Reversals of signal-posterior monotonicity imply a bias of screening

• 成果类型: Article
• 署名作者: Heinsalu, Sander
• 署名单位: Australian National University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2020.105073
• 发表日期: 2020
• 关键词: filtering; Bayes' rule; updating; Posterior beliefs; stochastic dominance; screening

摘要

The main result of Lagziel and Lehrer (2019) (LL) A bias in screening is generalized, and also derived using Chambers and Healy (2011) (CH) Reversals of signal-posterior monotonicity for any bounded prior. LL show that the conditional expectation of an unobserved variable of interest, given that a noisy signal of it exceeds a cutoff, may decrease in the cutoff. CH prove that the distribution of a variable given a lower signal may first order stochastically dominate the distribution given a higher signal. The nonmonotonicity results of CH and LL are extended to unbounded variables of interest and a wide range of signals, including the empirically relevant exponential and thicker-tailed distributions. Applications from the tax evasion literature are provided. Crown Copyright (C) 2020 Published by Elsevier Inc. All rights reserved.