RE: st: appropriateness of cluster option with xtreg, fe

["Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>]

Jason et al.,

> -----Original Message-----
> From: Austin Nichols [mailto:austinnichols@gmail.com] 
> Sent: Monday, September 25, 2006 3:38 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: appropriateness of cluster option with xtreg, fe
> 
> Jason et al.--
> 
> I agree with Johannes that fixed effects and clustering 
> address related but separate concerns, and I think Mark 
> Schaffer could usefully weigh in on the smaller-sample 
> properties of clustering and fixed-effects estimation in an 
> IV regression (it seems OK, in short, and you can test 
> "enough" even when a test of the overall model is infeasible, 
> because there are more coefficients than degrees of freedom 
> when the number of clusters is the same as the number of 
> fixed effects).

Just to follow up on Austin's suggestion - yes, the cluster-robust estimator is useable with fixed effects, and indeed, as Johannes implies, is pretty standard in this literature.  For the asymptotics to kick in, the number of clusters needs to go off to infinity, but the count starts at 1 and not at, e.g., the number of fixed effects or regressors.  The little evidence that I've seen is that you can (not necessarily will!) start getting reasonable results even with a modest number of clusters (say, 50).

It's also worth adding that Stock and Watson, in an important little paper that appeared earlier this year, showed that the standard heteroskedasticity-robust estimator, available in Stata with the -robust- option, is inconsistent for the fixed effects estimator.  Interestingly, the problem does not extend to the cluster-robust estimator, which is also heteroskedasticity-robust.  Thus, if you are doing fixed effects and want your SEs to be robust to heteroskedasticity, you should avoid -robust- and use -cluster()- instead, and get SEs that are robust to both heteroskedasticity as well was intra-group correlation.

HTH,
Mark

James H. Stock, Mark W. Watson (2006), "Heteroskedasticity-Robust Standard Errors for Fixed Effects Panel Data Regression", NBER Technical Working Paper No. 323.
http://www.nber.org/papers/T0323

> But the second paragraph of Johannes' email seems to imply 
> you should "always cluster your standard error on the same 
> level on which you would use fixed effects" which is not the 
> case.  For example, if you observed individuals (who didn't 
> move) over time, and you regressed their outcomes on 
> county-level variables, you might want to include fixed 
> effects for individual people, but cluster on the county 
> level (accounting for the intra-county clustering of errors 
> over time and people).
> 
> A useful treatment for the general case is "Robust Standard 
> Error Estimation in Fixed-Effects Panel Models,"
> by G�bor K�zdi (sometimes Gabor Kezdi), originally published 
> as a working paper in about 2001, and usually cited that way, 
> but now with a publication date of 2004, and a ridiculously long URL:
> http://portal.ksh.hu/pls/portal/docs/PAGE/STATSZEMLE/STATSZEML
> E_ARCHIVUM/2004_ARCHIVUM/2004_SPECIAL_S9_ARCHIVUM/KEZDI.PDF
> but available here for a limited time:
> http://tinyurl.com/l8vbg
> 
> Another frequently cited source is
> Arellano (1987). "Computing robust standard errors for 
> within-groups estimators." Oxford Bulletin of Economics and 
> Statistics. Vol. 49. No.
> 4. p. 431-434
> 
> On 9/24/06, Johannes Schmieder <jfs2106@columbia.edu> wrote:
> <snip>
> > I would say that in applied microeconometricians it is very much 
> > standard today to always cluster your standard error on the 
> same level 
> > on which you would use fixed effects. Of course if you use several 
> > fixed effects (e.g. in an education framework you might have grade, 
> > school and year fixed effects) you have to put some 
> thinking into the 
> > question on which level it is best to cluster. Generally it is not 
> > only fine to use FE and cluster together, I would go as far 
> as saying 
> > that not doing it is a bit fishy. I think this trend in 
> economics is 
> > only a couple of years old when a paper by duflo, bertrand and 
> > mullainathan pointed out the severity of this problem. 
> Maybe in other 
> > disciplines this is not (yet) standard.
> >
> > best, Johannes
> 
> 

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