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When data are clustered, common practice has become to do OLS and use anestimator of the covariance matrix of the OLS estimator that comes close tounbiasedness. In this paper we derive an estimator that is unbiased when therandom-effects model holds. We do the same for two more general structures. Westudy the usefulness of these estimators against others by simulation, the sizeof the $t$-test being the criterion. Our findings suggest that the choice ofestimator hardly matters when the regressor has the same distribution over theclusters. But when the regressor is a cluster-specific treatment variable, thechoice does matter and the unbiased estimator we propose for the random-effectsmodel shows excellent performance, even when the clusters are highlyunbalanced.

Unbiased estimation of the OLS covariance matrix when the errors are clustered