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Presented By: Department of Economics

A Prior-Agnostic Test for Bayesian Updating (by Cheaheon Lim and Tomasz Strzalecki)

Tomasz Strzalecki, Harvard University

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We develop a test of Bayesian updating “in the field,” where the analyst observes neither the likelihood function nor the realized signals. Our test works ex post, conditional on every realized state, and is prior-agnostic in the sense that its validity does not require the agent’s prior to be “correct.” We compare our procedure to tests based on the martingale property of beliefs, which are valid only ex ante, before the state is realized, and only if the prior is correct. Whereas martingale tests are sensitive to correlation between issues, our test is robust to such dependence. Even when issues are independent, we find that our test typically has greater power relative to the martingale-based tests. In an empirical application using individual-level belief data, we illustrate how our procedure provides a more direct test of Bayesian updating than the martingale-based alternatives.

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