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Re: st: size of cluster robust SEs relative to regular SEs


From   David Quinn <dxquinnx@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: size of cluster robust SEs relative to regular SEs
Date   Thu, 28 Oct 2010 14:34:15 -0400

Thanks again, Stas.  I fear that this small N problem is really
trapping me, then.

I do notice that the most significant amount of fluctuation in
directionality occurs with a suite of dummy variables that were
constructed out of a categorical variable, wherein I excluded all but
one of the dummies to prevent perfect collinearity.  Hence, by their
nature, each of the dummies in the suite contain more zeroes than
ones.  Not sure if the fluctuation in that regard is natural or not.

On Thu, Oct 28, 2010 at 11:21 AM, Stas Kolenikov <skolenik@gmail.com> wrote:
> On Thu, Oct 28, 2010 at 11:08 AM, David Quinn <dxquinnx@gmail.com> wrote:
>> I do only have two dozen clusters, so perhaps that is driving the
>> issue. Maybe I am misunderstanding something, but I thought that if
>> this was the case, the cluster robust standard errors would all be
>> biased in the same way.  And by that I mean that all of the cluster
>> robust standard errors would either be: A.) Smaller than the regular
>> standard errors, or B.) Larger than the regular standard errors but
>> not as large as they should be.  Hence, they would be exhibiting
>> downward bias. But maybe I am wrong.
>>
>> Anyhow, if it is a case of intra-cluster correlation that is driving
>> the issue instead, I am not sure what could be causing the alternating
>> change in directions, since the pattern is not consistent across all
>> regressors. Maybe it is a case of a mix of negative ICCs and positive
>> ICCs canceling each other out?
>
> Something like that. You have an interplay of the regression error
> ICCs, regressor ICCs, and the ICCs of the combination x'e (while
> E[x'e] = 0, it is a random vector with its own covariance). Depending
> on the magnitudes of those ICCs and the severity of the small sample
> issues, it can go either way. With larger # of clusters, you would
> expect the standard errors to go up.
>
> --
> Stas Kolenikov, also found at http://stas.kolenikov.name
> Small print: I use this email account for mailing lists only.
>
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