Identifiability of the instrumental variable model with the treatment and outcome missing not at random

Music City Center 

The instrumental variable model of Imbens and Angrist (1994) and Angrist et al. (1996) allow for the identification of the local average treatment effect, also known as the complier average causal effect. However, many empirical studies are challenged by the missingness in the treatment and outcome. When the treatment and outcome are missing not at random (MNAR), the CACE is in general not identifiable because the underlying data distribution can not be identified without further assumptions. We study the identifiability of the CACE even when the treatment and outcome are MNAR. Through an exhaustive search, we identify all MNAR mechanisms that enable the identification of the CACE without the need for auxiliary information. This is achieved under the following two scenarios: (1) when missing data are present exclusively in either the treatment or the outcome, and (2) when missing data occur in both the treatment and outcome in the context of prospectively collected data. We review the existing results and obtain many new results to complete the discussion.

MNAR

instrumental variable