An Adversarial Approach to Identification

TL;DR

This paper presents a novel adversarial framework for characterizing identified sets in econometric models, unifying various identification problems and enabling computation via linear programming.

Contribution

It introduces a set membership reformulation of identification problems using an adversarial approach, applicable to diverse econometric models with different error structures.

Findings

Applicable to nonlinear panel models with fixed effects

Enables computation of identified sets via linear programming

Versatile across models with parametric and nonparametric errors

Abstract

We introduce a new framework for characterizing identified sets of structural and counterfactual parameters in econometric models. By reformulating the identification problem as a set membership question, we leverage the separating hyperplane theorem in the space of observed probability measures to characterize the identified set through the zeros of a discrepancy function with an adversarial game interpretation. The set can be a singleton, resulting in point identification. A feature of many econometric models, with or without distributional assumptions on the error terms, is that the probability measure of observed variables can be expressed as a linear transformation of the probability measure of latent variables. This structure provides a unifying framework and facilitates computation and inference via linear programming. We demonstrate the versatility of our approach by applying it to nonlinear panel models with fixed effects, with parametric and nonparametric error distributions, and across various exogeneity restrictions, including strict and sequential.