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Re: st: Comparison of robust and cluster-robust standard errors when the number of clusters is small

From   Austin Nichols <>
Subject   Re: st: Comparison of robust and cluster-robust standard errors when the number of clusters is small
Date   Fri, 4 Jan 2013 10:35:55 -0500

Tobias Pfaff <>:
As the FAQ says,
"See the manual entries [R] regress (back of Methods and Formulas),
[P] _robust (the beginning of the entry), and [SVY] variance
estimation for more details."
and see an article referenced there (and by
as well):
--Rogers 1993 is still the best intro, though the commands are all obsolete.
Also see Kish 1965
for an early explanation of one way to measure [possibly negative]
intracluster correlation of x*e, using a quantity which Kish calls roh

On Thu, Jan 3, 2013 at 11:43 AM, Tobias Pfaff
<> wrote:
> Hi all,
> The Stata FAQ explains nicely why cluster-robust standard errors
> (-vce(cluster clustvar)-) can be smaller than robust standard errors
> (-vce(robust)-):
> -option/
> The FAQ's answer is negative correlation within cluster.
> But could it be that in cases with small number of clusters this answer is
> not sufficient?
> Consider a setting with a small number of clusters (in my case 12 clusters)
> and the following standard errors:
> Ordinary (OLS) SE: .1109
> Robust SE: .1268
> Cluster-robust SE: .0414
> The literature says that an insufficient number of clusters (approximately
> less than 50) can lead to standard errors that are downward biased (e.g.,
> Cameron et al. 2008).
> Is it correct to say that my cluster-robust SE is smaller than the robust SE
> due to negative correlation within cluster OR due to downward bias of the
> cluster-robust SE in the case with few clusters?
> If the statement is correct, can I find out if one of the reasons can be
> ruled out? Can I measure the negative correlation? Or can I measure the
> downward bias due to few clusters?
> In this regard, maybe you guys have a hint for me why (mathematically) the
> SE are downward biased in the case with few clusters? I didn't find an
> answer so far in the literature.
> Any comments are appreciated!
> Thanks very much,
> Tobias
> Literature cited:
> Cameron, Gelbach, Miller (2008), Bootstrap-Based Improvements for Inference
> with Clustered Errors. The Review of Economics and Statistics, 90 (3),
> 414-427.
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