Gender wage and longevity gaps and the design of retirement systems

We study the design of pension benefits for male and female workers. Women live longer than men but have a lower wage. Individuals can be single or live in couples who pool their incomes. Social welfare is utilitarian but an increasing concave transformation of individuals' lifetime utilities introduces the concern for redistribution between individuals with different life-spans. We derive the optimal direction of redistribution and show how it is affected by a gender neutrality rule. With singles only, a simple utilitarian solution implies redistribution from males to females. When the transformation is sufficiently concave redistribution may or may not be reversed. With couples only, the ranking of gender retirement ages is always reversed when the transformation is sufficiently concave. Under gender neutrality pension schemes must be self-selecting. With singles only this implies distortions of retirement decision and restricts redistribution across genders. With couples, a first best that implies a lower retirement age for females can be implemented by a gender-neutral system. Otherwise, gender neutrality implies equal retirement ages and restricts the possibility to compensate the shorter-lived individuals. Calibrated simulations show that when singles and couples coexist, gender neutrality substantially limits redistribution in favor of single women and fully prevents redistribution in favor of male spouses.