An Adversarial Approach to Identification and Inference

We introduce a novel framework to characterize identified sets of structural and counterfactual parameters in econometric models. Our framework centers on a discrepancy function, which we construct using insights from convex analysis. The zeros of the discrepancy function determine the identified set, which may be a singleton. The discrepancy function has an adversarial game interpretation: a critic maximizes the discrepancy between data and model features, while a defender minimizes it by adjusting the probability measure of the unobserved heterogeneity. Our approach enables fast computation via linear programming. We use the sample analog of the discrepancy function as a test statistic, and show that it provides asymptotically valid inference for the identified set. Applied to nonlinear panel models with fixed effects, it offers a unified approach for identifying both structural and counterfactual parameters across exogeneity conditions, including strict and sequential, without imposing parametric restrictions on the distribution of error terms or functional form assumptions.