8
Excess Fertility, Unintended Births, and Children's Schooling

Mark R. Montgomery and Cynthia B. Lloyd

Introduction

Consensus prevails as to the benefits of education: it is believed to promote economic development, speed the completion of the demographic transition, and enhance individual well-being. Where the determinants of education are concerned, however, no similar consensus has yet taken shape. The process by which individuals acquire education is exceedingly complex, involving their motivations and abilities, the goals and resources of their families, and the actions taken, or not taken, by the state. Among the many factors that may affect children's schooling, few have emerged in the literature as clearly decisive, and the role of demographic determinants has yet to be fully understood. In this chapter, we consider two demographic determinants of children's schooling: unintended and excess fertility within the family. Our analysis is empirical in nature and relies on Demographic and Health Survey (DHS) data for four developing countries. To our knowledge, this research is the first to combine data on children's schooling with data on excess fertility and the intendedness status of recent births. We show that in two of the four countries studied—the Dominican Republic and the Philippines—unintended and excess fertility have sizeable negative impacts on children's schooling. In the other two countries—Kenya and Egypt—we do not find such effects. It appears that these fertility effects can be important, but vary in strength according to socioeconomic context.

Our focus on fertility can be understood as follows. Developing-country parents, who face resource constraints in much of their behavior, may find their plans for children's schooling disrupted or compromised by the arrival of unin-



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--> 8 Excess Fertility, Unintended Births, and Children's Schooling Mark R. Montgomery and Cynthia B. Lloyd Introduction Consensus prevails as to the benefits of education: it is believed to promote economic development, speed the completion of the demographic transition, and enhance individual well-being. Where the determinants of education are concerned, however, no similar consensus has yet taken shape. The process by which individuals acquire education is exceedingly complex, involving their motivations and abilities, the goals and resources of their families, and the actions taken, or not taken, by the state. Among the many factors that may affect children's schooling, few have emerged in the literature as clearly decisive, and the role of demographic determinants has yet to be fully understood. In this chapter, we consider two demographic determinants of children's schooling: unintended and excess fertility within the family. Our analysis is empirical in nature and relies on Demographic and Health Survey (DHS) data for four developing countries. To our knowledge, this research is the first to combine data on children's schooling with data on excess fertility and the intendedness status of recent births. We show that in two of the four countries studied—the Dominican Republic and the Philippines—unintended and excess fertility have sizeable negative impacts on children's schooling. In the other two countries—Kenya and Egypt—we do not find such effects. It appears that these fertility effects can be important, but vary in strength according to socioeconomic context. Our focus on fertility can be understood as follows. Developing-country parents, who face resource constraints in much of their behavior, may find their plans for children's schooling disrupted or compromised by the arrival of unin-

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--> tended births. Moreover, as the broader macroeconomic context changes, parents may find themselves situated in new and possibly unanticipated circumstances. In the light of these circumstances, current family size may be revealed to be excessive and may then present an obstacle to desired educational investments. Thus we consider two conceptually distinct measures of fertility: (1) unintended fertility, or the birth of children whom the mother reports were either unwanted at the time of conception or whose conception was reported to be mistimed; and (2) excess fertility, or the birth of a larger number of children than is implied by the mother's expressed family-size ideal. The essence of our approach is to compare the schooling achieved by children in families with and without such fertility. For developing countries, the gap between desired and actual fertility is surprisingly large, with recent estimates suggesting that as many as one birth in five is unwanted (Bongaarts, 1990) and an even greater fraction unintended. As Bankole and Westoff (1995) demonstrate, in many middle-income developing countries, declines in desired family size now appear to be outpacing declines in fertility. The long-term educational implications of these trends deserve consideration. Viewed from a broader perspective, our research addresses the individual welfare rationale that supports family planning programs. That rationale is based on the costs imposed by imperfect fertility control on women and their families. Our findings show that in some settings, at least, the rationale can be strengthened: effective family planning may improve the prospects for investment in children's human capital. It follows that if the fullest advantage is to be gained from public-sector investments in schooling, parents must have the means to limit their fertility to the levels they desire. The remainder of the chapter is organized as follows. The next section provides a conceptual overview of the linkages among family size, excess fertility and unintended births, and human capital investments in children. It also reviews the rather meager literature that has addressed such questions. The third section presents a descriptive overview of the fertility and schooling environments in the four countries studied. The fourth section outlines the statistical model that motivates our empirical work; the results derived from that model are then given. The final section presents conclusions and suggestions for further research. Review Of Concepts And Literature Children with many or closely spaced siblings are often thought to be disadvantaged with respect to their schooling in comparison with other children. The disadvantages are believed to be due mainly to resource constraints, with children in larger families receiving smaller shares of total family resources. Economists have written about such issues under the rubric of the quantity,-quality tradeoff (see, among others, Becker and Lewis, 1973; Hanushek, 1992; Parish and Willis,

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--> 1993). As used in this literature, the term tradeoff refers not to any fixed or mechanistic causal relationship between fertility and children's schooling, but rather to the often-found negative association between the two. A tradeoff—a systematic negative association—between fertility and children's schooling is evident in many settings, but there are important exceptions to the general rule. In recent reviews, Lloyd (1994) and Kelley (1996) document a considerable range of empirical associations between fertility and children's schooling at the family level. The associations are usually negative, but they are not always statistically significant or quantitatively large, and positive associations appear as well (Hermalin et al., 1982; Parish and Willis, 1993; Montgomery et al., 1995a, 1995b; see also Diamond et al., this volume). When the results of many studies are summarized, the relationship between fertility and children's education is seen to vary over time and among countries according to several factors: the stage of economic development, the role played by the state, the phase of demographic transition, and the nature of the family system (Lloyd, 1994). It appears that some threshold level of development must be attained before fertility comes to be strongly negatively associated with children's schooling. If the surrounding environment is one of few schools and few skilled jobs, parents will have neither the opportunity nor the incentive to invest in their children's education, irrespective of whether resources are to be spread over many children or only a few (Desai, 1995). Another consideration is the role played by the state in school provision and finance. In countries in which a high proportion of the money costs of schooling are borne by parents, parental resource constraints are more important in determining which children attend school than is the case in countries in which education is provided free by the state. If the benefits of schooling are substantial, then it is the former situation, with parents responsible for the money costs of schooling, in which one would expect a negative association between fertility and children's education to emerge. Finally, in family systems involving sibling chains of support or child fostering, parents can distribute the costs of schooling and childrearing among a network of relatives, thereby escaping the constraints imposed by their individual family budgets. Consequences of Unintended and Excess Fertility Economic models are built on the premise that fertility and children's schooling are jointly determined outcomes of a common set of exogenous determinants. According to this way of thinking—see Appendix A for an extended discussion—a negative association between fertility and schooling is only one of any number of associations that might emerge from family productive and reproductive strategies. Fertility is not, in itself, a causal determinant of children's schooling, nor is schooling a causal determinant of fertility. It is therefore not meaningful to ask how desired fertility might affect desired children's schooling. The

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--> question is ill defined; it confuses association with causation. It is appropriate, however, to ask how the exogenous determinants of desired fertility might affect desired schooling. When the issue is posed in these terms, there is a proper causal linkage to be considered. In short, it is only the unintended or excess aspects of fertility that can act as causal determinants of children's schooling. An unintended birth imposes new and unanticipated demands on the resources that can be marshaled for schooling. Parents of unintended or excess children may be less able, and perhaps less willing, to increase the total resources devoted to their children or to reallocate resources among children on a particular child's behalf.1 To approach this issue more formally (see Appendix A for further discussion), let us imagine that parents make decisions so as to maximize a unitary utility function V(C, N, S, H), in which C refers to the level of parental consumption, N to the number of their children, S to the children's schooling, and H to the children's health or some other dimension of human capital investment.2 Parents face a budget constraint and must restrict their total expenditures to no more than Ω, the level of their exogenous income. The decision problem yields a set of optimal or desired values C*, N*, H*, S*, where N* represents the desired number of children. These optimal values yield utility level V*. Now suppose an unintended birth occurs, so that family size exceeds the optimal value N*. Actual fertility is then N = N* + 1. All else being equal, this additional birth must reduce parental well-being, causing actual utility to fall below V*. How are we to gauge the magnitude of the impact? One approach is to ask what increment in income, DW, would be required to restore utility to V*, that is, to just compensate the parents for the additional child. The required compensation will depend on numerous factors: the initial level of income Ω; the many childrearing prices and constraints faced by the parents; and the nature of the utility function V, in particular its curvature in the neighborhood of N* with respect to the number of children. This theoretical framework suggests an empirical model of the consequences of unintended fertility. In such an empirical model, the actual level of schooling S is a function not of actual fertility N = N* + U, where U is unintended fertility, but rather of U itself, 1   For the purposes of argument, we are here making a sharper distinction between unintended and intended fertility than may exist in the minds of the decision makers concerned. 2   The simple model to be outlined here assumes that parents act as a unit in making decisions about family size and child investments. If mothers and fathers differ in their desires—and there is much evidence to suggest that this is often the case with expressed family-size ideals (see Lloyd, 1993, for a review)—the question arises of whether the couple strives for compromise, or one partner tends to override the wishes of the other. Likewise, the model abstracts from issues such as sibling chains of support, transfers of resources among the wider family, and child fostering.

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--> This specification isolates the unintended, exogenous component of fertility. The coefficient γ associated with U thus measures the direct consequences of unintended fertility for children's schooling.3 The set of other covariates X includes all exogenous factors (such as income Ω) that affect the desired level of schooling S* and, likewise,0 the desired level of fertility N*. Although not shown in this formulation, interactions of U and X could also enter the empirical model. These concepts are easily generalized to the situation in which parents have, say, two life-cycle periods in which they can bear children. In period 1 they might desire to have N1* children and in period 2, N2* children. Associated with these fertility desires are the desired levels of schooling for the different sets of children, that is, S1* and S2*. (The subscripts on S* refer to the period of the child's birth.) These educational investments are planned to take place in periods 2 and 3. Among other things, optimal choices about fertility and schooling depend on the anticipated sequence of parental incomes, Ω1, Ω2, and Ω3. Suppose that the parents succeed in having Nl* births in period 1, but in period 2 have U2 unintended births, so that N2 = N2* + U2. The unintended births may then affect the schooling of both older and younger children, as indicated in the following pair of equations: Although the model as first written required that the effects of unintended or excess fertility be the same for all children in the family, differential effects among siblings, as shown in this expanded version, are perhaps more plausible. Going further, one might distinguish effects felt mainly by the unintended child herself (or himself) from those felt by other children in the family, as when an 3   Rather little of the literature, unfortunately, has considered the consequences of unwanted fertility from this point of view. What is usually done is to estimate an equation of the form This specification is theoretically inappropriate, since children ever born, N, includes both the desired level of fertility N* and U. It is also statistically inappropriate, given the likelihood of correlation between the choice variable N* and e0. See Montgomery and Lloyd (1996) for a fuller discussion and an approach that uses the concept of measurement error in attempting to interpret results from this conventional framework.

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--> older child is withdrawn from school to help care for a younger sibling whose conception was unintended. The effects considered here may also be produced by changes in circumstances that render the parents' initially desired levels of fertility nonoptimal. Other than the arrival of an unintended birth, this is the primary reason for excess fertility as we have defined the term. Suppose that, anticipating life-cycle income levels of Ω1, Ω2 and Ω3, parents initially desire to have N1* and N2* children. Imagine that they succeed in meeting exactly these fertility goals. Upon entering period 3, however, the parents encounter an unanticipated shortfall in their income. This shortfall in Ω3 imposes new constraints on the remaining schooling investments they can afford and find it rational to make. Had the actual level of income been known in advance, the parents' desired fertility levels might well have differed from N1* and N2*. Our point is that although births N1* and N2* may have been fully desired at the time of their conception, later events may bring about revisions in desired family size and force a rethinking of educational investments. Viewing the situation in retrospect, the parents might well say in response to a survey question that the number of children they actually bore exceeded their ideal number. They would thus experience excess fertility even though, strictly speaking, no birth was unintended. Consequences of Unintended or Excess Fertility Remarkably little research has examined directly the consequences of unintended or excess fertility for developing-country families and children. This is surprising in view of the central role played by the elimination of such fertility in the rationale for family planning and in the emerging literature on unmet need. For example, much of the work on the health implications of birth spacing (see Montgomery and Lloyd, 1996, for a review) draws no distinction between intended and unintended fertility, although it can be assumed that very short birth intervals must generally be unintended. Much of the research on the consequences of imperfect fertility control is concerned with the developed-country situation.4 For instance, the vast literature on the consequences of teenage pregnancy and birth (see Brown and Eisenberg, 4   Whatever the differences between the developed- and developing-country contexts, it seems that the incidence of unintended fertility is high in both. A recent Institute of Medicine study of unintended pregnancy in the United States (Brown and Eisenberg, 1995) documents that 57 percent of all pregnancies in recent years were unintended, that is, either unwanted at conception or mistimed. Evidently, even in a country that has achieved replacement-level fertility and in which abortion and birth control are readily available, the goal of full control over reproduction remains elusive for many women. These figures are based on current reports by women on the status of all pregnancies in the previous 5 years. Of the U.S. pregnancies that resulted in live births in 1988 to 1993, some 11 percent were unwanted and 33 percent mistimed.

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--> 1995, for a review) is dominated by studies of the United States. This literature has been concerned mainly with the consequences of teen births for the mothers, although a number of studies have examined effects on young children as well. Relatively few efforts have been made to distinguish intended from unintended births, as it has been assumed, quite plausibly, that the great majority of teen births in the United States are unintended. A handful of studies in a variety of settings have documented negative effects for unwanted children, whether in terms of heightened mortality risks (Frenzen and Hogan, 1982, for Thailand), poor social development (Baydar and Grady, 1993; Baydar, 1995), poor psychological development (David et al., 1988), or greater risks of physical abuse and neglect (Zuravin, 1991).5 Yet we are aware of only one study, from Finland, that explores the consequences of a child's wantedness for educational attainment (Myhrman et al., 1995). This study is based on a unique longitudinal design that began in 1966 with interviews of women who were then in their sixth or seventh month of pregnancy.6 At the time of the first interview, the wantedness of each woman's pregnancy was ascertained. Some 63 percent of the pregnancies were reported to have been wanted at that time, 12 percent unwanted, and 25 percent mistimed. The study continued to monitor the women (all of whom gave birth) and their children, with assessments taking place in 1980-1981 and 1990, at which point the children were age 24. Myhrman et al. found that the children who were unwanted during pregnancy were subsequently less likely than their wanted counterparts to progress beyond the basic 9 years of education. The education of children who were mistimed fell between that of the other two groups. Among the young men surveyed in 1990, differentials in schooling by wantedness status were apparent only in larger families (those with three or more children). However, young women born into smaller families (two or fewer children) following an unwanted pregnancy had a particularly high risk of stopping after 9 years of compulsory schooling. We know of no similar studies in the developing-country context. On occasion, however, ingenious efforts have been made to tease out the effects of unintended fertility by indirect means. In the case of India, Rosenzweig and Wolpin (1980) examined the educational consequences stemming from twin births, whose simultaneous arrival was clearly unintended. These consequences were negative, if not especially large, although one wonders whether an analysis focusing on unwanted fertility as well as spacing might have found more substantial impacts. In another interesting study, Rosenzweig and Schultz (1987) estimated levels of fecundability among Malaysian mothers, this being one of the 5   For interesting recent research on unwantedness and investments in children's health in the Philippines using an approach that parallels our own, see Jensen et al. (1996). 6   These children were born at a time when access to abortion was highly restricted in Finland; abortion had to be authorized by two physicians and could be granted only for medical reasons.

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--> exogenous factors that might lead to unintended or excess births, and found a modest negative association between fecundability and children's schooling. Fertility And Schooling In The Study Countries The countries examined for this study—the Dominican Republic, Egypt, Kenya, and the Philippines—would seem to form an eclectic group, and one might wonder what features unite them. Four general criteria guided their selection. First, we required that several types of data be available: on the educational levels and enrollment of school-age children, on the fertility preferences of their mothers, and on access within the community to family planning and schooling. Surprisingly few DHS surveys gather this range of data, with data on children's schooling the most likely to be lacking. Second, these are countries in which the proportion of unwanted births is relatively high, in the range of 20-35 percent (Bankole and Westoff, 1995). Third, the study countries exemplify settings in which abortion is illegal.7 And fourth, taken together, these countries represent each of the major regions of the developing world. Fertility In these four countries, total fertility rates (TFRs) for the 3 years before the respective DHS survey dates range from a low of 3.7 in the Dominican Republic to a high of 5.2 in Kenya, with the TFR for the Philippines being 4.1 and that for Egypt 4.7. In each of the surveys, women of reproductive age were asked about the intendedness of all pregnancies resulting in live births during the 5 years preceding the survey. Women were asked whether, at the time they became 7   The illegality of abortion is a key consideration in our research. Where access to abortion is legal, conceptions that are most unwanted or most grievously mistimed will have a greater likelihood of ending in abortion. For example, in the United States, where abortion is legal, 51 percent of unintended pregnancies ended in abortion in 1987 (Brown and Eisenberg, 1995). Abortion induces a type of selection bias: the conceptions that presumably would have the most negative consequences never become births. In a setting in which abortion is illegal, by contrast, a greater percentage of such conceptions will be taken to term because of the risks and costs of illegal abortion. This reduces the selection bias, even if it does not entirely eliminate it, and permits the consequences of unintended conception to be more fully understood. The penal codes in all four countries of this study prohibit abortion (United Nations, 1992. 1993, 1995). In the Dominican Republic, however, abortion is permitted to save the life of the mother. The grounds for this exception appear to be interpreted liberally, as abortion is reported to be widely performed in both public hospitals and clinics, and cases are rarely brought to the courts. In the Philippines, despite the severity of the law, abortion appears to be widely practiced and cases rarely prosecuted, although the surrounding climate is one of fear and shame. In Kenya, hospital-based studies show that illegal abortion is a growing health problem. Little information is available on the extent of illegal abortion in Egypt.

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--> pregnant but before they gave birth, they wanted the birth then, later, or not at all. If a woman said she wanted the birth later, she was asked how much longer she would like to have waited.8 These retrospective data provide the basis for our measures of unintended fertility. The measurement of excess fertility is based on the difference between cumulative fertility and the woman's report of her ideal family size, both being measured at the date of the survey. Appendix B examines at some length the conceptual and empirical differences between measures of unintended and excess fertility. Our view is that although these measures have certain elements in common, each presents distinctive features. The differences between the two are sufficient, we believe, to justify separate analyses. Both measures suffer from incomplete information on timing, that is, on the dates at which the attitudes in question were held. For instance, no data were collected on the intendedness of births that occurred before the 5-year retrospective window adopted by the DHS. Thus, the wantedness status of children over age 5 cannot be assessed by the same means as that applied to younger children. Likewise, information on a woman's current family-size ideal is solicited by the DHS, but no inquiries are made about how long she has maintained that ideal or about the nature of the ideals that were previously held. Moreover, the attitudes measured are those of the women respondents. Independent questions were not asked of fathers, and it cannot be determined whether the views women express are uniquely their own or reflect a consensus forged between spouses (and perhaps involving others). Table 8-1 presents summary statistics on the extent of unintended fertility among the births occurring in the 5 years before the DHS surveys. The percentage of such births that were unwanted at conception varies from 15 percent in the Dominican Republic to 22 percent in Egypt. Because of ex post rationalization, this is likely to be an underestimate of the actual level of unwanted childbearing at the time of pregnancy (see Bankole and Westoff, 1997, for longitudinal evidence from Morocco). However, the children still labeled as unwanted as of the survey date are those that were probably most intensely unwanted at the time of conception. Another 13 to 35 percent of births are reported to have been mistimed, with 8 to 24 percent mistimed by more than 2 years. The total percentage of recent births that were unintended ranges from 52 percent in Kenya, to 45 percent in the Philippines, to 38 in the Dominican Republic, to 35 in Egypt. Kenya, with the highest fertility overall, also has the highest percentage of unintended pregnancy. Table 8-2 presents these data from another perspective, that of the women who might experience either unintended or excess fertility. A substantial percentage of women in each country (from 41 to 63 percent) had no births during 8   No follow-up question on the preferred timing of mistimed births was asked in the Egyptian survey.

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--> TABLE 8-1 Intendedness Status of Births in 5 Years Before Survey Wantedness at conception Dominican Republic (1991) Egypta (1988) Kenya (1993) Philippines (1993) Number of births 4,216 8,716 6,115 9,152 Wanted at conception 61% 65% 49% 55% Mistimed 2 years 16 13b 11 10 Mistimed >2 years 8 13b 24 19 Unwanted 15 22 17 16 Total 100% 100% 100% 100% n.a. = not available a Based on ever-married women only. b Desired time to next birth not asked. TABLE 8-2 Incidence of Unintended and Excess Fertility Among Women Variable Dominican Republic (1991) Egypta (1988) Kenya (1993) Philippines (1993) Number of women 7,318 8,911 7,540 15,029 Number of births in last 5 years (Percent) 0 63 41 48 61 1 21 30 27 21 2 13 22 21 14 3 3 7 4 4 Of women with births in last 5 years At least 1 unwanted birth At least 1 unwanted or 18 28 20 21 mistimed by more than 2 years 28 n.a.a 48 40 For all women, ideal family size and fertility Number of births at survey > Ideal family size 22 52 30 20 Surviving children at survey > Ideal family size 19 42 25 16 n.a. = not available a Only ever-married women interviewed; no data on desired time to next birth.

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--> the preceding 5 years. Among those who did give birth, 18 to 28 percent had at least one unwanted birth; 28 to 48 percent had either one or more unwanted births or one birth mistimed by more than 2 years. From 43 to 59 percent of women (not shown) had at least one unintended birth. Egypt had the highest incidence of recent unwantedness and the Dominican Republic the lowest. Mistimed pregnancies were most prevalent in Kenya and least prevalent in the Philippines. With regard to excess fertility, two measures are shown in Table 8-2, one based on children ever born and the other on surviving children.9 Egypt displays the highest levels of excess fertility, with 42 or 52 percent of women reporting a number of children that exceeded their current family-size ideal. The figure for Egypt is more than double that shown for the Dominican Republic and the Philippines. Schooling Our analyses are focused on children of school age—those aged 6 or 7 to 18, with the lower end of the range depending on the normal age for starting the first grade of primary school. The DHS surveys gather limited information, through their household rosters, on current educational status. Unfortunately, no educational histories are available for children. Thus we cannot determine the ages at which children passed important educational milestones, and issues related to age at first enrollment, dropout and reentry, or grade repetition can be studied only indirectly. To understand school enrollment and educational attainment in the four study countries, one must be familiar with certain structural aspects of their educational systems, such as school starting ages, grade-to-grade promotion policies, the duration of primary and secondary levels, and the critical transition points at which performance on national exams may limit opportunities for advancement. Each of the countries is distinctive with regard to such structural features. Table 8-3 summarizes the main elements of the educational systems of the four countries, not only at the time of the DHS surveys, but also for the relevant school years of all children in the sample aged 6-18.10 Egypt and Kenya have 9   See McClelland (1983) for a discussion of the potential differences in these indicators of excess fertility. In our empirical work we employ the measure based on children ever born. 10   In 1985, primary school in Kenya was expanded from 6 to 8 years. Because the DHS data were collected in 1993, all children aged 18 at the time of the survey (the oldest children in our sample) would have been 10 in 1985; this ensures that they would have been full participants in the transition to 8 grades. A reduction in the years of primary schooling in Egypt from 6 to 5 years came in 1989, the year after the 1988 DHS was conducted, thus allowing us to use the old system to analyze the full sample of children. Recent changes in the Dominican Republic's system have not been fully implemented, and it appears that two parallel systems are currently in place: the traditional system had an intermediate phase of 2 years before full secondary, whereas the reform plan has 4 years of secondary following 6 years of primary, with two additional years for university-bound students.

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--> consequences of unwanted fertility (or other exogenous shocks) during the reproductive life cycle on subsequent fertility and subsequent child investments. These consequences might well depend on the level and age pattern of the wanted births that had already occurred at the time of the exogenous shock. Such earlier births (likewise, earlier child investments) would function as predetermined constraints (or sunk costs) that could limit the scope and nature of any post-shock adjustments on the part of parents. Moreover, in a dynamic decision problem in which the spacing and arrival of wanted births is not fully controllable by parents, it becomes conceptually appropriate to ask how the timing of wanted births affects subsequent fertility, child schooling, and parental consumption. Likewise, one can ask how imperfectly predictable factors, such as a child's educational abilities, might affect the parents' fertility as these factors become known. Given that this chapter is mainly empirical in nature and based on cross-sectional data sets, we have chosen not to pursue the theoretical possibilities afforded by dynamic modeling. The empirical concerns are indeed difficult to address. If lagged, predetermined values of ex ante choice variables are to be included in the empirical model, a means must be found to protect the estimates against the effects of persistent omitted variables, which would be expressed first in the lagged values of the choice variables and again in the current values being modeled. Thus, demanding data requirements must be met to permit consistent estimation of such models. Longitudinal data are required, at a minimum, and the DHS data used here simply do not meet these requirements. With richer data, one could begin to ask a richer set of causal questions. Elements of the One-Period Model We begin by separating the one-period parental utility function into two factors. The first factor, denoted here by U, measures the utility that parents derive from the number of children and their education. We follow Behrman (1988) in using the constant elasticity of substitution (CES) specification, that is, in which i is a subscript for child i, and si is the education of that child. Here n is the total number of children. The parameter p of this subutility function serves to index the degree of parental aversion to inequality in the distribution of resources among their children. It ranges from -∞ to 1, with the case of ρ = 1 representing no aversion to inequality and, at the opposite end, the case of p →∞ representing no tolerance of inequality, that is, Leontief preferences.22 22   This specification has one awkward feature: if si = 0. then child i provides no utility benefits to the parents. In other words, there is a utility return to increasing the number of children only if the

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--> In addition to U, the utility of the parents is affected by their own consumption C. We assume that the full utility function can be expressed in a Cobb-Douglas form, V = UCa where the parameter α gives the subjective weight parents attach to their own consumption. The full parental utility function is therefore a composite in which a CES factor, having to do with child services, is nested within a Cobb-Douglas function in which the two arguments are the child services aggregate U and parental consumption C. The budget constraint for this problem allows for both discretionary and exogenous components of expenditure on children. Each child is assumed to require a fixed amount w in childrearing expenditures; in addition, a child-specific net price pi is associated with each unit of education si. The rationale for making the net price of education child-specific is to account for differences across children in the expected future benefits of schooling. We could accomplish the same goal by elaborating the model in the time dimension, with the nature of the future benefits made explicit, but the current specification should suffice for the purposes of illustration. The budget constraint can then be expressed as where W is total parental income. Solving the Utility Maximization Problem The utility maximization problem can now be divided into discrete stages that correspond to the alternative numbers of children that parents could contemplate having. For any given number of children n, parents face the task of optimally dividing their discretionary income, Ω - wn, between child services U and their own consumption C. The Cobb-Douglas specification for the full utility function implies that with n given,     additional children receive a strictly positive amount of schooling. In future work, we will study more general specifications that do not impose this requirement.

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--> and what remains of household resources is then available to be distributed among the n children for their schooling. The properties of the CES framework (see Varian, 1984, for details) imply that each child will receive in education, where r = ρ/(ρ - 1) and Y = (Ω- wn)/(1 + α) is the total amount of discretionary income available for schooling. We refer to this as the schooling demand equation, where by demand we mean demand that is conditional on a particular fertility level n. The conditional indirect utility derived from child services is then We can now summarize the overall parental utility derived from n children as This is a conditional indirect utility function, giving maximum parental utility as a function of the number of children, which is itself a choice variable. Using this expression, the task that remains is to search over discrete values of n to find the optimal value—the level of fertility that maximizes parental utility. In the main text, we refer to the optimal value of n as wanted fertility. Since n is discrete, no analytic expression for wanted fertility is available, but for given parameter values, it is straightforward to find the level of wanted fertility by numerical means.23 Let n* denote the level of wanted fertility. The wanted level of children's education, which will in general differ across children, is then determined by substituting n* for n in the denominator of the schooling demand equation above. Likewise, the optimal level of parental consumption is given as C = α/(1 + α) (Ω - wn*). Since n* is a function only of the set of exogenous factors (Ω, p, w, ρ, α), wanted schooling and consumption are also fully determined by these factors. It is in this sense that wanted fertility and schooling are jointly determined. 23   Note that the expression applies to values of n > 1.

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--> Some Properties of the Solution As Behrman (1988) demonstrates in a related context, parental aversion to inequality has a potentially important role to play in allocating educational investments among a set of children. This role emerges in situations in which the net price of schooling, pi, differs across children, so that there is an economic incentive to invest differentially. The extent to which such differential investment takes place depends on ρ, the utility parameter that expresses whether parents are indifferent to inequality (ρ = 1) or would tend to resist allocating resources in an unequal manner (ρ < 1), other things being equal. When parents are wholly indifferent to inequality, educational resources are concentrated in the child whose net price of schooling pi is lowest. When they resist such a concentration of resources, by contrast, educational investments tend to be spread more equally among children, although the child with the lowest net price will generally continue to receive more in the way of parental investment (apart from the extreme case of Leontief preferences). The discrete nature of fertility also influences patterns of child investment. To see this, consider the comparative statics of the response to a change in parental income Ω. Suppose that Ω is reduced. In addition to reducing their own consumption, parents faced with lower income have the option to adjust to the situation in two ways that affect their children: on the extensive margin, by reducing the desired number of children, and on the intensive margin, by leaving the number of children unchanged and reducing educational investments. For certain combinations of parameters, as income Ω falls, parents will adjust first by cutting back on children's schooling. After a certain point, however, income will be low enough that parents will find it necessary to reduce fertility. A one-child reduction in fertility frees an amount w in exogenous childrearing expenses. Once that fertility reduction has been made, a portion of the freed w can be used to increase children's schooling, that is, to increase it relative to what it was before the fertility reduction took place. Thus, if we were to graph the relationship between Ω and children's schooling, the graph could exhibit a sawtooth pattern whose shape would reflect both the intensive and the extensive margins of adjustment. A similar pattern could characterize the parental response in own consumption as Ω varies. As far as we are aware, these potentially complex responses have not been much studied, whether from a theoretical or an empirical perspective. Parental Responses to Unwanted Fertility The conceptual approach developed here can be used to study the consequences of unwanted fertility for parental consumption and children's educational investments. As above, let n* denote the level of wanted fertility. If an unwanted birth occurs, actual fertility is then n' = n* + 1. Returning to the

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--> expressions above concerning children's education, we can determine the education response to unwanted fertility by inserting n' in the demand equation where n* had appeared; we can do likewise for parental consumption. The implied adjustments in education and consumption will depend on a number of factors: the level of exogenous childrearing costs w, the child-specific net prices for education pi, the level of income Ω, and so on. The full welfare cost for parents can be summarized in terms of compensating variation, that is, in terms of the additional level of income Ω that would be required to leave the parents as well off with n' children as they would have been with the number of children they actually wished to have, or n*. It is possible to calculate the required compensation by using the conditional indirect utility function V*(n) shown above. This compensation can then be interpreted as a summary measure of parental motivation to avoid unwanted fertility. Alternatively, it can be interpreted as the monetized welfare costs (again from the parents' point of view) that are imposed by unwanted fertility.

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--> Appendix B Measurement Of Unintended And Excess Fertility In the main text, we focus on two distinct concepts—excess fertility and unintended fertility. As noted, the former is measured by the extent to which a woman's cumulative fertility exceeds her expressed ideal family size at the time of the survey. Reports on ideal family size are elicited by the following DHS question: ''If you could go back to the time you did not have any children and could choose exactly the number of children to have in your whole life, how many would that be?" Unintended fertility, by contrast, is typically measured with reference to the 5-year window of time ending at the survey. Within that window, the intendedness of each birth is determined by asking the mother to think back to her feelings at the time she was first pregnant with the child and to report whether she wanted the pregnancy at that time. If the pregnancy was wanted, she is asked whether it was wanted then or later. Concerns about the measurement of unwantedness have focused primarily on the problem of ex post rationalization. Rationalization is a potential problem when respondents who already have children are asked questions about desired or ideal family size or about the unwanted status of specific surviving children (McClelland, 1983). In particular, the questions on unintended fertility are asked on a child-by-child basis, and in answering them, the woman may feel that she is being required, in effect, to affix a label to each child. Yet a child whose conception was unwanted might have grown up to become a loved and much "wanted" member of the family. The woman might therefore feel some reluctance to label the child's conception as unwanted, and the approach might produce underreports of unwanted conceptions. (No similar bias would be expected to distort estimates of birth timing.) The DHS questions were worded so as to minimize ex post rationalization, and there is some evidence from experimental studies in Peru and the Dominican Republic (Westoff et al., 1990) that the emphasis on feelings at the time of conception helps reduce the problem. The fact that substantial numbers of women report excess fertility and unwanted births appears to be ample proof that family-size desires represent considerably more than rationalization. Another form of rationalization could lead to biases in the opposite direction. Rosenzweig and Wolpin (1993) have conjectured that women may be overly optimistic at the time of pregnancy about the endowments of their unborn children. They suggest that retrospective reporting of unwantedness at the time of pregnancy may produce an overestimate rather than an underestimate of the actual level of unwantedness prior to birth. The possibilities for ex post revisionism, regardless of the direction of the possible bias, are what make the kind of longitudinal data available in the Finnish survey ideal for the study of the consequences of unwantedness.

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--> Apart from considerations of recall error and ex post rationalization, a woman's reports on the intendedness of a particular child's conception should not change over time. Such reports are based on the memory of feelings held at a particular fixed point in the past. We do, however, expect to observe changes over time in measures of excess fertility for an individual woman, even if her actual fertility remains unchanged. A woman's desire for children, as expressed in her ideal family size, can be altered by changes in economic, marital, or health circumstances, or by the receipt of new information or knowledge, even if her underlying preferences are held constant (McClelland, 1983). Thus a woman could report her last birth as being wanted at the time of conception and during the same survey interview report excess fertility in the present. She might do so if, in the interim, she faced deteriorating economic conditions, gained new skills in the labor market that increased the opportunity costs of childbearing, absorbed new ideas about the advantages of small families from the media, or lost a husband through death or divorce. Similarly, a woman who reports not having wanted a particular pregnancy in the past could report no excess fertility in the present for a variety of reasons, including an improvement in her own or her community's economic circumstances that allows her to afford more children than previously, the arrival of a new husband who is eager for her to have children with him, or a change in government policies. It is therefore quite difficult to determine from the survey questions themselves whether a woman is inconsistent in her responses. The fact that a woman currently views her family size as excessive does not necessarily mean that any particular child was unwanted at the time of conception, nor does it mean that any particular child is unwanted now. Excess fertility indicates only that the woman now sees her family size as being too large in relation to current ideals. Of course, if fertility ideals and intentions are wholly transitory, their measurement as of a particular point in time will not provide a reliable guide to either past or future behavior. Recent evidence from Peru suggests that desired fertility is reasonably stable in the short run (Mensch et al., 1995). In this study, over 80 percent of women reinterviewed after 3 years provided consistent responses to a question about future fertility intentions. When responses to the question about future childbearing desires from the 1991-1992 DHS were compared with responses to the same question in the 1994 follow-up survey, 72 percent of women gave the exactly the same response. Of those who did not want more in 1994 but had wanted more in 1991-1992, roughly half had had a child in the interval or had experienced a marital disruption; thus an additional 7-8 percent gave consistent answers. Therefore, roughly 80 percent of women gave consistent answers between the two surveys. This provides some evidence to suggest that women's fertility desires do not change wholesale over 3 years. Casterline et al. (1996) examined changes in the Philippines over a shorter reinterview period—6 weeks—and also found considerable evidence of stability. Although Bankole and Westoff (1995) consider recent births, the aggregate

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--> measures of unwanted fertility reported elsewhere in the literature are not based on reports on the wantedness status of particular births, but rather on measures of ideal family size (Lightbourne, 1985) or the desirability of the next birth (Bongaarts, 1990). In the terms we have employed, the Lightborne measures are measures of excess fertility. Bongaarts (1990) compared such excess fertility measures with alternative, forward-looking measures based on the desirability of a next birth. He found strong correlations between these two alternatives, but much weaker correlations between the desire for a next birth and the wantedness status of recent births. Evidently, the alternative measures must tap different concepts; in addition, they are differentially affected by changing events and by recall or misreporting error. To obtain a sense of the empirical overlap between measures of excess and unintended fertility, we examined the DHS data from our four study countries. We investigated whether women who say they currently have excess fertility also report as unwanted at conception those recent births whose parity exceeds the mother's current ideal. The proportion of such recent births reported to be unwanted at the time of conception ranges from 35 percent in the Philippines to 65 percent in the Dominican Republic. In light of the above discussion, it should be clear that such differences in the fertility measures can be interpreted in various ways. One possibility among many is that ideal family size may have declined over the 5 years preceding the survey (Bankole and Westoff, 1995), perhaps as economic circumstances changed. Thus some children who were wanted prior to their birth may now be found in a family that is larger than their mother would view as ideal under her present circumstances. In summary, it appears reasonable to proceed with the excess and unintended fertility measures, each taking a place in the analysis. These measures are fundamentally different in character, and as just shown, they are sufficiently different empirically to warrant separate consideration.

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--> Appendix C Endogeneity Tests Using Generalized Residuals In Schooling Equations

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--> APPENDIX C Endogeneity Tests Using Generalized Residuals in Schooling Equations Measure of Unwantedness χ2 on family planning access in incidence equation (p-value) Generalized residual coefficient, years equation (z stat.) Generalized residual coefficient, secondary school equation (z stat.) Dominican Republic 0, 1, or 2+ unwanted births in last 5 years 23.6 0.022 0.354 (0.07) (0.15) (0.79) Any unwanted births or births or more years mistimed by 3 17.6 -0.109 0.752 (0.29) (-0.66) (1.50) Number of births exceeds family-size ideal 31.0 0.170 0.100 (0.01) (1.08) (0.57) Egypt 0, 1, or 2+ unwanted births in last 5 years 50.5 -0.173* -0.327* (0.00) (-3.23) (-2.37) Any unwanted births or births mistimed by 3 or more years 61.2 -0.175* -0.384* (0.00) (-2.68) (-2.21) Number of births exceeds family-size 85.9 -0.141 -0.447 (0.00) (-1.94) (-1.98)

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--> Measure of Unwantedness χ2 on family planning access in incidence equation (p-value) Generalized residual coefficient, years equation (z stat.) Generalized residual coefficient, secondary school equation (z stat.) ideal Kenya 0, 1, or 2+ unwanted births in last 5 years 21.8 -0.238* 0.218 (0.02) (2.57) (0.46) Any unwanted births or births mistimed by 3 or more years 17.5 -0.172 0.093 (0.06) (-1.26) (0.12) Number of births exceeds family-size ideal 27.2 -0.162 0.438 (0.00) (-1.89) (0.71) Phillippines 0, 1, or 2+ unwanted births in last 5 years 27.0 -0.059 -0.129 (0.04) (0.71) (0.20) Any unwanted births or births mistimed by 3 or more years 29.3 -0.202* -0.001 (0.02) (-2.18) (-0.01) Number of births exceeds family-size ideal 34.7 0.324* 0.440 (0.01) (3.17) (1.22) * Significant at p < .05.