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Re: st: Fixed Effect Estimation Results


From   "Joana Quina" <joana.statalist@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Fixed Effect Estimation Results
Date   Mon, 3 Apr 2006 11:01:22 +0100

This is a follow-up question to a recent(ish) query:

Given that a high corr(u_i,Xb) suggests a model is a poor candidate
for random effects, how should one interpret a Hausman test that fails
to reject random effects?
It seems counter-intuitive. Any suggestions would be much appreciated.

Thanks,
Joana

On 14/03/06, William Gould, Stata <wgould@stata.com> wrote:
> Sam Rawlings <sr3209@bristol.ac.uk> asked,
>
> > I have estimated (several) sub-samples for a fixed effects model using
> > panel data. However, in order to interpret my results, I'm slightly
> > confused about one of the statistics given - corr(u_i, Xb). Is there any
> > chance anyone could enlighten me, [...]
>
> and following that Sam included some -xtreg, fe- output, the header of
> which reads,
>
> > Fixed-effects (within) regression           Number of obs      =   560
> > Group variable (i): country                 Number of groups   =   112
> >
> > R-sq:  within  = 0.6385                     Obs per group: min =   5
> >        between = 0.9909                                    avg =   5.0
> >        overall = 0.9694                                    max =   5
> >
> >                                             F(3,445)           =   62.01
> > corr(u_i, Xb)  = 0.9249                     Prob > F           =  0.0000
>
> In terms of the fixed-effects model, that corr(u_i, Xb) = .9249 is just a
> fact, one among many.  Sam could interpret it as a country's residual
> positively renforces the a country's expected outcome based on its
> characteristics.  Countries that have a high expected value vased on their
> characteristics also tend to have positive residuals, so their outcome is even
> higher.
>
> That's interesting, but that is not why Stata reports it.  No doubt there are
> many other interesting implications of Sam's model.
>
> Many researchers, however, use fixed-effects regression on their way to
> estimating a random-effects model, both because the random-effects model is
> more efficient and because the random-effects model allows estimating
> coefficients for variables that are constant within group (country).
> To obtain these advantages, the random-effects model makes additional
> assumptions, one of them being that the fixed-effects residuals are
> uncorrelated with the fixed-effects predicted values, X*b.
>
> That corr(u_i, Xb) = .9249 reveals that the model estimated by Sam would be a
> poor condidate for estimating with -xtreg, re-.  Sam has estimated a model
> that virtually demands estimation by -xtreg, fe-, which Sam did.
>
> Thus, in answering Sam's question, "What does corr(u_i, Xb) mean?", we have
> answered a question Sam did not ask, "Could I have estimated my model
> by random-effects regression?  Should I?"
>
> -- Bill
> wgould@stata.com
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