Introduction
Much of what looks like changing marriage preferences over the twentieth century is actually demographics. Variation in sex ratios and mortality across U.S. birth cohorts—driven by immigration and differential longevity gains—accounts for two-thirds of the cross-cohort differences in marriage and divorce behavior, with no change in behavioral parameters at all. This paper provides the first joint identification of marriage preferences, match quality dynamics, and the costs of marriage and divorce in a unified equilibrium framework, exploiting the large demographic variation across the 1870, 1930, and 1950 birth cohorts.
The variation we exploit is plausibly exogenous to marriage preferences. The sex ratio at marriageable ages fell from 1.056 men per woman (1870 cohort) to 0.942 (1950 cohort)—a swing from male surplus to female surplus driven by the closing of the frontier, declining male immigration, and faster female mortality improvements. These forces operate through the population’s age and sex structure, not through tastes over partners. They change who is scarce and who must compete in the marriage market, so that equilibrium marriage and divorce patterns shift even if no one’s preferences change. We estimate a dynamic general equilibrium model of marriage and divorce, matching 84 moments of marriage and divorce behavior across the three cohorts. Beyond the aggregate role of demographics, the estimates reveal sharp findings about what people value and how relationships work:
• Women’s preferences changed; men’s did not. Women in the 1870 cohort placed a premium on older over younger husbands large enough to delay marriage by several years relative to a world with symmetric preferences (Figure 3). By 1950 this premium had collapsed to near zero. Men’s preferences over partner age are essentially constant across all three cohorts. The marriage age gap is driven not by men preferring younger (more fecund) women, as Siow (1998) suggests, but by women’s preference for older, more established men—a preference that erodes as women gain economic independence.
• Love that survives becomes permanent—but surviving got harder. A good match, once achieved, is permanent: the implied duration exceeds the remaining lifetime. But in the 1870 cohort a new marriage had a 97% probability of reaching the good state; by 1950, this had fallen to 44%. The 1950 cohort uniquely allowed recovery from bad matches with 16% chances, generating dynamics that resemble cohabitation.
• Divorce costs depend on life stage. The middle-age group (“young” in our model) faces the 2 Throughout we consider only opposite-sex couples, reflecting the historical period studied. For historical mortality rates, see Haines (1998) and Arias (2012); for historical patterns of gender-biased immigration to the U.S., see Donato and Gabaccia (2015). 2 highest effective divorce cost—roughly six times the utility value of a standard-deviation match shock—substantially above both adolescents and the old. This generates the age-declining divorce rate profile observed in every cohort. The base cost declined six-fold across cohorts, with a structural break between 1910 and 1930 coinciding with the liberalization of divorce laws and the entry of women into the labor force.
• Divorce costs and match quality are substitutes. Cohort-specific match quality process alone— without any cohort variation in divorce costs—achieves the same fit as the Baseline specification. Both channels govern marital dissolution, one through the price of exit, the other through the probability of wanting to exit. Combining both yields a further 14% improvement, revealing two independent dimensions of social change: the liberalization of exit and the increasing uncertainty of relationships.
How can these mechanisms be separately identified? The key is that different moments respond
to different parameters, and the three cohorts provide 84 moments under very different demographic
conditions. Marriage rates by age for male and female reveal how each sex values partners of different
maturities: when the sex ratio shifts from male surplus to female surplus, the scarce sex becomes pickier
and marriage patterns change in ways that depend on the preference parameters. Divorce rates and
their age profile reveal the cost of exit: the pervasive pattern that divorce declines with age identifies
the age-dependent component of divorce costs, because without it the model would predict flat or
rising divorce with age. The fraction never married by age 50 disciplines marriage frictions: a high
never-married fraction signals that substantial frictions prevent matches from forming. The persistence
of marriages—how quickly divorce rates fall with duration—reveals match quality dynamics: if good
matches are permanent but medium matches are fragile, divorce concentrates in the early years. The
cross-cohort variation in these moments overdetermines the parameter vector. [...]
This paper contributes to the literature on marriage and matching in three ways. First, it provides a framework to separate demographic forces from behavioral responses in equilibrium matching markets. Second, it identifies the dynamics of match quality and the role of divorce costs using variation that is orthogonal to preferences. Third, it shows that much of the long-run change in marriage and divorce patterns can be understood as the consequence of demographic shifts rather than changes in tastes.
