This note strengthens the main result in Lagziel and Lehrer (2019) `` A bias in screening '' by deriving it as a corollary of Chambers Healy (2011) `` Reversals of signal-posterior monotonicity for any bounded prior '' .
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. This note transforms the density of a modified CH signal into the cumulative distribution of the LL signal .
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". 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. This note transforms the density of a modified CH signal into the cumulative distribution of the LL signal