Identification and Inference in Nonlinear Panel Models: An Adversarial Approach
Coauthors: Irene Botosaru and Isaac Loh
Abstract:
In nonlinear panel models with fixed effects, structural parameters and counterfactual objects such as the average structural function are typically partially identified, and restrictions imposed conditional on the fixed effects induce a continuum of moment conditions. Existing approaches to identification and inference are largely model-specific. We propose a unifying approach that formulates identification as a set-membership question in the space of probability measures on observables. The central object is an adversarial discrepancy function whose zero set sharply characterizes the identified set. Point identification need not be established a priori.
The discrepancy function is the value of a semi-infinite linear program, which we solve by row-and-column generation with optimality certificates. For discrete outcomes, the sample analogue admits the same representation. We derive its limiting distribution and a uniformly valid penalized bootstrap whose contact-set penalty mitigates conservativeness. Applied to binary choice panels, the framework delivers the first sharp identification under sequential exogeneity with unrestricted errors and the first sharp identified set for probit with interval-censored covariates, while nesting classical point-identification results, including conditional logit, as special cases.
Organized by: Vadim Marmer
