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st: Re: other ways in dealing with endogeneity other than IV?


From   Kit Baum <baum@bc.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: Re: other ways in dealing with endogeneity other than IV?
Date   Wed, 7 May 2008 06:35:06 -0400

In Austin's excellent Stata Journal (7:4, 2007) article, he discusses the usefulness of fixed effects models to deal with a certain kind of 'endogeneity', which he describes as correlation between regressor and error. It is true that in the model

y_it = X_it b + u_it

on panel data, with X strictly exogenous, there will be an endogeneity problem if there is unobserved heterogeneity that depends only on who you are (only on i). This arises because the true DGP is

y_it = X_it b + [ a_i + u_it]

and if a_i (individual-specific characteristics) are correlated with observed X's, the error term is correlated with the regressors and OLS is inconsistent. That can be dealt with, as he discusses, with fixed effects, expressing a_i as a parameter to be estimated using individual-specific dummy variables or the within transformation, a la -xtreg, fe- or -areg-.

BUT if the original assumption that X is exogenous -- uncorrelated with u -- is not appropriate, then there is conventional endogeneity in the equation as well as unobserved heterogeneity. Fixed effects will deal with the latter, but not the former, and fixed effects will be just as inconsistent as pooled OLS. That is the point I was making. In that circumstance you need an IV fixed-effects estimator such as that implemented by -xtivreg, fe- or -xtivreg2, fe-, or an estimator implementing the first difference transformation with IV (- xtivreg, fd- or -xtivreg2, fd-).


Kit Baum, Boston College Economics and DIW Berlin
http://ideas.repec.org/e/pba1.html
An Introduction to Modern Econometrics Using Stata:
http://www.stata-press.com/books/imeus.html


On May 7, 2008, at 02:33 , Austin wrote:

Kit et al.--
A fixed-effects model deals with one very specific type of endogeneity
due to omitted variables that vary only across groups in i() and not
within.  Hence the discussion of -xtreg- in
http://www.stata-journal.com/article.html?article=st0136
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