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Inference under covariate‐adaptive randomization with multiple treatments

Author

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  • Federico A. Bugni
  • Ivan A. Canay
  • Azeem M. Shaikh

Abstract

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.

Suggested Citation

  • Federico A. Bugni & Ivan A. Canay & Azeem M. Shaikh, 2019. "Inference under covariate‐adaptive randomization with multiple treatments," Quantitative Economics, Econometric Society, vol. 10(4), pages 1747-1785, November.
  • Handle: RePEc:wly:quante:v:10:y:2019:i:4:p:1747-1785
    DOI: 10.3982/QE1150
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    References listed on IDEAS

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    1. Miriam Bruhn & David McKenzie, 2009. "In Pursuit of Balance: Randomization in Practice in Development Field Experiments," American Economic Journal: Applied Economics, American Economic Association, vol. 1(4), pages 200-232, October.
    2. Esther Duflo & Pascaline Dupas & Michael Kremer, 2015. "Education, HIV, and Early Fertility: Experimental Evidence from Kenya," American Economic Review, American Economic Association, vol. 105(9), pages 2757-2797, September.
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    4. Berry, James & Karlan, Dean & Pradhan, Menno, 2018. "The Impact of Financial Education for Youth in Ghana," World Development, Elsevier, vol. 102(C), pages 71-89.
    5. Ali Hasanain & Saad Gulzar & Arman Rezaee & Yasir Khan, 2015. "Personalities and Public Sector Performance: Evidence from a Health Experiment in Pakistan," Working Papers id:6690, eSocialSciences.
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    7. Max Tabord-Meehan, 2018. "Stratification Trees for Adaptive Randomization in Randomized Controlled Trials," Papers 1806.05127, arXiv.org, revised Jan 2020.
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    Cited by:

    1. Athey, Susan & Imbens, Guido W. & Bayati, Mohsen, 2019. "Optimal Experimental Design for Staggered Rollouts," Research Papers 3837, Stanford University, Graduate School of Business.
    2. Azeem M. Shaikh, 2019. "Inference in Experiments with Matched Pairs," CeMMAP working papers CWP19/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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