Sample selection models are a widely used approach for correcting bias caused by data that are missing not at random. Their formulation requires specifying the variables that influence the outcome and those that drive the selection process. This specification is often based on expert knowledge, which can result in the inclusion of irrelevant variables or the omission of important ones. Moreover, to avoid inferential problems such as practical non-identifiability, practitioners frequently impose exclusion restrictions, that is, model specifications in which certain variables predict selection but have no effect on the outcome of interest. A recent proposal employs adaptive LASSO to select the variables that enter into the outcome and selection equations, but its performance depends on the so-called covariance assumption, which can be violated in small to moderate samples. To address these challenges, we propose two families of spike-and-slab priors to conduct Bayesian variable selection in sample selection models. These prior structures allow for constructing a Gibbs sampler with tractable conditionals, which is scalable to the dimensions of practical interest. We illustrate the performance of the proposed methodology through a simulation study and present a comparison against adaptive LASSO and stepwise selection. We also provide two applications using publicly available real data.

翻译：样本选择模型是纠正非随机缺失数据所引起偏差的常用方法。该模型的构建需要指定影响结果变量和驱动选择过程的变量集合，而这种指定通常依赖专家知识，可能导致纳入无关变量或遗漏重要变量。此外，为规避实际非可识别性等推理问题，研究者常施加排除限制条件，即特定变量仅预测选择过程而无关结果变量。现有研究采用自适应LASSO选择结果方程与选择方程中的变量，但其性能依赖于协方差假设，这在中小样本条件下可能无法满足。针对这些挑战，我们提出两类尖峰-平板先验结构，用于实现样本选择模型中的贝叶斯变量选择。这些先验结构可构建具有可处理条件分布的吉布斯采样器，且能扩展至实际应用所需的维度规模。通过模拟研究验证所提方法的性能，并与自适应LASSO及逐步选择方法进行对比，同时基于公开真实数据提供两项应用实例。