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Re: st: Using the cluster command or GLS random effects?


From   Mark Schaffer <M.E.Schaffer@hw.ac.uk>
To   statalist@hsphsun2.harvard.edu, Joseph Coveney <jcoveney@bigplanet.com>
Subject   Re: st: Using the cluster command or GLS random effects?
Date   Fri, 18 Jul 2003 15:26:32 +0100 (BST)

Joseph,

Quoting Joseph Coveney <jcoveney@bigplanet.com>:

> 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: m.e.schaffer@hw.ac.uk
web: http://www.sml.hw.ac.uk/ecomes
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