A characterization of "Phelpsian" statistical discrimination

TL;DR

This paper characterizes when statistical discrimination can occur, linking it to the identifiability of signal structures and the existence of fair wages, and connects these ideas to Bayesian persuasion theory.

Contribution

It provides a precise condition for the possibility of statistical discrimination based on signal identifiability and relates it to fair remuneration and Bayesian persuasion.

Findings

Discrimination occurs if signal structures are not identifiable.

Fair, skill-dependent wages imply no statistical discrimination.

Optimal signaling yields linear payoff functions when discrimination is absent.

Abstract

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 workers. Finally, we connect the statistical discrimination literature to Bayesian persuasion, establishing that if discrimination is absent, then the optimal signaling problem results in a linear payoff function (as well as a kind of converse).