A Characterization of "Phelpsian" Statistical Discrimination

We establish that statistical discrimination is possible if and only if it is impossible to uniquely identify the signal structure observed by an employer from a realized empirical distribution of skills. The impossibility of statistical discrimination is shown to be equivalent to the existence of a fair, skill-dependent remuneration for every set of tasks every signal-dependent optimal assignment of workers to tasks. Finally, we connect this literature to Bayesian persuasion, establishing that if the possibility of discrimination is absent, then the optimal signalling problem results in a linear payoff function (as well as a kind of converse).