Joseph,
Quoting Joseph Coveney <[email protected]>:
> Mark Schaffer followed-up Buzz Burhans's response to a question
> about the
> differences between -xtreg, re- and -regress , cluster()-. Mark
> brought up
> differences in consistency and efficiency between the two methods.
> Excerpting
> Mark's post:
>
> --------------------------------------------------------------------------
------
>
> Trade offs:
>
> -xtreg- gives you more efficient estimates if your modelling of the
>
> correlation caused by clustering is correct. If it isn't, your
> coeffs and
> SEs are wrong.
>
> -regress- with -cluster- gives you consistent estimates across a
> broad
> range of possible forms of the correlation, but they won't be as
> efficient
> as when you know the exact form (and you're right).
>
> --------------------------------------------------------------------------
------
>
>
> I have a follow-up question on consistency: random effects
> regression gives
> inconsistent results when there is substantial correlation between a
> fixed-
> effect regressor and the random effect; will -regress , cluster()-
> overcome
> this liability and provide consistent estimators when there is a
> correlation
> between a regressor and an (un-modeled) random effect? As an
> extension, if you
> get a significant Hausman test after -xtreg , re-, would a
> reasonable back-up
> approach--albeit taking a hit in efficiency--be to resort to
> -regress ,
> cluster()-?
>
> Joseph Coveney
Well spotted! In fact, I think my earlier posting was inaccurate. The
argument I presented was correct (I hope!) for cluster-robust OLS vs.
random effects GLS. I mentioned fixed effects in passing, but shouldn't
have.
The case of cluster-robust OLS vs. fixed effects is different. One way to
see this is to point out that -areg, absorb(id) cluster(id)- estimates a
cluster-robust fixed-effects model, where the fixed effects and the
clustering are based on the same grouping of observations (id in this
case). What's the consistency-efficiency trade-off here?
-regress, cluster(id)- can still give you consistent coeffs and SEs in the
presence of intra-group correlation, but not when the individual-specific
effect is correlated with the general error term u (i.e., there's an
endogeneity problem). It is not only consistent but also efficient if the
individual-specific effects are in fact zeros. Makes sense - if the
individual-specific effects aren't there, you don't lose by leaving them
out.
-areg, absorb(id) cluster(id)- also gives you consistent coeffs and SEs in
the presence of intra-group correlation. As Joseph points out, it will
still give you consistent estimates even if the individual-specific effects
are correlated with u. However, if the individual-specific effects are in
fact zeros, then it's less efficient than -regress-, basically because you
waste information trying to accommodate something (the indiv-specific
effects) when they aren't actually there.
...I think I've got it right this time around!
BTW, -xtreg- doesn't allow use of the -cluster- option, which is why -areg-
is needed. The Stata 7 description of -areg- says "See the command xtreg,
fe in help xtreg for an improved version of areg", but in this respect
-areg- is superior.
--Mark
>
>
>
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>
Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3008
email: [email protected]
web: http://www.sml.hw.ac.uk/ecomes
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