Treatment effects with targeting instruments

Multivalued treatments are commonplace in applications. We explore the use of discrete-valued instruments to control for selection bias in this setting. Our discussion revolves around the concept of targeting: which instruments target which treatments. It allows us to establish conditions under which counterfactual averages and treatment effects are point- or partially-identified for composite complier groups. We illustrate the usefulness of our framework by applying it to data from the Head Start Impact Study. Under a plausible positive selection assumption, we derive informative bounds that suggest less beneficial effects of Head Start expansions than the parametric estimates of Kline and Walters (2016).