Sibling Spillovers: Having an Academically Successful Older Sibling May be More Important for Children in Disadvantaged Families

Abstract

This paper examines causal sibling spillover effects among students from different family backgrounds in elementary and middle school. Family backgrounds are captured by race, household structure, mothers’ educational attainment, and school poverty. Exploiting discontinuities in school starting age created by North Carolina school-entry laws, we adopt a quasi-experimental approach and compare test scores of public school students whose older siblings were born shortly before and after the school-entry cutoff date. We find that individuals whose older siblings were born shortly after the school-entry cutoff date have significantly higher test scores in middle school, and that this positive spillover effect is particularly strong in disadvantaged families. We estimate that the spillover effect accounts for approximately one third of observed statistical associations in test scores between siblings, and the magnitude is much larger for disadvantaged families. Our results suggest that spillover effects from older to younger siblings may lead to greater divergence in academic outcomes and economic inequality between families.

1. Introduction

Social scientists have long been concerned about economic inequality. While contexts such as neighborhoods and schools are important, family is the major channel through which economic inequality patterns are shaped (Duncan, Boisjoly, and Harris 2001). Existing scholarship on how family shapes inequality has focused on correlations between older and younger generations within the same household, namely intergenerational transmission and mobility (Blau and Duncan 1967; Bloome 2014; Mare 2011; Sharkey 2008; Solon 1992; Song 2016; Warren and Hauser 1997), and how much couples have in common, namely assortative mating (Mare 1991; Kalmijn 1991; Schwartz and Mare 2005; Eika, Mogstad, and Zafar 2019; Breen and Salazar 2011). In the late 2010s, approximately 60% of households with children in the United States have more than one child. Strong sibling correlations in long-term cognitive ability and economic outcomes have been documented, and these correlations account for as much as half of economic inequality in the U.S. (Mazumder 2008; Hauser and Mossel 1985; Hauser and Sewell 1986). The social process behind sibling correlations could be a key understudied pathway for both inter- and intra-generational transmission of (dis)advantages. Conventional wisdom assumes that sibling correlations mainly reflect similarities in biological endowment and shared family and school environmental characteristics. But an emerging literature provides evidence that inter-sibling influences (i.e., sibling spillovers) exist for a range of human capital outcomes (Joensen and Nielsen 2018; Qureshi 2018; Karbownik and Ozek 2021; Black et al. 2021; Breining et al. 2021; Fletcher, Hair, and Wolfe 2012).

Despite these latest studies, when siblings influence each other and which siblings influence each other most are still unclear (Conley and Glauber 2005). Two questions in particular are relatively unexplored: does inter-sibling influence vary by children’s school levels? Conditional on school levels, is sibling influence stronger or weaker in advantaged families or in disadvantaged families? The answers to these questions have important theoretical implications. The first question brings a life course perspective into our understanding of how siblings influence each other at different developmental stages in childhood. The second question can help us understand whether and to what extent having siblings can mitigate or exacerbate disadvantages and how that varies as a function of family backgrounds. Broader social context in America, such as gender expectations, a high divorce rate, a declining marriage rate, a rising economic cost of schooling, and structural racism shapes family backgrounds. Different family backgrounds further generate differential dynamics of sibling interactions and outcomes in advantaged and disadvantaged families.

In order to address these questions, this research explores how sibling spillover effects interact with both children’s school levels and family backgrounds, focusing on elementary and middle school children in the North Carolina public school system. We focus on four important aspects of family backgrounds among American youth: race, mothers’ educational attainment, family structure, and school poverty. We isolate the causal effect of sibling spillovers on children’s educational outcomes using a quasi-experimental approach based on discontinuities in school starting ages created by North Carolina school-entry laws. The state of North Carolina assigns a cutoff date by which children must have reached the age of five in order to start kindergarten. Children born shortly after the cutoff date are typically not permitted to enroll in school till the following year and are therefore older compared to their classmates. Because of the relative age advantage and potential adjustments made in family and school contexts in response to this later date of initial enrollment, these children have substantially better school outcomes than those born shortly before the cutoff date, despite sharing similar household socioeconomic profiles (Bedard and Dhuey 2006; Cook and Kang 2016; Elder and Lubotsky 2009; Tan 2017; Dhuey et al. 2019). We use a unique dataset developed from information provided by the North Carolina Education Research Data Center (NCERDC). This dataset links birth certificate data and school administrative records, which allows us to estimate the impact of having older siblings born after the cutoff date on younger siblings’ test scores at the elementary and middle school levels for socially advantaged (i.e., White, mother with more than high school education, two-parent, or non-poverty school) and disadvantaged (i.e., Black, mother with high school education or lower, single-mother, or high-poverty school) families.

We find that individuals whose older siblings were born shortly after the school-entry cutoff date have significantly higher test scores in middle school but not in elementary school. In contrast with most existing theories that assume homogeneous sibling spillover effects, our results show a larger absolute spillover effect among disadvantaged families. We further provide estimates of the contribution of sibling spillovers to sibling correlations in test scores, relative to the contributions of shared biological and environmental characteristics. Our findings suggest that sibling spillovers are an important channel through which inequality between families is produced, most likely when younger siblings are in middle school rather than earlier in elementary school. In addition, older siblings in disadvantaged families are not only more likely to have worse outcomes, such as lower test scores, to begin with (Conley 2004), but also, as our findings suggest, have greater (negative) spillovers on their younger siblings’ outcomes. By contrast, resources in advantaged families may buffer the influence of older siblings on younger siblings’ performance, by, for example, allowing siblings to have separate rooms, or paying for younger siblings’ extracurricular activities that allow them to spend more time outside the home with other children. Findings from this study have important implications for how we should think about the production of inequality and the way we examine inequality.

2. Theoretical Framework

How might having an older sibling born after the school-entry cutoff date affect a younger sibling’s test scores? And does the effect vary by school levels and family backgrounds? Older siblings’ school starting ages could affect younger siblings’ test scores through multiple channels, including the older sibling’s own academic performance and non-academic outcomes, family outcomes (e.g., parents’ employment, parents’ divorce risks, family income), and time spent together among family members (e.g., children’s time spent with parents, siblings’ time spent together) (Landersø, Nielsen, and Simonsen 2019; Gelbach 2002; Fitzpatrick 2010; Elder and Lubotsky 2009). For example, in the US context where robust public childcare programs are often not available, delaying school entry for a year implies that the older sibling spends an extra year in expensive childcare facilities or at home instead of going to public schools, which may negatively affect younger siblings’ academic performance through lowering family income (Gelbach 2002). Relatedly, the increased financial and mental pressure associated with an older sibling spending an extra year in expensive childcare facilities or at home may potentially lower marital stability among parents (Landersø, Nielsen, and Simonsen 2019), and therefore negatively affect younger siblings. In addition, considering the high cost of pre-school childcare, delaying school entry may delay mothers’ plans to participate in the labor force because they need to spend time on childcare, and for mothers who already have a job, it may delay their plans to work longer hours or to switch from part-time jobs to full-time ones (Ruppanner, Moller, and Sayer 2019; Gelbach 2002), which is a relevant consideration because mothers’ labor force participation appears to affect younger siblings’ academic performance in several ways (Dunifon et al. 2013; Hill et al. 2005).

However, based on our literature review, spillovers of older siblings’ school starting ages are most likely to impact younger siblings’ test scores through improving older siblings’ educational performance and health, especially mental and behavioral health (Fletcher, Hair, and Wolfe 2012; Breining 2014; Breining et al. 2021; Black et al. 2021; Dee and Sievertsen 2018; Balestra, Eugster, and Liebert 2020). Other channels have been proposed and investigated but appear to be less supported by empirical evidence. For example, in a paper using data from Florida close in spirit to this study, Karbownik and Ozek (2021) provided evidence that family income is unlikely to be a major mechanism by showing that older siblings’ delayed school entry does not affect younger siblings’ eligibility for free or reduced priced lunch. Findings from previous studies also show that parents’ employment status and divorce risks are unlikely to be affected by older siblings’ school starting age (Landersø, Nielsen, and Simonsen 2019). Therefore, we focus on potential mechanisms through which older siblings’ improved school performance and health are most likely to affect younger siblings’ test scores directly and indirectly (through parental investment decisions). Although sibling configuration, such as sibship size, birth order, and gender composition, matters when it comes to sibling dynamics, we simplify our theoretical discussions by comparing school levels and family backgrounds conditional on sibling configuration.

Older siblings’ academic performance may positively affect younger siblings’ performance through role modeling or positive attitudes towards school.¹ According to the confluence theory (Zajonc and Markus 1975; Zajonc 1976), improved academic performance of the older sibling will improve the intellectual environment of the family, which will improve the younger sibling’s academic performance. The role-modeling theory provides another type of interaction through which family intellectual environment may affect children’s intellectual development -- as similar-aged family members going through relevant current life experiences, older siblings provide salient points of reference as role models (Bank and Kahn 1975; Brim 1958; Benin and Johnson 1984; Hauser and Wong 1989). An academically successful older sibling may set high standards for achievement, raising younger siblings’ expectations and aspirations for themselves. A related possibility is that older siblings who earn good grades and are promoted on time will be more likely to have a positive attitude toward school. This positive attitude is likely to be contagious and can be communicated to younger siblings.²

Older siblings’ improved mental and behavioral health may also positively affect younger siblings’ academic performance. Studies have consistently shown that having a disabled or learning disordered sibling, particularly an older one, leads to weaker academic achievement, potentially through day-to-day sibling interactions (Black et al. 2021; Breining et al. 2021; Breining 2014; Fletcher, Hair, and Wolfe 2012). Conversely, an older sibling with better mental and behavioral health may exhibit better attitudes and behaviors towards schools, which can be contagious to younger siblings. Because we do not have good measures of siblings’ health to directly test this mechanism, the rest of our theoretical discussion focuses on the role of older siblings’ improved academic performance.

In addition to direct interactions between siblings, older siblings can affect younger siblings indirectly through parents’ decisions on allocation of household resources. An emerging literature has shown that children’s characteristics, such as child gender and the genetic profile of the child, affect parents’ investment and other behaviors (Breinholt and Conley 2020; Raley and Bianchi 2006), but this literature has generally not considered the characteristics of siblings. The parental preference model provides two parental investment strategies (Becker and Tomes 1976). Parents who hold child-neutral preferences may invest disproportionally in the child with the greatest talent. In this case, an older sibling’s better academic performance may lead parents to divert household resources away from younger siblings (Grätz and Torche 2016). If, on the other hand, parents hold child-equality preferences, they may invest more resources in the less talented child to equalize siblings’ success. In this case, having an academically strong older child may allow parents to devote more resources to the younger child (Grätz 2018; Conley 2008; Yi et al. 2015). Also relevant is the sociological resource dilution model, which emphasizes the family’s function of distributing resources to its members and has been most successful in explaining the negative relationship between sibship sizes and educational attainments (Powell and Steelman 1993; Blake 1989; Steelman and Powell 1989; Conley 1999, 2001).

The strength of inter-sibling influences may vary by children’s school levels. The Akers social learning theory posits that in formative years, young children are heavily influenced by both positive and negative portrayals of behaviors from parents and other authority figures, who reinforce these portrayals with rewards and encouragement or disciplinary actions (Ardelt and Day 2002). By early adolescence, however, children increasingly seek independence from their parents and look more to their peers and older siblings for approval, especially individuals of the same gender or with similar interests (Ardelt and Day 2002). One study, using similar data to the current study, found that the effects of classroom peer characteristics increase nearly threefold for reading and fivefold for math test scores during middle school, while the importance of family backgrounds diminishes at this stage (Sorensen, Cook, and Dodge 2017). Siblings, particularly those closely spaced, are a special type of peer. Older siblings’ influence becomes more important when they reach middle-school grades because they are more likely to be viewed as role models. A large number of studies have documented the importance of older siblings’ role modelling function among adolescents, even after taking the influence from peers into account (Needle et al. 1986; Windle 2000; Conger and Rueter 1996; Duncan, Duncan, and Hops 1996; Giordano, Cernkovich, and DeMaris 1993; Slomkowski et al. 2001; Averett, Argys, and Rees 2011; Low, Shortt, and Snyder 2012; Ardelt and Day 2002). There is no theory or empirical evidence showing how other mechanisms (e.g., parental investment decisions) may vary in elementary and middle schools. Therefore, we hypothesize that sibling spillover effects are strong in middle school, but not in elementary school (H1).

It is unclear how we should conceptualize the social processes through which sibling influences take place in different family contexts. The Wisconsin model of socioeconomic attainment, which has deeply influenced how sociologists think about the production and persistence of inequality, posits that the influence of significant others is dependent on family origins (Blau and Duncan 1967; Sewell, Haller, and Portes 1969; Sewell and Hauser 1975). A related theory in economics provides a useful framework to think about disparities in achievements between siblings. Becker et al. argue that parents in both disadvantaged and advantaged families tend to invest disproportionally in the human capital of the better-endowed child, but families with higher socioeconomic status (SES) will compensate other siblings later with non-human capital goods such as cash transfers or gifts whereas poor families do not have the resources to do so (Becker and Tomes 1976, 1986; Becker 1993). However, this model focuses narrowly on the economic-resource aspect of family backgrounds and the relationship between parents and children. Other dynamics in family life shaped by different backgrounds that may transmit (dis)advantages to children, particularly the interactions among siblings and the role of children in shaping their siblings’ achievements, are largely ignored.

We propose an alternative theoretical framework to explain the functional roles of siblings in advantaged and disadvantaged families. Rather than isolating a single mechanism, our framework incorporates multiple mechanisms while, importantly, allowing the relative strength or role of each mechanism to vary as a function of family backgrounds. Although all families may strive to balance efficiency and equality of investment between siblings, we argue that differences in family resources and social environments may impact how that process influences the strength of sibling spillovers. Specifically, four aspects of family backgrounds of interest in this paper -- race, family structure, maternal education, and school poverty -- may create differential family experience and culture by affecting how parents define their own roles and their children’s roles in family life as well as time spent with children (Lareau 2011, 2002; Ridgeway 2014; Schneider, Hastings, and LaBriola 2018; Weininger and Lareau 2009). In most families, regardless of background, parents are fond of all their children and want all of them to do well, but in practice parenting practice is influenced by family resources. Our theory is inspired by the rich discussions in the culture and family literature on how family SES affects children’s life experiences, as among the four aspects of family backgrounds we are interested in, race and family structure are statistically associated with SES and the other two directly measure SES. We hypothesize that positive sibling spillover effects are greater in disadvantaged families than in advantaged families (H2).

We argue that among disadvantaged families, parents divert their limited resources to the child they believe has better chances of achieving upward mobility, with an expectation that this child will compensate other siblings’ human capital (e.g., academic performance) or non-human capital in the future (e.g., gifts). This expectation has been documented in qualitative studies. A relatively successful individual who is a person of color and/or from a poor family is more likely to be expected to help other siblings compared to an individual in a rich or White family (Conley 2004). Ethnographic work suggests that in the face of structural racism, Black families often see their children as vulnerable and at risk (Anderson 2015; Anderson et al. 2012; Anderson 2012). As a result, poor Black families often encourage their children to help each other, and older siblings tend to have a substantial influence on younger siblings (Brody and Murry 2001; McHale et al. 2007; Stormshak, Comeau, and Shepard 2004; Whiteman, Bernard, and McHale 2010; Brody et al. 2003; McHale, Updegraff, and Whiteman 2012; Mwangi 2015; Loury 2004). Consistent with this argument, Black adolescents report higher levels of intimacy with family members and lower levels of intimacy with friends than Whites, and therefore are more likely to depend on older siblings rather than school peers (Ardelt and Day 2002; Giordano, Cernkovich, and DeMaris 1993). Qualitative research also shows that older siblings in disadvantaged families often take the role of the parents (Burton 2007), and older brothers often take the role of the father in single-mother families (Conley 2004). More generally, parents in disadvantaged families may not participate in children’s activities as often as their counterparts in advantaged families, “leaving child’s play to children” (Lareau 2011). This means that siblings spend more time together in disadvantaged families compared to advantaged ones.³ By contrast, higher-SES parents typically pursue a “cultivation” approach, which emphasizes individualism within the family and encourages children to seek adult role models (Lareau 2011, 2002). Among advantaged families, parents more heavily invest in better-endowed children’s human capital to obtain higher returns, but their investment in less-talented siblings may not necessarily be reduced much.⁴ This is consistent with existing evidence that parents, especially higher-SES ones, invest more in the education of the sibling with better health endowment, but more in the health of the sibling with lower health endowment (Yi et al. 2015).

In addition, sibling role modeling and contagious positive attitudes towards schools may be particularly salient among disadvantaged families because in these families, parents may not be good role models or may not be around much, and the effects will impact sibling relationships. By contrast, although these mechanisms may also occur among advantaged families, their impacts should be relatively small: Children in these families can more readily find high achieving school peers or adults to be role models, obtain positive attitudes towards school, as well as accessing other resources, such as tutors.⁵ Finally, when the older sibling is a bad role model, disadvantaged families do not have the same resources that advantaged families have to buffer negative sibling spillovers. By contrast, younger siblings from advantaged families may have a “compensatory advantage” and be less affected by older siblings’ negative outcomes (Bernardi 2014; Boudon 1998).

3. Background on North Carolina School-entry Laws

Prior to cohorts born in 2004, the North Carolina school attendance law specified that children born after October 16 could not start kindergarten until the year they turned five years old. Therefore, a child born on October 16 was eligible to start kindergarten in August prior to their fifth birthday, whereas a child born on October 17 was not eligible until the following year. All individuals in our dataset were born before 2004 and hence bound by the October 16 cutoff date.⁶

Compliance was not perfect for two main reasons: academic redshirting (i.e. delaying school entry on purpose) and grade retention in kindergarten (Cook and Kang 2020). Existing studies generally find that non-compliance is more common among White, male, and high-SES children (Bassok and Reardon 2013; Dobkin and Ferreira 2010; Huang 2015). In the context of North Carolina, Cook and Kang (2020) find that among children born between 2003 and 2004 who attended grades 1–3 in North Carolina public schools, 92.5% of them started school on time, 0.8% of children started early, and 6.7% started late. In our own sample, approximately 92% of older siblings started school on time. The older third graders were disproportionally White boys, especially those in higher-SES families but with relatively lower academic abilities (Cook and Kang 2020). However, the relationship between non-compliance and different aspects of family backgrounds is complex. For example, Cook and Kang (2020) find that coming from low-income families is associated with compliance for White and Hispanic males but delayed school entry for Black males, and makes little difference for females.

Despite imperfect compliance, studies consistently show that school-entry laws have substantial effects on the academic performance of individuals born shortly after the cutoff date, which diminish but remain highly significant up to the eighth grade (Bedard and Dhuey 2006). In the context of North Carolina, studies consistently show that individuals born right after the cutoff date experience a substantial increase in test scores. The estimated effect sizes are 6 and 4.5 percentage points in sixth and eighth grade reading scores according to Cook and Kang (2016), and 0.35 and 0.2 standard deviations in third and eighth grade scores according to Tan (2017).

The increase in test scores is likely due to a relative age advantage. As students born after the cutoff date are older than their classmates at the time of testing, they have higher levels of human capital accumulated prior to kindergarten (Elder and Lubotsky 2009) and higher levels of cognitive development (Dhuey et al. 2019). Older siblings born shortly after the cutoff date also tend to exhibit better health and school-related behaviors, including higher task persistence, lower inattentiveness or hyperactivity, better mental health, and a lower probability of being diagnosed with special educational needs (Dee and Sievertsen 2018; Mühlenweg et al. 2012; Black et al. 2021; Balestra, Eugster, and Liebert 2020; Elder 2010; Elder and Lubotsky 2009; Evans, Morrill, and Parente 2010). Some scholars have also argued that the age effects are not only biological but also reflect potential adjustments made by families and schools in response to children’s school starting ages (Cook and Kang 2020).

4. Data

NCERDC provided our dataset, which linked North Carolina birth certificate data and school administrative records and removed personal identifiers, with permissions from the NC Department of Public Instruction (NCDPI) and the NC Department of Health and Human Services (NCDHHS). The birth certificate data provide information including a child’s birth weight and family backgrounds in terms of mother’s race, age, educational attainment, and marital status at the time of birth. Crucially, the birth certificate data also allows us to identify siblings born to the same mother. We do not have birth certificate records for individuals who were not born in North Carolina or not born to mothers residing in North Carolina. The public-school records provide individual-level data on all end-of-grade (EOG) reading and math test scores from third to eighth grades. All North Carolina public school students in the same grade in the same year take the same EOG tests. If a child repeats a grade and re-takes the EOG test, results from the first test are used. The public-school data also provide information on school and school district characteristics in terms of student poverty rates and proportion of students passing EOG tests, as well as number of crimes per 100 students in a school and percentage of students living with one parent in a school district.

The birth cohorts included in the final sample were born in 1988–2003. We restrict the sample to individuals born to non-Hispanic White and non-Hispanic Black mothers, because a large proportion of Hispanic and Asian public-school students in these birth cohorts were born out of state (i.e., we do not have their birth certificate records). We also exclude students attending charter schools or schools in correctional facilities due to differences in testing requirements. Because about 61% of students with siblings only have one sibling, for the sake of simplicity, our main analysis is based on students who have exactly one sibling who also appears in the dataset. We extend our analysis to include students from larger families in Appendix A1, which shows qualitatively similar results. We further exclude twins and siblings born more than 6 years apart.⁷ For the latter, older siblings are unlikely to be viewed as younger siblings’ peers and their interactions may therefore be very limited (Hoffman and Teyber 1979; Dunifon, Fomby, and Musick 2017).⁸

We measure each student’s educational performance as z-scores relative to the test scores of all students who took the same test, including students not included in the final sample.⁹ Z-scores are calculated for each grade by subject. Because elementary and middle schools represent different developmental stages and school environments for children, we then averaged z-scores across grades 3 through 5 for elementary school and grades 6 through 8 for middle school.¹⁰ Besides math and reading z-scores, we create a variable using the average of reading and math z-scores to summarize overall achievement. Data on EOG test scores are only available up to and including 2017. Because we have fewer students who have completed higher grades by 2017, the sample size is slightly smaller at higher grade levels. The attrition is unlikely due to selection, since the vast majority of students remain in the sample until age 17, including students born shortly before or after the cutoff date (Tan 2017). In addition, because a substantial proportion of students born after 2002 would not take the EOG test until 2018, eighth grade test scores are computed only for cohorts born in 2002 or earlier.

Our main independent variable is an indicator of whether the older sibling was born after the cutoff date, October 16, which was the North Carolina kindergarten entry cutoff date prior to year 2009. We also control for the following sociodemographic characteristics and social contexts that are available through the administrative data: the older and younger siblings’ relative ages, conditions at the time of birth (i.e. birth weight, mother’s age, mother’s education, and mother’s marital status), school characteristics (i.e., school poverty rates, proportion of school students who passed EOG tests, and number of crimes per 100 school students), and school district characteristics (i.e., school district poverty rates, proportion of school district students who passed EOG tests, and proportion of school district students in single parent homes). Among all available variables in our data, based on previous studies (Tan 2017), these variables are theoretically predictive of students’ test scores, and therefore controlling for them in our quasi-experimental design can improve the precision of our estimates (Lee and Lemieux 2010). Because indicators for school and school district characteristics are not available in every year,¹¹ we generate the averages of each indicator across all years of data available. A flow of sample restrictions is provided in Appendix Figure A1.

Table 1 provides summary statistics of individual, school, and school district characteristics of younger siblings whose older siblings were born within 60 days before or after the North Carolina school-entry cutoff date. The two groups are similar in terms of individual and school district characteristics, with t-tests showing statistically insignificant differences at the 10% level. Students whose older siblings were born shortly after the cutoff date (hereafter the “treatment group”) tend to be slightly more disadvantaged: The percentages of them attending schools with high student poverty rates, high crime rates, and low EOG passing rates are higher. However, the differences are small compared to statewide proportions. While the differences are significantly different from zero, suggesting that the two groups are systematically different, the differences are so small that they are arguably not substantively meaningful. Furthermore, to the extent that there is a slight tendency for children born shortly after October 16^th to be more disadvantaged than those born shortly before, if anything, that difference tends to reduce the observed advantages of starting school late. A number of the observed effects are nonetheless significant.

Table 1:

Summary Statistics

	Older sibling born up to 60 days before cutoff date	Older sibling born up to 60 days after cutoff date	Difference
	(1)	(2)	(3)
Panel A: Individual characteristics
Female (%)	48.967	48.971	0.000
Birth weight (grams)	3395.882	3393.305	2.577
Mother is White (%)	72.711	72.427	0.003
Maternal age at time of birth	27.390	27.355	0.035
Maternal education at time of birth (years)	13.082	13.082	−0.001
Mother was married at time of birth (%)	75.293	74.698	0.006
Panel B: School characteristics
Students living in poverty (%)	58.011	58.338	−0.003**
No. of crimes (per 100 students)	0.579	0.588	−0.009*
Students passed end-of-grade tests (%)	75.102	74.931	0.002**
Panel C: School district characteristics
Students living in poverty (%)	16.214	16.216	0.000
Students with one parent (%)	22.223	22.232	0.000
Students passed end-of-grade tests (%)	82.424	82.394	0.000
N	29,481	27,792

Note:

^{***, **, and *}correspond to statistical significance at 1%, 5% and 10% level respectively.

5. Empirical Specification

Sibling spillover effects are difficult to distinguish from other factors that account for the similarity in academic performance between siblings. We consider four broad categories of explanations for sibling correlations in academic outcomes: unobserved biological endowment, observed family and school environmental characteristics (e.g., parental marital status and education, schoolmates’ socioeconomic status and academic performance), unobserved family and school environmental characteristics (e.g., parenting style and values), and influence of older siblings on younger siblings (both direct and indirect).

An ordinary least squares (OLS) regression model with a younger sibling’s academic performance as the dependent variable and an older sibling’s performance as the independent variable reflects all four categories. The goal of this paper is to isolate the effect of inter-sibling influence, which in the absence of an experimental manipulation cannot be reliably obtained, given that some family and environmental characteristics are unobserved or poorly measured. Fortunately, there is a source of exogenous variation in the academic performance of the older sibling, which occurs as the result of the interaction between legislated age cutoff at which a child can begin public school, and the near-randomness of the child’s exact birth date. Discontinuities in the older sibling’s school starting age resulting from the cutoff are a source of variation in his or her academic performance that is exogenous to both observed and unobserved characteristics of the siblings. Variation from this source arguably affects the younger sibling’s academic performance exclusively through inter-sibling influence – a claim for which we provide a variety of supporting evidence.

We begin by using an OLS regression model on a sample of students whose older sibling was born within 60 days on either side of the cutoff date for starting school. The younger sibling’s test scores in primary (grades 3–5) and middle school (grades 6–8) are regressed on an indicator of whether the older sibling was born before or after the cutoff date, together with other variables. This model identifies the reduced form effects of an older sibling’s school starting age, which can affect the younger sibling’s academic performance through multiple channels. Covariates are included to capture sociodemographic characteristics and social contexts described in the previous section to account for observed characteristics, and cohort fixed effects to partially account for unobserved characteristics. To use the same sample as our regression discontinuity (RD) analysis introduced below, we limit our sample to younger siblings whose older siblings were born within 60 days of the cutoff date on either side. However, the analysis includes younger siblings who were born throughout the year.

As an alternative method for estimating the older sibling’s influence on younger sibling’s test scores, we employ an RD model, which estimates the causal impact of discontinuities in an older sibling’s school starting age due to the school-entry cutoff date. Based on Buckles and Hungerman (2013)’s evidence that babies born in different seasons of the year tend to have mothers with significantly different SES, and graphical evidence from previous work using similar data from North Carolina (Tan 2017), our main specification employs a linear local RD specification. Robustness checks using a quadratic functional form in Appendix Table A3 show highly consistent results. Algebraically, the local RD model chooses parameter values that minimize the following:

$$\begin{gathered} {\Sigma }_i{\left(Testscor{e}_i-{\beta }_{1}Sibcutof{f}_i-{\beta }_{2}Sibag{e}_i-{\beta }_{3}Sibcutof{f}_i*Sibag{e}_i-{\mathit{\beta }}_{\mathbf{4}}{\mathit{X}}_{\mathit{i}}- \\ {\mathit{\theta }}_{\mathit{i}}\right)}^2{K}_h\left(Sibag{e}_i\right) \end{gathered}$$ (1)

where $Testscor{e}_i$ is a younger sibling’s test score in elementary or middle school, and $Sibcutof{f}_i$ is a dichotomous indicator for whether his or her older sibling was born after the school-entry cutoff date. $Sibag{e}_i$ refers to the exact age in days of the older sibling relative to the rest of his or her school cohort. It is measured using the number of days they were born before or after July 2^nd (the middle point of a year) to allow for a monotonic effect on the outcome. We include the term $Sibcutof{f}_i*Sibag{e}_i$ to allow for changes in the running variable $Sibag{e}_i$ before and after the cutoff date. ${\mathit{X}}_{\mathit{i}}$ is a vector of control variables as described above, and ${\mathit{\theta }}_{\mathit{i}}$ is a set of birth cohort fixed effects. Although it is not necessary for obtaining consistent treatment effects, including covariates in the RD model can reduce sampling variability and therefore increase precision of the estimates (Lee and Lemieux 2010). To account for potential sibling correlations in date of birth, we also control for whether the younger sibling was born after the school-entry cutoff date, and his or her exact age in days relative to the rest of the school cohort (calculated by counting the number of days from Oct 17th to Oct 16th of the following year).

Following previous related literature (Cook and Kang 2016; McCrary and Royer 2011; Tan 2017), we use a triangular kernel, which assigns more weights to data points closer to the cutoff date:

$$K_h\left(Sibag{e}_i\right)=\left(1-\frac{\left|Sibag{e}_i\right|}{h}\right)\mathbf{1}\left[\frac{\left|Sibag{e}_i\right|}{h}<1\right]$$ (2)

where $h$ is the bandwidth or smallest number of days the older sibling is born before or after the cutoff date which are assigned zero weight. Following previous studies, we use 60 days as the bandwidth in the main analyses (Tan 2017; Cook and Kang 2016). Robustness checks using alternative bandwidths are provided in Appendix Table A4 and the results are highly consistent. Standard errors are estimated using the jackknife method and are clustered by the older sibling’s exact age in days relative to the rest of his or her school cohort. Various robustness checks such as sibling correlations in time of birth and season of birth effects are provided in Appendix A2 and A3, respectively, and show highly consistent results.

To examine H1, we conduct subgroup analyses for younger siblings in elementary and middle schools. To examine H2, we compare estimates between advantaged and disadvantaged families conditional on school levels. We consider four aspects of family backgrounds: maternal race (non-Hispanic White vs. non-Hispanic Black), education (more than high school vs. high school degree or less) and marital status (married vs. not married) at the time of birth, and whether the younger sibling attends a school with high vs. low levels of poverty among students. A low level of student poverty is defined as having a below-average poverty rate in our sample. Among these family background indicators, maternal race, mothers’ education, and school poverty have been used by previous studies examining educational spillover effects among siblings to capture students’ social backgrounds (Karbownik and Ozek 2021; Qureshi 2018; Goodman et al. 2019; Nicoletti and Rabe 2019), but the inclusion of mothers’ marital status at the time of birth is novel. Maternal education strongly predicts other key aspects of family SES (e.g., income, occupation), and among these key aspects, maternal education has been shown to be one of the strongest predictors of children’s educational and health outcomes (Reardon 2011; Harding, Morris, and Hughes 2015; Jackson, Kiernan, and McLanahan 2017).

Our main analysis focuses on effects of older siblings on younger siblings because the literature suggests that educational spillover effects tend to operate in this direction (Fletcher, Hair, and Wolfe 2012; Qureshi 2018; Breining et al. 2021; Abramovitch, Corter, and Lando 1979). In addition, our identification method relies on variation from school-entry laws, which affect not only older siblings’ test performance, but also their age at school entry and hence the spacing between siblings’ grade levels. Existing evidence suggests that birth spacing between siblings is positively associated with educational outcomes among older siblings but has negligible effects on younger siblings (Buckles and Munnich 2012). Since having a younger sibling born after the cutoff date is associated with increased spacing between grade levels, our identification method is likely to overestimate spillover effects from younger siblings to older siblings. Therefore, we confine our main analysis to older siblings affecting younger siblings. Results on younger siblings affecting older siblings are shown in Appendix Table A5. We observe some positive spillover effects on reading scores in this direction but not for math or total scores.

6. Main Results

We first confirm the relationship between older siblings being born shortly after the cutoff date and their own test scores suggested in previous studies (e.g., Tan 2017). Results are shown in Appendix Table A6 and are plotted in Appendix Figure A2. On average, students born right after the cutoff date have test scores higher by a fifth of a standard deviation in elementary school, which diminishes slightly by middle school.¹² By comparison, the difference in the mean test scores between White and Black students is three-fifths of a standard deviation, estimated from a nationally representative dataset (Orr 2003). Hence, our school-entry cutoff effect represents around a third of the Black-White test score gap in the US. Heterogeneous effects by family backgrounds are presented in Appendix Table A7, which shows that older siblings from disadvantaged families benefit more from being born shortly after the cutoff date compared to those from advantaged families. The difference in the magnitudes between students attending high-poverty schools (0.18) and low-poverty schools (0.11), for example, is 0.07. This suggests that being born shortly after the cutoff date improves the total test score of an older sibling attending a high-poverty school by an additional 0.07 standard deviation compared to one attending a low-poverty school, which is roughly 14.2% of the gap in the mean test scores of older siblings between high-versus low-poverty schools.

Panel A1 of Table 2 displays the statistical associations between having an older sibling born shortly after the cutoff date and a younger sibling’s test scores, estimated using an OLS model. Significant associations at the 5% significance level are observed for middle school students but not for elementary school students. Having an older sibling born shortly after the cutoff date is associated with an increase in a younger sibling’s reading and math scores by 0.03–0.04 of a standard deviation. The magnitude of the association for reading is larger and more robust than that for math. The association remains robust after controlling for individual, school, and school district characteristics in Panel A2, providing further evidence that an older sibling’s time of birth provides an exogenous source of variation.

Table 2:

Impact of Having an Older Sibling Born After School Entry Cutoff Date on Younger Sibling’s Test Scores

	Elementary School			Middle School
	Reading	Math	Total	Reading	Math	Total
	(1)	(2)	(3)	(4)	(5)	(6)
Panel A1: OLS without controls
Older sibling born after
cutoff date	0.021	0.017	0.018	0.037**	0.025	0.030*
	(0.018)	(0.016)	(0.016)	(0.017)	(0.016)	(0.016)
Panel A2: OLS with controls
Older sibling born after
cutoff date	0.019	0.016	0.017	0.035**	0.021*	0.027**
	(0.015)	(0.013)	(0.013)	(0.014)	(0.012)	(0.012)
Panel B1: RD without controls
Older sibling born after
cutoff date	0.021	0.011	0.016	0.041**	0.025	0.032*
	(0.020)	(0.018)	(0.018)	(0.019)	(0.019)	(0.018)
Panel B2: RD with controls
Older sibling born after
cutoff date	0.025	0.016	0.020	0.043***	0.027**	0.034**
	(0.016)	(0.014)	(0.015)	(0.016)	(0.013)	(0.014)
N	54,622	54,722	54,878	52,527	52,589	52,703

Note:

^{***, **, and *}correspond to statistical significance at 1%, 5% and 10% level respectively. Standard errors are clustered by older sibling’s relative age. In all models, we control for whether older sibling was born after cutoff date and older sibling’s relative age. In Panels A2 and B2, we also control for whether younger sibling was born after cutoff date, younger sibling’s relative age, conditions at the time of birth, school and school district characteristics, as well as cohort fixed effects. In the RD models, interactions between older sibling’s relative age and whether they were born after cutoff date are also included. The sample is restricted to sibling pairs where older sibling was born within 60 days of the cutoff date.

Our results are consistent with Figure 1, which plots the average test scores of younger siblings for each exact date of birth of older siblings. The dotted line at zero indicates the school cutoff date and the two dotted lines near it define a 60-day window before and after the school cutoff date. The average test scores range from zero to 0.2, reflecting a small variance of test score means among younger siblings against their older siblings’ birth dates. The school-entry cutoff date and the 60-day window are illustrated. Two features of the figure stand out. First, there is a hump in test scores between day −200 and −100. This observed pattern is highly consistent with seasonality patterns documented in Buckles and Hungerman (2013). Second, the variation in test scores is more monotonic within the 60-day window. This is consistent with our assumption that the individuals in our sample share more similar family backgrounds. The discontinuity at the cutoff date, indicating that younger siblings in the treatment group tend to perform better, is larger in middle school than in elementary school. The positive discontinuities in middle school appear for both reading and math, but especially for reading (see Appendix Figure A3).

Figure 1: Younger Sibling’s Test Scores by Older Sibling’s Exact Date of Birth.

Note: The analysis is restricted to sibling pairs where older sibling was born within 60 days of the North Carolina school entry cutoff date, indicated by the middle vertical dotted line.

As an alternative identification strategy, we estimate regression discontinuity models. Panel B1 and B2 of Table 2 show RD estimates with and without control variables by school level, respectively.¹³ The results are consistent with the OLS estimates. The effects are significant at the 5% level for middle school but not for elementary school. The magnitudes of the effects are between 0.025 and 0.043 of a standard deviation, with the magnitude for reading larger and more robust than that for math. Having an older sibling born shortly after the cutoff date is associated with an increase in a younger sibling’s total scores by 0.034 of a standard deviation. By one comparison, this represents around 6% of the Black-White achievement gap. Our results are consistent with H1 and indicate that a considerable portion of the academic gains of older siblings born after the school-entry cutoff date spill over to their younger siblings. If we, for example, compare the coefficients for total scores in middle school in Panel B2, 23% of the positive effects gained by older siblings spill over to younger siblings (0.034/0.15 = 0.23). It is interesting to note that the effect of being born shortly after the cutoff date on older siblings’ own test scores is greater in elementary school than in middle school, whereas the spillover effect on younger siblings’ test scores is only statistically significant when they were in middle school. This finding further suggests that, as argued in H1, younger siblings are more affected by older siblings in middle school due to their developmental stages.

Results by grade are provided in Appendix Table A8. These results confirm that spillovers occur mostly in middle school. Because sibling spillover effects exist across grades in middle school but only exist for the last year of elementary school, it is quite plausible that school levels empirically correspond to meaningful stages in cognitive development. From the magnitudes of the coefficients for each grade, the cognitive progression throughout childhood is not linear. The sixth grade, which marks the transition from elementary to middle school, appears to be a key transition in sibling relationships with the greatest magnitude of sibling spillover effects. Previous studies have documented the multiple transitions and challenges students face when transitioning from elementary to middle schools (Rudolph et al. 2001; Cook et al. 2008; Alspaugh 1998; Barber and Olsen 2004). It is possible that when transitioning between school levels, in response to uncertainty and challenges, younger siblings may be especially influenced by older siblings’ advice or experience. Previous studies have also identified the sixth grade as a critical turning point towards peer influence on academic outcomes (Sorensen, Cook, and Dodge 2017; Berndt 1979).

We move on to examine H2 by looking at heterogeneous effects by family background conditional on school levels. We find consistent positive spillover effects among disadvantaged families in middle school, but not among advantaged families (see Table 3). Among advantaged families, only the sibling spillover effect for those whose mother has a higher than high school degree at birth is statistically significant, with the magnitude of 0.036. By contrast, among disadvantaged families, the sibling spillover effects across all four dimensions are statistically significant. The magnitude of the effect is 0.063 for Black families, 0.036 for those whose mother has a high school degree or lower, 0.065 for those with unmarried mothers at birth, and 0.055 for those attending a high-poverty school.

Table 3:

Impact of Having an Older Sibling Born After School Entry Cutoff Date on Younger Sibling’s Test Scores, by Family Background

	Elementary School				Middle School
	Reading	Math	Total	p-value comparing Panels A and B in Column (3)	Reading	Math	Total	p-value comparing Panels A and B in Column (7)
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
Panel A: Socioeconomically Advantaged
Mother is non-Hispanic White	0.020	0.013	0.015	0.62	0.032*	0.017	0.024	0.20
	(0.020)	(0.019)	(0.019)		(0.017)	(0.017)	(0.016)
N	39,823	39,890	39,991		38,120	38,152	38,235
Mother has a higher than high school degree at birth	0.042**	0.022	0.030*	0.46	0.054**	0.020	0.036*	0.99
	(0.020)	(0.020)	(0.018)		(0.023)	(0.022)	(0.022)
N	25,870	25,873	25,939		24,622	24,620	24,661
Mother is married at birth	0.019	0.012	0.014	0.55	0.035**	0.016	0.024	0.08
	(0.019)	(0.017)	(0.017)		(0.017)	(0.015)	(0.015)
N	41,089	41,145	41,252		39,404	39,429	39,508
Low-poverty school	0.019	0.004	0.009	0.48	0.026	0.003	0.013	0.16
	(0.022)	(0.018)	(0.018)		(0.022)	(0.015)	(0.017)
N	26,630	26,661	26,720		25,688	25,698	25,747
Panel B: Socioeconomically Disadvantaged
Mother is non-Hispanic Black	0.039	0.021	0.031		0.074**	0.053*	0.063**
	(0.030)	(0.028)	(0.027)		(0.029)	(0.028)	(0.027)
N	14,799	14,832	14,887		14,407	14,437	14,468
Mother has a high school degree or lower	0.012	0.013	0.012		0.036*	0.036**	0.036**
	(0.024)	(0.017)	(0.020)		(0.022)	(0.017)	(0.018)
N	28,752	28,849	28,939		27,905	27,969	28,042
Mother is unmarried at birth	0.039	0.025	0.032		0.067**	0.061***	0.065***
	(0.032)	(0.026)	(0.027)		(0.027)	(0.022)	(0.023)
N	13,533	13,577	13,626		13,123	13,160	13,195
High-poverty school	0.031	0.027	0.030		0.060**	0.050**	0.055**
	(0.025)	(0.024)	(0.023)		(0.027)	(0.022)	(0.024)
N	27,992	28,061	28,158		26,839	26,891	26,956

Note:

^{***, **, and *}correspond to statistical significance at 1%, 5% and 10% level respectively. Standard errors are clustered by older sibling’s relative age. In all models, we control for whether older and younger sibling were born after cutoff date, older and younger siblings’ relative ages, conditions at the time of birth, school and school district characteristics, cohort fixed effects, and an interaction between older sibling’s relative age and whether they were born after cutoff date. The sample is restricted to sibling pairs where older sibling was born within 60 days of the cutoff date.

Although many differences between family background subgroups are not significant at the 10% level, the estimates among disadvantaged families are more robust and have larger effect sizes than those of advantaged families. In addition, positive spillover effects are significantly larger at the 10% level for single-mother families compared to two-parent families. These results suggest that in advantaged families, compared to disadvantaged ones, not only there is a smaller effect on older siblings to begin with that can be spilled over to younger siblings (see Appendix Table A7), but also the proportion of the effect that spills over to younger siblings is smaller. Take the coefficients of total scores for high-versus low-poverty schools in middle school as an example: the proportions are 11.8% for advantaged families (0.013/0.11=0.118) and 30.6% for disadvantaged families (0.055/0.18=0.306). The difference in the magnitudes between students attending high-poverty schools (0.055) and low-poverty schools (0.013) is 0.042. This suggests that having an older sibling born shortly after the cutoff date improves the total test score of a younger sibling attending a high-poverty school by an additional 0.042 standard deviation compared to one attending a low-poverty school, which is roughly 8.3% of the gap in the mean test scores of young siblings between high-versus low-poverty schools.

An interesting observation here is that the coefficients of both reading and math scores for students in disadvantaged families are significant, whereas for those in advantaged families, only the coefficients of reading scores are often significant. One potential explanation is that there may be more role modeling in studying math from older siblings to younger siblings, or older siblings may be more effective in conveying positive attitudes to math learning in disadvantaged families than in advantaged families. Considering that there are typically more students from advantaged families than from disadvantaged families in our sample, the heterogeneous effects by family background explain our finding in Table 2 that sibling spillover effects are generally larger and more robust for reading scores than for math scores.

Because of the importance of the sixth grade, we also look at the patterns for spillover effects by family background just for this grade. Results are shown in Table 4. We find evidence at this point that sibling spillover effects are stronger among disadvantaged families compared to advantaged families. Specifically, the effects are larger in non-Hispanic Black families than in non-Hispanic White families, in single-mother families than in two-parent families, and for students attending schools with high-poverty levels than those attending schools with low-poverty levels. All these results support H2. Compared to whether a mother has a high school degree, maternal race, marital status, and school poverty levels are stronger proxies of the availability of positive adult male figures or high-performing peers in family and school environments. In the relative absence of these figures, an academically successful older sibling may make a greater difference as a much-needed positive role model and gateway to beneficial networks for developing educational goals. This finding is also consistent with existing psychological literature showing that parental characteristics tend to be less important to adolescents’ development compared to older siblings’ and peers’ (Ardelt and Day 2002), and that the difference in siblings’ time spent together by mothers’ educational attainment is small (Dunifon, Fomby, and Musick 2017).

Table 4:

Impact of Having an Older Sibling Born After School Entry Cutoff Date on Younger Sibling’s Test Scores in Grade 6, by Family Background

	Middle School
	Reading	Math	Total	p-value comparing Panels A and B in Column (3)
	(1)	(2)	(3)	(4)
Panel A: Socioeconomically Advantaged
Mother is non-Hispanic White	0.032**	0.032	0.030*	0.10
	(0.015)	(0.020)	(0.016)
N	36,461	36,344	37,022
Mother has a higher than high school degree at birth	0.058***	0.035	0.045**	0.89
	(0.022)	(0.021)	(0.019)
N	23,718	23,606	23,965
Mother is married at birth	0.032**	0.024	0.027*	0.01
	(0.016)	(0.016)	(0.014)
N	37,677	37,548	38,224
Low-poverty school	0.020	0.023	0.018	0.06
	(0.018)	(0.019)	(0.017)
N	24,525	24,452	24,890
Panel B: Socioeconomically Disadvantaged
Mother is non-Hispanic Black	0.079**	0.094***	0.086***
	(0.031)	(0.033)	(0.028)
N	13,508	13,493	13,818
Mother has a high school degree or lower	0.033* (0.018)	0.065*** (0.017)	0.048*** (0.016)
N	26,251	26,231	26,875
Mother is unmarried at birth	0.080*** (0.027)	0.130*** (0.027)	0.100*** (0.024)
N	12,292	12,289	12,616
High-poverty school	0.068*** (0.026)	0.077*** (0.021)	0.072*** (0.022)
N	25,444	25,385	25,950

Note:

^{***, **, and *}correspond to statistical significance at 1%, 5% and 10% level respectively. Standard errors are clustered by older sibling’s relative age. In all models, we control for whether older and younger sibling were born after cutoff date, older and younger siblings’ relative ages, conditions at the time of birth, school and school district characteristics, cohort fixed effects, and an interaction between older sibling’s relative age and whether they were born after cutoff date. The sample is restricted to sibling pairs where older sibling was born within 60 days of the cutoff date.

7. Auxiliary Analysis: Sibling Spillover Effects by Sibling Configuration

Because sibling spillover effects may depend on sibling configurations, we present subgroup analyses by sibling configuration variables. We first compare our results for siblings who are two or fewer years apart with those who are three or more years apart. On the one hand, closely spaced siblings may share more similar interests and peer networks, increasing the amount of social interactions, and the ability of younger siblings to relate to their older siblings and their experiences. On the other hand, larger age gaps may give older siblings greater authority and opportunities to take on teaching and leadership roles (Altonji, Cattan, and Ware 2017). Previous studies suggest that educational spillover effects tend to be larger when siblings are closely spaced (Joensen and Nielsen 2018; Nicoletti and Rabe 2019). Table 5 shows sibling spillover effects by sibling age gap and tests for equality of coefficients across panels. While the point estimates of spillover effects between closely spaced siblings are larger, we do not find significant differences between coefficients across panels. We have also conducted additional analyses considering the interaction effects between age spacing and family backgrounds, as siblings’ age spacing patterns may differ systematically across family backgrounds. Results are highly consistent with those in Table 3.

Table 5:

Impact of Having an Older Sibling Born After School Entry Cutoff Date on Younger Sibling’s Test Scores, by Age Gap

	Elementary School			Middle School
	Reading	Math	Total	Reading	Math	Total
	(1)	(2)	(3)	(4)	(5)	(6)
Panel A: Age gap <=2
Older sibling born after cutoff date	0.031	0.019	0.024	0.052*	0.028	0.041*
	(0.029)	(0.020)	(0.022)	(0.029)	(0.025)	(0.025)
N	18,063	18,092	18,146	17,390	17,414	17,446
Panel B: Age gap >2
Older sibling born after cutoff date	0.021	0.013	0.017	0.038**	0.026	0.030*
	(0.018)	(0.018)	(0.017)	(0.017)	(0.018)	(0.017)
N	36,559	36,630	36,732	35,137	35,175	35,257
Comparison between Panels A and B
p-value	0.74	0.81	0.74	0.66	0.94	0.71

Note:

^{***, **, and *}correspond to statistical significance at 1%, 5% and 10% level respectively. Standard errors are clustered by older sibling’s relative age. In all models, we control for whether older and younger sibling were born after cutoff date, older and younger siblings’ relative ages, conditions at the time of birth, school and school district characteristics, cohort fixed effects, and an interaction between older sibling’s relative age and whether older sibling was born after cutoff date. The sample is restricted to sibling pairs where older sibling was born within 60 days of the cutoff date.

We then look at heterogeneous effects across sibling sex compositions. Findings on the effect of sibling sex composition on academic outcomes have been mixed (Steelman et al. 2002), with more recent studies finding larger effects between brothers (Joensen and Nielsen 2018) and more generally between siblings of the same sex compared to those of different sexes (Nicoletti and Rabe 2019; Qureshi 2018). These results suggest that mixed-sex pairs in general may share fewer activities together, where sibling spillovers typically take place. Our results generally support these findings but also point to a more complicated picture, as shown in Table 6. We do not find unambiguously larger effect sizes between brothers compared to between sisters or between older sister/younger brother pairs. However, positive sibling spillover effects are significantly stronger for brother pairs compared to those for older brother/younger sister pairs. For the latter, the point estimates of spillover effects are even negative. One potential interpretation is that boys are favored to some extent over girls in many households due to gender norms, and therefore having an academically successful brother, particularly an older one, may lead parents to divert more resources to him (Powell and Steelman 1989, 1990).

Table 6:

Impact of Having an Older Sibling Born After School Entry Cutoff Date on Younger Sibling’s Test Scores, by Gender Composition

	Elementary School			Middle School
	Reading	Math	Total	Reading	Math	Total
	(1)	(2)	(3)	(4)	(5)	(6)
Panel A: Brothers
Older sibling born after cutoff date	0.022	0.033	0.030	0.071**	0.047*	0.057**
	(0.032)	(0.032)	(0.031)	(0.029)	(0.027)	(0.024)
N	13,537	13,568	13,624	12,944	12,970	13,002
Panel B: Sisters
Older sibling born after cutoff date	0.036	0.019	0.026	0.057**	0.043	0.050*
	(0.029)	(0.030)	(0.028)	(0.026)	(0.031)	(0.026)
N	12,634	12,631	12,666	12,089	12,082	12,109
Comparison between Panels A and B
p-value	0.75	0.73	0.91	0.70	0.93	0.84
Panel C: Older brother and younger sister
Older sibling born after cutoff date	−0.029	−0.033	−0.033	−0.0038	−0.027	−0.016
	(0.028)	(0.032)	(0.027)	(0.028)	(0.034)	(0.030)
N	14,367	14,382	14,411	13,839	13,850	13,872
Comparison between Panels A and C
p-value	0.22	0.14	0.13	0.06	0.10	0.06
Panel D: Older sister and younger brother
Older sibling born after cutoff date	0.056	0.042	0.047	0.037	0.039	0.039
	(0.036)	(0.031)	(0.032)	(0.035)	(0.033)	(0.033)
N	14,084	14,141	14,177	13,655	13,687	13,720
Comparison between Panels A and D
p-value	0.46	0.85	0.68	0.39	0.84	0.61

Note:

^{***, **, and *}correspond to statistical significance at 1%, 5% and 10% level respectively. Standard errors are clustered by older sibling’s relative age. In all models, we control for whether older and younger sibling were born after cutoff date, older and younger siblings’ relative ages, conditions at the time of birth, school and school district characteristics, cohort fixed effects, and an interaction between older sibling’s relative age and whether they were born after cutoff date. The sample is restricted to sibling pairs where older sibling was born within 60 days of the cutoff date.

8. Auxiliary Analysis: Relative Importance of Inter-Sibling Influence in Explaining Sibling Correlations

How much does inter-sibling influence explain sibling correlations in test scores? The category of inter-sibling influence increases this correlation and hence increases inequality between families beyond the contributions of shared family and community characteristics. Appendix A4 presents a formal model to better define the effect of inter-sibling influence on inequality among families.

Here, we focus on two comparisons that have important implications for inequality patterns in the United States: single-mother vs. two-parent families, White vs. Black families. We know a mother’s marital status at the time she gave birth, which could be informative of current single-mother household status. Since mothers’ marital statuses may subsequently change, the magnitude of the larger positive spillover effect found among siblings with unmarried mothers at birth likely underestimates the life-course effect of mothers’ marital statuses.

To estimate the relative importance of sibling spillovers, we examine how much younger siblings’ test scores will change if their older siblings’ test scores at the same school level improved by one standard deviation. This can be achieved by estimating an instrumental variable (IV) model if we assume having an older sibling born after the cutoff date affects a younger sibling’s test scores mainly through improving the older sibling’s test scores. This assumption can be strong considering that it is almost impossible to rule out all the other potential mechanisms, and therefore our IV results may be considered as an upper bound. In the IV model, the independent variable is older siblings’ test scores, the dependent variable is younger siblings’ test scores at the same school level, and the instrument is whether a child has an older sibling born right after the cutoff date. We use the same set of control variables. The interpretation of the IV estimates also makes it useful for comparison with estimates presented in previous studies (e.g. Joensen and Nielsen (2018), Qureshi (2018). Full results are provided in Appendix Table A9.

Figure 2 summarizes our findings for middle school students. The raw sibling correlation in middle school test scores is 0.55 in our sample. Interestingly, the magnitude is consistent with studies on sibling correlations in cognitive abilities in Europe and the United States (Anger and Schnitzlein 2017; Mazumder 2008; Paul 1980). The IV estimate of inter-sibling influence using the full sample is 0.16, which is generally comparable to the effect size of 11% of a SD in Nicoletti and Rabe (2019) based on an older sample of older siblings at age 16. These results suggest that nearly one third of the sibling correlation in test scores can be explained by inter-sibling influence (0.16/0.55 = 0.29). If we restrict the sample to siblings whose mothers were married at birth, the correlation in test scores is 0.54, which is just slightly smaller. The estimate of inter-sibling influence is 0.12, which suggests that approximately one fifth of the sibling correlation in test scores can be explained by inter-sibling influence (0.12/0.54 = 0.22). By contrast, the correlation between siblings whose mothers were unmarried at birth is much smaller (0.34). However, inter-sibling influence explains approximately 76% of the sibling correlation in test scores (0.26/0.34 = 0.76). One possible explanation for the greater relative importance of shared biological and environmental characteristics for two-parent families is that siblings in these families are more likely to have the same father, and hence have a greater genetic overlap.

Figure 2: Comparison of Sibling Correlations and Inter-Sibling Influences.

Similarly, if we compare non-Hispanic White with non-Hispanic Black families, the sibling correlation in test scores is larger in the former (0.53) compared to the latter (0.38), but inter-sibling influence accounts for 63% of the sibling correlation for non-Hispanic Blacks whereas it only accounts for 25% for non-Hispanic Whites. All these results suggest that sibling correlation in test scores is larger for advantaged families than disadvantaged families. While sibling correlation is mainly driven by shared biological, family, and community environments for advantaged families, it is mainly driven by inter-sibling influence for disadvantaged families.

8. Discussion and Conclusions

This study is the first to explore how sibling spillover effects in education vary by both school level and family background, measured by maternal education, race, marital status, and school poverty context. Using a North Carolina dataset which links birth certificate data to public school records, we compare test scores of students with older siblings born shortly before and after the school-entry cutoff date. We find that there are positive sibling spillovers on younger siblings in middle school but not in elementary school, and a quarter of a change in the older sibling’s academic performance spills over to younger siblings’ performance in middle school. The magnitude of the sibling spillover effect is comparable to approximately 6% of the Black-White achievement gap in the US. Assuming that older siblings’ school starting ages affect younger siblings’ test scores primarily through affecting older siblings’ educational performance, we estimate that sibling spillover effects account for approximately one third of observed statistical associations in test scores between siblings.

We also find that the positive spillover effects are larger among disadvantaged families than in advantaged families. Sibling correlations in test scores are stronger in advantaged families compared to the disadvantaged ones (Conley 2004), but in contrast with most existing theories that assume homogeneous sibling effects, our results show a larger absolute spillover effect among disadvantaged families. Hence, inter-sibling influence is not only stronger in an absolute sense but also accounts for a much larger share of the sibling correlation in test scores among disadvantaged families. In other words, sibling correlation in test scores for disadvantaged families is largely driven by inter-sibling influence whereas it is mainly driven by shared biological and environmental characteristics for advantaged families.

The big picture story of this study is the following: older siblings born shortly after the school-entry cutoff date delayed one year to enter schools, and therefore they became the oldest in their class. Because of the relative age, these older siblings tended to perform better in school. The improved academic performance among older siblings spilled over to their younger siblings in middle school, particularly among disadvantaged families, most likely through mechanisms such as sibling role modeling, attitudes towards schools, and parental investment decisions. Although we do not directly examine these mechanisms in this study, we find suggestive evidence that sibling role modeling might be a more important mechanism among disadvantaged families compared to advantaged families. For example, we find significant spillover effects from older to younger siblings on math scores, but not the other way around (see Appendix Table A5), which points to the importance of role modeling from older to younger siblings. However, the positive spillover effects on reading scores from younger to older siblings, shown in Appendix Table A5, suggest that role modeling is not the only mechanism, as this mechanism mostly occurs in older to younger sibling spillovers. The spillover effects from younger to older siblings are likely driven by contagious attitudes towards schools, and/or parental investment decisions favoring equality between siblings.

Our findings are consistent with existing evidence showing positive educational spillover effects from older to younger siblings among economically disadvantaged families (Karbownik and Ozek 2021; Qureshi 2018; Goodman et al. 2019). However, in contrast with most of these studies finding no spillovers among advantaged families, we find weaker but positive spillover effects among these families, especially for reading scores. The difference in the results may be due to differential identification strategies, family background measures, or local contexts. In previous studies, family background measures are mainly SES-focused, such as eligibility for reduced-price/free school lunches, parental education, neighborhood deprivation, immigration status, or probabilities of college enrollment. In this study, in addition to parental education and neighborhood deprivation (measured as school poverty level), we consider maternal race and marital status as important aspects of family backgrounds. More importantly, we further discussed the relative importance of inter-sibling influence in explaining sibling correlations in test scores in Black vs. White and single-mother vs. two-parent families, which, for the first time, explains how much the observed inequality between these families are shaped by inter-sibling influence.

There are several limitations of this study. First, results in this study apply specifically to public school children in North Carolina and may not be generalized to other settings. In the past decade, approximately 80% of students in North Carolina attend public schools.¹⁴ A large portion of the remaining 20% likely attend private schools or are home schooled and therefore are likely from more advantaged families than those in our sample.¹⁵ However, based on our finding that family SES appears to be negatively associated with sibling spillover effects, if students from private schools were added to our sample, the difference in sibling spillover effects between students from advantaged and disadvantaged families would have been even greater. Therefore, we may have underestimated the heterogeneity in sibling spillover effects. In addition, we are able to observe students who attended public schools in earlier grades but left public schools later. We find that these students tended to have relatively worse academic performance compared to those who stayed in public schools, but they did not necessarily have more advantaged family backgrounds. Restricting the sample to students who never left public schools gives highly consistent results as our main results.

In addition, North Carolina is relatively representative of the nation in many aspects, but is not in some other aspects. In Appendix Table A10, we compare key demographic, birth, and educational characteristics among students in North Carolina and in the nation. North Carolina is similar to the nation (i.e., the absolute difference in the means is smaller than 2) in terms of birth rate, infant birth weight, mother’s marital status at birth, proportion of children born in the United States, number of children in the household, birth spacing, and dropout rate among 9^th-12^th graders. However, compared to the nation, North Carolina has a higher proportion of non-White mothers, a slightly higher level of poverty rates among students, a lower proportion of students attending private elementary or secondary schools, and a higher rate of school suspension. Therefore, future studies in other locations with a broader range of family backgrounds represented are needed to confirm our results.

Second, compliance with the school-entry law was imperfect and was potentially stratified by family SES, which may account for part of the differences between advantaged and disadvantaged families observed in Figure 2. Although the Cragg-Donald F statistics (see Appendix Table A9) suggest that compliance to the school-entry law among advantaged families may be higher than that among disadvantaged families, Cook and Kang (2020) find that this relationship was confounded by academic ability. Using the same data from North Carolina, Cook and Kang (2020) find that boys with low academic ability from advantaged families, such as non-Hispanic White families, were most likely to redshirt. Through redshirting, these boys, who were born before the cutoff date, may have improved their academic performance, and therefore reduced the difference in test scores between those born shortly before and after the cutoff date among students from advantaged families. This smaller gap may translate into a smaller difference in their siblings’ test scores. By contrast, redshirting was much less likely among students from disadvantaged families, and therefore it has limited impacts on the estimated effects. As a result, the difference in sibling spillover effects between students from advantaged and disadvantaged families might be smaller than we estimated. However, it is unlikely to substantially bias our estimates because only 6.7% students started late (Cook and Kang 2020). In addition, because economic disadvantages appear to make little difference in the probability of non-compliance for females (Cook and Kang 2020), we provide a robustness check using only female samples in Appendix Table A11. Results further confirm that the differential sibling spillover effects we found by family background cannot be largely driven by SES-based selective non-compliance.

Third, due to data limitations, we were only able to examine individuals born to non-Hispanic White and non-Hispanic Black mothers in North Carolina. Future studies are needed to examine students from other racial/ethnic groups, as well as students who were born outside of North Carolina. Fourth, although the RD design provides causal estimates, our analyses are restricted to academic performance in elementary and middle schools. Future studies are needed to examine the long-term sibling spillover effects, such as the effect of older siblings’ school-entry ages on younger siblings’ high school performance, college attendance, and earnings. Finally, we adopt a reduced form approach to identify sibling spillover effects, which limits our ability to directly examine the relative importance of various mechanisms proposed in our theoretical framework. Future studies may consider adopting a structural approach or conduct randomized control trials to examine whether certain mechanisms are more important in disadvantaged families than advantaged families (for example, see Berry, Dizon-Ross, and Jagnani (2020)).

Despite these limitations, the findings of this paper have broader significance for social inequality. First, our results suggest that approximately one third of the strong resemblance between sibling cognitive ability documented in previous studies may be driven by inter-sibling influence. What does it mean to intergenerational transmission of (dis)advantages? Differential parental investment in children’s human capital is a major channel through which intergenerational inequality is shaped (Downey, Von Hippel, and Broh 2004; Schneider, Hastings, and LaBriola 2018). Previous studies estimated that parental investment of each additional year of education is associated with a 10.5 percent increase in children’s hourly earnings, assuming no sibling spillovers (Psacharopoulos and Patrinos 2018). Our results imply that returns to parental investment in children’s human capital should be even higher.

What does it mean to intragenerational transmission of advantages? The life course literature has documented the importance of early life conditions on later life outcomes. The sibling spillover effects found in middle school may lead to cumulative advantages later in life. Previous studies have estimated that children who perform one standard deviation better in school are 16 percentage points more likely to attend college (Dynarski, Hyman, and Schanzenbach 2013), and that a standard deviation increase in test scores is associated with higher future earnings by 5–9 percent (Watts 2020). Our finding that having an older sibling born shortly after the cutoff date is associated with an increase in a younger sibling’s total scores by 0.034 of a standard deviation thus translates to a higher probability of college attendance by 0.5 percentage points (0.034*16 = 0.544) and increased earnings by 0.2–0.3 percent. Considering that we are only capturing sibling spillovers associated with one source of variation in the performance of older siblings in this study, namely school starting ages, if the same fraction of all sources of variation spills over, sibling spillovers would be far greater. Hence, sibling spillovers provide an important additional channel through which inequality of wealth and income translates to inequality of social and economic opportunity for the next generation. We also show this more formally in Appendix A4.

Second, our results suggest that when bad things happen to older siblings, younger siblings in disadvantaged families suffer more compared to those in advantaged families. Existing studies have also shown that disadvantaged families, particularly older siblings in these families, are likely to suffer substantially from family tragedies such as illness, death, and parental unemployment (Conley 2004). This suggests that younger siblings in these families may not only directly suffer from family tragedies, but also experience negative spillovers from their older siblings. Some statistics from our data further confirm our argument that sibling spillover effects contribute to the gap in test scores among children in advantaged and disadvantaged families. Because we only find sibling spillover effects in middle school but not in elementary school, if our argument holds, we would expect the test score gap to be greater among children in middle school than those in elementary school due to negative spillovers in disadvantaged families in middle school. Indeed, we find test score gaps in our data for students from disadvantaged and advantaged families to be greater in middle school for all four aspects of family backgrounds. Therefore, it is important to provide a strong social safety net to disadvantaged families.

Conversely, our findings suggest that a public investment in educational achievement of the older sibling in a household will have the knock-on benefit of improving test scores of the younger sibling. This benefit will be particularly strong for Black, single-mom, and low-income families. For example, we estimated a much larger effect size for students attending high-poverty schools (0.055) than those in low-poverty schools (0.013, the difference is 0.042), which translates to an additional increase in the probability of college attendance by 0.7 percentage points (0.042*16 = 0.672, based on the estimates in Dynarski, Hyman, and Schanzenbach (2013)) and additional increase in earnings by 0.3 percent (0.042*8 = 0.336, based on the estimates in Watts (2020)). Therefore, investments such as smaller class sizes, which tend to benefit Black students more (Dynarski, Hyman, and Schanzenbach 2013), could be directed to help close the test-score gap among children in Black versus White, poor versus nonpoor, and single-mother versus two-parent households. In other words, it will benefit the kids we worry about the most.

Third, social scientists have used sibling correlations as a proxy to measure shared family and community environments over the past 30 years (Corcoran et al. 1990; Solon et al. 1991; Teachman 1995; Warren, Sheridan, and Hauser 2002). A related practice is the widely-adopted sibling fixed effects model aiming to remove variation due to shared family and community environments and, to some extent, genetic factors between siblings to obtain causal estimates. For these practices to be valid, the role of inter-sibling influence has to be small in explaining sibling correlations. Given the spillover effects found in this study and the heterogeneous patterns among families with different backgrounds, sibling correlations as a proxy for shared family and community environments and sibling fixed effects models may be biased, particularly for disadvantaged families. It might be possible to use the sibling spillover effects estimated in this study to correct the bias in sibling fixed effects models.

Fourth, this study contributes to the long-standing interest among sociologists in understanding how siblings affect individual outcomes (Dumont 1890; Galton 1874). Much of the focus in this line of research has been on the effect of sibling configuration, such as sibship size, sex composition, birth order, and birth interval, on individuals’ academic achievement (Steelman et al. 2002; Powell and Steelman 1990, 1993; Maralani 2008; Lu and Treiman 2008; Yu and Su 2006; Park 2008; Marteleto and de Souza 2012; Blake 1981, 1989). These structural variables, though important, do not explain the social and psychological processes through which siblings influence each other (Buhrmester and Furman 1990). Our study adds to this literature by looking at the role of policy interventions on siblings in explaining educational attainments conditional on sibling configuration variables, which provides us a better understanding of the underlying process of sibling influence on school achievement.

Finally, this study also ties into the literature on the effects of school starting age. Most existing studies in this literature have focused on the effects of school starting age on students’ own outcomes and their parents’ outcomes such as employment, income, and divorce (Black, Devereux, and Salvanes 2011; Fredriksson and Ockert 2005; Dee and Sievertsen 2018; Landersø, Nielsen, and Simonsen 2016; Landersø, Nielsen, and Simonsen 2019; Dhuey et al. 2019; Bernardi 2014), whereas spillover effects on other siblings are less studied. We are aware of only two existing studies that have examined the sibling spillover effects of school starting age, with one using data from Florida and the other using data from Denmark (Landersø, Nielsen, and Simonsen 2019; Karbownik and Ozek 2021). Our study adds to this literature by examining the spillover effects in a different context, where the percentages of non-Whites and single-mother households are much higher, and providing first comparisons by school levels between White and Black families as well as single-mother and two-parent families.

In addition, White males are more likely to have a relative age advantage because of the higher prevalence of redshirting practice (Cook and Kang 2020). This may create a relative age disadvantage for Black students, which may negatively affect their test scores and lead to negative spillovers on their younger siblings’ test scores. Policies increasing the absolute school starting ages by shifting the school-entry cutoff date have been shown to reduce the redshirting practice and therefore reduce the Black-White test score gap among boys in North Carolina (Cook and Kang 2020). This kind of policies are also likely to have positive sibling spillovers in Black families, further closing the racial achievement gap.