  Combining short-term experimental data with observational data enables
credible long-term policy evaluation. The literature offers two key but
non-nested assumptions, namely the latent unconfoundedness (LU; Athey et al.,
2020) and equi-confounding bias (ECB; Ghassami et al., 2022) conditions, to
correct observational selection. Committing to the wrong assumption leads to
biased estimation. To mitigate such risks, we provide a novel bracketing
relationship (cf. Angrist and Pischke, 2009) repurposed for the setting with
data combination: the LU-based estimand and the ECB-based estimand serve as the
lower and upper bounds, respectively, with the true causal effect lying in
between if either assumption holds. For researchers further seeking point
estimates, our Lalonde-style exercise suggests the conservatively more robust
LU-based lower bounds align closely with the hold-out experimental estimates
for educational policy evaluation. We investigate the economic substantives of
these findings through the lens of a nonparametric class of selection
mechanisms and sensitivity analysis. We uncover as key the sub-martingale
property and sufficient-statistics role (Chetty, 2009) of the potential
outcomes of student test scores (Chetty et al., 2011, 2014).
