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Wang and Tchetgen Tchetgen (2017) studied identification and estimation ofthe average treatment effect when some confounders are unmeasured. Under theiridentification condition, they showed that the semiparametric efficientinfluence function depends on five unknown functionals. They proposed toparameterize all functionals and estimate the average treatment effect from theefficient influence function by replacing the unknown functionals withestimated functionals. They established that their estimator is consistent whencertain functionals are correctly specified and attains the semiparametricefficiency bound when all functionals are correctly specified. In applications,it is likely that those functionals could all be misspecified. Consequentlytheir estimator could be inconsistent or consistent but not efficient. Thispaper presents an alternative estimator that does not require parameterizationof any of the functionals. We establish that the proposed estimator is alwaysconsistent and always attains the semiparametric efficiency bound. A simple andintuitive estimator of the asymptotic variance is presented, and a small scalesimulation study reveals that the proposed estimation outperforms the existingalternatives in finite samples.

A Simple and Efficient Estimation of the Average Treatment Effect in the Presence of Unmeasured Confounders