We propose a method for estimation and inference for bounds for heterogeneous causal effect parameters in general sample selection models where the treatment can affect whether an outcome is observed and no exclusion restrictions are available. 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 effects. We use a flexible debiased/double machine learning approach that can accommodate non-linear functional forms and high-dimensional confounders. Easily verifiable high-level conditions for estimation, misspecification robust confidence intervals, and uniform confidence bands are provided as well. Re-analyzing data from a large scale field experiment on Facebook, we find significant depolarization effects of counter-attitudinal news subscription nudges. The effect bounds are highly heterogeneous and suggest strong depolarization effects for moderates, conservatives, and younger users.

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