Semiparametric Bayesian Instrumental Variables Estimation for Nonignorable Missing Instruments
This paper considers the case where instrumental variable (IV) are available to infer the e¤ect of interested variable to the outcome (or the causal e¤ect), 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 identi ed. We use the IV distribution of original population as an auxiliary information, and show that missing mechanism can be represented as identi able nonparametric generalized additive model. We also introduce MCMC algorithm that impute the missing values and simultaneously estimate parameters of interested.
Instrumental variable; Missing not at random; Auxiliary information
Research Institute for Economics and Business Administration
Rokkodai-cho, Nada-ku, Kobe
Department of Economics, Keio University
RIKEN Center for Advanced Intelligence Project