An Adversarial Approach to Identification, Computation, and Inference in Models with a Linear-in-Measures Representation

2026-09-25

AI Summary

This study addresses the identification, computation, and inference challenges inherent in linear measurement representation models. It proposes a linear measurement framework for nonlinear outcome equations, constructing an adversarial discrepancy function to characterize the identified set. By integrating adversarial machine learning, finite-dimensional linear programming, and the penalized bootstrap, the method achieves efficient computation and valid confidence inference while supporting certified bound estimation under infinitely supported latent inputs. The approach successfully recovers known sharp identified regions in binary choice panel data and entry games with multiple equilibria, and constructs confidence sets with uniform coverage. Ultimately, this work provides a general, computationally tractable theoretical and algorithmic framework for partially identified models.

Abstract

We develop a framework for identification, computation, and inference in econometric models with a linear-in-measures representation. These models express maintained restrictions as moment conditions linear in the joint probability measure of observed and latent inputs, and map that measure linearly to the distribution of outputs, even with nonlinear outcome equations. We construct an adversarial discrepancy function whose zeros characterize the identified set for structural and counterfactual parameters. With finite output support, finite linear programs compute the discrepancy function or provide certified bounds even when latent inputs have infinite support, and a penalized bootstrap yields confidence sets with uniform per-point coverage. We apply the framework to two open cases in binary choice panels with fixed effects and discrete covariates: sequential exogeneity with unspecified conditional marginal error distributions, and known conditional marginal error distributions with unrestricted serial dependence. In an entry game with multiple equilibria, the framework recovers the known sharp identification region.

Problem

• linear-in-measures representation
• identification
• econometric models
• inference
• partial identification

Innovation

• Adversarial discrepancy function
• Linear-in-measures representation
• Finite linear programs
• Penalized bootstrap
• Partial identification