Filtered and Unfiltered 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 stresses the role of assumptions on targeting (which instruments target which treatments) and filtering (limits on the analyst's knowledge of the treatment assigned to a given observation). It allows us to establish conditions under which counterfactual averages and treatment effects are identified for composite complier groups. We illustrate the usefulness of our framework by applying it to data from the Head Start Impact Study and the Student Achievement and Retention Project.