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

TL;DR

This paper introduces a bootstrap-based method for valid inference on linear functionals of set-identified parameters defined by linear moments, avoiding grid searches and ensuring reliable coverage.

Contribution

It presents a novel perturbation approach for constructing confidence sets with guaranteed coverage, simplifying computation and relaxing assumptions compared to existing methods.

Findings

Achieves uniform validity for inference on set-identified parameters.

Provides confidence sets with coverage probability of 1 over the identified set.

Method is computationally simple and does not require gridding the parameter space.

Abstract

This paper 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.