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.

翻译：本文提出了一种在一般样本选择模型中对异质性因果效应参数边界进行估计与推断的方法，其中处理可能影响观测结果是否被观测到，且不存在可用的排他性约束。该方法提供了作为政策相关预处理变量函数的条件效应边界。它允许对未识别的条件效应进行有效的统计推断。我们采用一种灵活的纠偏/双重机器学习方法，能够适应非线性函数形式和高维混杂因子。同时提供了易于验证的估计高阶条件、对错误设定稳健的置信区间以及一致置信带。我们重新分析了Facebook上一项关于反态度新闻订阅的大规模现场实验数据（存在样本流失问题）。与传统方法相比，我们的方法产生了显著更紧的效应边界，并表明对年轻用户存在去极化效应。