An Age-Structured Two-Sex Population Model with Endogenous Forces of Attraction

ABSTRACT : In age-structured two-sex population models, couple formation is modeled as a two-step process in which pairs first meet and then determine whether to match. The probability that a female of age i meets a male of age j depends on the relative numbers of such individuals, while the probability that this pair matches conditional on meeting -- the "force of attraction" for an ij pair -- is exogenously given and time independent. However, adopting a search-theoretic perspective, matching probabilities should also vary with marriage-market conditions. Intuitively, singles facing better marriage prospects should become more selective, setting a higher reservation match quality, and hence have a lower force of attraction. To address these search-theoretic considerations, we incorporate value functions into a conventional age-structured two-sex model, allowing endogenous determination of the forces of attraction. These value functions, which characterize the expected value of continued search by singles at each age, are determined through a process of adaptive expectations, with current marriage-market conditions used as a proxy for future conditions. The model is illustrated with a series of hypothetical examples involving change in the sex ratio at birth (which eventually creates a "marriage squeeze"), an important context in which endogenous attraction may be consequential for population projections.