z_2, as the sector of
activity is by construction not available for those who are out of the
labour market.

How can I address the problem?? can I run the "years of education"
equation with Z_1 but without Z_2? if not, what would you reccomend?

Thanks alot for your help, any little hint will be appreciated
Margherita







--
Margherita Comola
Paris School of Economics
Email: comola@pse.ens.fr
http://www.pse.ens.fr/comola/index.html
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