Identification and Bayesian inference for heterogeneous treatment effects under non-ignorable assignment condition
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We provide a sufficient condition for the identification of heterogeneous treatment effects (HTE) where the missing mechanism is nonignorable and information is available on the marginal distribution of the untreated outcome. We also show that under such a condition, the same result holds for the identification of average treatment effects (ATE). By exposing certain additivity on the regression function of the assignment probability, we reduce the identification of HTE to the uniqueness of a solution of some integral equation, and we discuss this based on the idea borrowed from the identification of nonparametric instrumental variable models. In addition, our result is extended to relax several assumptions in data fusion. We propose a quasi-Bayesian estimation method for HTE and examine its properties through a simple simulation study.
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