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Experiments that use covariate adaptive randomization (CAR) are commonplacein applied economics and other fields. In such experiments, the experimenterfirst stratifies the sample according to observed baseline covariates and thenassigns treatment randomly within these strata so as to achieve balanceaccording to pre-specified stratum-specific target assignment proportions. Inthis paper, we compute the semiparametric efficiency bound for estimating theaverage treatment effect (ATE) in such experiments with binary treatmentsallowing 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 thoseused in practice. The stratum-specific target proportions play the role of thepropensity score conditional on all baseline covariates (and not just thestrata) in these experiments. Thus, the efficiency bound is a special case ofthe bound in Hahn (1998), but conditional on all baseline covariates.Additionally, this efficiency bound is shown to be achievable under the sameconditions as those used to derive the bound by using a cross-fittedNadaraya-Watson kernel estimator to form nonparametric regression adjustments.

Efficient Semiparametric Estimation of Average Treatment Effects Under Covariate Adaptive Randomization