Sharp instruments for classifying compliers and generalizing causal effects
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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.
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