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
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