Simple Inference on Functionals of Set-Identified Parameters Defined by Linear Moments

This article proposes a new approach to obtain uniformly valid inference for linear functionals or scalar subvectors of a partially identified parameter defined by linear moment inequalities. The procedure amounts to bootstrapping the value functions of randomly perturbed linear programming problems, and does not require the researcher to grid over the parameter space. The low-level conditions for uniform validity rely on genericity results for linear programs. The unconventional perturbation approach produces a confidence set with a coverage probability of 1 over the identified set, but obtains exact coverage on an outer set, is valid under weak assumptions, and is computationally simple to implement.

本文提出了一种全新方法，可对由线性矩不等式（linear moment inequalities）定义的部分识别参数（partially identified parameter）的线性泛函（linear functionals）或标量子向量（scalar subvectors）实现一致有效推断。该方法等价于对随机扰动线性规划问题（randomly perturbed linear programming problems）的价值函数进行自助法（Bootstrap）推断，无需研究者在参数空间（parameter space）上开展网格化操作。支撑该方法一致有效性的低阶条件，依赖于线性规划的通有性结果（genericity results）。这种非常规的扰动方法可生成覆盖概率（coverage probability）在识别集（identified set）上恒为1的置信集（confidence set），同时在外集（outer set）上实现精确覆盖；该方法在弱假设条件下具备有效性，且计算实现简便易行。