  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.
