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Efficient Semiparametric Estimation of Average Treatment Effects Under Covariate Adaptive Randomization

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  • Ahnaf Rafi

Abstract

Experiments that use covariate adaptive randomization (CAR) are commonplace in applied economics and other fields. In such experiments, the experimenter first stratifies the sample according to observed baseline covariates and then assigns treatment randomly within these strata so as to achieve balance according to pre-specified stratum-specific target assignment proportions. In this paper, we compute the semiparametric efficiency bound for estimating the average treatment effect (ATE) in such experiments with binary treatments allowing for the class of CAR procedures considered in Bugni, Canay, and Shaikh (2018, 2019). This is a broad class of procedures and is motivated by those used in practice. The stratum-specific target proportions play the role of the propensity score conditional on all baseline covariates (and not just the strata) in these experiments. Thus, the efficiency bound is a special case of the bound in Hahn (1998), but conditional on all baseline covariates. Additionally, this efficiency bound is shown to be achievable under the same conditions as those used to derive the bound by using a cross-fitted Nadaraya-Watson kernel estimator to form nonparametric regression adjustments.

Suggested Citation

  • Ahnaf Rafi, 2023. "Efficient Semiparametric Estimation of Average Treatment Effects Under Covariate Adaptive Randomization," Papers 2305.08340, arXiv.org.
    • Handle: RePEc:arx:papers:2305.08340
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    References listed on IDEAS

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    1. Jinyong Hahn & Keisuke Hirano & Dean Karlan, 2011. "Adaptive Experimental Design Using the Propensity Score," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 96-108, January.
    2. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(3), pages 726-748, June.
    3. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Kato, Kengo, 2015. "Some new asymptotic theory for least squares series: Pointwise and uniform results," Journal of Econometrics, Elsevier, vol. 186(2), pages 345-366.
    4. Michael Kohler, 2002. "Universal Consistency of Local Polynomial Kernel Regression Estimates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(4), pages 879-899, December.
    5. Komunjer, Ivana & Vuong, Quang, 2010. "Semiparametric Efficiency Bound In Time-Series Models For Conditional Quantiles," Econometric Theory, Cambridge University Press, vol. 26(2), pages 383-405, April.
    6. Max Tabord-Meehan, 2023. "Stratification Trees for Adaptive Randomisation in Randomised Controlled Trials," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(5), pages 2646-2673.
    7. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, February.
    8. 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.
    9. Rothe, Christoph & Firpo, Sergio, 2019. "Properties Of Doubly Robust Estimators When Nuisance Functions Are Estimated Nonparametrically," Econometric Theory, Cambridge University Press, vol. 35(5), pages 1048-1087, October.
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    Cited by:

    1. Yuehao Bai & Azeem M. Shaikh & Max Tabord-Meehan, 2024. "A Primer on the Analysis of Randomized Experiments and a Survey of some Recent Advances," Papers 2405.03910, arXiv.org, revised Apr 2025.
    2. Yuehao Bai & Jizhou Liu & Azeem M. Shaikh & Max Tabord-Meehan, 2023. "On the Efficiency of Finely Stratified Experiments," Papers 2307.15181, arXiv.org, revised Nov 2025.
    3. Undral Byambadalai & Tomu Hirata & Tatsushi Oka & Shota Yasui, 2025. "Beyond the Average: Distributional Causal Inference under Imperfect Compliance," Papers 2509.15594, arXiv.org, revised Oct 2025.

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