Bias of the regression estimator for experiments using clustered random assignment

This paper shows that regression may be biased for cluster randomized experiments. For one application bias tends to zero when the number of clusters is large but for another, regression is not consistent. Results underscore Freedman’s [Freedman D.A., 2008. On regression adjustments to experimental data. Advances in Applied Mathematics 40, 180–193] insight that randomization does not justify regression assumptions.