On 8/25/06, Guido Heineck <Guido.Heineck@gmx.net> wrote:
> IMHO you don't need to bootstrap the multinomial logit either. I
> cannot really see the use of it.
I am just anticipating the referees' comments?! :-D
I'd support Jeane. The similarity here is quite superficial: you don't
really have the first step regression, so you don't have much to
correct for. Alternatively, if you had access to the original data
used in NBER, you could run a calibration regression on a bootstrap
subsample of that data, and use the results on an independent
bootstrap subsample of your own data; that would make it a valid
procedure. Otherwise, the bootstrap is no better asymptotically than
the MLE standard errors. (Feel free to use this piece in an answer to
the editor as to why you did not do the bootstrap.)
Other approaches for incorporating the first stage estimates would be:
(1) Murphy and Topel (1985), doi:10.2307/1391724. They derive an
estimator which, as far as I can recall, is a sum of two sandwich
estimators for two stages. If the full covariance matrix is reported
in the NBER paper you mentioned (I adore it personally when economists
come to social sciences and teach people what to do and what not to
do...), then you can use it to correct the standard errors. You can
even try to feed them back to Stata with -ereturn post- commands,
which you would have come across if you've written your own
estimators.
(2) Bayesian inference, where the reported results can be used as a
prior on the measurement equation. That would be a pretty complicated
model, but you can push it through with some help of Bayesian-inclined
econometricians/statisticians. Basically, this is a rigorous way to
follow up on Jeane's second suggestion.
(3) Structural equation models: you have BMI (or whatever) measured
with error, but you know the properties of the measurement error
process (SEM folks would say that you know the reliability of your
measure). See if you can find some sociologists or psychologists to
talk about your model, as they are more familiar with the types of
models I am mentioning than ecoomists are (at least in the US, the
disciplines are somewhat more interpenetrating in Europe).
Other models for estimation with the measurement error may also be
appropriate; see a recent book by Carroll, Stefanski, Ruppert and
Cianicianu -- I think those guys are known in econometric world, too.
--
Stas Kolenikov
http://stas.kolenikov.name
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