Reversals of signal-posterior monotonicity imply a bias of screening

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.