  Many treatment variables used in empirical applications nest multiple
unobserved versions of a treatment. I show that instrumental variable (IV)
estimands for the effect of a composite treatment are IV-specific weighted
averages of effects of unobserved component treatments. Differences between IVs
in unobserved component compliance produce differences in IV estimands even
without treatment effect heterogeneity. I describe a monotonicity condition
under which IV estimands are positively-weighted averages of unobserved
component treatment effects. Next, I develop a method that allows instruments
that violate this condition to contribute to estimation of treatment effects by
allowing them to place nonconvex, outcome-invariant weights on unobserved
component treatments across multiple outcomes. Finally, I apply the method to
estimate returns to college, finding wage returns that range from 7\% to 30\%
over the life cycle. My findings emphasize the importance of leveraging
instrumental variables that do not shift individuals between versions of
treatment, as well as the importance of policies that encourage students to
attend "high-return college" in addition to those that encourage "high-return
students" to attend college.
