  It is well-known that, without restricting treatment effect heterogeneity,
instrumental variable (IV) methods only identify "local" effects among
compliers, i.e., those subjects who take treatment only when encouraged by the
IV. Local effects are controversial since they seem to only apply to an
unidentified subgroup; this has led many to denounce these effects as having
little policy relevance. However, we show that such pessimism is not always
warranted: it is possible in some cases to accurately predict who compliers
are, and obtain tight bounds on more generalizable effects in identifiable
subgroups. We propose methods for doing so and study their estimation error and
asymptotic properties, showing that these tasks can in theory be accomplished
even with very weak IVs. We go on to introduce a new measure of IV quality
called "sharpness", which reflects the variation in compliance explained by
covariates, and captures how well one can identify compliers and obtain tight
bounds on identifiable subgroup effects. We develop an estimator of sharpness,
and show that it is asymptotically efficient under weak conditions. Finally we
explore finite-sample properties via simulation, and apply the methods to study
canvassing effects on voter turnout. We propose that sharpness should be
presented alongside strength to assess IV quality.
