Fertility in Denmark has fallen despite educational attainment increasing and educational attainment being positively correlated with fertility. In a descriptive decomposition, lower partnership formation accounts for about as much of the decline as lower fertility within couples, while the shift toward higher education partly offsets it. We develop and estimate an equilibrium model of education, marriage, labor supply, and fertility with imperfectly transferable utility and unobserved heterogeneity in fertility preferences. We identify women’s and men’s preferences for children separately from couples’ joint choices using variation in local marriage market conditions that shifts bargaining power. The estimated model attributes the decline mainly to falling preferences for children among women, while men’s preferences change little. In policy counterfactuals, free childcare raises fertility by 3.4 percent, and partnership formation accounts for 41 percent of that gain. Joint taxation weakens incentives for education and marriage and, as a result, lowers fertility in equilibrium more than three times as much as in a benchmark that holds couples fixed. Closing the gender wage gap reduces fertility 2.8 times as much as in that benchmark, in part through a shift in bargaining power toward wives.

We examine marital sorting using novel data from a marriage-matching platform that records both a dating-to-marriage pipeline and pre-marital attributes, including preferences for children and for the division of housework and childcare. Unlike census or post-marital surveys, characteristics are collected before matching, and objectively measurable attributes are verified using official documents, providing an ideal setting to study matching and sorting free from post-marital adjustment. Using a multidimensional matching framework across twelve attributes, we find assortative matching along all dimensions. Age is the most salient trait, while preferences for children are second—exceeding education—an economically important margin invisible in standard data. A low-dimensional factor representation shows that fertility preferences constitute a distinct sorting dimension. Exploiting the platform’s dating-to-marriage pipeline, we show that sorting on fertility preferences emerges at later serious-relationship stages. A theoretical analysis suggests that the magnitude of sorting along this margin is consistent with the veto model of fertility decisions.

Women have overtaken men in education, yet the marriage market has adjusted only partly. Using Danish administrative registers for 1980–2013, we document that the share of couples in which the wife is more educated (female hypogamy) rose from 15 to 27 percent and overtook the reverse pattern (female hypergamy) around 2004. Hypogamy, however, remains less common than under random matching. Investigating this puzzle, we document new facts on the distribution of singles, marriage formation, and heterogeneous, duration-dependent divorce risk. These facts motivate an equilibrium search model of the marriage market with transferable utility, household production, endogenous divorce, and dynamic selection. Decomposing the hypogamy trend with the estimated model, we find that changes in the education mix account for about three quarters of the rise. Net of composition, the trend is driven by changing norms regarding partnership formation, partly offset by more low-educated men remaining single; wages, household technology and bargaining power play only minor roles.

We study how people search for partners and how beliefs about their own attractiveness shape whom they approach, using the detailed search log of a marriage matching platform. Requests to more popular partners are less likely to be accepted, but members at every popularity level send most of their requests to the most popular partners. This could reflect a strong preference for popular partners over remaining single, or optimistic beliefs about their chances of being accepted. The strength of the data is that search behavior over time is directly observed rather than inferred from final matches, so we can distinguish between these explanations. Members gradually target less popular partners, especially after unexpected rejections. A predictable rejection has little effect, and an unexpected acceptance raises their aim. This pattern is consistent with belief updating, because unexpected outcomes carry more information than predictable ones. We develop and estimate an equilibrium search model in which members are uncertain about their own attractiveness and learn from the responses they receive. The model recovers members’ beliefs, so we can separate their effect on search from that of preferences. We then use the model to quantify how optimistic beliefs at entry affect the timing and quality of the final match as well as the decision to quit the platform. We also evaluate policies that provide feedback on acceptance probabilities or limit monthly requests, allowing beliefs and acceptance rates to change in equilibrium.

We examine how working from home (WFH) affects men’s participation in childcare and housework and their attitudes toward family. Because WFH is an endogenous decision, we apply a first-difference instrumental variable estimator, taking the degree to which one can work from home, measured at the individual level, as the instrument. We find that WFH increases the time that men spend on household chores and with family, and the fraction of men who consider life more important than work. Although WFH decreases their commuting time, we find no evidence that it reduces working hours or self-perceived productivity.