## Abstract

In sub-Saharan Africa, 60 % of child deaths are preventable by investments in child health as simple as immunizations, bed nets, or water purification. This article investigates how a household’s decisions regarding such investments are affected by the size and gender composition of a child’s cohort. I focus on a previously overlooked type of investment: nonrival, child-specific goods (club goods). I empirically estimate the response of immunization status to cohort characteristics. I carefully address the problem of endogenous fertility, which is common in cohort studies. Because most rural Senegalese households are composed of multiple nuclear families, a child’s cohort is composed of both siblings and nonsibling children. Estimating within households, I instrument cohort characteristics with those of the nonsibling (exogenous) portion. I find that children with larger (or more predominantly male) cohorts of vaccine-eligible age are significantly more likely to receive immunization. These findings suggest that children with larger cohorts may be better off in terms of club investments; this is a significant finding for child health given that many illness prevention methods are of a club good nature.

## Introduction

Evidence suggests that human capital investments beginning at the earliest stages of childhood translate into success in adulthood (see Alderman et al. 2006; Black et al. 2007; Case and Paxson 2008). Parents’ decisions regarding investments in nutrition, health, and education for their children determine the productivity of the next generation. This is particularly salient in sub-Saharan Africa, where the cost of even a small investment can be a significant burden and child development lags. As such, the complex processes that affect child investment decisions in poor households are of utmost interest to studies of economic development.

Since the nineteenth century, researchers have recognized that such investment decisions are affected by household composition, particularly by the number of children in the household (Engel 1895). Becker’s (1960) seminal work suggested that parents trade off between quantity and quality of children, implying that parents invest less in children in larger families.

Becker’s theory assumes that investments in children are strictly private goods and, as such, children are in explicit competition with one another for resources. However, many child investments can be considered “club” goods for kids—that is, child-specific goods that are nonrival. Unlike private goods, one person’s consumption of club goods does not diminish the amount available for others. Also unlike public goods, club goods are excludable: they are available or useful only to those in the “club.” Any nonrival good that disproportionately benefits the health of young children over other members of the household could be considered a club good for children. This applies to many investments that are critical for early childhood health in poor countries. Some examples include improved flooring, improved cook stoves, treated bed nets, or a method for purifying drinking water. Such investments can prevent or reduce the leading causes of childhood morbidity and mortality in the developing world: worms, respiratory tract infections, malarial illness, and water-borne diseases.

Certainly, a household with an additional child, ceteris paribus, will have fewer resources available per child. In this sense, a child is directly affected by the size of her cohort. Here, I use the term cohort to mean the group of children with whom a child is growing up and who are living in her household, rather than the generational meaning of the term. Given the competition for resources, a larger cohort would clearly predict reduced investment in private goods per child. However, the expected result with regard to club goods is less clear. A larger cohort would reduce available resources per member, but would simultaneously increase the returns to club investments in kids.

The question of how a cohort affects investment in club goods follows directly from the research on household economies of scale. Barten’s (1964) model of household economies of scale predicts that, holding total income constant, a change in family composition will change the household’s consumption choices across goods. He likened these “family effects” to price effects: greater household size reduces the per person cost of public goods. This is analogous to the proposition that a larger cohort of children effectively makes club goods cheaper relative to private goods for children. Gustafsson and Kjulin (1994) showed evidence that such economies of scale do exist for adult time spent on child care, based on their analysis of families in Sweden. In the context of a poor country, such potential economies may have a significant impact on investment affordability.

Thus, with regard to club goods, a child may benefit from, rather than compete with those in her cohort. If so, club goods will respond to cohort characteristics in the opposite manner of private goods, and accounting for this response may change the net effect of one’s cohort. Such issues may explain the seemingly inconsistent results when researchers have sought causal evidence of the quantity-quality trade-off.

### Contribution

The primary contribution of this work is to estimate the effects of cohort size and gender composition on investment in club goods for children in sub-Saharan Africa. The central challenge in estimating such effects is that the parents making the investment decisions have also (to some degree) chosen these cohort characteristics. Therefore, many unobserved characteristics and preferences will affect both cohort and investments.

This endogeneity of siblings plagues many empirical studies of cohort effects. Previous efforts to address this endogeneity have relied on twinning as an exogenous determinant of total fertility (Black et al. 2005, 2010; Caceres-Delpiano 2006). Although the use of twin studies is a creative and rigorous solution to the endogeneity problem, it is difficult to know whether results are applicable to nontwin families. Further, this methodology is infeasible in the context of poor countries, where twin data sets are generally unavailable. Other researchers have used China’s one-child policy as an exogenous determinant of cohort size (Qian 2009; Rosenzweig and Zhang 2009). For this method too, it is difficult to know whether results are generalizable beyond China.

A second contribution of this paper is the introduction of a new method for dealing with this endogeneity. I exploit the large households that are the norm in Senegal, generally composed of extended families and containing multiple mothers of young children. These are generally sisters-in-law. In these households, a child’s nonsibling coresident children provide similar cohort effects with regard to club goods as would her siblings. However, when estimating within-household, these nonsibling coresident children are exogenous with respect to the fertility decisions of the child’s mother. The characteristics of this exogenous portion of the cohort are used as an instrument for the full cohort measures in a two-stage least squares estimation.

In the next section, I discuss the existing literature regarding cohort effects on child investment. The following sections present the empirical analysis and offer conclusions.

## Existing Evidence of Cohort Effects

The theory of a quantity-quality trade-off in child-rearing, first proposed by Becker (1960) and then formalized by Becker and Lewis (1973), suggests that investments in children decrease with the increasing size of their cohort. It can be easily shown in a broad range of settings that family size and child outcomes exhibit a negative correlation. However, few researchers have been able to establish a causal effect of cohort size on investments. For example, studies of the Matlab family planning experiment in Bangladesh have examined an exogenous change in fertility, but the implementation of child health services alongside family planning services makes it impossible to ascribe the estimates of improved child health outcomes (or investments) solely to reduced family size (Joshi and Schultz 2013).

The most common way to address the endogeneity of fertility choices in this literature is to exploit the exogenous increase in fertility that occurs with twinning. However, the results of “twin studies” regarding the impact of cohort size on child outcomes are mixed. Although some researchers (Rosenzweig and Wolpin 1980; Rosenzweig and Zhang 2009) have found decreased schooling for children from families with twins, others (Angrist et al. 2010; Black et al. 2005, 2010; Caceres-Delpiano 2006; Qian 2009) have not found significantly negative effects of increased cohort size on schooling or health outcomes. Using an alternative method, Rosenzweig and Schultz (1987) estimated a woman’s fecundity and used it as an instrument for total fertility in Malaysia, where fertility control is incomplete; they found that increased cohort size reduces schooling.

These studies have generally focused on outcomes for children, rather than investments per se. Outcomes such as schooling attainment or achievement are, of course, the result of both private and club investments. Thus, if cohort effects that decrease investment in private goods are offset by increased club goods, one would expect these ambiguous or indistinguishable effects on such aggregate outcomes. One exception is a secondary result found by Rosenzweig and Zhang (2009), who examined actual investments, such as adult time spent helping with homework and the likelihood of having an Internet connection. Both of these investments could be considered club goods, and Rosenzweig and Zhang found a positive effect of cohort size on both investments.

In addition to cohort size, a child’s own gender may also affect parental decisions regarding allocation of resources. Several empirical studies have shown evidence of son preference in child investment in diverse cultural contexts (Edmonds 2006 (based in Nepal); Ono 2004 (Japan); Yount 2003 (Egypt); Lundberg 2005 (United States); Gong et al. 2005 (China); Asfaw et al. 2010 (India); Duraisamy and Duraisamy 1995 (India); Rose 2000 (India)). In the presence of son preference, sons may command a greater share of household resources than daughters, leading some scholars to suggest that girls who have more brothers are worse off (holding total cohort size constant). That is, assuming that parents allocate a fixed share of resources to children, the resources available for a given child are decreasing in the share of her cohort that is male.

Evidence for such gender “crowding out” has been mixed. Although some studies focusing solely on education have found negative effects of a male cohort (Bommier and Lambert 2004; Dayioglu et al. 2009; Kambhampati and Rajan 2008; Morduch 2000; Ota and Moffatt 2007; Parish and Willis 1993; Rammohan and Dancer 2008), effects on other composite outcomes, such as health and mortality, are ambiguous. Makepeace and Pal (2008) showed evidence of gender crowding out in India: boys with a more dominantly male sibship have higher mortality rates.1 Both Pande (2003) and Mishra et al. (2004) examined anthropometric measures for children in India and found that girls are in some cases actually disadvantaged by sisters but not brothers.2 Garg and Morduch (1998) found that in Ghana, anthropometric measures for children were 25 % to 40 % worse for a child with an all-boy cohort (versus an all-girl cohort). However, they also found a contrasting positive effect of the indicator for having any brothers. Such seemingly contradictory results might be explained by corresponding increases in investments in club goods and decreases in private investments in response to the male composition of the cohort.

## Empirical Analysis

The purpose of the empirical exercise is to test how investment in club goods responds to cohort size and gender composition. Although some club goods for children are physical, such as a household water sanitation system, many nonrival investments in children are composed of adult time in some form (e.g. supervision, reading, transportation). The club good I examine here is the transportation of children from rural areas in Senegal to a health clinic for immunizations. Although immunization may be seem to be a private good, the injection itself is generally costless in this context because of government subsidization (Save the Children 2012). However, the adult time required to obtain the immunization (via transport and wait time) may be many hours. Pande (2003) noted that in India, differential immunization rates by gender, despite decades of free provision, imply significant opportunity costs of adult time. Further, it seems likely that parents traveling to the clinic would bring all children in the household in need of an immunization. Therefore, as the explicit cost of the injection gets close to zero, a vaccine becomes (very nearly) a nonrival good for children of a relevant age. In the upcoming section Immunizations as a Club Good, I provide suggestive evidence that immunizations are a club good in the context of this analysis.

### Data

This analysis is set in Senegal, where households are large and are often composed of multiple families. These household characteristics, which are not unusual in the developing world, enable me to resolve an inherent challenge of estimation (as discussed in the upcoming section Methodological Challenge). Senegal is an appropriate context for this analysis given that its total fertility rate is more than double the world average (5.2 children per woman in 2005), so that children have large cohorts of varying sizes.

Evidence also suggests preferences for having and investing in sons relative to daughters in this context. Household composition in Senegal suggests the presence of differential stopping behavior, a practice induced by a preference to have sons (discussed further in the section Methodological Challenge). Indeed, self-reported fertility preferences show that the average ideal number of boys is significantly higher than the ideal number of girls (2.9 vs. 2.2; p = 0). Further, greater investment in boys is evidenced by the higher rate of immunization for boys in these data (by 0.5 percentage points, p = .03).

The data are drawn from two cross-sectional household surveys, the Senegalese Demographic and Health Surveys (DHS) in 1993 and 2005 (Ndiaye et al. 1994; Ndiaye and Ayad 2006).3 The DHS interviews all women aged 15-49 from a nationally representative sample of households on topics relevant to fertility, reproductive health, marital relations, and childhood health and nutrition. Specifically, the two surveys used here recorded whether each child under age 5 received each vaccine recommended by the Senegalese National Immunization Schedule as shown in Table 1. Although a single household can appear in both data sets, households cannot be linked across data sets. Therefore, the two cross-sections are pooled for estimation purposes. Given that the estimation is based only on children under 5, however, no child appears in both sets of data; thus, each child-observation is truly unique.

Table 1 also presents a summary of the coverage of immunizations in rural households. Overall coverage of immunizations is low, although it increased from 60 % to 75 % over the 12-year period. Vaccines for which a child is not yet due are excluded from the mean, producing the slight decline in sample size for vaccines due at older ages. Additional details regarding sample size are show in Table 2. A decline in sample size results also from nonresponse to some items regarding immunization. However, children with data missing for any of the 10 vaccines make up less than 10 % of the sample. The last two rows of Table 2 show the sizes for the two samples used in most specifications: 92,643 child-vaccine observations, and 50,602 child-vaccine observations for children with a nonzero cohort size.

### Immunizations as a Club Good

Why would immunizations act as a club good in this setting? I argue here that the principal cost of immunizing a child is the cost of adult time to wait at the clinic, which, in addition to travel time, is nonrival for any children who need to be taken. Certainly, immunizations are not perfectly nonrival because there may be some positive marginal cost per child. These costs, however, are likely small relative to the total cost. Because mothers’ transportation to the clinic is likely to be primarily by foot, walking children will exert zero marginal cost. Nonwalking children will exert some positive marginal cost in terms of adult effort, although nearly zero cost in terms of adult time. However, there is an upper bound for nonwalking children that can be carried; thus, the cost per child that is associated with immunizations as a club good would be decreasing in cohort size, but at a decreasing rate. This is supported by results presented in the section Specification Checks that suggest a nonlinear relationship between immunizations and cohort size.

What would be the total cost in terms of adult time? Community-level data collected with the 1993 DHS include information on distance to the nearest health facility. On average, these rural communities are 5.4 km from a service access point. At this distance, most individuals would travel by foot,4 equating to a mean one-way travel time of 81 minutes.

Systematic data on clinic wait times in Senegal are not available. However, one document reported a nearly three-hour (171-minute) average visit time for each of four urban family planning clinics in Senegal (SEATS 2000). This is consistent with evidence from other African countries: client wait times in two clinics in Nairobi, Kenya, were 140 minutes, for only 16 minutes of service time, on average (Lynam et al. 1994); the wait time at an urban HIV-treatment clinic in Nigeria was 6.48 hours, on average (Umar et al. 2010). Given the lower provider-to-client ratio in rural areas, an appointment at a rural clinic could easily take half the day or longer (Clemens 2009:15–16). In a study of rural health clinics in Mozambique, 43 % of patients reported that either the lengthy travel or the long wait time was the most significant barrier affecting their utilization (Newman et al. 1998). Based on the evidence presented here, it seems reasonable to expect that a rural Senegalese mother would require five to seven hours for accessing vaccination services, a large cost for a service with an unseen benefit.

In this analysis, immunizations are considered a club good for children in a relevant age group. Although the vaccines considered here are all due by age 9 months, in practice, the children in these data continue receiving vaccines up to 4 years of age. However, over 95 % of vaccines administered are received by age 2 years, and this will be the default age group used in this analysis.5 Therefore, for a given child, i, the relevant age-cohort6 is composed of all other children in the household within 24 months of his or her age: that is, coresident children potentially needing vaccines at any time during which child i is due for a vaccine.

To demonstrate that immunizations operate as a club good, I examine the proportion of children receiving vaccines on the same day as a cohort member. For approximately half of the full sample, the enumerator was able to view the health card that lists the immunization history of a child. For this health card subsample, the data contain the date on which each immunization was received. Among rural children with age-mates, 44 % of those that have completed their vaccines received one or more vaccine at the same time as another child in the household. In contrast, urban children are 30 % less likely to have done so (p = .00). This difference likely reflects the increased opportunity cost involved for rural residents to reach and wait at a health clinic. This motivates the restriction of this analysis to the rural areas and suggests that, in rural areas, travel to the clinic is a nonrival good for children in need of immunizations.

### Methodological Challenge

In any empirical estimation of the response of resource allocation to household composition, one must account for the fact that neither the number of children in the household nor their age distribution is exogenous. Specifically, unobserved factors that determined parents’ past fertility choices will also affect current allocation decisions.

It is uncontroversial to state that parents choose, to some degree, the number of children they bear. Perhaps less obvious but also true is that parents choose the gender composition of their children as well, within some bounds. If parents have a greater desire for sons, they will likely continue childbearing until they achieve some target number of sons. Yamaguchi (1989) developed a formal model of how son preference can affect the gender ratio even when manifest only through such differential stopping behavior (DSB). DSB predicts that girls will end up with more siblings than will boys and that families with greater son preference will have a more male-skewed composition. Filmer et al. (2009), using DHS data from 65 low-income countries, presented empirical evidence that DSB is practiced on a significant scale. Although DSB seems most prevalent in South and Central Asia, evidence suggests that DSB is practiced in rural Senegal. In the data used here, boys are significantly more likely to be last-born than are girls, suggesting that the birth of a girl is more likely to induce a continuation in childbearing. Girls in this sample, on average, have more sibling age-mates than boys, and a negative correlation between parity and male composition is observed.7 When DSB is practiced to any degree, it creates a correlation between parental preferences and observed gender composition of children.

Correlations between preferences and both number and gender of children can seriously confound efforts to estimate how child composition affects intrahousehold allocations or child outcomes. Ejrnaes and Portner (2004) simulated the relationship between birth order and schooling investment in children based on a model of household allocation in which fertility is endogenous. They found that accounting for endogenous fertility reverses the direction of correlation between birth order and schooling; that is, when fertility is assumed to be exogenous, empirical estimates are seriously biased.

#### Solutions

To avoid confounding by unobserved household characteristics, I use a within estimator using household fixed effects to compare across children within the same household. In combination with an indicator for a child’s birth order, this holds constant the total number of children in the household when the child is due for immunizations, as well as time-invariant household characteristics. The within-household estimation is possible only because the cohort of interest is defined by age and therefore varies across children within the same household.

However, because many households in the sample include multiple mothers of young children, one may still be concerned that unobservable differences between mothers within a household could confound the estimation.8 For example, a mother that has a high concern for child health may be careful to space births according to public health recommendations (at least three years apart). She would also be sure to immunize her children, creating a spurious negative correlation between age-cohort size and immunizations. Mother fixed effects could remedy this problem but are not feasible in this sample. Variation in age-cohort composition across a mother’s children would require her to have at least three children in the sample. Because vaccination information is available only for children born within five years of the survey, fewer than 10 % of mothers have three or more children in the sample. This is, of course, merely a problem of lacking data that contain detailed immunization information for all of a woman’s children. Additional data collection would allow a more ideal estimation. What is presented here is a novel method for achieving causal estimates based on data that are currently available.

Mother fixed effects being infeasible, I contend with this potential endogeneity by exploiting a unique characteristic of households in Senegal. As shown in Table 3, 56 % of mothers of children under age 5 coreside with one or more other mothers of young children.

#### Multifamily Households

Who are these coresident families? The data do not provide information explicitly on relations between household members, but instead provide information only on each member’s relation to the household head. For households that have more than one mother of young children, however, I can partially determine which result from polygyny according to the method described in the notes of Table 4. Although some of these households result from polygynous unions, three-quarters of them do not. Compared with other rural women, women in households with multiple mothers (who are not cowives) are much more likely to be the daughter-in-law or a foster daughter of the household head, as shown in Table 4. This suggests that many coresident mothers are often sisters-in-law, foster sisters, or other relatives.

I assume that a family is unitary. Thus, what I describe as mothers’ decisions throughout the text are actually the outcome of some joint decision-making or bargaining process between mother and father. I also assume that within a household, separate families coordinate on the provision of goods and services for the household but do not coordinate on matters of sex and procreation. Evidence that coresident families do not coordinate fertility timing is provided in the Appendix.

If families coordinate on provision of goods, a trip to the health clinic would be nonrival for all children of an eligible age within the household. Therefore, the benefit of time spent traveling to and waiting at the clinic will have a value that depends on the total number of eligible children in the household. Thus, all age-mates in the household (sibling or not) would be the relevant cohort for evaluating the cohort composition effects of club good consumption.

As discussed earlier, the sibling portion of the cohort is endogenous. By using household fixed effects, however, I hold constant any unobserved preferences that are in common within the household, so that the timing of nonsibling coresident children is exogenous. I can then use the number and gender of the nonsibling age-mates as an instrument for the characteristics of the full cohort.

The primary identification assumption is thus: controlling for anything common across mothers in a household by the use of household fixed effects, the immunization decisions of mother A are impacted by the fertility decisions of mother B only through the economies of scale effects that are proposed here. If any unobserved preferences that affect both fertility and immunization are shared across mothers (because they share a husband, for example), this will be absorbed by the household fixed effect.

Three possible threats to this identification exist. The first is the case in which three or more coresident mothers reside in a household and at least two but not all of them share a husband. In this case, the two wives sharing a husband could have correlated preferences that are not captured by the household fixed effect. As shown later in the article, however, the results are robust to the exclusion of households potentially fitting this unique profile.

The second case is the possibility that the assumptions about household dynamics are wrong. That is, instead of being unitary families that are independent within households, the households themselves may in fact be unitary. If there is a single patriarch making the primary decisions for everyone in the household, then these preferences or decisions will be captured by the household fixed effect. In this case, there are certainly some smaller decisions that are made independently by mother-father pairs, and these smaller decisions will be the source of variation and identification for my estimations. In the Appendix, I provide basic evidence that heterogeneity exists within households regarding immunization decisions, indicating that there is some parental autonomy within the household.

The third case is a threat of reverse causality: perhaps the immunization decisions of mother A are affecting the fertility of mother B. That is, if A has a strong preference for investing in club goods for children and will certainly do so, B may calculate that her own costs of investing in her children are lower (resulting from free-riding). If these savings reduce the expected costs of child-rearing significantly, it is possible that this may induce mother B to coordinate her fertility timing with mother A. In this case, a similar positive correlation between mother A’s investment and mother B’s cotimed fertility would be observed, but the direction of causation would be opposite. However, as shown in the Appendix, conception is not significantly predicted by recent conception of a coresident woman in nonpolygynous households, suggesting that coresident women are not coordinating fertility timing, either to have coincident or spaced births.

### Estimation

Absent the aforementioned endogeneity issues, the model I would like to estimate is
(1)
where Rijv is a binary indicator of whether child i in household j received vaccine v. The outcome is predicted by Nij, the size of child i’s age-cohort within the household; Zij, the share of that cohort that is male; child characteristics contained in the vector Kij, as discussed later; and household and vaccine fixed effects, ηj and ηv. is a mean-zero error term. However, given the potential endogeneity of Nij and Zij, the model I estimate instead is
(2)
where and are the analogs to measures Nij and Zij for the exogenous portions of the age-cohort (the nonsibling coresident children). For comparison, I also estimate the same equation using only the endogenous portion of the age-cohort (the age-mate siblings). That is,
(3)
where $N˙ij$ and $Z˙ij$ are the relevant size and gender composition measures for the sibling age-cohort. In this equation, represents the predicted change in the probability of receiving a vaccine for each additional nonsibling (sibling) member in a child’s age-cohort. The coefficient represents the difference in that same probability for a child who has nonsibling (sibling) age-mates that are all boys versus all girls. In this setting, I assume that the true effects are the same for sibling and nonsibling age-mates within the household, that is, and . However, I expect that the coefficient estimates based on sibling age-mates will be confounded by unobserved maternal characteristics, so that and . That is, I expect that estimates of will be biased but that the estimates of will be unbiased. If parental concern for child health induces both lower fertility and increased investment, the bias on will be downward.
Although ordinary least squares (OLS) estimation is useful for recovering unbiased estimates of based on the nonsibling age-mates, I am more interested in estimates of —that is, the effects of the characteristics of the full age-cohort. Thus, I use a two-stage least squares (2SLS) estimation to recover the coefficients. I use the exogenous portion of the age-cohort to predict the measures Nij and Zij for the full age-cohort. I estimate
(4)
(5)
(6)
so that and have similar identification as and but are now appropriately scaled to represent effects of the full age-cohort.

Given that an increase in cohort size would reduce available resources per child but also reduce the price of club goods per child relative to private goods, the expected sign of will be the net of income and substitution effects. will be positive if the substitution effect dominates the income effect. Similarly, the expected sign of is ambiguous. An increase in the male share of the cohort makes club goods relatively cheaper than private goods to boys but more expensive than private goods to girls. Absent any son preference, this would predict that resources would be diverted from boy goods to girl goods , or possibly also diverted from club goods to girl goods . However, households with son preference would prefer to shift resources from boy goods to club goods that also benefit boys, rather than goods benefiting only girls. will be positive if son preference dominates the price effect.

A final concern for the estimation of is that one-third of the children in the sample have no age-mates within the household. For these children, the gender composition of their age-cohort is meaningless. Therefore, to accurately estimate , the effect of gender composition, I restrict the sample to those children with a nonzero cohort size (NZC sample). To accurately measure , I use the full rural sample and thus must exclude Zij. Thus, for each of the preceding equations, two estimations are shown: (1) the full sample, excluding Zij, and (2) the restricted NZC sample, including both Nij and Zij.9

#### Control Variables

Certainly there are some child characteristics that affect a child’s probability of immunization beyond her cohort size and gender composition. I include such child characteristics, which may also be correlated with these cohort characteristics, to ensure they do not confound the estimate of interest. The primary characteristic of concern is the child’s gender: boys are more likely to be immunized and, because of differential stopping behavior, have slightly smaller and more male-dominated age-cohorts than girls. I thus control for child gender to ensure that the impact of age-cohort size is not underestimated and that the impact of age-cohort male composition is not overestimated. Birth order to a particular mother and birth order within the household also predict both immunization and age-cohort size, to lesser degrees. Children later in the birth order to a particular mother or within the household are less likely to be immunized. Children later in a mother’s birth order have smaller age-cohorts. Children later in the household birth order have larger age-cohorts. As such, these controls are also included in the fully specified model. Finally, although age is also a predictor of immunizations, I do not include it because it is highly collinear with mother’s and household birth order. Table 8 shows that the main results are not dependent on the inclusion of these controls.

## Results

Table 5 shows results from estimations of Eqs. (2), (3), and (6). Estimates of the effect of cohort size, using the full rural sample, are shown in columns 1, 3, and 5. Estimates of the effect of cohort gender composition use data from the subsample with a nonzero cohort size (NZC sample) and are shown in columns 2, 4, and 6. Columns 1 and 2 show estimates of Eq. (3), taking only a child’s siblings as her cohort. As noted earlier, such estimates are expected to be significantly downward biased. Columns 1 and 2 show negative point estimates for the effect of cohort size and a small positive effect of male composition that is not distinguishable from zero.

The results in columns 3 and 4 are based on only the exogenous portion of a child’s cohort: the nonsibling age-mates. Although these children would exert similar cohort effects within the household, their presence is uncorrelated with unobserved parental preferences (within household fixed-effects estimations). The estimated effects are significantly different from the biased estimations using siblings. Each additional nonsibling age-mate predicts an increase in probability of immunization of about 2.5 percentage points. This estimate is robust to whether I control for the gender composition and to whether I exclude children without any age-mates. In column 4, the sample includes only children who have exogenous age-mates in order to examine gender composition effects. Controlling for cohort size, having an all-male cohort predicts a 3.6 percentage point greater probability of immunization than having all-female age-mates.

To estimate the effect of an age-mate more generally, I show in columns 5 and 6 estimates that instrument full cohort characteristics with those of just the exogenous portion (nonsibling age-mates). These are the second-stage estimations of Eq. (6).10 The coefficients of interest have increased in magnitude relative to the OLS estimation, although the 95 % confidence intervals overlap. These results suggest that any additional age-mate will increase the probability of immunization by about 3 percentage points. Further, for children having any age-mates, an all-boy cohort predicts a 4.6 percentage point increase in the likelihood of immunization relative to an all-girl cohort.

Given an immunization coverage rate of only 70 %, the magnitudes of these effects are significant. Consider a child that has one female age-mate with R = .70, where R is the probability of receiving a given vaccine. Then a child with four female age-mates would have R = .79, an increase of 13 %. Further, if those age-mates were all boys, then R = .836. That is, the child would be nearly 20 % more likely to be immunized than the child in the baseline case.

### Heterogeneous Effects

Table 6 repeats the 2SLS estimations for various samples that are assumed to have different costs associated with taking children for immunizations. The greater the share of the cost that is nonrival, the more immunizations are a club good. For example, having access to a health clinic within one’s village significantly reduces the travel time required to receive immunizations, thus reducing the share of the cost that is nonrival. Thus, households with a clinic in the same village should exhibit smaller effects of cohort size. Because information on distance to clinic is available only in the 1993 round of data, I examine this heterogeneity within the 1993 sample.11

Columns 1 and 2 of Table 6 show estimates for households in villages that reported having a health clinic 0 km away. For both estimates based on the full sample and those based on the subsample of children with a nonzero cohort size (NZC sample), the impact of cohort size is reduced by about 50 % and is no longer statistically distinguishable from zero. Within the NZC sample, the impact of cohort gender composition is inflated. It is not clear why households nearer to clinics would exhibit a stronger impact of gender composition, except for the possibility of differential son preference. However, the point estimate is also less precise and not distinguishable from zero at any standard level of significance.

Another factor that determines the nonrival share of cost for immunization is the opportunity cost of adult time. For mothers with a higher cost of time, the share of immunization cost that is adult time increases. I separate children by an indicator of the potential opportunity cost of adult time: mother’s level of education. Because the vast majority of mothers report no education, the sample for those with any education is small. Nonetheless, the point estimate on cohort size more than doubles for those whose mother has any education versus those with an uneducated mother and remains statistically significant at the 1 % level. The coefficient on gender composition also increases, by 70 %; the coefficient, however, has an increased standard error and I can no longer reject that it is zero. Although the standard errors do not allow me to reject that the effect is the same across the two groups, the increased point estimates are consistent with a higher valuation of time for women with education (based on a higher potential for gainful employment) and thus a greater share of the immunization cost that is nonrival.

In sum, I interpret these results as evidence that the impacts of cohort characteristics on immunization are rooted in the club-good nature of immunizations and their potential economies of scale in terms of adult time.

### Specification Checks

Table 7 presents several alternative specifications of Eq. (6) designed to check for significant interactions or nonlinearities. Column 1 suggests that the effect of gender is linear with respect to the share of the cohort that is male. Neither the indicator nor its square is statistically significant, although they are jointly significant. There is weak evidence, however, of diminishing marginal returns to cohort size. It seems sensible that there would be a limit on the number of children one adult could take to the clinic at one time, which would produce this shape. The point estimates suggest a concave response function that levels off at around 10, turning around completely at 12.25. Although diminishing marginal returns seem plausible, one would expect the function to level off somewhat earlier. However, the squared term is not very precisely estimated, and a turnaround at 3.7 is within the 90 % confidence interval.

In column 2, the specification includes interactions of the variables of interest with the gender of child i. The signs of the coefficients on the interaction terms suggest that cohort effects may be slightly stronger for girls than boys. However, because these effects are not at all precisely estimated, I cannot reject that the effects are the same for boys and girls.

Column 3 investigates whether there is any interaction between the effects of cohort size and cohort gender composition. The positive coefficient on the interaction suggests that (1) the effect of an additional age-mate is larger if that age-mate is a boy, and (2) the effect of gender composition is stronger for larger cohorts. Yet again, I cannot reject that there is no interaction whatsoever, given the rather large standard error on the interaction term. The lack of significance of the coefficient on male share is inconsequential because that estimate represents the effect of cohort gender when the cohort is of size zero. More meaningful is that the coefficients on male share and the interaction are jointly significant at the 5 % level.

### Robustness Checks

#### Sample Selection on Survival

The DHS data used here contain information on immunizations for all living children under age 5. Therefore, children born within the past five years that have since died are present in the data but have no immunization information and are thus excluded from the estimations. If we assume that the excluded children received immunizations with the same likelihood as surviving children, this sample selection should not be a source of bias.

However, immunizations are intended to prevent potentially fatal illnesses. Therefore, a negative correlation between vaccine status and child death is possible. Further, if a child is born weak or sickly, she may be less likely to be immunized and also less likely to survive. Yet, in order to bias the results presented here, death must also be correlated with the size and/or gender of one’s age-cohort. If the excluded children had significantly smaller (or more-female) age-cohorts, then these results are downward biased and serve as a lower-bound effect. If excluded children had larger (or more-male) age-cohorts, then these effects are overestimates.

As shown in column 1 of Table 8, deceased children had smaller age-cohorts, suggesting that the results presented here are a lower bound on the effect of cohort size on immunization. There is also a negative, albeit insignificant, correlation between survival and gender composition of one’s cohort.

#### Polygyny

As stated earlier, a possible violation of the identification assumption arises from polygynous marriages in which mothers of young children share a husband. If all the mothers of young children in the household share the same husband, however, the commonalities in preferences are captured by the household fixed effect. The potential violation occurs when two or more mothers share a husband and (at least) one other mother in the household has a different husband. There are 119 households in the sample that meet these criteria. Column 2 of Table 8 shows the estimation of Eq. (6) based on children with exogenous age-mates, excluding the households that potentially violate the identification assumption. The coefficient estimates of interest are not significantly changed by this exclusion.

#### Within-Household Health Externalities

Many of the vaccines examined here prevent diseases that are transmitted human-to-human via airborne transmission (tuberculosis, pertussis, measles, diphtheria), direct contact (diphtheria), or the fecal-oral route (polio). For these diseases, one could imagine that children with larger cohorts are simply at higher risk of disease, given their increased potential exposure.12 If so, then perhaps these results can be attributed to this unique nature of vaccines, rather than to the club nature of the investment.

I test for this possibility by exploiting data for a vaccine that protects against vector-borne rather than human-to-human transmission.13 Yellow fever is contracted from the bite of an infected mosquito. Certainly, proximity to other infected humans is a factor in vector-borne transmission. However, Anopheles gambiae, the primary malaria vector in Africa, has a maximal flight distance of 10 km (Kaufmann and Briegel 2004). This implies that exposure is based on infection rates within a village more so than within the household, so that vaccinating against yellow fever should offer fewer within-household health externalities. If such externalities are driving the results, estimating based on yellow fever immunization alone should produce a lower point estimate for cohort size, as compared with the main estimations for all vaccines. As shown in column 3 of Table 8, the point estimate for cohort size is identical to that from the main estimation, with a very similar standard error and statistical significance remaining at the 5 % level.14 In addition, the estimate for gender composition is not statistically distinguishable from the originally estimated effect, although it is less precise because of the 90 % reduction in sample size for this estimation.

Given that within-household transmission can result in increased disease severity, regardless of transmission mechanism (Aaby et al. 1984), I cannot fully rule out that some externalities may be at work. Nonetheless, if such externalities were fully driving the results, one would expect the results to be stronger for diseases transmitted by human-to-human contact, and I do not find that this is the case.

#### Age-Cohort Definition

Another assumption of this empirical test has been that the age-cohort that is relevant for immunizations as a club good is defined as all children in the household within 24 months of one’s age. As shown in the remaining columns of Table 8, whether a child’s age-mates are defined as children within 36, 30, 18, or 12 months of his or her age (columns 4–7), the results do not differ significantly from those based on the 24-month definition. Coefficients on cohort gender range from 0.035 to 0.062; none are significantly different from the originally estimated 0.046 (or from each other), and all are different from zero at standard levels of significance. Similarly, effects of cohort size range from 0.014 to 0.038 and do not differ significantly from the originally estimated 0.029. Although only the estimations based on the NZC sample are shown (in order to show the gender effects), estimates of cohort size effects based on the full sample generally do not differ from the estimates shown in columns 4–7. The only exception is the precision of the coefficient estimate for cohort size under the 12-month definition. The final column of Table 8 shows that the effect of cohort size is statistically different from zero in the full sample; the lack of precision in the 12-month NZC sample is likely due to the reduced sample size.

## Conclusions

In this study, I considered how investment in children is affected by the number and gender composition of children within a household. The literature has offered (at least) two theories on this: that (1) children receive less investment as their cohort increases in size (i.e., Becker’s theory of quantity-quality trade-offs), and (2) given any preference for sons, children with more boys in their cohort will receive relatively less (i.e., gender crowding-out).

Evidence for these theories based on rigorous empirical work has been mixed at best, tending to reject more often than support them. I propose that in focusing exclusively on competition for private goods, these theories are missing a key element of child investment: investment in club goods. Further, the effects of one’s cohort on the provision of goods can work in opposite directions for private and club goods. Because of economies of scale, investment in club goods may increase as their price relative to private goods decreases under larger cohorts.

Many significant investments in children are not strictly private. The primary causes of childhood morbidity and mortality are diarrhea, acute respiratory infections, malarial illness, and parasitic worms. Such ailments result from the lack of key investments that are nonrival and disproportionately benefit the children of the household: immunizations, water purification, improved cook stoves, treated bed nets, and improved flooring. As such, it is crucial to understand how households make decisions regarding club good investments, especially as they may differ significantly from private goods.

This study provides evidence that investments in a certain club good, immunizations, increase with cohort size and male composition. The results are robust and do not rely on unique properties of immunizations. Further explorations of these results support the proposition that the increase in immunization is rooted in its club-good nature: those with a greater share of the cost that is nonrival exhibit greater effects of cohort size.

The magnitudes of the estimated effect sizes are reasonably large. If a child with one female age-mate has a 70 % chance of immunization, she has a 3 % chance of dying from a vaccine-preventable disease by age 5. If that child had three more age-mates or all age-mates are boys, immunization increases to 79 % and 83 %, respectively. With 83 % immunization, the chance of vaccine-preventable death drops to 1.7 %—a 44 % reduction over the baseline case. Thus, at least with respect to certain investments, children with larger cohorts may fare better.

Finally, the effects presented here are estimated based on exogenous nonsibling age-mates and, as such, do not warrant direct conclusions regarding the effects of fertility on child investment. Nonetheless, many programs assume that reducing fertility and increasing birth spacing (thereby reducing cohort sizes) would automatically improve child outcomes, an assumption that ignores potential club goods benefits. I leave for future work the collection of adequate data that would allow a more direct test of how sibships affect investments in club goods.

## Acknowledgments

I am grateful to Elisabeth Sadoulet, Alain de Janvry, Jeremy Magruder, Ted Miguel, Abdoulaye Sy, Clair Null, Erick Gong, Meredith Fowlie, and seminar participants at UC Berkeley and IFPRI for their helpful comments and suggestions. All remaining errors are my own.

### Appendix

#### Are Coresident Families’ Fertility Decisions Correlated?

In this section, I present evidence that nonpolygynous multifamily households are not coordinating on fertility timing. This is a key assumption underlying this analysis: the birth timing of coresident children is assumed to be reasonably exogenous after time-invariant household characteristics have been controlled using household fixed effects. If coresident families were coordinating birth timing, conception by one woman would predict either the conception or nonconception of another woman in the household within 12 or fewer months (depending on whether the household preferred coincident or spaced births).

I create a woman-by-month panel of fertility outcomes for rural, ever-married women based on the full birth histories collected in the Senegal DHS. For each woman in each month, the panel contains her age, parity, ever-married status, and whether she conceived in that month (calculated as 9 months prior to observed births). For each woman-month observation, I create an indicator for whether another woman in her household conceived within the 6 or 12 months prior to that month. Using a linear probability model, I regress whether a woman conceives in a given month on an indicator for recent conception by another woman in her household, controlling for age, parity, and ever-married status.

Fifty-three percent of women in multifamily households are not in a polygynous marriage. For these women, the results in Table 9 show that whether a woman conceives in a given month is not significantly predicted by whether another woman in her household conceived in the past 6 or 12 months. Despite very large sample sizes, these estimates fail to provide evidence that multifamily households are coordinating birth timing to achieve either coincident or spaced births.

For women in polygynous marriages, I do find evidence of fertility coordination. These women are significantly more likely to conceive if a cowife has conceived within the past 6 or 12 months (9 % and 5 % more likely, respectively). This predictive effect is no longer significant when household fixed effects are included.15 That is, fertility correlations are driven by the household commonalities (e.g., the husband) that are controlled by the household fixed effect.

#### Parental Autonomy Within the Household

As an indicator of the ability of parents to make child investment decisions independently from the household, I examine differences in immunization records within a household. I focus on rural households that have multiple mothers of children under age 5. I categorize mothers as (1) having a perfect record (i.e., all children are current on all immunizations), (2) having a zero record (no children have any immunizations), or (3) having a mixed record (children have some immunizations for which they are due). Perfectly homogenous households contain women who all have perfect or zero records. These households make up 7 % and 4 % of all rural households with multiple mothers, respectively. Households with some intermediate or unknown level of homogeneity are those in which all mothers have mixed records (45 %). Households with the greatest heterogeneity of immunizations across mothers are those in which a mother with a perfect record or a mother with a zero record coresides with mothers who have the opposite records or mixed records. These households combine to make up 44 % of all households. Figure 1 shows these categorizations graphically, with the white areas being homogenous households and successively darker shades indicating increasing levels of heterogeneity. The highest level of heterogeneity is when a mother with a perfect record coresides with a mother with a zero record (5 % of households).

## Notes

1

In this study, gender composition of sibship is proxied by gender of the first-born.

2

The authors’ explanation is that selective neglect arises from a desire for gender balance, rather than a pure desire for sons.

3

Other SDHS rounds were not used for the following reasons: 2008, 2006 and 1997 did not collect immunization information; 1986 collected immunization information only for a small subsample.

4

Tanser et al. (2006) used GIS and transportation modeling for rural sub-Saharan Africa and predicted that for distances of 5 km, only 20 % of individuals will use public transportation.

5

Results are robust to age groups defined over the range of 12 to 36 months.

6

This terminology is not meant to imply any relation to age-period-cohort analysis.

7

Girls have an average of 0.49 sibling age-mates vs. 0.46 for boys (equality rejected with p = .0539). Among women with reasonably completed fertility (aged 48+), each additional child is associated with a reduction in male share of .022 (on a mean of .47; p = .03).

8

In this analysis (as in the data), a family is defined as a mother and her children. A household is defined as members who coreside: generally extended families, as discussed in the next subsection.

9

The exclusion of Zij from the full sample estimation may bias the estimate of β1 slightly downward because (as discussed earlier) Nij and Zij are correlated as a result of differential stopping behavior.

10

Estimations of first-stage Eqs. (4) and (5) are shown in the Appendix.

11

Main results disaggregated by survey round (shown in the Appendix) are consistent with the aggregated estimates. However, the impact of gender composition is not statistically significant when only the 2005 data are used.

12

Evidence also suggests that diseases transmitted within the household can be more severe than the same disease contracted from a casual contact (Aaby et al. 1984).

13

Tetanus is also not passed by human-to-human transmission, but the vaccine for tetanus is combined with diphtheria and pertussis in the DPT series.

14

One would not expect this pathway to generate the main results found regarding cohort gender composition. Nonetheless, I include the full specification, including gender composition, in the presented results based on yellow fever alone. The point estimate for gender composition (0.05) is similar to the original (0.036) and robustness-checked (0.044 and 0.063) estimates, although the standard error is slightly higher (p = .102).

15

I also included household fixed effects in the nonpolygynous estimations, and the results are not different from those presented.

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