At What Level Should One Cluster Standard Errors in Paired Experiments, and in Stratified Experiments with Small Strata?

Abstract

In paired experiments, units are matched into pairs, and one unit of each pair is randomly assigned to treatment. To estimate the treatment effect, researchers often regress their outcome on a treatment indicator and pair fixed effects, clustering standard errors at the unit-of-randomization level. We show that the variance estimator in this regression may be severely downward biased: under constant treatment effect, its expectation equals 1/2 of the true variance. Instead, we show that researchers should cluster their standard errors at the pair level. Using simulations, we show that those results extend to stratified experiments with few units per strata.

Keywords: clustered standard errors, clustering, paired experiments, stratified experiments, randomized experiments, RCT

JEL Classification: C01, C12, C21, C9