CFDP 2328R

Distributions of Posterior Quantiles and Economic Applications


Publication Date: March 2022

Revision Date: July 2022

Pages: 46


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

Supplemental material

Supplement pages: 10

Keywords: Posterior quantiles, stochastic dominance, gerrymandering, Bayesian persuasion, two-sided markets, quantile regression

JEL Classification Codes: C31, D72, D82, D83, G28, L12, M41

See CFDP Version(s): CFDP 2328