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Title: A simple and efficient estimation of the average treatment effect in the presence of unmeasured confounders Authors:  Zheng Zhang - Renmin University of China (China) [presenting]
Chunrong Ai - University of Florida (United States)
Lukang Huang - Renmin University of China (China)
Abstract: Identification and estimation of the average treatment effect has been studied previously when some confounders are unmeasured. Under an identification condition, it has been shown that the semiparametric efficient influence function depends on five unknown functionals. It has been proposed to parameterize all functionals and estimate the average treatment effect from the efficient influence function by replacing the unknown functionals with estimated functionals. The proposed estimator has been established to be consistent when certain functionals are correctly specified and attains the semi-parametric efficiency bound when all functionals are correctly specified. In applications, it is likely that those functionals could all be misspecified. Consequently, the estimator could be inconsistent or consistent but not efficient. An alternative estimator is proposed which does not require parameterization of any of the functionals. We establish that the proposed estimator is always consistent and always attains the semiparametric efficiency bound. A simple and intuitive estimator of the asymptotic variance is presented, and a small scale simulation study reveals that the proposed estimation outperforms the existing alternatives in finite samples.