At What Level Should One Cluster Standard Errors in Paired and Small-Strata Experiments?

Abstract

In matched-pairs experiments in which one cluster per pair of clusters is assigned to treatment, to estimate treatment effects, researchers often regress their outcome on a treatment indicator and pair fixed effects, clustering standard errors at the unit-ofrandomization level. We show that even if the treatment has no effect, a 5%-level t-test based on this regression will wrongly conclude that the treatment has an effect up to 16.5% of the time. To fix this problem, researchers should instead cluster standard errors at the pair level. Using simulations, we show that similar results apply to clustered experiments with small strata.