  A fundamental question underlying the literature on partial identification
is: what can we learn about parameters that are relevant for policy but not
necessarily point-identified by the exogenous variation we observe? This paper
provides an answer in terms of sharp, analytic characterizations and bounds for
an important class of policy-relevant treatment effects, consisting of marginal
treatment effects and linear functionals thereof, in the latent index selection
model as formalized in Vytlacil (2002). The sharp bounds use the full content
of identified marginal distributions, and analytic derivations rely on the
theory of stochastic orders. The proposed methods also make it possible to
sharply incorporate new auxiliary assumptions on distributions into the latent
index selection framework. Empirically, I apply the methods to study the
effects of Medicaid on emergency room utilization in the Oregon Health
Insurance Experiment, showing that the predictions from extrapolations based on
a distribution assumption (rank similarity) differ substantively and
consistently from existing extrapolations based on a parametric mean assumption
(linearity). This underscores the value of utilizing the model's full empirical
content in combination with auxiliary assumptions.

Econometrics