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

49 Pages Posted: 10 Feb 2020 Last revised: 16 Sep 2020

See all articles by Clément de Chaisemartin

Clément de Chaisemartin

University of California, Santa Barbara (UCSB) - Department of Economics

Jaime Ramirez-Cuellar

University of California, Santa Barbara (UCSB) - Department of Economics

Multiple version iconThere are 2 versions of this paper

Date Written: September 15, 2020

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

Suggested Citation

de Chaisemartin, Clément and Ramirez-Cuellar, Jaime, At What Level Should One Cluster Standard Errors in Paired Experiments, and in Stratified Experiments with Small Strata? (September 15, 2020). Available at SSRN: https://ssrn.com/abstract=3520820 or http://dx.doi.org/10.2139/ssrn.3520820

Clément De Chaisemartin

University of California, Santa Barbara (UCSB) - Department of Economics ( email )

2127 North Hall
Santa Barbara, CA 93106
United States

Jaime Ramirez-Cuellar (Contact Author)

University of California, Santa Barbara (UCSB) - Department of Economics ( email )

2127 North Hall
Santa Barbara, CA 93106
United States

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