Policy Relevant Treatment Effects with Multidimensional Unobserved Heterogeneity

This paper provides a framework for the policy relevant treatment effects using instrumental variables. In the framework, a treatment selection may or may not satisfy the classical monotonicity condition and can accommodate multidimensional unobserved heterogeneity. We can bound the target parameter by extracting information from identifiable estimands. We also provide a more conservative yet computationally simpler bound by applying a convex relaxation method. Linear shape restrictions can be easily incorporated to further improve the bounds. Numerical and simulation results illustrate the informativeness of our convex-relaxation bounds, i.e., that our bounds are sufficiently tight.