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Discussion Paper

Distributions of Posterior Quantiles and Economic Applications

We characterize the distributions of posterior quantiles under a given prior. Unlike
the distributions of posterior means, which are known to be mean-preserving contractions
of the prior, the distributions of posterior quantiles coincide with a first-order
stochastic dominance interval bounded by an upper and a lower truncation of the
prior. We apply this characterization to several environments, ranging across political
economy, Bayesian persuasion, industrial organization, econometrics, finance, and