Abstract: This paper presents a simple and efficient estimation of the average treatment effect (ATE) and local average treatment effect (LATE) in models with unmeasured confounders. In contrast to existing studies that estimate some unknown functionals in the influence function either parametrically or semiparametrically, we do not model the influence function nonparametrically. Instead, we apply the calibration method to a growing number of moment restrictions to estimate the weighting functions nonparametrically, and then estimate the ATE and LATE by substitution. The calibration method is similar to the covariate-balancing method in that both methods exploit the moment restrictions. The difference is that the calibration method imposes the sample analogue of the moment restrictions, whereas the covariate-balancing method does not. A simulation study reveals that our estimators have good finite-sample performance and outperform existing alternatives. An application to an empirical analysis of return to education illustrates the practical value of the proposed method.

Key words and phrases: Average treatment effect, endogeneity, local average treatment effect, semiparametric efficiency, unmeasured confounders.