Tuesday, March 14, 2006
Re: st: Fixed Effect Estimation Results
Sam Rawlings <firstname.lastname@example.org> 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?"
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