I have a sample with little over 100 observations and 50 clusters, one quarter of which have only one observation. Is it correct to calculate clustered standard errors in a linear regression that uses this data or are there some requirements for minimum cluster size and sample size that I am violating? Any references in support of answers provided would be great!
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Angrist and Pischke's Mostly Harmless Econometrics semi-jokingly gives the number of 42 as the minimum number of clusters for which the method works. Jeff Wooldridge had a review of clustered standard errors published in AER, he might be mentioning some other considerations there. A concise presentation on many issues surrounding clustered standard errors was given at 2007 Stata User Group meeting by Austin Nichols and Mark Schaffer.
A small number of observations within a cluster will lead to problems if you need to estimate the within-cluster variability, but if that is not of your interest, you should be good with what you have. This seems like an awkward design, at any rate. No survey statistician would intentionally design a survey with one observation per cluster. It may also be that you are worrying about a cluster effect that is non-existent, like you decided to cluster on something post-hoc as this seemed like a good idea. "These days, everybody is clustering on state". Or on school. Or on the day of the week. Or on the color of the individual's hair. If the tool is out there, it does not mean it should be applied to every problem: if you have a hammer in your hand, all problems look like nails to you. A test for clustering effects, akin to White's heteroskedasticity test, is mentioned in the above presentation by Nichols and Schaffer (2007).
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$\begingroup$ StasK, thank you for the answer and the references. I have another question, related to this one, but also to the answer you gave on August 10 to the question "When to use Student's or Normal distribution in linear regression?". There you imply that in the presence of clustered standard errors, one should use the normal, rather than the t-distribution for testing hypotheses about population parameters. Why then do software packages report "t-values" and probabilities in the output of regressions with cluster option? And one more question: can you test that a cluster-effect is not present? $\endgroup$– ChrisCommented Oct 4, 2011 at 18:59
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$\begingroup$ Using t-distribution rather than z-distribution is rooted in a common (and not unreasonable) belief that t-distributions work better with finite samples. I have seen examples in survey statistics where in inference for the mean problem, you can arrive at t-distribution with clustered standard errors exactly. (You probably need balanced cluster sizes both in the sample and in the population, and equal variances across clusters, but don't quote me on that.) As for the tests, see my update on presentation materials where the test is discussed. Try searching for it on RePEc to see if it came out. $\endgroup$– StasKCommented Oct 4, 2011 at 20:44