NBER Program Affiliations: ED
NBER Affiliation: Faculty Research Fellow
Institutional Affiliation: University of California at Santa Barbara
|At What Level Should One Cluster Standard Errors in Paired Experiments, and in Stratified Experiments with Small Strata?|
with : w27609
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.
|Estimating the Effect of Treatments Allocated by Randomized Waiting Lists.|
with : w26282
Oversubscribed treatments are often allocated using randomized waiting lists. Applicants are ranked randomly, and treatment offers are made following that ranking until all seats are filled. To estimate causal effects, researchers often compare applicants getting and not getting an offer. We show that those two groups are not statistically comparable. Therefore, the estimator arising from that comparison is inconsistent when the number of waitlists goes to infinity. We propose a new estimator, and show that it is consistent, provided the waitlists have at least two seats. Finally, we revisit an application, and we show that using our estimator can lead to significantly different results from those obtained using the commonly used estimator.
|Two-way Fixed Effects Estimators with Heterogeneous Treatment Effects|
with : w25904
Linear regressions with period and group fixed effects are widely used to estimate treatment effects. We show that they identify weighted sums of the average treatment effects (ATE) in each group and period, with weights that may be negative. Due to the negative weights, the linear regression estimand may for instance be negative while all the ATEs are positive. In two articles that have used those regressions, half of the weights are negative. We propose another estimator that solves this issue. In one of the articles we revisit, it is of a different sign than the linear regression estimator.