This paper proposes and estimates a static non-parametric transferable utility model of the marriage market. The model rationalizes the standard interpretation of marriage rate regressions as well as pointing out its limitations. The model was used to estimate US marital behavior in 1971/72 and 1981/82. The estimates show that the gains to marriage for young adults fell substantially over the decade. It also showed that the legalization of abortion had a significant quantitative impact on the fall in the gains to marriage for young adults.

We use marriage matching functions to study how marital patterns change when population supplies change. Specifically, we use a behavioral marriage matching function with spillover effects to rationalize marriage and cohabitation behavior in contemporary Canada. The model can estimate a couple's systematic gains to marriage and cohabitation relative to remaining single. These gains are invariant to changes in population supplies. Instead, changes in population supplies redistribute these gains between a couple. Although the model is behavioral, it is nonparametric. It can fit any observed cross-sectional marriage matching distribution. We use the estimated model to quantify the impacts of gender differences in mortality rates and the baby boom on observed marital behavior in Canada. The higher mortality rate of men makes men scarcer than women. We show that the scarceness of men modestly reduced the welfare of women and increased the welfare of men in the marriage market. On the other hand, the baby boom increased older men's net gains to entering the marriage market and lowered middle-aged women's net gains.

We develop and estimate an empirical collective model with endogenous marriage formation, participation, and family labor supply. Intrahousehold transfers arise endogenously as the transfers that clear the marriage market. The intra-household allocation can be recovered from observations on marriage decisions. Introducing the marriage market in the collective model allows us to independently estimate transfers from labor supplies and from marriage decisions. We estimate a semi-parametric version of our model using 2000 US Census data. Estimates of the model using marriage data are much more consistent with the theoretical predictions than estimates derived from labor supply.

This supplement provides details and extensions omitted from the main paper. I first provide a literature review on closed-form matching functions derived from dynamic equilibrium model of firms-workers matching, and I attempt to draw connections with the dynamic marriage matching function in this paper. Section S.2 relaxes the i.i.d. distributional assumption and considers correlation in the idiosyncratic shocks using the Generalized Extreme Value Distribution. In Section S.3, I propose a bootstrap procedure to derive the standard errors of the marriage gains. Finally, Section S.4 details the estimation results of the logit model used to parameterize the divorce hazard in the dynamic model.

Our article investigates the variation of winning bids in slave auctions held in New Orleans from 1804 to 1862. Specifically, we measure the variation in the price of slaves conditional on their geographical origin. Previous work using a regression framework ignored the auction mechanism used to sell slaves. This introduced a bias in the conditional mean of the winning bid because it depended on the number of bidders participating in the auction. Unfortunately, the number of bidders is unobserved by the econometrician.We adopt the standard framework of a symmetric independent private value auction and propose an estimation strategy to attempt to deal with this omitted variable bias. Our estimate of the mean number of bidders doubled from 1804 to 1862. We find the number of bidders had a significant positive effect on the average winning bid. An increase from 20 to 30 bidders in an auction raised the average winning bid by around 10%. The price variation according to the geographical origin of slaves found in earlier work continues to persist after accounting for the omitted variable. We also find a new result that a considerable premium is paid for slaves originating from New Orleans. However, this price variation disappears once we account for regional productivity differences.