Abstract

This paper considers the case where instrumental variable (IV) are available to infer the effect of interested variable to the outcome (or the causal effect), but some components of IV are missing with the missing mechanism of not missing at random (NMAR). Although NMAR requires the analysis to prespecify the missing mechanism, it is unknown for us and what is worse, it is generally not identified. We use the IV distribution of original population as an auxiliary information, and show that missing mechanism can be represented as identifiable nonparametric generalized additive model. We also introduce MCMC algorithm that impute the missing values and simultaneously estimate parameters of interest.