Inference in partially identified moment models via regularized optimal transport

TL;DR

This paper introduces a novel approach for inference in partially identified models using regularized optimal transport, enabling efficient estimation and hypothesis testing with broad empirical applications.

Contribution

It develops a new methodology combining entropic regularization and optimal transport for identification, estimation, and inference in partially identified GMM models.

Findings

Efficient computation via Sinkhorn algorithm.

Valid hypothesis testing with bootstrap and CLT.

Applicable to diverse empirical models.

Abstract

Partial identification often arises when the joint distribution of the data is known only up to its marginals. We consider the corresponding partially identified GMM model and develop a methodology for identification, estimation, and inference in this model. We characterize the sharp identified set for the parameter of interest via a support-function/optimal-transport (OT) representation. For estimation, we employ entropic regularization, which provides a smooth approximation to classical OT and can be computed efficiently by the Sinkhorn algorithm. We also propose a statistic for testing hypotheses and constructing confidence regions for the identified set. To derive the asymptotic distribution of this statistic, we establish a novel central limit theorem for the entropic OT value under general smooth costs. We then obtain valid critical values using the bootstrap for directionally differentiable functionals of Fang and Santos (2019). The resulting testing procedure controls size locally uniformly, including at parameter values on the boundary of the identified set. We illustrate its performance in a Monte Carlo simulation. Our methodology is applicable to a wide range of empirical settings, such as panels with attrition and refreshment samples, nonlinear treatment effects, nonparametric instrumental variables without large-support conditions, and Euler equations with repeated cross-sections.