The informativeness of combined experimental and observational data under dynamic selection
中文摘要
处理组幸存者平均处理效应(Average Treatment Effect on the Treated Survivors, ATETS; Vikström et al., 2018)刻画了时变处理与动态选择进入幸存者群体的复合效应。我们研究在缺乏长期实验数据的情况下识别这一处理效应参数的问题,转而利用可获得的长期观测数据。这在实践中构成一个不小的挑战,因为动态选择会加剧观测数据中的静态选择。我们建立了两个理论结果。第一,若没有模型约束或辅助数据,便不可能得到有信息量的界。第二,为扭转这一否定性结果,我们考察了实验数据与观测数据相结合的计量经济学最新进展(如 Athey et al., 2025; 2024),将其视为一条有前景的路径;我们发现,在不施加经典模型约束的情况下,利用短期实验数据也能提供有信息量的结果。在 Chesher and Rosen (2017) 的基础上,我们进一步探讨如何系统地推导尖锐识别界,同时借助新颖的数据组合原则与经典模型约束。本文还给出了估计与推断程序。应用所提出的方法,我们考察了在缺乏长期实验数据的情况下,能够就职业培训项目对就业的长期效应了解到什么。
Abstract
The Average Treatment Effect on the Treated Survivors (ATETS; Vikström et al., 2018) captures a composite effect of time-varying treatment and dynamic selection into the survivor population. We address the problem of identifying this treatment-effect parameter in the absence of long-term experimental data, utilizing available long-term observational data instead. This poses a nontrivial challenge in practice, as dynamic selection compounds static selection in observational data. We establish two theoretical results. First, it is impossible to obtain informative bounds without model restrictions or auxiliary data. Second, to overturn this negative result, we explore the recent econometric developments in combining experimental and observational data (e.g., Athey et al., 2025; 2024) as a promising avenue; we find that exploiting short-term experimental data can be informative without imposing classical model restrictions. Building on Chesher and Rosen (2017), we further explore how to systematically derive sharp identification bounds, leveraging both novel data-combination principles and classical model restrictions. Estimation and inference procedures are also provided. Applying the proposed method, we investigate what can be learned about the long-run effects of job training programs on employment in the absence of long-term experimental data.