Modern Marriage:
Labor Market Sorting and the
Intergenerational Transmission of Health†
Molly K Candon‡
University of Georgia
September 22, 2015
†
Special thanks to Ian Schmutte, David Bradford, David Mustard, and Jon Baio. Some data are generously
provided by the Autism and Developmental Disabilities Monitoring Network. Reported findings do not represent any position of the Center for Disease Control and Prevention. All errors are my own.
‡
Department of Public Administration and Policy, 203D Baldwin Hall, Athens, GA 30602, mkcandon@uga.edu
Abstract
This paper explores the labor market’s role in assortative mating and the intergenerational transmission of health. To begin, I develop a model of marriage in which agents
sort in labor markets based on their genetics and skill, thereby increasing the likelihood that they match with a genetically similar agent. Wages, the dispersion of skill,
and moving costs can induce agents to directly change sectors and indirectly change
the next generation’s genetic composition. For additional motivation, I then estimate
the mental, physical, cognitive, and noncognitive skill composition within and across
marriages using couples in the Current Population Survey and skill measures from the
O*NET Content Model. I assume that these measures serve as a proxy for one’s underlying genetic make-up. There is more similarity by mental and cognitive skill, both of
which enjoy a higher conditional correlation with earnings than physical and noncognitive skill. Additionally, I find that broad segments of the labor market sort differently
along these dimensions. Finally, I ask whether children and adolescents’ mental health
outcomes are driven, at least in part, by their parents’ assortative mating by skill.
Given data limitations, I employ two separate empirical strategies. First, I consider
a development psychological theory that argues autism is associated with assortative
mating by the ability to systemize and empathize. Using the CDC’s Autism and Developmental Disabilities Monitoring Network, I find higher rates of autism in Census
tracts with a more systemizing strength. Second, I extend the theory to other mental
health disorders, including ADHD, anxiety disorders, and mood disorders. Using the
Medical Expenditures Panel Survey, I find that a parent’s mental and noncognitive skill
measure has a significant and positive relationship with the incidence of any mental
disorder in their children, though the relationship is subject to diminishing returns.
Combined, the results of this paper suggests an unexplored research arc: as we play to
our comparative advantage, are we also shaping public health?
JEL Codes: J12, J13, J24, I19
Keywords: Marriage, Labor Market Sorting, Children, Skills, Mental Health
“Selection is probably the most important factor in evolution.”
(Cavalli-Sforza & Bodmer 1971, 44)
1
Introduction
The labor market influences who we meet, how we’re similar, when and with whom we have
children, and the traits that we pass on from generation to generation. In this paper, I ask
whether labor market sorting segments the ‘modern’ marriage market, thereby increasing
positive assortative (non-random) mating and shaping the intergenerational transmission
of health. In particular, I focus on parental sorting by different occupational-specific skill
measures in an attempt to explain children and adolescents’ mental disorders, currently “the
most prevalent and costly of all chronic illnesses in youth” (Blau et al. 2010).
Marriage and mating have changed substantially in the last half century. Access to
tertiary education and the work force in developed countries increases the likelihood that
labor market sorting occurs before one marries and/or has a child, especially if the median
age at first marriage and first child continues to rise (Baker & Vélez 1996; Hymowitz et al.
2013). In particular, women’s attachment to the labor market has grown precipitously. In
1950, 68 percent of married women stayed at home. By 2012, 30 percent of married women
stayed at home (Thompson 2012). An increase in women’s relative wages has likely induced
positive selection into the labor market; the falling wage gap is discussed by Mulligan and
Rubinstein (2008), who show that women’s selection was negative in the 1970s and positive
in the 1990s. The diffusion of easy and affordable birth control has also led to increased
and prolonged labor market participation and further delays of marriage for women, as
documented by Goldin and Katz (2002).
For additional motivation, consider the original genetic theory of assortative mating
developed by Fisher (1918) and Wright (1921).
The tendency toward phenotypic similarity of mating pairs may be a direct consequence of genetic relationship. For example, in a subdivided population there
will generally be a greater phenotypic similarity among the members because
they share a common ancestry [...] On the other hand, there may be assortative
mating based on similarity for some trait, and any genetic relationship is solely
the consequence of similar phenotypes (Crow & Felsenstein 1968, 85).
A phenotype is any observable trait, while a genotype includes every inherited instruction of
the genetic code. Extending this definition to marriage, there are two types of sorting that
1
influence positive assortative mating. First, marriage markets are defined over “a subdivided
population” due to a variety of institutional factors – including labor market sorting. As
such, individuals with similar occupational-specific traits are more likely to meet, match,
and have children. Second, individuals can directly observe traits and any match may be
“solely the consequence of similar” traits. Positive assortative mating has important genetic
implications because it often decreases genotypic variance, allowing recessive genes to be
expressed (Crow & Felsenstein 1968).
The ‘classic’ marriage market, first developed by Becker (1974), only models the
second route to an assortative match: agents observe a trait, then match positively or negatively on that trait. While a number of papers have since incorporated a labor market into
the marriage decision, many assume marital outcomes occur before labor market outcomes,
as in Chiappori (1992) and Choo, Seitz, and Siow (2008), or that marital and labor market outcomes are determined simultaneously, as in van der Klaauw (1996). Labor market
sorting should be considered in any model of assortative mating – it can affect the genetic
distribution of a population because it segments the marriage market, typically decreasing
within-group variance and increasing between-group variance.
As a first step, I develop a stylized model of ‘genetic output,’ a term I use to describe
the intergenerational transmission of genotypes. Agents sort in labor markets based on
their phenotype, thereby increasing the likelihood that they match with agents with similar
genotypes. Wages, the dispersion of skill, and moving costs can induce agents to directly
change sectors and indirectly change the next generation’s genotype. For example, suppose
a sector experiences an increase in wages due to a change in consumer tastes: if certain
individuals have phenotypes that are well-suited to the tasks rewarded in that sector, they
are more likely to select the sector and match with genetically similar individuals.
I then consider the relationship between labor market characteristics and assortative
mating. In particular, I use couples in the Current Population Survey and their respective
occupational-specific skill measures from the O*NET Content Model to estimate the mental
and physical skill composition within marriages. O*NET measures different task requirements by occupation; I assume that these characteristics are correlated with individuals’
phenotypes, thus serving as proxies for individuals’ genotypes. There is consistently more
sorting on mental skill, which enjoys a higher conditional correlation with earnings. Sorting
by physical skill is positive but smaller in magnitude, which coincides with a lower conditional correlation with earnings. This suggests that characteristics of the labor market can
induce sorting by skill, and therefore, sorting by genotype. Overall, there is more assorta-
2
tivity on each skill measure than earnings and less assortativity on each skill measure than
age and education.1
In addition to mental and physical skill, I examine sorting by cognitive and noncognitive skill. Cognitive skill is defined as general intelligence, while noncognitive skill refers to
personality traits that may be correlated with cognitive skill, including persistence, empathy,
and dependability. Sorting by cognitive and noncognitive skill plays a crucial role in today’s
labor market because technology continues to increase the return to mental specialization.
According to Autor and Dorn (2013), “computerization has reduced the demand for [middleskilled] jobs, but it has boosted demand for workers who perform ‘nonroutine’ tasks that
complement the automated activities.” Most high-skilled occupations require the ability to
think abstractly and problem solve using “intuition, persuasion, and creativity” that no computer can (currently) replicate. The literature has yet to cleanly divide occupational-specific
skill measures between cognitive and noncognitive skill. In this paper, I use inductive reasoning, perceptual speed, analyzing data, mathematical ability, and creativity to construct
cognitive skill and persuasion, interpersonal skill, judgment and decision making, time management, and assisting others to construct noncognitive skill. I consistently find more sorting
on cognitive skill than noncognitive skill. Like mental skills at large, cognitive skill enjoys a
higher conditional correlation with earnings than noncognitive skill.
Next, I ask whether broad segments of the labor market sort differently. Younger,
college-educated couples are indicative of a modern marriage market, while older, non-college
educated couples are indicative of a classic marriage market. I find that couples who have
both attended college are more similar along mental dimensions and noncognitive dimensions,
while couples with at least one member who has not attended college are more similar along
physical dimensions and, interestingly, cognitive dimensions. Younger couples are more
similar along mental and cognitive dimensions. Older couples are more similar along physical
dimensions. When decomposing the variance in skill across college-educated couples, I find
that between-group variation explains between 10 and 25% of the variance in skill. When
decomposing the variance in skill across older versus younger couples, between-group variance
explains less than 1% of the total variance in skill.
The mechanisms by which labor market segmentation influences genetic variation
may be similar to those mechanisms that influence income inequality. Card, Heining, and
1
Recently, Domingue et al. (2014) estimate the genetic similarity in couples using more than a million
single-nucleotide polymorphisms (SNPs) in individual DNA – SNPs are the A, T, C, and G sequences. Their
results are remarkably similar to the results of this paper: married couples are more genetically similar than
random couples, though the similarity in genotype was only one-third of the similarity in education.
3
Kline (2012) attribute increasing income inequality in West Germany to the assignment of
high- and low-skilled workers to firms. If, in the marriage market, couples are increasingly
sorting along some dimension, differences across segments of the marriage market will be
amplified. Though Kremer (1997) fails to find that sorting by education has large effects
on education inequality, he does note that sorting has a more significant effect on intergenerational mobility. While an increase in couples’ correlation in education from 0.6 to 0.8
increases the its children’s standard deviation of education by 1%, the same increase could
lead to a 3.5% increase within families in the long run.2
Finally, I ask whether mental disorders in children and adolescents are driven, at least
in part, by the assortative match on skill by their parents. Since 1994, the prevalence of
nearly every mental disorder has increased (Perou et al. 2013). Overall, between 13% and
20% of children and adolescents are diagnosed with a mental disorder in the US (Perou et
al. 2013). To my knowledge, there are no US data that provide both detailed occupational
information of parents and the health outcomes of their children. Given empirical limitations,
I employ two separate datasets and estimation strategies.
First, I explore a development psychological theory that suggests autism is a hypersystemizing condition that may result from an assortative match of two high systemizers
(Baron-Cohen 2006). High systemizers search data for patterns and regularities and are
often attracted to science, technology, engineering, and mathematical (STEM) occupations.
I argue that assortative mating by the ability to systemize has likely increased due to labor
market sorting and the recent expansion of the STEM sector, especially for women. Using
data from the CPS and O*NET, I find that the ability to systemize is higher and more
evenly distributed in the STEM sector. Using data from the Metropolitan Atlanta site of
the Autism and Developmental Disabilities Monitoring Network, I also find an increased
prevalence of autism in Census tracts with more systemizing strength.
Second, I extend Baron-Cohen’s theory to other mental disorders, including attention
deficit/hyperactivity disorder (ADHD), anxiety disorders, and mood disorders (depression,
mania, and bipolar disorder). Instead of parents’ systemizing, I utilize the broader measures
of parents’ mental, physical, cognitive, and noncognitive skill. Using the Medical Expenditure
Panel Survey, I find that parents’ mental and noncognitive skill has a significant and positive
2
Fernandez and Rogerson (2001) claim that marital sorting unequivocally increases education and income
inequality in the short- and long-run, perhaps due to the measures that Kremer leaves out of his analysis:
the correlation between fertility and education, the marginal effect of parental education on their children’s
years of education, and the process of wage determination. They argue that the first is negative, the second
is declining, and the third is particularly sensitive to the relative supply of skilled to unskilled workers.
4
relationship with the incidence of mental disorders in their children, though the relationship is
subject to diminishing returns. Additionally, parents’ cognitive skill is negatively associated
with the incidence of anxiety disorders.
This paper makes a number of contributions to the literature. First and foremost,
the results of this paper suggest an unexplored and important research arc: as we play to
our comparative advantage and sort through the labor market, are we also shaping public
health? Second, I bridge the gap between the genetic and economic definitions of assortative
mating by fully considering the first route to a positive assortative match – as the labor
market subdivides the marriage market, it increases the likelihood that genetically similar
couples meet, match, and have children. Third, I develop a modern marriage market in
which labor market outcomes are determined prior to marital outcomes. Unlike the classic
marriage market, this framework can explain assortative mating by traits without consistently positive marginal products, which is well documented in the sociology and psychology
literature but theoretically impossible in many economic models of marriage.3 Fourth, I use
rich and detailed data from O*NET to estimate the composition of skill within marriages.
To my knowledge, no paper has used these data to consider mental, physical, cognitive, or
noncognitive skill compositions within or across marriages.4 Finally, I extend the framework described by Baron-Cohen to other mental health outcomes, including ADHD, anxiety
disorders, and mood disorders.
2
Review of the Literature
There is substantial sociologic evidence of labor market sorting and its role in assortative
mating. Schools promote assortative mating by age, class, religion, and education, while work
promotes assortative mating by class. This “generally confirm[s] the notion that mating requires meeting: the pool of available interaction partners is shaped by various institutionally
organized arrangements and these constrain the type of people with whom we form personal
relationships” (Kalmijn & Flap 2001, 1,289). Assortative mating by broad education category has increased by 20% since 1960 and that college graduates are less likely than ever
3
For example, there is evidence of positive marital sorting by weight, mental disorders, and drug use
(Buss 1985; Baron et al. 1981; Yamaguchi & Kandel 1993).
4
Kambourov, Siow, and Turner (2013) use O*NET to show that strong partnering skills reduce the probability of divorce and job turnover conditional on couples’ market wages and education levels. Van Kammen
and Adams (2014) measure occupational distance using O*NET and find that couples with occupational
compatibility are less likely to divorce.
5
to marry non-graduates, largely due to the earnings gaps between educational categories
and reduced gender inequality (Mare & Schwartz 2006). More recently, Xuet et al. (2015)
extend the Gale-Shapley model to allow for “structural forces that sort individuals into separate social contexts by similarity in attributes” (5,974). The authors find that assortative
mating exists even when assortative preferences do not thanks to the “dynamic changes of
those waiting for marriage in a closed system” (5,978).
There is growing economic evidence of the phenomenon. Using data from a speed
dating agency, Belot and Francesconi (2013) find that individuals sort by physical attributes
and education, but meeting opportunities are the most important factor in determining dates.
Jacquemet and Robin (2013) also suggest the importance of a first route: “it is extremely
difficult to separate the meeting probability from the probably of matching given meeting”
(16). Mansour and McKinnish (2014) find that individuals are more likely to match with
those who share their occupation due to lower search costs within occupation. The authors
note that marriage markets are rarely frictionless and “are much more local than typically
modeled by economists. This implies that choices about where to work or where to go to
school can have important consequences for matching by changing the group of people with
whom one interacts most easily” (21).
Theories of social interaction are also linked to modern marriage. Easley and Kleinberg (2013) clearly define the first route to an assortative match in their discussion of social
networks and the tendency of people to form friendships with others who are like themselves.
Selection may be active, with people picking those who are most similar from a pool of potential friends, or implicit, with social environments enhancing the opportunity of forming
friendships with those who are similar.5 In an analysis of email networks, Kleinbaum et al.
(2013) find higher rates of assortative matching within organizational units and a higher rate
of assortative matching within larger organizations. Assortative matching “is a twin-engine
phenomenon. The motors are individual preference to interact with similar others and differential opportunities to associate based on how people sort, self-select, or are selected into
physical and social locations” (1,331).
While not an explicit focus of this paper, modern marriage may be tied to the economics of identity. Akerlof and Kranton (2000) incorporate one’s sense of self, which presumably includes one’s comparative advantage, into an economic framework of social interaction.
5
The intuition of this paper is akin to an implicit focal closure within a social-affiliation network, which
contains both “a social network on the people and an affiliation network on the people and foci” (Easley
& Kleinberg 2013, 96). Focal closure refers to the increased likelihood that two individuals with a common
focus – work or school, for example – will form a link at some point.
6
Utility is derived from one’s own actions, others’ actions, and one’s self-image – which is further derived from assigned social categories, the quality of match between the individual
and the assignment, and the extent to which actions deviate from the “prescribed behavior”
expected within categories (719). Identity can fundamentally alter outcomes and potentially
explain counterintuitive observations in at least four ways: first, one’s actions can affect one’s
own payoff; second, others’ actions can affect one’s own payoff; third, a governing entity can
affect everyone’s payoffs; and fourth, individuals may have the ability to “choose who they
want to be” (718).
3
Theory: Modern Marriage
In this section, I develop a stylized model of labor market sorting that describes the genetic
distribution across sectors. Predictions show that sectoral wages, the distribution of skill,
and the cost of moving sectors can influence the share of genetic types within sectors, thereby
increasing or decreasing the likelihood that genetically similar individuals meet.
3.1
Genetic Output
Moving forward, I use the term genetic output to describe the intergenerational transmission of genotypes. This stage describes the effect of parents’ matching on their children’s
genotype. To do so, consider a simple and intuitive model of Mendelian inheritance, which
describes traits that are attributable to one gene (Cavalli-Sforza & Bodmer 1971).6 A genotype includes 46 chromosomes and over 20,000 genes, all of which include multiple alleles
(NIH 2007). These alleles – or allelomorphs – are alternative forms of a gene along a given
chromosome. Agents inherit an allele from their father and mother, meaning an agent has
at least two alleles per gene. If both alleles are the same (AA or BB), agents are homozygous. If the alleles are different (AB of BA), agents are heterozygous. Most alleles offer no
observable variation, while some result in different and observable phenotypes (Crow and
Kimura 1970).
While one can restrict the marriage (or cohabitation7 ) market as he or she sees fit,
I focus solely on couples who have or will have a biological child. Suppose a population of
6
Most traits with a continuous distribution are polygenic because they are influenced by more than one
gene (Cavalli-Sforza & Bodmer 1971).
7
A quarter of never-married 25- to 34-year-olds in the U.S. currently live with their partner. The share
of adults over 25 that has never married was 20% in 2012, compared to 9% in 1960 (Wang & Parker 2014).
7
size N is evenly distributed across two genders (Nm = Nf , where Nm refers to males and Nf
refers to females) and three genetic types (AA, BB, and AB). AA individuals receive an A
allele from both their father and mother, and so on. The B allele is assumed to be dominant,
so AB individuals are identical to BB individuals. The population shares are given by πAA ,
πBB , and πAB , where πAA + πBB + πAB = 1.
In the first generation, six types of matches can occur: AA×AA, AA×BB, AA×AB,
BB × BB, BB × AB, and AB × AB. The outcome space is described in Figure 1. The
distribution of marital matches is given by
2
γAAAA = πAA
;
(3.1.1)
γAABB = 2πAA πBB ;
(3.1.2)
γAAAB = 2πAA πAB ;
(3.1.3)
2
γBBBB = πBB
;
(3.1.4)
γBBAB = 2πBB πAB ;
(3.1.5)
2
γABAB = πAB
;
(3.1.6)
Assume that N2 marriages are randomly distributed and that each marriage involves
biological offspring. Further, assume that each child randomly receives one of the two alleles
from his or her biological father and mother. For example, an AA child will result from
100% of AA × AA matches, 50% of AA × AB matches, and 25% of AB × AB matches. As
such, the share of each population type in the following generation is given by:
∗
πAB
1
1
∗
πAA
= γAAAA + γAAAB + γABAB ;
2
4
1
1
∗
πBB
= γBBBB + γBBAB + γABAB ;
2
4
1
1
1
= γAABB + γAAAB + γBBAB + γABAB .
2
2
2
(3.1.7)
(3.1.8)
(3.1.9)
Suppose some mechanism increases the likelihood that an AA × AA match occurs – the
distribution of matches in the second generation is shown in Figure 2.
8
3.2
Labor Market Sorting
Labor market sorting can affect the types of matching that occur. Here, I employ a Roy
model in which agents select the sector with the highest payoff given their idiosyncratic skill.
The decision depends on the distribution of skills and abilities, the correlation of these skills
in the population, technology, and consumer tastes that affect demand for output (Autor
2003). Agents have multiple skills and are aware of these skills, but can only join one sector
in one market at a time. Output is assumed to be log normal (Roy 1951).
Following Borjas (1987), suppose there are two sectors. Type AA agents have different average sectoral wages (µ1 and µ2 ) and/or moving costs (C) than type BB – and,
equivalently, type AB – agents. For now, wages in sector 1 for type AA agents are
AA AA
lnW1AA = µAA
1 + σ1 1 ,
(3.2.1)
where µAA
is the mean wage of AA agents in sector 1 if no AA agents move from sector 1
1
to sector 2. Wages in sector 2 are
AA AA
lnW2AA = µAA
2 + σ2 2 ,
(3.2.2)
is the mean wage of agents in sector 1 if every AA agent from sector 1 moves to
where µAA
2
sector 2. Earnings are linear in characteristics with no explicit externalities built into individuals’ utility (Heckman and Sedlacek 1985). Further, labor exhibits diminishing marginal
returns at the firm and industry level (Cicala et al. 2011). The distribution of skill, which
is akin to a price effect, is assumed to be equivalent for AA, AB, and BB types in sectors 1
and 2, so σ1 = σ1AA = σ1AB = σ1BB and σ2 = σ2AA = σ2AB = σ2BB .
Traditionally, AA
and AA
are the mean zero equivalent of workers’ income in each
1
2
σ AA
AA
AA
AA
sector and are correlated by ρ
= σ112σ2 , where σ12
= cov(AA
1 2 ). While equivalent in
nature, I refer to the errors as workers’ skill. As in Mulligan and Rubinstein (2008), skill
follows a standard bivariate normal distribution:
AA
1
AA
2
!
"
∼
0
0
!
,
1
ρAA
ρAA
1
!#
.
(3.2.3)
Skill for AB and BB agents also follows a standard bivariate normal distribution with mean
zero, variance one, and correlation ρAB = ρBB .
9
Agents play to their comparative advantage. The decision to switch sectors hinges
on the following index variable:
I = ln
W2AA
(W1AA + C AA )
C AA
AA
AA
AA
= µ2 − µ1 − AA + (AA
2 − 1 ),
W1
where C AA includes pecuniary and non-pecuniary moving costs and
C AA
W1AA
C AA
W1AA
(3.2.4)
is its time-equivalent
measure. For simplicity, I can assume that
is equal for all AA agents from sector 1. If
I > 0, an AA agent will move to sector 2. If I < 0, an AA agent will stay in sector 1. An
index variable can be constructed similarly for BB and AB agents.
The share of AA migrants is denoted by:
Pr ν AA
 AA
− µAA
AA
2 − µ1 −
C
AA
AA
> − µ2 − µ1 − AA
= 1 − Φ
σν
W1
C AA
W1AA

 = 1 − Φ(z AA ),
(3.2.5)
p
AA
and σν2 = (σ12 + σ22 − 2ρAA σ1 σ2 ). Φ is the standard normal distriwhere ν AA = AA
2 − 1
bution function, while z AA is akin to the cost of moving sectors given agents’ idiosyncratic
skill. Since the standard normal is symmetric, 1 − Φ(z AA ) is the equivalent of Φ(−z AA ).
As z AA decreases, the probability of moving to sector 2 for AA agents increases. This
AA
< 0). This could also result from
could result from lower mean wages in sector 1 ( δP
δµAA
1
AA
( δP
δµAA
2
AA
δP
higher mean wages in sector 2
> 0) or from a lower cost of moving ( δC
AA < 0). As
AA
z increases, the probability of moving to sector 2 for AA agents decreases.
Ultimately, I am interested in the probability that AA and BB or AB agents are
located in each sector. Given random matching, the distribution of types within sectors will
determine the genetic output. If something induces AA agents to switch sectors without also
inducing BB and AB agents, the AA × AA match will be more likely to occur. Following
Bayes’ Rule and beginning with AA types in Sector 2, I have
P r(AA|2) =
P r(2|AA)P r(AA)
,
P r(2)
(3.2.6)
where P r(AA) = πAA . The conditional probability of being in Sector 2 given AA status is


C AA
AA
−(µAA
)
−
µ
−
2
1
W1AA
.
P r(2|AA) = P r  p 2
2
AA
σ1 + σ2 − ρ σ1 σ2
10
(3.2.7)
The unconditional probability of being in sector 2 is given by
P r(2) = Φ(−z AA )πAA + Φ(−z BB )πBB + Φ(−z AB )πAB ,
(3.2.8)
where Φ(−z BB ) and Φ(−z AB ) are derived similarly to Φ(−z AA ). The conditional probability
of being in sector 2 is:
P r(AA|2) =
Φ(−z AA )πAA
Φ(−z AA )πAA + Φ(−z BB )πBB + Φ(−z AB )πAB
.
(3.2.9)
I can also derive the conditional probability of being in sector 2 for BB and AB types:
P r(BB ∪ AB|2) =
Φ(−z BB )πBB + Φ(−z AB )πAB
Φ(−z AA )πAA + Φ(−z BB )πBB + Φ(−z AB )πAB
.
(3.2.10)
Turning to sector 1 and again following Bayes’ Rule, I have
P r(BB ∪ AB|1) =
P r(1|BB ∪ AB)P r(BB ∪ AB)
,
P r(1)
(3.2.11)
where P r(BB ∪ AB) = πBB + πAB . The conditional probability of being in Sector 1 given
BB or AB status is


BB,AB
C BB,AB
−(µBB,AB
−
µ
)
−
BB,AB
2
1
W1
.
P r(1|BB ∪ AB) = P r  q
(3.2.12)
BB,AB BB,AB
2
2
BB,AB
σ1 + σ2 − ρ
σ1
σ2
The unconditional probability of being in sector 1 is given by
P r(1) = Φ(z AA )πAA + Φ(z BB )πBB + Φ(z AB )πAB .
(3.2.13)
Therefore, I have
P r(BB ∪ AB|1) =
Φ(z BB )πBB + Φ(z AB )πAB
Φ(z AA )πAA + Φ(z BB )πBB + Φ(z AB )πAB
11
.
(3.2.14)
Finally, I can derive the unconditional probability of being in sector 1 for AA agents:
P r(AA|1) =
3.3
Φ(z AA )πAA
Φ(z AA )πAA + Φ(z BB )πBB + Φ(z AB )πAB
.
(3.2.15)
Comparative Statics
Now, consider how changes in parameters will influence the share of agents in each sector.
While I focus on AA agents, it is easy to show the comparative statics for BB and AB
agents. As z AA increases, the share of sector 1 AA agents will increase and the share of
sector 2 AA agents will decrease. More formally, I have
δP r(AA|2)
< 0.
δz AA
(3.3.1)
Assuming positive selection, the main predictions are as follows: first, higher wages in sector
2 induce AA agents to select sector 2; second, fewer AA agents will move sectors when there
is more skill dispersion in sector 2 relative to sector 1, so long as wages are higher for those in
sector 2; third, lower moving costs (which could occur as women infiltrate the labor market)
draw more AA workers into sector 2.8
Moving from sector 1 to sector 2 can be influenced by the average wage in either
AA
AA )
−(µAA
2 −µ1 −C
, it is easy to show
sector. Remembering that z AA =
σν
δz AA
> 0;
δµAA
1
(3.3.2)
δz AA
< 0.
δµAA
2
(3.3.3)
Higher wages for AA agents in sector 1 keep more AA agents in sector 1, while higher wages
in sector 2 induce more AA agents to move to sector 2.
Changes in the dispersion of skill can also affect the distribution of skill. So long as
the distribution of skill is related to the distribution of one’s genotype, changes in the skill
8
As in Borjas (1987), these results will not hold up under negative sorting or refugee sorting. Due to
discrimination and societal norms, women’s labor market participation may have resembled refugee sorting.
12
distribution will also influence genetic output. I have:
1 AA
δz AA
AA
AA
)
σ2 = (µ2 − µ1 − C
δ σ1
2
σ2
σ1
2
σ2
− 2ρ
σ1
− 32 σ2
AA σ2
2 − 2ρ
,
σ1
σ1
(3.3.4)
which depends on the sign of 2 σσ12 − 2ρAA σσ21 . In the case that ρAA is between 0 and 1 and
the skills rewarded in sectors 1 and 2 are positively correlated, a decrease in dispersion in
sector 2 relative to sector 1 will induce the AA agents to move to sector 2. In the case that
ρAA is between -1 and 0 and the skills rewarded in sectors 1 and 2 are negatively correlated,
a decrease in dispersion in sector 2 relative to sector 1 will deter the AA agents from moving
to sector 2. These results require that µAA
> µAA
2
1 .
Finally, if moving costs change:
δz AA
> 0.
δC AA
(3.3.5)
Thus, lower moving costs induce more AA agents to move to sector 2.
3.4
Results & Discussion
According to the previous section, higher wages for AA agents in sector 1 keep more AA
agents in sector 1, while higher wages for AA agents in sector 2 induce AA agents to move
to sector 2; more AA agents will move when there is relatively more dispersion in sector 2
than sector 1, so long as wages are higher in sector 2; and lower moving costs for AA agents
induce AA workers to move to sector 2. These results hold so long as changes in zAA do not
affect BB or AB agents. If σσ21 were to change, the comparative static depends on the sign
and µAA
of ρ and the relative magnitudes of µAA
2 .
1
AA
Recall that as z
decreases, the probability of moving from sector 1 to sector 2
increases for AA agents. More explicitly, I have
−1
δP r(AA|2)
AA
BB
AB
=
φ(−z
)π
Φ(−z
)π
+
Φ(−z
)π
+
Φ(−z
)π
AA
AA
AA
BB
AB
δΦ(−z AA )
−2
−φ(−zAA )πAA Φ(−zAA )πAA + Φ(−z BB )πBB + Φ(−z AB )πAB
> 0.
13
(3.4.1)
For BB and AB agents, I have
δP r(BB ∪ AB|2)
= −φ(−zAA )πAA
δΦ(−z AA )
−2
Φ(−zAA )πAA + Φ(−z BB )πBB + Φ(−z AB )πAB
< 0.
(3.4.2)
Thus, as z AA decreases – either due to a change in relative wages, more skill dispersion
in sector 2, or lower moving costs – the composition of sectors 1 and 2 change. Sector
1 will have a larger share of AB and BB agents and sector 2 will have a larger share of
AA agents. Given random matching, this increases the number of AA × AA matches and
decreases the number of AA × BB and AA × AB matches. Positive assortative mating by a
homozygous trait increases, thereby decreasing the number of heterozygous matches. This
reduces genetic variety since couples with similar phenotypes are often similar in genotypes.
In fact, assortative mating can have “generally the same consequences as inbreeding” (Crow
& Felsenstein 1968, 85).
Similarly, I can show the composition of agents in sector 1:
−1
δP r(AA|1)
= −φ(zAA )πAA Φ(z AA )πAA + Φ(z BB )πBB + Φ(z AB )πAB
AA
δΦ(−z )
−2
+φ(zAA )πAA Φ(zAA )πAA + Φ(z BB )πBB + Φ(z AB )πAB
< 0;
(3.4.3)
−2
δP r(BB ∪ AB|1)
BB
AB
=
φ(z
)π
Φ(z
)π
+
Φ(z
)π
+
Φ(z
)π
> 0.
AA
AA
AA
AA
BB
AB
δΦ(−z AA )
(3.4.4)
3.5
The STEM Effect
Since many recessive genes are harmful in some way, assortative mating and reduced heterozygosity can affect the genetic fitness of a population. Fitness is a broad term encompassing genetic success and can be defined absolutely (the number of progeny) or relatively (surviving progeny of a particular genotype compared to other genotypes). Reed and Frankham
(2003) find that decreased heterozygosity has a significant and “deleterious effect on population fitness” in 34 separate studies of genetic diversity in insects (230). More recently, Joshi
et al. (2015) examine the effects of homozygosity on a variety of health indicators, including
height, blood pressure, cholesterol, and educational attainment. Using over 350,000 genomes
14
from 100 cohorts, they find significant and negative associations between homozygosity and
height, expiratory lung capacity, general cognitive ability, and educational attainment. In
particular, they show that the offspring of first cousins are half an inch shorter and earn
nearly a year’s less educational attainment.
Labor market sorting could increase homozygosity and influence genetic fitness. Consider a development psychological theory developed by Baron-Cohen (2006), who argues
that autism is a hyper-systemizing conditions resulting, at least in part, from the assortative match of two high systemizers. His theory assumes every individual is born with a
unique ability to systemize, which refers to analyzing changing inputs for possible structure,
and that individuals with autism have an extreme ability to systemize. A high systemizer searches data for patterns and regularities, and is therefore attracted to the rigidity of
science, technology, engineering, and mathematical (STEM) occupations.
Suppose sector 2 includes STEM occupations and AA agents are high systemizers. If
the returns to systemizing increase, particularly for women, high systemizers are more likely
to select sector 2, thus shaping the next generation’s ability to systemize. The continued expansion of the STEM sector is well documented: since 2008, areas with a high concentration
on STEM occupations have experienced positive job growth, less unemployment, and higher
real wages (Rothwell 2013). While the share of STEM occupations has doubled since 1850,
the composition of the STEM sector has changed substantially. In 1950, women earned only
5.9% of Physical Science PhDs. By 2005, it had grown to 34.3% (Chiswick et al. 2010).
Golden (2012) finds that an increasing correlation of systemizing within couples (from 0.3
to 0.4) could eventually double the prevalence of autism without significant changes to the
overall ability distribution. What’s more, “increasing the returns to a trait for women alone
will also increase assortative mating” (43). Figure 3 describes the STEM effect.
4
Empirics: Sorting by Skill
This section examines the relationship between labor market characteristics and the skill
compositions within and across marriages. In particular, I focus on sorting by mental,
physical, cognitive, and noncognitive skill.
15
4.1
Data
I employ two datasets: the O*NET Content Model and the Current Population Survey
Merged Outgoing Rotation Groups (CPS ). O*NET measures different task requirements
for every occupation. I assume these measures are correlated with individuals’ phenotypes
and therefore serve as proxies for individuals’ genotypes. O*NET considers every occupation in the Standard Occupational Classification (SOC) system, which includes nearly 1,000
occupations. Reports are initially collected from occupation analysts then updated using
surveys of worker populations. These data are updated annually in order to consider changing requirements within occupations. O*NET defines the features of an occupation using a
standardized set of variables on a 0 to 100 scale.
To roughly measure genetic compositions within marriages, I first consider sorting
by mental and physical skill in an attempt to measure a latent characteristic (individuals’
genotypes) using occupational-specific task measures (individuals’ phenotypes) as proxies.
I define mental skill as the average of accuracy, analyzing data, assisting others, creativity,
developing strategies, inductive reasoning, mathematical reasoning, memorization, organization, originality, perceptual speed, persuasion, processing information, time management,
and updating and using relevant knowledge. I define physical skill as the average of arm
hand steadiness, control precision, dynamic strength, dynamic flexibility, explosive strength,
finger dexterity, gross body coordination, gross body equilibrium, manual dexterity, multilimb coordination, rate control, reaction time, speed of limb movement, stamina, and static
strength.
In addition to mental and physical skill, I examine sorting by cognitive and noncognitive skill. Cognitive skill refers to general intelligence, while noncognitive skill includes
‘softer’ skills, including grit and empathy. I average cognitive skill across inductive reasoning, perceptual speed, analyzing data, mathematical ability, and creativity. I average
noncognitive skill across persuasion, interpersonal skill, judgment and decision making, time
management, and assisting others.
Households are taken from the CPS for the years 2001 through 2010, which uses
3-digit codes for the 472 occupations in the 2000 Census. The CPS includes extracts from
monthly CPS surveys; each month, the Bureau of Labor Statistics surveys between 50,000
and 60,000 households about their labor force participation and other economic variables of
interest. I focus on married households in which both spouses are present and employed.
In order to merge the two datasets, I convert the SOC codes to Census codes using
16
the Census 2000 Occupational Categories, With Standard Occupational Classification Equivalents. If an SOC occupation was not a Census occupation, I use the closest SOC code to
best align the occupation. For example, Water Resource Specialists (SOC 11-9121.02) are
now considered Natural Sciences Managers (SOC 11-9121.00, Census Code 036). Because the
SOC system includes more occupations, many of the O*NET skill measures are aggregated.
For example, Chief Executives and Chief Sustainability Officers have different SOC codes
but both have a Census code of 001. Therefore, skill measures for both Chief Executives
and Chief Sustainability Officers is an average of both O*NET entries.
4.2
Estimation Strategy
I first estimate the correlation of heads and spouses’ skill:
corr(mh , ms ) =
cov(mh , ms )
;
σh σs
(4.2.1)
corr(ph , ps ) =
cov(ph , ps )
;
σh σs
(4.2.2)
corr(ch , cs ) =
cov(ch , cs )
;
σh σs
(4.2.3)
corr(nh , ns ) =
cov(nh , ns )
;
σh σs
(4.2.4)
where mh , ms , ph , ps , ch , cs , nh , and ns are the measures of mental, physical, cognitive, and
noncognitive skill, as described above. A positive correlation implies the presence of positive
assortative mating. Correlations are located in Table 1.
Next, I apply a post hoc procedure developed by Lubotsky and Wittenberg (2006) in
an attempt to minimize measurement error.9 Instead of using multiple skill proxies for some
unobserved independent variable, I can estimate a single measure of skill based on linear
regressions of skill measures on earnings, using the estimated coefficients as weights in an
aggregation. Thus, the Lubotsky-Wittenberg index can be interpreted as an income-weighted
skill index.
When profit-maximizing agents select occupations, they are likely thinking of the
9
Lubotsky and Wittenberg (2006) apply this procedure to the effect of wealth on children’s school attendance in India. Proxies of wealth include the presence of refrigerators, VCRs, access to drinking water,
seeing machines, the type of toilet, electricity, and livestock.
17
payoffs to their skills rather than their skills themselves. Some skills (inductive reasoning
and time management) have higher payoffs than others (memorization and assisting others).
Extending the theoretical predictions, I expect more sorting on those skills with a higher
conditional correlation with earnings.10 By giving additional weight to those skills that
provide more explanatory power, the Lubotsky-Wittenberg index may provide an advantage
over crude measures of skill because it better captures real-world behavior. Correlations of
the Lubotsky-Wittenberg indices are located in Table 2.
More formally, suppose we have J proxies for skill for every ith agent:
lnYi = αi +
J
X
βj mij + i ,
(4.2.5)
j=1
where mij include the different occupational-specific mental skills taken from O*NET. To
have a single measure of skill for each agent, I then estimate
mentali =
J
X
βj
j=1
cov(lnYi , mij )
.
cov(lnYi , mi1 )
(4.2.6)
The indices for physical skill, cognitive skill, and noncognitive skill are aggregated similarly.
This method minimizes attenuation bias because the coefficients include both the variances
and covariances of the error components in the aggregation (Lubotsky & Wittenberg 2006).
The measure is normalized by cov(lnY, s1 ) in order to interpret the results. I perform the
above regression separately for mental, physical, cognitive, and noncognitive skill. In the
mental skill aggregation, s1 is mathematical ability. In the physical skill aggregation, s1
is dynamic strength. In the cognitive skill aggregation, s1 is inductive reasoning. In the
noncognitive skill aggregation, s1 is assisting others.
One concern regarding job-specific skill aggregations is the inherent bias given endogenous mobility, which is difficult to sign for a number of reasons. Gathmann and Schönberg
(2007) explain: “on the one hand, workers who are well matched are less likely to switch
occupations or move to a distant occupation. This implies a positive (partial) correlation
between occupation and task tenure and the match quality, and thus to an upward bias in
the return to occupation- and task-specific human capital. On the other hand, workers may
have switched occupations or moved to a distant occupation because they are particularly
10
The data support this: couples’ correlation of inductive reasoning and time management are slightly
higher than the correlation of memorization and substantially higher than the correlation of assisting others.
18
well matched with the new occupation. Hence, workers with low levels of occupation and
task tenure may have particularly high task matches, leading to a downward bias in the
return to occupation- and task-specific human capital” (25–26).
To more fully consider labor market’s role in assortative mating, I also ask whether
broad segments of the labor market sort differently in marriage markets. Since positive
sorting segments a marriage market, it also decreases within-group variance and increases
between-group variance. Decreasing within-group variance further increases the rate of positive assortative mating and has important genetic consequences.
I define a household’s skill endowment to be the head’s skill plus the spouse’s skill.
Couples who have both attended college enjoy a higher mental skill endowment (114.70
versus 100.52), cognitive skill endowment (109.50 versus 94.00), and noncognitive skill endowment (115.29 versus 104.46), while couples who have at least one member with no college
education have a higher physical skill endowment (52.02 versus 33.08). The difference in skill
is substantially smaller for couples over 40 versus couples with at least one member under 40,
but older couples have a higher mental skill endowment (107.42 versus 105.88), cognitive skill
endowment (101.36 versus 100.03), and noncognitive skill endowment (110.36 versus 108.78),
while younger couples have a higher physical skill endowment (45.66 versus 42.04).11
Correlations for couples who have some college education and couples with at least
one member who has no college education are listed in Table 3, while correlations for couples
who are over 40 and couples with at least one member under 40 are listed in Table 4.
Segmenting populations by college education highlights the role of labor market institutions:
extending the theoretical predictions, I expect college-educated couples to be more similar
in skill because they enjoy higher wages and lower moving costs. Segmenting populations
by age focuses on intergenerational changes to the marriage and labor market: women and
minorities enjoy higher wages and lower moving costs today than they did in the past. As
such, I expect younger couples to be more similar in skill.
Finally, I decompose the within- and between-group variance of skill endowments
across college education and older versus younger couples. The higher the between-group
variance is relative to the within-group variance, the more the distribution of skill across
segments differ. Total variance for mental skill is given by:
Vt = Vb + Vw =
J X
C
X
(mcj − m̄)2 ,
j=1,2 c=1
11
These skill endowments are from the 2001 CPS, but the relationships are stable over time.
19
(4.2.7)
where mcj is the average or Lubotsky-Wittenberg skill endowment of couple c in group j
and m̄ is the overall mean of mental skill. The between-group variance is given by:
J X
C
X
Vb =
(m̄j − m̄)2 ,
(4.2.8)
j=1,2 c=1
where m̄j is the mean mental skill in group j. The within-group variance is given by:
Vw =
J X
C
X
(mcj − m̄j )2 .
(4.2.9)
j=1,2 c=1
The total variance is decomposed similarly for physical, cognitive, and noncognitive skill.
Variances for Lubotsky-Wittenberg skill measures are in Tables 5 and 6.
This empirical strategy faces a few estimation issues, the first of which is fit. Fit
considers “the extent to which an individual’s physical abilities, cognitive skills, education,
and work experience match the demands of the work environment” (Vogel & Feldman 2009,
3). Fit is highest for young workers: because the job requirements typically change over
the course of one’s tenure, fit tends to decay as workers age (Vogel & Feldman 2009). The
results for those couples under age 40 are more likely to avoid this issue. Second, O*NET
only provides up-to-date skill measures and does not provide detailed information on how
those skill measures are determined, nor offers any longitudinal changes to skill measures.
4.3
Results & Discussion
Table 1 reports the correlation of income, age, education, and average skill measures. There
is more assortativity for education and age, ranging from 0.619 to 0.634 for education and
from 0.923 to 0.931 for age. The correlation of couples’ earnings is lower, ranging from
0.082 in 2004 to 0.186 in 2010. The correlation of average mental skill is roughly twice the
correlation of average physical skill, ranging from 0.311 to 0.341 versus 0.113 to 0.163. The
correlation of cognitive skill is higher than the correlation of noncognitive skill, ranging from
0.281 to 0.334 versus 0.192 to 0.225. While the correlation of earnings is increasing between
2001 and 2010, the correlations of education and age are stable.
Table 2 measures the correlation of the Lubotsky-Wittenberg indices of skill. The
correlation of skill is still higher than earnings – from 0.215 to 0.252 for mental skill and
from 0.193 to 0.227 for physical skill – but approximately 50% lower than average skill
20
measures. This suggests that there may be more sorting on skills with lower labor market
returns. As with average skill, the correlation of mental skill is consistently higher than
the correlation of physical skill and the correlation of cognitive skill is consistently higher
than the correlation of noncognitive skill. Unlike average skill measures, there is an upward
trajectory across time. Between 2001 and 2010, the correlation of mental skill increased
from 0.215 to 0.237, the correlation of physical skill increased from 0.195 to 0.213, and the
correlation of noncognitive skill increased from 0.100 to 0.145. This suggests that the labor
market’s promotion of assortative mating may be increasing.
Tables 3 and 4 include the Lubotsky-Wittenberg skill indices for those couples who
have attended college versus couples with at least one member who has not attended college
and correlations for those couples who are above age 40 versus those couples with at least
one member under age 40. Generally, college-educated couples are more similar with regard
to earnings, mental skill, and noncognitive skill, while non-college educated couples are more
similar with regard to physical skill and cognitive skill. In most years, younger couples are
more similar in earnings, mental skill, physical skill, cognitive skill, and noncognitive skill.
These results suggest an increasing presence of labor market segmentation. If sorting is different among modern couples (younger, college-educated couples) compared to classic (older,
non-college-educated) couples, there will be shifts in the intergenerational transmission of
health.12
The variance of skill is decomposed across college education and age in Tables 5
and 6. Overall, there is more variation in mental skill than physical skill and in cognitive
skill than noncognitive skill. When decomposing across college-educated couples, I find that
between-group variation explains roughly 20% of the variance in mental skill, 10% of the
variance in physical skill, 20% of the variance in cognitive skill, and 25% of the variance in
noncognitive skill. When decomposing across older and younger couples, the between-group
variance is negligible: in every year, the between-group variance explains less than 1% of the
total variance in mental, physical, cognitive, and noncognitive skill.
To summarize, individuals sort more positively on those skills with higher conditional
correlations with earnings. In college-educated and younger populations, the rate of positive
assortative mating on mental skill is even higher – consistent with the notion of a modern
marriage market. In addition to mean differences in skill, some segments also differ in terms
of skill dispersion. In particular, skill is distributed more equally across college-educated
12
Referring to the previous discussion of occupational fit, this could also be a result of better measurement.
21
couples than non-college educated couples. Combined, these results suggest that the labor
market is playing some role in marriage selection.
5
Application: Children’s Mental Health
I now ask whether parents’ sorting by skill is associated with their children’s mental health
outcomes. To my knowledge, there are no US data that includes both detailed occupational
information of parents and health outcomes of children. As such, I use two separate estimation strategies. First, I use data from the Autism and Developmental Disabilities Monitoring
(ADDM) Network to ask whether autism spectrum disorders are associated with sorting
by the ability to systemize. Second, I use data from the Medical Expenditure Panel Survey
(MEPS) to ask whether mental disorders, including attention deficit/hyperactivity disorder (ADHD), anxiety disorders, and mood disorders, are associated with sorting by mental,
physical, cognitive, or noncognitive skill. In the ADDM Network data, the dependent variable is the tract-level percentage of 8 year olds with autism. In the MEPS, the dependent
variable is a household-level dummy variable of children’s diagnosed mental disorders.
5.1
Background
Mental disorders are “serious deviations from expected cognitive, social, and emotional development” and cost society nearly $250 billion annually (Perou et al. 2013). Since 1994,
the prevalence of nearly every mental disorder has increased – the most commonly occurring
disorders in children and adolescents include attention-deficit/hyperactivity disorder (6.8%),
behavioral or conduct problems (3.5%), anxiety (3.0%), depression (2.1%), autism spectrum
disorders (1.1%), and Tourette syndrome (0.2%) (Perou et al. 2013). In total, between 13%
and 20% of children living in the US experience a mental disorder in any given year (Perou
et al. 2013).
In addition to mental disorders at large, I focus on four groups of disorders: autism
spectrum disorders, ADHD, anxiety disorders, and mood disorder. Autism is diagnosed
on the basis of abnormal social and communicative development, as well as the presence
of narrow, restricted interests and repetitive activity (APA 2013). ADHD is characterized
by inattention, difficulty controlling behavior, and, at times, hyperactivity (APA 2013).
Any disorder marked by excessive worry, including panic disorders, phobias, and obsessivecompulsive disorder, falls under the umbrella of anxiety disorders (APA 2013). Mood disor22
ders – sometimes referred to as affective disorders – encompass those diagnoses in which the
most prevalent symptom is a disturbance in mood. The most common mood disorders are
major depressive disorder, manic disorder, and bipolar disorder (APA 2013).
While the nature versus nurture debate remains, there is substantial evidence of
genetic components to three of the four disorders: siblings of children with autism are only
3 to 6% more likely to receive the diagnosis, while an identical twin of a child has a 40-90%
likelihood of the same diagnosis (Dougherty 2013); four genes – the dopamine D4 and D5
receptors, and the dopamine and serotonin transporters – have been consistently linked to
ADHD (Bobb et al. 2005); and the heritability of mood disorders, or the degree to which
differences in the occurrence of the disorder are associated with differences in the genetic
code, is over 40% for women and nearly 30% for men (Barnett & Smoller 2009).
5.2
Is Assortative Mating Linked to Mental Health Outcomes?
Thus far, the clinical literature has provided detection-based explanations for increases in
the prevalences of children’s mental health disorders. For example, there are three accepted
explanations for increasing prevalence of autism: more awareness, a broader diagnostic standard, and diagnostic substitution (Fombonne 2009). In the fourth Diagnostic and Statistical
Manual of Mental Disorders (DSM-IV), the criteria for an autism diagnosis were extended to
include higher-functioning individuals with issues of social interaction. The DSM-V imposes
stricter standards and eliminates a separate diagnosis for Asperger syndrome (APA 2015).13
Diagnostic substitution occurs when individuals are first diagnosed with another condition
before being properly diagnosed with autism. King and Bearman (2009) find that a quarter
of the observed increase in autism prevalence California between 1992 and 2005 is due to
diagnostic substitution from mental retardation (King & Bearman 2009).
Assortative mating by mental traits may be driving part of the increasing prevalence
of autism and other mental disorders. The prevalence of mental health varies geographically,
within and between countries. Recent evidence suggests that parental backgrounds play an
important role, at least for autism: Durkin et al. (2010) find that children with autism are less
likely to live in poverty and more likely to live in neighborhoods with higher adult educational
achievement, while Van Meter et al. (2010) find clusters of autism in areas with older, highly
educated parents. The highest autism prevalence recorded is in Goyang City, near Seoul,
South Korea, where Kim et al. (2011) estimate that 2.64% children (approximately 1 in
13
However, Huerta et al. (2012) use the proposed DSM-V criteria on children diagnosed with DSM-IV
criteria and find that 91% of children diagnosed with DSM-V criteria.
23
38) have autism. This body of evidence suggests parents in certain places have an increased
likelihood of having children with autism. Sorting by the ability to systemize is one possible
explanation, especially given the high incidence of autism in South Korea – a “high-tech
utopia” (O’Connell 2005).
Baron-Cohen (2006) argues that autism is a hyper-systemizing conditions resulting, at
least in part, from the assortative match of two high systemizers. His theory assumes every
individual is born with a unique ability to systemize, which refers to analyzing changing
inputs for possible structure, and that individuals with autism have an extreme ability to
systemize. A high systemizer searches all data for patterns and regularities.14 Gender plays
a crucial role in the theory, as men tend to be better at systemizing. Studies show that males
are superior to females in spatial tasks, including Euclidian geometric navigation and finding
a part within a whole. Individuals with autism perform better than developmentally normal
males in these spatial tasks (Baron-Cohen 2002). The theory also maintains that autism is
a hypo-empathizing condition resulting from the assortative match of two low empathizers.
Evidence of the theory is limited, but growing. Baron-Cohen et al. (1998) find
that both mothers and fathers of children with autism have elevated rates of systemizing
occupations (physics, engineering, and math) among their fathers. Roelfsema et al. (2012)
estimate that two to four times as many children are diagnosed with autism in Eindhoven,
the Dutch Silicon Valley, than in Haarlem and Utrecht, areas of equivalent size but without
the high concentration of information technologists and engineers. Most recently and using
the ADDM Network, Golden (2012) finds a higher rate of autism in Census block groups
with a mathematically-strong occupational composition. While this paper uses the same
geographic area, I utilize skill measures that are better aligned with Baron-Cohen’s theory
of assortative mating.
Apart from autism, there are a few pieces of evidence that link assortative mating by
skill to mental health outcomes. Baron et al. (1981) find that assortative mating by affective
disorders may increase the intergenerational transmission of affective disorders. Andreasen
(1987) finds that writers had a substantially higher rate of affective disorders, especially
bipolar disorder. In an autism-based study, Baron-Cohen et al. (1998) find twice as many
cases of bipolar disorder in the families of literature students.
14
Systemizing comes in many forms: sensory (repeatedly touching surfaces), motoric (spinning), mechanical (ease with electronics), vocal or auditory (echolalia), and environmental (lining up toys) systemizing are
very common in children with autism.
24
5.3
5.3.1
Autism Spectrum Disorders
Data
Authorized by the Children’s Health Act of 2000, the ADDM Network is a group of programs
funded by Center for Disease Control and Prevention (CDC) that estimate the number of
8-year-olds with autism and other developmental disabilities living in different areas of the
US. Currently, the ADDM Network sites span fourteen states: AL, AZ, AR, CO, FL, GA,
MD, MO, NJ, NC, PA, SC, UT, and WI. As of 2008, the total population of 8-year-olds
was 289,287. The ADDM Network’s goals are to measure autism prevalence across sites
and time period, to describe the population of children with autism, to compare how autism
prevalence differs across the country, and to identify changes in autism occurrence over time.
The ADDM Network uses a clinician-based approach. Parent-based surveys report
higher prevalence (nearly 4% in the National Survey of Children’s Health) and clinician
versus parent-based surveys can range by a factor of four or more, in part due to parents’
misunderstanding of what constitutes a medical diagnosis (Candon & Bradford 2015). In
the ADDM Network, children are diagnosed based on public school and medical records. On
average, clinicians spend more than 45 minutes with each child in question without a clinical
diagnosis of autism (Van Naarden Braun et al. 2007).
Occupational compositions and controls are taken from the 2000 and 2010 Decennial
Census. The population’s occupational shares are available at the 2-digit level for Census
tracts. To measure the occupational composition within Census tracts, I average systems
analysis and social perceptiveness within the twenty-three occupational sectors, then multiply each average by the sector’s share in the tract and aggregate to a single measure of
systemizing and empathizing strength. These measures provide an advantage over Golden
(2012), who only uses mathematical ability. Summary statistics for the ADDM Network are
in Table 7.
5.3.2
Estimation Strategy
To apply Baron-Cohen’s theory of assortative mating, I use two skills from O*NET : systems
analysis, which is determining how a system should work and how changes in conditions,
operations, and the environment will affect outcomes; and social perceptiveness, or being
aware of others’ reactions and understanding why they react as they do. According to the
25
2010 CPS, the correlation of systemizing and empathizing within couples is roughly equal:
0.186 for systemizing and 0.185 for empathizing.
My equation of interest is:
autismt = α + βsystemizingt + λsocial perceptivenesst + γXt + t .
(5.3.1)
where autismt is the percentage of 8 year olds with autism in Census tract t pooled across
five years (2000, 2002, 2004, 2006, and 2008), systemizingt and social perceptivenesst are
measures of systemizing and empathizing strength given the occupational composition of
Census tracts, and Xt includes controls commonly used in the literature: median income,
the poverty rate, the percentage of individuals who have completed a Bachelor’s, and county
fixed effects. Results of equation 5.3.1 are located in Table 8.
5.3.3
Identification Issues
The identifying assumption of this framework is that t is uncorrelated with the systemizing
and empathizing strength of tracts. Endogeneity will be an issue if something besides a job
opportunity were to drive the parents of children with autism to locate within these tracts.
The literature shows that access to health care, like hospitals, can affect the likelihood of an
autism diagnosis (Candon & Bradford 2015). While the causes of autism remain unidentified,
there is some evidence linking air pollution to autism. Volk et al. (2013) find that children
with autism in California were more likely to live in homes in the highest quartile of trafficrelated pollution exposure during pregnancy and the first year of life. In particular, regional
exposure measures of nitrogen dioxide and particulate matter less than 2.5 and 10 microns
in diameter were correlated with autism during gestation.
As another example, consider the Marcus Autism Center in DeKalb County, a large,
successful non-profit focused on the diagnosis and treatment of autism. Presumably, the
Marcus Autism Center also employs high systemizers, particularly for research-intensive
jobs. If families were more likely to move to DeKalb county to seek out resources offered
by the Marcus Autism Center and if high systemizers were more likely to move to DeKalb
county to take advantage of the job opportunities provided by the Marcus Autism Center,
then higher autism prevalence would be incorrectly associated with systemizing strength.
26
5.3.4
Results & Discussion
First, I consider the skill composition in the STEM sector using the CPS and O*NET.
Both members of the STEM sector have a higher ability to systemize than their non-STEM
counterparts: 51.53 versus 37.60 for males and 50.55 versus 37.32 for females. This suggests
that labor market sorting increases the likelihood that two high systemizers meet, match,
and have a child with an extreme ability to systemize – hence the potential of a STEM effect
on autism spectrum disorders.
Results are in Table 8. In every specification, a tract’s systemizing strength is statistically significant and positive. In the first specification (without controls and county fixed
effects), a tract’s empathizing strength is statistically significant and negative. Both signs
are consistent with Baron-Cohen’s theory of assortative mating. Additionally, tracts with
higher poverty rates have a lower incidence of autism. To interpret the coefficients, recall
that systemizing and empathizing are scored on a 0 to 100 basis in O*NET. As a tract’s
systemizing strength increases by 5, autism prevalence increases by approximately 1% based
on the final specification.
Notably, the magnitude of the systemizing effect increases when county fixed effects
are included. Controlling for geography improves the link between skill and genetic output,
as any county-specific incentives that draw in both families with an autistic child and high
systemizers are addressed. Failing to include fixed effects in the analysis leads to a downward
bias on the systemizing strength of Census tracts.
5.4
5.4.1
ADHD, Anxiety Disorders, and Mood Disorders
Data
The Medical Expenditure Panel Survey (MEPS ) is a nationally representative survey of
households, medical providers, and employers. The households surveyed are drawn from a
subsample of households interviewed in the previous year’s National Health Interview Survey. Households are surveyed five times in two and a half years. In 2012, 14,763 families
(and 37,182 persons) were interviewed in the MEPS. Questions relate to “demographic characteristics, health conditions, health status, use of medical services, charges and source of
payments, access to care, satisfaction with care, health insurance coverage, income, and
employment” (AHRQ 2009). I use the Medical Conditions file to identify children with
mental health disorders through the International Statistical Classification of Diseases and
27
Related Health Problems (ICD-9) condition code. There are four health outcomes of interest: ADHD (ICD-9 314), anxiety disorders (ICD-9 300), mood disorders (ICD-9 311); and
all mental disorders (ICD-9 294–319). I use data from the years 2003 through 2010.
Summary statistics are located in Table 9. Approximately 5% of children had a diagnosed mental disorder, which includes ADHD, anxiety disorders, mood disorders, schizophrenia, paranoid states, personality disorders, drug and alcohol dependence, eating disorders,
sleep disorders, conduct disorders, specific delays in development, and mental retardation.
Nearly half of the diagnosed cases were ADHD, while anxiety and mood disorders accounted
for 0.7% and 0.8% of cases, respectively.
Because of crude occupational measures, O*NET skill measures are averages for each
SOC occupation in the 1-digit MEPS occupational code. I use averages of the 15 mental
skills, 15 physical skills, 5 cognitive skills, and 5 noncognitive skills, as described in Section
4. I do not use Lubotsky-Wittenberg skill indices, which are difficult to construct given
collinearity issues. The average mental skill for parents is 47.98. The average physical skill
is lower, at 26.61. The average cognitive skill is 48.23, while the average noncognitive skill is
52.44. The difference in skill ranges from 1.06 for mental skill to 4.55 for noncognitive skill.
5.5
Estimation Strategy
Baron-Cohen (2006) argues that an assortative match between two high systemizers leads
to an extreme ability to systemize in biological offspring. I now extend his theory to other
mental disorders and broad measures of mental, physical, cognitive, and noncognitive skill.
There are four outcome variables of interest: whether a child has been diagnosed with any
mental disorder, ADHD, an anxiety disorder, or a mood disorder. The first equation is:
disordercjt = α + βmpjt + λppjt + γZjt + cjt ,
(5.5.1)
where disordercjt is a dummy for the disorder in question for a child c in household j, mpjt
and ppjt are the average mental and physical skill for couples in household j, and Zjt is a
vector of controls for household j in year t, including the child’s race, age, and sex and the
head of household’s age, income, marital status, education, and hours worked. Results of
equation 5.5.1 are in Tables 10 and 11.
Next, I focus on cognitive and noncognitive skill:
disordercjt = α + θcpjt + ψnpjt + λph + γZ + cjt ,
28
(5.5.2)
where cpjt , npjt , and ppjt are the measures of couples’ average cognitive, noncognitive, and
physical skill and disorder1jt and Zjt are as described above. Results of equation 5.5.2 are
in Tables 12 and 13.
5.5.1
Identification Issues
The identifying assumption of this framework is that cjt is uncorrelated with the mental,
physical, cognitive, and noncognitive skill requirements of their parents’ jobs. There is significant evidence that the parents of children with health issues work less: Gould (2004) shows
how children with time-intensive and unpredictable illnesses negatively influence parents’ labor supply. In particular, single mothers work fewer hours if their child has a time-intensive
illness and married mothers are less likely to work and work fewer hours if their child has
an unpredictable illness. To my knowledge, there is no evidence linking children’s health to
parents’ specific occupational choice. Thus, I assume parents do not select into occupations
based on their child’s mental health.
5.6
Results & Discussion
Tables 10 and 11 include the logistic regressions of mental and physical on mental disorders,
ADHD, anxiety disorders, and mood disorders. Parents’ mental skill is associated with a
broad indicator of children’s mental disorders, though the relationship is subject to diminishing returns. A one-unit increase in parents’ mental skill increases the odds of being diagnosed
with a mental disorder by 26%. Age, gender, and race also matter: the odds of developing a
mental disorder increase by 14% annually; the odds of developing a mental disorder increase
by 84% for boys; and the odds of developing a mental disorder are 29% lower for blacks and
41% lower for Hispanics. Children with older parents, lower-income parents, and single parents are less likely to be diagnosed with a mental disorder. Parents of children with mental
disorders work less – the direction of causation is questionable, but Gould (2004) finds that
parents may work less for unpredictable illnesses and more for financially-straining illnesses.
The likelihood of mental disorders is consistently increasing over the time horizon.
When ADHD, anxiety disorders, and mood disorders are analyzed separately, only
mood disorders are associated with the mental skill of parents. The effect is larger in magnitude: a one-unit increase in parents’ mental skill increases the odds of being diagnosed
with a mood disorder by 101%. ADHD, anxiety disorders, and mood disorders are more
likely to occur in older children and to children of single parents. Males are more likely to
29
be diagnosed with ADHD, Hispanics are less likely to be diagnosed with ADHD and anxiety
disorders, and black children are less likely to be diagnosed with anxiety or mood disorders.
ADHD and mood disorders are associated with lower parental incomes, while anxiety disorders are associated with less parental education. While ADHD is consistently increasing over
the time horizon – likely driving the increase of mental disorders at large – mood disorders
are falling at the end of the time horizon.
Tables 12 and 13 provides estimates of the logistic regressions of cognitive skill and
noncognitive skill on mental health outcomes. Parents’ noncognitive skill is positively associated with the incidence of mental disorders in children – a one-unit increase in noncognitive
skill increases the odds being diagnosed with a mental disorder by 76%. As with mental
skill, the relationship is subject to diminishing returns. Parents’ noncognitive skill is also
associated with the incidence of ADHD. Interestingly, parents’ cognitive skill decreases the
likelihood that children are diagnosed with an anxiety disorder. A one-unit increase in
cognitive skill decreases the odds of being diagnosed with an anxiety disorder by 36%.
These results suggest a positive relationship between parents’ mental and noncognitive
skill and the incidence of mental health disorders. Additionally, I find a negative relationship
between cognitive skill and the incidence of anxiety disorders. While the effects cannot be
decomposed into genetics, the environment, and their match, this doesn’t negate the public
health implications: if labor market sorting promotes sorting by nature or nurture, labor
market sorting can also affect the intergenerational transmission of health.
5.7
Limitations
This paper’s application to mental health faces two main limitations: first, there is a general lack of suitable and easily accessible data, particularly in the US; second and given
these data limitations, any identified effects include nature, nurture, and the idiosyncratic
match between nature and nurture. Turkheimer (2000) highlights the crux of the problem:
“[i]f the underlying causal structure of human development is highly complex [...] the relatively simple statistical procedures employed by developmental psychologists, geneticists,
and environmentalists alike are being badly misapplied” (163).
In some European countries, registry data are readily available and growing in popularity.15 Given the falling cost of genetic coding, these registries are allowing for more
15
For example, Denmark instituted the Danish Cyrogenetic Central Register in 1960, which collects prenatal and postnatal blood samples for chromosomal analysis “that provide a unique opportunity to collect
patient data at the individual level routinely, in some cases at the family level, and to carry out reliable
30
genome sequencing of large populations. Recently, a group in Iceland sequenced the entire
genome for more than 2,500 Icelander and sequenced parts of the genome for more than
100,000 Icelanders. There are a variety of public health benefits: “[l]arge scale whole genomic sequencing has allowed the detection of rare sequence variants that range in effect
from causing diseases to modifying complex disease risk-variants that would recently either
not have been observed or could not be tested for association with disease on a sufficiently
large scale” (Gudbjartsson et al. 2015, 1). The scope of these registries is politically infeasible in the US, as the public share of the private health insurance market is substantially
lower. However, Beauchamp et al. (2011) discuss the efforts taken by the National Longitudinal Study of Adolescent Health, the Wisconsin Longitudinal Study, and the Health and
Retirement Survey to collect genetic markers in addition to economic information.
Unfortunately, the explosion of genetic data does not circumvent all of the difficulty in
measuring heritability. “There are myriad confounds to a causal interpretation [...] because
of the way DNA is transmitted from parents to children, the genotype [...] is often highly
correlated with the genotypes of nearby [single-nucleotide polymorphisms (SNPs), necessitating follow-up work to any robustly detected association to identify which SNP is actually
responsible” (Benjamin et al. 2012, 644).16 Another issue is the endogeneity of nature and
nurture: parents’ genotypes correlate with both children’s genotypes and environments.
6
Policy Implications
The direct cost of mental health is large. In a large European study, the direct costs of
depression were over $2,000 per diagnosis – with half going toward outpatient care, a quarter
going toward inpatient care, and a quarter going toward prescriptions (Sobocki et al. 2006).
The indirect costs may be even larger, as individuals with depression average 5 hours of
productivity loss per week; overall, lost time costs US employers of $50 billion annually
(Stewart et al. 2003). The direct cost of anxiety disorders was $42 billion in 1990, with
approximately 10% of these costs associated with lost productivity (Greenberg et al. 1999).
Another implication involves newborn screening. Currently, Georgia offers screenings
for amino acid disorders, organic acidemias, fatty acid defects, galactosemia, biotinidase
kinship tracking” (Nguyen-Nielsen et al. 2013, 1). This register has over 300,000 registrations, with 10,000
new registrations each year. Additionally, Denmark collects registries for nonpolyposis colorectal cancer,
breast and ovarian cancer, Huntington’s, cystic fibrosis, eye diseases, retinitis pigments, von Hippel-Lindau
disease, Fabry disease, angiodema, and prophyria (Nguyen-Neilson et al. 2013).
16
SNPs are the A, T, C, and G sequences in DNA.
31
deficiency, endocrine disorders, hemoglobinopathies, and cystic fibrosis (Georgia Department
of Public Health 2014). Though biomarkers for many mental disorders have yet to be
identified, this line of research could provide better information to parents17 In the case
of autism, early intervention is crucial, as a younger age at diagnosis is one of the bestknown predictors of functional outcome (Harris & Handleman 2000). Though the differences
between infants with and without autism can be detected at less than a year of age, fewer
than half of children with autism are diagnosed before 5 years of age (Werner et al. 2000;
Maenner et al. 2013). Benjamin et al. (2012) offer another example: “if dyslexia can
eventually be predicted sufficiently well by genetic screening, parents with children who
have dyslexia-susceptibility genes could be given the option of enrolling their children in
supplementary reading programs, years before a formal diagnosis of dyslexia” (640).
Next, consider a major player in modern marriage: the computer. Between 1995 and
2005, the share of couples who met online grew from 0 to 22 percent (Rosenfeld & Thomas
2012). Online dating sites like Match.com use algorithms to match individuals along similar
dimensions. These dimensions include preferences and attitude, which are undoubtedly
correlated to one’s phenotype and genotype. Presumably, these algorithms do not currently
consider the potential health outcomes of biological offspring.
Finally, the conclusions of this paper may shed light on our society’s growing mental
health problem. As labor market sorting increases – particularly for women in developing
countries – we should expect changes in the genetic distribution of the population and,
perhaps, the growth and wane of certain disorders. Evidence of the theory of assortative
mating is limited and based mainly in Europe. Researchers in the US need to fully consider
the possibility that genetic similarities of parents may cause genetic extremes in children.
7
Conclusion
Marriage has changed. In this paper, I develop a model of marriage in which agents sort in
labor markets based on their genetics and skill, thereby increasing the likelihood that they
match with a genetically similar agent. The theory predicts that wages, the dispersion of
skill, and moving costs can induce genetically similar agents to match and shape the genetic
composition of the following generation. I then estimate the skill compositions within and
across marriages. I assume that these skill measures serve as a proxy for one’s underlying
17
In my opinion, the information set should also include the challenges and benefits of neurodiversity, as
described by Ortega (2009).
32
genetic make-up. There is more similarity by mental and cognitive skill, which both enjoy
a higher conditional correlation with earnings than physical and noncognitive skill. Finally,
I ask whether children and adolescents’ mental health outcomes are driven, in part, by the
assortative match of their parents using the CDC’s Autism and Developmental Disabilities
Monitoring Network and the Medical Expenditures Panel Survey. I find higher rates of autism
in Census tracts with a more systemizing strength. I also find that a parent’s mental and
noncognitive skill measure has a significant and positive relationship with the incidence of
mental disorders in their children, though the relationship is subject to diminishing returns.
Combined, the results of this paper suggests an unexplored research arc: as we play to our
comparative advantage in the labor market, are we also shaping public health?
33
8
Tables and Figures
1
AA × AB
BB × AB AB × AB
AA × BB
BB × BB AB × BB
AA × AA
BB × AA AB × AA
πBB
πAA
0
πAA
πBB
1
Figure 1: Outcome Space in Sector 2, First Generation
1
AA × AB
BB× AB×
AB AB
AA × BB
BB× BB×
BB AB
AA × AA
AA× AA×
BB AB
∗
πBB
∗
πAA
∗
∗
πAA
πBB
0
1
Figure 2: Outcome Space in Sector 2, Second Generation
34
w1 (i)
w2 (i)
φ(i)
w1 (i∗ )
w2 (i∗ )
φ(i) =
0
w1 (i∗ )
0
w2 (i∗ )
θ(i)
θ0 (i)
0
i∗
non-STEM
i
i∗
STEM
Figure 3: The STEM Effect
35
φAA
2 (i)
φAA
1 (i)
Table 1: Correlation of Couples’ Average Skill, CPS
earnings
education
age
mentala
physicalb
cognitivec
noncognitived
obs
2001
0.129
0.624
0.931
0.319
0.163
0.293
0.212
14,112
2002
0.107
0.619
0.928
0.312
0.163
0.288
0.197
13,576
2003
0.129
0.629
0.928
0.305
0.130
0.281
0.192
13,607
2004
0.082
0.623
0.928
0.317
0.132
0.287
0.210
14,030
2005
0.108
0.619
0.925
0.311
0.115
0.301
0.200
17,587
2006
0.118
0.634
0.923
0.323
0.130
0.307
0.193
12,871
2007
0.154
0.634
0.927
0.328
0.124
0.307
0.226
12,842
2008
0.139
0.632
0.927
0.322
0.115
0.304
0.208
12,791
2009
0.147
0.634
0.921
0.311
0.115
0.295
0.202
12,740
2010
0.186
0.625
0.924
0.341
0.113
0.334
0.219
12,437
a The
average mental skill measure includes accuracy, analyzing data, assisting others, creativity, developing strategies,
inductive reasoning, mathematical reasoning, memorization, organization, originality, perceptual speed, persuasion, processing information, time management, and updating and using relevant knowledge.
b The average physical skill measure includes arm hand steadiness, control precision, dynamic strength, dynamic flexibility, explosive strength, finger dexterity, gross body coordination, gross body equilibrium, manual dexterity, multilimb
coordination, rate control, reaction time, speed of limb movement, stamina, and static strength.
c The average cognitive skill measure includes inductive reasoning, perceptual speed, analyzing data, mathematical ability, and creativity.
d The average noncognitive skill measure includes persuasion, interpersonal skill, judgment and decision making, time
management, and assisting others.
36
Table 2: Correlation of Couples’ Skill, CPS †
earnings
education
age
mental
physical
cognitive
noncognitive
obs
2001
0.129
0.624
0.931
0.215
0.195
0.424
0.100
14,112
2002
0.107
0.619
0.928
0.221
0.193
0.445
0.107
13,576
2003
0.129
0.629
0.928
0.215
0.197
0.460
0.113
13,607
2004
0.082
0.623
0.928
0.216
0.202
0.456
0.097
14,030
2005
0.108
0.619
0.925
0.231
0.210
0.494
0.122
17,587
2006
0.118
0.634
0.923
0.232
0.203
0.483
0.139
12,871
2007
0.154
0.634
0.927
0.235
0.205
0.423
0.127
12,842
2008
0.139
0.632
0.927
0.227
0.194
0.423
0.118
12,791
2009
0.147
0.634
0.921
0.243
0.207
0.436
0.119
12,740
2010
0.186
0.625
0.924
0.237
0.213
0.391
0.145
12,437
† The skill measures are constructed using the Lubotsky-Wittenberg procedure, in which the coefficients from a linear
regression of each mental and physical dimension on log(earnings) are used as weights in the aggregation into a single index. Mental skills include accuracy, analyzing data, assisting others, creativity, developing strategies, inductive
reasoning, mathematical reasoning, memorization, organization, originality, perceptual speed, persuasion, processing information, time management, and updating and using relevant knowledge. Physical skills include arm hand
steadiness, control precision, dynamic strength, dynamic flexibility, explosive strength, finger dexterity, gross body
coordination, gross body equilibrium, manual dexterity, multilimb coordination, rate control, reaction time, speed of
limb movement, stamina, and static strength. Cognitive skills include inductive reasoning, perceptual speed, analyzing data, mathematical ability, and creativity. Noncognitive skills include persuasion, interpersonal skill, judgment
and decision making, time management, and assisting others.
37
Table 3: Correlation of Couples’ Skill by College Education, CPS †
total earnings
mental
physical
observations
college
no college
college
no college
college
no college
college
no college
2001
0.075
0.059
0.124
0.095
0.129
0.141
6,107
8,005
2002
0.043
0.047
0.150
0.117
0.128
0.154
5,877
7,699
2003
0.097
0.065
0.142
0.120
0.147
0.147
5,942
7,665
2004
0.026
0.024
0.149
0.113
0.144
0.158
6,206
7,824
2005
0.040
0.041
0.145
0.134
0.145
0.167
8,164
9,423
2006
0.093
0.025
0.160
0.134
0.154
0.149
5,953
6,918
2007
0.085
0.108
0.160
0.116
0.154
0.141
6,019
6,823
2008
0.084
0.082
0.158
0.123
0.138
0.143
6,148
6,643
2009
0.094
0.088
0.158
0.139
0.142
0.154
6,181
6,559
2010
0.148
0.117
0.160
0.128
0.150
0.158
5,967
6,470
total earnings
cognitive
noncognitive
observations
college
no college
college
no college
college
no college
college
no college
2001
0.075
0.059
0.345
0.462
0.090
0.023
6,107
8,005
2002
0.043
0.047
0.393
0.474
0.112
0.018
5,877
7,699
2003
0.097
0.065
0.390
0.498
0.130
0.012
5,942
7,665
2004
0.026
0.024
0.392
0.493
0.092
0.025
6,206
7,824
2005
0.040
0.041
0.424
0.537
0.117
0.046
8,164
9,423
2006
0.093
0.025
0.422
0.522
0.147
0.034
5,953
6,918
2007
0.085
0.108
0.349
0.467
0.128
0.020
6,019
6,823
2008
0.084
0.082
0.339
0.476
0.128
0.020
6,148
6,643
2009
0.094
0.088
0.378
0.472
0.116
0.040
6,181
6,559
2010
0.148
0.117
0.318
0.441
0.147
0.033
5,967
6,470
† The
skill measures are constructed using the Lubotsky-Wittenberg procedure, in which the coefficients from a linear regression of each mental and physical dimension on log(earnings) are used as weights in the aggregation into a
single index. Mental skills include accuracy, analyzing data, assisting others, creativity, developing strategies, inductive reasoning, mathematical reasoning, memorization, organization, originality, perceptual speed, persuasion,
processing information, time management, and updating and using relevant knowledge. Physical skills include arm
hand steadiness, control precision, dynamic strength, dynamic flexibility, explosive strength, finger dexterity, gross
body coordination, gross body equilibrium, manual dexterity, multilimb coordination, rate control, reaction time,
speed of limb movement, stamina, and static strength. Cognitive skills include inductive reasoning, perceptual
speed, analyzing data, mathematical ability, and creativity. Noncognitive skills include persuasion, interpersonal
skill, judgment and decision making, time management, and assisting others.
38
Table 4: Correlation of Couples’ Skill by Age, CPS †
total earnings
mental
physical
observations
year
over 40
under 40
over 40
under 40
over 40
under 40
over 40
under 40
2001
0.137
0.126
0.194
0.238
0.190
0.197
7,172
5,195
2002
0.100
0.114
0.209
0.240
0.189
0.209
7,184
4,724
2003
0.136
0.138
0.196
0.223
0.199
0.178
7,367
4,577
2004
0.063
0.118
0.209
0.237
0.192
0.226
7,862
4,562
2005
0.090
0.139
0.209
0.263
0.202
0.221
9,965
5,589
2006
0.087
0.173
0.227
0.233
0.207
0.188
7,229
4,148
2007
0.170
0.150
0.214
0.267
0.196
0.213
7,412
4,066
2008
0.123
0.190
0.207
0.243
0.183
0.204
7,382
4,001
2009
0.130
0.178
0.225
0.271
0.202
0.217
7,431
3,947
2010
0.177
0.196
0.214
0.273
0.211
0.200
7,440
3,715
total earnings
cognitive
noncognitive
observations
year
over 40
under 40
over 40
under 40
over 40
under 40
over 40
under 40
2001
0.137
0.126
0.412
0.436
0.068
0.131
7,172
5,195
2002
0.100
0.114
0.421
0.470
0.095
0.120
7,184
4,724
2003
0.136
0.138
0.429
0.494
0.093
0.125
7,367
4,577
2004
0.063
0.118
0.484
0.508
0.117
0.127
7,862
4,562
2005
0.090
0.139
0.447
0.467
0.083
0.114
9,965
5,589
2006
0.087
0.173
0.476
0.492
0.118
0.163
7,229
4,148
2007
0.170
0.150
0.402
0.452
0.116
0.142
7,412
4,066
2008
0.123
0.190
0.417
0.432
0.125
0.109
7,382
4,001
2009
0.130
0.178
0.426
0.451
0.103
0.142
7,431
3,947
2010
0.177
0.196
0.378
0.409
0.106
0.147
7,440
3,715
† The
skill measures are constructed using the Lubotsky-Wittenberg procedure, in which the coefficients from a
linear regression of each mental and physical dimension on log(earnings) are used as weights in the aggregation
into a single index. Mental skills include accuracy, analyzing data, assisting others, creativity, developing strategies, inductive reasoning, mathematical reasoning, memorization, organization, originality, perceptual speed,
persuasion, processing information, time management, and updating and using relevant knowledge. Physical
skills include arm hand steadiness, control precision, dynamic strength, dynamic flexibility, explosive strength,
finger dexterity, gross body coordination, gross body equilibrium, manual dexterity, multilimb coordination,
rate control, reaction time, speed of limb movement, stamina, and static strength. Cognitive skills include inductive reasoning, perceptual speed, analyzing data, mathematical ability, and creativity. Noncognitive skills
include persuasion, interpersonal skill, judgment and decision making, time management, and assisting others.
39
Table 5: Variance Decomposition of Skill by Education, CPS †
total variance
within-group
between-group
mental
physical
mental
physical
mental
physical
obs
2001
4,323.1
2,516.7
3,531.0
2,215.2
792.2
301.6
14,112
2002
4,274.0
2,516.5
3,552.6
2,272.3
721.5
244.1
13,576
2003
4,352.6
2,547.3
3,663.4
2,299.6
699.1
247.7
13,607
2004
4,476.6
2,607.4
3,743.1
2,353.8
733.4
253.6
14,030
2005
6,134.0
3,583.5
5,075.4
3,226.1
1,058.5
367.5
17,587
2006
4,224.6
2,404.5
3,538.3
2,161.5
686.2
243.1
12,871
2007
4,385.5
2,527.7
3,502.2
2,236.0
803.3
291.7
12,842
2008
4,261.5
2,537.9
3,561.9
2,271.9
699.6
265.9
12,791
2009
4,382.1
2,668.8
3,605.9
2,365.3
776.2
303.4
12,437
2010
4.648.1
2,668.8
3,825.4
2,365.3
822.7
303.4
12,437
cognitive
noncognitive
cognitive
noncognitive
cognitive
noncognitive
obs
2001
0.286
8.301
0.282
7.720
0.006
0.580
14,112
2002
0.294
8.751
0.292
8.230
0.002
0.521
13,576
2003
0.381
8.342
0.377
7.865
0.003
0.477
13,607
2004
0.365
8.585
0.362
8.083
0.002
0.502
14,030
2005
0.532
12.175
0.526
11.442
0.005
0.733
17,587
2006
0.347
8.328
0.344
7.811
0.003
0.517
12,871
2007
0.302
8.886
0.299
8.288
0.003
0.598
12,842
2008
0.352
8.563
0.349
8.088
0.003
0.475
12,791
2009
0.300
9.156
0.298
8.616
0.002
0.539
12,437
2010
0.245
7.705
0.244
7.199
0.001
0.506
12,437
† The
skill measures are constructed using the Lubotsky-Wittenberg procedure, in which the coefficients from a linear regression of each mental skill on log(earnings) are used as weights in the aggregation into a single index. Variances are estimated across those couples who both attended college and couples with at least one person who did
not attend college. Mental skills include accuracy, analyzing data, assisting others, creativity, developing strategies,
inductive reasoning, mathematical reasoning, memorization, organization, originality, perceptual speed, persuasion,
processing information, time management, and updating and using relevant knowledge. Physical skills include arm
hand steadiness, control precision, dynamic strength, dynamic flexibility, explosive strength, finger dexterity, gross
body coordination, gross body equilibrium, manual dexterity, multilimb coordination, rate control, reaction time,
speed of limb movement, stamina, and static strength. Cognitive skills include inductive reasoning, perceptual
speed, analyzing data, mathematical ability, and creativity. Noncognitive skills include persuasion, interpersonal
skill, judgment and decision making, time management, and assisting others.
40
Table 6: Variance Decomposition of Skill by Age, CPS †
total variance
within-group
between-group
mental
physical
mental
physical
mental
physical
obs
2001
4,323.1
2,516.7
4,312.3
2,507.1
10.9
9.6
14,112
2002
4,274.6
2,516.5
4,255.6
2,500.0
18.5
16.5
13,576
2003
4,362.6
2,547.3
4,221.8
2,525.1
30.7
22.2
13,607
2004
4,476.6
2,607.4
4,460.6
2,591.1
16.0
16.2
14,030
2005
6,134.0
3,593.5
6,100.3
3,566.3
33.7
27.2
17,587
2006
4,224.6
2,404.5
4,209.1
2,391.1
15.5
13.4
12,871
2007
4,385.5
2,527.7
4,367.4
2,512.3
18.1
15.4
12,842
2008
4,261.5
2,537.9
4,250.3
2,526.4
11.2
11.5
12,791
2009
4,382.1
2,655.9
4,371.8
2,655.9
10.3
12.8
12,437
2010
4,648.4
2,668.8
4,637.4
2,655.8
10.7
12.8
12,322
cognitive
noncognitive
cognitive
noncognitive
cognitive
noncognitive
obs
2001
0.286
8.301
0.286
8.310
0.000
0.000
14,112
2002
0.294
8.751
0.294
8.748
0.000
0.003
13,576
2003
0.381
8.751
0.380
8.331
0.000
0.011
13,607
2004
0.365
8.585
0.365
8.578
0.000
0.008
14,030
2005
0.532
12.175
0.365
12.159
0.000
0.016
17,587
2006
0.347
8.328
0.347
8.315
0.000
0.013
12,871
2007
0.302
8.886
0.302
8.872
0.000
0.014
12,842
2008
0.352
8.563
0.352
8.550
0.000
0.013
12,791
2009
0.300
9.156
0.300
9.142
0.000
0.013
12,437
2010
0.245
7.705
0.245
7.694
0.000
0.011
12,322
† The skill measures are constructed using the Lubotsky-Wittenberg procedure, in which the coefficients from a linear
regression of each mental skill on log(earnings) are used as weights in the aggregation into a single index. Variances
are estimated across those couples above age 40 and those couples with at least one person below age 40. Mental
skills include accuracy, analyzing data, assisting others, creativity, developing strategies, inductive reasoning, mathematical reasoning, memorization, organization, originality, perceptual speed, persuasion, processing information,
time management, and updating and using relevant knowledge. Physical skills include arm hand steadiness, control
precision, dynamic strength, dynamic flexibility, explosive strength, finger dexterity, gross body coordination, gross
body equilibrium, manual dexterity, multilimb coordination, rate control, reaction time, speed of limb movement,
stamina, and static strength. Cognitive skills include inductive reasoning, perceptual speed, analyzing data, mathematical ability, and creativity. Noncognitive skills include persuasion, interpersonal skill, judgment and decision
making, time management, and assisting others.
41
Table 7: Summary Statistics, ADDM Network
autism
0.009
(0.007)
systemizing
39.496
(3.729)
empathizing
56.439
(2.085)
median income, in thousands
59.389
(30.677)
percent in poverty
10.579
(12.588)
percent with Bachelors
21.996
(12.782)
Clayton County
0.079
Cobb County
0.182
DeKalb County
0.241
Fulton County
0.349
Gwinnett County
0.149
observations
474
Standard deviations are provided in parentheses. Systemizing
and empathizing is measured on a 0-100 scale.
42
Table 8: Autism Prevalence and Systemizing Strength, ADDM Network
%8 year olds with autism
systemizing
0.00121∗∗∗
0.00115∗∗∗
0.00213∗∗∗
(0.00025)
(0.00035)
(0.00080)
-0.00059
-0.00150
(0.00050)
(0.00114)
-0.00002
-0.00003
(0.00002)
(0.00005)
∗∗∗
empathizing
-0.00121
(0.00046)
median income ($1,000s)
∗∗∗
%poverty
-0.00013
(0.00003)
%Bachelor’s
-0.00012
∗
(0.0007)
Cobb
-0.00018∗∗∗
(0.00009)
-0.00023
(0.00016)
0.00224
(0.00304)
DeKalb
-0.00042
(0.00289)
Fulton
0.00046
(0.00299)
0.00541∗
Gwinnett
(0.00306)
observations
R
2
Robust standard errors are provided in parentheses.
∗∗∗
indicates statistical significance at the 1% level.
indicates statistical significance at the 5% level.
indicates statistical significance at the 10% level.
∗∗
∗
43
474
474
474
0.110
0.146
0.097
Table 9: Summary Statistics, MEPS
child
any mental disorder
0.052
(0.221)
adhd
0.023
(0.151)
anxiety disorder
0.007
(0.081)
mood disorder
0.008
(0.086)
age
8.317
(5.157)
male
0.515
(0.500)
Hispanic
0.296
(0.456)
black
0.163
(0.369)
age
39.028
(10.830)
grade completed
12.441
(3.222)
annual income (in $1000s)
29.445
(32.180)
married
0.610
(0.488)
hours worked
38.527
(11.929)
average mental skill
47.981
(4.196)
average physical skill
26.609
(7.340)
average cognitive skill
48.228
(4.857)
average noncognitive skill
52.439
(3.528)
head
parents
Standard errors are provided in parentheses. Skill is measured on a 0-100 scale.
44
Table 10: Logit of Any Mental Disorder and Mental/Physical Skill, MEPS
parents’ mental skill
parents’ mental skill
2
0.230∗∗
(0.107)
∗∗
(0.001)
-0.002
parents’ physical skill
2
parents’ physical skill
0.007
(0.018)
0.000
(0.000)
age
0.131
∗∗∗
(0.004)
male
0.609∗∗∗
(0.033)
-0.500
∗∗∗
(0.044)
-0.335
∗∗∗
(0.047)
∗∗
(0.002)
∗∗∗
(0.001)
Hispanic
black
head’s age
0.005
head’s income
-0.003
head’s education
0.004
(0.007)
head’s marital status
-0.499
∗∗∗
(0.036)
head’s hours worked
-0.003∗∗
(0.001)
2004
0.137∗∗
(0.062)
2005
∗∗
(0.063)
∗∗∗
(0.062)
∗∗∗
(0.064)
∗∗∗
(0.062)
2009
0.127
∗∗
(0.062)
2010
0.308∗∗∗
(0.063)
0.128
2006
0.193
2007
0.261
2008
0.273
constant
-10.093
observations
R
∗∗∗
99,413
2
0.070
Standard errors are provided in parentheses.
∗∗∗
indicates statistical significance at the 1% level.
indicates statistical significance at the 5% level.
indicates statistical significance at the 10% level.
∗∗
∗
(2.622)
45
Table 11: Logit of ADHD, Anxiety, and Mood Disorders
and Mental/Physical Skill, MEPS
ADHD
0.229
(0.153)
parents’ mental skill
anxiety
-0.409
(0.280)
mood
0.699
∗∗
(0.300)
∗∗
(0.003)
2
-0.003
parents’ physical skill
-0.043
(0.025)
0.075
(0.048)
0.012
(0.048)
parents’ physical skill2
0.001
(0.000)
-0.001
(0.001)
-0.000
(0.001)
parents’ mental skill
age
male
Hispanic
black
head’s age
head’s income
head’s education
head’s marital status
head’s hours worked
(0.002)
0.121
∗∗∗
(0.005)
1.152
∗∗∗
(0.052)
-0.616
∗∗∗
(0.067)
-0.026
(0.062)
∗
(0.003)
0.005
∗∗∗
-0.004
0.004
∗∗∗
0.153
-0.103
∗∗∗
-0.450
∗∗∗
-0.971
0.003
(0.003)
(0.010)
-0.007
∗∗∗
0.236
(0.012)
(0.084)
-0.106
(0.080)
(0.121)
-0.080
(0.103)
(0.164)
(0.006)
-0.563
∗∗∗
0.002
(0.005)
(0.001)
0.001
(0.001)
-0.003
0.010
0.064∗∗∗
(0.021)
-0.017
(0.017)
-0.340∗∗∗
(0.052)
-0.409∗∗∗
(0.096)
-0.731∗∗∗
(0.090)
(0.002)
∗∗
(0.004)
-0.002
(0.004)
-0.003
-0.009
-0.004
∗∗
(0.132)
(0.002)
0.213
∗∗
(0.096)
-0.134
(0.156)
-0.015
(0.141)
0.200
∗∗
(0.098)
-0.172
(0.162)
-0.046
(0.146)
∗∗∗
(0.097)
-0.004
(0.154)
-0.079
(0.146)
2007
∗∗∗
0.472
(0.091)
-0.105
(0.164)
-0.090
(0.154)
2008
0.589∗∗∗
(0.091)
-0.044
(0.157)
-0.172
(0.152)
2009
∗∗∗
2004
2005
2006
2010
constant
0.250
0.504
∗∗∗
0.665
-10.321
observations
R
2
∗∗∗
(0.090)
(0.093)
(3.757)
-0.211
2.450
(0.160)
(0.170)
(6.925)
-0.545
(0.152)
∗∗
(0.166)
∗∗∗
(7.269)
-0.330
-24.135
99,413
99,413
99,413
0.079
0.067
0.110
Standard errors are provided in parentheses.
∗∗∗
indicates statistical significance at the 1% level.
indicates statistical significance at the 5% level.
indicates statistical significance at the 10% level.
∗∗
∗
-0.264
∗∗∗
46
Table 12: Logit of Any Mental Disorder and Cognitive/Noncognitive Skill, MEPS
parents’ cognitive skill
parents’ cognitive skill
2
parents’ noncognitive skill
2
parents’ noncognitive skill
-0.035
(0.077)
0.000
(0.001)
0.565
∗∗∗
(0.154)
∗∗∗
(0.001)
-0.005
parents’ physical skill
-0.017
(0.020)
parents’ physical skill2
0.000
(0.000)
age
∗∗∗
(0.004)
∗∗∗
(0.033)
∗∗∗
(0.044)
∗∗∗
(0.047)
∗∗
(0.002)
∗∗∗
(0.001)
0.131
male
0.608
Hispanic
-0.506
black
-0.342
head’s age
0.005
head’s income
-0.003
head’s education
0.005
(0.007)
∗∗∗
(0.036)
∗
(0.001)
0.138
∗∗
(0.062)
0.130
∗∗
(0.063)
0.193
∗∗∗
(0.062)
2007
0.260
∗∗∗
(0.064)
2008
0.274∗∗∗
(0.062)
2009
∗∗
(0.062)
∗∗∗
(0.063)
head’s marital status
-0.483
head’s hours worked
-0.003
2004
2005
2006
0.125
2010
0.304
∗∗∗
constant
-18.395
observations
R
99,413
2
0.071
Standard errors are provided in parentheses.
∗∗∗
indicates statistical significance at the 1% level.
indicates statistical significance at the 5% level.
indicates statistical significance at the 10% level.
∗∗
∗
(3.884)
47
Table 13: Logit of ADHD, Anxiety, and Mood Disorders
and Cognitive/Noncognitive Skill, MEPS
parents’ cognitive skill
ADHD
0.024
(0.113)
anxiety
-0.441∗∗
(0.196)
mood
0.210
(0.217)
parents’ cognitive skill2
-0.000
0.004∗∗
(0.002)
-0.002
(0.001)
(0.002)
parents’ noncognitive skill
0.491
∗∗
(0.217)
0.271
(0.407)
0.646
(0.042)
parents’ noncognitive skill2
-0.005∗∗
(0.002)
-0.002
(0.004)
-0.006
(0.004)
parents’ physical skill
-0.067∗∗
(0.027)
0.045
(0.055)
0.006
(0.005)
∗∗
(0.001)
-0.001
(0.001)
0.000
(0.001)
2
parents’ physical skill
age
male
Hispanic
0.001
∗∗∗
(0.005)
∗∗∗
(0.052)
0.121
1.151
∗∗∗
-0.619
(0.067)
∗∗∗
0.153
-0.104
∗∗∗
-0.461
0.236
(0.012)
(0.084)
-0.105
(0.080)
(0.121)
-0.090
(0.103)
black
-0.029
(0.063)
0.005∗
(0.003)
0.003
(0.006)
0.002
(0.005)
-0.004∗∗∗
(0.001)
0.001
(0.001)
-0.003∗∗
(0.002)
(0.021)
-0.013
(0.017)
head’s education
head’s marital status
head’s hours worked
-0.004
-0.335
∗∗∗
-0.003
(0.010)
(0.052)
(0.002)
0.067
∗∗∗
(0.164)
-0.574
∗∗∗
head’s age
head’s income
-0.981
∗∗∗
(0.010)
∗∗∗
∗∗∗
(0.097)
∗∗
(0.004)
-0.001
(0.004)
-0.396
-0.008
-0.701
∗∗∗
(0.133)
(0.090)
0.214
∗∗
(0.096)
-0.132
(0.156)
-0.011
(0.141)
2005
0.200
∗∗
(0.098)
-0.169
(0.161)
-0.041
(0.146)
2006
0.251∗∗∗
(0.097)
-0.004
(0.154)
-0.079
(0.146)
2007
0.472
∗∗∗
(0.096)
-0.105
(0.164)
-0.091
(0.154)
0.590
∗∗∗
(0.091)
-0.043
(0.157)
-0.170
(0.152)
0.504
∗∗∗
(0.090)
∗
0.664
∗∗∗
2004
2008
2009
2010
constant
∗∗∗
-17.846
-0.265
(0.160)
-0.547
∗∗∗
(0.163)
∗∗
(0.166)
(0.093)
-0.215
(0.170)
-0.336
(5.435)
-3.560
(10.320)
-30.044
(10.647)
observations
99,413
99,413
99,413
R2
0.080
0.063
0.111
Standard errors are provided in parentheses.
∗∗∗
indicates statistical significance at the 1% level.
indicates statistical significance at the 5% level.
indicates statistical significance at the 10% level.
∗∗
∗
48
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