On 7/27/06, Schaffer, Mark E <M.E.Schaffer@hw.ac.uk> wrote:
The intuition isn't hard: sigma_u=0 means no variance in the cohort
effect, which means they all have the same intercept, which means ...
OLS.
Different random-effects estimators will give you different estimates of
sigma_u. Try the others (sa and ml options) and see what you get.
Black Wooldridge gives three or four of those estimators, including
those that are guaranteed to be positive.
An estimate equal to zero may not necessarily mean that the population
value is equal to zero; that's only an estimate, in the end. E.g. if
the true variance were a small but positive number, the sampling
variability around it (asymptotically normal near the population mean,
and some non-trivial variance) may have support below zero, in which
case the panel estimators would constrain it to be zero, to make any
sense. If, on the other hand, it were exactly zero, you would need to
work out through the literature about estimation on the boundary (a
bunch of papers by Andrews in Econometrica in early 2000s is the best
set of references, at this point); at the very least see -help
j_chibar-.
My experience with structural equation models, where negative error
variance estimates are pretty common, suggests that there might be
some model misspecifications, too, when the population value of the
parameter is actually negative, because of an improperly specified
structure of the model. So by steering away from zero/negative error
variances, you may miss an important message the data, along with the
estimation procedure, are trying to tell you about your model.
--
Stas Kolenikov
http://stas.kolenikov.name
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