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Intersection Bounds, Robust Bayes, and Updating Ambiguous Beliefs.

This paper develops multiple-prior Bayesian inference for a set-identi…ed parameter whose identi…ed set is constructed by an intersection of two identi…ed sets. We formulate an econometrician’s practice of "adding an assumption" as "updating ambiguous beliefs." Among several ways to update ambiguous beliefs proposed in the literature, we consider the DempsterShafer updating rule (Dempster (1968) and Shafer (1976)) and the full Bayesian updating rule