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

63 Pages Posted: 10 Feb 2020 Last revised: 2 May 2022

See all articles by Clément de Chaisemartin

Clément de Chaisemartin

SciencesPo - Sciences Po - Department of Economics

Jaime Ramirez-Cuellar

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

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Date Written: May 5, 2021

Abstract

In clustered paired experiments, randomization units, say villages, 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 the treatment 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, researchers should cluster at the pair level. Using simulations, we show that those results extend to clustered 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 and Small-Strata Experiments? (May 5, 2021). Available at SSRN: https://ssrn.com/abstract=3520820 or http://dx.doi.org/10.2139/ssrn.3520820

Clément De Chaisemartin

SciencesPo - Sciences Po - Department of Economics ( email )

28, rue des Saints-Pères
Paris, Paris 75007
France

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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