Marriage Market Equilibrium and Bargaining in Marriage*

This paper examines marriage market equilibrium when allocation is determined by bargaining in marriage rather than binding agreements between prospective spouses. We view sorting in the marriage market and allocation in marriage as a two-stage game in which prospective spouses, when they meet in the marriage market, foresee the allocation that would emerge from bargaining in marriage, but are powerless to alter it. Our analysis is consistent with a wide range of noncooperative and cooperative bargaining models as well as with Becker's altruist model, in which one spouse has the power to impose his or her preferred allocation. Our approach is in contrast to the now-standard Beckerian assumption that prospective spouses, when they meet in the marriage market, make binding agreements about allocation in marriage. With binding agreements in the marriage market, the appropriate mathematical framework for analyzing the marriage market is the Koopmans-Beckmann assignment model and marriage market equilibrium is Pareto efficient. With bargaining in marriage, the appropriate mathematical framework for analyzing the marriage market is the Gale-Shapley matching model. Even if bargaining leads to Pareto-efficient allocations within each marriage, the marriage market equilibrium -who marries, and who marries whom-need not be Pareto efficient. The inability of prospective spouses to make binding agreements in the marriage market about allocation in marriage may explain behavior that otherwise appears anomalous. The standard Beckerian marriage market model predicts that in equilibrium there cannot be both unmarried men and unmarried women. Yet what demographers call the “European marriage pattern” is characterized by high rates of non-marriage for both men and women. Marriage Market Equilibrium and Bargaining in Marriage* Shelly Lundberg, University of Washington and Robert A. Pollak, Washington University in St. Louis We model sorting in the marriage market and allocation in marriage as a two-stage game. The first stage, the marriage market, determines who marries, and who marries whom. The second stage, bargaining in marriage, determines allocation within each marriage. Our analysis is consistent with a wide range of household allocation models, including noncooperative and cooperative bargaining models of marriage, Chiappori's collective approach, and Becker's altruist model. We assume that prospective spouses, when they meet in the marriage market, foresee the allocation that would emerge (e.g., from Nash bargaining) but are powerless to alter it. Our critical premise is the inability of individuals to make binding agreements before marriage about allocation during marriage. This implies that, with transferable utility and no search frictions, an appropriate framework for analyzing marriage market equilibrium is the Gale-Shapley (1962) matching model which they introduced and analyzed in “College Admissions and the Stability of Marriage.” We show that, without binding agreements in the marriage market, the implied marriage market equilibrium need not be Pareto efficient. The intuition is simple: even if marriage is productivity-enhancing, an individual may prefer to remain unmarried rather than enter a marriage in which his or her spouse has too much bargaining power. The standard assumption in the marriage market literature is that prospective spouses, when they meet in the marriage market, can make binding agreements about allocation in marriage. Becker (1973, 1991) was the first to recognize that, with binding agreements in the marriage market, the appropriate framework for analyzing marriage market equilibrium is the Koopmans-Beckmann (1957) assignment model. The behavioral foundations of the Choo and Siow (2006) marriage matching functions also assume that all match-specific returns are divided at marriage. With binding agreements in the marriage market, transferable utility, and no search frictions, the implied marriage