An Adversarial Approach to Identification and Inference

Abstract

This paper presents a framework for identification in nonlinear panel models with fixed effects. We characterize the identified set as the zero set of a discrepancy function constructed via a separating hyperplane argument. The characterization is sharp if the set of model-implied probability measures is convex. Our method applies to models with parametric or nonparametric error distributions, various exogeneity conditions, and diverse counterfactual parameters. The discrepancy function is computed efficiently using linear programming; we establish strong duality and show that standard cutting plane algorithms apply. For discrete data, we derive the limiting distribution of the empirical discrepancy function to construct uniformly valid bootstrap confidence sets. We apply the framework to binary choice panel models, obtaining sharp identification results with a tractable computation. The framework provides a unified approach to identification, computation, and inference.