A Characterisation of 'Phelpsian' Statistical Discrimination

Abstract

We establish that a type of statistical discrimination-that based on informativeness of signals about workers' skills and the ability appropriately to matchworkers to tasks-is possible if and only if it is impossible uniquely to identify the signal structure observed by an employer from a realised empirical distribution of skills. The impossibility of statistical discrimination is shown to be equivalent to the existence of a fair, skill-dependent, remuneration for workers. Finally, we connect the statistical discrimination literature to Bayesian persuasion, establishing that if discrimination is absent, then the optimal signalling problem results in a linear pay-off function (as well as a kind of converse).