  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. We re-analyze data from a large
scale field experiment on Facebook on counter-attitudinal news subscription
with attrition. Our method yields substantially tighter effect bounds compared
to conventional methods and suggests depolarization effects for younger users.
