Reversals of signal-posterior monotonicity imply a bias of screening

Abstract

This note strengthens the main result of Lagziel and Lehrer (2019) (LL) "A bias in screening" 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 result is also extended to the empirically relevant exponential and Pareto distributions, and a wide range of signals.