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.

翻译：我们提出了一种方法，用于在一般样本选择模型中对异质性因果效应参数进行边界估计与推断，其中处理变量可能影响结果是否被观测到，且不存在可用的排他性约束条件。该方法提供了以政策相关的预处理变量为函数的条件效应边界，允许对未识别的条件效应进行有效统计推断。我们采用灵活的去偏/双机器学习方法，能够处理非线性函数形式和高维混杂因素。此外，本文还提供了易于验证的高阶条件用于估计、对误设稳健的置信区间以及均匀置信带。通过重新分析Facebook大规模现场实验数据，我们发现反态度新闻订阅推送具有显著的去极化效应。效应边界表现出高度异质性，表明对温和派、保守派及年轻用户存在强烈的去极化效果。