11
Evolutionary Biology and Rational Choice in Models of Fertility

David Lam

There is perhaps no bigger challenge for any theoretical model of human fertility behavior than the model’s ability to explain the large fertility declines that have accompanied the enormous increases in human living standards in high-income countries since the 19th century and in low-income countries in more recent decades. Today, the great majority of couples in the high-income countries of the world are spectacularly rich by any historical standards, but most of them choose to have no more than one or two children. Similarly, fertility has fallen dramatically in virtually every developing country that has had significant increases in living standards in the past 20 years, with high-income couples generally leading the way to low fertility. Analyzed in the cross section, it is almost universally observed that higher-income, better-educated couples have lower fertility than poorer and less educated couples across a wide variety of cultural and institutional settings.

These stylized facts have been the focus of extensive theorizing from a wide variety of disciplinary and theoretical perspectives. The negative relationship between income and fertility has posed a particular challenge to economic and evolutionary models of fertility. Both economic and evolutionary models—at least in their most naive form—might have been expected to predict a positive relationship between income and fertility. Considerable effort has been put into fitting the observed empirical patterns into economic and evolutionary theoretical perspectives, with some important successes. One of the most important features of these analyses in both economic and evolutionary approaches has been the recognition that decreased fertility is almost universally associated with increased investments



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Offspring: Human Fertility Behavior in Biodemographic Perspective 11 Evolutionary Biology and Rational Choice in Models of Fertility David Lam There is perhaps no bigger challenge for any theoretical model of human fertility behavior than the model’s ability to explain the large fertility declines that have accompanied the enormous increases in human living standards in high-income countries since the 19th century and in low-income countries in more recent decades. Today, the great majority of couples in the high-income countries of the world are spectacularly rich by any historical standards, but most of them choose to have no more than one or two children. Similarly, fertility has fallen dramatically in virtually every developing country that has had significant increases in living standards in the past 20 years, with high-income couples generally leading the way to low fertility. Analyzed in the cross section, it is almost universally observed that higher-income, better-educated couples have lower fertility than poorer and less educated couples across a wide variety of cultural and institutional settings. These stylized facts have been the focus of extensive theorizing from a wide variety of disciplinary and theoretical perspectives. The negative relationship between income and fertility has posed a particular challenge to economic and evolutionary models of fertility. Both economic and evolutionary models—at least in their most naive form—might have been expected to predict a positive relationship between income and fertility. Considerable effort has been put into fitting the observed empirical patterns into economic and evolutionary theoretical perspectives, with some important successes. One of the most important features of these analyses in both economic and evolutionary approaches has been the recognition that decreased fertility is almost universally associated with increased investments

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Offspring: Human Fertility Behavior in Biodemographic Perspective in children. It is somewhat less surprising that humans would have chosen to have fewer children as their incomes increased when one recognizes that the decrease in numbers of children was offset by enormous increases in the amount of resources invested in each child. Quality-quantity trade-offs have been central to both economic and evolutionary models of fertility and arguably offer the most plausible way for reconciling both types of models with the observed empirical patterns. This chapter discusses the intersection between rational choice models of fertility—especially models developed by economists—and evolutionary biology models of human fertility. The focus is primarily on the issue of quantity-quality trade-offs, an area in which there is considerable theoretical overlap in the two approaches. A central motivating question is whether evolutionary perspectives on the biodemography of fertility can help us understand the negative relationship between income and fertility and how these evolutionary approaches compare to economic models of fertility behavior. The chapter begins with the presentation of a generic economic model of fertility that includes both quality-quantity trade-offs and the time cost of children. Particular emphasis is placed on the effect that increased productivity of parental time may have on choices about the quantity and quality of children and on time allocation. Then empirical evidence is presented from Brazil and South Africa that supports the view that quality-quantity trade-offs are fundamentally important in understanding fertility decline. The relationship between economic models and models drawn from evolutionary biology is then discussed. The paper points out the potential contributions that an evolutionary approach can make to economic models and considers potential differences in predictions coming from evolutionary and economic models. THE RELATIONSHIP BETWEEN INCOME AND FERTILITY The relationship between fertility and income has always been a fundamental issue for economists interested in fertility and the family. Becker’s seminal first paper on the economics of fertility (1960) heavily focused on the question of why we do not observe a stronger positive relationship between income and fertility. Becker found the observed lack of a positive relationship curious enough that he partially attempted to explain it as a statistical anomaly, suggesting that more complete data would in fact reveal a stronger positive association. But he also introduced the notion that quantity-quality trade-offs might be at the heart of the issue, noting that in the case of many goods that have an important quality dimension, higher incomes lead to much larger increases in quality than quantity. As will be discussed below, Becker would later appeal to evolutionary biology as part of the motivation for quality-quantity trade-offs in human fertility. In his

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Offspring: Human Fertility Behavior in Biodemographic Perspective later work on time allocation, Becker (1965) added another important piece of the story, noting that high-income couples are usually high-wage couples, making time-intensive commodities like children relatively more expensive than they are for low-wage couples. These two issues—quantity-quality trade-offs and the opportunity cost of time—continue to be the most important components of economic models of fertility, especially as they relate to explaining historical patterns in fertility and cross-section differentials as a function of income, wages, and schooling. An Economic Model of Quality-Quantity Trade-Offs It is useful to organize the discussion around a simple economic model of child quantity and quality of the type developed by Willis (1973), Becker and Lewis (1973), and Becker (1991). Assume that parents maximize a utility function U(N, Q, Z), where N is the number of children, Q is the children’s average quality (where quality refers to outcomes such as children’s health and schooling), and Z represents all nonchild uses of time and goods. The nature and origins of the preferences embedded in this utility function are taken as outside the model and are one area in which evolutionary models are potentially informative. One of the useful features of these types of models is that they can also incorporate issues of time allocation and the opportunity cost of children by assuming that child quality is produced using inputs of time and goods according to some production function: Q = Fq(Tqw, Tqh, Xq) where Tqw and Tqh are the amount of the wife’s time and the husband’s time used to produce child quality (summed across all children), and Xq is the amount of purchased goods used to produce child quality. Nonchild consumption, Z, is produced by an analogous production function. A standard simplifying assumption that keeps the analysis tractable is that the production functions for both child quality and nonchild consumption are constant returns to scale, implying that doubling all inputs causes a doubling of child quality, and that producing N children who are each of quality q requires exactly N times as much of all inputs as producing one child of quality q. This assumes that there is a unit production function q = fq(tqw, tqh, xq ), where tqw and tqh are the amount of the wife’s time and the husband’s time used for each unit of child quality per child, and xq is the amount of purchased goods used for each unit of quality. The wife’s total time, Tw, is allocated between market work, Tmw, children, and nonchild consumption, subject to the time constraint Tw = Tmw + NQTqw + ZTzw. An analogous time constraint describes the alloca-

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Offspring: Human Fertility Behavior in Biodemographic Perspective tion of the husband’s time, Th. The simplest case is to assume that both the wife and the husband are at an interior solution at which some time is allocated to all activities, implying that each partner’s market wage is an appropriate marginal valuation of his or her time. Labor market earnings of the husband and wife plus unearned income A are used to purchase the market inputs for children and nonchild consumption, A + wwTmw + whTmh = NQxqpx + Zxzpx. One of the important implications of the constant returns to scale assumption is that it means the choices of optimal inputs of time and goods into home production are a function only of the production technology and the input prices and can be separated from household consumption and fertility decisions. This separability implies that we can define the shadow price pq = wwtqw + whtqh + pxxq, the cost of producing one unit of child quality for a single child, a cost that is independent of the amount of quality produced. The shadow price of Q, the average quality of all children, is πq = Npq. This shadow price depends on N, child quantity, and thus cannot be separated from the household’s consumption decisions. Similarly, the shadow price of N is πn = Qpq and is directly dependent on the choice of child quality. The endogeneity of these shadow prices with respect to the chosen levels of quantity and quality is at the heart of the complex price and income responses implied by quality-quantity models, as discussed by Willis (1973), Becker and Lewis (1973), and Becker (1991). Several important points come out of analyzing a model such as this. The intrinsic interaction between quantity and quality means that a simple change like increasing unearned income can have complicated effects on quantity and quality. In contrast with simple models of consumer expenditures, for example, doubling income cannot lead to a doubling of both quantity and quality, since that would require four times—not two times— as much income.1 Becker argues that in the case of other goods that have both quantity and quality dimensions, there is strong empirical evidence that increases in income lead to much larger increases in quality than quantity. The same might plausibly be expected for children. Given the nonlinearities of the model, it is possible to generate a negative effect of income on child quantity even in the case where both child quantity and child quality are “normal” goods in the usual economic sense. Lam and Duryea (1999) and Lam and Anderson (2002) adapt this type of model to consider the impact of parental schooling on quantity-quality 1   Although this may seem to be making too much of the simple multiplicative model of quantity and quality, the basic point will be true for more general representations of the problem. As long as couples care about both the number of children and the amount invested in them, complex nonlinearities will be introduced into the usual consumer demand analysis.

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Offspring: Human Fertility Behavior in Biodemographic Perspective trade-offs, looking at empirical evidence from Brazil and South Africa. The case of schooling is interesting in the context of evolutionary approaches, since it might be thought of as representing the general class of increases in parental productivity in producing healthy and productive children. In the case of the model outlined here, an increase in the schooling of either parent may lower the amount of time or goods required to produce a unit of quality, thus reducing the shadow price of a unit of quality, pq. Market wages may increase at the same time, with the partial effect of raising pq. Whatever the resulting change in pq, the effects of this price change on Q and N are complicated by the nonlinearity of the budget constraint. A reduction in pq will reduce the shadow price of both quality and quantity, which are intrinsically connected, and any adjustments in N or Q in response to the change can be thought of as causing further changes in these endogenous shadow prices. A large increase in Q, for example, implies a large increase in the shadow price of N. As shown in Lam and Anderson (2002), it is theoretically possible that an increase in parents’ ability to produce higher-quality children may lead to a decrease in either fertility or child quality but not both. An additional implication of this type of quality-quantity model is that responses can be greatly exaggerated beyond those of a standard linear budget constraint. This effect, as noted by Becker (1991), may help explain the rapid declines in fertility and corresponding rapid increases in children’s human capital in response to relatively modest changes in the shadow price of children. It is entirely reasonable in the context of an economic model of quantity-quality trade-offs that we could observe substantial decreases in child quantity offset by large increases in child quality in response to increased productivity of parents in producing child quality. Labor Market Productivity and the Price of Children It is often remarked that children are much more expensive today than they were 100 years ago, an observation that in turn is often used to help explain why fertility is so low in today’s high-income countries. The quantity-quality model outlined above provides some useful insights into the issue of the cost of children. One of the most important points is that the “price” of children is an endogenous outcome of the parents’ trade-off between quantity and quality. While it is fair to say that people who choose high-quality children have “expensive” children, it is quite misleading in the context of the model presented above to say that it is the high price of children that explains the low quantity. They might have chosen a combination of low quality and high quantity, in which case it would be similarly misleading to say that they had many children because they were so cheap.

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Offspring: Human Fertility Behavior in Biodemographic Perspective It should also be noted that even the high-quality children being chosen by the rich today probably consume a substantially smaller proportion of parents’ lifetime income than did the children of 100 or 1,000 years ago. The model also helps us think about other components of the price of children that are more exogenous, and some important points are worth noting. In addition to trading off child quality for child quantity, the second dimension in which couples are making trade-offs is in the allocation of time between the labor market and care for children. The mother’s schooling may have important effects here, as emphasized in many economic theories of fertility decline. As noted above, increases in a mother’s schooling can be expected to simultaneously increase her productivity in home production (including child care) and in the labor market. It is often assumed that increases in market wages associated with higher schooling represent an increase in the relative price of labor market time versus home production time. This clearly does not have to be the case, however, since it is possible that an increase in schooling raises home productivity by as much as it raises wages. This could occur because wages do not adjust to the actual increase in productivity or simply because the increase in home productivity is as large as the increase in labor market productivity.2 A woman will work in the labor market if and only if her labor earnings are worth more to the couple than the foregone productivity of her time at home. Increased schooling will increase the probability that a woman works in the labor market if that schooling causes a larger increase in her market wage than in her home productivity. While the experience of high-income countries suggests that labor market productivity increases faster than home productivity, it may well be the case that for women with low levels of schooling (and large numbers of children) the increase in home productivity from an additional year of schooling is large. It may also be the case that, while all levels of schooling raise labor market productivity, the effects of schooling on home productivity face diminishing returns. It may thus be the case that increased schooling causes home productivity to rise as fast as market productivity at low levels of schooling, but market productivity eventually rises faster at higher levels of schooling. In this case increases in schooling would not increase labor force participation at low levels of schooling but would increase participation at higher levels of schooling. 2   Although it is simplest to think of the labor market as the alternative use of a mother’s time, a very similar story could be told about a mother’s decision of how much time to spend in agricultural cultivation or even food gathering, if these activities compete with time invested in children.

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Offspring: Human Fertility Behavior in Biodemographic Perspective The important point of this case is that children do not necessarily become relatively more expensive as market wages increase. If the mother’s home productivity (including her productivity in producing high quality-children) is rising as fast as the market wage, the decline in the time inputs to produce child quality can offset the higher wage. For women who are not in the labor market initially, the increased home productivity will lower the effective price of child quality. This can plausibly lead to an increase in child quality, a decrease in child quantity, and no change in the amount of time spent in the labor market. In this economic model, then, the effect of schooling on fertility, child quality, and women’s labor supply can be viewed theoretically as being driven by trade-offs along two margins. On the one hand is the race between home productivity and labor market productivity, driving the extent to which better-educated women are pulled into the labor force by higher wages. On the other hand is the adjustment in child quality and child quantity that results from the effects of schooling on home productivity. It is important to note that the economic model offers no strong unambiguous predictions regarding the effect of income or schooling on either child quantity or quality. If the total fertility rate in Italy today were 6.0, we could easily explain it in this model as resulting from a positive income elasticity of demand for children, whether child quality were higher or lower than is observed under the current low-fertility regime. While the model does not make sharp a priori predictions, it does suggest that decisions about child quality, child quantity, and time allocation are best analyzed jointly, with a great deal potentially learned from looking at the combined set of outcomes. One prediction the model does make is that we should never see both the numbers of children and the quality of children fall in response to increases in income or schooling. The joint responses in fertility, investments in children, and women’s employment can potentially be informative about the mechanisms that drive fertility decline. EMPIRICAL EVIDENCE FROM BRAZIL AND SOUTH AFRICA The observed cross-sectional relationship between schooling and fertility is potentially informative about the kinds of changes that may take place during the demographic transition and therefore provides a useful reference point for thinking about the relationship between economic and evolutionary models of fertility. Figures 11-1 to 11-4 present empirical patterns from Brazil and South Africa. These are particularly interesting cases to consider because their extremely high levels of inequality generate a distribution of education that has significant percentages of adults spread across the schooling distribution from zero years to university. Both countries also have

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Offspring: Human Fertility Behavior in Biodemographic Perspective FIGURE 11-1 Number of live births by years of schooling for married women, ages 45 to 54, in Brazil 1984, and for black South Africans, 1995-1998. SOURCE: 1984 Brazil PNAD and 1995-1998 South Africa October Household Survey. FIGURE 11-2 Employment rates by years of schooling for married women, ages 35 to 44, in Brazil, 1984, and for black South Africans, 1995-1998. SOURCE: 1984 Brazil PNAD and 1995-1998 South Africa October Household Survey.

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Offspring: Human Fertility Behavior in Biodemographic Perspective FIGURE 11-3 Natural logarithm of monthly wages by years of schooling (relative to women with zero schooling) for married women, ages 35 to 44, with positive wages, in Brazil, 1984, and for black South Africans, 1995-1998. SOURCE: 1984 Brazil PNAD and 1995-1998 South Africa October Household Survey. FIGURE 11-4 Mean years of schooling of 15-year-olds by mother’s education, in Brazil, 1984, and for black South Africans, 1995-1998. SOURCE: 1984 Brazil PNAD and 1995-1998 South Africa October Household Survey.

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Offspring: Human Fertility Behavior in Biodemographic Perspective large nationally representative household surveys that make it possible to look at detailed relationships between schooling and fertility.3 Figure 11-1 shows the number of children ever born by years of completed schooling for women ages 45 to 54 in Brazil in 1984 and for black women in South Africa using pooled data from the October household surveys for 1995, 1997, and 1998. The results for Brazil are similar to those of Lam and Duryea (1999). The results for South Africa are similar to those of Lam and Anderson (2002). The figure demonstrates the large differences in fertility across years of women’s schooling in both countries. For Brazilian women in 1984 there was a decline of over three births between women with zero years of schooling and women with 8 years of schooling. The schooling gradient in contemporary black South Africa is more modest, but there is still a decline of about 0.75 births over the first 8 years of schooling. The difference between black women who have completed grade 12 and black women with no schooling is about 1.5 births. Regression analysis using additional control variables indicates that these simple bivariate relationships between schooling and fertility are somewhat attenuated but remain substantial when controls for region, husband’s schooling, and husband’s income are included (Lam and Duryea, 1999; Lam and Anderson, 2002). Although fertility falls relatively steeply with schooling in both Brazil and South Africa, there is surprisingly little effect of the first 8 years of schooling on the probability that women are employed in the labor market. Figure 11-2 plots the proportion of all women ages 35 to 44 that reported being employed in the previous 7 days by years of schooling. Very similar patterns are observed at both younger and older ages in both countries. The patterns for Brazil and South Africa are surprisingly similar, with the proportion of women employed being between 30 and 40 percent until about 8 years of education. Employment rates increase dramatically at higher levels of schooling in both countries, reaching levels typical of high-income countries. Employment rates among university-educated women are two to three times as high as employment rates among women with primary schooling or less. Comparing Figures 11-1 and 11-2, there is surprisingly little relationship between fertility and employment as schooling increases. This pattern is even more surprising when the effect of schooling on wages is taken into account. Figure 11-3 plots the mean log wage for employed women reporting nonzero wages relative to women with no schooling. In both countries there is a strong positive relationship between schooling and wages. In Brazil this positive relationship is observed beginning at grade 1, with 3   The Brazil results are based on the 1984 Pesquisa Nacional por Amostra de Domicilios (PNAD), a nationally representative survey of over 100,000 households. The South African results are based on the pooled October household surveys from 1995, 1997, and 1998, a pooled dataset of about 80,000 households.

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Offspring: Human Fertility Behavior in Biodemographic Perspective increases on the order of 15 to 20 percent per year of schooling over the first seven grades. In South Africa the implied rate of return to schooling is in the range of 15 to 25 percent per completed grade after grade 4. Comparing Figures 11-2 and 11-3, it is striking that employment rates for women remain low and relatively constant over ranges of schooling in which wages are rising substantially. In both Brazil and South Africa, among 35- to 44-year-old women who work, those with 8 years of schooling report wages about 1.0 log points higher than those with zero years of schooling, implying about three times higher wages. The percentage of women working at these two schooling levels is almost identical, however, only slightly above 30 percent. Women with 8 years of schooling have considerably fewer births in both countries, but this lower fertility does not translate into higher involvement in the labor force. In both Brazil and South Africa we observe a situation in which schooling appears to have a negative effect on fertility over ranges in which there is very little relationship between employment and fertility. This suggests that the effect of education on fertility is not working primarily through price-of-time effects. Wages increase substantially over this range, without any corresponding increase in women’s employment, additional evidence that there is some aspect of women’s time allocation other than labor market activity to explain the link between education and fertility. As suggested in the theoretical discussion above, investments in child quality may be the margin in which education and time allocation interact with fertility. Figure 11-4 plots the schooling attainment of 15-year-old children as a function of their mother’s schooling. The gradient of children’s schooling by mother’s schooling is substantial in both countries, with stronger effects in Brazil. In Brazil in 1984, 15-year-old children whose mothers had 12 years of schooling were about four grades ahead of children whose mothers had no schooling. The gap in South Africa between these extremes is about two grades. One of the important features of Figure 11-4 is that the gradient is quite steep over the range of schooling in which fertility falls without any corresponding change in women’s employment, the range up to 8 or 9 years of schooling. These empirical patterns suggest that an increase in the opportunity cost of children due to rising wages is unlikely to be the major reason that increases in women’s schooling are associated with declines in fertility in Brazil and South Africa. Despite increases in market wages, women do not substantially increase their market labor supply as their schooling increases. The evidence suggests that quality-quantity trade-offs are a more plausible explanation for the link between maternal schooling and fertility. These results suggest there is a strong link between fertility and investments in children. Increases in schooling at low levels lead to increases in the productivity of both mothers and fathers in producing better-educated

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Offspring: Human Fertility Behavior in Biodemographic Perspective children. Parents respond to this increased productivity in a way consistent with the theoretical model outlined above—they choose higher levels of child quality and reduce the number of children. As argued by Becker (1991), one of the interesting implications of a model of quality-quantity interactions is that an increase in income or a reduction in the unit price of quality can lead to large responses, with large increases in quality and large decreases in quantity. Increases in women’s schooling also lead to increased labor market productivity, as evidenced by the large rise in wages. In making labor supply decisions, however, women are faced with simultaneous increases in home productivity and labor market productivity. Over a large range of schooling it appears that increases in home productivity are large enough to offset even large increases in wages. Until about 8 years of schooling we do not see women responding to rising wages with significant increases in labor supply. The driving mechanism through which schooling reduces fertility, then, does not appear to be rising opportunity cost of time due to rising wages. Rather, couples respond to their increased productivity in producing child quality by reducing the number of children and investing more resources in each child. QUALITY-QUANTITY TRADE-OFFS AND FERTILITY DECLINE While the cross-sectional relationships between education and the quality and quantity of children shown in Figures 11-1 to 11-4 do not necessarily have implications for the time series changes observed across populations, there would seem to be at least a rough correspondence between the cross-sectional and time series patterns over the broad sweep of historical fertility declines. Declining fertility has almost universally gone hand in hand with increased investments in children, as indicated by improvements in child health, survival, and education. While the specific causal mechanisms are difficult to identify, it is virtually impossible to separate declining numbers of children from the increased investments in those children in any population in which fertility has declined. Indeed, it is the almost universal increase in the “cost” of children that has caused many observers to see this higher cost as a mechanism inducing parents to have fewer children. In the context of the economic model of quality-quantity trade-offs, however, this higher cost is itself a matter of choice, with the simultaneous decisions about quantity and quality impossible to separate from each other. Evolutionary Approaches to Quality-Quantity Trade-Offs The trade-off between the quality and quantity of offspring plays an important role in evolutionary biology, including applications of evolutionary biology to human fertility. As argued by Kaplan and Lancaster else-

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Offspring: Human Fertility Behavior in Biodemographic Perspective where in this volume, evolutionary forces may well have produced a tendency to trade off child quality and quantity in hunting and gathering populations, with parents responding to the perceived payoff to investments in quality given environmental conditions. For example, humans may have adapted to postpone subsequent births in favor of increased investment in existing children when perceived payoffs to such investments were high. Such trade-offs may well have been fitness maximizing in a hunting and gathering setting. From an evolutionary perspective, the link between the quantity and quality of offspring may offer one of the most plausible mechanisms for explaining the reductions in fertility that have accompanied the large increase in standards of living in both high-income and low-income countries. In developing his economic model of fertility, Becker (1991) suggests that the quantity-quality trade-off can help provide a link between Darwinian theory and the decline in family size associated with rising family incomes in the past hundred years. In A Treatise on the Family, Becker (1991:137) argues, “a reduction in the number of children born to a couple can increase the representation in the next generation if this enables the couple to invest sufficiently more in the education, training, and ‘attractiveness’ of each child to increase markedly their probability of survival to reproductive ages and the reproduction of each survivor.” The quantity-quality calculus may be affected by the environment in which parents make such decisions, including factors that affect their ability to produce child quality and the returns to those investments. Writing from an evolutionary perspective, Low (2000:144-145) writes that “complexities in either the ecological or social environment that result in increased effectiveness of parental investment should result in more investment, even at the expense of fertility itself.” Low’s discussion suggests that high eventual reproductive payoffs to trading off child quantity for child quality in the current generation might hold the promise of reconciling evolutionary models of fertility with the awkward empirical evidence of declining fertility in the face of rapidly rising incomes over time. Parents might find it optimal to reduce child quantity in favor of quality in their own offspring, with the payoff coming in the form of increased numbers of grandchildren born to their well-endowed children. As noted by Kaplan and Lancaster (this volume), however, the weight of empirical evidence suggests that the payoff to increased investments in child quality in terms of increased numbers of grandchildren or other descendants is very unlikely to make up for the direct effect of reduced numbers of children in the next generation, at least in contemporary high-income settings. The study by Kaplan et al. (1995) of Albuquerque men indicates that the men who had the greatest number of grandchildren were those who had the greatest number of children. The argument that investments in child quality may increase the num-

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Offspring: Human Fertility Behavior in Biodemographic Perspective ber of offspring in the long run raises theoretical complications as well. A model in which numbers of children are reduced as a strategy to maximize numbers of grandchildren (or great grandchildren) has the unappealing feature that it requires children to make the opposite calculation from their parents, producing large quantities of children at the expense of child quality. This implies a kind of dynastic time inconsistency that seems unlikely to generate a stable equilibrium path within a lineage and is unlikely to be consistent with adaptive evolutionary processes. If it were rational for high-income couples in the current generation to reduce quantity in favor of quality, given the observed trade-offs in the environment, why wouldn’t their highly endowed children come to the same conclusion? The payoff must come in some generation eventually having very high fertility, with an ever-increasing baby boom required to generate a sufficient return on the initial investment as more generations choose low fertility. It seems unlikely, then, that reductions in fertility in favor of child quality are ever likely to be fitness maximizing in a modern setting, at least not to a degree that can fit the large fertility reductions of the past 100 years into a simple evolutionary framework. In this sense it might be concluded that the issue of quantity-quality trade-offs cannot rescue an evolutionary model from a fundamental inconsistency with the observed declines in fertility that have accompanied large increases in income. It might further be argued that the rational choice economic model is therefore better able to explain modern low fertility than is the evolutionary model, since the observed fertility behavior is consistent with standard economic models. The apparent superiority of the economic model should not be overstated, however. Low fertility is consistent with an economic model simply because almost any level of fertility is consistent with the economic model, as long as both quantity and quality are not simultaneously reduced in response to increases in income. Evolutionary Origins of Indifference Curves Although economic and evolutionary models might be viewed as offering competing approaches to understanding the trade-off between quality and quantity of children, they may in fact be highly complementary. As noted above, Becker (1991) appealed to evolutionary interpretations in discussing his own economic model of quality-quantity trade-offs. Economists have generally been much more attracted to evolutionary models of demographic behavior than most noneconomist demographers. As Bergstrom (1996:1903) writes in his survey of evolutionary and biological approaches to the family, “Because of the intimate connection between reproduction and the family, it should not be surprising that the theory of evolutionary biology has fundamental implications for the economics of the

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Offspring: Human Fertility Behavior in Biodemographic Perspective family.” One of the important contributions of evolutionary models is that they potentially help explain the origins of the utility functions that economists traditionally take as given. This could be especially valuable in developing models of fertility and the family, since evolutionary approaches may provide guidance in thinking about issues such as intrafamily altruism, preferences about having children, and the trade-off between child quantity and child quality. In the case of quantity-quality trade-offs, the focus of this paper, it is worth considering whether evolutionary biology can help inform the economic model laid out above. While one does not necessarily need an evolutionary approach to explain why there might be a utility trade-off between the quantity and quality of children—any more than one needs an evolutionary approach to explain a utility trade-off between the quantity and quality of televisions—it is nonetheless useful to realize that a quality-quantity trade-off in offspring is a highly plausible evolutionary adaptation. Even if observed quality-quantity trade-offs in the modern environment do not appear to be fitness maximizing, this does not imply that these behaviors do not have an evolutionary origin. We may be observing an evolutionary adaptation operating in a very different environment than the environment in which it evolved. As argued by Kaplan and Lancaster, it may well have been fitness maximizing in a hunting and gathering setting to shift from quantity of offspring to quality of offspring when the rate of return to investments in quality was high. In economic terms the “indifference curves” describing the trade-off between quantity and quality may have been developed in this early human environment. The returns to investments in child quality today, as measured for example by returns to giving a child a college education, may be many times higher than the returns ever experienced in early human populations. The response to these high returns, given the indifference curves developed in a very different setting, is to reduce fertility to very low levels and make very large investments in each child. This behavior is not in fact fitness maximizing, but it may reflect trade-offs that have an evolutionary origin. A strong quantity-quality fertility trade-off that responds to high returns to investments in children may be one of the most fundamental elements in the biodemography of fertility, helping us understand both the time series and the cross-section relationships between income and fertility. While this argument has considerable appeal, a criticism of this sort of explanation is that it allows the evolutionary model to potentially fit almost any kind of observed relationship between income and fertility. We may have a story of where the utility function came from, but we have no sharp predictions about what that utility function might imply in any particular setting. This is a criticism of both the economic and the evolutionary mod-

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Offspring: Human Fertility Behavior in Biodemographic Perspective els, since both models can potentially be reconciled with any relationship between income and fertility. The trade-off between quality and quantity appears to be a compelling piece of the puzzle, but we are left with models from both economic and evolutionary approaches that in principle are consistent with either a positive or a negative relationship between income and fertility. CONCLUSIONS This paper has explored how economic rational choice models and evolutionary biology models can be used to explain the widely observed negative relationship between income and fertility within populations and over time. The focus has been on quality-quantity trade-offs, an issue that has been fundamental in both economic and evolutionary models. Standard economic models of fertility are theoretically consistent with a negative relationship between income and fertility, especially if there is a positive relationship between income and investments in children. This prediction can also be applied to the effects of increased productivity of parents, resulting for example from increased schooling. Empirical evidence from Brazil and South Africa suggests that the strong negative effect of mother’s schooling on fertility is the result of a strong quality-quantity trade-off over the first 8 years of schooling. Although women’s labor market productivity, as measured by the market wage, rises rapidly over the first 8 years of schooling in both countries, only about 30 percent of women are employed over the entire range. Child quality, as measured by the schooling of 15-year-olds, rises rapidly with mother’s schooling, however. If these cross-sectional patterns apply to historical changes over time, they suggest that increasing parental productivity leads to a large increase in child quality and an offsetting decrease in fertility. This quantity-quality trade-off appears to be far more important in explaining fertility decline than an increase in the price of children resulting from higher women’s wages. Evolutionary biology models have also emphasized quality-quantity trade-offs, which offer at least the potential to reconcile evolutionary predictions with an observed negative relationship between income and fertility over time. Some authors suggest that such trade-offs may in fact maximize reproductive fitness because of the eventual increase in the numbers of grandchildren or great-grandchildren resulting from increased endowments in current children. Empirical evidence suggests that payoffs in offspring from later generations are unlikely to be large enough to offset the reduction in current children in contemporary settings, however. A simple quantity-quality model is therefore unlikely to explain current low fertility as being adaptive in an evolutionary sense. This does not mean that quality-

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Offspring: Human Fertility Behavior in Biodemographic Perspective quantity trade-offs may not have been highly adaptive in hunting and gathering settings, however, and may therefore have had an important effect in shaping the preferences that guide the behavior of modern humans. We observe almost universal patterns of declining fertility and increased investments in children in response to rising incomes and rising productivity in a wide variety of cultural, environmental, and institutional settings. It does not seem unreasonable to believe that rational economic choices about quality-quantity trade-offs in our modern setting are being driven at least in part by preferences that were influenced by the process of evolution in a much different early human environment. REFERENCES Becker, G.S. 1960 An economic analysis of fertility. Pp. 209-231 in Demographic and Economic Change in Developed Countries. Princeton, NJ: National Bureau of Economic Research. 1965 A theory of the allocation of time. Economic Journal 75:493-517. 1991 A Treatise on the Family. Cambridge, MA: Harvard University Press. Becker, G.S., and H.G. Lewis 1973 On the interaction between the quantity and quality of children. Journal of Political Economy 81:S279-S288. Bergstrom, T.C. 1996 Economics in a family way. Journal of Economic Literature 34:1903-1934. Kaplan, H., J. Lancaster, J. Bock, and J. Johnson 1995 Does observed fertility maximize fitness among New Mexico men? A test of an optimality model and a new theory of parental investment in the embodied capital of offspring. Human Nature 6:325-360. Lam, D., and S. Duryea 1999 Effects of schooling on fertility, labor supply, and investments in children, with evidence from Brazil. Journal of Human Resources 34:160-192. Lam, D., and K. Anderson 2002 Women’s schooling, fertility, and investments in children in South Africa. Paper presented at the annual meeting of the Population Association of America, Atlanta, GA. Low, B. 2000 Why Sex Matters: A Darwinian Look at Human Behavior. Princeton, NJ: Princeton University Press. Willis, R.J. 1973 A new approach to the economic theory of fertility behavior. Journal of Political Economy (March-April):S14-S64.