At What Level Should One Cluster Standard Errors in Paired Experiments, and in Stratified Experiments with Small Strata?
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.
We are very grateful to Antoine Deeb, Jake Kohlhepp, Heather Royer, Dick Startz, Doug Steigerwald, Gonzalo Vasquez-Bare, members of the econometrics and labor groups at UCSB, participants of the Advances in Field Experiments Conference 2019, California Econometrics Conference 2019, LAMES 2019, and LACAE 2019 for their helpful comments. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.