Microeconomics of Demographic Behavior
MICROECONOMICS OF DEMOGRAPHIC BEHAVIOR
This article briefly surveys the intellectual development and empirical implications of the literature on the microeconomic theories of demographic behavior. The behaviors discussed in this article include fertility behavior, investment in the human capital of children, marriage, divorce, non-marital childbearing, and selected aspects of female labor supply. Other demographic variables such as mortality and migration have been analyzed using microeconomic theory, but are not treated in this article. This article begins with fertility, the first of these behaviors to be studied using the microeconomic approach.
Microeconomic Fertility Theory
The view that fertility behavior can be analyzed within the choice-theoretic framework of neoclassical economics originated in a model of fertility by economist Harvey Leibenstein (1922–1994) in 1957 that stressed the importance of intergenerational transfers from children as a form of old age security as a motivation for fertility in developing countries. A far more influential economic model of fertility was presented shortly thereafter in a pioneering paper by economist Gary Becker in 1960. Becker attempted to reconcile the prediction from demand theory that increases in income should raise the demand for children with the facts that income growth has been accompanied by secular decline of fertility and that family income is inversely associated with cross-section differentials in the industrialized countries. Becker sought to address this apparent paradox by applying the theory of the consumer to show that these secular changes and cross-sectional differences in the completed family sizes of households in developed countries were the result of variations in family incomes and the prices, or opportunity costs of children.
In his 1960 paper, Becker introduced two key elements of all microeconomic theories of household behavior: preferences and constraints. A household consisting of a husband and wife is assumed to have preferences for goods and services that contribute their own adult standard of living and, crucially, also to have preferences for children. The household faces a budget constraint determined by its lifetime resources and market prices or opportunity costs of these resources. Using terminology introduced by economist Pierre-Andre Chiappori in 1992, Becker assumed a unitary model of the household in which a husband and wife behave as if their preferences are described by a single household utility function. This common utility function might be justified by assuming that the husband and wife have identical preferences or that one of them controls the household's resources and has the power to dominate household decisions. Later, this article will consider "collective" household models in which husbands, wives, and even children all have their own preferences and household behavior that reflects the inter-action of these actors within some kind of bargaining model. Meanwhile, the unitary model is utilized as a convenient simplifying assumption to be replaced by more appropriate assumptions when the question under analysis requires separate consideration of the interests of the husband and wife as, for example, when considering the formation or dissolution of the household through marriage and divorce, the decision of whether to bear children within marriage, or out of wedlock, or how the allocation of resources to children may vary with the resources owned by the father and mother.
Quality versus Quantity of Children
In conventional economic theory, the demand function for a given good can be derived by assuming that a household maximizes its utility subject to its budget constraint. Hypotheses about observable behavior are then developed from comparative static analysis that shows how demand varies as the budget constraint shifts due to changes in income, the price of the given good, or prices of related goods. When this methodology is applied to fertility behavior, Becker noted an apparent conflict between the predictions of theory and empirical evidence. As income rises, theory predicts that the quantity of most goods should increase, with the exception of "inferior" goods that tend to be inferior members of a class–the potato as an inferior form of food is a common textbook example. Empirically, Becker noted that fertility had been declining secularly at the same time that incomes had grown enormously and, in cross-sections, that there appeared to be a negative correlation between family incomes and number of children.
Becker rejected the two most obvious ways to reconcile theory and data. He argued that the true effect of income on the demand for children is unlikely to be negative because children are not inferior members of some broader class of goods. He also rejected the idea that the price of children is higher because more is spent on them when incomes are high or in higher compared with lower income families. All families in a given market face the same prices regardless of their income. Expenditures on children are a matter of choice, not an exogenous component of the budget constraint.
Becker then introduced the important idea that the demand for children has a qualitative as well as a quantitative dimension such that total expenditures on children are equal to the number of children multiplied by quality per child and by a price index reflecting the cost of inputs into children relative to adult goods. Within the quality—quantity model, expenditures on children tend to increase with income, implying that children are normal goods, but most of the increase is due to rising child quality while fertility does not vary strongly with income.
Further analysis of the quality—quantity model by economist Robert Willis and by Becker and economist H. Gregg Lewis, all in 1973, provided an underlying reason for the differential magnitude of the income effects on the number and quality of children. Within this model, the marginal cost of an additional child is proportional to its quality while the marginal cost of an addition to quality per child is proportional to the number of children. It follows that the relative marginal cost of quantity to quality is equal to the ratio of quality to quantity. As income increases, the relative marginal cost of quantity to quality therefore must shift in favor of whichever of these aspects of children has the larger income elasticity, causing a substitution effect that reinforces the change in that attribute. Thus, if the true income elasticity of quality is larger than that of quantity, an increase in income causes an income effect plus an induced substitution effect tending to raise quality per child and an income effect minus an induced substitution effect that may even cause a reduction in fertility.
Household Production and Allocation of Time
The next major steps in the development of a microeconomic model of fertility involved a more careful specification of a household's resource constraints, a correspondingly richer definition of the cost of children, and a linkage of fertility to other household behaviors, especially female labor supply. The key idea in these developments is to consider the household as a productive unit as well as a consumption unit. In the first application of this idea to fertility behavior in 1963, economist Jacob Mincer argued that the mother's time was a crucial input to childcare and that the opportunity cost of this time is measured by the woman's potential market wage. Given that the husband's income and the wife's earnings potential tend to be positively correlated, the marginal cost of children will tend to be higher in higher income families, thus suggesting another reason for a negative correlation between family income and fertility. In a groundbreaking paper on married women's labor supply in 1962, Mincer argued that the productivity of nonmarket time for women led both to a lower level of market labor supply than for men and to greater responsiveness of labor supply to increased real wages than is true for male labor supply. Greater responsiveness arises from the high degree of substitutability between market and nonmarket goods ultimately satisfying the same needs (e.g., home-cooked meals vs. restaurant meals) whereas the relevant margin for male labor supply is more likely between goods and leisure, which are less substitutable. Secular growth of real market wages thus could consistently explain both the secular increase in female labor supply and secular decrease in male labor supply. Labor supplies of both sexes are reduced by the gain in real income and associated increase in the demand for leisure caused by rising real wage rates; however, the substitution effects in favor of work caused by higher real wages tend to outweigh the income effect for married women and to be outweighed by the income effect for married men.
In 1965 Becker produced a formal model of household production and time allocation in which he assumed that all commodities that a household ultimately values appear in the household's utility function. These are produced with inputs of purchased goods and time according to household production functions that reflect technology as distinct from the utility function that reflects taste. Within this framework, for example, differences in household demand for heating oil in Miami, Florida, and Minneapolis, Minnesota, are derived from the demand for the nonmarket household commodity, "comfortable temperature and humidity," which appears in the utility function. This approach provides a useful heuristic device for developing models of related investments such as furnaces and insulation or the study of the impact of air conditioning on the development of the U.S. Sunbelt.
More generally, the household production model, with its emphasis on time allocation, and its capacity to incorporate technological, environmental, and biological variables into economic models of household decisionmaking, has had broad influence on research on demographic behavior. Willis presented a model of fertility behavior that synthesizes the quality—quantity model of Becker using the concepts of household production and human capital investment. It emphasized the role of female time allocation between market and home work based on the earlier work of Becker in 1964 and 1965 and Mincer in 1963. The model assumes that the wife's time is combined with goods purchased in the market to produce two distinct household commodities: adult standard of living and child services where child services are the product of quality per child and number of children. A key technological assumption is that children are intensive users of female time relative to the adult standard of living from which it follows that increases in the marginal value of female time cause an increase in the ratio of the marginal cost of children to the marginal cost of adult standard of living. Increases in the cost of female time therefore tend to cause substitution effects weighted against children which, it is argued, will tend to induce quality—quantity interactions that reduce fertility while perhaps even raising quality per child.
Cost of Time and the Fertility Transition
The cost-of-time hypothesis is one of the leading hypotheses advanced to account for secular fertility decline and for the negative cross-sectional relationship between fertility and potential female market wage rates, often proxied by female education. Empirical tests of this hypothesis have been complicated by the fact that, according to the theory, variables such as the wife's labor supply and her market wage are chosen simultaneously with fertility and expenditures on children and that crucial prices that determine decisions are not directly observable. A woman will enter the labor force if her market wage exceeds the shadow price of time, an unobservable quantity that measures the marginal value of her time in household production, and, given that children are relatively time intensive, is positively related to the shadow price of children–another unobservable quantity. Women who do enter the labor force adjust their labor supply until the shadow price of time is equal to the market wage. Hence, the market wage, which is observable, can be used as a measure of the price of time and, indirectly, of the marginal cost of children. However, the value of time remains unobservable for nonworking women and, worse, these women are a self-selected non-random sample of all women so that the wage rates of observationally similar working women may not provide a suitable estimate of the time value of nonworking women. Methods to allow econometric estimation of theoretically relevant behavioral relationships in this situation were pioneered by economist James Heckman (1974a).
Another important issue, first analyzed by Mincer and economist Solomon Polachek in 1974, is that the value of a woman's time in market work depends on the human capital she acquires through labor market experience. Willis's 1973 study suggests that the dependence of the value of time on market experience may promote "corner solutions" in which some women pursue careers and remain childless while other women have large families and remain out of the labor force. In part, the tension between allocating time to children or to career development may be resolved through the purchase of childcare services in the market, as first analysed by Heckman in 1974. To the extent that market childcare can substitute for the mother's care, the household technology of families of high wage women may actually become relatively goods intensive. This is consistent with the declining negative correlation between market work and fertility, noted by economist V. Joseph Hotz, and his fellow researchers, in 1997, that has accompanied the dramatic increase in female labor force participation of mothers with young children.
If children are relatively goods intensive among high wage women who substitute market childcare for their own care, then increases in female wages reinforce income effects and the correlation between income and fertility may become positive in such groups. To the extent that lower wage women supply market childcare, however, the overall opportunity cost of children will increase over time as the real wage of women increases. An analysis by economist Dianne J. Macunovich in 1996, however, suggests that the real female wage, holding education constant, has not increased since the mid-1970s nor has U.S. fertility experienced major changes although rates of childlessness have increased and the mean age of childbearing has also increased.
The static models of fertility behavior described so far in this article make the highly unrealistic assumption that decisions about fertility, work, and other household life cycle decisions are made simultaneously at the beginning of marriage with perfect foresight. Recognizing this limitation, economists began to build dynamic models of fertility decisionmaking under uncertainty, shortly after static models had been introduced. An initial application to imperfect fertility control and contraception by Heckman and Willis, in 1975, built on stochastic models of reproduction developed in 1964 by biostatisticians Edward Perrin and Mindel Sheps with further developments described in more detail by Hotz, Jacob Klerman, and Willis in 1997. While dynamic models make more realistic assumptions, they can also be analytically intractable. In an important advance in the use of dynamic models in 1984, economist Kenneth I. Wolpin showed how numerically specified structural dynamic models of demographic behavior could be estimated and the estimates used to answer counterfactual policy questions. In 2002, economist Marco Francesconi provided an example of a dynamic model of the interaction between fertility and work decisions by married women.
Divergent Interests of Husband and Wife
An important limitation of the theories discussed so far is their assumption that the unit of analysis is a unitary household in which the interests or preferences of the husband and wife are not distinguished. As noted earlier in this article, this assumption must be abandoned before it is possible to analyze the formation and dissolution of households through marriage and divorce or a variety of questions concerning the division of labor, the allocation of household resources and the distribution of welfare among household members. Becker, as usual, made seminal contributions with his theories of marriage and divorce. In these theories, the household is viewed as a productive partnership. For a given marriage to be formed or maintained, each partner must perceive himself or herself to be better off than they could be in an alternative arrangement as single person or in another potential match. Becker shows that a marriage market equilibrium will result in an efficient assignment of males and females such that no alternative assignment could make any individual or set of individuals better off without making some others worse off.
These models allow analysts to address a number of new questions. One concerns sorting in marriage markets. Under what conditions does like marry like or, alternatively, do unlikes marry? One possibility analyzed by Becker emphasizes gains to specialization in market or nonmarket labor, reinforced by incentives to invest in acquiring skills that are proportional to the time spent in market or non-market activities. These incentives, Becker argues, lead to a sexual division of labor within the household and to a pattern of negative assortative mating in the marriage market such that the market wage rates of husbands and wives would be negatively correlated. Although a sexual division of labor within households is almost universally in evidence, there are few if any empirical instances of negative assortative mating either on actual market wages or on potential wages as measured by education. A theoretical explanation for this puzzle was provided by economist David Lam in 1988. Lam argued that economies of scale in household production, including the important special case of household public goods, create gains to positive assortative mating which, under plausible conditions, more than offset the gains from negative assortative mating associated with specialization of household labor. Evidence presented by demographers Lisa K. Jepsen and Christopher A. Jepsen in 2002, comparing the matching patterns of married couples, opposite-sex cohabiting couples, and same-sex couples, is broadly consistent with Lam's analysis. They found positive assortative mating on all traits for all couple types, but stronger correlations for nonmarket traits than for market traits and stronger correlations for married couples than opposite-sex couples and the weakest correlations for same-sex couples. Lam's model rationalizes these correlations because children are the most prominent examples of household public goods and match-specific investments in other collective household goods tend to be larger for more durable unions.
Divorce and Child Support
Models that allow for separate interests of men and women can help explain phenomena such as the failure of divorced fathers to pay child support and the rise of out-of-wedlock childbearing.
In 1985, Willis and economist Yoram Weiss showed that, relative to marriage, divorce reduces the incentives of both parents to devote resources to their children. In particular, it may cause a noncustodial father who served as an exemplary breadwinner for his wife and children during marriage to become, upon divorce, a "deadbeat dad" who fails to pay child support. This change in behavior upon divorce occurs even if it is assumed that the strength of the father's concern for his children's welfare remains unchanged.
The key assumption underlying their analysis is that children are "collective goods" from the standpoint of their parents because each parent values the welfare of the children. Because an additional expenditure on a child by one parent benefits the other parent, there is a potential gain to both parents in sharing in the cost of the child. The optimal level of child expenditure occurs when the sum of the marginal values of a dollar spent on the child of each parent is equal to one dollar.
Marriage provides an institutional setting that facilitates a cooperative allocation of resources to children. However, non-cooperative behavior by divorced parents tends to reduce child expenditures below the optimal level. For example, consider a divorced couple with one child in the mother's custody. Using only her own resources, the mother will spend on the child up to the point at which the marginal value of a dollar of expenditure equals one dollar. The father may endeavor to increase child expenditures by providing child support payments to the mother. Assuming the mother treats child support payments as ordinary income, she will tend to increase expenditures on both the child and her own consumption. For instance, suppose she receives one hundred dollars in child support leading her to increase expenditures on the child by twenty dollars and on her own consumption by eighty dollars, a response consistent with an analysis of household expenditures by economists Edward Lazear and Robert T. Michael in 1988. In this case, it will cost the father five dollars to increase expenditures on his child by one dollar as compared to a cost equal to a fraction of a dollar when he and the mother cooperatively shared child costs within marriage. Weiss and Willis's theory implies that the increased cost of children caused by non-cooperative behavior in divorce leads to a reduction in child well-being, as measured by total expenditures by both parents, and may also lead to an unwillingness of the non-custodial father to pay any child support voluntarily, thus tending to shift cost of children onto the custodial mother. In 1999, Willis extended this analysis to show how these factors may lead to out-of-wedlock childbearing among low income women under conditions in which such women are economically able to support children with their own resources (including receipt of welfare payments) and when they outnumber men in the marriage market.
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Robert J. Willis