In this chapter we discuss in more detail the determination of the division of the marital surplus and how it responds to market conditions. If each couple is considered in isolation, then, in principle, any efficient outcome is possible, and one has to use bargaining arguments to determine the allocation. From a global perspective, however, the stability of the assignments restricts the possible divisions because of the ability to replace one spouse by another one. The options for such substitution depend on the distributions of the marital-relevant attributes in the populations of men and women to be matched. In this chapter we precisely ask how the marriage market influences the outcome in the ideal, frictionless case discussed previously. Although the division within marriage is not always fully determined, some qualitative properties of the division can be derived from information on the joint distribution of male and female characteristics together with a specification of the household output function.

As before, we discuss separately the cases of discrete and continuous distributions. The general intuition goes as follows: in the discrete case, competition puts bounds on individual shares but does not completely determine them; this is so because on the marriage market, each potential spouse has only a finite number of “competitors,” none of whom is a perfect substitute – so some elements of “bilateral monopoly” persist.

Individuals in society have many potential partners. This situation creates competition over the potential gains from marriage. In modern societies, explicit price mechanisms are not observed. Nevertheless, the assignment of partners and the sharing of the gains from marriage can be analyzed within a market framework. The main insight of this approach is that the decision to form and maintain a particular union depends on the whole range of opportunities and not only on the merits of the specific match. However, the absence of explicit prices raises important informational issues. There are two main issues distinguishing the approaches used in the matching literature. The first issue concerns the information structure, and the second relates to the extent of transferability of resources among agents with different attributes. Specifically, models based on frictionless matching assume that perfect and costless information about potential matches is available to all participants; the resulting choices exclusively reflect the interaction of individual preferences. Such models may belong to several classes depending on whether or not compensating transfers are allowed to take place between individuals and, if so, at what “exchange rate.” Still, they all rely on a specific equilibrium concept, namely, stability. Formally, we say that a matching is stable if

1. There is no married person who would rather be single.

2. There are no two (married or unmarried) persons who prefer to form a new union.

The interest in stable marriage assignments arises from the presumption that in a frictionless world, a marriage structure that fails to satisfy (1) and (2) either will not form or will not survive.

Introduction

There is a growing concern that the higher turnover in the marriage market causes more children to live with single mothers or stepparents. In the United States in 2005, 68 percent of children younger than 18 years old lived with two parents (including stepparents), 23 percent lived only with their mother, 5 percent lived only with their father, and the rest lived in households with neither parent present. There is substantial evidence that children of divorced parents do not perform as well as comparable children in intact families. However, such empirical evidence does not necessarily imply a causal relationship. Indeed, Bjorklund and Sundstrom (2006) argue that inferior performances of divorced children can be attributed largely to selection effects.

The purpose of this chapter is to examine in more detail the impact of marriage and divorce on children. In particular, we wish to discuss the determination of expenditures on children and their welfare under various living arrangements, with and without the intervention of the courts. We take into account that parents continue to care about their natural children following separation, which may induce voluntary commitments of child-support transfers from fathers to their custodial ex-wives in the event that she remain single. Such conditional transfers can increase the bargaining power of the mother on remarriage and thus benefit the children. We then show that exogenous shocks that raise the divorce rate can increase the welfare of the children and their mothers because they provide incentive to fathers to raise their commitments.

Preferences

In Chapter 2 we informally reviewed the gains from marriage in some generality. The existence of potential gains from marriage is not sufficient to motivate marriage and to sustain it. Prospective mates need to form some notion as to whether families realize the potential gains and how they are divided. In this chapter we consider these issues in a very specific context. The context is a two-person (e.g., woman a and man b) household in which the only (static) decision is how much to spend on various market goods that are available at fixed prices, given fixed total household expenditure on all goods. Although very special, this context allows us to discuss formally many of the issues that will be used in other contexts in later chapters.

Some commodities are private and some public. Private goods are consumed nonjointly by each partner, and public goods, such as heating, are consumed jointly and nonexclusively by the two partners. In other words, private goods are characterized by an exclusion restriction property: the fact that I consume a particular apple de facto excludes anyone else from consuming the same apple. With public goods, on the contrary, no such restriction exists: that I enjoy seeing a beautiful painting on my wall does not preclude my spouse from enjoying it just as much (or even disliking it).

What Are the Objects of Interest?

We have seen earlier that various approaches can be used to describe household behavior, from the unitary setting to noncooperative approaches and the collective model. Ultimately, the choice among these various frameworks will rely on particular considerations. First, general methodologic principles may favor one approach over the others. For instance, one can argue that the unitary framework is not totally faithful to methodologic individualism, a cornerstone of micro theory that postulates that individuals, not groups, are the ultimate decision makers. A second requirement is the model's ability to generate testable predictions for observable behavior that can be taken to data using standard techniques. Standard consumer theory fares pretty well in this respect. Utility maximization under a linear budget constraint yields strong predictions (e.g., adding-up, homogeneity, Slutsky symmetry, and negative semidefiniteness and income pooling), and adequate methodologies have been developed for testing these properties. Finally, a crucial criterion is the fruitfulness of the approach, particularly in terms of normative analysis and policy recommendations. A remarkable feature of standard consumer theory is that individual preferences can be uniquely recovered from demand functions (if these satisfy the Slutsky conditions); it is therefore possible to analyze welfare issues from the sole knowledge of observed behavior. This is a particular case of the general requirement that the model be identifiable, that is, that it should be possible to recover the underlying structure from observed behavior.

The first line of argument, concerning methodologic individualism, was evoked earlier. In this chapter we concentrate on the remaining two aspects, namely, testability and identifiability of preferences and processes from observed behavior. Most of the existing knowledge for nonunitary models concerns the cooperative framework and especially the collective model. The testability requirement per se is not problematic. The idea that a model should generate predictions that can be taken to data belongs to the foundations of economics (or any other science!).

The purpose of this chapter is to present some basic and general facts about marriage and the family. The chapter is intended to motivate the analysis that follows in the rest of the book by showing how presumably noneconomic activities, such as marriage and fertility, interact with economic considerations such as work, wages, and schooling.

Marriage, Divorce, and Remarriage

Marital Status

Marriage is a “natural state.” Table 1.1 shows the proportions (the “stocks”) in each marital state for three different years for six high-income countries. These figures show that most of the adult population (aged 20 or older) is married at any given time (about 55 to 70 percent). However, the proportion of the adult population that is married has declined in all six countries over the last fifty years. This trend is accompanied by a larger proportion of never-married and a higher proportion of divorced individuals, with little change in the proportion of widowed (because of the offsetting effects of reduced marriage and mortality). In all countries and at all times, the proportion of never-married women is significantly lower than the proportion of never-married men; this is partially attributable to the fact that men marry later.

Explaining these cross-country regularities and trends is a major challenge for demographers and economists. Factors that may be related to the changes in marital status that we see in this table are changes in the age structure, delays in marriage, the relative attractiveness of alternative household arrangements, higher turnover, and longer life spans.

This chapter provides a simple model of the marriage market that includes fertility, divorce, and remarriage and addresses some of the basic issues associated with the higher turnover in the marriage market. For this purpose, we introduce search frictions, heterogeneity, and unexpected shocks to match quality. The model is simple enough to identify the welfare implication of increasing turnover. The main result is that the prospects of remarriage generate multiple equilibria due to a positive feedback whereby a higher aggregate divorce rate facilitates remarriage, which, in turn, raises the incentives of each couple to divorce. Moreover, when multiple equilibria exist, an equilibrium with higher divorce and remarriage rates generates higher expected welfare for all adult participants in the marriage market. This holds even though parents internalize the negative impact of divorce on their children. This result is a direct outcome of the positive search externalities that are embedded in the model. The main lesson is that a high aggregate divorce rate can be beneficial because it facilitates the recovery from negative shocks to match quality, allowing couples to replace bad marriages by better ones. In this chapter we make the strong assumption that conditional on marital status, the welfare of children is exogenous. A subsequent chapter will introduce postdivorce transfers between partners that can mitigate the negative impact of divorce on children.

From an economic point of view, marriage is a partnership for the purpose of joint production and joint consumption. However, consumption and production are broadly defined to include goods and services such as companionship and children. Indeed, the production and rearing of children are the most commonly recognized roles of the family. But there are other important gains from marriage, both economic and emotional. Although the economic gains may not be the most important motivation for living together with someone (“marrying”), we focus on them here and examine five broad sources of potential material gain from marriage, that is, why “two are better than one”:

1. The sharing of public (nonrival) goods. For instance, both partners can equally enjoy their children, share the same information, and use the same home.

2. The division of labor to exploit comparative advantage and increasing returns to scale. For instance, one partner works at home and the other works in the market.

3. Extending credit and coordination of investment activities. For example, one partner works when the other is in school.

4. Risk pooling. For example, one partner works when the other is sick or unemployed.

5. Coordinating child care. This is a public good for the parents.

We emphasize that the gains discussed here are only potential – if they are realized to their full extent and who benefits from them are the subject matter of much of the rest of this book. We shall cast our discussion in terms of two agents who choose to live together, but many of the points apply generally to a many-person household. We also note that the gains for someone may be different depending on the potential partner. In later sections of this book we will expand and elaborate on many of the issues presented in this chapter.