A Marriage Market Model for Clarifying Factors Contributing to Declining Marriage Rates: A Consideration of the Two-Sex Problem

The rate of marriage in Japan has been declining since the 1970s. In recent years, a similar trend manifests itself in other East Asian countries. This paper predicates such a phenomenon on the schematic proposed by Coleman (1986). In an effort to clarify factors contributing to declining marriage rates, we need to appropriately control the size of demographic cohorts for macro-level social changes so as to reinterpret them as aggregations of micro-level individual decisions. However, the respective rates for men and women being unmarried and the probability of first marriage used as explained variables in previous studies are only controlled by the population size of a single sex, and the influence of the population size of the other sex (possible marriage partner) has not been excluded. This problem is related to the so-called “two-sex” marriage problem, which remains an unresolved problem in demography.

Given this two-sex problem, this paper aims to construct a simple model based on the marriage market theory proposed by Becker (1973). Let Nf and Nm represent the unmarried populations of women and men, respectively, with y as the number of marriages. By letting Sf and Sm represent the benefit gained by women and men, respectively, who opt to remain single, and M as the benefit gained by men and women who marry, the marriage supply curves of women and men can be respectively represented by y = Nf{−exp(−x + Sf) + 1} and y = Nm{−exp(x + Sm − M) + 1}. Therefore, M − (Sf + Sm) = log[NfNm/{(Nf − y)(Nm − y)}]．The right-hand side represents the “tendency towards first marriage” controlled by the population size of both men and women. A multivariate analysis based on this equation will help us clarify the true factors contributing to the decline in the marriage rate.