  We study the identification and estimation of long-term treatment effects
when both experimental and observational data are available. Since the
long-term outcome is observed only after a long delay, it is not measured in
the experimental data, but only recorded in the observational data. However,
both types of data include observations of some short-term outcomes. In this
paper, we uniquely tackle the challenge of persistent unmeasured confounders,
i.e., some unmeasured confounders that can simultaneously affect the treatment,
short-term outcomes and the long-term outcome, noting that they invalidate
identification strategies in previous literature. To address this challenge, we
exploit the sequential structure of multiple short-term outcomes, and develop
three novel identification strategies for the average long-term treatment
effect. We further propose three corresponding estimators and prove their
asymptotic consistency and asymptotic normality. We finally apply our methods
to estimate the effect of a job training program on long-term employment using
semi-synthetic data. We numerically show that our proposals outperform existing
methods that fail to handle persistent confounders.
