Sharp bounds in the latent index selection model
在潜变量选择模型中推导出边际处理效应及其线性泛函的解析锐界，利用随机序理论，并应用于俄勒冈健康保险实验，发现基于分布假设的外推与基于参数均值假设的结果存在显著差异。
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.