Which wage distributions are consistent with statistical discrimination?

In this paper, we propose a general non-parametric model of statistical discrimination in the labor market, and derive a test for statistical discrimination that only requires cross-sectional data on wages. There are two groups whose productivity distributions have identical means, but can otherwise be different. The group identity is observable to employers, but productivities are not. Instead, there are group-dependent statistical experiments that generate signals about the underlying productivity. Signals induce posterior productivity distributions (via Bayes' rule) and, in particular, these can be used to compute posterior estimates (the mean of the productivity conditional on the signal) of the unobserved productivity. Therefore, each group's statistical experiment generates a distribution over posterior productivity estimates. Wages are then determined via a strictly increasing, continuous function of the posterior productivity estimate that, importantly, does not depend on the group. We say that two wage distributions - one for each of the two groups - are consistent with statistical discrimination if they can be rationalized by this model.