Family Decision Making

Abstract

The classic unitary model assumes that households maximize a household utility function and implies resource ‘pooling’ – household behaviour does not depend on individuals’ control over resources within the household. Since the 1980s, economists have modified the unitary model in ways that have theoretical, empirical and practical implications. Non-unitary alternatives based on joint decision-making by individual family members with distinct preferences broaden the range of observable behaviour consistent with economic rationality. Many non-unitary models imply that both individuals’ control over resources and ‘environmental factors’ can affect intra-household allocation. Empirical evidence has consistently rejected income pooling and, hence, the unitary model.

Economic models of consumer demand and labour supply begin with an individual economic agent choosing actions that maximize his or her utility subject to a budget constraint. How can we reconcile this individualistic theory of the consumer with the reality that people tend to live, eat, work and play in families? Economists have dealt with a possible multiplicity of decision-makers in the family in two ways. The first, in ascendancy until the 1980s, was the unitary approach – treating the family as though it were a single decision-making agent, with a single pooled budget constraint and a single utility function that includes the consumption and leisure time of every family member. The second approach, pioneered in the early 1980s by Manser and Brown and by McElroy and Horney, was to model family behaviour as the solution to a cooperative bargaining game. Other non-unitary approaches have subsequently been developed, including the ‘collective’ model of Chiappori, extensions of the cooperative models of Manser–Brown and McElroy–Horney, and various non-cooperative models.

Most non-unitary models of family behaviour allow two decision makers – the husband and the wife; children are customarily excluded from the set of decision-making agents, though they may be recognized as consumers of goods chosen and provided by loving or dutiful parents. Bargaining models have also been used to analyse interactions between parents and adolescent or young adult children, and between elderly parents and adult children. These interactions may involve family members living in different households, and, in many of these models, who lives with whom is endogenous. As a class, non-unitary models are consistent with a wider range of behaviour than unitary models. The empirical implications of specific non-unitary models of the family depend upon their assumptions about preferences, opportunities, and the form of the game.

Unitary Models

Two models provide the theoretical underpinning of the unitary, or common preference, approach to family behaviour: Samuelson’s (1956) consensus model and Becker’s (1974, 1981) altruist model. The consensus model was introduced by Samuelson to exhibit the conditions under which family behaviour can be rationalized as the outcome of maximizing a single utility function. Consider a two-member family consisting of a husband and a wife. Each partner has an individual utility function that depends on his or her private consumption of goods, but, by consensus, they agree to maximize a social welfare function incorporating their individual utilities, subject to a joint budget constraint that pools the income received by the two spouses. Then we can analyse the household’s observed aggregate expenditure pattern as though the family were a single agent maximizing a utility function (that is, the consensus social welfare function). That is, the household maximizes U (c^h, c^w), where c^h and c^w are the private consumptions of husband (h) and wife (w), subject to the budget constraint p(c^h + c^w)= y = y^h + y^w which pools the individual incomes of husband and wife. This problem generates demand functions cⁱ = fⁱ(p, y) that depend only on prices and total family income and that have standard properties provided the utility functions are well behaved. Thus, the comparative statics of traditional consumer demand theory apply directly to family behaviour under the consensus model. Samuelson did not, however, purport to explain how the family achieves a consensus regarding the joint welfare function, or how this consensus is maintained.

Becker’s (1974, 1981) altruist model addresses these questions, and also provides an account of how resources are distributed within the family. In Becker’s model, the family consists of a group of purely selfish but rational ‘kids’ and one altruistic parent whose utility function reflects his concern for the well-being of other family members. Becker argues that the presence of an altruistic parent who makes positive transfers to each member of the family is sufficient to induce the selfish kids to act in an apparently unselfish way. The altruistic parent will adjust transfers so that each ‘rotten kid’ finds it in his interest to choose actions that maximize family income. The resulting distribution is the one that maximizes the altruist’s utility function subject to the family’s resource constraint, so the implications of the altruist model for family demands coincide with those of the consensus model (see Bergstrom 1989 for a discussion of the conditions under which the rotten kid theorem holds and does not hold).

Unitary models provide a simple, powerful mechanism for generating demand functions and establishing their comparative statics for use in applied problems. Since the introduction of the bargaining paradigm however, these models have been criticized on both empirical and theoretical grounds. We first discuss the theoretical criticisms, and then turn to the accumulating empirical evidence inconsistent with the unitary model.

Dissatisfaction with unitary models on theoretical grounds has been the product of serious study of marriage and divorce. Models of marriage and divorce require a theoretical framework in which agents compare their expected utilities inside marriage with their expected utilities outside marriage, but the individual utilities of husband and wife outside marriage cannot be recovered from the social welfare function that generates consumption, labour supply, fertility, and other behaviour within marriage. If the analysis of marriage and divorce is awkward, the analysis of marital decisions in the shadow of divorce is even more so. If unilateral divorce is possible, individual rationality implies that marital decisions cannot leave either husband or wife worse off than they would be outside the marriage. This individual rationality requirement, however, alters the comparative statics of the model, and destroys the correspondence between the behaviour of a single utility maximizing agent and the behaviour of a family.

Non-unitary Models

Cooperative Bargaining Models

A viable alternative to unitary models of the family must recognize, in a non-trivial fashion, the involvement of two or more agents in determining family consumption. Bargaining models from cooperative game theory, first applied to marriage by Manser and Brown (1980) and by McElroy and Horney (1981), satisfy these conditions. A typical cooperative bargaining model of marriage begins with a family that consists of only two members, a husband and a wife. Each has a utility function that depends on his or her consumption of private goods (U^h(c^h) for the husband and U^w(c^w) for the wife). If agreement is not reached, then the payoff received is represented by the ‘threat point’, (T^h(Z), T^w(Z)) – the utilities associated with a default outcome of divorce or, in the ‘separate spheres’ model of Lundberg and Pollak (1993), a non-cooperative equilibrium within the marriage. The threat point depends, in turn, upon a set of exogenous distribution factors Z that influence individual well-being in the default outcome.

The Nash bargaining model provides the leading solution concept in bargaining models of marriage. Nash bargaining implies that the couple maximizes the Nash product function N = [U^h(c^h) − T^h(Z)] [U^w(c^w) − T^w(Z)] subject to a pooled budget constraint, and this results in demand functions of the form cⁱ = fⁱ(p, y, Z). Thus demands and individual utilities depend upon the distribution factors Z, which may include individual incomes y^h and y^w. This solution can be illustrated by a diagram in utility space (Fig. 1), where AB is the utility-possibility frontier. Nash (1950) shows that a set of four axioms, including Pareto efficiency – which ensures that the solution lies on the utility-possibility frontier – uniquely characterize the Nash bargaining solution.

Family Decision Making, Fig. 1

The Nash bargaining solution

The utility received by husband or wife in the Nash bargaining solution depends upon the threat point: the higher one’s utility at the threat point, the higher one’s utility in the Nash bargaining solution. This dependence is the critical empirical implication of Nash bargaining models: family demands depend, not only on prices and total family income, but also on determinants of the threat point.

In divorce-threat bargaining models, the threat point is the maximal level of utility attainable outside the marriage. Hence, the threat point depends on wage rates and on the assets each spouse would take if the marriage were to end in divorce. The divorce threat point is also likely to depend on environmental factors (extra-household environmental parameters, or EEPs, in McElroy’s 1990, terminology) that do not directly affect marital utility, such as conditions in the remarriage market and the income available to divorced men and women. The family demands that result from divorce-threat marital bargaining will therefore depend upon these parameters as well.

In the separate spheres bargaining model of Lundberg and Pollak (1993), the threat point is internal to the marriage, not external as in divorce-threat bargaining models. The husband and wife settle their differences by Nash bargaining, but the alternative to agreement is an inefficient non-cooperative equilibrium within marriage. In this non-cooperative equilibrium, each spouse voluntarily provides household public goods, choosing actions that are utility-maximizing, given the actions of their partner. Divorce may be the ultimate threat available to marital partners in disagreement, but a non-cooperative marriage in which the spouses receive some benefits due to joint consumption of public goods may be a more plausible threat in day-to-day marital bargaining.

The introduction of this internal threat point has important implications, because the separate spheres model generates family demands that, under some circumstances, depend not on who receives income after divorce, but on who receives (or controls) income within the marriage. Lundberg and Pollak assume gender specialization in the non-cooperative provision of household public goods, with the husband providing one good out of his own resources, and the wife providing a separate good from her individual resources. This specialization occurs because socially prescribed gender roles provide a focal point for non-cooperative bargaining. The individual reaction functions in this game determine a Cournot–Nash equilibrium in which the public goods contributions may be inefficiently low, and may depend upon the distribution of individual incomes within the family.

As the divorce-threat and separate spheres models show, cooperative bargaining does not necessarily imply income pooling, that is, the property that demands depend only on total household income, rather than its separate components. Bargained outcomes depend upon the threat point, and the income controlled by husband and wife will affect family behaviour (and the relative well-being of men and women within marriage) if this control influences the threat point. This dependence implies that public policy (for example, taxes and transfers) need not be neutral in their effects on distribution within the family. Also, the absence of pooling and the presence of extra-household environmental parameters in family demands yield a model that can be tested against the unitary alternative. For example, changes in the welfare payments available to divorced mothers, or in the laws defining marital property and regulating its division upon divorce, should affect distribution between men and women in two-parent families through their effect on the threat point.

The ‘Collective’ Approach

Most models of the family either assume or conclude that family behaviour is Pareto efficient. Unitary models ensure Pareto efficiency by assuming a family social welfare function that is increasing in the utilities of all family members: when such a utility function is maximized, no member can be made better off without making another worse off. Cooperative bargaining models characterize the equilibrium distribution by means of a set of axioms, one of which is Pareto efficiency.

Pareto efficiency is the defining property of the ‘collective model’ of Chiappori (1988, 1992). Rather than applying a particular cooperative or non-cooperative bargaining model to the household allocation process, Chiappori assumes only that equilibrium allocations are Pareto efficient. He demonstrates that, given a set of assumptions including weak separability of public goods and the private consumption of each family member, Pareto efficiency implies, and is implied by, the existence of a ‘sharing rule’. Under a sharing rule, the family acts as though decisions were made in two stages: first total family income is divided between public goods and the private expenditures of each individual, and then each individual allocates his or her share among private goods. The collective model implies a set of testable restrictions on the response of household demands to ‘distribution factors’ that affect the household’s sharing rule.

Non-cooperative Bargaining Models

The use of models that assume Pareto efficiency of outcomes relies on the judgement that information within families is relatively good (or at least not asymmetric) and that members are able to make binding, costlessly enforceable agreements. Since legal institutions do not provide for external enforcement of contracts regarding consumption, labour supply, and allocation within marriage, however, the binding-agreement assumption is unappealing.

Non-cooperative game theory focuses on self-enforcing agreements. It is possible for non-cooperative bargaining to yield Pareto efficient outcomes under certain conditions. For example, repeated non-cooperative games have multiple equilibria which are sustained by credible threats of punishment, and some of these equilibria are Pareto efficient. One of the benefits of modelling distribution within marriage as a non-cooperative game is the opportunity to treat efficiency as endogenous, potentially dependent upon the institutions and social context of marriage in a particular society and upon the characteristics of the marital partners.

The prevalence of destructive or wasteful phenomena such as domestic violence and child abuse, as well as the demand for marriage counselling and family therapy, suggests that we consider the possibility that family behaviour is sometimes inefficient. Other researchers have pointed to gender segmentation in the management of businesses or agricultural plots in many countries as evidence of an essentially non-cooperative, and possibly inefficient, family environment. One piece of evidence is provided by Udry (1996), who finds that in Burkina Faso the marginal product of land controlled by women is below the marginal product of land controlled by men and concludes that the household allocation of inputs to male- and female-controlled agricultural plots is inefficient.

Intertemporal Models

In dynamic bargaining models, decisions made in one period can alter the relative bargaining power of individual family members in future periods. If family members cannot agree on rules for sharing household resources in the future, and make credible promises to obey such rules, then inefficiencies of the standard ‘hold-up’ variety will result. Lundberg and Pollak (2003) model the two-earner couple location problem as a two-stage game in which a couple must decide where to live and whether to stay together without being able to make binding commitments about allocation in the new location. Lundberg and Pollak show that the equilibrium of this two-stage game need not be efficient even if the second-stage game is conditionally efficient (that is, efficient given the location determined at the first stage).

Even if prospective spouses can make binding agreements in the marriage market, they cannot make agreements with potential spouses they have not yet met. Konrad and Lommerud (2000) show that individuals will over-invest in education prior to marriage to increase their marital bargaining power, even if they expect to bargain cooperatively once they find and marry a spouse. Models of limited commitment in marriage can also be applied to decisions about childbearing, career choice and work effort.

Empirical Evidence

Recent empirical evidence suggests that the restrictions imposed on demand functions by unitary models are not well supported. Rejections of the family income pooling hypothesis, in particular, have been most influential in weakening economists’ attachment to unitary models. Unitary models imply that the fraction of income received or controlled by one family member should not influence demands, given total family income. A large number of recent empirical studies have rejected pooling, finding that earned and unearned income received by the husband or wife significantly affect demand patterns when total income or expenditure is held constant. Some studies find that children appear to do better when their mothers control a larger fraction of family resources (Thomas 1990; Haddad and Hoddinott 1994). These results are inconsistent with the unitary framework, but consistent with both bargaining models (provided individual incomes affect the threat point) and with the collective model (provided individual incomes are included among the ‘distribution factors’ that influence the household’s sharing rule).

The collective model imposes, in addition, a proportionality restriction on the influence of distribution factors on demands. The ratio of the marginal propensities to consume any two goods must be the same for all sources of income, for example, because individual incomes affect consumption only through the sharing rule. A generalization of Slutsky symmetry in price effects can also be derived (Browning and Chiappori 1998). A series of empirical tests have found that consumption expenditures in households reject the unitary framework but are generally consistent with the collective model (for example, Bourguignon et al. 1993; Browning and Chiappori 1998).

Tests of the unitary model against non-unitary alternatives require a measure of husband’s and wife’s relative control over resources. Relative earnings would seem to be an attractive candidate for this measure, since labour income is by far the largest component of family income, and earnings data are readily available and reliably measured. Also, the earnings of wives relative to husbands have increased dramatically in the United States and many other countries, and we would like to assess the distributional consequences, if any, of this change. The difficulty with this approach is that earnings are clearly endogenous with respect to household time-allocation decisions. Earnings are the product of hours worked, a choice variable, and hourly wage rates, which measure the prices of time for husband and wife and therefore enter demand functions directly in the unitary model. This implies that households with different ratios of wife’s earnings to husband’s earnings are likely to face different prices and may have different preferences.

One might try to avoid these problems by testing the pooling of unearned income rather than earnings. Unearned income is not contaminated by price effects, but most unearned income sources are not entirely exogenous with respect to past or present household behaviour. Schultz (1990), who like Thomas (1990) uses unearned income to test the pooling hypothesis, points out that variations in unearned income over a cross-section are likely to be correlated with other (possibly unobservable) determinants of consumption. For example, property income reflects, to a considerable extent, accumulated savings and is therefore correlated with past labour supply and, if those who worked a lot in the past continue to do so, with current labour supply. Public and private transfers may be responsive to household distress due to unemployment or bad health, and may be related to expenditures through the events that prompted them. Unexpected transfers such as lottery winnings, unexpected gifts or unexpected bequests will affect resources controlled by individuals without affecting prices, but are likely to be sporadic and unimportant for most families.

Other standard empirical proxies for the relative bargaining power of husbands and wives (or, in the terminology of the collective model, distribution factors) include the relative ages, educations, or measures of family background of husband and wife. The interpretation of these factors, however, is contaminated by assortative mating on unobserved characteristics. It would be unwise to assume that a highly educated woman married to a man with less education has relatively more control over the allocation of household resources without controlling for other personal characteristics that affected the decision of this couple to marry in the first place. The same critique applies to measures of relative assets brought to the marriage by the husband and wife, even when they maintain separate ownership of these assets during marriage and divorce.

The ideal test of the pooling hypothesis, and therefore of the unitary family model, would be based on an experiment in which some husbands and some wives were randomly selected to receive income transfers. A less-than-ideal test could be based on a ‘natural experiment’ in which some family members receive an exogenous income change, and one can study a constant population of families before and after the change. Several studies exploiting such policy changes have found evidence against income pooling, and have also supported the hypothesis that women have a greater propensity, on average, to spend on children’s goods.

Lundberg et al. (1997) examine the effects of a policy change in the United Kingdom that transferred a substantial child allowance from husbands to wives in the late 1970s. They find strong evidence that a shift towards relatively greater expenditures on women’s goods and children’s goods coincided with this income redistribution, and interpret this as a rejection of the pooling hypothesis. Duflo (2000) studied the effect of an extension of the South African Old Age Pension on children’s health and nutrition, and found that payments to grandmothers had a substantial effect on these outcomes, especially for girls, while payments to grandfathers had no effect. These results both reject a unitary framework for multi-generation families, and support the hypothesis that children benefit from female control of household resources. Tests of pooling using PROGRESA, a public cash transfer programme in Mexico directed at women, have been more complicated. A random assignment social experiment, PROGRESA had a substantial income effect and benefits were conditional on child school enrolment. Attanasio and Lechene (2002) reject household pooling using PROGRESA data, and Rubalcava et al. (2004) find that these transfers to women were more likely to be spent on child goods, improved nutrition, and investments in small livestock than other household income.

One important implication of non-unitary models of the household is that government programmes targeted to particular individuals within households may affect the intra-household allocation. Even if, as rejections of the unitary model suggest, targeted transfers are effective in the short run, we cannot conclude that targeted transfers will be effective in the long run. Lundberg and Pollak (1993) show that the long-term effects of such policy changes on intra-household allocation may be very different from the short-term effects, as adjustments occur in the marriage market of subsequent cohorts. If prospective couples can make binding agreements when they marry, then the distributional effects of policy can be offset by subsequent generations of families. Even if such marital agreements are not possible, changes in the expected gains to marriage will affect who marries whom and who marries at all, and this will also affect the long-run distributional effects of policy. Cross-sectional studies of intra-household allocation that use state variation in policy or laws (such as divorce laws or property settlement rules) will be estimating the equilibrium effects of long-standing differences in policy, including any marital sorting effects.

Conclusion

The classic unitary model assumes that households maximize a household utility function subject to household resource and technology constraints. Unitary models imply income or resource ‘pooling’ – household behaviour does not depend on individual control over resources within the household. Since the 1980s, economists have modified the unitary model in ways that have theoretical, empirical and practical implications. Non-unitary alternatives based on joint decision-making by individual family members with distinct preferences broaden the range of observed behaviour consistent with economic rationality. Non-unitary models also permit the analysis of marriage and divorce within the same framework as household demands and the labour supply of household members. Unlike unitary models, many non-unitary models imply that both individual control over resources and ‘environmental factors’, such as divorce laws, that affect the well-being of individuals outside the household can affect intrahousehold allocation. Empirical evidence has consistently rejected income pooling and, hence, the unitary model.

See Also

• Collective Models of the Household

• Family Economics

• Intrahousehold Welfare

• Marriage and Divorce