Identification of heterogeneous treatment effects as a function of potential untreated outcome under the nonignorable assignment condition

JELコード : C13,C31,C83

We provide sufficient conditions for the identification of hetero-geneous treatment effects (HTE), in which the missing mechanism is nonignorable, when the information on the marginal distribution of untreated outcome is available. It is also shown that, under such a situ-ation, the same result holds for the identification of average treatment effects (ATE). Exposing certain additivity on the regression function of the assignment probability, we reduce the identication of HTE to the uniqueness of a solution of some integral equation, and discuss it borrowing the idea from the literature on statistical inverse prob-lems. Our result contributes to theoretical understandings in causal inference with heterogeneity and also the relaxation of the conditional independence assumption in statistical data fusion or statistical data combination.