The health and behavioral outcomes of out-of-wedlockchildren from families of social fathers
Kwok Ho Chan • Ka Wai Terence Fung •
Ender Demir
Received: 18 May 2013 / Accepted: 9 January 2014
� Springer Science+Business Media New York 2014
Abstract There is abundant evidence that childhood health status affects socio-
economic status (income, wealth and academic results) in later stages of life. This
study examines the potential impact of social fathers on children’s health and
behavioral outcomes. The current family and health literature mostly focuses on the
impact of social fathers on the well-being of older children or adolescents. Using the
data from the Fragile Families and Child Wellbeing Study, we examine the health
and behavioral outcomes of younger children (3-year olds) whose mothers marry (or
live with) social fathers after the children are born. Moreover, most of the past
studies neglect the self-selection problem; we apply the propensity score matching
method to address the sample bias issue of the child’s mother self-selecting to have
a new partner. We found that children with social fathers did not differ significantly
in terms of the probability of having asthma, measures of depressive, aggressive
behavior and positive attitude, from children living with only biological mothers.
Keywords Child welfare � Family structure � Fragile Families � Non-marital
childbearing
JEL Classification J12 � J13
K. H. Chan � K. W. T. Fung (&)
Division of Business and Management, United International College, Zhuhai, China
e-mail: [email protected]
K. H. Chan
e-mail: [email protected]
E. Demir
Faculty of Tourism, Istanbul Medeniyet University, Istanbul, Turkey
e-mail: [email protected]
123
Rev Econ Household
DOI 10.1007/s11150-014-9238-9
1 Introduction
Without a doubt, shifts in family structures are a contributing factor to the level of
well being in children. In the United States, family demography has undergone
drastic changes during recent decades. For example, only 5 % of children were born
to unwed parents in 1960. That share rose to 18 % in 1980 and a stunning 40 % in
2007, which is more than an eightfold increase (Waldfogel et al. 2010). These
changes in family formation in the past several decades have increased children’s
exposure to the partnership instability of mothers (Cooper et al. 2011). Since unwed
mothers tend to be younger than married women, they are likely to get married or
engage in a romantic relationship with a cohabiting partner (Fomby and Osborne
2010; Osborne and McLanahan 2007). If the mother is married to or cohabiting with
a new partner, the latter is defined as a social father.
The current study uses US longitudinal data from a cohort of 3-year-old children,
the majority of which were born to unwed parents, to examine the association
between family instability patterns and physical health. We focus on the impact of
social fathers on the well-being of young children using data from the Fragile
Families and Child Wellbeing Study (FFCWS). The four measures are whether the
child has asthma, internalizing and externalizing behavioral scores, and the
Adaptive Social Behavior Inventory (ASBI, which measures children’s social
competence) by Hogan et al. (1992).
Several important questions will be addressed. Is the existence of social fathers
beneficial because children fare better if a mother and father (even though non-
biological) dwell together? Does the social father increase the economic resources
devoted to the stepchildren? Do children born to unwed parents that later live with a
social father exhibit more behavioral problems at age 3 than children who remain in
a single-mother family? Does moving to a new environment cause more stress or
interruption in the children’s original routines? The answers to these questions have
very different policy implications.
The analysis makes several contributions to the literature. Most early studies
generally showed that older children living with cohabiting parents fared less well than
their counterparts with married parents in various aspects (Brown 2004; Manning
2002). This paper aims to extend previous research by focusing on 3-year-old children
born to unmarried parents and by considering how resident social fathers affect
children’s well-being. One of the advantages is that we can avoid the confounding
effect of family instability with that of family structural change. Children may not have
the capacity to comprehend the difference between a social and biological father at
such a young age; thus there will be less resistance to involvement by a social father
than older children usually exhibit (Bzostek 2008). Most current studies used married
couples as a reference group focusing on divorce and separation. We focus on the
relationship between a child’s health outcomes and a more detailed category of family
structures, namely families with single mother versus families with social fathers.
Actually, some studies that have compared children in different familial structures
failed to distinguish between biological and non-biological cohabiting parents (Adlaf
and Ivis 1997; Guterman et al. 2009). This study examines only the effect of non-
biological fathers on the health and behavioral outcomes of young children. In order to
K. H. Chan et al.
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identify the effect of social fathers on the children, we compare out-of-wedlock
children in families with a biological mother and a social father to out-of-wedlock
children in families with only a biological mother.
The assignment of children to have social fathers can be endogenous; that is,
potentially related to the characteristics of the mothers, such as education level,
employment status, and income level. The outcome difference between children
with social fathers and children without social fathers may be caused by those
characteristics of the mothers regardless of the presence of social fathers.
Conventional least square estimation may lead to a biased estimate. To address
the selection bias, we adopted a methodology similar to Liu and Heiland (2012),
using the propensity score matching method1 to estimate the effect of social fathers
on the children’s wellbeing. The method estimates the average treatment effect by
constructing a setting similar to an experiment in which the treatment (the presence
of social fathers in this study) is randomly assigned. We are different from Liu and
Heiland (2012) in an important aspect. While Liu and Heiland (2012) examined the
causal effect of unwed mothers getting married with the biological father, this study
analyzes the impact of unwed mothers cohabiting with or marrying a new partner.
We found that the presence of social fathers did not have any significant negative
effect on children’s health and behavior. Children aged three living in families with
social fathers have similar outcomes in health and behavior as those living only with
their biological mothers. Health and behavior of the children are not the only aspects
that can be affected by social fathers, but those will not be addressed in this paper.
The number of social fathers can be expected to rise due to the increase in single
parent births. Any potentially negative effect caused by the social fathers will affect
a large portion of the future population of children.2
2 Background
2.1 Why interest in early childhood health?
According to the Social Stress Theory, partnership transitions lead to changes in
material and social resources which then create stress and diminish the psycholog-
ical functioning of mothers’ positive interactions with the children (George 1989).
This ultimately affects parenting quality. Children’s health and behavioral outcomes
can worsen when the mothers, who are supposed to provide meals and nutrition,
manage child healthcare and provide guidance for exercise and television, are less
nurturing. This is important because the literature has documented a strong
correlation between children’s initial health and socioeconomic status (income,
academic achievement and wealth) in later age (Currie and Madrian 1999). One of
the economic rationales is the life course hypothesis. Poorer childhood health can
1 See Rosenbaum and Rubin (1983), Heckman et al. (1998) and Imbens (2004) for details of propensity
score matching method.2 Around 4.2 million children under age 18 in the United States were living with biological mother and a
social father, as shown by Data from the 2004 Survey of Income and Program Participation (Sweeney
2010).
The health and behavioral outcomes of out-of-wedlock children
123
translate into chronic health problems throughout adulthood. Moreover, health
problems deprive the child’s opportunity to receive education (for instance,
increasing absence) which leads to poor labor skills and lower wage compensation.
Psychological evidence also indicates that children are very responsive to changes
in their immediate environment during the period from infancy to preschool
(Duncan et al. 1994). Instability and stress in childhood may lead to continued
destabilizing events in the future.
For instance, using a cohort of British-born children in 1958 and keeping their
health records until adulthood, Case et al. (2005) found that people who had a low-
birth weight or chronic health conditions during childhood are more likely to have
persistent health problems when reaching adulthood. Moreover, their academic
performance (by means of public exam results), working hours and occupational status
is inferior. It is also possible that behavioral problems such as childhood aggression at
a young age can translate into anti-social behavior in adolescence and adulthood
(Moffitt et al. 2002). Lundberg (1993), using a representative sample from Sweden,
showed that conflicts in the family during childhood, having a broken family and
economic hardship were associated with illness later in life. Black et al. (2007)
examined the impact of low-birth weight using a sample of sets of twins from Norway.
They found that underweight newborns tended to have a higher mortality rate and
inferior academic and work outcomes later in life. To control for unmeasured family
attributes, Smith (2005) used the Panel Survey of Income Dynamics (PSID) to
estimate how childhood health can affect levels and trajectories of education, family
income, household wealth, individual earnings, and labor supply. Except education,
Smith (2005) found signficant effects on all measures of socioeconomic status.
2.2 Health outcome: asthma
The first variable of interest is whether the child has asthma (as reported by the
mother) by age three. Asthma is one of the most common chronic illnesses among
young children. It is generally believed that family structure and instability increase
the risk of asthma. A large-scale survey using five data sources from the US
National Health Center of Statistics found that 7.5 % of young children from age
0–17 have reported asthma. There was clear evidence of racial disparity. Young
black children were more likely to have asthma (Akinbami and Schoendorf 2002).
How can family instability be related to the occurrence of asthma in children? It is
well known that asthma triggers include pet dander, cockroaches and dust mites.
Children who have multiple relocation experiences are exposed to more settings
with asthma triggers. Moreover, children born in stable two-parent families may
experience less stress and more stability in their household arrangements. Medical
evidence reveals that psychological stress can weaken the immune processes,
leading to asthma (Chen et al. 2006). Maternal stress during pregnancy and
parenting quality may affect the immune system in ways that can be associated with
a higher risk of asthma (Klinnert et al. 2001). While familial dissolution clearly has
a negative impact on children’s health outcomes, familial union may reduce
children’s asthma risk due to the economic resources gained through a new
partnership. For instance, the children may move to a better housing environment.
K. H. Chan et al.
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Evidence from prior research using data from the National Health Interview
Survey has suggested a correlation between single-mother families and children’s
chances of getting asthma (Dey et al. 2004; Newacheck and Halfon 2000). Harknett
(2009) found children born to married parents have the lowest likelihood of being
diagnosed with asthma and experiencing asthma-related emergencies, followed by
cohabiting mothers and single mothers. Parental coresidence, demographics and the
mother’s socioeconomic status are the key determinants.
2.3 Behavioral outcomes
How do structural changes in the family affect children’s behavior? The core
concept of union stability is that children and parents form a functioning system.
Interruption in this system, regardless of the union or separation of parents or
partners, may lead to long-term deleterious behaviors in children. A child’s mental
and psychological stability may be disrupted either through the child’s direct
observation of family conflict or through the influence of conflict on parenting style
and parenting stress (Fomby and Osborne 2010). Prior research shows that family
structure instability is correlated to externalizing behavior problems (Fomby and
Cherlin 2007). There is evidence that young children from cohabiting families have
more reported behavioral problems than those growing up in a family where parents
are married. Most of the differences come from household income, parental
background and pre-existing maternal health outcomes (Osborne et al. 2004). Beck
et al. (2010) examined how a mother’s partnership changes and parenting behavior
affects children’s outcomes. Controlling for race, maternal education and initial
family structure, the authors contend that both union and dissolution are associated
with significantly higher rates of maternal parenting stress and harsh discipline.
Waldfogel et al. (2010) contended that young children’s behavioral problems are
a combined result of family structure and stability because prior studies indicate that
behavioral problems are more intense in both stable single-mother and unstable
cohabitating families (Osborne and McLanahan 2007). Cooper et al. (2011) using
the FFCWS data, investigated the relationship between a mothers’ partnership
instability and children’s school readiness and behavioral problems. It was found
that partnership transitions of mothers (both co-residential and dating transitions)
are positively related to behavioral problems and negatively related to verbal ability.
This impact is higher for boys than for girls. Some studies did not find evidence that
family instability affects young children’s behavior. Osborne and Mclanahan (2007)
provided supportive evidence for the positive association between partnership
transitions and aggressive and anxious/depressive behavior of children at age 3. Wu
et al. (2008) supported the strong harmful effect of marital disruption on children’s
psychological functioning in Canada, whereas cohabitation breakdown is found to
be uncorrelated with children’s well-being.
2.4 Social father involvement
This study examines the impact of a more detailed category of family instability–a
transition from single mother to cohabiting family with a non-biological father–on
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young children’s risk of asthma and behavioral problems. Admittedly, both union
entrances and exits are possible causes of stress and interruption in family routines.
However, it is more likely that the former effect trumps because social fathers
potentially provide more economic and social resources that eventually outweigh
the negative consequences of stress (Bzostek and Beck 2011). Perceived paternal
support (particularly emotional support) has also been linked with more positive
maternal attitudes and practices. Mothers with more partner support tend to be less
power-assertive (Brunelli et al. 1995). The presence of social fathers may enhance
parenting quality and lower children’s behavioral problems.3
There is another possibility that, since unwed mothers are more likely to separate
from partners in the future; the children may go through more family conflicts
before and after their parents’ marriage dissolution. Some studies suggest that social
fathers invest less in their children than biological fathers do (Coleman et al. 2000).
The new romantic relationship with the social father can possibly distract the
mothers’ attention from the children. In fact, research has been mixed regarding the
effect of social fathers’ involvement with the children.
Bzostek (2008) tested whether the cohabiting social fathers have the same
positive effect on children’s well-being as cohabiting biological fathers. Children’s
well-being is evaluated by behavioral outcomes and an overall measure of health.
The involvement of fathers was measured by the number of days in a week the
fathers were involved in some activities with the children. Bzostek (2008) found
that the social fathers were as beneficial for children’s well-being as biological
fathers. Artis (2007) showed that kindergarten children’s well-being measures
(except reading skills) were similar in cohabiting families and married stepfamilies
as compared to married biological parents after controlling other factors. Vogt Yuan
and Hamilton (2006) using the National Longitudinal Study of Adolescent Health,
found that stepfather involvement is similar to biological parental involvement and
strongly associated with adolescent well-being. More specifically, adolescents’
closeness to a stepfather led to lower depression and less behavioral problems;
whereas conflicts with stepfathers resulted in higher depression and more behavioral
problems. Harknett (2009) found that children whose biological parents were living
apart were at the highest risk of asthma diagnosis; however, the risk of asthma
diagnosis in married and cohabiting parents did not differ significantly when
demographic, socioeconomic, and insurance differences were controlled. Cobb-
Clark and Tekin (2014) found that adolescent boys engaged in less delinquent
behavior with stepfather in the family compared to those with only biological
mother in the family.
Some recent studies found a negative effect of social fathers. Chan and Fung
(2013) found that children living with social fathers scored around three points less
in a cognitive ability test than children living with only biological mothers did.
Berger et al. (2009) examined whether children faced a higher risk of maltreatment
in families with social fathers. The risk of maltreatment was evaluated by whether
the families had been contacted by Child Protective Services (CPS). They found that
3 Guterman et al. (2009) even argue that fathers’ availability and contributions to the family can lower
the risk of child abuse.
K. H. Chan et al.
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the presence of social fathers increased the probability of being contacted by CPS,
compared to families with a cohabiting or married biological father.
Others do not find evidence that family instability affects young children’s
behavior. Bzostek and Beck (2011) examined the relationship between family
instability and physical health at the age of 5 by using the FFCWS. Children living
with biological parents with a stable marriage have the lowest odds for asthma
diagnosis and obesity. However, the health status of children from a cohabiting
family (stable or unstable) was no different from the reference group–stable single-
mother family. However, an analysis by Liu and Heiland (2012) found no evidence
that family structural change (unwed mothers getting married to the biological or
social father) affected the risk of child asthma once mother’s health, education and
socioeconomic background and self-selection are controlled. Marriage does not
improve behavioral problems either.
3 Method
3.1 Study design and sample
This study examines whether the presence of social fathers has any negative effect
on health and behavioral outcomes for young children born to unwed parents. We
used data from the FFCWS, which tracks a cohort of 4,898 children born between
1998 and 2000 in 20 US cities (for a detailed description of the sample and design,
see Reichman et al. 2001). The FFCWS provides detailed information on the
marriage, fertility, and socioeconomic status of the biological mothers of the
children. It oversamples single mothers and minorities. Before the FFCWS, research
on stepparents mostly focused on children who experienced the divorce (or union)
of biological parents and the remarriage of the parents who lived with them. For
instance, the emotional trauma and stress after and during separation and divorce
adversely affect the children (Dawson 1991). With the FFCWS, the effect of divorce
can be separated from the effect of stepparents’ presence. Researchers can focus
only on the effect of stepparents on out-of-wedlock children. The availability of the
Fragile Families Study also permits an investigation of how various family
structural changes shape children early on.
About 3,700 baseline interviews were conducted at the time of childbirth with
both of the biological, unmarried parents. Second and third interviews were
conducted when the child reached 1 and 3 years old, respectively. Information about
the characteristics of the parents, relationship between the parents, parent–child
relationship, socioeconomic activities, and child development were collected.
The ‘‘36-month In-Home Longitudinal Study of Pre-School-Aged Children’’, a
supplementary survey of FFCWS, was conducted to collect information about the
health and behavioral outcomes of the children at age 3. This supplementary survey
collected information from a random subsample4 of the baseline respondents. The
interviewers recorded details such as the children’s behavior and living environment.
4 2,368 children and their mothers participated in the supplementary survey.
The health and behavioral outcomes of out-of-wedlock children
123
The 3,700 household units are divided into two groups: out-of-wedlock children
in families with a biological mother and social father and out-of-wedlock children in
families with only a biological mother. Details of the children’s behavior and living
environment are only available for those who participated in the supplementary
survey. Further screening is processed to reduce sample bias: (1) 2,530 households
did not participate, (2) 51 cases are twin births, and (3) 49 children did not live with
the mothers most of the time. Since our focus is on the well-being of out-of-wedlock
children with social fathers, we excluded 495 cases in which the biological parents
were married at baseline. In order to limit the influence of the biological father on
the children, children whose biological parents were married at year 1 (127 cases);
and biological fathers who were married to the mothers or living with the children at
year 3 (542 cases) were excluded. Due to missing information on the dependent or
independent variables, 242 cases were dropped. Another 29 observations have a
propensity score falling outside the region of common support. A final sample of
833 children was analyzed. Among these, 163 children were living with the
presence of social fathers; 670 children were living with the biological mothers
only.
3.2 Child outcome measures
Health and behavioral outcomes are used as the measures of children’s well-being.
Whether a child has asthma is used to indicate a child’s health condition. A child is
classified as having asthma if the mother was informed by a doctor or health
professional that the child has asthma. Children’s behavioral outcomes are
evaluated by several measures. Items from the Age 2–3 Child Behavior Checklist
(CBCL) by Achenbach (1992) were asked in the FFCWS. Mothers responded to
each item with the following: 0 = not true of my child; 1 = sometimes/somewhat
true; 2 = very/often true. The scores from the items were summed up to calculate
Anxious/Depressed and Withdrawn (internalizing behavior) as well as Aggressive
and Destructive (externalizing behavior) subscales. A measure to assess children’s
positive behavior was also included in the survey. Items from the Express subscale
of the Adaptive Social Behavior Inventory (ASBI) by Hogan et al. (1992) were
asked in the FFCWS. The ASBI subscale can measure children’s social competence
and prosocial skills with peers and adults. The Cronbach’s alphas5 were calculated
for each measure and the numbers showed that the items used in each measure are
reliable in the sample. The detailed list of items for each measure is presented in the
‘‘Appendix’’.
3.3 Control variables
The main independent variable for the analyses is the presence of a social father,
represented by a dummy variable. The mothers were asked to report their
relationship status at the third interview. If they were coresiding with a social father,
then the dummy variable will be one.
5 The Cronbach’s alpha examines the internal consistency of a psychometric test score of a sample.
K. H. Chan et al.
123
We include three variables to control for children’s characteristics. Since
previous research has found a correlation between being born with a low birth
weight and asthma6 (Brooks et al. 2001; Harknett 2009), we added a low-birth-
weight dummy to the model. The child’s gender is included as it was found to have
an effect on the involvement of biological fathers (Lundberg et al. 2007). This may
then affect the presence of social fathers. Having other children before the focal
child may increase the need of having a father; therefore, a first-born dummy is
included. Obviously, the mothers’ characteristics will influence both the well-being
of the child and the decision to have a social father. Most of the unwed parents are
less educated, have lower income and are more likely to be black (McLanahan and
Sandefur 1994). Demographics such as age, race, education, birthplace, religion and
PPTV score (a measure of cognitive ability) are included.
Since child well-being can be adversely affected by mothers’ physical and mental
health problems (Downey and Coyne 1990; Osborne et al. 2004), three mothers’
health measures were added to the model. These are indicator functions of whether
the mother meets depression criteria and had a prenatal smoking or drinking habit.
There is well-documented evidence that prenatal smoking is associated with serious
child behavioral problems, especially aggressive behavior (Wakschlag et al. 2002).
A mother who reports more depression and psychological problems clearly
functions less well as a parent as a result (Waldfogel et al. 2010).
Not only does the availability of economic resources affect the choice of mating
partners, it also directly affects child well-being by enabling mothers to spend more
time with their children and to purchase more resources, including higher quality
childcare (Becker 1991). The amount of economic resources can be proxied by
whether the mother is working or directly measuring household income and the
poverty ratio. We divided the household income and poverty ratio into three and
four categories, respectively. The number of adults and kids are included to account
for the economic burden of the household. Five mediating factors—whether the
biological parents are in a romantic relationship at childbirth, how many days in a
week the mother tells stories, whether the child uses the biological father’s last
name, whether the biological father’s name is on the birth certificate and whether
paternity is officially established–are included in the analysis. These factors account
for how close the relationship is between the biological father and the family, as
well as the closeness of relationship between the biological mother and the child.
3.4 Analytic strategy
A simple linear equation augmented with an indicator function can be used to
estimate the impact of social fathers on the well-being of the child:
Yi ¼ a0 þ a1Gi þ a2Xi þ ei ð1ÞGi ¼ Iðc0 þ c1Xi þ li [ 0Þ ð2Þ
where i denotes the household unit; Yi is the well-being of the child; Gi indicates the
presence of social fathers, who can be a cohabiting partner of the mother or a
6 Low-birth-weight baby is defined as baby weighing less than 5lbs 8 oz at birth.
The health and behavioral outcomes of out-of-wedlock children
123
husband of the mother. A value of zero for Gi means that the mother remains single.
This function is usually estimated by a logistic or probit estimation. The covariate
Xi is a controlling factor of the household characteristics. ei and li are two error
terms with zero mean and normal distribution. The variable of interest is a1 cap-
turing the relationship between the presence of social fathers and the well-being of
the child. However, the ordinary least square estimation method may render the
coefficients biased due to the self-selection problem.
In the statistical analysis of randomized experiments, a certain status is viewed as
having a treatment and the rest as the control. Randomization enables an unbiased
estimation of treatment effects; for each covariate, it implies that the treatment
group will be balanced on average due to the law of large numbers. Biostatistics has
plenty of examples.7 Unfortunately, for observational studies, the assignment of
treatments to research subjects is, by definition, not randomized. One may attempt
to compare similar groups before they were exposed to treatments. The assignment
of treatments cannot be controlled, thus randomization cannot be used to ensure
comparability.8 Analytical adjustments are required to account for baseline
(covariate) differences in the groups. Matching is a common practice to mimic
randomization by creating a sample of units that receives the treatment that is
comparable on all observed covariates to a sample of units that does not receive the
treatment.
In the context of this paper, the presence of a social father is not randomly
assigned to the children. Without doubt, the mothers’ socioeconomic factors will
affect the decision to remain single or accept a new partner and the well-being of the
child. The independence assumption of li and ei will be violated, rendering the
ordinary least squares estimate of the coefficient a1 biased; and failing to identify
the pure effect of social fathers on the well-being of the child. The ordinary least
squares estimate will be a combination of the effect of social fathers and factors
affecting the marriage decisions of mothers.
We use the propensity score matching method to identify the pure effect of
having a social father on a child’s well-being. The technique was first published by
Rosenbaum and Rubin (1983) and implemented in the Rubin causal model for
observational studies. Propensity score matching is a statistical matching technique
that attempts to estimate the effect of a treatment, policy, or other intervention by
accounting for the covariates that predict receiving the treatment. It employs a
predicted probability of group membership based on some factors usually obtained
from logistic regression to create a counterfactual group.
To be specific, the presence of social fathers (Gi) represents the treatment;
households without social fathers belong to the control group. Yi(1) and Yi(0) denote
the health and behavioral outcomes of the child in household i if the child is under
the treatment and the control group, respectively. Ordinary least squares estimates
7 For instance, Cameron and Pauling (1976) offered vitamin C to patients in final phases of cancer.
Patients’ age, gender, cancer site and tumor type were controlled; these factors were obviously not related
to the assignment of vitamin C.8 For example, one may be interested in evaluating the effectiveness of a job training program. The
treatment effect estimated by simply comparing a particular outcome can be affected by the covariates
that dictate the decision to participate in the program.
K. H. Chan et al.
123
give the simple average outcome difference between the treatment group and the
control group: a1;OLS ¼ E½Yið1ÞjGi ¼ 1� � E½Yið0ÞjGi ¼ 0�, which is the average
treatment effect (ATE). As the treatment status is the result of self-selection rather
than a random assignment, average treatment effect (ATE) is not able to capture the
pure effect of treatment. Additional effort is needed to estimate the average
treatment effect on the treated (ATET), defined as:
a1;ATET ¼ E½Yið1ÞjGi ¼ 1� � E½Yið0ÞjGi ¼ 1� ð3Þ
which is the difference between the expected outcome of the child with the treat-
ment and the expected outcome of the same child if the child receives no treatment.
While the first term on the right side of Eq. (3) is an observable variable; the
expected outcome of a child in the treatment group if the child receives no treatment
is unobservable. This value has to be estimated from the outcome of the control
group. A match from the control group will be found for every observation in the
treatment group by propensity score matching.
A critical assumption underlying propensity score matching is Conditional
Independence, which implies that conditional on the observed covariate X, the
outcomes are not contingent on the treatment status. In another words, the outcome
of the control group is what the outcome of the treatment group would have been if
the treatment group did not receive the treatment. Rosenbaum and Rubin (1983)
showed that Conditional Independence Assumption held for a general class of
functions. The propensity score, the probability of selection into treatment, is one of
those. The main advantage of propensity score matching is the limited loss of
observations. By reducing a multi-dimensional matching procedure to a scalar in the
form of probability, researchers can easily balance treatment and control groups on
a large number of covariates without losing a large number of observations. If units
in the treatment and control groups were balanced on a large number of covariates
one at a time, large numbers of observations would be needed to overcome the
‘‘dimensionality problem’’ whereby the introduction of a new balancing covariate
increases the minimum necessary number of observations in the sample
geometrically.
Like other matching algorithms, propensity score matching employs nonpara-
metric kernel matching using a weighted average of almost all observations in the
control group to create the counterfactual outcomes for the observations in the
treatment group. Smith and Todd (2005) contend that the weights depend on
the propensity score distance between the observations in the control group and the
targeted observation in the treatment group for which the counterfactual outcome
was estimated. For instance, a symmetric, nonnegative, unimodal kernel gives
higher weight to individuals with propensity scores closer to that of the targeted
observation in the treatment group, but lower weight to individuals with propensity
scores further away to that of the targeted observation in the treatment group.
To test for robustness, three kernels, namely Gaussian, Epanechnikov and
uniform kernels are used to estimate the propensity score. Two bandwidths (0.1 and
0.001) are used for each kernel. On the other hand, the matching method with
replacement is used because of the small sample size. Caliendo and Kopeinig (2008)
argued that matching with replacement could lead to estimates with lower bias and
The health and behavioral outcomes of out-of-wedlock children
123
higher variance. For comparison purpose, we will also estimate Eq. (1) by ordinary
least squares.
3.5 Empirical results
Descriptive statistics of all independent variables are reported in Table 1. Summary
statistics are reported for the whole sample in the first column. Conditional statistics
are also reported separately for children with social fathers and children without
social fathers in the second column and third column, respectively. Certain
characteristics of the sample can be observed. For example, nearly 40 % of the
households in the sample have a household income under ten thousand dollars.
Also, around 35 % of the households in the sample are in poverty, for which they
have a ratio of total household income to the official poverty thresholds9 of under
50 %. Apart from household characteristics, we can also observe that mothers with
a lower education level are over-represented in the sample. The same thing applies
to mothers whose ethnicity is black. In short, the sample is over-represented with
households of inferior socioeconomic status.
We observe systematic differences between children with social fathers and
children without social fathers in some independent variables. For example, mothers
of children without social fathers are significantly older than mothers of the children
with social fathers. Also, the former are more likely to have some college education
than the latter. There are also some differences between the two groups of children
in terms of variables related to the biological father. For example, for children
without social fathers, their biological parent was significantly more likely to be in a
romantic relationship when the child was born, compared to children with social
fathers. It is also more likely for the children without social fathers to have the
biological father’s name on the birth certificate and to have paternity established,
compared to children with social fathers. These variables indicate that the
relationship of the biological father with the biological mother was very close
before and when the child was born. With a closer link with the biological father,
the mother may be more reluctant to start a new relationship.
The measures of health and behavioral outcomes used in this paper include
whether the child has asthma, a scale measure of Anxious/Depressed and
Withdrawn (internalizing behavior), a scale measure of Aggressive and Destructive
(externalizing behavior), as well as a measure of Adaptive Social Behavior
Inventory (ASBI). Table 2 presents the summary statistics of these outcomes.
Summary statistics are reported for the whole sample in the first column, for the
sample with social fathers in the second column and for the sample without social
fathers in the third column. Obviously, the proportion of children having asthma is
relatively high at 24.69 %. The reason may be that children from families with low
socioeconomic status are over-represented in the sample. Simple statistics show that
there is no significant difference for children with and without social fathers for all
four measures of health and behavior outcomes.
9 The official poverty thresholds are established by the U.S. Census Bureau.
K. H. Chan et al.
123
Table 1 Summary statistics of the FFCWS sample
Sample mean With social
father
Without social
father
Presence of social father 0.1957 (0.397) Nil Nil
Child is of low birth weight 0.1092 (0.3121) 0.0982 (0.2984) 0.1119 (0.3155)
Child is a boy 0.533 (0.4992) 0.5521 (0.4988) 0.5284 (0.4996)
Child is mother’s first birth 0.4034 (0.4909) 0.3865 (0.4884) 0.4075 (0.4917)
Mother’s age*** 23 (5.03) 21.93 (4.38) 23.26 (5.15)
Mother is white 0.1056 (0.3076) 0.1411 (0.3492) 0.097 (0.2962)
Mother is Hispanic 0.1657 (0.372) 0.1411 (0.3492) 0.1716 (0.3774)
Mother is black 0.7095 (0.4543) 0.6871 (0.4651) 0.7149 (0.4518)
Mother is of other race 0.0192 (0.1373) 0.0307 (0.173) 0.0164 (0.1272)
Mother’s education: less than HS 0.4406 (0.4968) 0.4847 (0.5013) 0.4299 (0.4954)
Mother’s education: HS 0.3169 (0.4656) 0.3252 (0.4699) 0.3149 (0.4648)
Mother’s education: some college** 0.2185 (0.4135) 0.1534 (0.3615) 0.2343 (0.4239)
Mother’s education: college 0.024 (0.1532) 0.0368 (0.1889) 0.0209 (0.1431)
Mother is foreign born 0.036 (0.1864) 0.0368 (0.1889) 0.0358 (0.186)
Mother is Catholic 0.1753 (0.3804) 0.1595 (0.3673) 0.1791 (0.3837)
Mother is Protestant 0.4358 (0.4962) 0.4049 (0.4924) 0.4433 (0.4971)
Mother is of other religion 0.1801 (0.3845) 0.2025 (0.4031) 0.1746 (0.3799)
Mother has no religion 0.2089 (0.4068) 0.2331 (0.4241) 0.203 (0.4025)
Mother attends religious activity 0.5558 (0.4972) 0.5583 (0.4981) 0.5552 (0.4973)
PPVT score of the mother 87.16 (11.19) 87.5 (10.85) 87.07 (11.27)
Mother meets depression criteria 0.2533 (0.4352) 0.2209 (0.4161) 0.2612 (0.4396)
Prenatal smoking by mother 0.2485 (0.4324) 0.2883 (0.4544) 0.2388 (0.4267)
Prenatal drinking by mother 0.1044 (0.306) 0.1043 (0.3066) 0.1045 (0.3061)
Mother is working 0.5522 (0.4976) 0.5215 (0.5011) 0.5597 (0.4968)
Household income (B$10,000) 0.3914 (0.4883) 0.362 (0.482) 0.3985 (0.49)
HH’s inc. ($10,000–$25,000) 0.3601 (0.4803) 0.3374 (0.4743) 0.3657 (0.482)
HH’s inc. ([$25,000)* 0.2485 (0.4324) 0.3006 (0.4599) 0.2358 (0.4248)
HH’s poverty ratio (0–49 %) 0.3565 (0.4793) 0.362 (0.482) 0.3552 (0.4789)
HH’s poverty ratio (50–99 %) 0.2437 (0.4296) 0.2209 (0.4161) 0.2493 (0.4329)
HH’s poverty ratio (100–199 %) 0.2425 (0.4289) 0.2393 (0.4279) 0.2433 (0.4294)
HH’s poverty ratio (C200 %) 0.1573 (0.3643) 0.1779 (0.3836) 0.1522 (0.3595)
No. of adults in household 1.7899 (0.9696) 2.0859 (0.6885) 1.7179 (1.0139)
No. of kids in household 2.4202 (1.4087) 2.4049 (1.3592) 2.4239 (1.4214)
Parents in romantic relationship at
childbirth***
0.7587 (0.4281) 0.6564 (0.4764) 0.7836 (0.4121)
Days in a week mother tells story 5.2005 (2.1263) 5.3129 (2.1301) 5.1731 (2.126)
Child uses father’s last name 0.7503 (0.4331) 0.7239 (0.4484) 0.7567 (0.4294)
Father’s name on birth cert.* 0.8451 (0.362) 0.7975 (0.4031) 0.8567 (0.3506)
Paternity established** 0.605 (0.4891) 0.5276 (0.5008) 0.6239 (0.4848)
The health and behavioral outcomes of out-of-wedlock children
123
Although the unconditional mean shows that the presence of social fathers does
not make any difference in the children in terms of health and behavioral outcomes,
we have to investigate in detail the effect of social fathers on the children’s
condition using a set of variables about the children and the families. Tables 3, 4, 5,
6 shows the OLS results of health and behavior outcomes. Results show that the
presence of social fathers is positively related to children having asthma, though the
estimate is not significant. Similar results have been found on the behavioral
outcomes. The presence of social fathers does not have a significant effect on the
children’s scores of internalizing behavior, externalizing behavior and ASBI. It
means that children in families with social fathers are not significantly different
from children in families with only the biological mother in terms of health and
behavioral outcomes, after controlling for a set of household socioeconomic
variables.
In order to control the self-selection problem, the propensity score matching
method is used in the following analysis. The first step of the propensity score
matching method is to estimate the propensity scores for having a social father in
the household. A probit model is used to estimate the propensity score, defined as
the probability of having a social father in the household. All the variables in
Table 1 are included in the probit estimation.
A condition of common support is needed for using the propensity score
matching. This can guarantee that the observations in the treatment group and those
in the control group are comparable with sufficient overlap in their propensity
scores. Observations having propensity scores outside the common support region
are excluded from the analysis. The common support region has a lower bound and
an upper bound. The upper bound is defined as the highest propensity score obtained
by the observations in the control group. The lower bound is defined as the lowest
propensity score obtained by the observations in the treatment group. Using this
method,10 the common support region is [0.0299251, 0.6773368]. A total of 833
observations have propensity scores falling within this region.
Table 1 continued
Sample mean With social
father
Without social
father
Number of observations 833 163 670
Standard deviations are reported in parentheses
Statistical tests on the equality of proportions/mean between sample with social father and sample without
social father
*** Denotes statistical significance at the 1 % level
** Denotes statistical significance at the 5 % level
* Denotes statistical significance at the 10 % level
10 This method of defining a common support region of propensity score is also used in a study by Liu
and Heiland (2012).
K. H. Chan et al.
123
Table 7 summarizes the results from the probit estimation. The marginal effects
of the variables are reported. The probit estimates show that several factors have
significant effects on the presence of social fathers. For example, a social father is
less likely to be present if the child is his/her mother’s first birth. The reason is that
having other children before the focal child may increase the financial need of
having a new partner in the household. Also, the child is less likely to have a social
father if the biological parents were in a romantic relationship at childbirth. This is
consistent with usual behavior as people need time to accept a new partner after just
ending a romantic relationship. The mothers’ age, religion, income, prenatal
drinking and smoking habits do not seem to matter.
The second step of the propensity score matching method is to find the estimated
effect of having a social father in the household on the well-being of the child.
Table 8 summarizes the results on the estimated effect of social fathers on
children’s health and behavioral outcomes. Column 1 of the table shows the
ordinary least squares estimate for comparison purpose. Columns 2–7 show the
propensity score matching estimates using Gaussian kernel, Epanechnikov kernel
and uniform kernel, each with two different bandwidths.
Using the propensity score matching method, we found that children in families
with social fathers are more likely to have asthma compared to children in
families without social fathers. However, the estimates are not significantly
different from zero. Apart from that, none of the estimates concerning behavioral
outcomes is significant, suggesting that the presence of social fathers does not
have any significant effect on the behavioral outcomes of the children. Results
show that the presence of social fathers does not have any effect on children’s
health and behavioral outcomes. Results from both OLS and the propensity score
matching method failed to find any significant effect of social fathers on health
and behavior outcomes. It showed that the result is robust and not dependent on
the method used.
Table 2 Summary statistics on health outcome and behavioral outcomes
Sample mean With social father Without social father
Asthma 0.2469 (0.4314) 0.2547 (0.4371) 0.2451 (0.4304)
CBCL internalizing
Behaviors 10.66 (6.16) 10.59 (5.66) 10.68 (6.28)
CBCL externalizing
Behaviors 14.97 (8.20) 15.71 (7.93) 14.81 (8.26)
ASBI 15.09 (2.71) 15.11 (2.65) 14.81 (2.72)
Standard deviations are reported in parentheses
Statistical tests on the equality of proportions/mean between sample with social father and sample without
social father
*** Denotes statistical significance at the 1 % level
** Denotes statistical significance at the 5 % level
* Denotes statistical significance at the 10 % level
The health and behavioral outcomes of out-of-wedlock children
123
Table 3 Ordinary least squares
estimates on asthma
Robust standard errors are
reported in parentheses
*** Denotes statistical
significance at the 1 % level
** Denotes statistical
significance at the 5 % level
* Denotes statistical significance
at the 10 % level
Variable Estimate (standard
error)
Social father is present 0.0187 (0.0401)
Child is of low birth weight 0.0689 (0.0533)
Child is a boy 0.1232 (0.0301)***
Child is mother’s first birth -0.0555 (0.0436)
Mother’s age 0.0124 (0.0254)
Mother’s age square -0.0003 (0.0005)
Mother’s race (Ref: Other race)
White 0.049 (0.0806)
Hispanic 0.1772 (0.0768)**
Black 0.1659 (0.0718)**
Mother’s education (Ref: College)
Less than High School -0.0832 (0.104)
High School -0.0397 (0.1009)
Some College -0.0926 (0.0961)
PPVT score of the mother -0.0007 (0.0017)
Mother is working -0.0351 (0.0329)
Prenatal smoking by mother 0.0326 (0.0398)
Prenatal drinking by mother -0.0538 (0.0498)
Mother is foreign born -0.1092 (0.068)
Mother’s religion (Ref: No Religion)
Catholic 0.0142 (0.0548)
Protestant -0.0279 (0.0442)
Other religion -0.0038 (0.0522)
Mother attends religious activity 0.0585 (0.032)*
Child’s Household Income (Ref: [ $25,000)
B$10,000 0.1717 (0.0905)*
$10,000–$25,000 0.0763 (0.0565)
Child’s Household Poverty Ratio (Ref: [=200 %)
0–49 % -0.1284 (0.1004)
50–99 % -0.0664 (0.0756)
100–199 % -0.0287 (0.0534)
Days in a week mother tells story 0.008 (0.0072)
No. of adults in household -0.019 (0.016)
No. of kids in household 0.0098 (0.0132)
Mother meets depression criteria 0.0179 (0.0356)
Parents in romantic relationship at
childbirth
0.0033 (0.0388)
Child uses father’s last name -0.0288 (0.044)
Father’s name on birth cert. 0.0557 (0.0521)
Paternity established 0.0021 (0.0346)
K. H. Chan et al.
123
4 Discussion
The study aims to show how the presence of social fathers affects the health and
behavior outcomes of out-of-wedlock children. Because of the widespread
occurrence of non-marital births, young children living with social fathers are
likely to become more common in the future. Statistics in this paper also showed
that a very large percentage of these children are living in families with a low
socioeconomic status. Possible negative effects caused by the presence of social
fathers would create double disadvantages for these children. It is possible that they
will be more likely to face inferior outcomes in school or the job market in the
future.
Previous studies focused more on the effect of stepparents on older children or
adolescents. This study extends the literature to examine the effect of social fathers
on children born to unmarried parents by using a large representative sample of out-
of-wedlock children. For these children, the occurrence of social fathers happens
early in their lives without going through the divorce or separation of the biological
parents. This can identify the pure effect of a social father’s presence independent of
the change of family structure or the effect of divorce.
One should notice that the presence of social fathers is the result of self-selection.
To address the selection issue, prior studies adopted a different strategy. For
example, some studies estimate the impact of a variable of interest on children’s
well-being by using more detailed subgroups of the sample to separate the effect
from family instability and structure (Fomby and Osborne 2010; Thomson et al.
1994). The most common approach is including as many known and observable
socio-economic variables of the sample as possible to capture the correlation
between household characteristics and the choice of social fathers (Bzostek and
Beck 2011; Guterman et al. 2009; Hofferth 2006). Following Liu and Heiland
(2012), we used propensity score matching—a semi-parametric method—to handle
self-selection. There is one restrictive assumption of the propensity score matching
method namely, self-selection based on observables. An alternative is instrumental
variable estimation based on selection by unobservable. However, this methodology
has bias toward non-rejection of the null hypothesis (Cerulli 2011).
With selection issues being addressed by the propensity score matching method,
we found that children in families with social fathers are more likely to have asthma
than children in families with only the biological mother. Nonetheless, this effect is
not statistically significant. On the other hand, the presence of a social father has no
significant effect on children’s behavioral outcomes.
What are the possible reasons that the presence of social fathers does not affect
children’s health and behavioral outcomes? On one hand, the social father can
provide more financial resources for the new family.11 With more financial
resources, the family can seek for appropriate child care that is beneficial for the
11 Contradictory result has also been found before. For example, Akashi-Ronquest (2009) found that an
increase in the father’s wage rate won’t improve the family’s investment in the child when the child is a
stepchild of the father.
The health and behavioral outcomes of out-of-wedlock children
123
Table 4 Ordinary least squares
estimates on Internalizing
Behaviors
Robust standard errors are
reported in parentheses
*** Denotes statistical
significance at the 1 % level
** Denotes statistical
significance at the 5 % level
* Denotes statistical significance
at the 10 % level
Variable Estimate (Standard
Error)
Social father is present -0.5089 (0.566)
Child is of low birth weight 1.1093 (0.7005)
Child is a boy 0.3997 (0.4273)
Child is mother’s first birth -0.0221 (0.6129)
Mother’s age -0.2705 (0.3567)
Mother’s age square 0.0044 (0.0064)
Mother’s race (Ref: Other race)S
White -1.2235 (1.7008)
Hispanic -1.4204 (1.6675)
Black -2.4779 (1.5862)
Mother’s education (Ref: College)
Less than High School 3.716 (0.9574)***
High School 2.5347 (0.8535)***
Some College 1.3776 (0.8219)*
PPVT score of the mother -0.1385 (0.0269)***
Mother is working -0.7482 (0.4634)
Prenatal smoking by mother -0.3221 (0.5223)
Prenatal drinking by mother 0.4462 (0.7031)
Mother is foreign born -2.0638 (1.0415)**
Mother’s religion (Ref: No Religion)
Catholic -0.2247 (0.8287)
Protestant 0.1238 (0.6305)
Other religion -0.5901 (0.6752)
Mother attends religious activity -0.5093 (0.4606)
Child’s Household Income (Ref: [ $25,000)
\= $10,000 -1.7769 (1.2622)
$10,000–$25,000 -1.7389 (0.7943)**
Child’s household poverty ratio (Ref: [=200 %)
0–49 % 1.5867 (1.3826)
50–99 % 0.8516 (1.0586)
100–199 % -0.4525 (0.7897)
Days in a week mother tells story -0.0941 (0.1105)
No. of adults in household 0.0834 (0.237)
No. of kids in household -0.0456 (0.204)
Mother meets depression criteria 1.3807 (0.5297)***
Parents in romantic relationship at
childbirth
-1.0387 (0.5847)*
Child uses father’s last name -1.4896 (0.6396)**
Father’s name on birth cert. 0.5018 (0.8632)
Paternity established 0.3689 (0.4983)
K. H. Chan et al.
123
Table 5 Ordinary least squares
estimates on Externalizing
Behavior
Robust standard errors are
reported in parentheses
*** Denotes statistical
significance at the 1 % level
** Denotes statistical
significance at the 5 % level
* Denotes statistical significance
at the 10 % level
Variable Estimate (Standard
Error)
Social father is present 0.2816 (0.7634)
Child is of low birth weight 1.8349 (1.0099)*
Child is a boy 1.0418 (0.5948)*
Child is mother’s first birth -1.3323 (0.7872)*
Mother’s age -0.0066 (0.5216)
Mother’s age square -0.0029 (0.0096)
Mother’s race (Ref: Other race)
White -3.1107 (2.0363)
Hispanic -2.3013 (1.979)
Black -3.2684 (1.8755)*
Mother’s education (Ref: College)
Less than high school 2.1082 (2.059)
High school 2.246 (1.9809)
Some college 1.152 (1.9382)
PPVT score of the mother -0.0739 (0.0338)**
Mother is working -1.0711 (0.6919)
Prenatal smoking by mother 0.3595 (0.7148)
Prenatal drinking by mother -0.0719 (1.0347)
Mother is foreign born -2.0518 (1.8376)
Mother’s religion (Ref: No Religion)
Catholic 0.0101 (1.1148)
Protestant -0.3208 (0.8396)
Other religion -0.4414 (0.9747)
Mother attends religious activity -0.8333 (0.6385)
Child’s household income (Ref: [ $25,000)
B$10,000 0.6094 (1.7089)
$10,000–$25,000 -0.6725 (1.0935)
Child’s household poverty ratio (Ref: [=200 %)
0–49 % -1.3617 (1.9528)
50–99 % -0.7485 (1.4991)
100–199 % -1.441 (1.1241)
Days in a week mother tells story -0.4442 (0.1504)***
No. of adults in household 0.5629 (0.3538)
No. of kids in household -0.0177 (0.281)
Mother meets depression criteria 1.9663 (0.7219)***
Parents in romantic relationship at
childbirth
-1.4974 (0.7868)*
Child uses father’s last name -2.7939 (0.8796)***
Father’s name on birth cert. 1.9139 (1.1297)*
Paternity established 0.3238 (0.669)
The health and behavioral outcomes of out-of-wedlock children
123
Table 6 Ordinary least squares
estimates on ASBI
Robust standard errors are
reported in parentheses
*** Denotes statistical
significance at the 1 % level
** Denotes statistical
significance at the 5 % level
* Denotes statistical significance
at the 10 % level
Variable Estimate (Standard
error)
Social father is present 0.053 (0.2677)
Child is of low birth weight -0.1122 (0.2861)
Child is a boy -0.4903 (0.19)***
Child is mother’s first birth -0.1361 (0.2615)
Mother’s age -0.4119 (0.1545)***
Mother’s age square 0.007 (0.0028)**
Mother’s race (Ref: Other race)
White 1.1574 (0.7814)
Hispanic 0.71 (0.7603)
Black 0.6371 (0.7395)
Mother’s education (Ref: College)
Less than High School -1.1243 (0.6499)*
High School -0.9332 (0.6192)
Some College -0.6539 (0.6096)
PPVT score of the mother 0.0466 (0.0109)***
Mother is working 0.0406 (0.2068)
Prenatal smoking by mother 0.0014 (0.2379)
Prenatal drinking by mother 0.082 (0.3176)
Mother is foreign born -0.0049 (0.6313)
Mother’s religion (Ref: No Religion)
Catholic -0.3083 (0.3581)
Protestant 0.0847 (0.2722)
Other religion 0.6004 (0.2916)**
Mother attends religious activity -0.0601 (0.196)
Child’s household income (Ref: [ $25,000)
B$10,000 0.1053 (0.6137)
$10,000–$25,000 0.2376 (0.341)
Child’s household poverty ratio (Ref: [=200 %)
0–49 % -0.7391 (0.6675)
50–99 % -0.2095 (0.4555)
100–199 % 0.0768 (0.3256)
Days in a week mother tells story -0.0055 (0.0435)
No. of adults in household -0.107 (0.1042)
No. of kids in household -0.0248 (0.0919)
Mother meets depression criteria -0.3195 (0.2265)
Parents in romantic relationship at
childbirth
0.2227 (0.2705)
Child uses father’s last name 0.3226 (0.2652)
Father’s name on birth cert. -0.3173 (0.3471)
Paternity established 0.3695 (0.2356)
K. H. Chan et al.
123
Table 7 Probit estimates of
propensity score
Marginal effects instead of the
coefficients are reported
Standard errors are reported in
parentheses
*** Denotes statistical
significance at the 1 % level
** Denotes statistical
significance at the 5 % level
* Denotes statistical significance
at the 10 % level
Variable Estimate (Standard
error)
Child is of low birth weight -0.0202 (0.0424)
Child is a boy -0.0034 (0.0275)
Child is mother’s first birth -0.1013 (0.0345)***
Mother’s age -0.0147 (0.0245)
Mother’s age square 0.0001 (0.0005)
Mother’s race (Ref: Other race)
White -0.0449 (0.0886)
Hispanic -0.1232 (0.0658)
Black -0.1216 (0.1114)
Mother’s education (Ref: College)
Less than High School -0.1019 (0.0883)
High School -0.0918 (0.0781)
Some College -0.1294 (0.0619)*
PPVT score of the mother 0.0004 (0.0014)
Mother is working -0.0126 (0.0308)
Prenatal smoking by mother 0.0383 (0.036)
Prenatal drinking by mother -0.0015 (0.0477)
Mother is foreign born -0.0449 (0.0646)
Mother’s religion (Ref: No Religion)
Catholic -0.066 (0.0433)
Protestant -0.0344 (0.0375)
Other religion 0.0115 (0.0452)
Mother attends religious activity 0.009 (0.0291)
Child’s household income (Ref: [ $25,000)
\= $10,000 0.0851 (0.068)
$10,000–$25,000 0.1168 (0.1034)
Child’s household poverty ratio (Ref: C 200 %)
0–49 % 0.0988 (0.0657)
50–99 % 0.0076 (0.0499)
100–199 % 0.036 (0.0795)
Days in a week mother tells story 0.0061 (0.0066)
No. of adults in household 0.0624 (0.0156)***
No. of kids in household -0.0111 (0.0122)
Mother meets depression criteria -0.0473 (0.0301)
Parents in romantic relationship at
childbirth
-0.1243 (0.0403)***
Child uses father’s last name 0.0306 (0.0376)
Father’s name on birth cert. -0.0242 (0.049)
Paternity established -0.0444 (0.0316)
The health and behavioral outcomes of out-of-wedlock children
123
child.12 At the same time, potential harmful effects from the presence of the social
father are conceivable. For instance, the mothers may spend less time with the child
because of the new romantic relationship, indirectly affecting parenting quality.
Unwed mothers have a higher probability of separation with partners (Manning
et al. 2004). The child may be exposed to frequent conflict between parents as the
Table 8 Estimated effect of social father on child health and behavioral outcomes
OLS Gaussian Epanechnikov Uniform
0.1 0.01 0.1 0.01 0.1 0.01
Asthma
Estimate 0.0187 0.0119 0.0028 0.0129 0.0026 0.0106 0.0052
Standard error 0.0401 0.0418 0.0448 0.0433 0.0514 0.0439 0.0499
No. of Obs. treated 157 157 157 157 155 157 155
No. of Obs. control 661 661 661 661 656 661 656
% Matched treated Nil 100 100 100 99 100 99
Internalizing
Estimate -0.5089 -0.4097 -0.3778 -0.5269 -0.3122 -0.5013 -0.3944
Standard error 0.5659 0.5532 0.7402 0.5719 0.7446 0.6742 0.6653
No. of Obs. treated 137 137 137 137 133 137 133
No. of Obs. control 598 598 598 598 585 598 585
% Matched treated Nil 100 100 100 97 100 97
Externalizing
Estimate 0.2815 0.5007 -0.1063 0.3006 -0.1065 0.3221 -0.2347
Standard Error 0.7633 0.7601 0.9964 0.8599 1.046 0.7516 0.9298
No. of Obs. treated 134 134 134 134 130 134 130
No. of Obs. control 599 599 599 599 587 599 587
% Matched treated Nil 100 100 100 97 100 97
ASBI
Estimate 0.053 0.0716 0.0638 0.0859 0.0933 0.0762 0.0485
Standard Error 0.2676 0.2935 0.3262 0.3035 0.2955 0.2848 0.3104
No. of Obs. treated 137 137 137 137 135 137 135
No. of Obs. control 605 605 605 605 593 605 593
% Matched treated 100 100 100 98 100 98
Robust standard error is reported for the OLS estimates
Bootstrap standard errors based on 100 replications are reported for the propensity score matching
estimates
*** Denotes statistical significance at the 1 % level
** Denotes statistical significance at the 5 % level
* Denotes statistical significance at the 10 % level
12 For example, Brilli et al. (2014) found that child care availability has a positive and significant effect
on children’s language test scores.
K. H. Chan et al.
123
marriage is dissolving. Sometimes moving to reside with social fathers means that
the mothers’ and children’s ties to family and neighborhood may be disrupted. The
beneficial and harmful effects of social fathers may cancel each other. In fact, some
prior studies indicate that socioeconomic characteristics of family matter more than
family structure to predict children’s health and behavioral outcomes. Once
sufficient economic and financial variables of the household are controlled, family
structure has little impact on children’s well-being (Osborne and McLanahan 2007;
Osborne et al. 2004). Waldfogel et al. (2010) provide another possibility that
instability seems to be more important than family structure to determine health
outcomes.
It was suggested that the relationship between a social father and a child is not as
close as the one between a biological parent and a child (Hofferth and Anderson
2003). The benefit of having a social father in the family would probably not be as
large as having the biological father in the family. The differences in the benefit of
having a biological father versus a social father have been found in many past
studies. In terms of health and behavioral outcomes, Liu and Heiland (2012) found
that the marriage of biological parents after childbirth did not have any significant
benefit on the children. As a biological father can’t benefit the children in terms of
health and behavioral outcomes, the non-existence of benefit by a social father
would not be too surprising.
Both this study and Liu and Heiland (2012) imply that marrying the biological
father or starting a new family with a social father do not improve children’s health
and behavioral outcomes. Policies promoting marriage of single mothers may not be
effective. Reducing the rate of births outside of marriage in the first place, boosting
financial resources for single mothers and high-quality early childhood education
seem to be more desirable policies. Also, the measures of health and behavioral
outcomes we used are not broad enough. A non-existent effect using these measures
does not rule out possible significant effects using other measures. Future research
using a wider range of children’s health and behavioral outcomes would complete a
clearer picture on how social fathers affect the well-being of children.
Acknowledgments We are deeply grateful to Donald Cox, Arthur Lewbel and Zhijie Xiao for their
valuable advice. We would also like to thank Wei Sun, Arlene Anderson and two anonymous referees for
their helpful comments.
Appendix
See Table 9.
The health and behavioral outcomes of out-of-wedlock children
123
Table 9 Detailed description for items used in behavior outcomes
Item description
Internalizing behavior (a = 0.822)
Clings to adults or is too dependent
Feelings are easily hurts
Gets too upset when separated from parents
Looks unhappy w out good reason
Nervous, high strung, or tense
Overtired
Self-conscious or easily embarrassed
Too shy or timid
Too fearful or anxious
Unhappy, sad, depressed
Wants a lot of attention
Acts too young for age
Avoids looking others in the eye
Doesn’t answer when people talk to (him/her)
Doesn’t get along with other children
Doesn’t know how to have fun, or acts like little adult
Doesn’t seem to feel guilty after misbehaving
Refuses to play games
Seems unresponsive to affection
Shows little affection toward people
Shows little interest in things around (him/her)
Stubborn, sullen, or irritable
Uncooperative
Under active, slow moving, or lacks energy
Withdrawn—does not get involved with others
Externalizing behavior (a = 0.890)
Defiant
Demands must be met immediately
Disobedient
Easily frustrated
Easily jealous
Gets in many fights
Hits others
Has angry moods
Punishment doesn’t change (his/her) behavior
Screams a lot
Selfish or won’t share
Has sudden changes in mood or feelings
Has temper tantrums or hot temper
K. H. Chan et al.
123
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