Intersection Bounds, Robust Bayes, and Updating Ambiguous Beliefs
نویسنده
چکیده
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 econometricians 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 (Fagin and Halpern (1991) and Ja¤ray (1992)), and argue that the Dempster-Shafer updating rule rather than the full Bayesian updating rule better matches with an econometricians common adoption of the analogy principle (Manski (1988)) in the context of intersection bound analysis. Keywords: Intersection Bounds, Multiple Priors, Bayesian Robustness, Dempster-Shafer Theory, Updating Ambiguity, Imprecise Probability, Gamma-minimax, Random Set, JEL Classi cation: C12, C15, C21. Email: [email protected]. Financial support from the ESRC through the ESRC Center for Microdata Methods and Practice (CEMMAP) (grant number RES-589-28-0001) is gratefully acknowledged.
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