Data on fertility and mortality in various parts of the world (see handout on "Fertility and Mortality - 1996") make it clear that these different regions may be seen as being in different stages of the demographic transition. Among the nonindustrialized (less developed) parts of the world, sub-Saharan Africa constitutes the only major region yet to experience the onset of fertility decline, while Latin America seems furthest along.
Consideration of the relationships between these demographic phenomena and GNP per capita (a crude measure of economic well-being) makes it clear that mortality and economic well-being are strongly inversely related, while fertility and economic well-being also appear to be inversely related (Figure I.B.1; note why crude rates are not used).
Earlier we noted that conventional demand theory looks at demand as a function of income, prices, and tastes. From the perspective of the home production framework, the positive relationship between life expectancy and economic well-being suggests that survival is a normal commodity -- i.e., as incomes rise, people have a higher demand for (and realization of) survival.
But does this mean that children are an inferior commodity? This doesn't seem very palatable. Clearly, increases in income tend to be associated with reductions in fertility. Do such increases in income somehow bring about changes in people's preferences for children?
The economic approach to fertility that we will examine here seeks to provide an analytical framework that can explain observed fertility behavior, past and present, with emphasis on economic considerations (i.e., not appealing to changes in preferences or tastes as an explanatory factor).
We will focus on the Easterlin model (first laid out in 1975) as a broad economic framework for fertility analysis. Easterlin's model was designed to incorporate Becker's earlier work focused on the demand for children. At the same time, Easterlin also sought to develop a model that would be compatible with the approaches to fertility used in other disciplines.
In brief, the Easterlin model emphasizes three broad categories through which the "basic determinants" of fertility operate and which influence, in turn, the "proximate determinants" of fertility. These three categories are the demand for children (the number of surviving children parents would want if fertility regulation were costless); the supply of children (the number of surviving children parents would have if they did not deliberately limit fertility); and the costs (subjective and objective) of fertility regulation.
Following Becker, a couple's demand for children is treated as analogous to the demand for goods and services. In particular, demand depends on household income, on the cost (price) of children, and on parents' tastes or preferences for children relative to other goods and services that provide satisfaction (utility) to the couple.
Other things equal, higher income is expected to be associated with a greater demand for children (i.e., children are assumed to be a normal good). However, greater demand for children may be realized at least in part by greater resource endowments per child rather than simply by an increase in the number of children. In this respect, the demand for children or "child services" may be seen as comparable to the demand for consumer durable goods more generally, where higher income often translates into increased demand for quality rather than simply increased quantity.
Greater resource endowments (i.e., higher expenditures) per child are typically described in the economics literature on fertility as child "quality," and there is considerable discussion in the literature of quality-quantity tradeoffs (e.g., see Becker's analysis of the demand for children in A Treatise on the Family).
The greater the cost of children, the lower is the quantity demanded. The cost of children includes not simply the direct costs of goods and services that are complementary to children, but also the indirect or opportunity cost of the mother's time spent in child care (often measured using estimates of the woman's earning power, or potential wage rate, in the labor market). Indeed, for children of given "quality," it is typically differences among women in the opportunity cost of time that result in differences across households in the cost of children.
The stronger are a couple's (relative) preferences for children, the greater the demand for children, other things equal. In considering this aspect of the demand for children, it is necessary to take into consideration tastes relating to child "quality." More generally, economics does not have a lot to say about tastes, but presumably this factor is likely to be related to cultural factors such as ethnicity or religion, and it may also be related to individual factors such as educational attainment.
The supply of children reflects two factors: a couple's natural fertility and the chances of child survival. Natural fertility refers to the number of births a couple would have if they took no action aimed at limiting fertility behavior (e.g., as with the Hutterites, or in societies in which deliberate fertility control is not practiced). Cultural differences in behaviors that influence the likelihood of a birth (e.g., in duration of breastfeeding or in the observance of periods of postpartum abstinence) can lead to differences in natural fertility between different natural fertility populations.
Since the potential supply of children in the Easterlin framework refers to the number of children surviving to adulthood, it is clear that supply varies inversely with the level of mortality. Hence, reductions in mortality increase the supply of children.
The costs of fertility regulation incorporate a couple's attitudes toward and access to fertility control methods and supplies. There are two types of costs of fertility regulation: psychic costs and market costs. Psychic costs refer to the displeasure associated with the practice or idea of fertility control, while market costs are the money and time costs necessary to learn about and use specific contraceptive techniques.
Couples have a motivation for fertility regulation if the potential supply exceeds the quantity of children demanded. This does not necessarily translate into efforts to control fertility -- that depends also on the costs of fertility regulation. Given the extent of the motivation to limit fertility, the lower the costs of fertility regulation the more likely a couple is to opt for contraception. In this framework, then, family planning programs can lead to fertility reduction via reducing both the market costs and the psychic costs of contraception.
The "basic determinants" of fertility behavior include underlying socioeconomic conditions, or what Easterlin and Crimmins describe as "modernization variables" such as education, urbanization, and modern sector employment, as well as cultural factors such as ethnicity and religion, and other determinants such as genetic factors. These basic determinants influence fertility through their impact on the demand for children, the supply of children, and/or the costs of fertility regulation.
Between the basic determinants of fertility and realized fertility behavior are the "proximate determinants" of fertility. That is, the basic determinants influence fertility only indirectly, through their influence on the proximate determinants. It is these proximate determinants which are seen as determining fertility directly.
Following Davis and Blake (1956) and Bongaarts (1978), the proximate determinants include factors such as extent of exposure to intercourse (heavily influenced by age at marriage, but note that cultural practices regarding intercourse outside of marriage will also be relevant here as well), fecundability (including frequency of intercourse), duration of postpartum infecundability (related especially to breastfeeding durations), sterility, and the use of deliberate fertility control including contraception and induced abortion.
As a prelude to considering applications of the Easterlin model and its usefulness in accounting for the relationships we observed earlier, it is desirable to begin with a formal look at Becker's theory of the allocation of time and its application to considering the demand for children. This is laid out in the mathematical handout entitled "Fertility and Female Labor Force Participation in the Context of the Theory of the Allocation of Time."
Children constitute a home-produced commodity (one of Becker's Zs), and the demand for children can be analyzed like the demand for any other commodity (cf., children as analogous to durable consumer goods). The production of children is typically assumed to involve a high time input on the part of the mother.
In terms of the mathematics of the model, this assumption means that when Zj represents children, the partial derivative of wife's time with respect to production of the commodity will be large. This, in turn, means that the opportunity cost of the wife's time will be a major component of the full price of children (cf., middle element of the numerator of equation 13 in the mathematical handout).
Indeed, empirical studies that attempted to quantify the costs of children in terms of the present value of direct and opportunity costs have typically found that the opportunity costs of the mother's time exceeded the direct costs.
Further, from equation (10) of the mathematical handout it should be evident that increases in the potential wage rates of women, other things equal, will create pressures to economize on the wife's time in the production of children. That is, given diminishing marginal productivity, reduced wife's time inputs to production of children will result in higher marginal productivity of her time and allow the household to reach a new equilibrium.
At the same time, the wife's potential market wage (as well as the husband's) are important because they indicate the household's ability to buy market goods (cf., full income:
I* = Wf Tf + Wm Tm +V). Hence, the wife can work at home engaged in home production and/or work in the market to earn income to buy market goods to be used in home production.
Consider a given society. Market wages of women vary across households, due to differences in women's educational attainment and in their employment possibilities (regional and rural-urban differences in the industrial mix). Other things being equal, the full price of children will be greater in households with high-wage women, and we would expect such households to have a lower quantity of children demanded -- i.e., to manifest lower levels of fertility. The key assumption here, again, is that children as a home-produced commodity are time intensive with respect to mother's time.
Further, since childbearing and the raising of children is a major competitor with labor force activity for the wife's time, and since a higher wage increases the opportunity cost of not working in the market, high-wage women would be more likely to be employed in the labor market.
Hence, the theory of the allocation of time, along with the assumption that children are time intensive with respect to mother's time, implies that women's wages will be a key influence on fertility, and that fertility and female labor force participation will be inversely related.
A large number of studies have looked at the economic determinants of fertility and the relationship between women's childbearing and labor force behavior, in both industrialized and developing countries. In assessing this literature, however, there are a number of conceptual and methodological issues that need to be taken into consideration.
Some of these issues arise from conditions different from those assumed in the model, others arise from difficulties in observing or estimating values of certain key variables, and still others crop up once we allow for dynamic aspects of family formation, particularly as tied to labor force behavior. We turn now to an examination of these different issues.
In a developing-country context, one often finds certain important conditions different from those postulated in Becker's model. These differences may complicate the model sufficiently so as to reduce its predictive capabilities.
For example, consider the implications of joint production -- the act of engaging in multiple activities simultaneously. Labor-intensive agricultural production is the primary economic activity of much of the world's population in developing nations. Combination of child care with agricultural work is extremely common in the Third World, however.
This joint production means that children need not be (as) time intensive with respect to the time of rural agricultural women, and likewise there is not the same degree of competition between childbearing and labor force activity for the mother's time. Even in an urban setting, the existence of a large informal sector of employment permits child care to be accomplished simultaneously with labor force participation (cf., sidewalk mamas in Kinshasa).
Further, as children in agricultural settings get older, they may have value as producer goods -- i.e., they may be able to contribute to household income generation. In Becker's original (1960) analysis of fertility, he noted that the net cost of children was equal to the present value of expected direct expenditures on children plus the imputed value of the parents' services, minus the present value of the expected money return from children minus the imputed value of children's services.
Clearly, to the extent that children contribute to household income, their net cost is lowered. The value of children as producers of income depends on both the age at which they begin to contribute to production and the marginal product of child labor (cf., determinants of MPL). This factor provides one reason for expecting rural fertility to be higher than urban fertility.
Another relevant consideration in developing-country settings is the extended family. If there are other adults (or older children) in the household besides the parents who can participate in child care, this will reduce the importance of the opportunity cost of the mother's time as an influence on fertility behavior. It will also weaken the hypothesized inverse association between the mother's fertility and her labor force behavior (cf., Kalombo family, child fostering).
Social insurance for old age is also relevant here. Formal old-age insurance generally does not exist or is inadequate in many less developed countries. Traditionally, children provide this insurance, and hence, this is an additional motivation for high fertility (cf., implications for future US fertility).
More specifically, frequently old-age support for parents in developing countries comes from surviving sons. This introduces an additional element into fertility behavior: sex preferences on the part of the parents. In particular, if a shortage of sons is viewed as much more undesirable than a surplus (cf., Kalonji, Bentsh, and Sekimonyo stories; problems in Asia), the existence of sex preferences will likely have an independent positive effect on fertility.
In order for the theory of the allocation of time and the economic approach to fertility to provide a useful framework for examining fertility in developing countries, then, we need to take into consideration the various factors just discussed. Further, there are difficulties in observing or estimating values of certain key variables, even in industrialized economies, that complicate empirical estimation of the model.
First, we can't observe the full price of children. Indeed, as Pollak and Wachter have pointed out in a broad-ranging critique of Becker's approach, the full price at the margin is endogenous and depends upon how many children parents choose to have.
If we take a step back from the full price, we can focus on a critical determinant: the opportunity cost of a woman's time. We typically want to measure this with the woman's (potential) market wage rate, but for women not working in the labor market we can't observe a wage.
One way of estimating a wage for nonemployed women that was used by some researchers early on was to impute a wage rate to these women based on their personal and labor market characteristics. This imputed wage was based on the assumption that they could earn the same wage as their employed counterparts with comparable characteristics.
However, this assumption -- that the wage-offer distribution was identical for the employed and the nonemployed -- was called into question by Heckman in a series of papers in the mid- to late-1970s. Concerned by the possibility of sample selection bias or selectivity bias, Heckman argued that the structure of wages among employed women was probably different from the wage structure for all women (see Fig. I.B.2).
This argument implies that the imputation procedure just described would give biased estimates of the opportunity cost of time of nonemployed women. Heckman and others have since developed techniques to adjust for sample selection bias. These techniques typically entail a two-stage estimation procedure in which first the likelihood of a woman being in the work force is determined as a function of her characteristics, and then this likelihood is used to generate unbiased estimates of the opportunity cost of time for all women.
A third set of issues arises when we take into consideration dynamic aspects of family formation. The model as laid out implicitly assumed full or perfect information, in the sense that parents' lifetime choices regarding fertility would be made based on their knowledge of the utility derived from children relative to the utility from other commodities. In essence, we had a one-period model with no revisions.
Suppose, however, that during the process of family formation, parents' assessment of the utility of children relative to other commodities changes. That is, at the outset of the life cycle there may be imperfect information, and in turn there may be revisions to tastes that take place during family formation. Further, as a consequence of early decisions about labor force activity, an individual's earning power in the labor market may change over time (cf., on-the-job training and human capital accumulation), thus altering the full cost of children.
The implication, then, is that dynamic considerations will be relevant to a household's completed level of fertility. That is, completed fertility in this view is not simply the outcome of a single lifetime choice made early in a couple's life cycle. Rather, it is the outcome of a series of sequential decisions that may reflect both accumulation of knowledge (revision of tastes?) and changes in the market opportunities and wages available to different family members (these changes may be exogenous as well as endogenous).
Having considered these various issues, I'd now like to return to consideration of the Easterlin approach and its implications for fertility behavior in the course of economic development. The key here is to think about how demand for children and supply of children are likely to change as economic development and modernization proceed. The behavior of demand and supply will determine the existence and magnitude of the motivation to control fertility, and in conjunction with the costs of fertility regulation this will determine the onset of fertility control.
In brief, as shown in Fig. I.B.3 (from Easterlin), modernization and development, typically associated with increasing urbanization and education of the population, would be expected to result eventually in declines in the number of children demanded. This would reflect the increase in the net cost of children (higher opportunity cost, lower monetary and nonmonetary returns from children) in conjunction with growth of returns (payoffs) to children's schooling (cf., technological advances) and hence emergence of quality-quantity tradeoffs.
At the same time, improvements in the material standard of living (and advancement of science in combating infectious diseases) should lead to increases in the supply of children, via reductions in infant and child mortality in particular. Modernization may also result in cultural changes that influence natural fertility and hence supply (cf., breastfeeding durations, postpartum abstinence).
Hence, while in earlier times there is likely to be an excess demand for children, eventually the combination of decreasing demand and increasing supply results in an excess supply of children and hence the emergence of a motivation to control fertility. At this point, however, the costs of fertility regulation (psychic and direct) are likely to be high. In effect, initially the cost of unwanted children is likely to be less than the cost of fertility regulation. In this situation, fertility control is not practiced, and the actual number of children is equal to supply. Eventually, however, the objective and subjective cost of fertility regulation declines and is exceeded by the cost of unwanted children, and fertility control begins. This reduces the actual number of children below the supply level, and as control is practiced by a growing proportion of the population, the number of children approaches demand.
[My lecture on the research on women in Kinshasa that Dr. Tambashe and I have been doing since 1990, plus our forthcoming paper on the reading list provide an overview of an empirical study grounded in the economic approach to fertility.]
There is one final issue that I'd like to discuss in this section on fertility, and that is the question of measuring the costs of children. Consider again Becker's original definition of the net cost of children: the present value of expected direct expenditures plus the imputed value of the parents' services minus the present value of the expected money return from children minus the imputed value of the children's services.
As noted above, early studies in the U.S. that attempted to quantify the first two elements, with forgone labor market earnings of the wife as the second element, found wife's forgone earnings to be the major component of the cost of children. For example, a study done for the U.S. Commission on Population Growth and the American Future concluded that as of the late 1960s, the present value of the costs of a first child was nearly $60 thousand, with $20+ K in direct costs and $39+ K in opportunity cost.
[Note how direct and opportunity costs might be estimated -- taking account of the household income level (L/M/H) for the former; potential selection bias issue for the latter; note implications of the fact that now 50% of mothers of children under age 1 are in the labor force.]
In a developing-country context, the latter two elements of Becker's definition come into play. Consider results from a cost-benefit analysis carried out some years ago for a proposed family planning project in Haiti. This analysis essentially was a crude application of Becker's approach focused on the first and third elements of his definition of net costs of children.
Figure I.B.4 shows a stylized representation of per capita consumption and production over the course of the life cycle. If the production level is treated as the expected money return from children (i.e., children's future earnings) and the consumption level is treated as the expected direct expenditure or cost, then attaching numbers to the graph allows one to calculate the net cost of children.
That net cost was substantial. This is in large part the consequence of the time patterns of costs (front-loaded) and returns (delayed). That is, with a positive discount rate, the present value of the costs will exceed the present value of the returns, where PV = "SUM" (Yt/(1+r)"exp"t).
In the context of the proposed family planning project, the net cost of a child was compared to the estimated cost per birth averted associated with implementing the project (note how cost per birth averted was estimated, CYP measure and adjustments). The net cost of a child was treated as the benefit of the family planning project in avoiding an unwanted birth. The fact that this benefit exceeded the cost per birth averted was taken as an indication that the project was desirable from an economic point of view.
An alternative and more sophisticated approach to measuring the cost of children may be illustrated by the issues raised in a consultation I did in Tunisia in the late 1980s. There was an active governmental family planning organization in Tunisia, the ONFP, which was under pressure from elsewhere within the government to justify its budget expenditures. Some other government agencies felt that they were more directly involved in economic development activities, and wished to have their budgets increased at the expense of ONFP.
The perspective at ONFP was that their activities over the years had resulted in a large number of births averted, and that the cost of children provided an indication of the value of each birth averted. Data from a household budget and consumption survey were available as a source for estimating the cost of children. However, there was a disagreement between ONFP and USAID, an external funder supporting ONFP operations research, as to whether those data would be adequate.
More specifically, a local economist/demographer who was serving as a consultant to ONFP held that the household budget and consumption study data were inadequate to the task, because the data were aggregated at the household level. His view was that since the data were not disaggregated to the individual level, it would not be possible to accurately measure the cost of children, and especially the marginal cost of the nth child. Consequently, he argued that a new survey focused on measuring costs at the individual level should be carried out.
The USAID project officer was not convinced of the need for a new survey, and her response was to solicit an expert opinion. This is where I came in, my mandate being to determine if the existing household budget and consumption study could serve as the basis for measuring the cost of children.
With a little reflection, it should be clear that even an individual-oriented survey will have trouble directly measuring the cost of food and items like hand-me-down clothing at the individual level. However, regression analyses of household expenditures on various categories in relation to household demographic composition can be used to infer the direct costs of individual children for those types of expenditures (note how).
More fundamentally, as noted in a very informative paper by Deaton and Muellbauer (D & M), efforts to identify the direct costs of individual children encounter a big conceptual problem with respect to the existence of household public (i.e., shared) goods. In fact, D & M note that there have been two distinct sets of literature on the costs of children: one from demography, and the other from economists' consumer demand analysis. What's described at the end of the previous paragraph and also the earlier discussion has been from the demography literature; now we'll consider the consumer demand approach.
A starting point here is to recognize that since the arrival of a child does not, in and of itself, alter the resources (income) available to the household, the cost of a child may be viewed as being reflected in a reallocation of household expenditures toward the child and away from the parents. Conceptually, we can imagine a potential compensation (payment) to the parents that will bring some measure of their welfare (well-being) back to the level it was at prior to the birth of the child.
This compensation amount may be thought of as the cost of the child. A key point here is that the measure of parental welfare should be a narrow one. In particular, it should not include the utility derived from the presence of the child.
Ideally, this narrow measure of parental welfare should be directly related to parents' expenditures on themselves. However, this requires distinguishing expenditures on adults from expenditures on children, and as noted already, the existence of household public goods makes this an impossible task.
As D & M point out, one has to define an alternative means of measuring the economic welfare of adults, and then be able to evaluate this measure at different household compositions in order to assess the cost of the change in composition. In this context, then, the cost is the compensation required to equalize parental welfare before and after the change in composition.
The two methods that have been used to estimate child costs in the consumer demand literature are the Engel method and the Rothbarth method. Engel's method takes the share of the household budget devoted to food as an inverse indicator of parents' level of economic well-being.
This is based on two pieces of empirical evidence: 1) given the household demographic composition, the food share of total household expenditures varies inversely with total household income or expenditures (Engel's Law); and 2) given total household income or expenditure, the food share increases with the number of children.
Fig. I.B.5 depicts this situation. Given an arbitrary food share wf0, expenditure of x0 is required by the reference household (size N) and expenditure of x* is required by the larger household (size N+1). Hence, by Engel's method the cost of the additional child is given by (x* - x0).
D & M argue that this is an upward-biased measure of the cost of the child, however, since children's consumption is more food-intensive than that of adults, especially in developing countries. They cite empirical evidence to support this contention regarding the food intensity of children.
But now consider the implications of this food intensity. If the parents were indeed compensated so as to be as well off as before the child, their own food consumption would presumably be the same as before; but adding in a largely food-consuming child raises the household's overall food share.
That is, with a correct compensation for the cost of the child, the household of size N+1 should have a higher food share than the N-sized household. In terms of Fig. I.B.5, this means that the correct compensating expenditure level for the additional child will be less than (to the left of) x*.
The Rothbarth method focuses instead on a pre-selected set of adult goods, with the idea that total expenditures on these goods correctly indicate adult welfare. Rothbarth used a broad definition of adult goods, including all luxury goods and saving, while others have used narrower definitions such as alcohol and tobacco.
The basic idea, though, is that since children will not consume these goods, the presence of children affects expenditures on adult goods only via income-like effects (due to the "siphoning" of income to pay the direct costs of children). Hence, calculating the amount of money needed to restore expenditures on adult goods gives the Rothbarth estimate of the cost of children.
D & M argue that the Rothbarth method may understate the costs of children, to the extent that children make pure adult goods less expensive relative to goods shared with children. They explore more complex considerations, but acknowledge that as a practical matter the Engel and Rothbarth methods are likely to remain popular because of their empirical tractability. They conclude that the Rothbarth approach is superior to the Engel approach.
The issues raised here highlight the empirical difficulties of answering what at first glance seems to be a straightforward question: what is the cost of children? They also emphasize some broader issues in making welfare comparisons across households. One of these issues is how to balance the additional costs of children against the utility they presumably provide to parents.
A second issue is how to compare standards of living across households of different compositions. For example, we often observe a tendency for larger households to have incomes that are higher, but not proportionately higher, than those of smaller households. Hence, if per capita income of the household is used as the measure of economic well-being, this means that larger households will be classified as poorer. However, recognizing the existence of household public goods and differential consumption (cf., adult-equivalent consumption) makes it clear that this will not necessarily be the case.
© 1997 David Shapiro
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