  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 instruments: 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).
