Working Paper: NBER ID: w27609
Authors: Clément de Chaisemartin; Jaime Ramirezcuellar
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; Paired experiments; Stratified experiments; Statistical inference
JEL Codes: C01; C21
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Incorrect clustering methods (C38) | Bias introduced in treatment effect estimation (C21) |
| Clustering standard errors at the unit-of-randomization level (C38) | Downward biased variance estimator (C51) |
| Pair-clustered variance estimator (C59) | Unbiased variance of treatment coefficient (C21) |
| Using pair-clustered standard errors (C21) | Decrease in significant effects found at the 5% level (C29) |
| Stratum-clustered variance estimators (C21) | Maintain correct size in hypothesis testing (C12) |