Multivalued treatments are commonplace in applications. We explore the use of discrete-valued instruments to control for selection bias in this setting. We establish conditions under which counterfactual averages and treatment effects are identified for heterogeneous complier groups. These conditions require a combination of assumptions that restrict both the unobserved heterogeneity in treatment assignment and how the instruments target the treatments . We introduce the concept of filtered treatment, which takes into account limitations in the analyst's information  . Finally, we illustrate the usefulness of our framework by applying it to data from the Student Achievement and Retention Project and the Head Start Impact Study.
Multivalued treatments are commonplace in applications. We explore the use of discrete-valued instruments to control for selection bias in this setting. We establish conditions under which counterfactual averages and treatment effects are identified for heterogeneous complier groups. These conditions restrict (i) the unobserved heterogeneity in treatment assignment , (ii) how the instruments target the treatments , and optionally (iii) the extent to which counterfactual averages are heterogeneous. We allow for limitations in the analyst's information via the concept of a filtered treatment . Finally, we illustrate the usefulness of our framework by applying it to data from the Student Achievement and Retention Project and the Head Start Impact Study.
R
require a combination of assumptions that restrict both
restrict (i)
R
and
, (ii)
R
. We introduce the concept of filtered treatment, which takes into account
, and optionally (iii) the extent to which counterfactual averages are heterogeneous. We allow for
A
via the concept of a filtered treatment