Estimating Heterogeneous Bounds for Treatment Effects under Sample Selection and Non-response

In this paper we propose a method for nonparametric estimation and inference for heterogeneous bounds for causal effect parameters in general sample selection models where the initial treatment can affect whether a post-intervention outcome is observed or not. Treatment selection can be confounded by observable covariates while the outcome selection can be confounded by both observables and unobservables. The method provides conditional effect bounds as functions of policy relevant pre-treatment variables. It allows for conducting valid statistical inference on the unidentified conditional effect curves. We use a flexible semiparametric de-biased machine learning approach that can accommodate flexible functional forms and high-dimensional confounding variables between treatment, selection, and outcome processes. Easily verifiable high-level conditions for estimation and misspecification robust inference guarantees are provided as well.