Signals, Indices, and Statistical Discrimination in Hiring

Some scholars conjectured that Spence's signaling games with an index would serve as a model of statistical discrimination in the hiring processes, which should explain the following facts observed in industrialized societies: first, the mean educational level for men is greater than that for women; second, the mean wage for men is greater than that for women. In order to examine whether the conjecture is supported or not, I formulated a generalized version of these games, assuming that the educational level is a signal of productivity while the gender is an "index" of productivity, and followed the procedure of refinements of perfect Bayesian equilibria to eliminate unreasonable outcomes. My analysis reveals that a "curious" consequence is derived from the separating equilibrium that survives the Intuitive Criterion in the refinements: the mean wage for men would be equivalent to that for women. As the employers are assumed to know that the educational costs for women are greater than those for men, they would believe that women with shorter years of education have the same productivity as men with longer years of education and therefore offer the same wage for the men and the women. I also examined some modifications of the model that might resolve the difficulty in explaining the gender gaps in education and wage.