Abstract

Research on the schooling implications of fertility transitions often faces an aggregation problem: despite policy interest in macro-level outcomes, empirical studies usually focus on the micro-level effects of sibsize on schooling. This article proposes an aggregation framework for moving from micro- to macro-level associations between fertility and schooling. The proposed framework is an improvement over previous aggregation methods in that it considers concurrent changes in the effects of sibsize, socioeconomic context, and family structure. The framework is illustrated with data from six sub-Saharan countries. Possible extensions are discussed.

Whereas concern [over high fertility in developing countries] is based on the macroeconomic consequences of population growth, it is at the level of the family that fertility decisions take place. (King 1987:373)

Research on the schooling implications of fertility transitions still faces the “level of analysis” quandary noted by King more than two decades ago. On the one hand, fertility transitions are inherently a macroscopic phenomenon, and policy debates over their consequences often focus on macro-level outcomes. On the other hand, fertility decisions and their consequences occur most directly within households. The question, therefore, is whether the schooling consequences of fertility transitions are best studied from a macro- or a micro-perspective. Put differently, can studies reconcile the rigor of micro-level analysis with the policy interest in macro-level answers?

This dilemma can be addressed in three ways. One can forgo the micro-level detail and simply study macro-level associations (NRC 1986). Conversely, one can embrace the micro-analytical rigor, even if results remain silent about macro-level implications (Cassen 1994; Lloyd 1994). More comprehensively, one can attempt to bridge the micro-macro gap by aggregating the micro-level evidence in order to achieve both statistical detail and policy relevance (Knodel and Wongsith 1991; Knodel et al. 1990; Lam and Marteleto 2005). Our research extends this latter effort.

To situate our contribution to this bridging effort, let us consider four main reasons why the micro-level effects of sibsize are insufficient to infer the societal implications of fertility transitions on schooling (hereafter labeled “fertility transition effect”).1 First is a distribution issue: how declines in national fertility affect schooling depends on whether these declines occur among subpopulations with lower versus higher fertility (Birdsall et al. 2001; Knodel et al. 1990; NRC 1986). Second, the effects of sibsize on schooling can change over time, and such change matters (Knodel et al. 1990). Third, these effects might likewise vary across subpopulations (King 1987; NRC 1986). Fourth and finally, if fertility transitions affect both the size and structure of families, the latter could have additional effects (McLanahan 2004). All four problems have been acknowledged in past studies, but only the first has been resolved (Knodel et al. 1990).

Our article attempts to address these unresolved problems by proposing a framework for aggregating the micro-level estimates of sibsize effects to infer the fertility transition effect. The framework links sibsize effects (the usual focus of empirical research) to the macro-level fertility transition effect (an important focus of policy). It shows how this macro-level effect depends not only on the magnitude and distribution of changes in family size but also on historical changes in sibsize effects. More broadly, it captures the effects of fertility transitions contingent on, and relative to, other socioeconomic changes. Altogether, it addresses three fundamental questions about the magnitude, variability, and relative importance of the fertility transition effect on schooling:

  • (1) Magnitude: How large is the fertility transition effect, and how does it relate to the micro-level effect of sibsize?

  • (2) Variation: How does this effect vary with key features of transitions, such as their evenness (how evenly fertility declines within the national population) or multidimensionality (whether the decline in fertility is accompanied by changes in family structure)?

  • (3) Relative importance: How does the magnitude of this effect compare with the influence of other socioeconomic changes?

These questions have practical relevance in high-fertility countries striving to raise the levels of school enrollment under tight budget constraints. They also inform scientific debates about the socioeconomic consequences of fertility transitions. In theory, declines in birth rates can enhance national rates of school participation partly by averting the dilution of family resources across multiple children (Blake 1989).2 Empirically, many studies have explored this family-level dilution (e.g., Lloyd 1994), but few have explicitly derived its national-level implications. We fill this gap by examining these aggregate implications. We explore the question conceptually and with an empirical illustration.

This article is structured as follows. First, we discuss why evidence of family-level dilution (alone) is insufficient to infer national-level implications of fertility declines. Second, we build on previous research to propose a more complete approach for aggregating micro-level evidence. Third, we illustrate this approach with data from six African countries. We conclude with the framework’s key insights and possible extensions.

A Hypothetical Illustration

Our premise is that micro-level estimates of sibsize effects are insufficient to infer aggregate transition effects. This basic point is illustrated with the hypothetical examples in Fig. 1. Imagine a country with an average sibsize effect (βs) of –5 at the onset of its fertility transition: that is, each additional sibling reduces the probability of school enrollment by 5 percentage points. If the average number of siblings in the country (F) fell from 6 to 4, how much would this decline boost schooling? The intuitive expectation (scenario A in Fig. 1) is a 10-point gain. Sensible as it seems, this intuition is accurate only if βs values remain constant throughout the demographic transition, if they are invariant across subpopulations, and if fertility declines evenly across the national population.

These assumptions are questionable. Sibsize effects (βs) change over time (Lloyd 1994; Lu and Treiman 2005; Maralani 2008); they might be curvilinear, or depend on sex, ethnicity, rural residence, or income (Anh et al. 1998; King 1987); and fertility may decline unevenly (Bongaarts 2003; Kirk and Pillet 1998; Shapiro and Tambashe 2002). For these reasons, one must consider how less-restrictive assumptions affect conclusions about macro-level effects. Scenario B in Fig. 1 relaxes the assumption of a constant βs, positing instead an increase from –5 at the onset of the fertility transition to –10 points at the end of the study period. Although the initial sibsize effect (βs) and the national fertility decline (∆F) remain the same as in scenario A, the predicted outcome under scenario B reverses dramatically to become a 10-point decline in schooling.3 Scenarios C and D further consider what happens if βs and ∆F vary across subpopulations. Whereas scenario A posits a homogenous population with an even decline in fertility and an even sibsize effect (∆F = –2 and βs = –5 in both subgroups), scenarios C and D assume no sibsize effect (βs = 0) in one subgroup and a strong effect (βs = –10 point) in the other. Furthermore, the fertility decline in scenario C is relatively even but highly uneven in scenario D. The predicted outcomes under these new conditions become +15 and +25, respectively. In other words, scenarios A–D yield very different conclusions, even as they assume exactly the same fertility decline and initial sibsize effect. Clearly, information about the average magnitude of the initial sibsize effect and the fertility decline is insufficient to infer the fertility transition effect. Other characteristics of transitions must be considered.

Previous Research

Granted that micro-level sibsize effects are not enough to infer transition effects, how have previous studies inferred these transition effects? The simplest approach, which relies on cross-country regressions, is deemed statistically unreliable (Rodrik 2005). Micro-level studies can be more detailed and rigorous (Cassen 1994), but they have shortcomings of their own. First, they focus on family-level dilution as the lone pathway, thereby overlooking such macro-level influences as changes in age-dependency. Second, despite methodological inroads, researchers still debate how to best estimate the causal effects of sibsize. Efforts to establish causation have used modeling strategies that focus on reportedly unintended fertility (Montgomery and Lloyd 1999) or instrumental variables, such as twin births (Angrist et al. 2010; Black et al. 2005; Li et al. 2008; Rosenzweig and Wolpin 1980), the sex composition of siblings (Angrist et al. 2010; Conley and Glauber 2006), or miscarriages (Maralani 2008). All three instruments are plausible sources of exogenous fertility, but their application must be considered carefully. Detailed and reliable data on miscarriage might be unavailable; twin births are a rare event, and there exist biological differences and cultural differences in treatment between twins and nontwins; one must make arbitrary assumptions about parental preferences for sex composition; and imbalance in the sex composition of the first two children, for instance, is less likely to shape the rates of parity progression beyond two children in countries where ideal family size is high. So far, there is little consensus on the best instrument (Schultz 2007) or how findings change with alternative modeling strategies. Some studies show little change when instruments are used (Lee 2004; Li et al. 2008). Even where a change is observed, the lessons are not straightforward. In Black et al. (2005), for instance, the use of an instrumental variable wipes out the apparent sibsize effect found with simpler ordinary least squares (OLS) methods with few controls, but the study itself and its replication with the same data and instruments (Mogstad and Wiswall 2009) underscores the value of also attending to simpler concerns, such as extensive controls (birth order, for instance) or the functional form of sibsize effects. Other worthy concerns include using event-history frameworks and adjusting for fixed characteristics of parents, including their propensity to trade child quality for quantity (Eloundou-Enyegue and Williams 2006; Guo and VanWey 1999).

A third limitation of previous research—most relevant to this article—is that even if a reliably causal estimate is obtained at the micro level, aggregate implications remain unclear. Analysts who infer aggregate transition effects from micro-level studies risk both a historical and an ecological fallacy. The first fallacy arises when drawing historical conclusions from cross-sectional evidence (Thornton 2001). The second might occur when using micro-level evidence to infer national outcomes (Berry and Martin 1974) because such inferences ignore the distributional aspects of fertility transitions. As the U.S. National Academy of Sciences (NRC 1986:57) intimated, “If a nation achieves lower fertility rates, the impact on the education and health of children will be determined in part by the class distribution of the fertility reduction.”

A few studies have accordingly sought to bridge this micro-macro gap (Knodel and Wongsith 1991; Knodel et al. 1990). The idea is to express changes in national schooling as the aggregate result of changes in the relative size and fertility levels of different subgroups. This strategy permits four key advances: (1) it makes explicit the individual experience of fertility transitions—declines in national fertility “[lead] to a major increase in the proportion of children who come from small families” (Knodel and Wongsith 1991:119); (2) it pays due attention to the difference between changes in fertility rates (the macro-level process) and family size (the child-level experience), a distinction also stressed in other studies (Lam and Marteleto 2005); (3) it aggregates micro-level outcomes more reliably because it considers distribution; and (4) it reconciles interest in national-level outcomes with the rigor of micro-level evidence. Essentially, this new perspective traces how the effects of fertility transitions are mediated through the changing sibsize experiences of children. It aptly shifts from macro-level transitions down to the individual experiences and back up to macro-level outcomes. Still, the approach retains two limitations readily acknowledged by the authors. First, it adjusts for neither “the variety of influences operating simultaneously, most of which also contribute to rising levels of education for children” nor the possibility for “the effects of family size on children’s education [to] change during the course of fertility transition” (Knodel et al. 1990:52). Further, it narrowly equates fertility transitions with changes in birth rates, even as contemporary transitions also involve changes in family structure. Our framework addresses these three limitations.

Proposed Extension

Let family structure be a variable defined by an exhaustive set of mutually exclusive family types j. Family types can be defined on the basis of parents’ marital status but also other markers of resources available to children, including parents’ socio-economic status (SES), employment, or education, for instance. If wjt and sjt are, respectively, the proportion of children and the average schooling in family type j at time t, then the average schooling (S) at the national level is
formula
(1)
The historical change in national schooling between two time points is
formula
(2)
where barred variables represent averages over the two time points—for example,
formula
As in other basic decompositions, Eq. (2) expresses the total change in schooling in two components: change in group composition (left bracket) and change in schooling within group (right bracket). The rightmost bracket can be expanded by considering the dilution function linking children’s schooling to their sibsize. Assuming linear dilution (a tenable assumption if one has a dichotomous outcome expressed in logit units), then
formula
(3)
where αjt, the baseline, indicates the group-specific enrollment rate for an only child; and βst and βjt are dilution coefficients associated with sibsize (Fj) and family type (j), respectively. Plugging Eq. (3) into Eq. (2), the historical change in national schooling then becomes
formula
or
formula
With a slight reordering,
formula
(4)

The formulation in Eq. (4) thus splits a country’s historical change in schooling into four components capturing the influences of both fertility transitions and socioeconomic change (see Fig. 2). Fertility components include changes in (A) the level and distribution of fertility and (B) family structure. Socioeconomic changes include change in (C) dilution environment (i.e., the schooling penalty associated with the addition of a sibling or with change in family structure), and (D) the baseline probability of school enrollment. This decomposition can help answer our study questions about the influences of fertility transitions on schooling. For now, we briefly describe these four components.

Component A is the aggregate effect of changing family size. All else equal, the larger the decline in family size (ΔF), the larger the overall implications for schooling. Importantly, this effect of ΔF depends not on the initial βs value, but rather on the average () during the study period. Thus, ignoring the changes in βs would bias the estimation of the fertility transition effect. The bias is downward (underestimation) if βs strengthens over time, and vice versa.

Component B represents the effects of changing family structure (∆wj). It deserves attention if the changes in family structure are viewed as an integral aspect of fertility transitions. As Eq. (4) shows, the changes in family structure enhance the transition effect if they raise the proportion of births occurring in less vulnerable families (∆wj > 0 for families with above-average s values).

Component C, the dilution effect, reflects the changes in the schooling penalty from family size and/or family structure (Δβs and Δβj) during the transition. Accounting for changes in dilution helps address the situations envisioned under scenario B of Fig. 1. Besides modulating the effects of falling sibsize, changes in βs have a main effect. Even if fertility levels and family structure remain unchanged, national schooling levels might change solely in response to change in the penalty associated with high fertility.

Component D represents socioeconomic changes that affect the baseline schooling opportunity for children (∆αj). One such factor is the public education funding per child, itself determined by changes in the national economy, public commitment to education, and size of youth cohorts. Because fertility transitions affect the size of these cohorts, they also contribute to D. Although we focus on the contributions of fertility transitions via A and B, there is a possible contribution through D as well.

Illustrative Country Cases

Sub-Saharan Africa is a good illustrative setting. First, the region has a clear policy interest in possible schooling gains from transitions. With one-half of its residents living on less than $1.25 USD per day, a total fertility rate of 5.3, and a gross secondary enrollment ratio of 30 % (World Bank 2005), the region combines the highest fertility and the lowest secondary enrollment rates among major world regions. In spite of Africa’s commitment to Millennium Development, the gains in reducing poverty and expanding quality schooling remain slow (UN 2009; UNECA 2009). Whether fertility transitions boost schooling is therefore relevant.

Second, this region remains in the early stages of its transition. In the past two decades, the region’s total fertility rate fell by about 20 % from 6.4 births per woman two decades ago, but national experiences vary. Countries such as Zimbabwe, Ghana, and Botswana have reduced birth rates by more than one-third since 1985, but others have witnessed modest declines. Family structure is also changing. Ghana saw a 45 % increase in unmarried mothers over the past 15 years, contrasting with Madagascar’s 21 % decline (DHS 2010). Further differences are found within countries, in places where transitions began among urban or educated elites. The result, in such cases, was a “three-stage transition process, with fertility initially declining in urban areas while remaining stable in rural areas, then fertility falling in both settings but more rapidly among urban dwellers, and finally with fertility declining more in rural than in urban areas” (Shapiro and Tambashe 2002:111; see also Bongaarts 2003; Kirk and Pillet 1998).

Third, African transitions began under a variety of contexts, including unexpected circumstances, such as economic downturns, famines, health crises, wars, or weak family planning infrastructure (Bongaarts and Watkins 1996; Cohen 1998; Kirk and Pillet 1998; Lesthaeghe 1993; Lindstrom and Berhanu 1999; Locoh and Makdessi 1996; NAS 1993). They also unfolded under diverse dilution environments; some began at a time when extended-family supports were buckling under the strain of economic and health crises (Lesthaeghe 1993; Lindstrom and Berhanu 1999). As these supports eroded, the economic burden of childrearing fell back to biological parents, often raising the penalty of large sibsize for children’s schooling. This growing significance of sibsize had been expected, and it has since been documented (Desai 1995; Eloundou-Enyegue and Williams 2006; Lloyd 1994; Montgomery and Kouame 1993). In this light, the diversity of African fertility transitions facilitates the study of contextual variation. Our illustrative countries (Burkina Faso, Ghana, Kenya, Madagascar, Tanzania, and Zambia) capture this diversity. All six countries experienced some decline in fertility rates, from –1.5 % (Burkina Faso) to –15.4 % (Ghana) (see Fig. 3). Their transitions occurred in diverse dilution environments. Sibsize effects were worsening in some countries (Madagascar, Ghana, Kenya, and Zambia) but becoming milder elsewhere (Burkina Faso and Tanzania). Economic trends also varied. GDP per capita and public funding of education were declining in Madagascar and Zambia, growing in Ghana and Kenya, and stable in Tanzania and Burkina Faso. Many African countries were rescinding primary school tuition and fees (Minten et al. 2005), and some—such as Burkina Faso and Tanzania—were coping with unexpected flows of refugees and returnees from war-stricken neighboring countries (UNHCR 2009). Reflecting this economic and policy diversity, this decade witnessed both dramatic gains and reversals in enrollments (DeRose and Kravdal 2007; Lloyd and Hewett 2003). Although our sample does not represent sub-Saharan Africa as a whole, its diversity can illustrate how fertility transition effects vary with features of national transitions.

Data and Measures

The study data come from the Demographic and Health Surveys (DHS). The DHS are nationally representative surveys fielded over the past two decades across Africa, Asia, and Latin America. Beyond fertility and health data, some DHS have collected schooling data. Their replication across and within countries facilitates comparative historical analysis. We sought to restrict analysis to countries with reliably mergeable data for more than two survey rounds, but only four countries met this criterion at the time of our study (Ghana, Kenya, Madagascar, and Tanzania). Burkina Faso and Zambia were added to expand the sample, despite their having only two rounds. Zambia was a particularly weak addition because of its much shorter intersurvey interval of four years, compared with a decade for the other countries. Nonetheless, this country was interesting for its marked economic reversal during this period. The main dependent variable was school enrollment. Predictors, as per Eq. (4), include key descriptors of fertility transitions, notably changes in sibsize and family structure, as well as changes in dilution environment and socioeconomic context. These variables were measured as follows.

The main outcome, child schooling (sij), was measured by enrollment status among 10- to 21-year-olds. We chose this wide range4 because our interest extends beyond basic education and because the 10–21 age range limits the confounding effects of delayed school entry while maximizing variation across sampled countries and over time. Schooling entry is delayed in many African countries, and enrollments have been found to peak at ages 10–11 even where the official starting age stands at 6–7 (Lloyd and Blanc 1996). Setting 21 as the upper-age boundary helps capture cross-country variation or the historical swings in enrollment seen in some of these countries during the 1990s (Lloyd and Blanc 1996; DeRose and Kravdal 2007; DHS 2010; Lloyd et al. 2000). School quality is a better indicator of the schooling resources availed to children, and studies have begun to note the emerging differences in school quality in Africa, questioning whether some of the recent gains in enrollment came at the expense of quality (Michaelowa 2001). Unfortunately, we did not model school quality because of lack of data.

Fertility was captured by sibsize, specifically the number of living siblings, including the index child. Sibsize was calculated both nationally and within each family type (Fij). It could not be established for orphans and foster children in the absence of data links to mothers. The imputed value in these cases was the national average family size: that is, orphans and foster children could be disadvantaged only because of family structure, not family size.

Family structure was measured by the distribution of families of different types. Family types (j) were defined on the basis of mother’s marital status, father’s employment, and residence, which are three variables chosen for their relevance to the material resources available to children. All three variables were dichotomized to index currently married women, employed fathers, and urban residence, respectively. These three dummy variables should in theory generate six categories, but we placed all rural married women into one category because relatively few rural women had unemployed partners. Conversely, we created a separate category for orphans and foster children in light of their large numbers and expected educational disadvantage (Case et al. 2004; Isiugo-Abanihe 1985). Our six family types thus included (1) orphans and fostered children; and children whose mothers were (2) rural and unmarried, (3) rural and married, (4) urban and unmarried, (5) urban and married to an unemployed partner, and (6) urban and married to an employed partner.

Effects of sibsize and family structure were indicated by the regression coefficients (βs and βj, respectively) obtained from regressing enrollment status on family size and family type (results in Online Resource 1). The β values generated by OLS show an association but do not warrant causal claims. In other words, the lower schooling found in larger families might simply signal an endogenous parental tradeoff between high fertility and child quality. Other studies have similarly struggled with establishing causation, and we used the most extensive controls and rigorous methods available to us while refraining from strong causal claims. We controlled for several correlates of children’s schooling or parental preference for child quality (sex, age, education of the household head, and family wealth) and adjusted for the fixed effects of households. We further controlled for community characteristics: specifically, average enrollment rates in the cluster of residence. These multiple controls reduce the risk of spurious covariation, but causality is not established because of a lack of data on a convincing instrument. This limitation must be remembered. However, the point of this article is less about causal estimation than it is about macro-level implications: assuming that a researcher can estimate the micro-level effects of sibsize on schooling, what do these estimates imply for the aggregate schooling impact of a fertility transition?

Socioeconomic context was captured by baseline enrollment opportunities (αj). These were computed from the predictive equation generated by the regression results, and they were generated for each family type. Specifically, the number of siblings and family structure are set to 0, and the other covariates are set to their group-specific means. These baseline enrollments (αj) reflect group circumstances with respect to family SES, parental education, and community-level opportunity; in other words, the change in baseline enrollment reflects historical changes in family and community-level circumstances.

Methods of Analysis

Beyond the regressions used to obtain the dilution coefficients (Online Resource 1), this study used aggregation, simulation, and decomposition methods. Aggregation was used to answer the first study question about the magnitude of the fertility transition effect in the study countries. This effect was computed by applying the A and B components of Eq. (4). Conclusions from this new aggregation procedure were compared with results obtained with previous approaches.

Simulation was used to explore how various characteristics of a fertility transition modulate its schooling implications. Simulations were run for each study country. The baseline simulation involved plotting the expected change in national schooling if fertility declined by 2.5 children but other characteristics of the transition remained the same as were actually observed. Additional scenarios assumed situations where national fertility declined evenly across all family types, β remained constant over time, or family structure did not change during the transition. Comparing these alternatives with the baseline scenario helps appraise the importance of various characteristics of transitions.

Finally, decomposition was used to assess the relative importance of fertility transitions in driving changes in schooling. Using the full Eq. (4), we apportion each country’s total change in schooling into the influences of national change in fertility (A), family structure (B), dilution environment (C), or socio-economic context (D).

Findings

Total Change in Schooling

Table 1 summarizes the background data on fertility and schooling for the study countries. For each family type, the first block of columns shows the relative representation (wjt), average sibsize (Fjt), net association with schooling (βjt), net association between sibsize and schooling (βst), and baseline probability of enrollment (αjt). For instance, rural unmarried families in Madagascar (1992–1993) accounted for 8.1 % of all sampled children; they had an average sibsize of 5 children; they were 37 % less likely to be enrolled than children from urban married and employed families; each additional sibling was associated with a 0.06 decline in the logit of enrollment; and the baseline logit of enrollment was –0.31 (i.e., an enrollment probability of 0.42). Using this information, we calculated the enrollment logits and odds for each family type (second block of columns). The national odds of enrollment (St) are then obtained as a weighted average of the group-specific data, as per Eq. (1), and they are shown at the bottom of the column. The procedure is repeated for the last survey year (third and fourth block of columns). Data for the intermediate survey are excluded for space considerations. Finally, using data from these four blocks, we calculated the intersurvey change in enrollment. Although sibsize declined in all six countries, the schooling trends diverged. The national odds of enrollment increased in Madagascar (+88 %), Ghana (+8 %), and Tanzania (+72 %), but they declined in Zambia (–17 %), Kenya (–25 %), and Burkina Faso (–20 %). Having thus documented the total change in school enrollment, we can now examine how much of this change is specifically associated with the change in fertility.

Magnitude of the “Transition” Effect

Using the background data in Table 1, Table 2 examines the relationship between fertility transitions and schooling trends in the study countries. Its purpose is to compare the results from different analytical approaches. In the first approach (column 1a), fertility is assumed to be the only relevant change during the study period. In this case, the change in enrollments is entirely imputed to the fertility transition. However, historical changes in schooling likely reflect multiple influences. The methods used in past research to capture the net contributions of fertility include macro-level regression, micro-level regression, or simple aggregation. The results from these alternative approaches are shown in Table 2 (columns 1b, 2, and 3, respectively), and they are compared with the results obtained with our proposed aggregation scheme (column 4).

Macro-Level Regression (Column 1b)

The focus here is on the macro-level association between changes in fertility and the logit of national enrollments in the study countries. Results (data not shown but available on request) showed a weak association (R2 = .01) but a regression coefficient b = 0.20. The result of applying this coefficient to changes in national sibsize is shown in column 1b. The observed gains in enrollment logits range from 0 (Burkina Faso) to a high of 0.16 (Kenya). All values here are positive, whereas some in 1a are negative: although total enrollment declined during the study period in some countries (Kenya, Burkina Faso, and Zambia), a positive association exists between declines in national fertility and gains in schooling. Clearly, a decline in enrollments during a transition does not rule out the possibility of a schooling boost from the falling birth rates because this boost can be muted by other socioeconomic changes. Although the approach in 1b represents an improvement over 1a, it is flawed in assuming that national declines in fertility have the same average effect across countries.

Micro-Level Regression (Column 2)

In this approach, the micro-level association between sibsize and schooling is used to directly infer the macro-level fertility transition effect. In Madagascar (1992–1993), this micro-level association is –0.06: having one additional sibling is, on average, associated with a 0.06-unit decline in the logit of enrollment. When applied to the country’s decline in sibsize (0.6 children), the estimated transition effect is +0.036 logit units (–0.06 × –0.6) (column 2). Unlike 1b, this approach recognizes national differences in the micro-level associations between fertility and schooling. Thus, even as Zambia’s fertility decline was larger than Ghana’s during the study period (–0.26 vs. –0.16), Ghana registered a larger gain in enrollment (+.014 logits, as opposed to 0.00) because of its larger βs value.

Simple Aggregation (Column 3)

Contrary to the previous approach, the analysis under column 3 relaxes the assumption of an even fertility decline. It is analogous to Knodel et al.’s (1990) approach but differs slightly because it considers both family size and structure.5 Here, the aggregate effect of fertility transitions equals the A component of Eq. (4) except that βs values remain constant over time. In this case, Madagascar’s effect becomes 0.033 units versus the earlier 0.036 value. The observed differences between columns 2 and 3 are small in our illustrative case studies, but they could become large if the fertility declines are very uneven. The approach in column 3 makes more realistic assumptions than the approach used in column 2, but it still ignores possible historical change in the associations between sibsize and schooling.

Fuller Aggregation (Column 4)

Because the associations between sibsize and schooling change over time (Table 1), the fertility transition effect can be measured by component A in Eq. (4). The new estimates are shown under column 4a. Madagascar, for instance, now shows a larger effect 0.061 because the country’s βs values grew stronger over time. Where these values weakened (Tanzania and Burkina Faso), the transition effect is smaller than the value under column 3. The differences are not trivial. In Kenya and Madagascar, the estimated logits are 54 % and 85 %, respectively, higher than in column 3. By ignoring the historical changes in βs values, one might substantially alter conclusions about the magnitude of fertility transition effects.

Finally, transitions also involve changes in family structure. If these are incorporated in the analyses, the estimated transition effect (column 4b) becomes the sum of A and B in Eq. (4). The numerical value for Madagascar becomes 0.14. Not only are the differences large, but the effect is occasionally reversed compared with scenario 4a. This is true of Kenya and Zambia, where adverse changes in family structure accompanied the decline in fertility. The final story about the transition effect can thus vary noticeably if transitions are defined more broadly to include change in family structure. More generally, results can be distorted if one restrictively assumes that fertility transitions are even, unidimensional, or involve no change in β values. Simulation analysis was used to further clarify how each of these assumptions matters.

Simulation Results

Simulation analysis was used to examine how the schooling effect of transitions varies with their characteristics. Figure 4 describes the simulation results for a 2.5-unit decline in sibsize, under four scenarios. The baseline scenario (gray solid line with no markers) shows the estimated schooling gains under the actual circumstances of the country’s transition. The remaining scenarios show results under hypothetical circumstances that assume transitions that are even across all family types (dotted line with no markers), involve no change in βs values (black solid line with markers), or involve no change in family structure (broken line with markers). By varying one factor at a time, simulations reveal the unique implications of each assumption. Looking at the baseline curve, the effects of a 2.5-unit reduction in sibsize range from negligible in Burkina Faso and Tanzania (0.3 and 1.2 percentage points, respectively) to substantial in Ghana and Madagascar (5.2 and 5.7 percentage points, respectively).

Distribution of Fertility Decline

The importance of distribution is gauged by comparing the baseline to the finely dotted line. As Fig. 4 shows, these two curves overlap for all study countries. Although such results seem to downplay the importance of distribution, they reflect the relative evenness of these countries’ fertility declines, at least across the family categories used in our analysis. In this particular case, failure to consider the distribution of the fertility decline would not skew the results.

Historical Change in βsValues

To gauge the importance of ignoring the historical change in βs values, we compare the baseline with the black solid line with square markers. The wider the angle between the two lines, the greater the bias from ignoring change in βs values. Angles are visible for all countries, but they are most meaningful in Ghana and Madagascar. Had βs not changed in Madagascar, for instance, the transition effect associated with a 2.5-unit decline in sibsize would have been nearly one-half (3 percentage points) the value under the baseline scenario (5.7 points). Transition effects are underestimated in countries where βs values grow over time (Kenya, Ghana, and Madagascar) and overestimated where βs values weaken over time (e.g., Tanzania). Although past studies have been most concerned with finding reliable estimates of βs values, our results warrant attention to change in βs values during the transition. If these values grow (Lloyd 1994), prognoses based solely on pretransitional βs would underestimate the changes in schooling associated with fertility transitions. In that sense, one can still expect a country’s fertility transitions to be associated with rising schooling levels, even if this country’s sibsize effects are weak at the onset of the transition.

Changes in Family Structure

If changes in family structure are viewed as an intrinsic component of fertility transitions, this aspect must also be considered. In Fig. 4, its influence is reflected in the difference between the baseline and the dotted line with markers. Family structure has both main and interactive influences. Its main influence reflects change in the distribution of children across family types (Δw in component B of Eq. (4)). Its interactive influence reflects how family structure modulates the effects of changing fertility (w in component A). In Fig. 4, the main influence is reflected in the vertical distance between the two curves at origin, and the interactive influence is reflected in the angle between the two curves. Results mostly suggest a “main influence” except in Tanzania and perhaps Burkina Faso. In Kenya and Zambia, the dotted line sits well above the baseline curve. Had the fertility transition in these countries involved no change in family structure, it would have been associated with greater gains in enrollments. The reverse is true in Ghana and Madagascar. Thus, changes in family structure can substantially add to, or remove from, the total changes in schooling associated with changing sibsize.

Decomposition Results

Using decomposition methods, we examined the relative contributions of fertility transitions versus other socioeconomic changes to national trends in schooling. The results are shown (Table 3) in nominal values and in percentages. The interpretation of percentages is straightforward, except when they exceed 100 % or fall below 0. A positive value indicates a contribution in the direction of the total trend. A negative value indicates a contribution against the total trend. When the total change in national enrollment is very small (as in Ghana), decomposition can yield very large and meaningless percentages because the denominator is close to 0. Results suggest the following. First, the share of total change in enrollments associated with changing sibsize was generally small. The largest shares were seen in Kenya and Madagascar (–14 % and 8 %, respectively). The shares attributed to changes in family structure were a little larger but less consistent. They raised enrollment logits in Ghana (+0.06) and Madagascar (+0.08) but reduced them in Kenya (–0.08), Burkina Faso (–0.08), and Zambia (–0.11). Even if they are added together, changes in family size and structure do not account for the majority of the observed change in enrollments in the study countries.

Far more influential were the changes in dilution environment (βs). These were the dominant source of change, notably in Zambia, Kenya, and Tanzania (101 %, 110 %, and 157 % of the total change in enrollment, respectively). Dilution became more severe in the first two countries and worked to reduce enrollments, but it became less severe and worked to raise enrollments in Tanzania. Although this change in dilution environment itself is unexplained here,6 it clearly seems to shape the national trends in enrollments.

Socioeconomic context also mattered. It drove much (147 %) of Madagascar’s growth in school enrollment, and it braked what would have otherwise been a greater decline in enrollment in Kenya (–23 %) and Zambia (–28 %). Conversely, a worsening socioeconomic environment reduced enrollments trends in Tanzania (–0.373; –57 %) and Burkina Faso (–1.14; 415 %). It is unclear which socioeconomic factors were at work. The positive influence of socioeconomic circumstances in Madagascar is consistent with the policy provision of tuition-free education during these years (Minten et al. 2005), but it is surprising in Zambia given the country’s economic and policy trends during the study period (see Fig. 3). Presumably, socioeconomic factors other than GDP and education budgets were influential.

Conclusion

This study proposed a framework for inferring the macro-level implications of fertility transitions from micro-level studies of sibsize effects. The framework advances previous aggregation schemes by considering the historical changes in sibsize effects, the unique features of each transition, as well as concurrent socioeconomic change. The framework also helps gauge the relative influence of fertility transitions vis-à-vis other socioeconomic changes. In particular, it can help decompose historical changes in national schooling into the influences of changes in fertility, sibsize effects, family structure, or baseline opportunities for schooling.

The study generates two main insights, one conceptual and the other empirical. The conceptual insight is that sibsize effects are necessary but insufficient to infer the aggregate effect of fertility transitions; no one-to-one connection exists between the micro-level sibsize effect and the macro-level impact of a transition. A country with initially large sibsize effects might reap modest schooling dividends from its transition if these sibsize effects erode during the transition, if its fertility decline is uneven, or if the decline is accompanied by adverse changes in family structure. Conversely, countries with modest sibsize effects at the onset of the transition may turn out to have substantial schooling dividends if the effects of sibsize increase during the course of transitions. Analyses must therefore consider historical change in sibsize effects, and not just the effects at a single point in time as has often been the implicit practice. Where sibsize effects increase during transitions, analysts would underestimate the schooling gains from fertility transitions if they base their prognoses solely on the sibsize effects observed before the onset of the transition.

A second and far more tentative insight is suggested by our empirical findings: looking at our illustrative case studies, the changes in schooling associated with fertility transitions appear to be smaller than those associated with other socioeconomic change. Our decomposition results suggest that reductions in sibsize per se accounted for small percentages of the total change in enrollments. Much of the change was instead associated with changes in dilution or socioeconomic environment. This conclusion is far more tentative for four reasons: it strongly depends on accurate estimation of the effects of sibsize and family structure; it may depend on the criterion used to classify families into various types; it is based on a nonrandom sample of six countries, most taken at fairly early stages in their fertility transitions; and it applies specifically to the age range (10–21) and schooling outcome (enrollment) used in this research. Because choices about age range, sampled countries, and measure of schooling might affect the estimated βs value, the relative magnitude of the resulting transition effect will be affected accordingly. A priori, larger βs values are expected for wider age intervals, higher levels of schooling, school quality, or countries with weaker social supports for poor and large families. All else equal, these larger βs values would yield larger transition effects. For these reasons, we cannot assert that the effects of socioeconomic change always dwarf those of fertility transitions. At a minimum, however, this finding underscores the need to pay attention to other socioeconomic changes during the course of fertility transitions. Even if one is mostly interested in fertility transitions, it is useful to appraise their effects relative to those of concurrent socioeconomic change.

More than its empirical conclusions, the study’s contribution is perhaps more methodological. Research in this area is striving to refine methods that generate causal estimates of the effects of sibsize on children. As this quest comes to fruition, the next challenge is to derive macro-level implications. Because micro-level relationships do not univocally translate into macro-level ones, some aggregation scheme is necessary. We proposed just such a scheme. It improves earlier aggregation efforts by considering the historical changes in sibsize effects, family structure, and socioeconomic environment.

In turn, the proposed framework can be improved in at least three directions. One is to consider other pathways through which fertility transitions affect schooling. Changes in age-dependency ratios are one such pathway (Bloom et al. 2002). They are implicitly embedded in the D component of Eq. (4), and if researchers can estimate how changing age dependency ratios affect baseline opportunities for enrollment, this influence is easily added to the total effect of fertility transitions. A second extension is to consider implications for schooling inequality. Much work on the human-capital effects of fertility declines has focused on averages. However, asymmetric fertility declines might worsen inequality among children. Fortunately, the framework (see Online Resource 2) can be expanded to address these implications for schooling inequality. As a third extension, one might further distinguish between dilution from family size versus family structure. This too, can be easily achieved by separating these two factors in the C component of Eq. (4).

Still, even in its current form, the proposed framework advances research on the schooling impacts of fertility transitions by bridging some of its micro-macro divide. It offers a relatively simple way to reconcile the potential rigor and detail of micro-level analysis with the policy interest in national level outcomes. This advance is both practical and timely. Its application is facilitated by a growing availability of repeated demographic surveys; and it is made urgent by current questions in higher-fertility countries about the socioeconomic dividends from ongoing demographic transitions.

Acknowledgments

The authors thank MACRO/DHS for making the data available. This research was supported by Cornell’s Bronfenbrenner Life Course Center, the Polson Institute for Global Development, and the Hewlett Foundation. Previous versions of this article were presented at the 2007 and 2011 meetings of the Population Association of America (in New York and Washington, DC, respectively). Thanks to the anonymous reviewers and the editors of Demography for greatly improving the paper’s content and presentation. We also received useful comments from Lindy Williams, Shannon Stokes, Julie DaVanzo, Cheikh Mbacké, Florencia Torche, Lisa Dundon, and Mary Eloundou. Remaining errors are ours.

Notes

1

Because the term “effect” has a strong causal connotation, we use it only in the theoretical sections of the article. When discussing findings, the term “association” is preferred.

2

Another pathway, not examined here, is to reduce the size of school-age cohorts (Birdsall et al. 2001; Bloom et al. 2002).

3

One way to calculate these transition-related gains is to estimate, for each time period and each subpopulation, the reduction in enrollment rates relative to a baseline situation of no siblings. In scenario A (Time 1), this reduction is 6 siblings × (–5): that is, –30. At Time 2, the reduction is 4 siblings × (–5): that is, –20. The change associated with the transition is thus [(–30) – (–20)]. In scenario B, the reductions are –30 [(6 siblings) × (–5)] at Time 1, and –40 [(4 siblings) × (–10)] at Time 2, giving a transition-related decline of 10 points in enrollments. The same logic applies in C and D except that population weights of 0.5 are applied. In scenario C, the reduction at Time 1 is [(0.5 × 8 × –10)] + [(0.5 × 4 × 0)] = –40. At Time 2, it becomes [(0.5 × 5 × –10)] + [(0.5 × 3 × 0)] = –25. The change between the two times is thus [(–25) – (–40)]. A more systematic calculation method, shown later herein, begins by expressing national schooling as a weighted average of group-specific enrollments (Eq. (1), upcoming). Because group-specific enrollments are themselves a function of baseline enrollment opportunities (α), sibsize (F), and the schooling effects of sibsize (βs), one can express the change in national schooling in terms of change in group weights (Δw), baseline enrollment opportunities (Δα), sibsize effects (Δβs), and sibsize (ΔF) (see upcoming Eq. (4)). For scenario C, in which group size, sibsize effects, and baseline opportunities do not change (i.e., Δw = Δβs = Δα = 0), Eq. (4) reduces to , for a numerical result of [(–10) × (0.5) × (–3)] + [(0) × (0.5) × (–1)] = + 15.

4

Studies on Africa’s basic schooling trends have used a variety of age ranges: for example, 7–14 (Lloyd et al. 2000), 10–14 (Lloyd and Blanc 1996), 15–19 (Lloyd et al. 2000), and 15–24 (DeRose and Kravdal 2007). Choosing a higher age boundary here was needed to maximize cross-country and historical variability and to increase sample size. Ideally, one would include a sensitivity analysis for various choices of age range, but such analyses were not included in this research.

5

In Knodel et al. (1990), weights were based on the distribution of children across different family sizes. Here, we monitor change in the representation of children across both family sizes and types.

6

In Zambia and Kenya, informal support networks available to large and poor families may have weakened, or perhaps schooling costs increased. In Tanzania, new policies might have subsidized the schooling of needy children.

References

Angrist, J., Lavy, V., & Schlosser, A. (
2010
).
Multiple experiments for the causal link between the quantity and quality of children
.
Journal of Labor Economics
,
28
,
773
824
. 10.1086/653830
Anh, T. S., Knodel, J., Lam, D., & Friedman, J. (
1998
).
Family size and children’s education in Vietnam
.
Demography
,
35
,
57
70
. 10.2307/3004027
Berry, K. J., & Martin, T. W. (
1974
).
The synedochic fallacy: A challenge to recent research and theory-building in sociology
.
The Pacific Sociological Review
,
17
,
139
166
. 10.2307/1388339
Birdsall, N., Kelley, A., & Sinding, S. (
2001
).
Population matters. Demographic change, economic growth, and poverty in the developing world
.
New York
:
Oxford University Press
.
Black, S., Devereux, P. J., & Salvanes, K. G. (
2005
).
The more the merrier? the effect of family composition on children’s education
.
Quarterly Journal of Economics
,
120
,
669
700
.
Blake, J. (
1989
).
Family size and achievement
.
Berkeley
:
University of California Press
.
Bloom, D., Canning, D., & Sevilla, J. (
2002
).
The demographic dividend. A new perspective on the economic consequences of population change
.
Santa Monica
:
Rand Corporation
.
Bongaarts, J. (
2003
).
Completing the fertility transition in the developing world: The role of educational differences and fertility preferences (Policy Research Division Working Paper No. 177)
.
New York
:
Population Council
.
Bongaarts, J., & Watkins, S. C. (
1996
).
Social interactions and contemporary fertility transitions
.
Population and Development Review
,
22
,
639
682
. 10.2307/2137804
Case, A., Paxson, C., & Ableidinger, J. (
2004
).
Orphans in Africa: Parental death, poverty, and school enrollment
.
Demography
,
41
,
483
508
. 10.1353/dem.2004.0019
Cassen, R. (
1994
).
Population and development: Old debates, new conclusions
.
New Brunswick
:
Transaction
.
Cohen, B. (
1998
).
The emerging fertility transition in sub-Saharan Africa
.
World Development
,
26
,
1431
1461
. 10.1016/S0305-750X(98)00058-8
Conley, D., & Glauber, R. (
2006
).
Parental educational investment and children's academic risk: Estimates of the impact of sibship size and birth order from exogenous variation in fertility
.
Journal of Human Resources
,
41
,
722
737
.
Demographic and Health Surveys (DHS). (2010). Statcompiler, ORC Macro. Retrieved from http://www.statcompiler.com
DeRose, L. F., & Kravdal, O. (
2007
).
The effects of educational reversals on first births in sub-Saharan Africa: A dynamic multi-level perspective
.
Demography
,
44
,
59
77
. 10.1353/dem.2007.0001
Desai, S. (
1995
).
When are children from large families disadvantaged? evidence from cross-national analyses
.
Population Studies
,
49
,
195
210
. 10.1080/0032472031000148466
Eloundou-Enyegue, P. M., & Williams, L. B. (
2006
).
Family size and schooling in sub-Saharan African settings: A reexamination
.
Demography
,
43
,
25
52
. 10.1353/dem.2006.0002
Guo, G., & VanWey, L. K. (
1999
).
Sibship size and intellectual development: Is the relationship causal?
.
American Sociological Review
,
64
,
169
187
. 10.2307/2657524
Isiugo-Abanihe, U. C. (
1985
).
Child fosterage in West Africa
.
Population and Development Review
,
11
,
53
73
. 10.2307/1973378
King, E. (
1987
).
The effect of family size on family welfare: What do we know?
. In Johnson, D. G., & Lee, R. D. (Eds.),
Population growth and economic development: Issues and evidence
(pp.
373
411
).
Madison
:
The University of Wisconsin Press
.
Kirk, D., & Pillet, B. (
1998
).
Fertility levels, trends, and differentials in sub-Saharan Africa in the 1980s and 1990s
.
Studies in Family Planning
,
29
,
1
22
. 10.2307/172178
Knodel, J., Havanon, N., & Sittitrai, W. (
1990
).
Family size and the education of children in the context of rapid fertility decline
.
Population and Development Review
,
16
,
31
62
. 10.2307/1972528
Knodel, J., & Wongsith, M. (
1991
).
Family size and children’s education in Thailand: Evidence from a national sample
.
Demography
,
28
,
119
131
. 10.2307/2061339
Lam, D., & Marteleto, L. (
2005
).
Small families and large cohorts: The impact of the demographic transition on schooling in Brazil
. In Lloyd, C. (Ed.),
Growing up global: The changing transitions to adulthood in developing countries
(pp.
56
83
).
Washington
:
National Academy Press
.
Lee, J. (
2004
).
Sibling size and investment in children’s education: An Asian instrument (IZA Discussion Paper 1323)
.
Bonn
:
Institute for the Study of Labor
.
Lesthaeghe, R. (1993). Are there crisis-led transitions? Paper presented at the 1993 annual meeting of the Population Association of America, Cincinnati, Ohio.
Li, H., Zhang, J., & Zhu, Y. (
2008
).
The quantity-quality trade-off of children in a developing country: Identification using Chinese twins
.
Demography
,
45
,
223
243
. 10.1353/dem.2008.0006
Lindstrom, D. P., & Berhanu, B. (
1999
).
The impact of war, famine, and economic decline on marital fertility in Ethiopia
.
Demography
,
36
,
247
261
. 10.2307/2648112
Lloyd, C. B. (
1994
).
Investing in the next generation: The implications of high fertility at the level of the family (Research Division Working Papers No. 63)
.
New York
:
The Population Council
.
Lloyd, C. B., & Blanc, A. K. (
1996
).
Children’s schooling in sub-Saharan Africa: The role of fathers, mothers, and others
.
Population and Development Review
,
22
,
265
298
. 10.2307/2137435
Lloyd, C. B., & Hewett, P. (
2003
).
Primary schooling in sub-Saharan Africa: Recent trends and current challenges (Research Division, Working Papers No.176)
.
New York
:
The Population Council
.
Lloyd, C. B., Kaufman, C. E., & Hewett, P. (
2000
).
The spread of primary schooling in sub-Saharan Africa: Implications for fertility change
.
Population and Development Review
,
26
,
483
515
. 10.1111/j.1728-4457.2000.00483.x
Locoh, T., & Makdessi, Y. (
1996
).
Population policies and fertility decline in sub-Saharan Africa (CEPED Series, No. 2)
.
Paris
:
Centre Français sur la Population et le Développement
.
Lu, Y., & Treiman, D. J. (2005, March–April). The effect of family size on educational attainment in China: Cohort variations. Paper presented at the annual meeting of the Population Association of America, Philadelphia, PA.
Maralani, V. (
2008
).
The changing relationship between family size and educational attainment over the course of socioeconomic development: Evidence from Indonesia
.
Demography
,
45
,
693
717
. 10.1353/dem.0.0013
McLanahan, S. (
2004
).
Diverging destinies: How children are faring under the second demographic transition
.
Demography
,
41
,
607
627
. 10.1353/dem.2004.0033
Michaelowa, K. (
2001
).
Primary education quality in francophone sub-Saharan Africa: Determinants of learning achievement and efficiency considerations
.
World Development
,
29
,
1699
1716
. 10.1016/S0305-750X(01)00061-4
Minten, B., Francken, N., & Ralison, E. (
2005
).
Dynamics in social services delivery and the rural economy of Madagascar: Descriptive results of the 2004 communes surveys (Cornell ILO Policy Brief)
.
Ithaca
:
Ilo
.
Mogstad, M., & Wiswall, M. (
2009
).
How much should we trust linear instrumental variables estimators? an application to family size and children’s education (IZA Discussion Paper No. 4562)
.
Bonn
:
Institute for the Study of Labor
.
Montgomery, M. R., & Kouame, A. (
1993
).
Fertility and schooling in Côte d'Ivoire: Is there a tradeoff? (Technical Working Paper No 11)
.
Washington
:
The World Bank
.
Montgomery, M. R., & Lloyd, C. B. (
1999
).
Excess fertility, unintended births, and children’s schooling
. In Bledsoe, C., Casterline, J. B., Johnson Kuhn, J. A., & Haaga, J. G. (Eds.),
Critical perspectives on schooling and fertility in the developing world
(pp.
216
266
).
Washington
:
National Academy Press
.
Demographic effects of economic reversals in sub-Saharan Africa
. (
1993
).
Washington
:
National Academy Press
.
Population growth and economic development: Policy questions
. (
1986
).
Washington
:
National Academy Press
.
Rodrik, D. (2005). Why we learn nothing from regressing economic growth on policies. Unpublished document. Kennedy School of Government, Cambridge, MA.
Rosenzweig, M. R., & Wolpin, K. I. (
1980
).
Testing the quantity/quality fertility model: The use of twins as a natural experiment
.
Econometrica
,
48
,
227
240
. 10.2307/1912026
Schultz, T. P. (
2007
).
Population policies, fertility, women’s human capital, and child quality
.
Handbook of Development Economics
,
4
,
3249
3303
. 10.1016/S1573-4471(07)04052-1
Shapiro, D., & Tambashe, B. O. (
2002
).
Fertility transition in urban and rural sub-Saharan Africa: Preliminary evidence of a three-stage process
.
Journal of African Population Studies
,
7
(
2&3
),
111
135
.
Thornton, A. (
2001
).
The developmental paradigm, reading history sideways and family change
.
Demography
,
38
,
449
465
. 10.1353/dem.2001.0039
The millennium development goals report 2009
. (
2009
).
New York
:
United Nations
.
Assessing progress in Africa toward the millennium development goals
. (
2009
).
Addis Ababa
:
UNECA
.
Global trends report: 2008
. (
2009
).
New York
:
United Nations
.
World Bank. (2005). World development indicators. Retrieved from http://devdata.worldbank.org/dataonline

Supplementary data