Research

Recent U.S. marital matching exhibits three known facts: (i) marriage has declined while cohabitation has risen at every education level; (ii) both unions have become more stable; and (iii) union formation passes through two regimes dividing at 2008—substitution from marriage toward cohabitation, then a retreat from partnership altogether. Static models of marriage matching, such as that of Choo and Siow (2006), explain the decline of marriage as a fall in the gains to marriage. But a fall in the gains to marriage cannot explain the concurrent increase in the duration of marriages. To fit the data, this paper estimates time-varying match values together with match-formation and dissolution costs for different marital matches. The retreat from marriage operates through entry. Marriage-formation costs rose past marriage gains that were themselves rising, most sharply for the less-educated, while stability rose because unions became more valuable, not harder to leave. Cohabitation's rise is mostly its own market with higher value, greater durability, and a costlier upgrade to marriage. I use the estimates to test a number of explanations for these changes. I find that only men's declining labour-force attachment robustly moves the net gain to forming a match, and the bulk of the transition remains unexplained.

Since 2008, U.S. birth rates have fallen nearly twice as fast as fertility intentions. Is the shortfall delay, marriage postponed so that fewer childbearing years are spent where births are most likely, or decline, fewer births at a given age whether married or not? I estimate a dynamic marriage matching model with endogenous divorce and fertility on U.S. survey data for 2008–2023, then hold each estimated component at its 2008 value in turn, re-solving the marriage market and retracing the fertility decisions that follow. Of the fall the model explains, a third is delay and two thirds decline. The delay comes from the cost of forming a marriage, which rose faster than the payoff to a match. The decline lies outside marriage, where the net gain to a birth fell; within marriage there is little to explain. Both movements are concentrated among adults under thirty.

We study the nonparametric identification of skill distributions and the revenue function in a discrete Roy model with matching, in which participants choose between managing and working and firms pair one manager with one worker. The econometrician observes each firm's revenue and the wage it pays, as in matched employer–employee records with occupations. Under a single restriction on the skill distribution—jointly high-skilled types are rarest, jointly low-skilled types most common—the equilibrium takes one of five observable regimes, and we derive the sharp identified set in closed form for each. When participants sort perfectly, the identified set is two-dimensional; when they mix, it shrinks to a line segment. The analysis extends to any number of skill levels, where the sharp set is a polytope of known dimension, increasing in the number of occupationally indifferent skill pairs. The dependence between skills is not identified nonparametrically, and we discuss parametric assumptions that locally identify it.

Between 1966 and 1980 the regional land-use plans of Flanders set aside land as residential reserve, designated for future housing but held back from building until the authorities release it. We show that the share of each municipality held in reserve shaped how much house prices rose during the housing boom of the 2000s, with prices rising less where the share was larger. We use that share, interacted with regional house-price growth, as an instrument for local price growth. The share was set decades before our study period by planning bureaus that sized the reserve in different ways from one part of Flanders to the next, and it is only weakly related to the characteristics of municipalities in 2001. With register data on all women in Flanders at risk of a first birth from 2001 to 2018, we find that first births rose less where the reserve held price growth down. Prices rising 10 per cent faster over a year raise the rate of first conceptions in the following quarter by about 9 per cent, an elasticity of about 0.9. The increase is persistent and holds when we control for local characteristics that could link reserve to housing demand. The relationship also holds for homeowners and non-owners and across age groups, with varying magnitudes. The results illustrate how land-use planning affects family formation through the housing market.

Place-based designs assign treatment to a spatial unit and measure outcomes aggregated over its residents at a later date, but people migrate between treatment and measurement. We show that in a general setting the coefficient such a design reports is the true effect scaled by a mobility factor and displaced by a selection term. Following the same individuals recovers the true effect exactly when movers' outcomes depend only on the treatment they received before moving. When individuals cannot be followed, the mobility factor is identified from aggregate migration flows. The selection term is not identified, but it can be bounded by the typical difference in outcomes between movers and stayers and this difference's correlation with treatment. The mobility factor and the bound give an identified set and the level of selection at which the reported sign would reverse. In Belgian register data, ignoring migration biases the estimated effect of home prices on first births at ages 25–29 by 16 per cent over one year and 93 per cent over five. The identified set contains the estimate from following individuals in nineteen of twenty age-by-horizon cells. Migration is prevalent, but its selectivity is almost uncorrelated with prices, so the reported sign survives everywhere except at ages 30–34 beyond the first year, where the effect is close to zero.

We study distribution of labor with a model relying on one-to-one matchings of workers on which occupational choice is a constraint. We show this formulation of the model to be consistent with empirical observations of skill-based wage inequalities observed in the American market. We study theoretical properties, like existence and uniqueness of optimal solutions and stability results which indicate the behaviour of the labor market when either the original population or the production function changes. The techniques used to investigate such a model rely on optimal transport methods which allow us to provide quantitative tools to analyze and predict these changes. This model provides new understanding of wage inequalities across and within firms relating them to relative skill contributions to production (through matched worker-firm pairs). 

Non-marital cohabitation is a central feature of contemporary household formation in the United States, yet it is not directly observed in nationally representative data prior to 1990 and remains imperfectly measured thereafter. This paper develops a consistent historical measure of cohabitation by constructing a stable risk set of candidate dyads and estimating a pair-level classifier of latent cohabitation status using the Current Population Survey. A conservatively regularized gradient-boosted tree model (XGBoost), validated using rolling-origin procedures that respect the time-series structure of the data, produces well-calibrated individual-level probabilities that are portable across Census waves. The reconstructed series indicates that cohabitation existed at non-negligible levels throughout the twentieth century, declined modestly into mid-century, and rose sharply after 1960—consistent with, but now directly measurable beyond, prior conjecture. I then apply the reconstructed measure to examine the repeal of anti-miscegenation laws using a staggered event-study design. Legalization produces large increases in interracial marriage but no discrete response in interracial cohabitation. The evidence suggests that marriage law primarily affected the formal recognition of interracial unions rather than their underlying formation. Methodologically, the paper demonstrates how machine learning can be used not merely for prediction, but to reconstruct latent social states in historical data, thereby enabling the study of long-run union dynamics beyond the limits of contemporaneous survey design.