A Parametric Two-Sided Model of Marriage

John Allen Logan, Peter D. Hoff, and Michael A. Newton

We propose a method to simultaneously estimate men's and women's
preferences for marriage partners using data on the characteristics of
married couples and single individuals. Underlying our method is a
parametric version of a two-sided matching model of marriage
considered in game theory.  There are two matching populations, men
and women. Members of each population have utilities for pairing with
members of the other population, which results in a stable set of
matches between the two populations.  The estimated preference
coefficients determine the degree to which measured characteristics of
individuals affect choices of marital partners. We also discuss
possible uses of such estimates for projections of formations and
dissolutions of marriages. Our method should be useful in many
situations in which voluntary pairings have arisen through some
complex process whose details have not been recorded. Besides marriage
and cohabitation, data on employment, college attendence, and
coresidence of elderly parents with adult children often have this
character, as do some biological data on non-human mating. Only
cross-sectional information, rather than observations over time, is
required. By assuming each individual chooses freely and knowledgeably from
the set of potential partners he or she finds available,
we estimate
preferences without having either to observe these sets or to specify
any details of the matching process. This makes our method robust to
unknown features of the process. Unlike a two-sided logit model
previously introduced for employment data, our method does not require
categorization of alternatives on one side of the marriage market, but instead
uses individual-level, quantitative characteristics symmetrically on
both sides.  We test our method on simulated marriage data and 
illustrate its use with marriage and cohabitation data from the 1993
Panel Study of Income Dynamics.

KEY WORDS: Two-sided matching; Multinomial choice; 
Two-sided probit; Two-sided logit; Data augmentation; 
Metropolis algorithm; Gibbs sampler.