The informativeness of combined experimental and observational data under dynamic selection

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.