Instrumental Variable-based Identification for Causal Effects using Covariate Information

This paper deals with the identification problem of causal effects in randomized trials with noncompliance. In this problem, generally, causal effects are not identifiable and thus have been evaluated under some strict assumptions, or through the bounds. Different from existing studies, we propose a novel identification condition of joint probabilities of potential outcomes, which allows us to derive a consistent estimator of the causal effect. Regarding the identification conditions of joint probabilities of potential outcomes, the assumptions of monotonicity (Pearl 2009), independence between potential outcomes (Robins and Richardson 2011), gain equality (Li and Pearl 2019) and specific functional relationships between cause and effect (Pearl 2009) have been utilized. In contrast, without such assumptions, the proposed condition enables us to evaluate joint probabilities of potential outcomes using an instrumental variable and a proxy variable of potential outcomes. The result of the present paper extends the range of solvable identification problems in causal inference.