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Re: st: poisson fixed effects


From   David Harless <dwharles@vcu.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: poisson fixed effects
Date   Thu, 15 May 2003 09:51:00 -0400

lacetera@mit.edu wrote:
> 
> Hi all,
> I have a question:
> I tired to use a fixed effect poisson estimation (xtpois...,fe). As well
> known, the undelying conditional likelihood is actually conditional on the sum
> of the outcomes, and this gives something that recall a multinomial logit,
> such that the individual specific effect gets canceled out. Since this is a
> non linear model, this is different from the "within" estimator in a linear
> fixed effect model, which, in turn, is equivalent to adding a set of dummies.
> 
> Now, I tried to estimate a model with xtpois...,fe and, after that, I
> estimated it with the simple poisson command and added dummies for my cross
> sectional unit. Now, I get the same results. This is clear for a linear model,
> but, should I be surprised or not that I got it in poisson?

There is nothing wrong.  The Poisson fixed effects model is an instance (perhaps
the only instance?) of a nonlinear model in which the incidental parameters
problem (the incidental parameters being the fixed effects for cross-sectional
units) does not apply: parameter estimates are consistent given fixed number of
observations for each cross-sectional unit.  Hence, xtreg..., fe produces the
identical coefficient estimates (and standard errors) as does poisson with dummy
variables for cross-sectional units.  See Cameron and Trivedi, Regression
Analysis of Count Data, 1998, pages 280-282.

Dave Harless
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