Inference in partially identified moment models via regularized optimal transport

2025-12-19

AI Summary

This paper addresses the local identification problem in moment-based models arising solely from marginal distribution information. We propose a novel framework for identification, estimation, and inference grounded in support functions and entropic optimal transport (ENTROPIC OT). First, we embed ENTROPIC OT into partially identified generalized method of moments (GMM) inference; second, we establish a central limit theorem for ENTROPIC OT with smooth cost functions; third, we develop boundary-uniformly valid hypothesis tests. Our approach innovatively integrates the Sinkhorn algorithm, bootstrap inference for directionally differentiable functionals, and support function representations—yielding computationally tractable and statistically robust inference. Monte Carlo experiments confirm excellent size control of the proposed test statistics. The methodology accommodates empirically relevant settings including panel data with missing outcomes, nonlinear treatment effects, and weak instrumental variables.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements

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.

Problem

• Develops methodology for identification, estimation, and inference in partially identified GMM models
• Characterizes sharp identified sets via support-function and optimal transport representation
• Proposes hypothesis testing and confidence region construction using entropic regularization

Innovation

• Entropic regularization for smooth optimal transport approximation
• Sinkhorn algorithm enables efficient computation of regularized transport
• Bootstrap method for directional derivatives ensures valid inference