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A fundamental question underlying the literature on partial identificationis: what can we learn about parameters that are relevant for policy but notnecessarily point-identified by the exogenous variation we observe? This paperprovides an answer in terms of sharp, analytic characterizations and bounds foran important class of policy-relevant treatment effects, consisting of marginaltreatment effects and linear functionals thereof, in the latent index selectionmodel as formalized in Vytlacil (2002). The sharp bounds use the full contentof identified marginal distributions, and analytic derivations rely on thetheory of stochastic orders. The proposed methods also make it possible tosharply incorporate new auxiliary assumptions on distributions into the latentindex selection framework. Empirically, I apply the methods to study theeffects of Medicaid on emergency room utilization in the Oregon HealthInsurance Experiment, showing that the predictions from extrapolations based ona distribution assumption (rank similarity) differ substantively andconsistently from existing extrapolations based on a parametric mean assumption(linearity). This underscores the value of utilizing the model's full empiricalcontent in combination with auxiliary assumptions.

Sharp Bounds in the Latent Index Selection Model