JOB MARKET PAPER
Parental Investment and the Birth Order Gap in Cognitive Skill
Formation: The Role of Resource Dilution
Abstract
Siblings compete for limited parental time and financial resources, so that investments
available to each child decline as the number of children in the family increases. This
resource dilution is present for secondborns throughout their life, whereas firstborns have
the natural advantage of experiencing a period alone with parents. This paper shows that
resource dilution is a quantitively convincing mechanism to explain why firstborn children
tend to outperform their secondborn siblings on cognitive exams. Using a framework
similar to Del Boca, Flinn, and Wiswall (2014), structural estimates of the child quality
production function suggest an extra (counterfactual) year alone with parents for the
firstborn leads to a 0.12 standard deviation increase of the birth order gap in child quality
between the ages of 6 and 12. This effect accounts for a little over 1/3 of the observed gap
in cognitive ability test scores for a US representative sample of two-child families of white
mothers from the (C)NLSY79. Investment spillovers between siblings add to the dynamic
impacts of resource dilution and make the uplift of the firstborn’s relative position persist
over time.
1 Introduction
Earlier-born children tend to outperform their younger siblings on measures of academic
achievement and labor market outcomes.1 An important determinant of birth order differences
in cognitive ability test scores has been attributed to the level of parental investment received
by siblings in early childhood (see Pavan, 2016; Lehmann, NuevoChiquero, and Vidal-
Fernandez, 2018). However, the mechanism that leads parents to invest relatively less in later-
born children remains unclear. This paper proposes that the decline in per-child parental inputs
as the number of children in the family increases explains a quantitively convincing share of the
1 See, for instance, Kantarevic and Mechoulan (2006), Booth and Kee (2009), Black, Devereux, and Salvanes
(2005), Black, Devereux, and Salvanes (2011), Hotz and Pantano (2015), Pavan (2016), Lehmann, Nuevo-Chiquero,
and Vidal-Fernandez (2018), Bagger et al. (2020). On the noncognitive side, Black, Grönqvist, and Öckert (2018)
document birth order effects on personality traits, while Breining et al. (2020) find that among boys, the secondborn
is more likely to develop delinquent behavior than the firstborn.
1
,birth order gap in cognitive ability scores observed at ages when children attend elementary
school. While both siblings are alive, they compete for limited parental time and financial
resources, so the investment accrued to each child declines. This effect is present for secondborn
children throughout their life, whereas firstborns experience a period without resource dilution.
Relying on information about parental investments and children’s cognitive ability test
scores from the Children of the National Longitudinal Survey of Youth (CNLSY79), structural
estimates of a child quality production function are obtained using a framework similar to Del
Boca, Flinn, and Wiswall (2014). To measure how resource dilution generates a birth order gap
in cognitive ability, I simulate a counterfactual time delay between births in a two-child
household choice model where parents invest in the production of children’s quality. Results
suggest that an extra year spent alone with parents for the firstborn leads to a 0.12 standard
deviation increase of the birth order gap in child quality between the ages of 6 and 12. This
resource dilution effect accounts for a little over 1/3 of the observed gap in standardized
cognitive ability test scores for a US nationally representative sample of two-child families of
white mothers.
Moreover, predictions from the model indicate that a longer delay between births generates
an uplift of the relative position in accumulated child quality for the firstborn, while that of the
secondborn remains broadly unchanged. This asymmetric birth spacing effect across siblings is
in line with causal estimates of Buckles and Munnich (2012), who instrument the time between
births using variation in whether a miscarriage is experienced during that period. Approximately
50% of the cognitive ability score gap implied by their causal birth spacing estimates can be
explained by the dynamic impacts of an extra year without having to compete for parental
resources for the firstborn in the model.
The role of parental investment as determinant of birth order differences in cognitive ability
scores is among several proposed mechanisms2. Pavan (2016) demonstrates the importance of
considering the dynamic impacts of parental investment to explain the observed birth order gap
in later childhood. By allowing the child development process to depend on past development
2 The confluence model (Zajonc and Markus, 1975; Zajonc, 1976) proposes that child development depends on
the average intelligence level of the household, detrimental to later-born siblings in families of larger sibship size.
Ejrnæs and Pörtner (2006) show that birth order effects can arise from an optimal stopping fertility behavior based
on the genetic endowments of children. Price (2008) observes that the overall involvement in children decreases over
time, which advantages earlier-born siblings. Hotz and Pantano (2015) show that parents illustrate a more stringent
disciplinary attitude towards the firstborn to deter bad behavior in later-born children. Works in evolutionary
psychology (Sulloway, 1995) also explore determinants of birth order effects, while medical outcomes are attributed
in specific settings (Jayachandran & Pande, 2017).
2
,stages, parental inputs in early childhood can have lasting and multiplying effects on the path of
human capital accumulation.
In addition to the dynamic impacts of child-specific parental inputs, this paper considers a
child quality production function with spillovers from investment directed to the other sibling.
Model predictions suggest that more than 1/3 of the superior accumulated child quality retained
by the firstborn from the period spent alone with parents is explained by spillovers from parental
inputs dedicated to the second child. Even if parents find it more productive to invest in the
secondborn when both siblings are alive, the birth order gap persists over time because the
firstborn benefits from a share of investments directed to her/his younger sibling. Moreover,
spillovers have a dual role in the model in that they introduce economies of scale in parental
investments. As opposed to the case considering only child-specific inputs in the production
function, the scale effects make it such that the per-child level of investment in the model is not
restricted to fall after the second child’s birth.
Following Del Boca, Flinn, and Wiswall (2014) and Caucutt et al. (2020), the structural
estimation of the child quality production function accounts for measurement error in the
mapping between child quality and cognitive ability test scores, the opportunity costs of time
and expenditure inputs in children, and their substitutability/complementarity. Although actual
time and expenditure in children are not directly observed in the CNLSY79, parental input
choices in the model are tied to corresponding items of the Home Observation Measurement of
the Environment (HOME), extending the approach utilized by Del Boca, Flinn, and Wiswall
(2014) to measure child quality from observed cognitive ability test scores.
The proposition advanced by this paper ties the birth order gap in cognitive ability scores to
the natural advantage of the firstborn to enjoy the early years of her/his life without having to
compete for parental resources. After accounting for economies of scale in parental investments,
structural estimates of the child quality production function suggest that the second child never
receives an equivalent level of inputs. Counterfactual simulations of the model predict that the
longer this advantage lasts for the firstborn, the more distant the relative position with her/his
sibling becomes in terms of accumulated child quality at any given age. This result is a direct
implication of findings by Cunha and Heckman (2008) and Cunha, Heckman, and Schennach
(2010), who demonstrate that the cognitive (and non-cognitive) skill formation process is to a
large extent shaped by the early childhood environment. This paper adds to the study of how
fertility timing impacts disparities in parental investment and academic achievement across
siblings (Price, 2008, 2010; Buckles and Munnich, 2012) and relates more generally to the
3
, family quantity-quality trade-off (Becker and Lewis, 1973; Becker and Tomes, 1976; Hanushek,
1992) and resource dilution theories (Blake, 1981; Downey, 1995, 2001).
Section 2 proceeds with a description of the data and a reduced form analysis motivating the
structural environment. Section 3 presents the model, with a focus on the structural determinants
of per-child investments before and after the second child’s birth. Section 4 covers the details
of measurement, identification and estimation of the model parameters. The interpretation of
the parameter estimates governing the child quality production function is presented in section
5, joint with the sample fit and external validity of model predictions. In section 6, the resource
dilution effect is measured, followed by a brief discussion on implications for family-related
policies. Section 7 concludes.
2 Data
This section presents the data and describes key features that motivate the structural approach
used to measure how resource dilution generates a birth order gap in cognitive ability. For two-
child families of white mothers, I document that the per-child level of parental investments
declines after the second child’s birth. Families with longer time between births illustrate larger
birth order gaps in average measures of parental investments and cognitive skills. While
financial expenditures are similar across siblings, firstborns benefit from having more time spent
on them over childhood.
Sample Description
This study uses mother-child matched data from the National Longitudinal Survey of Youth
1979 (NLSY79) and the Children of the NLSY79 (CNLSY79). The NLSY79 is a US nationally
representative panel of 12,686 respondents aged between 14 and 21 in 1979. Respondents were
surveyed periodically throughout their lives on education, labor market outcomes, family
structure, and other background characteristics.
The CNLSY79 follows 11,504 children of 79% of mothers in the NLSY79, surveyed from
an early age up to their early adult life. For this study, useful variables consist of the Home
Observation Measurement of the Environment (HOME), household background characteristics,
and a rich set of cognitive ability test scores. HOME scores consist of child-specific proxies for
the level of parental investment. They are constructed by summing 0-1 recoded measures on
criteria such as the time parents spend reading to a child, the number of books the child has
access to, or the number of times the child is taken to an outing, among others. Items that
4
Parental Investment and the Birth Order Gap in Cognitive Skill
Formation: The Role of Resource Dilution
Abstract
Siblings compete for limited parental time and financial resources, so that investments
available to each child decline as the number of children in the family increases. This
resource dilution is present for secondborns throughout their life, whereas firstborns have
the natural advantage of experiencing a period alone with parents. This paper shows that
resource dilution is a quantitively convincing mechanism to explain why firstborn children
tend to outperform their secondborn siblings on cognitive exams. Using a framework
similar to Del Boca, Flinn, and Wiswall (2014), structural estimates of the child quality
production function suggest an extra (counterfactual) year alone with parents for the
firstborn leads to a 0.12 standard deviation increase of the birth order gap in child quality
between the ages of 6 and 12. This effect accounts for a little over 1/3 of the observed gap
in cognitive ability test scores for a US representative sample of two-child families of white
mothers from the (C)NLSY79. Investment spillovers between siblings add to the dynamic
impacts of resource dilution and make the uplift of the firstborn’s relative position persist
over time.
1 Introduction
Earlier-born children tend to outperform their younger siblings on measures of academic
achievement and labor market outcomes.1 An important determinant of birth order differences
in cognitive ability test scores has been attributed to the level of parental investment received
by siblings in early childhood (see Pavan, 2016; Lehmann, NuevoChiquero, and Vidal-
Fernandez, 2018). However, the mechanism that leads parents to invest relatively less in later-
born children remains unclear. This paper proposes that the decline in per-child parental inputs
as the number of children in the family increases explains a quantitively convincing share of the
1 See, for instance, Kantarevic and Mechoulan (2006), Booth and Kee (2009), Black, Devereux, and Salvanes
(2005), Black, Devereux, and Salvanes (2011), Hotz and Pantano (2015), Pavan (2016), Lehmann, Nuevo-Chiquero,
and Vidal-Fernandez (2018), Bagger et al. (2020). On the noncognitive side, Black, Grönqvist, and Öckert (2018)
document birth order effects on personality traits, while Breining et al. (2020) find that among boys, the secondborn
is more likely to develop delinquent behavior than the firstborn.
1
,birth order gap in cognitive ability scores observed at ages when children attend elementary
school. While both siblings are alive, they compete for limited parental time and financial
resources, so the investment accrued to each child declines. This effect is present for secondborn
children throughout their life, whereas firstborns experience a period without resource dilution.
Relying on information about parental investments and children’s cognitive ability test
scores from the Children of the National Longitudinal Survey of Youth (CNLSY79), structural
estimates of a child quality production function are obtained using a framework similar to Del
Boca, Flinn, and Wiswall (2014). To measure how resource dilution generates a birth order gap
in cognitive ability, I simulate a counterfactual time delay between births in a two-child
household choice model where parents invest in the production of children’s quality. Results
suggest that an extra year spent alone with parents for the firstborn leads to a 0.12 standard
deviation increase of the birth order gap in child quality between the ages of 6 and 12. This
resource dilution effect accounts for a little over 1/3 of the observed gap in standardized
cognitive ability test scores for a US nationally representative sample of two-child families of
white mothers.
Moreover, predictions from the model indicate that a longer delay between births generates
an uplift of the relative position in accumulated child quality for the firstborn, while that of the
secondborn remains broadly unchanged. This asymmetric birth spacing effect across siblings is
in line with causal estimates of Buckles and Munnich (2012), who instrument the time between
births using variation in whether a miscarriage is experienced during that period. Approximately
50% of the cognitive ability score gap implied by their causal birth spacing estimates can be
explained by the dynamic impacts of an extra year without having to compete for parental
resources for the firstborn in the model.
The role of parental investment as determinant of birth order differences in cognitive ability
scores is among several proposed mechanisms2. Pavan (2016) demonstrates the importance of
considering the dynamic impacts of parental investment to explain the observed birth order gap
in later childhood. By allowing the child development process to depend on past development
2 The confluence model (Zajonc and Markus, 1975; Zajonc, 1976) proposes that child development depends on
the average intelligence level of the household, detrimental to later-born siblings in families of larger sibship size.
Ejrnæs and Pörtner (2006) show that birth order effects can arise from an optimal stopping fertility behavior based
on the genetic endowments of children. Price (2008) observes that the overall involvement in children decreases over
time, which advantages earlier-born siblings. Hotz and Pantano (2015) show that parents illustrate a more stringent
disciplinary attitude towards the firstborn to deter bad behavior in later-born children. Works in evolutionary
psychology (Sulloway, 1995) also explore determinants of birth order effects, while medical outcomes are attributed
in specific settings (Jayachandran & Pande, 2017).
2
,stages, parental inputs in early childhood can have lasting and multiplying effects on the path of
human capital accumulation.
In addition to the dynamic impacts of child-specific parental inputs, this paper considers a
child quality production function with spillovers from investment directed to the other sibling.
Model predictions suggest that more than 1/3 of the superior accumulated child quality retained
by the firstborn from the period spent alone with parents is explained by spillovers from parental
inputs dedicated to the second child. Even if parents find it more productive to invest in the
secondborn when both siblings are alive, the birth order gap persists over time because the
firstborn benefits from a share of investments directed to her/his younger sibling. Moreover,
spillovers have a dual role in the model in that they introduce economies of scale in parental
investments. As opposed to the case considering only child-specific inputs in the production
function, the scale effects make it such that the per-child level of investment in the model is not
restricted to fall after the second child’s birth.
Following Del Boca, Flinn, and Wiswall (2014) and Caucutt et al. (2020), the structural
estimation of the child quality production function accounts for measurement error in the
mapping between child quality and cognitive ability test scores, the opportunity costs of time
and expenditure inputs in children, and their substitutability/complementarity. Although actual
time and expenditure in children are not directly observed in the CNLSY79, parental input
choices in the model are tied to corresponding items of the Home Observation Measurement of
the Environment (HOME), extending the approach utilized by Del Boca, Flinn, and Wiswall
(2014) to measure child quality from observed cognitive ability test scores.
The proposition advanced by this paper ties the birth order gap in cognitive ability scores to
the natural advantage of the firstborn to enjoy the early years of her/his life without having to
compete for parental resources. After accounting for economies of scale in parental investments,
structural estimates of the child quality production function suggest that the second child never
receives an equivalent level of inputs. Counterfactual simulations of the model predict that the
longer this advantage lasts for the firstborn, the more distant the relative position with her/his
sibling becomes in terms of accumulated child quality at any given age. This result is a direct
implication of findings by Cunha and Heckman (2008) and Cunha, Heckman, and Schennach
(2010), who demonstrate that the cognitive (and non-cognitive) skill formation process is to a
large extent shaped by the early childhood environment. This paper adds to the study of how
fertility timing impacts disparities in parental investment and academic achievement across
siblings (Price, 2008, 2010; Buckles and Munnich, 2012) and relates more generally to the
3
, family quantity-quality trade-off (Becker and Lewis, 1973; Becker and Tomes, 1976; Hanushek,
1992) and resource dilution theories (Blake, 1981; Downey, 1995, 2001).
Section 2 proceeds with a description of the data and a reduced form analysis motivating the
structural environment. Section 3 presents the model, with a focus on the structural determinants
of per-child investments before and after the second child’s birth. Section 4 covers the details
of measurement, identification and estimation of the model parameters. The interpretation of
the parameter estimates governing the child quality production function is presented in section
5, joint with the sample fit and external validity of model predictions. In section 6, the resource
dilution effect is measured, followed by a brief discussion on implications for family-related
policies. Section 7 concludes.
2 Data
This section presents the data and describes key features that motivate the structural approach
used to measure how resource dilution generates a birth order gap in cognitive ability. For two-
child families of white mothers, I document that the per-child level of parental investments
declines after the second child’s birth. Families with longer time between births illustrate larger
birth order gaps in average measures of parental investments and cognitive skills. While
financial expenditures are similar across siblings, firstborns benefit from having more time spent
on them over childhood.
Sample Description
This study uses mother-child matched data from the National Longitudinal Survey of Youth
1979 (NLSY79) and the Children of the NLSY79 (CNLSY79). The NLSY79 is a US nationally
representative panel of 12,686 respondents aged between 14 and 21 in 1979. Respondents were
surveyed periodically throughout their lives on education, labor market outcomes, family
structure, and other background characteristics.
The CNLSY79 follows 11,504 children of 79% of mothers in the NLSY79, surveyed from
an early age up to their early adult life. For this study, useful variables consist of the Home
Observation Measurement of the Environment (HOME), household background characteristics,
and a rich set of cognitive ability test scores. HOME scores consist of child-specific proxies for
the level of parental investment. They are constructed by summing 0-1 recoded measures on
criteria such as the time parents spend reading to a child, the number of books the child has
access to, or the number of times the child is taken to an outing, among others. Items that
4
