Reversals of signal-posterior monotonicity imply a bias of screening

Sander Heinsalu

Papers from arXiv.org

Abstract: This note strengthens the main result of Lagziel and Lehrer (2019) (LL) "A bias in screening" using Chambers 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 conditional on a lower signal may first order stochastically dominate the distribution conditional on a higher signal. The nonmonotonicity result is also extended to the empirically relevant exponential and Pareto distributions, and to a wide range of signals.

Date: 2019-10, Revised 2019-11
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Journal Article: Reversals of signal-posterior monotonicity imply a bias of screening (2020)
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