Quantitative Economics
Journal Of The Econometric Society
Edited by: Stéphane Bonhomme • Print ISSN: 1759-7323 • Online ISSN: 1759-7331
Edited by: Stéphane Bonhomme • Print ISSN: 1759-7323 • Online ISSN: 1759-7331
Quantitative Economics: Nov, 2019, Volume 10, Issue 4
Federico A. Bugni, Ivan A. Canay, Azeem M. Shaikh
This paper studies inference in randomized controlled trials with covariate‐adaptive randomization when there are multiple treatments. More specifically, we study in this setting inference about the average effect of one or more treatments relative to other treatments or a control. As in Bugni, Canay, and Shaikh (2018), covariate‐adaptive randomization refers to randomization schemes that first stratify according to baseline covariates and then assign treatment status so as to achieve “balance” within each stratum. Importantly, in contrast to Bugni, Canay, and Shaikh (2018), we not only allow for multiple treatments, but further allow for the proportion of units being assigned to each of the treatments to vary across strata. We first study the properties of estimators derived from a “fully saturated” linear regression, that is, a linear regression of the outcome on all interactions between indicators for each of the treatments and indicators for each of the strata. We show that tests based on these estimators using the usual heteroskedasticity‐consistent estimator of the asymptotic variance are invalid in the sense that they may have limiting rejection probability under the null hypothesis strictly greater than the nominal level; on the other hand, tests based on these estimators and suitable estimators of the asymptotic variance that we provide are exact in the sense that they have limiting rejection probability under the null hypothesis equal to the nominal level. For the special case in which the target proportion of units being assigned to each of the treatments does not vary across strata, we additionally consider tests based on estimators derived from a linear regression with “strata fixed effects,” that is, a linear regression of the outcome on indicators for each of the treatments and indicators for each of the strata. We show that tests based on these estimators using the usual heteroskedasticity‐consistent estimator of the asymptotic variance are conservative in the sense that they have limiting rejection probability under the null hypothesis no greater than and typically strictly less than the nominal level, but tests based on these estimators and suitable estimators of the asymptotic variance that we provide are exact, thereby generalizing results in Bugni, Canay, and Shaikh (2018) for the case of a single treatment to multiple treatments. A simulation study and an empirical application illustrate the practical relevance of our theoretical results.
Covariate‐adaptive randomization multiple treatments stratified block randomization Efron's biased‐coin design treatment assignment randomized controlled trial strata fixed effects saturated regression C12 C14
March 5, 2024
The terms of the Editors of the Econometric Society's three journals end June 30, 2025. We are pleased to announce the incoming Editors and to thank the outgoing Editors for their excellent and continuing service.
Econometrica: Since 2019, Guido Imbens has served as the 14th Editor of Econometrica. On July 1, 2025, Marina Halac will become the Editor.
Quantitative Economics: Stéphane Bonhomme has been the Editor of Quantitative Economics since 2021. His successor will be Bernard Salanié.
Theoretical Economics: The Editor of Theoretical Economics since 2021 has been Simon Board. Taking over for him in July 2025 will be Federico Echenique.
Guido, Stéphane, and Simon have been outstanding Editors. We are grateful to them for the work they have done and will continue to do, and we look forward to further congratulating them next year. We believe Marina, Bernard, and Federico will be outstanding successors and we thank them in advance for their service.
Finally, we are grateful to Larry Samuelson for chairing all three search committees, and we thank the search committee members for their hard and fruitful work:
Econometrica: Christian Dustmann, Lars Hansen, Alessandro Lizzeri, George Mailath, Ariel Pakes, Helene Rey, and Elie Tamer.
QE: Kate Ho, Michael Keane, Felix Kubler, Whitney Newey, and Frank Schorfheide.
TE: Jeff Ely, Johannes Horner, Gilat Levy, Meg Meyer, and Ran Spiegler.