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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