metadata: authors: 0: author: Jakiela,Pamela
1: author: Ozier,Owen
2: author: Fernald,Lia C.
3: author: Knauer,Heather Ashley
count: Kenya
docna: 0: docna: Big Sisters
docty: Policy Research Working Paper
subtopic: Gender and Development,Social Protections & Assistance,Early Child and Children's Health,Nutrition,Early Childhood Development,Reproductive Health,Inequality
teratopic: Social Protections and Labor,Health, Nutrition and Population,Education,Poverty Reduction,Gender
abstracts: cdata!: This paper models household investments
            in young children when parents and older siblings share
            caregiving responsibilities and when investments by older
            siblings contribute to young children's human capital
            accumulation. To test the predictions of the model, the
            paper estimates the impact of having one older sister (as
            opposed to one older brother) on early childhood development
            in a sample of rural Kenyan households with otherwise
            similar family structures.  Older sibling gender is not
            related to household structure, subsequent birth spacing, or
            other observable characteristics, so the presence of an
            older girl (as opposed to an older boy) is treated as
            plausibly exogenous. Having an older sister rather than an
            older brother improves younger siblings' vocabulary and
            fine motor skills by more than 0.1 standard deviations.
            Viewed through the lens of the model, the empirical pattern
            shown here suggests that: (i) older siblings'
            investments in young children contribute to their human
            capital accumulation, and (ii) households perceive lower
            returns to investing in older girls than in older boys.
geo_reg_key: 517191
repnme: repnme: Big Sisters
display_title: Big Sisters
listing_relative_url: /research/2020/10/32516723/big-sisters
topicv3: Inequality under Law m1326002 925,Education, Skills Development and Labor
            Market m1326135 1484,Gender m1327621 615,Early Child Development m1327727 479,Early Childhood m1582438 4408
publishtoextweb_dt: 2020-10-27T00:00:00Z
historic_topic: Social Protections and Labor,Health, Nutrition and Population,Education,Poverty Reduction,Gender
origu: DECRG: Human Development (DECHD)
no_of_pages: 45
author_keys: 0: author_key: 1149895
1: author_key: 691398
2: author_key: 794716
3: author_key: 1319053
model_extractions: Policy Research Working Paper 9454

# Big Sisters

_Pamela Jakiela Owen Ozier Lia Fernald Heather Knauer_ Development Economics Development Research Group October 2020
Policy Research Working Paper 9454

# **Abstract**

This paper models household investments in young children when parents and older siblings share caregiving responsibilities and when investments by older siblings contribute to young children’s human capital accumulation. To test the predictions of the model, the paper estimates the impact of having one older sister (as opposed to one older brother) on early childhood development in a sample of rural Kenyan households with otherwise similar family structures. Older sibling gender is not related to household structure, subsequent birth spacing, or other observable characteristics, so the presence of an older girl (as opposed to an older boy) is treated as plausibly exogenous. Having an older sister rather than an older brother improves younger siblings’ vocabulary and fine motor skills by more than 0.1 standard deviations. Viewed through the lens of the model, the empirical pattern shown here suggests that: (i) older siblings’ investments in young children contribute to their human capital accumulation, and (ii) households perceive lower returns to investing in older girls than in older boys.

This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at pamela.jakiela@williams.edu, owen.ozier@williams.edu, fernald@berkeley.edu, and heather.knauer@gmail.com.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Big Sisters**

Pamela Jakiela, Owen Ozier, Lia Fernald, and Heather Knauer<sup>_∗_</sup>

**JEL codes:** O12, J13, J16, D13

**Keywords:** sisters, girls, girl effect, girl power, Family Care Indicators, early childhood, human capital, household structure, parental investments, natural experiment

> _∗_ Jakiela: Williams College, BREAD, CGD, IZA, and J-PAL, email: pamela.jakiela@williams.edu; Ozier: Williams College and the World Bank Development Research Group, BREAD, IZA, and J-PAL, email: owen.ozier@williams.edu; Fernald: University of California at Berkeley, email: fernald@berkeley.edu; Knauer: University of Michigan, email: heather.knauer@gmail.com. Orazio Attanasio, Maya Eden, Dave Evans, Deon Filmer, Joe Henrich, Amanda Glassman, Matthew Jukes, Vikram Maheshri, John Ototo, Ania Ozier, Justin Sandefur, Dana Schmidt, and Tara Watson provided helpful comments. We are grateful to William Blackmon, Julian Duggan, Laura Kincaide, and Elyse Thulin for excellent research assistance. IRB approval for the larger RCT was provided by the University of California at Berkeley, by the Maseno University Ethics Review Committee, and by Innovations for Poverty Action. This research was funded by Echidna Giving and by the Strategic Impact Evaluation Fund and the Early Learning Partnership at the World Bank. All errors are our own.

The findings, interpretations and conclusions expressed in this paper are entirely those of the authors, and do not necessarily represent the views of the World Bank, its Executive Directors, or the governments of the countries they represent.
# **1 Introduction**

Investments in early childhood are a critical determinant of later life outcomes, and stimulating activities — for example, shared reading and infant-directed speech — are an important way that older family members invest in young children (Knudsen, Heckman, Cameron, and Shonkoff 2006, Grantham-McGregor _et al_ . 2007, Almond and Currie 2011, Walker _et al_ . 2011, Aizer and Cunha 2012). Underinvestment in early childhood is an acute problem in low- and middle-income countries (LMICs), where an estimated 43 percent of children are at risk of failing to meet their developmental potential because of inadequate nutrition and cognitive stimulation (Black _et al_ . 2017). A growing interdisciplinary literature examines the causes and consequences of parental investments in young children in LMICs, seeking to identify interventions that can change parenting practices to improve developmental outcomes in children and increase incomes in adulthood (cf. Gertler _et al_ . 2014, Black _et al_ . 2017, Andrew _et al_ . 2018). However, parents are not the only caregivers in most societies — in many low-income contexts, much of that work is done by older siblings, particularly sisters (Weisner _et al_ . 1977, Lancy 2015). Though this pattern is well-documented in the anthropology literature, older siblings’ role in childrearing is often ignored in academic and policy discussions of investments in early childhood.<sup>1</sup> We model older siblings’ contributions to the human capital accumulation of young chil-

> 1Though older siblings are known to play an important role in caring for young children in LMIC contexts, standard approaches to quantitative measurement frequently ignore both the investments older children make in their younger siblings and the impacts that early childhood interventions (including those that seek to change childrearing practices) might have on sibling caregivers. For example, the standard format of the Family Care Indicators, one of the most widely used measures of early childhood stimulation, does not record stimulating activities carried out by household members under 15 years old (Hamadani _et al_ . 2010, Kariger _et al_ . 2012). Researchers also tend to ignore the potential impacts of parenting interventions on sibling caregivers. For example, a recent systematic review of 466 impact evaluations of early childhood development interventions in LMICs found that only four measured indirect effects on older siblings in middle childhood or adolescence (Evans, Knauer, and Jakiela 2020). This tendency to ignore the caretaking role of older siblings is at least partially attributable to the widespread perception that parental stimulation is more beneficial to young children than stimulation by older children (though it may also entail a higher opportunity cost). In a published response to Weisner _et al_ . (1977), Brian Sutton-Smith argued that “Maximal personal and social development of infants is produced by the mother (or caretaker) who interacts with them in a variety of stimulating and playful ways. Unfortunately the intelligence to do this with ever more exciting contingencies is simply not present in child caretakers,” Weisner _et al_ . (1977, p. 184). Thus, sibling caregiving, though widespread, is often considered a second-best alternative to greater maternal investment — particularly since childcare responsibilities might limit older siblings’ ability to invest in their own human capital through formal schooling.

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dren. Our model extends existing work in economics by incorporating several insights from anthropology and psychology. First, older children do much of the childcare in many LMIC settings, and the quality of their caregiving practices impacts the human capital accumulation of their younger siblings (Weisner _et al_ . 1977, Maynard 2002, Maynard and Tovote 2010, Lancy 2015). Second, households where older siblings are involved in caregiving make active tradeoffs, deciding how much older children should invest in their own human capital and how much they should invest in their younger siblings (Brody 2004, Bock 2010). Third, even when older children are less effective than parents at building younger children’s human capital (Ellis and Rogoff 1982), it may be optimal to delegate some childrearing to older siblings when the opportunity cost of their time is low relative to that of adults (Chick 2010, Lancy and Grove 2010).

We extend a simple model of parental investments in children to consider the direct contributions of older siblings and the tradeoffs that arise when siblings and parents share caregiving responsibilities. Parental investments in both older and younger children entail opportunity costs in foregone domestic production, while older siblings’ investments in their younger siblings come at the expense of their own human capital. At the optimum, these marginal costs are equated with the marginal benefit of greater human capital accumulation in young children. We show that parental investments in the youngest household members cannot be interpreted as measures of parental preferences in such settings. Because parents’ and siblings’ investments are substitutes, having an older child who is an effective caregiver allows parents to increase their labor supply and shift some caregiving responsibilities to older children without compromising young children’s human capital.

In most societies where older children play a substantial caretaking role, older sisters do more childcare than older brothers (Weisner _et al_ . 1977, Hrdy 2009, Lancy 2015). Our model demonstrates that this can occur because older sisters are more effective caregivers than older brothers, or because households perceive a lower return to investing in the human capital of older girls than older boys. In either case, young children with an older sister (rather than an older brother) are likely to benefit, receiving more cognitive stimulation 3
as a result. Having an older sister rather than an older brother can have a causal impact on young children’s development even in settings where older children do not contribute to human capital accumulation in their younger siblings. If older siblings’ investments in young children’s human capital are not productive, any treatment effect of having an older sister must be driven by parental investments: parents would invest more in young children when they have an older girl rather than an older boy because they have less incentive to invest in their older child. In contrast, when older siblings contribute to the development of young children’s human capital, parents with an older girl may actually invest _less_ time in their young children — because they have an effective substitute. Our model illustrates that any treatment effect of older sisters (on child development) that is not explained by differential investments by parents can be attributed to — and provides evidence of — the contributions of older siblings.

To test the empirical predictions of our model, we estimate the impact of older sisters on early childhood development in a sample of rural Kenyan households that have one or two young children aged three to six and exactly one older sibling aged seven to 14.<sup>2</sup> In this sample, we show that the gender of the older sibling is unrelated to household or community characteristics — and hence plausibly exogenous.<sup>3</sup> We find that young children with one older sister experience significantly more cognitive stimulation than those with one older 2 Reviewing ethnographic evidence from 50 traditional societies, Rogoff _et al_ . (1975) report that the typical age at which societies begin assigning older children childcare responsibilities is between five and seven years old. Ominde (1952) reports that in an area near Kisumu, Kenya, the “school-going age for the Luo girl” was the “age to which society has assigned the duty of nursing,” with the girls’ interest in this responsibility peaking at age “eight to nine years.” Capen (1998) records that the term _japidi_ is used for a “girl who cares for a child,” “nurse,” or “nanny.” Nearby, (Weisner _et al_ . 1977) report that (Kenyan) Luhya girls aged 6–8 years old spent 60 percent of their waking hours looking after younger children, though this caretaking was often under the explicit or implicit supervision of nearby adults. Similarly-aged boys (6–8 years old) and younger girls (aged 3–5) spent about half as much time caring for small children. Apoko (1967) and Lijembe (1967) also relate how in neighboring Acholi communities (where the role is called the _lapidi_ ) as well as in Idakho communities, young girls are usually tasked with caring for infants; if there is no appropriately-aged older sister, the task may fall to an older brother.

> 3An extensive literature treats the sex composition of children as a source of exogenous variation (cf. Angrist and Evans 1998, Washington 2008, Glynn and Sen 2015). However, the assumptions required for such estimates to identify causal impacts are unlikely to hold in general (Bisbee, Dehejia, Pop-Eleches and Samii 2017, Clarke 2018). In the United States, Dahl and Moretti (2008) show that having a firstborn daughter increases the likelihood of parental separation. In India, existing evidence suggests that son preference influences birth spacing and total fertility (Clark 2000, Jayachandran and Kuziemko 2011), so households with a firstborn son may not be comparable to households with a firstborn daughter.

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brother. This pattern results from increased stimulation by older sisters, not by parents. Our model suggests that this empirical pattern will arise when both parents and older siblings perceive a gender gap in the return to investing in older children’s human capital, and parents know that stimulating activities with older siblings increase the youngest children’s human capital.

Differential patterns of household investment translate into meaningful impacts on child development. An aggregate index of language and motor development is more than 0.1 standard deviations higher when a young child’s older sibling is a sister and not a brother. In our sample, the magnitude of this difference is commensurate with that between children of mothers who completed primary school and children of those who did not. Impacts on fine motor skill development are concentrated in the bottom half of the distribution, but impacts on language skills are not. Our results suggest that older siblings play an important role in shaping younger children’s human capital in this context, and that optimizing households are well aware of this fact.

Though economic models of investments in children typically focus on parents’ investment decisions, several recent papers have highlighted the important role played by older sisters in LMIC settings. In Turkey, Alsan (2017) shows that a nationwide vaccination campaign targeting young children improved literacy and educational attainment among adolescent girls — who are often forced to stay home tending sick younger siblings. In Mozambique, Martinez, Naudeau, and Pereira (2017) find that the construction of new community-based preschools increased the likelihood that older children had ever attended school, decreased their childcare hours, and increased the amount of time spent on school work. In Pakistan, Qureshi (2018) demonstrates that increasing older girls’ educational attainment has positive impacts on the literacy and numeracy of younger brothers. In Kenya, Ozier (2018) shows that infants and toddlers whose older siblings were exposed to a schoolbased deworming program saw improvements in cognitive development, and that gains were larger among children with more older sisters. In Brazil, Attanasio _et al_ . (2019) find that access to publicly-provided daycare increased employment and income among older sisters 5
(aged 15 and above). These papers highlight the special alloparenting role played by older girls in many LMIC contexts, showing that it has empirical implications for both the girls themselves and their younger siblings.

Our work is related to several broader strands of literature. First, we contribute to the growing body of work on early childhood development in low-income settings (Heckman 2007, Almond and Currie 2011, Black _et al_ . 2017), specifically research analyzing the human capital production function (cf. Cunha, Heckman and Schennach 2010) and recent evaluations of interventions intended to change parenting practices (cf. Chang _et al_ . 2015, Weisleder _et al_ . 2017, Hamadani _et al_ . 2019, Attanasio _et al_ . 2020, Doyle 2020). Second, our work relates to the wider literature on gender norms affecting children in LMIC contexts (cf. Dhar, Jain and Jayachandran 2018), particularly work on factors constraining girls’ education (cf. Kremer, Miguel and Thornton 2009, Baird, McIntosh and Ozler 2011, Jensen 2012)<sup> ̈</sup> and on the differential chore and carework responsibilities of male and female children (cf. Edmonds 2006, Montgomery 2010).<sup>4</sup> Finally, our work builds on literature in demography, economics, political science, and sociology using quasi-experimental variation in the sex composition of children to identify the impact of daughters on parents’ attitudes and behaviors (cf. Dahl and Moretti 2008, Washington 2008, Glynn and Sen 2015).

The rest of this paper is organized as follows. Section 2 presents our model of familial investments in young children and our empirical tests of the model. Section 3 describes our study setting and data set. Section 4 presents our empirical results, and Section 5 concludes.

> 4Beyond the large literature on gender differences in schooling around the world (cf. Psaki, McCarthy and Mensch 2018, Evans, Akmal and Jakiela forthcoming), there is of course a rich literature on gender differences in adult behavior (cf. Pitt, Rosenzweig and Hassan 2012, Alesina, Giuliano and Nunn 2013), but those topics are not the emphasis of the present paper.

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# **2 Conceptual Framework**

## **2.1 A Simple Model of Parental Investment**

We first consider a simple model in which stimulating activities performed by older siblings do not contribute to the human capital accumulation of the youngest family members. In this setting, only parents can intentionally invest in the human capital of young children, and any effect of older siblings is explained by changes in parental investment.

Consider a unitary household comprising a parent, an older (school-aged) child, and a younger (not yet school-aged) child. Parental investments increase child ability, leading to higher incomes (or greater overall welfare) in adulthood. The parent divides their time between household production and investing in their two children. The household utility function is given by subject to the constraint _Lp ≥_ 0 is the amount of time allocated to home production, and _y_ ( _·_ ) is a strictly concave production function satisfying Inada conditions. Let _k ∈{o, y}_ index children within the household, indicating whether a child is the older or younger sibling. _pk_ is the parent’s investment of time in the human capital of child _k_ , and _h_<sup> ̃</sup> _k_ ( _·_ ) is a strictly concave human capital production function satisfying Inada conditions.<sup>5</sup> To model gender gaps, we let for _k ∈{o, y}_ and _z ∈{G, B}_ , where _z_ indicates whether child _k_ is a girl or a boy.<sup>6</sup>

> 5Many models of human capital formation divide childhood into multiple periods (cf. Heckman 2007). We abstract from the intertemporal dynamics of investment in a particular child to focus on the intrahousehold process of building young children’s human capital. An extension to our model would allow for consideration of dynamic effects in setting where older children contribute to the production of younger children’s human capital.

> 6Because _z_ always appears as a superscript on a parameter that is also indexed by a subscript _k_ , we omit the subscript _k_ (on _z_ ) to simplify notation.

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Thus, age-specific human capital production functions are identical up to a parameter characterizing the relative returns by gender (as perceived by the parent).<sup>7</sup> Inada conditions guarantee an interior optimum characterized by the first-order condition: Three results are immediately apparent. First, a younger sibling’s human capital only depends on the gender of the older sibling if there are gender differences in the human capital production function (as perceived by the parent): if _λ_<sup>_G_</sup> _o_ = _λ_<sup>_B_</sup> _o_<sup>and</sup><sup>_λG_</sup> _y_ = _λ_<sup>_B_</sup> _y_<sup>,</sup> parental investments in human capital do not depend on the gender of either child. Second, if parents prefer boys — or, equivalently, if the returns to investments in human capital are systematically lower for girls than for boys at all ages — parents will invest less in girls and more in boys (conditional on child age). So, if _λ_<sup>_G_</sup> _o_<sup>_<λB_</sup> _o_<sup>and</sup><sup>_λG_</sup> _y_<sup>_<λB_</sup> _y_<sup>,parentswillinvest</sup> less in older girls than in older boys, they will invest less in younger girls than in younger boys, and — conditional on the gender of the younger child — they will invest more in young children with an older sister than in young children with an older brother. Finally, if _λ_<sup>_G_</sup> _o_<sup>_<λB_</sup> _o_<sup>and</sup><sup>_λG_</sup> _y_<sup>=</sup><sup>_λB_</sup> _y_<sup>,parentalinvestmentsinbothchildrendependonthegenderof</sup> the older sibling: if the older sibling is a girl, parents will invest less in her and more in her younger sibling — irrespective of the gender of the younger child. Thus, we would expect to see a treatment effect of older sibling gender on the developmental outcomes of young children, and this effect would be driven by differences in parental investments in those children. If the marginal return to investing in older girls is relatively low (i.e. when one assumes that _λ_<sup>_G_</sup> _o_<sup>_<λB_</sup> _o_<sup>and</sup><sup>_λG_</sup> _y_<sup>=</sup><sup>_λB_</sup> _y_<sup>),parentswitholdergirlshavemoretimeavailable</sup> to invest in their younger children. However, because _λ_<sup>_G_</sup> _y_<sup>=</sup><sup>_λB_</sup> _y_<sup>,parentswouldnotinvest</sup>

> 7In this framework, lower objective returns — for example, gender differences in the return to schooling — are equivalent to lower subjective parental valuation of (objective) returns. For example, in a patrilocal society, parents’ private return to educating a daughter may be low because the return is captured by the girl’s husband’s family. Alternatively, parents who simply prefer boys might place more weight on their sons’ future income and wellbeing (relative to their daughters’ future income and wellbeing). The utility weights _λ_<sup>_z_</sup> _k_<sup>reflectbothobjectiveandsubjectivefactorsinfluencingparents’perceptionsofthereturnto</sup> investing in a child’s human capital.

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more in young boys than in young girls (on average, holding the gender of the older sibling constant).

# **2.2 The Contributions of Older Siblings**

We now extend the model to consider the contributions of older children in a framework that characterizes the active tradeoffs made by both parents and older siblings. Again, we consider a unitary household comprising a parent, an older child, and a younger child, but now we allow the actions of the older child to influence both their own human capital accumulation and the human capital of their younger sibling.<sup>8</sup> Familial (rather than parental) investments in children increase child ability, leading to higher adult welfare. The parent divides their time between household production and investing in their two children, and the older child divides their time between schoolwork (i.e. investing in their own human capital) and engaging in stimulating activities with the younger sibling.

The younger child’s human capital depends only on investments by older family members — since preschool-aged children do not make active choices (e.g. how hard to work in school) that increase human capital. The younger child’s human capital production function is given by where _hy_ ( _·_ ) is assumed to be an increasing, concave function that satisfies Inada conditions. _Iy_ = _py_ + _δo_<sup>_zoy_where</sup><sup>_py_istheparent’sinvestmentintheyoungerchild,</sup><sup>_oy_istheolder</sup> sibling’s investment in her younger sibling, and _δo_<sup>_z<_1isaqualityparameterindexingthe</sup> productivity (with respect to human capital production) of investments made by an older sibling of gender _z_ (relative to investments by adults in the household). Later, we will refer to _Iy_ and its component _δo_<sup>_zoy_as</sup><sup>_stimulation_,todistinguishthemfromtheunderlying</sup> _investment_ , _oy_ . Thus, parents and older siblings are assumed to be perfect substitutes in

> 8Because we consider a unitary household, there is no distinction between an older child who makes a tradeoff and a parent who dictates a tradeoff to an older child. In our model, parents and older children have the same preferences, so agency is irrelevant. In Section 2.3, we consider the consequences of relaxing this assumption by allowing parents and older children to have divergent preferences.

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the production of younger children’s human capital — though parents may have an absolute advantage.<sup>9</sup> Older children invest in their own human capital by exerting effort in school, and they also benefit from investments (in them) made by the adults in their household. The older sibling’s human capital production function is given by where _Eo_ is the child’s level of investment in their own human capital (e.g. in schoolwork) and _po_ is the parent’s investment in the older child. Thus, _ho_ ( _Eo, po_ ) is assumed to be additively separable in child and adult investments in human capital.<sup>10</sup> Both _ho→o_ ( _Eo_ ) and _hp→o_ ( _po_ ) are increasing and concave functions satisfying Inada conditions.

The parent divides one unit of time between household production and stimulating her children (as in Section 2.1). Household utility is given by: where and We assume a unitary household at this point in our exposition, deferring relaxation of this

> 9When _δoG_ and _δo_<sup>_B_</sup> are sufficiently small, investments made by the older sibling do not improve the younger siblings’ human capital, and the model reduces to the version considered in Section 2.1 — as we discuss further below.

> 10Cases where child effort and parental investment are complements have an intuitive appeal — for example, if parents assist school-aged children with their homework. However, such complementarities allow for the possibility of multiple equilibria. For this reason, we focus our analysis on the determinants of investments in younger children and simplify the rest of the environment as much as possible.

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assumption until Section 2.3. If an interior solution ( _p_<sup>_∗_</sup> _o_<sup>_, p∗_</sup> _y_<sup>_, o∗_</sup> _y_<sup>) exists, the following are true</sup> at the optimum: first, households equate the marginal product of parental labor with the marginal product of additional parental time invested in each child by setting and second, households equate the marginal product of older children’s investments in their own human capital with the marginal product of their investments in younger siblings by setting Two corner solutions are also possible: at the optimum, either _o_<sup>_∗_</sup> _y_<sup>or</sup><sup>_p∗_</sup> _y_<sup>(butnotboth)</sup> might be equal to 0. If older children are sufficiently proficient at stimulating their younger siblings, parents may delegate this task to them by setting _p_<sup>_∗_</sup> _y_<sup>=0.Ontheotherhand,</sup> when older children’s investments in their younger siblings are sufficiently unproductive, (i.e. when _δo_<sup>_G_and</sup><sup>_δ_</sup> _o_<sup>_B_aresufficientlysmall),oldersiblingswilldevotealltheirtimeto</sup> building their own human capital by setting _o_<sup>_∗_</sup> _y_<sup>to0and</sup><sup>_Eo_to1.</sup> For the rest of this exposition, we focus on the interior solution.<sup>11</sup> When _δo_<sup>_G_</sup> = _δo_<sup>_B_</sup> = 0, the model reduces to simple case described in Section 2.1.<sup>12</sup> Reviewing those predictions: if human capital production functions do not differ by gender (i.e. if _λ_<sup>_G_</sup> _k_<sup>=</sup><sup>_λB_</sup> _k_<sup>for</sup><sup>_k∈{o, y}_),wewouldnotexpectgendergapsinparentalinvestment</sup> or treatment effects of older sibling gender; when parents favor boys over girls (i.e. when _λ_<sup>_G_</sup> _y_<sup>_< λB_</sup> _y_<sup>and</sup><sup>_λG_</sup> _o_<sup>_< λB_</sup> _o_<sup>), they invest more in boys than girls at all ages, and they also invest</sup> more in the younger siblings of older girls; finally, when _λ_<sup>_G_</sup> _y_<sup>=</sup><sup>_λB_</sup> _y_<sup>and</sup><sup>_λG_</sup> _o_<sup>_< λB_</sup> _o_<sup>,parentsdo</sup> not invest more in younger boys than in younger girls on average, but they invest more in the younger siblings of older girls — because they perceive a low return to spending time

> 11Beyond the interior solution that is our emphasis here, one might note that a sufficient (but not necessary) condition under which this latter corner solution occurs is when _δo_<sup>_z_=0.Onewaytoguaranteethat</sup> the corner solution is inapplicable is to assume that _h_<sup>_′_</sup> _o→o_<sup>(</sup><sup>_E_</sup> _o_<sup>)</sup><sup>_→_0as</sup><sup>_E_</sup> _o_<sup>_→_1.Relaxingthisassumption</sup> does not change our analysis substantively, so we entertain the corner solutions no further here.

> 12Specifically, Equation 4 is the special case of Equation 11 that occurs when _δoG_<sup>=</sup><sup>_δ_</sup> _o_<sup>_B_= 0.</sup>

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building the human capital of school-aged girls; thus, in summary, there is a treatment effect of older siblings that is mediated by parental investments.

# **2.2.1 Gender Differences in Productivity**

We now characterize behavior when older children can improve their younger siblings’ human capital by engaging in stimulating activities with them. In our framework, there are two reasons older girls might stimulate their younger siblings more than older boys. First, girls might be better at producing younger siblings’ human capital with a given level of (time) investment ( _δo_<sup>_G> δ_</sup> _o_<sup>_B_).Alternatively,olderboysandgirlsmightbeequallygoodat</sup> caring for younger siblings, but the return to human capital might be lower for (older) girls than for (older) boys ( _λ_<sup>_G_</sup> _k_<sup>_< λB_</sup> _k_<sup>).13We have already considered the implications of the latter</sup> possibility, letting _λ_<sup>_G_</sup> _k_<sup>_< λB_</sup> _k_<sup>, in the special case when</sup><sup>_δ_</sup> _o_<sup>_G_and</sup><sup>_δ_</sup> _o_<sup>_B_are both equal to 0.We now</sup> consider the first of these possibilities: the consequences of gender differences in _δo_<sup>_z_, the rela-</sup> tive productivity of older siblings’ investments in young children’s human capital (compared to the parents’ investments), when human capital production functions do not differ by gender. Specifically, let _δo_<sup>_G> δ_</sup> _o_<sup>_B_,</sup><sup>_λG_</sup> _o_<sup>=</sup><sup>_λB_</sup> _o_<sup>=</sup><sup>_λ_ ̄</sup><sup>_o_,and</sup><sup>_λG_</sup> _y_<sup>=</sup><sup>_λB_</sup> _y_<sup>=</sup><sup>_λ_ ̄</sup><sup>_y_.Let</sup><sup>_p∗_</sup> _o_<sup>(</sup><sup>_δ_</sup> _o_<sup>_z,_ ̄</sup><sup>_λo,_ ̄</sup><sup>_λy_)denote</sup> the optimal level of parental investment in an older child of gender _z_ (given our assumptions about _δo_<sup>_z_and</sup><sup>_λz_</sup> _k_<sup>).Define</sup><sup>_p∗_</sup> _y_<sup>(</sup><sup>_δ_</sup> _o_<sup>_z,_ ̄</sup><sup>_λo,_ ̄</sup><sup>_λy_)</sup><sup>_, o∗_</sup> _y_<sup>(</sup><sup>_δ_</sup> _o_<sup>_z,_ ̄</sup><sup>_λo,_ ̄</sup><sup>_λy_)</sup><sup>_, L∗_</sup> _p_<sup>(</sup><sup>_δ_</sup> _o_<sup>_z,_ ̄</sup><sup>_λo,_ ̄</sup><sup>_λy_)</sup><sup>_, E_</sup> _o_<sup>_∗_(</sup><sup>_δ_</sup> _o_<sup>_z,_ ̄</sup><sup>_λo,_ ̄</sup><sup>_λy_), and</sup> _Iy_<sup>_∗_(</sup><sup>_δ_</sup> _o_<sup>_z,_ ̄</sup><sup>_λo,_ ̄</sup><sup>_λy_)analogouslyfor</sup><sup>_z∈{G, B}_.14</sup> In Proposition 1, we show that when older sisters are more productive than older brothers (when it comes to improving younger siblings’ human capital), children with older sisters

> 13It is apparent that one could extend the model to introduce other reasons that girls might spend more time stimulating younger siblings. In a model of occupational specialization, girls who expect to specialize in home production might see a high return to the development of home-specific human capital (such as child-rearing skills). Alternatively, one could introduce social norms that make it costly for boys or girls to engage in behaviors commonly associated with the opposite gender (see the model presented in Jakiela and Ozier (2019) for a simple example). Many of these theoretical extensions yield predictions that are identical to those derived here. Indeed, the _δo_<sup>_z_parametercapturessomeofthesesocialnormeffectsinasimplified</sup> way if we interpret as a measure of the amount of stimulation (for example, singing or storytelling) an older sibling engages in per unit of time spent caring for a younger sibling. If stimulating activities are perceived as feminine because they are often done by mothers, older brothers may be less likely to engage in such socially costly behaviors.

> 14An equilibrium is fully characterized by _p∗y_<sup>,</sup><sup>_p∗_</sup> _o_<sup>,and</sup><sup>_o∗_</sup> _y_<sup>.Theoptimal</sup><sup>_L∗_</sup> _p_<sup>,</sup><sup>_E_</sup> _o_<sup>_∗_,and</sup><sup>_I_</sup> _y_<sup>_∗_arethendefined</sup> by Equations 11 and 12.

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receive more stimulation overall. However, parents with an older daughter substitute away from investing their time in early childhood stimulation because their older child is a good substitute, investing more in the older child’s human capital and increasing their own their own labor supply in consequence. Impacts on older siblings’ time allocation are ambiguous and depend on the functional forms of the production functions, but the overall quantity of stimulation by older siblings ( _δo_<sup>_zo∗_</sup> _y_<sup>)ishigherwhentheoldersiblingisfemale.</sup>

**Proposition 1.** _Let δo_<sup>_G>δ_</sup> _o_<sup>_B>_0</sup><sup>_,andfurtherassumeδ_</sup> _o_<sup>_Bissufficientlyfarabovezeroto_</sup> _guarantee that o_<sup>_∗_</sup> _y_<sup>(</sup><sup>_δ_</sup> _o_<sup>_B, λB_</sup> _o_<sup>_, λz_</sup> _y_<sup>)</sup><sup>_>_0</sup><sup>_and o∗_</sup> _y_<sup>(</sup><sup>_δ_</sup> _o_<sup>_B, λB_</sup> _o_<sup>_, λz_</sup> _y_<sup>)</sup><sup>_>_0</sup><sup>_.Let λG_</sup> _o_<sup>=</sup><sup>_λB_</sup> _o_<sup>=</sup><sup>_λ_ ̄</sup><sup>_oλG_</sup> _y_<sup>=</sup><sup>_λB_</sup> _y_<sup>=</sup><sup>_λ_ ̄</sup><sup>_y._</sup> _The following are true:_

# _Proof._ See Appendix.

When girls are more productive caregivers than boys, young children benefit from having an older sister: they receive more stimulation from their older sibling and more stimulation overall. Parents also benefit because older girls provide more effective support at home. As a result, gender differences in older children’s effectiveness as caregivers translate into empirical predictions about both younger siblings’ development and parents’ responses.<sup>15</sup> Optimizing parents delegate more early childhood stimulation to more competent sibling caregivers, substituting toward other activities that cannot be done by their older children. Thus, if older girls are more effective caregivers than older boys, parents will appear to favor

> 15We consider the case of gender differences, but the proof is equally valid if other observable factors (e.g. older sibling age) generate systematic differences in _δo_<sup>_z_.</sup>

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older girls by investing more in their human capital — but this appearance is deceptive because it results from gender differences in children’s productivity rather than parents’ preferences. This highlights the importance of explicitly modeling the human capital production function within the household, and accounting for the role that older children play in shaping younger children’s human capital.

# **2.2.2 Gender Differences in the Returns to Human Capital**

Thus far, we have seen that a treatment effect of having an older sister could be explained by two different mechanisms: either a gender gap in the return to human capital investment among older children when older siblings do not contribute to building younger children’s human capital, or a gender gap in productivity where older sisters are better than older brothers at improving their younger siblings’ human capital. We have considered each mechanism in isolation, and seen that the models make divergent predictions about parental investments in young children. Here, we characterize household behavior when the returns to human capital investments in school-aged children differ by gender _and_ older siblings contribute to the development of human capital in young children by engaging in stimulating activities with them.

In Proposition 2, we show that when returns to human capital are lower for girls than for boys and older boys and girls are equally efficient at improving younger children’s human capital, children with older sisters receive more stimulation overall. When returns to older siblings’ human capital differ by gender, parents invest less in older sisters (relative to older brothers). However, when older children contribute to human capital accumulation in their younger siblings in this context, older sisters also invest less in their own human capital and more in the human capital of their younger siblings — breaking the link between the gender gap in the returns to investing in older children’s human capital and parental investments in younger children.

Let _δo_<sup>_G_=</sup><sup>_δ_</sup> _o_<sup>_B_=</sup><sup>_δ_ ̄</sup><sup>_o>_0,</sup><sup>_λG_</sup> _y_<sup>=</sup><sup>_λB_</sup> _y_<sup>=</sup><sup>_λ_ ̄</sup><sup>_y_,and</sup><sup>_λG_</sup> _o_<sup>_< λB_</sup> _o_<sup>.Paralleling our analysis in Section</sup> 2.2.1, we let _p_<sup>_∗_</sup> _o_<sup>( ̄</sup><sup>_δo, λG_</sup> _o_<sup>_,_ ̄</sup><sup>_λy_) denote the optimal level of parental investment in an older girl un-</sup> 14
der these assumptions, and we define _p_<sup>_∗_</sup> _y_<sup>( ̄</sup><sup>_δo, λ_</sup> _o_<sup>_z,_ ̄</sup><sup>_λy_)</sup><sup>_, o∗_</sup> _y_<sup>( ̄</sup><sup>_δo, λ_</sup> _o_<sup>_z,_ ̄</sup><sup>_λy_)</sup><sup>_, L∗_</sup> _p_<sup>( ̄</sup><sup>_δo, λ_</sup> _o_<sup>_z,_ ̄</sup><sup>_λy_)</sup><sup>_, E_</sup> _o_<sup>_∗_( ̄</sup><sup>_δo, λz_</sup> _o_<sup>_,_ ̄</sup><sup>_λy_),</sup> and _Iy_<sup>_∗_( ̄</sup><sup>_δo, λ_</sup> _o_<sup>_z,_ ̄</sup><sup>_λy_)analogouslyfor</sup><sup>_z∈{G, B}_.</sup>

**Proposition 2.** _Let λ_<sup>_G_</sup> _o_<sup>_<λB_</sup> _o_<sup>_,andletλG_</sup> _y_<sup>=</sup><sup>_λB_</sup> _y_<sup>_andδ_</sup> _y_<sup>_G_=</sup><sup>_δ_</sup> _y_<sup>_B>_0</sup><sup>_,andassumeδ_ ̄</sup><sup>_ois_</sup> _sufficiently far above zero to guarantee that o_<sup>_∗_</sup> _y_<sup>( ̄</sup><sup>_δo, λ_</sup> _o_<sup>_G, λz_</sup> _y_<sup>)</sup><sup>_>_0</sup><sup>_ando∗_</sup> _y_<sup>( ̄</sup><sup>_δo, λ_</sup> _o_<sup>_B, λz_</sup> _y_<sup>)</sup><sup>_>_0</sup><sup>_.The_</sup> _following are true:_

# _Proof._ See Appendix.

Proposition 2 highlights the importance of older siblings’ investments in young children — even when the treatment effect of older sisters is driven by gender differences in the return to education as opposed to productivity. As discussed in Section 2.1, when _δo_<sup>_G_=</sup><sup>_δ_</sup> _o_<sup>_B_=0,</sup> parents respond to gender gaps in the return to parental investment in older children by investing more in their younger children. Incorporating the tradeoffs made by older siblings into the model changes this prediction because older girls also invest less in themselves — and more in their younger siblings — than older boys.

We have considered the _δo_<sup>_G_=</sup><sup>_δ_</sup> _o_<sup>_B>_0case,butresultsaresimilarwhen</sup><sup>_δ_</sup> _o_<sup>_G_and</sup><sup>_δ_</sup> _o_<sup>_B_are</sup> not exactly equal. If older girls are substantially more effective caregivers than older boys (i.e. if _δo_<sup>_G_issubstantiallylargerthan</sup><sup>_δ_</sup> _o_<sup>_B_),thegendergapinsiblingproductivitywillbe</sup> more important than the gender gap in the return to schooling, so parents of older girls 15
will invest less in their young children than parents of older boys. The opposite is true if older boys are substantially more effective sibling caregivers than older girls. In both cases, any gender gap in the returns to investing in older children’s human capital may offset the effect of the gender gap in productivity. The key insight is that when households trade off older siblings’ investments in their own human capital with their investments in the human capital of their younger siblings, the effect of older sibling gender on parental investments in younger siblings is ambiguous because older sisters facing a lower return to investing in their own human capital invest more in the human capital of their siblings.

# **2.3 Extensions to the Model**

In much of our analysis, we have assumed that parents are not inherently prejudiced against girls. If gender differences were driven by parental bias, we would expect parents to invest less in older girls than in older boys, and we would also expect them to invest less in younger girls than in younger boys. In our framework, _λ_<sup>_G_</sup> _y_<sup>_<λB_</sup> _y_<sup>impliesaloweroptimallevelof</sup> familial investment in young girls than in young boys — a prediction that is testable in our data.

We have also assumed a unitary household that can be represented by a single utility function. However, if parents perceive a low return to investing in the human capital of older girls (relative to older boys) but older girls do not, the unitary household assumption may be inappropriate. If older girls perceive a higher return to investing in their own human capital than their parents do, this will tend to shift older girls toward investing more in their own human capital relative to the parental optimum; parents will partially offset this by investing more in the younger siblings of an older girl than they would under the unitary model — though the overall treatment effect of older sibling gender on parental investments in young children remains ambiguous. Importantly, this channel can only matter when older siblings contribute to the human capital of the young children. If they did not, older siblings would invest all their time in building their own human capital irrespective of the gender gap in the returns to schooling.

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# **2.4 Summary of Predictions**

Table 1 summarizes the theoretical predictions that we will test empirically.<sup>16</sup> As discussed below, our data set includes information on the amount of early childhood stimulation done by parents, by older siblings, and by other individuals. The model summarizes predictions about three outcomes: _p_<sup>_∗_</sup> _y_<sup>,theamountofparentalstimulationofyoungchildren,</sup><sup>_δ_</sup> _o_<sup>_zo∗_</sup> _y_<sup>;</sup> the amount of stimulation done by the older sibling; and _Iy_<sup>_∗_,thetotalamountofearly</sup> childhood stimulation experienced by the youngest family members. When either _δo_<sup>_G> δ_</sup> _o_<sup>_B_</sup> or _λ_<sup>_G_</sup> _o_<sup>_<λB_</sup> _o_<sup>,youngchildrenwithanoldersisterwillreceivemorestimulationthanyoung</sup> children with an older brother. Where this increase in overall stimulation comes from provides information about the underlying parameter values. When _δo_<sup>_G_=</sup><sup>_δ_</sup> _o_<sup>_B_=0,older</sup> siblings’ investments are not productive, so they do not invest time in stimulating their younger siblings. Hence, any overall impact of an older sister is mediated by parental investments. On the other hand, when _δo_<sup>_G> δ_</sup> _o_<sup>_B>_0and</sup><sup>_λG_</sup> _o_<sup>=</sup><sup>_λB_</sup> _o_<sup>,thetreatmenteffectof</sup> an older sister results from the fact that older sisters are more productive caregivers, and they do more stimulation of their younger siblings than older brothers. Parents respond to this by investing less in their younger children and more in their older children. Finally, when _λ_<sup>_G_</sup> _o_<sup>_<λB_</sup> _o_<sup>and</sup><sup>_δ_</sup> _o_<sup>_G≥δ_</sup> _o_<sup>_B>_0,bothmechansimsareatplay.Youngchildrenreceive</sup> more stimulation from older sisters than older brothers. Because of this, parents may invest either more or less in their younger children. The fact that _λ_<sup>_G_</sup> _o_<sup>_<λB_</sup> _o_<sup>pushesthemtoward</sup> investing less in their older daughters and more in their younger children. However, older daughters also invest less in themselves and more in their younger siblings, lowering the marginal return to parental investments in young children. Thus, the overall impact on parental investments in young children cannot be signed when both mechanisms are at work.<sup>17</sup>

> 16The full set if theoretical predictions is presented in Table A1.

> 17This is true for any values of _λGo_<sup>and</sup><sup>_λB_</sup> _o_<sup>suchthat</sup><sup>_λG_</sup> _o_<sup>_≥λB_</sup> _o_<sup>_>_0.</sup>

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# **3 Data**

Our sample includes data on 699 young children in 552 households from 73 rural communities in western Kenya. Data were collected during the baseline survey that preceded a pre-literacy intervention (Jakiela, Ozier, Fernald and Knauer 2020). Households living within 750 meters of the local government primary school were included in the sample if they had children between three and six years old. Here, we restrict attention to those households which also had exactly one older child between the ages of seven and 14. Our treatment of interest is an indicator for having an older child who is female. In this restricted sample of households, having an older child who is female is uncorrelated with a range of covariates, as we discuss further below.

Our data set includes information on household and parental characteristics (e.g. household assets and mother’s education) as well as multiple measures of child development and familial investments in young children. We consider two main developmental outcomes that can be measured in preschool-aged children: vocabulary and fine motor skills. Both are measured through direct child assessment.

Our vocabulary index combines includes three sub-scales: expressive vocabulary and receptive vocabulary in English (one of Kenya’s national language and the primary language of instruction at upper levels of primary school) and Luo (a Nilotic language that is the mother tongue of all of the children in our sample). Receptive vocabulary is the ability to understand words, while expressive vocabulary is the ability to produce words — for example, to identify familiar objects. Children begin developing receptive vocabulary before they begin to express themselves through speech (Fernald, Prado, Kariger and Raikes 2017). To measure receptive vocabulary in English and Luo, we adapted items from the British Picture Vocabulary Scale, a version of the Peabody Picture Vocabulary Test suitable for speakers of British or Commonwealth English (Dunn and Dunn 1997; Dunn, Dunn and Styles 2009; Knauer et al. 2019b). We assessed expressive vocabulary through a 37-item assessment developed and validated as part of an ongoing evaluation of an early literacy 18
intervention (Knauer, Kariger, Jakiela, Ozier and Fernald 2019b).

We assessed children’s fine motor skills using a subset of items from the Malawi Developmental Assessment Test (Gladstone et al. 2010). Specifically, the survey included six questions from the MDAT fine motor sub-scale that showed high predictive power (in terms of other development outcomes) in a pilot study (Knauer et al. 2019a). The items measure young children’s ability to build simple structures (e.g. a tower) with blocks and to use a pencil to make elementary drawings (e.g. a circle). Both vocabulary and fine motor indices were converted into age-normalized z-scores. We then average the individual (z-score) components to construct an overall measure of child development.

To understand the mechanisms through which sibling gender impacts child development, we collected data on early childhood stimulation using an expanded version of the Family Care Indicators (FCI) questionnaire (Hamadani et al. 2010, Kariger et al. 2012). The FCI asks about six types of stimulating activities: for example, reading, singing, storytelling, and physical play. We expanded this set to include additional stimulating activities more appropriate for slightly older children: for instance, teaching a child letters or English words (Knauer et al. 2019a). Based on extensive piloting, we also expanded the questionnaire to better capture the full range of family members who engage in early childhood stimulation. While the original instrument asks about stimulation by a child’s mother, father, and by other adults aged 15 and over, we also ask about stimulating activities by older sisters, older brothers, and grandparents. Summary statistics on who engages in early childhood stimulation are shown in Appendix Figure A1. On average, older sisters engage in more stimulating activities with young children than any other household members. Though older sisters do the most, even older brothers play an important role: older brothers do more than fathers or grandparents.

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# **4 Analysis**

## **4.1 Empirical Strategy**

To estimate the impact of big sisters on child development, we assume that child gender is plausibly exogenous.<sup>18</sup> We estimate the regression equation: where _Sisteri_ is an indicator equal to one if the older sibling in household _i_ is female. Parents cannot control the sex of any given child, and households in our study area have little access to sex-selection technologies — so gender is not explicitly endogenous. Nevertheless, our estimates of the treatment effect of older sisters will be biased if _Sisteri_ is correlated with any (observed or unobserved) covariates that also predict outcomes. For example, if adolescent girls were more likely to live at home in wealthier households, _β_<sup>ˆ</sup> would not capture the causal impact of having an older sister on child development. We test for this by comparing the observable characteristics of households with and without an older sister.

Summary statistics comparing households with an older sister to households with an older brother are presented in Table 2. Households are broadly similar in terms of family structure, parental characteristics, and living conditions; and younger children are similar in terms of gender, age, and school enrollment. Older sisters and older brothers are also similar in age, suggesting comparable patterns of fertility and birth spacing in the two types of households. Since families with older sisters and older brothers look similar in terms of observable characteristics, we treat the gender of the older child as plausibly exogenous in our subsequent analysis.<sup>19</sup>

> 18See Washington (2008) for a similar estimation approach.

> 19Our sample is also demographically similar to families sampled in the 2014 Kenya Demographic and Health Survey (DHS) (Kenya National Bureau of Statistics 2015). For example, in the DHS, among women age 15-49 in the former Nyanza province who had given birth at least once, the average number of years of schooling was 7.8, the average age was 31.7 years, and 82.6 percent had a latrine or toilet (author’s calculations); this is similar to the present sample, in which, on average, mothers have 7.9 years of schooling, are 30.5 years old, and have a latrine or toilet 79.3 percent of the time.

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# **4.2 The Impact of Big Sisters on Child Development**

Kernel density estimates of our early childhood development index are presented in Figure 1. Negative z-scores are more common among young children with older brothers, and z-scores are more concentrated about zero among children with older sisters. The density functions are quite similar for z-scores above one. Thus, the graphical evidence suggests that poor early childhood development outcomes are less common in families with an older child who is female.

Regression estimates of the impact of older sisters on younger siblings’ development are reported in Table 3. Having an older sister rather than an older brother has a statistically significant effect on younger siblings. Estimates of Equation 13 suggest that young children with an older sister score 0.129 standard deviations higher on our aggregate measure of early childhood development (p-value 0.035). In specifications that include controls for child gender, age (fixed effects for child age in months), mother’s education, and an index of household assets, the estimated impact of big sisters rises to 0.141 (p-value 0.023). The magnitude of the coefficients suggests that the treatment effect of having a big sister is developmentally meaningful. For comparison, the estimated effect is roughly equivalent to the difference in development between children whose mothers completed primary school and those whose mothers had less than eight years of education.<sup>20</sup> Quantile regressions of the early childhood development index on the indicator for having an older sister rather than an older brother are summarized in Panel A of Figure 2. We estimate one regression for every quantile between 0 _._ 05 and 0 _._ 95. The pattern suggests that impacts are largest at the bottom of the distribution. For the lowest quantiles, the estimated treatment effects are large but imprecisely estimated. For quantiles between about 0.2 and 0.5, estimated treatment effects are positive and confidence intervals typically exclude zero. Above the median, estimated treatment effects are closer to zero and never statistically significant. Thus, results from quantile regressions formalize the evidence from

> 20In OLS specifications including controls for child gender, age (fixed effects for child age in months), and an index of household wealth, the coefficient on the indicator for completing primary school is 0.135 (p-value 0.030).

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the kernel density estimates: the treatment effects of older sisters appear to be concentrated on the bottom half of the distribution.

In Panel B of Table 3, we decompose the underlying elements of the early childhood development index, estimating the treatment effect of big sisters on young children’s vocabulary and fine motor skills. Results show that having an older sister leads to improvements in both outcomes. In specifications including controls (child gender, child age, mother’s education, and an index of household assets), having an older sister as opposed to an older brother is associated with a 0.130 standard deviation increase in vocabulary (p-value 0.042) and a 0.151 standard deviation increase in fine motor skills (p-value 0.063).

In Panels B and C of Figure 2, we present quantile regressions of the impact of older sisters on vocabulary and fine motor skills. In both cases, the largest point estimates occur near the bottom of the distribution. However, impacts on the quantiles of fine motor skills are precise zeros in the top half of the distribution, while estimated impacts on quantiles below the median are substantially larger and often statistically significant. Thus, having an older sister appears to improve fine motor skills, but only below the median. In contrast, estimated impacts on vocabulary skills are consistently small and positive, though they are rarely statistically significant above the 20<sup>th</sup> percentile.

# **4.3 The Impact of Big Sisters on Investments in Young Children**

As discussed in Section 2, there are several different reasons that younger siblings might benefit from having an older sister. One possibility is that older sisters are more effective than older brothers at improving younger siblings’ human capital. Alternatively, older girls and their parents might believe that the returns to investing in their human capital are relatively low (as compared with similarly aged boys). If older siblings’ investments in young children are not productive, parents who invest less in their older girls will invest more in their youngest children. On the other hand, if older children contribute to the human capital accumulation of their younger siblings, older girls will invest less in themselves and more in their younger siblings — and the impact of older sibling gender on parental 22
investment will be ambiguous.

We test the predictions of the model using data on early childhood stimulation — both the overall amount of stimulation received by each young child, and the amount of stimulation done by different family members (e.g. the mother, the father, the older siblings, etc.). Estimates of the impact of having an older daughter on the overall level of early childhood stimulation are reported in Panel C of Table 3. We find large and statistically significant impacts of older sisters on the level of early childhood stimulation a child experiences. Having an older sister increases the number of different stimulating activities (out of 12) over the three days prior to the survey by between 0.637 (without controls, p-value 0.006) and 0.703 (with controls, p-value 0.002). Among households where the older child is male, the mean number of stimulating activities if 5.147; hence, the estimated treatment effect of having an older sister represents more than a ten percentage point increase in early childhood stimulation. From a theoretical perspective, this suggests that we can rule out the possibility that both _δo_<sup>_G_=</sup><sup>_δ_</sup> _o_<sup>_B_and</sup><sup>_λG_</sup> _o_<sup>=</sup><sup>_λB_</sup> _o_<sup>—sinceweobservea</sup> clear treatment effect of older sibling gender on early childhood stimulation.

Next, we test whether parents are the main channel of impact. In Figure 3, we summarize the estimated treatment effect of having an older sister on 10 different outcome variables. First, we present the treatment effect on the overall level of early childhood stimulation (replicating the specification in Panel C of Table 3 that was discussed above). Then, we present treatment effects on the amount of early childhood stimulation done by parents and the amount done by siblings. Finally, we present treatment effects on the amount of early childhood stimulation done mothers, by fathers, by sisters, by brothers, by grandmothers, by grandfathers, and by other individuals. Having an older sister does not impact the amount of stimulation young children receive from their parents, nor does it impact the amount received from the mother or father specifically, from either grandparent, or from others. All estimated coefficients are relatively precise zeros. Instead, having an older sister leads to a significant increase in the amount of stimulation received from siblings. Having an older sister increases the amount of stimulation done by sisters and 23
decreases the amount done by brothers, but the positive impact on stimulation by sisters is larger — leading to a positive impact on the overall level of sibling stimulation.<sup>21</sup> Seen through the lens of our theoretical model, this pattern of empirical results suggests two things. First, older siblings contribute to the human capital accumulation of their young siblings, and households know it. If this were not the case, we would expect a treatment effect of older siblings on parental investments in young children. Second, both parents and older siblings perceive lower returns to investments in older girls’ human capital relative to older boys. If this were not the case — and the treatment effect of older sisters was driven entirely by gender differences in the productivity of human capital investments by sisters vs. brothers — we would expect a negative treatment effect of older sisters on stimulation (of young children) by parents. We do not observe this, suggesting that part of the effect is attributable to gender gaps in the returns to human capital investments among older children, which lead older sisters to invest less in themselves and more in their young siblings while discouraging parents from ramping up their investments in older girls.

# **5 Conclusion**

Older sisters have a positive and significant impact on their younger siblings’ development. Our results are not consistent with a model in which parents of older sisters invest more in young children only because of a relaxed budget constraint associated with lower perceived labor market returns to investment in the older sister. Instead, our results suggest that older siblings and parents _both_ contribute to the development of young children’s human capital, and that households know the productive value of these contributions. Importantly, the empirical patterns we observe can only arise if households perceive a lower return to human capital investments in older girls, relative to older boys. Older sisters invest less in their own human capital than older brothers, and they invest more in their younger siblings. This changes the marginal utility of parental investments, so parents of older girls may or

> 21 Since our measure also captures stimulation by adult siblings, the level of stimulation by older sisters is not zero in households where the older child is male.

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may not invest more in their youngest progeny than parents of older boys.

Our results highlight the critical importance of older children (both sisters and brothers) in child rearing in developing country contexts. In our sample, siblings do more cognitive stimulation than any other household member — but their role is typically ignored in models of household investments in children and policy discussions about early childhood. Our results suggest that evaluations of early childhood interventions are unlikely to fully capture effects on households if they do not take account of older siblings, and the critical role that they play in childrearing in many LMIC contexts. In addition, evaluations targeting older children should explicitly consider impacts on younger siblings in critical stages of child development. Our findings are consistent with recent evidence from Pakistan showing that educating girls has positive spillover effects on younger siblings (Qureshi 2018), and with evidence from Mozambique and Turkey demonstrating that early childhood interventions that improve child health or increase preschool availability can have positive spillover effects on older children’s educational outcomes (Alsan 2017, Martinez, Naudeau and Pereira 2017). Siblings, particularly sisters, play an important role in shaping the developmental trajectories of young children in many developing country contexts, and researchers seeking to understand households’ investments in young children or the constraints on older girls’ educational attainment cannot fully capture these dynamics while ignoring the special role that older children play in caring for their younger siblings.

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