  It is important to draw causal inference from observational studies, which,
however, becomes challenging if the confounders have missing values. Generally,
causal effects are not identifiable if the confounders are missing not at
random. We propose a novel framework to nonparametrically identify causal
effects with confounders subject to an outcome-independent missingness, that
is, the missing data mechanism is independent of the outcome, given the
treatment and possibly missing confounders. We then propose a nonparametric
two-stage least squares estimator and a parametric estimator for causal
effects.

Methodology