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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