  For counterfactual policy evaluation, it is important to ensure that
treatment parameters are relevant to policies in question. This is especially
challenging under unobserved heterogeneity, as is well featured in the
definition of the local average treatment effect (LATE). Being intrinsically
local, the LATE is known to lack external validity in counterfactual
environments. This paper investigates the possibility of extrapolating local
treatment effects to different counterfactual settings when instrumental
variables are only binary. We propose a novel framework to systematically
calculate sharp nonparametric bounds on various policy-relevant treatment
parameters that are defined as weighted averages of the marginal treatment
effect (MTE). Our framework is flexible enough to fully incorporate statistical
independence (rather than mean independence) of instruments and a large menu of
identifying assumptions beyond the shape restrictions on the MTE that have been
considered in prior studies. We apply our method to understand the effects of
medical insurance policies on the use of medical services.
