Kernel estimation of average treatment effects in models with unmeasured confounders

Wang and Tchetgen Tchetgen proposed a parametric estimation of average treatment effects in models with unmeasured confounders. This article presents a kernel estimation of average treatment effects for the same model and establishes their asymptotic properties. We consider three estimators: (i) the inverse probability estimator, (ii) the regression estimator, and (iii) the efficient score estimator. We show that all three estimators are asymptotically equivalent when using an under‐smoothed bandwidth. However, the first two estimators are biased, whereas the third is unbiased, when the bandwidth is cross‐validated. A small‐scale simulation study reveals that the results are consistent with the theoretical findings. To illustrate the practical value of the proposed approach, we apply it to the CFPS dataset to evaluate the causal effect of mobile internet use on the subjective well‐being of older Chinese adults.