The Maternal and Sibling Spillover Effects in Educational Attainment

doi:10.21203/rs.3.rs-5263529/v1

This study rigorously examines educational spillovers within families using Inverse Prob- ability Weighted Regression Adjustment, Propensity Score Matching, and an innovative In- strumental Variable strategy. We find that children whose mothers have more than 12 years of schooling gain approximately 0.385 to 0.396 years of schooling, while younger siblings of firstborns with over 12 years of schooling gain 0.505 years. IV regressions further suggest that each additional year of maternal education leads to a 0.367-year increase in children’s schooling, and each additional year of firstborn’s education results in a 0.333-year gain for younger siblings. These results, robust across multiple estimation techniques, underscore the significant role of maternal and sibling education in shaping children’s outcomes. This study advances methodological approaches, enriches the literature on family influences in education, and offers new insights into the mechanisms driving educational attainment within families.

JEL classification: I21, I25, J13, J24

Maternal spillover effects

Sibling spillover effects

Education

Endogeneity

Economists have long been interested in estimating externalities in educational outcomes, rec- ognizing their importance for policymakers, educators, and parents when conducting cost-benefit analyses of public and private investments in education. Education externalities have been docu- mented in various contexts, such as school peer effects (Calvo´-Armengol et al., 2009; Goldsmith- Pinkham and Imbens, 2013; Lavy et al., 2012; Zimmerman, 2003), neighborhood effects (Bobonis and Finan, 2009; Lalive and Cattaneo, 2009; Wantchekon et al., 2015), and within-family spillovers (Black et al., 2005; Goodman et al., 2015; Nicoletti and Rabe, 2019; Qureshi, 2018; Gurantz et al., 2020; Dahl et al., 2020; Altmejd et al., 2021). While considerable attention has been given to spillovers in educational achievement and school major choices, spillovers in educational attain- ment remain less explored. This article aims to fill this gap by providing empirical evidence on family spillovers—both intergenerational and within-generational—in educational attainment.

A substantial body of literature highlights the significant role of family background in shap- ing educational success. Researchers have extensively explored the causal effects of various family characteristics, such as income, parents’ labor supply, and the home environment, on children’s ed- ucational outcomes (Blau, 1999; Acemoglu and Pischke, 2001; Ruhm, 2004; Blanden and Gregg, 2004; Cunha and Heckman, 2008; Dahl and Lochner, 2012; Duncan et al., 2011). However, rel- atively few studies have focused on establishing a causal relationship between the educational attainment of parents and that of their children. These studies generally do not report large causal effects of parental education, and as noted in the literature review by Holmlund et al. (2011), there are concerns about the validity of the identification strategies used. The three primary strategies include using differences in schooling between the children of twin parents, leveraging samples of adoptees, and employing education reforms as instrumental variables (IV). Each approach has potential limitations: the twin studies may suffer from unobserved heterogeneity bias; the use of adoptee samples could be subject to endogenous selection; and IV estimates using education reforms might be confounded by changes in other factors, such as teacher quality or concurrent re- forms, challenging the exclusion restriction. These challenges underscore the need for more robust

identification strategies.

In the context of sibling spillovers, numerous studies have documented significant sibling cor- relations across various socioeconomic outcomes using variance component models (Solon, 1999; Bjo¨rklund et al., 2002; Raaum et al., 2006; Mazumder, 2008; Nicoletti and Rabe, 2013). Bjo¨rklund and Salvanes (2011) write ‘The sibling correlation tells us what fraction of the total variance of years of schooling is attributable to factors that siblings share. Such factors can be of many differ- ent types, and include common genes, a common environment, and the influence of one sibling on another.’ Distinguishing causal sibling influence from these common factors like genetic transmis- sion or shared home environment has been notably challenging. It has been relatively recently that economists have focused on developing methodologies to estimate causal sibling spillover effects. Evidence of such influences has emerged in areas such as teenage substance use (Altonji et al., 2017), test scores (Nicoletti and Rabe, 2019), college choice (Aguirre and Matta, 2021; Good- man et al., 2015) and major choice (Dahl et al., 2020; Altmejd et al., 2021). However, empirical investigations of sibling spillover effects in educational attainment remain sparse. One notable exception is the study by Qureshi (2018), which finds that the schooling of the oldest sister sig- nificantly improves younger brothers’ literacy and years of schooling. This study leverages the distance to girls’ schools as an instrument, conditional on household location controls, to account for the gender segregation of schools in rural Pakistan.

Our study aims to provide an estimation of spillover effects within families by employing a rigorous identification strategy incorporating inverse-probability weighted regression adjustment (IPWRA), propensity-score matching (PSM), and a novel instrumental variable approach. For both IPWRA and PSM estimators, we use a logit model to predict treatment status based on an extensive list of individual ability and behavioral characteristics, as well as demographic, family, neighborhood, and school factors. Moreover, we construct our IV, inspired by the linear-in-means models of Manski (1993) and Bramoulle´ et al. (2009), using the educational expectations of moth- ers (or firstborns) and their best friends during adolescence. First, we model the best friend’s expectations as an outcome variable, using the mother’s (or firstborn’s) expectations as a predic-

tor while controlling for mother’s (or firstborn’s) individual and family characteristics, as well as school and neighborhood influences. The IV is derived from the residuals of this regression, cap- turing unexplained variation influenced by the best friend’s familial factors. This residual serves as our IV for the mother’s (or firstborn’s) educational attainment, aligning with the methodology used by Bramoulle´ et al. (2009) in leveraging peer characteristics as IVs.

For empirical analyses, we make use of data from the National Longitudinal Surveys of Youth. Our results indicate significant spillover effects of both maternal and firstborn educational attain- ment on children’s schooling. The treatment effect estimates show that when mothers have more than 12 years of schooling, their children’s average years of schooling increase by approximately

0.385 to 0.396 years, with the effect being somewhat stronger for those directly experiencing higher maternal education. Similarly, for younger siblings, the presence of a firstborn with more than 12 years of schooling results in an increase of about 0.505 years in their own schooling. These findings are supported by both IPWRA and PSM estimates and are robust against unobserved confound- ing. Additionally, IV regressions suggest that each additional year of maternal schooling leads to a 0.367-year increase in children’s schooling, while an additional year of schooling for the first- born corresponds to a 0.333-year increase in younger siblings’ schooling. The results highlight the dynamic nature of educational interactions among siblings, demonstrating that the strong correla- tion in siblings’ education observed in previous studies is attributable not only to intergenerational mobility but also to within-generation sibling interactions.

This study’s methodological rigor and comprehensive analysis represent significant contribu- tions to multiple strands of literature, particularly in the field of education. The study advances methodological approaches by introducing a new instrumental variable strategy. By integrating a combination of empirical strategies, we offer a nuanced analysis of the impact of educational attainment within families.

The study also contributes to the literature on family influences by presenting new evidence of significant maternal effects on children’s educational outcomes. Furthermore, to our knowledge, this is the first study to estimate the effects of sibling spillovers on educational attainment within the

U.S. context, emphasizing the dual role of firstborns as both educational role models and influential family members. While growing up together, siblings share somewhat similar family experiences and generational trends. Therefore, younger children in the family are likely to consider the oldest one as a constant reference point for competition or imitation. Our findings of this within-family peer effect contribute not only to the emerging literature of sibling spillovers but also to the widely studied peer-effect literature.

In sum, our research advances the understanding of intra-family educational dynamics, provid- ing valuable insights into the mechanisms of educational attainment. The methodological innova- tions and empirical findings presented here offer a deeper comprehension of educational external- ities, with implications for both theoretical frameworks and practical policy interventions aimed at improving educational outcomes across generations.

The paper proceeds as follows: Section 2 introduces the data, details the sample selection pro- cess, and presents descriptive statistics. Section 3 discusses the identification strategies employed to estimate the spillover effects of first-borns and mothers. Section 4 reports and interprets the findings. Finally, Section 5 offers concluding remarks. Additional descriptions of the variables and identification strategies are available in the online appendix.

This study utilizes data from two cohorts of the National Longitudinal Survey of Youth: the 1979 cohort (NLSY79) and Children and Young Adults cohort (NLSY79-CYA). The NLSY79- CYA follows the biological children of female respondents from the NLSY79 cohort. Starting in 1986, the NLSY79-CYA was conducted biennially as a single survey until 1994, when it split into two subcategories: Children and Young Adults.

The Children survey targets children under the age of 15, collecting data from either the child or the mother on behavioral, intellectual, and developmental characteristics. The Young Adult survey interviews individuals who were at least 15 years old by December 31 of the survey year, gathering information on education, employment, health, and social-psychological factors. Data collection for both surveys has continued biennially from 1986 to 2016.

Each child in the NLSY79-CYA can be linked to their mother in the NLSY79 files and to their siblings within the NLSY79-CYA dataset. This linkage allows for the comparison of achievement measures among siblings. As of 2016, the dataset includes 11,530 children born to 4,937 mothers from the NLSY79 cohort.

For the analysis of maternal spillover effects, each mother-child pair is treated as an obser- vation. For firstborn spillover effects, each pair of firstborn and younger sibling serves as an observation. Thus, two separate samples are prepared for estimating these effects, with identical restrictions applied to both.

To ensure that the highest level of schooling is accurately assessed, only individuals aged 35 or older as of 2016 are included in both samples. For younger children, we verify their school enrollment status in 2016 and previous survey years. Children who were not enrolled in school for at least two consecutive survey years are considered to have completed their education and are included in the samples. After applying these criteria and considering the available data for our variables, the final samples consist of 1,845 firstborn-younger sibling pairs for estimating sibling spillovers and 5,257 mother-child pairs for estimating maternal spillovers. Figure ?? in the online appendix presents the age distribution of children, mothers, firstborn, and younger siblings in the respective sample.

Descriptive statistics for key characteristics are summarized in Table 1. In the sample for es- timating maternal spillover effects, the average years of schooling completed by children is 13.15 years. Notably, 47.4% of mothers have more than 12 years of schooling. The average age of chil- dren in this sample is 32.16 years, while the average age of mothers is 55.76 years. The sample includes 44.8% White, 19.5% Hispanic, and 35.7% Black individuals, with an equal gender distri- bution among children (51% male). The sample comprises 4,692 children from 2,402 mothers.

In the sample for estimating firstborn spillover effects, the average years of schooling com- pleted by firstborns is 12.80 years, while younger siblings complete 12.80 years on average. The sample includes 66.7% firstborns with 12 years of schooling or less and 33.3% with more than 12 years. The average age of firstborns is 36.94 years, and younger siblings are on average 31.76 years old. The sample consists of 37.3% White, 21.1% Hispanic, and 41.6% Black individuals. Gender distribution among firstborns is balanced (50% male). The sample includes 1,020 firstborns and 1,669 firstborn-younger sibling pairs.

In this study, we investigate two distinct types of spillover effects in educational attainment:

(i) maternal spillover effects and (ii) firstborn spillover effects. While the inclusion of paternal education would enhance the analysis, data constraints preclude its integration. The NLSY79 Child and Young Adult dataset dataset offers extensive information on maternal education and related background characteristics but lacks comprehensive data on paternal education and background. This limitation is inherent in the dataset’s design, which prioritizes maternal attributes and their influence on child outcomes.

The interpretation of ordinary least squares (OLS) estimates of these spillover effects as causal is fraught with challenges due to potential biases. OLS estimates may be prone to omitted variable bias, given that children’s educational attainment is associated with a multitude of unobservable individual, family, and neighborhood factors. Additionally, OLS estimates may be affected by attenuation bias resulting from measurement errors, such as rounding inaccuracies prevalent in survey data. To mitigate these issues, we employ treatment-effects estimators and a novel in- strumental variable (IV) strategy. Our methodology is consistent for both maternal and firstborn spillover effects. Section 3.1 outlines our treatment-effects estimators, while Section ?? describes our IV estimator for identifying the spillover effects.

3.1 Treatment-Effects Estimators

Our outcome variable is the years of schooling of the child (laterborn), treated as a contin- uous variable for maternal (firstborn) spillovers. The treatments are binary. Utilizing data from NLSY, we categorize maternal spillover treatments into two levels: (i) mothers with 12 years of schooling and (ii) mothers with more than 12 years of schooling. In our sample, 2,470 mothers have completed 12 years of schooling, while 2,222 mothers have completed more than 12 years. For firstborn spillovers, the sample sizes of the two treatment groups are not as balanced. We have 1,113 firstborns who completed 12 years of schooling and 556 firstborns who completed more than 12 years.

Here, we present two methods for estimating treatment effects: one utilizes a doubly robust weighting estimator, while the other employs a matching estimator. ¹

Inverse-probability weighted regression adjustment (IPWRA) estimator: IPWRA estimators use weighted regression coefficients to compute averages of treatment-level predicted out- comes, where the weights are the estimated inverse probabilities of treatment. The contrasts of these averages estimate the treatment effects. IPWRA estimators have the double-robust property.
Propensity-score matching (PSM) estimator: PSM estimators impute the missing potential outcome for each subject by using an average of the outcomes of similar subjects that re- ceive the other treatment level. Similarity between subjects is based on estimated treatment probabilities, known as propensity scores. The treatment effect is computed by taking the average of the difference between the observed and potential outcomes for each subject.

We use the STATA teffects command (StataCorp, 2015) to estimate average treatment effects (ATEs) and average treatment effects on the treated (ATTs) for IPW and PSM estimators. For each estimator, we use a logit model to predict treatment status based on the variables listed in appendix Table ?? for maternal spillover effects and appendix Table ?? for firstborn’s spillover effects. The caliper is set to one-quarter of the standard deviation of the propensity score², with three matches per observation for estimating maternal spillover effects. Due to the relatively small sample size for firstborn’s spillover effects, we relax the caliper restriction while maintaining three neighborhood matches per observation. Figures 1a and 1b are provided to verify the overlap assumption. The blue line in figure 1a (1b) represents the estimated density of the predicted probabilities that a high school graduate mother (firstborn) is a high school graduate, while the red line shows the estimated density of the predicted probabilities that a higher educated mother (firstborn) is a high school graduate. There is nearly complete overlap between the two groups, and no treated or control persons have very high or low p-values. Therefore, there is no indication that the overlap assumption is violated. Based on the good overlap shown in this figure, we judged that it was not necessary to trim the sample based on the propensity score.

Appendix tables ?? and ?? check for covariate balance over treatment groups. The matched sample results indicate that both IPWRA and PSM estimators balanced the covariates. The stan- dardized differences are all close to zero, and the variance ratios are all close to one. The weighted standardized differences are all close to zero and the variance ratios are all close to one.

3.1.1 Instrumental Variable

To construct our IV, we utilize the mother’s report of her own and best friend’s educational expectations during adolescence³. Drawing on Manski (1993), we recognize that similarities in behavior within a peer group can arise due to three primary effects: (i) contextual effects—–the influence of peer group characteristics; (ii) the influence of peer outcomes; and (iii) correlated ef- fects—similar behaviors resulting from shared environments or characteristics among individuals in the same reference group. Bramoulle´ et al. (2009) consider an extended version of the linear-in- means model where each individual has his specific friendship group in a directed social network and model an individual’s outcome as a function of the mean of the corresponding outcome of his friends’ group, by his family background, by the mean family background of his friends’ group and network fixed effects, defined by the individuals whose mean outcome and characteristics influence his own outcome.

Informed by these perspectives, we construct an instrumental variable using two steps:

(i) We begin by modeling the mother’s report of her best friend’s educational expectations

during adolescence, E_jm ,r, as an outcome variable. Specifically, we consider the following:

Here, r denotes the network or the common environment that might influence both mother m and her best friend r’s expectations. E_m,r denotes mother m’s educational expectation dur- ing adolescence, X_m denotes a vector of m’s individual, demographic and family characteristics, N_r denotes a vector of mother m’s school and neighborhood characteristics during adolescence. Appendix Table ??⁴ presents a rich set of variables that we use as various measures of X_m and N_r. X_j represents the best friend j’s characteristics which are not observable in NLSY data and, finally, ψ_jm ,r represents idiosyncratic error. As a first step, we regress E_jm,r on E_m,r, X_m, and N_rto estimate the predicted educational expectations of the mother’s best friend,

(ii) Next, we derive the instrumental variable by focusing on the unexplained variation in the best friend j’s educational expectation. Specifically, we estimate j’s family background predictor of j’s educational expectation by taking the difference between the raw E_jm ,r and the predicted one, which is, in other words, the residual of equation (1):

This residual serves as our instrumental variable for mother m’s educational attainment. The rationale is that this residual—–being influenced by the best friend’s characteristics—–should cor- relate with the mother’s educational attainment by the same argument as in step (1). Importantly, since the residual has been purged of the mother’s own characteristics, as well as her family, school, and neighborhood influences, it should not be correlated with her child’s educational attainment. Essentially, our IV is along the lines of Bramoulle´ et al. (2009) who use peer-of-peer’s character-istics as IVs.

4.1 Maternal Spillover Effects

Table 2 presents the treatment effect estimates for maternal spillover effects on children’s schooling. The estimates are as follows: IPWRA ATE is 0.396, IPWRA ATT is 0.510, PSM ATE is 0.385, and PSM ATT is 0.580. All estimates are significant at the 1% level.

Table 2: Treatment Effects: Mother’s Education

This table presents treatment effects of maternal education using inverse-probability weighted regression adjustmen (IPW) and propensity score matching (PSM) estimators. For each estimator, we use a logit model to predict treatment status based on the variables listed in appendix Table ??. The caliper is set to one-quarter of the standard deviation of the propensity score with three matches per observation for estimating maternal spillover effects. Standard errors in parentheses. * p<0.1, ** p<0.05, *** p<0.01.

	IPWRA	PSM
ATE
Mother’s schooling: 12 years vs. >12 years	0.396***	0.385***
	(0.072)	(0.106)
ATT
Mother’s schooling: 12 years vs. >12 years	0.510***	0.580***
	(0.099)	(0.193)
N	4,692	4,692
Mean child’s years of schooling:
Mother’s schooling: 12 years	12.658	12.658
Mother’s schooling: >12 years	13.697	13.697

The ATE estimates suggest that, on average, children’s years of schooling increase by approx- imately 0.385 to 0.396 years (a little over 4.5 months) when their mothers complete more than 12 years of schooling compared to those whose mothers completed only 12 years. This increase represents around a 3% increase in years of schooling for children in families where mothers have completed 12 years relative to their mean of 12.658, this translates to an approximate increase to

13.05 years of schooling when the mother has more than 12 years of schooling. This effect is both statistically and economically significant.

The ATT estimates indicate that for children whose mothers completed more than 12 years of schooling, the increase in their years of schooling is approximately 0.510 to 0.580 years (around 6 to 7 months) on average, compared to if these same children had mothers who completed only 12

years of schooling.

The ATT estimates being higher than the ATE estimates suggests that the effect of mothers completing more than 12 years of schooling is stronger for those who actually experienced this higher level of maternal education than for the general population. This implies that children of more educated mothers benefit more than the average child would if their mother completed more than 12 years of schooling.

The consistency between the IPWRA and PSM estimates strengthens the credibility of these findings, providing robust evidence of the positive effect of maternal education on children’s schooling.

Table 3: Maternal Spillover Effects: OLS and IV estimate

This table presents OLS and IV estimates of maternal spillovers. The OLS model includes all covariates listed in appendix Table ??. In the IV model, the instrument is the residual from regressing the mother’s educational expectations during adolescence on her best friend’s educational expectations, along with all covariates listed in appendix Table ??. The control variables and their coefficient estimates for both the first and second stages of the IV regression in column (2) are provided in Table ??. Standard errors are shown in parentheses. * p<0.1, ** p<0.05, *** p<0.01.

	Child’s Schooling
	(1) OLS	(2) IV
Mother’s schooling	0.174*** (0.025)	0.368** (0.177)
First Stage:
IV		0.081*** (0.024)
Weak IV test: Cragg-Donald Wald F statistic		29.458
Kleibergen-Paap rk Wald F statistic		11.651
N	4,692	4,692
Mean child’s years of schooling:	13.150	13.150

Table 3 presents results from OLS and IV regressions where both the outcome variable (chil- dren’s years of schooling) and the main regressor of interest (mother’s years of schooling) are con- tinuous variables. The IV estimate suggests that an additional year of maternal schooling causes an increase of 0.367 years in children’s schooling. This effect is statistically significant at the 5% level. Relative to the mean child’s years of schooling of 13.150, this effect represents an increase to

13.49 years of schooling. The first stage of the IV regression yielded a coefficient of 0.080, signifi-

cant at the 1% level, and the Cragg-Donald Wald F statistic is 29.46, indicating that the instrument is relevant and provides a strong enough exogenous variation to identify the causal effect. In com- parison, the OLS estimate for the same relationship is 0.174, significant at the 1% level. The likely reason for the IV estimate to be larger is that the IV estimates the local average treatment affect for a sub-population that has larger treatment effects, whereas OLS estimates the average treatment effect over the entire population. The downward bias may also result from omitted variable bias or measurement error.

Next, we analyze the potential mechanisms by which a mother’s educational attainment in- fluences her children’s educational outcomes, focusing on four primary channels: family income, cognitive stimulation at home, emotional support at home, and the overall home environment. In NLSY data, we have repeated measures of these variables collected from 1986 to 2014.⁵ Table 4 presents the instrumental variables (IV) estimates for the effects of maternal education on these out- comes. The results suggest that a one-year increase in maternal schooling causes a 19.8% increase in family income, statistically significant at the 5% level. Higher family income can enhance chil- dren’s educational attainment by providing better educational resources and opportunities. More- over, a one-year increase in maternal schooling leads to a 39.8% of one standard deviation increase in the cognitively stimulating home environment, a 14.0% of one standard deviation increase in the emotional support at home, and a 43.5% of one standard deviation improvement in the overall home environment. The effects on cognitive and overall home environment are statistically signif- icant at the 10% level but the effect on the emotionally supportive environment is not statistically significant. These findings underscore the multifaceted ways in which a mother’s educational at- tainment can benefit her children’s educational outcomes, primarily through economic means and the enhancement of the home learning environment.

5The Home Observation Measurement of the Environment is the primary measure of the quality of a child’s home environment included in the NLSY79 child survey. More than 25 items are used to construct each of the measures of cognitive stimulation, emotional support and overall home environment that a child experiences at home. These items are reported either by the mother or the interviewer.

Table 4: Channels for Maternal Spillovers (IV Estimates)

The samples in columns 1, 2, 3 and 4 include repeated observations of mothers, who are included in the sample corresponding to Table 3, over different time periods. The IV is same as in Table 3 where the instru- ment is the residual from regressing the mother’s educational expectations during adolescence on her best friend’s educational expectations, along with all covariates listed in appendix Table ??. In column 1, for family income we add reported income of the child’s mother and her spouse from the following sources in year t: (i) wages, salary and tips; (ii) business and farm income; (iii) unemployment income; (iv) income from savings, net rental income, and social security income; (v) veteran benefits, worker compensation, and disability payments; (vi) welfare/AFDC, food stamps, Supplemental Security Income or other public assis- tance; and (vii) child support. The control variables included in the regression for column 1 are: mother’s race (categorized as Hispanic, Black, and Non-Hispanic/non-Black), the number of children in the family at year t (categorized as 1, 2, 3, and ≥ 4), mother’s marital status at time t, year fixed effects, and mother’s birth year fixed effects. For the outcome variables in columns 2, 3, and 4, we use the standardized scores for cognitive stimulation, emotional support, and overall home environment. Appendix Table ?? provides a brief description of these variables. The control variables added in the regressions for columns 2-4 include child i’s gender, age at time t, and all controls from column 1. Standard errors are robust, clustered at the family level, and reported in parentheses. p<0.1; p<0.05; p<0.01.

	(1) Log Family Income	(2) Cognitive Stimulation at Home	(3) Emotional Support at Home	(4) Overall Home Environment
Mother’s Years of Schooling	0.198**	0.398*	0.140	0.435*
	(0.095)	(0.207)	(0.149)	(0.241)
First Stage:
IV	0.073***	0.052**	0.047*	.047*
	(0.0024)	(0.024)	(0.024)	(0.024)
Weak IV test: Cragg-Donald Wald F statistic	76.212	23.327	18.154	22.478
N	18,021	10,518	10,108	12,230

4.2 Sibling Spillover Effects

Table 5 presents the treatment effect estimates for the effect of the firstborn’s educational at- tainment on the younger sibling’s years of schooling. The estimates are as follows: IPWRA ATE is 0.505, IPWRA ATT is 0.571, PSM ATE is 0.505, and PSM ATT is 0.656. All estimates are significant at the 1% level.

The ATE estimates suggest that younger siblings have, on average, about half a year more schooling in families where the firstborn has more than 12 years of schooling compared to those in families where the firstborn has exactly 12 years of schooling. The ATT estimates indicate an

Table 5: Treatment Effects: Firstborn’s Education

This table presents treatment effects of Firstborn’s education using inverse-probability weighted regression adjustmen (IPW) and propensity score matching (PSM) estimators. For each estimator, we use a logit model to predict treatment status based on the variables listed in appendix Table ??. The caliper is set to one-quarter of the standard deviation of the propensity score with three matches per observation for estimating maternal spillover effects. Standard errors in parentheses. * p<0.1, ** p<0.05, *** p<0.01.

	IPWRA	PSM
ATE
Firstborn’s schooling: 12 years vs. >12 years	0.506***	0.505***
	(0.102)	(0.109)
ATT
Firstborn’s schooling: 12 years vs. >12 years	0.571***	0.656***
	(0.129)	(0.146)
N	1,669	1,669
Mean younger sibling’s years of schooling:
First-born’s schooling: 12 years	12.412	12.412
first-born’s schooling: >12 years	13.567	13.567

increase of 0.571 to 0.656 years in schooling for younger siblings in families where the firstborn’s schooling exceeds 12 years.

Additional PSM analysis yields an ATT estimate of 0.656, significant at the 1% level, suggest- ing an even larger effect size, with younger siblings gaining 0.656 years of schooling when the firstborn has more than 12 years of schooling.

To assess the robustness of the PSM results to unobserved confounding, Rosenbaum bounds analysis is performed with gamma values up to 1.5. For gamma = 1, the results are significant, with a Hodges-Lehmann point estimate of 12 years and a confidence interval of 12 to 12 years. For gamma = 1.5, the results remain significant, with a point estimate of 12 to 13 years and a confidence interval of 12 to 13 years. These findings suggest that the PSM estimates are robust to moderate levels of unobserved bias.

In Table 6 the IV estimate of 0.333 provides further evidence of the positive impact of the firstborn’s educational attainment on the younger sibling’s years of schooling. The estimate in- dicates that each additional year of schooling for the firstborn is associated with an increase of

0.333 years in the younger sibling’s schooling, significant at the 1% level. This effect represents a 2.60% increase relative to the mean years of schooling for younger siblings, which is 12.797 years.

In contrast, the OLS estimate is 0.162, also significant at the 1% level. The larger IV estimate suggests that the OLS method may underestimate the true effect of the firstborn’s education on the younger sibling’s schooling. This underestimation could result from unobserved factors that positively correlate with both the firstborn’s and younger sibling’s educational attainment, such as parental involvement, family values towards education, or socioeconomic status. By using an instrumental variable, the IV approach mitigates this bias, providing a more robust estimate of the causal effect of the firstborn’s education on the younger sibling’s educational outcomes. The first stage of the IV regression yielded a coefficient of 0.100, significant at the 5% level, and the Cragg- Donald Wald F statistic is 11.33, indicating that the instrument is relevant and provides a strong enough exogenous variation to identify the causal effect.

Table 6: Firstborn’s Spillover Effects: OLS and IV estimate

This table presents OLS and IV estimates of firstborn’s spillovers. The OLS model includes all covariates listed in appendix Table ??. In the IV model, the instrument is the residual from regressing the firstborn’s educational expectations during adolescence on their best friend’s educational expectations, along with all covariates listed in appendix Table ??. The control variables and their coefficient estimates for both the first and second stages of the IV regression in column (2) are provided in appendix Table ??. Standard errors are shown in parentheses. * p<0.1, ** p<0.05, *** p<0.01.

	Younger Sibling’s Schooling
	(1) OLS	(2) IV
Firstborn’s schooling	0.162*** (0.030)	0.333*** (0.105)
First Stage:
IV		0.100** (0.043)
Weak IV test: Cragg-Donald Wald F statistic		11.335
N	1,669	1,669
Mean child’s years of schooling:	12.797	12.797

4.3 Discussion

The findings of this study provide compelling evidence of the significant and multifaceted spillover effects of both maternal and firstborn educational attainment on the schooling outcomes of children and younger siblings. These results offer a nuanced understanding of how educational attainment within a family can shape educational trajectories and highlight the critical role of family dynamics in influencing educational outcomes.

Our analysis reveals that a child remains in school for approximately one additional year for every three years of maternal schooling. This finding contrasts with previous research that reports minimal spillover effects of maternal education (Holmlund et al., 2011). Our results contribute new evidence suggesting that maternal education has a substantial influence on children’s educa- tional attainment, consistent with the broader literature emphasizing the importance of maternal education in enhancing child development outcomes (Becker, 1991; Chevalier, 2004).

We find that family income and the quality of the home environment are critical channels through which maternal education impacts children’s educational outcomes. This aligns with re- search indicating that maternal education fosters enriched home environments that promote cog- nitive development and academic success (Haveman and Wolfe, 1995; Magnuson, 2007). Edu- cated mothers are better positioned to provide improved educational resources, allocate family in- come towards superior schools, safer neighborhoods, and better nutrition (Oreopoulos et al., 2006). Moreover, this enrichment includes not only increased monetary resources but also a greater in- vestment of time in children’s educational activities (Duncan and Murnane, 2011; Guryan et al., 2008).

In comparison, our study highlights significant spillover effects from the firstborn’s education on younger siblings. The evidence of substantial firstborn effects highlights the dual roles that firstborns may assume—as both family members and educational role models. Growing up to- gether, siblings share similar family experiences and generational trends, leading younger children to view the oldest sibling as a key reference point for competition and imitation. This role as both a peer and a resource enhances the educational outcomes of younger siblings through produc-

tivity spillovers, imitation, and information sharing (Sacerdote, 2011; Nicoletti and Rabe, 2019). The firstborn’s influence thus complements the impact of maternal education, demonstrating the multifaceted nature of familial educational dynamics. These complementary effects suggest that educational policies should address both maternal education and the role of older siblings to max- imize educational outcomes across generations.

The findings indicate the need for targeted policy interventions to enhance educational out- comes. Current U.S. tax incentives, such as the American Opportunity Tax Credit and the Lifetime Learning Credit, mainly support college education but fall short in addressing high school com- pletion and the needs of low-income families. Effective approaches could include implementing tax credits tied to high school completion by the firstborn, leveraging positive spillover effects on younger siblings. Additionally, adopting policies similar to the U.K.’s Education Maintenance Allowance (EMA), which provides cash assistance to students meeting attendance and achieve- ment criteria, could improve school participation and educational outcomes (Dearden et al., 2009; Crawford and Greaves, 2012).

Furthermore, addressing the spillover effects of maternal education could be achieved by sup- porting mothers in pursuing continuing education or vocational training. This could include subsi- dized tuition, childcare support, and flexible scheduling options. Additionally, promoting family- friendly work policies, such as flexible working arrangements and parental leave, would support mothers in balancing work and educational pursuits. These measures would not only improve maternal educational attainment but also positively impact children’s educational outcomes by fostering a more supportive home environment.

This study rigorously explores the significant spillover effects of maternal and firstborn edu- cational attainment on the educational outcomes of children and their younger siblings. By em- ploying a robust identification strategy that integrates treatment-effects estimators, such as inverse-

probability weighted regression adjustment and propensity-score matching, alongside a novel in- strumental variable approach, we effectively address potential biases and uncover substantial edu- cational spillovers within families.

The results reveal that children whose mothers have more than 12 years of schooling experience an increase in their average years of schooling by approximately 0.385 to 0.396 years. Younger siblings also benefit significantly from the educational attainment of firstborns, with an observed gain of about 0.505 years in their own schooling. Instrumental variable estimates further support these findings, indicating that each additional year of maternal schooling leads to a 0.37-year in- crease in children’s schooling, while each additional year of schooling for the firstborn corresponds to a 0.33-year increase in younger siblings’ schooling. These findings underscore the critical role of both maternal and sibling education in shaping educational trajectories within families.

The strength of this study lies in its methodological rigor and the comprehensive analysis of intra-family educational dynamics. The results suggest that educational policies and interventions should consider the dual impact of maternal and sibling education to enhance educational outcomes across generations, thereby fostering broader educational and social benefits.

Author Contribution

All authors contributed to the study design. Material preparation, data collection and analysis were performed by S.F. The first draft of the manuscript was written by S.F. and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Data Availability

We use publicly available data from the National Longitudinal Survey of Youth (NLSY) and adhere to its usage policies. No ethical approvals were required for our use of this public data source

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1 For further See StataCorp (2015) where the descriptions are taken from.

2 A caliper of 0.25 standard deviations of the logit transformation of the propensity score is generally effective (Rosenbaum and Rubin, 1985; Stuart and Rubin, 2008).

3 During the first few rounds of the NLSY79 interview, respondents were asked the following questions about themselves and their best friend– ‘As things now stand, what is the highest grade or year you think you will actually complete?’ and ‘Now think about your best or closest friend. What is the highest grade or year of regular school that this friend wants to complete?’ The mothers in our sample were aged 14-20 in 1979. The mothers’ reports of their own and their best friend’s educational expectations to the NLSY interviewers, and their actual educational attainment, are over 30 years apart.

4 Appendix Table ?? presents the variables used to calculate residuals from a similar regression of the firstborn’s educational expectations during adolescence on the best friend’s expectations and the listed variables.

5 The Home Observation Measurement of the Environment is the primary measure of the quality of a child’s home environment included in the NLSY79 child survey. More than 25 items are used to construct each of the measures of cognitive stimulation, emotional support and overall home environment that a child experiences at home. These items are reported either by the mother or the interviewer.

No competing interests reported.

AppendixEducationSpillovers.docx

The Maternal and Sibling Spillover Effects in Educational Attainment

Status:

Version 1

Abstract

Figures

1 Introduction

2 Data

3 Identification of Spillover Effects

3.1 Treatment-Effects Estimators

3.1.1 Instrumental Variable

4 Results

4.1 Maternal Spillover Effects

Table 2: Treatment Effects: Mother’s Education

Table 3: Maternal Spillover Effects: OLS and IV estimate

Table 4: Channels for Maternal Spillovers (IV Estimates)

4.2 Sibling Spillover Effects

Table 5: Treatment Effects: Firstborn’s Education

Table 6: Firstborn’s Spillover Effects: OLS and IV estimate

4.3 Discussion

5 Conclusion

Declarations

Author Contribution

Data Availability

References

Footnotes

Additional Declarations

Supplementary Files

Status:

Version 1