The Effect of Cohort Sizes on Marriage Markets in Twentieth Century Sweden

Large, short-run fluctuations in the birth rate have been an important demographic feature of industrialized, low-fertility populations in the twentieth century. Since females normally marry men who are two or three years older than themselves, these fluctuations result in large imbalances between the size of male and female cohorts who would normally marry each other. These imbalances must somehow be resolved, either by a change in traditional patterns of age at marriage or by changes in the proportions of the population of one sex or the other who ever marry. Following a suggestion of Becker (1974,1981), we have developed a developed an implementable general equilibrium model of marriage assignments, which can be used to predict the way in which marriage patterns adjust to change in the numbers of males and females in each cohort. This model poses equilibrium in the marriage market as and application of the {\it linear programming assignment problem}, which was introduced to economics by Koopmans and Beckman (1987). For the purposes of this paper, we suppose that persons of the same sex differ only by the year in which they were born. Each individual has a preferred age of marriage. Any two people who marry each other must, of course, marry at the same time. Therefore, the total payoff to a marriage between any male and female is a function of the age difference between them. The more their age difference diverges from the difference between their preferred ages at marriage, the greater the greater must be the loss of utility to one or both from marrying at an age that is not ideal. If we posit a particular payoff structure to marriages as a function of the age of marriage of each partner, then given the size of each cohort, we can compute the optimal assignment of marriage partners by cohort. The fit of the predicted assignments from our model can then be compared with actual marriage patterns.