The Informativeness of Combined Experimental and Observational Data under Dynamic Selection

This paper addresses the challenge of estimating the Average Treatment Effect on the Treated Survivors (ATETS; Vikstrom et al., 2018) in the absence of long-term experimental data, utilizing available long-term observational data instead. We establish two theoretical results. First, it is impossible to obtain informative bounds for the ATETS with no model restriction and no auxiliary data. Second, to overturn this negative result, we explore as a promising avenue the recent econometric developments in combining experimental and observational data (e.g., Athey et al., 2020, 2019); we indeed find that exploiting short-term experimental data can be informative without imposing classical model restrictions. Furthermore, building on Chesher and Rosen (2017), we explore how to systematically derive sharp identification bounds, exploiting both the novel data-combination principles and classical model restrictions. Applying the proposed method, we explore what can be learned about the long-run effects of job training programs on employment without long-term experimental data.