Family Labor Market Decisions and Statistical Gender Discrimination

We present a model where labor supply decisions are made jointly by couples, and firms which respond to the joint nature of these decisions. In our model, parenthood requires a parent of choice to take some time out of the labor force, while a contracting friction implies that leaving the labor force imposes a cost on firms that hired them. An efficiency wages mechanism arises when there is assortative mating in the productivity level of family members, as firms know that increasing the wage of their employees makes them less likely to leave the labor force. As a consequence, no equilibrium in pure strategies without discrimination is possible. If firms can condition wages on gender there exists an equilibrium where women are paid less than men at all productivity levels, while productive women always employed but paid less than men (glass ceiling) and less productive women are not employed. If firms can not condition on wages on gender but can do so on a characteristic (even if irrelevant for productivity) another equilibrium (akin to mixed strategies) arises. In it at each productivity level workers of both genders have heterogeneous wages with identical distribution. The efficiency effects of these equilibrium are complex as it worsens allocation within families, as it adds noise inducing in occasion the most productive member to leave the market. We extent the model allowing for differences in home and market productivity of genders and show that in the gender discrimination equilibrium a decrease in the gap of productivity induces female participation increases at low productivity levels while top female wages rise. Furthermore, increases in female participation increase male wage inequality. In a dynamic version of the model we hypothesize that if in the past, productivity differences made discriminatory equilibrium unique, then as productivities converge the discriminatory equilibrium remain unique. Instead of multiple equilibrium we may observe multiple steady states that make gender differences stable in the absence of policy changes.