  In many experiments and observational studies, the outcome of interest is
often difficult or expensive to observe, reducing effective sample sizes for
estimating average treatment effects (ATEs) even when identifiable. We study
how incorporating data on units for which only surrogate outcomes not of
primary interest are observed can increase the precision of ATE estimation. We
refrain from imposing stringent surrogacy conditions, which permit surrogates
as perfect replacements for the target outcome. Instead, we supplement the
available, albeit limited, observations of the target outcome (which by
themselves identify the ATE) with abundant observations of surrogate outcomes,
without any assumptions beyond random assignment and missingness and
corresponding overlap conditions. To quantify the potential gains, we derive
the difference in efficiency bounds on ATE estimation with and without
surrogates, both when an overwhelming or comparable number of units have
missing outcomes. We develop robust ATE estimation and inference methods that
realize these efficiency gains. We empirically demonstrate the gains by
studying the long-term-earning effects of job training.
