Identification and estimation of causal effects with confounders subject to instrumental missingness

Drawing causal inference from unconfounded observational studies is of great importance, which, however, is jeopardized if the confounders are subject to missingness. Generally, it is impossible to identify causal effects if the confounders are missing not at random. In this paper, we propose a novel framework to nonparametrically identify the causal effects with confounders missing not at random, but subject to instrumental missingness, that is, the missing data mechanism is independent of the outcome, given the treatment and possibly missing confounder values. The average causal effect is then estimated using a nonparametric two-stage least squares estimator based on series approximation.