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Michigan State
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This is to certify that the
dissertation entitled

EMPIRICAL ESSAYS IN FAMILY STRUCTURE AND EARLY
CHILD OUTCOMES

presented by

TERRY-ANN L. CRAIGIE

has been accepted towards fulfillment
of the requirements for the

Ph.D. degree in Economics

 

 

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June 12, 2009

 

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EMPIRICAL ESSAYS IN FAMILY STRUCTURE AND EARLY CHILD OUTCOMES
By

Terry-Ann L. Craigie

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Economics

2009

ABSTRACT

Empirical Essays in Family Structure and Early Child Outcomes
By
Terry-Ann L. Craigie
This dissertation empirically explores the issues surrounding family structure in the
United States and its consequences for the outcomes of young children. It highlights the
instability hypothesis, which holds that the father’s sporadic presence in the household
lowers cognitive performance and exacerbates behavioral problems in young children. In
addition, the de-institutionalization of marriage and the family in recent years has made
the study of committed unmarried couples relevant to the discussion of family structure
and child wellbeing. As a result, adverse outcomes for young children and factors linked
to family dissolution among married and cohabiting couples are studied in detail.

The first chapter investigates how a father’s presence in the household affects
child cognitive performance as measured by the revised version of the Peabody Picture
Vocabulary Test (PPVT-R). By meticulously defining all possible forms of paternal
presence, while holding mother’s presence in the household constant, the model
distinguishes between stability and family structure effects of paternal presence. The
empirical findings show that cognitive outcomes are statistically similar for children in
stable single-parent and stable two-parent households. However, unstable family
structures, characterized by a father’s sporadic presence in the home, are shown to have

adverse effects on cognitive performance compared to the stable single-parent family

structure. The profound implication of these findings is the importance of family stability
relative to family structure in producing positive child cognitive outcomes.

The second chapter empirically tests the long-held view that parental
incarceration negatively impacts child wellbeing. Stemming from the findings of the first
chapter, all absences are not created equal. As such, the study will distinguish between
the effect of a father’s incarceration on the cognitive and behavioral development of the
pre-school aged child and the effect of his absence in general. The findings suggest that
when both incarceration and absence are treated as endogenous in the model, where
identifying instruments are used for both in instrumental variables (IV) estimation, the
effect of paternal incarceration is not observed to be statistically different from the effect
of his subsequent absence.

The third chapter investigates the factors that influence the probability of family
dissolution and explore whether the hazard of dissolution is characterized by duration
dependence. Unlike previous works, this study goes beyond the examination of unions
formed through marriage only, in order to observe unions formed through cohabitation as
well. Factors such as age, race, education, religion and cohabitation are shown to
significantly influence the risk of union dissolution. Religion and religiosity are shown to
be especially important to union survival among cohabiting couples relative to married
couples. The study finds no evidence of duration dependence among unions once marital

status and other indicators of relationship quality are controlled for in the model.

Copyright by
TERRY-ANN L. CRAIGIE
2009

ACKNOWLEDGEMENTS
I would like to express my love and appreciation for my Rock and Shield, Jesus Christ.
Without His strength and guidance, I would not have been able to successfully complete
this journey.

In addition, I extend my sincerest gratitude to Dr. Jeff B. Biddle who has been an
excellent dissertation advisor. His guidance and instruction throughout this process was
invaluable. Dr. Stephen Woodbury and Dr. Thomas J eitschko were more than committee
members, but excellent counselors as well. Thank you all for transcending your generic
graduate school roles to being strong supporters of my academic and professional
choices. Dr. Tom Luster — you are gone but not forgotten. I am grateful to Barbara Ames,
Todd Elder, Steven Haider and Gary Solon for helpful comments on my dissertation.

Thanks to the secretaries, professors and students of the economics department.
To my classmates — you pushed me to the pinnacle of my potential (and sanity).

To my academic mentors — Charles Becker, Elizabeth Elmore, Reza Ghorashi,
Sonia Gonsalves, Kenneth Harrison, Janice Joseph, Melaku Lakew and Linda Nelson — I
would not have reached this milestone if you had not recognized that I was a diamond in
the rough. To Stephen Davis and Paulette Forbes-Igharo — I have not forgotten your
listening ear and tolerance of my whining. Thank you all for your support and
encouragement in the mountains and valleys of this journey.

To my parents and siblings -— thank you for your patience during my most
stressfirl times and your forgiveness when I forgot your birthdays — I love you all. Thanks

to my extended family for your prayers and continued support.

TABLE OF CONTENTS

LIST OF TABLES .................................................................................. vii
LIST OF FIGURES ................................................................................... ix
CHAPTER 1
EFFECTS OF PATERNAL PRESENCE AND FAMILY INSTABILITY ON CHILD
COGNITIVE PERFORMANCE ........................................................................................ 1
1.1 Introduction .................................................................................. l
1.2 Literature Review ........................................................................ 3
1.3 Simple Theoretical Framework ....................................................... 6
1.4 Econometric Approach ................................................................. 8
1.5 Data Description ...................................................................... 10
1.6 Results .................................................................................. 20
1.7 Summary ............................................................................... 25
CHAPTER 2
PATERNAL INCARCERATION, PATERNAL ABSENCE AND EARLY CHILD
DEVELOPMENT .................................................................................... 28
2.1 Introduction ................................................................................ 28
2.2 Background ............................................................................ 30
2.3 Data and Variable Descriptions ..................................................... 32
2.4 Econometric Issues and Methods ................................................... 37
2.5 Results .................................................................................. 46
2.6 Summary ............................................................................... 49
CHAPTER 3
AN ANALYSIS OF THE CAUSES AND CORRELATES OF FAMILY
DISSOLUTION ..................................................................................... 5 1
3.1 Introduction ................................................................................ 51
3.2 Literature Review ..................................................................... 52
3.3 Data ..................................................................................... 57
3.4 Econometric Specification .......................................................... 61
3.5 Results .................................................................................. 63
3.6 Summary ............................................................................... 67
APPENDICES ...................................................................................... 70
Appendix A .................................................................................. 112
Appendix B ............................................................................... 114
Appendix C ............................................................................... 1 15
BIBLIOGRAPHY .................................................................................. 116

vi

LIST OF TABLES

Table 1 Summary Statistics ....................................................................... 70
Table 2 Comparison of the Standardized PPVT-R Score by Family Structure ............ 73
Table 3 Summary Statistics of Independent Variables by Family Type .................... 74
Table 4 Replication of Columns (1) & (2) of Tables 3 & 4 of Lang and Zagorsky (2001) 6
......................................................................................................... 7
Table 5 Estimated Effects of Paternal Presence on Peabody Picture Vocabulary Test
(PPVT-R) Scores ................................................................................... 78
Table 6 Estimated Effects of Paternal Presence on Boys’ Peabody Picture Vocabulary
Test (PPVT-R) Scores .............................................................................. 80
Table 7 Estimated Effects of Paternal Presence on Girls’ Peabody Picture Vocabulary
Test (PPVT-R) Scores .............................................................................. 82
Table 8 Robustness Checks ....................................................................... 84
Table 9 Summary Statistics ....................................................................... 86
Table 10 Summary Statistics by Incarceration History ....................................... 88
Table 1 1 Average Non-Traffic Stops by City and Race/Ethnicity ........................... 90
Table 12 OLS Estimates of the Marginal Impact of Paternal Incarceration on Outcomes92
Table 13 Estimates of the Marginal Impact of Paternal Incarceration Ex Post by Father’s
Race/Ethnicity ....................................................................................... 95
Table 14 OLS and IV Regressions of the Effect of Incarceration Ex Post on Child
Outcomes ............................................................................................ 96
Table 15 Summary Statistics ..................................................................... 98
Table 16 Linear Probability Estimates of the Correlates of Union Dissolution .......... 100
Table 17 Linear Probability Estimates for Low-Educated and Black Mothers ........... 102

Table 18 Linear Probability Estimates for Couples Cohabiting and Married at Baseline
...................................................................................................... 104

vii

Table 19 Logit Estimates of Union Dissolution .............................................. 106

viii

LIST OF FIGURES

Figure 1.1 ........................................................................................... 108
Figure 2.1 .......................................................................................... 110
Figure 3.1 .......................................................................................... 111

ix

Chapter 1.
Effects of Paternal Presence and Family
Instability on Child Cognitive
Performance

1.1. Introduction

Non-traditional and single-parent family structures are a growing phenomenon in the
United States. According to the US. Census Bureau Current Population Reports, in
1996, 25.4% of all children under eighteen had only one parent in the household. This
figure rose to 27.3% in 2002; during this period, over 80% of single-parent family
households were headed by single mothers. The issue therefore remains as to how
children are being affected by the growing trend of family structures, in which the
father is seldom in residence. This study will examine how paternal presence in the
household and stability of the family structure impact the child’s cognitive
development.

The fundamental identification problem in answering this question is that
unobserved characteristics such as parental values, preferences and innate ability are
potentially correlated with both paternal presence and child outcomes — a situation
which could severely bias the estimated effect of paternal presence (Lang and Zagorsky,
(2001) and Painter and Levine, (2000)). The problem can be addressed by including

numerous family background and individual covariates to attenuate omitted variable

bias and subsequently make causal inferences (Antecol and Bedard, (2007); Lang and
Zagorsky (2001); Painter and Levine (2000)). I employ this approach to address the
identification problem using data from The Fragile Families and Child Wellbeing Study
(FFCWS), which provides very rich data on family structure as well as a plethora of
family background, household and individual correlates.

Prior studies have focused on the outcomes of adolescent children and the
outcomes of adults who grew up in single-parent households (Antecol and Bedard,
(2007); Corak, (2001); Lang and Zagorsky, (2001); Painter and Levine, (2000);
Sandefur and Wells, (1997)). However, there is still much to learn about the impact of
family structure on outcomes for young children, particularly pre-school aged children.
Parental investments during early childhood years may significantly impact the brain
development of the child, thus affecting cognitive skills and accordingly, human capital
accumulation (Heckman (2000); Ruhm, (2004)). It is therefore imperative to investigate
how the family setting affects early cognitive development due to the momentous
impact this may potentially have on skills of the future labor force.

The outcome variable used to evaluate cognition is the revised version of the
Peabody Picture Vocabulary Test (PPVT-R), as it conveniently serves as a measure of
cognitive ability and academic readiness. Unlike Antecol and Bedard (2007) and Lang
and Zagorsky (2001), the study finds no statistically significant effects of paternal
presence when the indicator is defined as a continuous variable. However, once the
model meticulously specifies all family structure types brought about by variations in
paternal presence, the stability effect is clearly observed. First, the study finds that child

cognitive performance within the stable two-parent family struCture is not statistically

different from performance within the stable single-parent family structure. Second,
unstable family structures, where paternal presence in the household is sporadic, yield
more negative outcomes for the child than the stable single-parent household. In
general, children of unstable families score on average about 1/5 of a standard deviation
lower than children of stable single-parent families. Two-parent families are not shown
to necessarily yield better cognitive outcomes than single-parent families and as such,
the family structure effect is not substantiated by this study. The main implication of
these findings is that when it comes to the cognitive development of pre-school aged
children, the stability of the family structure is more important than the family structure
type.

The paper is organized as follows. Section 1.2 provides a brief review of past
works that examine the effect of paternal presence in the home. Section 1.3 describes a
simple theoretical fi'amework from which the model specification was derived. Section
1.4 discusses the econometric issues associated with measuring the effect of paternal
presence. Section 1.5 gives the data description and descriptive statistics of the variables
used in the model. Section 1.6 discusses the OLS regression results and robustness
checks; Section 1.7 concludes with a summary of the findings and policy implications.
1.2. Literature Review
Child outcomes are not only shaped by the genetic endowments of parents, but also the
allocation of resources within the household. Parents have genetic endowments such as
health and intelligence that are considered heritable and thus, are passed on to children
directly (Haveman and Wolfe, (1995); Scott-Jones, (1994)). Therefore, a child will

inherit intellectual and health endowments from his/her parents regardless of the family

structure. However, parental genetic endowments also affect child outcomes by
influencing the level and allocation of resources within the household. Family
dissolution ultimately influences the resources devoted to child development. A highly
intelligent and healthy father living in the household could significantly increase
household income and subsequently the investments of both time and goods devoted to
the child (Haveman and Wolfe, (1995)). The mother could also increase her time
allocation within the household and her interaction with the child as a result (Scott-
Jones, (1994)).

These arguments suggest that paternal absence could have deleterious effects on
the cognitive performance of the child. Furthermore, the timing of paternal absence may
also have varying effects (Haveman and Wolfe, (1995); Seltzer, (1994)). Using sibling
comparisons, studies have shown that children exposed to paternal absence for a longer
period of time experience more pronounced negative effects (Ermisch and Francesconi,
(2001); Sandefirr and Wells, (1997); Sutton-Smith et al., (1968)). However, the
assumption must be made that siblings respond to paternal absence in the same way and
that parents treat all children equally. There is also the selection problem associated
with using sibling comparisons - it limits the analysis sample to families with multiple
children (Sigle-Rushton and McLanahan, (2002)).

Other studies examine and exploit the reasons for paternal absence. Divorce for
instance, as a cause of paternal absence, is much more endogenous than paternal loss
through death (Corak, (2001); Lang and Zagorsky, (2001)). Divorce or separation may
be caused by pre-existing factors and consequently, father absence would be

endogenous in the model. Paternal ab'sence through death, on the other hand, is arguably

more exogenous since it is not expected to be correlated with pre-existing factors’. Lang
and Zagorsky (2001) exploit the exogenous variation provided by paternal death and
concluded that this event decreased the probability of a son being married.

It is traditionally believed that paternal presence in the household yields positive
repercussions for family and child outcomes. However, it has been shown that father
presence may not be as important as previously thought (Corak, (2001); Lang and
Zagorsky, (2001)). Lang and Zagorsky (2001) found that when family background and
individual characteristics were controlled for, there was not much evidence of the
positive impact on outcomes that one would expect (with the exception of father’s death
lowering the chances of the son being married). In particular, paternal absence had only
modest effects on child cognitive ability as measured by the Armed Forces
Qualification Test (AF QT).

Using a similar methodology however, Antecol and Bedard (2007) buttressed
the traditional hypothesis on the importance of father presence, concluding that children
were indeed “better off” the longer the biological father lived in the household. They
found that an additional 5 years living with a biological father reduced the probability of
outcomes such as smoking, drinking, convictions, marijuana use and pre-marital sexual
activity.

Recently, there have emerged works that examine the stability of the family
structure. Cavanagh and Huston (2006) showed that family instability was strongly
associated with teacher and observer reports of child behavioral problems. Fomby and

Cherlin (2007) bolstered these findings, noting that multiple family transitions produced

 

.1 If father’s death is due to risky lifestyle choices such as dangerous occupations, criminal activities,
unhealthy eating or drinking, death is arguably no longer an exogenous event.

more negative developmental outcomes than stable two-parent and even stable single-
parent family structures. Similarly, Osborne and McLanahan (2007) concluded that
partnership instability moderately contributed to behavioral problems in young children
up to three years old.

Cavanagh and Huston (2006) hinted at the importance of unraveling family
structure as a dynamic process rather than observing it in its discrete form. Instead of
examining paternal presence as a continuous variable with a unique effect, the purpose
of this study is to explore the possibility of multiple effects on the child’s cognitive
development by meticulously detailing all family structure types generated from

variability in paternal presence over time.
1.3. Simple Theoretical Framework

The model is based on the following production function:
Yi = F (Tia Pia Hi: Xi) (1)

where Y denotes the child’s PPVT-R score as a measure of child output, T is a vector
of variables modeling family structures, P is a vector of parental attributes affecting the

productivity of time inputs, H denotes measures of household income and X is a vector

of individual and family background covariates affecting performancez.

The family structures are depicted as a tree diagram, in which the mother’s
presence is held constant while the father’s presence is allowed to vary (see Figure 1.1).

Binary variables are created to represent each form of paternal presence. Paternal

 

2 Leibowitz (1977) employs a similar theoretical framework to show the effect of quality of time inputs
on child output measured by the PPVT.

presence is specified in this way to examine how the stability and presence of a father
impact the child’s cognition simultaneously. These issues for children in their early
developmental stages of learning (pre-school) have yet to be critically analyzed
together, and this model specification will allow me to do exactly this.

It should be noted that these measures do not speak to the quality, but rather to
the quantity of time the father spends in the home. Nevertheless, we expect that paternal
presence (whether through marriage or common-law union) will have a positive impact
on child cognitive ability. It is also important to reiterate that if the father is not
consistently present in the home, a negative disruptive effect may ensue. The child’s
adjustment to untimely paternal shifts into or out of the household could detract from
the quality and quantity of interaction time between the parent and the child (Amato and
Booth, (1991); Cherlin, (1978); Seltzer, (1994)). In addition, family disruption may
cause stress for parents as well as the child, generating parental aggravation and even
child behavioral problems (McLanahan, (1985); Sandefur and Wells, (1997); Wu,

(1996)).

Parental attributes such as schooling and substance abuse, P, affect time inputs
and child cognitive ability and should be extensively controlled for in order to reduce
omitted variable bias. In addition, higher household income, H, is assumed to have a

positive effect on the child’s PPVT-R score because more goods and services that foster

educational development can be purchased (Leibowitz, (1977)). Individual and family
characteristics, X, include the child’s birth order, sex, race/ethnicity, father figures

present in the home and household size. (See Table 1 for the full list of control

variables.)

 

1.4. Econometric Approach

The production function (1) given above can be estimated as:

Yr :2 5k Tki + Pi I31 “I“ Hi [32 + Xi [33+ Hi + 3i (7—)
=1

where Y denotes the child’s PPVT-R score and T is the set of m family structure types

engendered by variability in paternal presence; 5k shows the effect of different family

structures on cognitive performance. Father’s time in the household as well as parents’

education and income are potentially correlated with time-invariant and unobserved
innate ability, parental values and preferences (captured by It).

Since the Fragile Families dataset includes the Wechsler Adult Intelligence
Scale — Revised (WAIS-R3) scores for both parents, I argue that these scores can be
used as proxy variables for parents’ cognitive ability. In addition, the dataset supplies

several proxy variables for parental values and preferences (see Table 1 (section D) for

the complete list of proxy variables, Z). If these variables are valid proxies for
unobserved characteristics, listed above, the OLS estimator, 5, will be arguably

unbiased: 5 is expected to be upwardly biased if unobserved heterogeneity is not

effectively addressed. The methodology of dealing with omitted variable bias in this

way is formally known as the Proxy- Variable OLS Solution (Wooldridge, (2002) pg.
63-64). I argue that the proxy variables for parental ability, tastes and preferences, Z,

are valid in that they are redundant (i.e. they can be ignored as long as u and the

 

3 The questions are acquired from the Similarities subtest expected to measure verbal concept formation
and reasoning abilities (Wechsler, (1981)).

independent variables are directly controlled for) and once they are accounted for in the

model, yield no correlation between u and the independent variables. Put simply, once

Z is incorporated into the model, the endogenous variables and Z should not be

correlated with 8.

The reduced-form model becomes:

Yi =33ka Tki + Pi (11 + Hi 0£2 + Xi 0£3 + Zr (14 + Vi (3)

where Z represents the proxy variables for innate ability, parental values and

preferences usually unmeasured in previous studies.

Prior studies have exploited variation fi'om parental loss through death as well as
sibling composition to attenuate omitted variable bias (Lang and Zagorsky, (2001);
Sandefur and Wells, (1997)). However, as discussed in section 1.2, using these methods
may introduce other sources of bias into the model. Exploiting sibling comparisons, for
instance, requires the assumption that siblings receive equal parental investments;
moreover, the analysis sample is restricted to only those families with multiple children
(Sigle-Rushton and McLanahan, (2002)). Paternal death may also be endogenous in the
model if death is caused by endogenous factors such as lifestyle and occupational
choices. Furthermore, it cannot be used to examine multiple effects of paternal
presence.

If the main observed and unobserved characteristics can be directly controlled
for in the model using a rich set of control variables along with the proxy-variable OLS

solution, then arguably the “true” impact of father’s presence on child cognitive

performance can be isolated. The FFCWS aptly offers a wealth of data in which once
unobserved and unmeasured characteristics can now be directly controlled for in the
model. Even though this econometric method is not as elaborate as those employed in
previous studies, omitted variable bias will be effectively attenuated without

introducing other sources of bias.

1.5. Data Description

The Fragile Families and Child Wellbeing Study (FFCWS) supplies rich and detailed
information on family structure, family characteristics and conditions. It follows a
sample of approximately 5,000 children born between 1998 and 2000. Follow-up
interviews were conducted at one, three and five years thereafter. For this analysis, I
will only use data from the baseline, the one-year and three-year follow-up interviews.

The baseline interviews of both parents occurred shortly after the child was
born, when both parents were likely to be present in the hospital for the birth of their
child. As a result, the study was able to interview about 75% of all unmarried fathers in
the sample - the cohort that is usually under-sampled in many surveys. Moreover,
because both parents were interviewed at the baseline, data on missing fathers are also
made available through the mother’s responses.

The FFCWS uses stratified random sampling as the means of recruiting parents
to be a part of the sample p0pulation. Of all 77 large cities in the United States with a
population of 200,000 or more, 16 of these were randomly sampled. It is important to

note that there are 20 cities that comprise the total FFCWS sample. However, 4 were

10

non-randomly selected as they were of special interest to specific foundations of this
Study“.

The cities were stratified according to policy milieu and labor market conditions.
All cities were scored on their welfare generosity, the strength of the child support
system and the state of the labor market. The indicators for welfare generosity are
measures of the dollar value of monthly welfare payments; the strength of the child
support system was determined by paternity establishment and the number of AFDC
cases given awards and payments; labor market conditions of a city were primarily
determined by unemployment rates.

For welfare generosity, the stringency of the child support enforcement system
and labor market conditions, cities were scored then ranked in categories of strong,
moderate or weak. A city is classified as ‘extreme’ if it ranked in the strong or weak
categories (top or bottom quartiles of total points respectively) for all three policy
regimes. Cities that had extreme values fell into one of eight possible cells. For
instance: (i) generous welfare, stringent child support enforcement, and strong labor
market; (ii) generous welfare, stringent child support enforcement, and weak labor
market; (iii) insufficient welfare, stringent child support enforcement and strong labor
market, etc. This represents different combinations of extreme forms of welfare, child
support, and labor market regimes. Within each of these eight ‘extreme’ cells, 1 city
was randomly chosen and over—sampled, providing about 325 births to the sample
population. These cities were over-sampled in order to maximize variation in policy

regimes. In total, there were 12 cities over-sampled — the 8 ‘extreme’ cities and the 4

 

4 These cities include: Detroit, MI; Oakland, CA; San Jose, CA; Newark, NJ

11'

selected for specific foundationss. Approximately 100 births were sampled from each of
the other 8 ‘non-extreme’ cities with moderate policy regimes or labor market
conditions; this helped facilitate the detection of non-linearities as well as create a
nationally representative sample of non-marital births.

After the cities were selected, hospitals were then sampled such that each city
sample was representative of non-marital births for that city. However, sampling
I hospitals within each of the twenty cities was not uniformly executed. First off, there
were five cities in which there were only 5 birthing hospitals or less: Oakland, CA;
Austin, TX; Newark, NJ; Richmond, VA and Corpus Christi, TX. Consequently, all
hospitals in these cities were sampled.

By contrast, the other 15 cities had more than 5 birthing hospitals. For 12 of
these, the hospitals were rank-ordered such that the hospital with the most non-marital
births was sampled first; sampling would continue in descending order until the sample
was representative of the non-marital births for that city — usually about 75%. Hospitals
in New York, NY and Chicago, IL, were not rank-ordered using this ru1e6. These cities
had numerous birthing hospitals and consequently, there was less need to secure the
participation of any one hospital. Only hospitals with over 1,000 non-marital births per
year were randomly sampled in New York, NY and Chicago, IL.

The sample frame for each hospital was a list of beds in the maternity ward. The
design of the Study was to over-sample non-marital births and as such, non-marital

births were sampled until a pre-set quota, based on 1996-1997 non-marital birth rates in

 

5 These 8 extreme cities are: Indianapolis, IN; Austin, TX; Boston, MA; Santa Ana, CA;
Richmond, VA; Corpus Christi, TX; Toledo, OH; New York, NY.

6 Hospitals in Philadelphia, PA, were also not rank-ordered using this rule. 63% of non-marital births to city
residents were sampled from six of the eighteen hospitals.

12

each hospital, was reached. Marital births were also sampled until a pre-set quota was
reached. Some parents were inevitably ineligible to be a part of the Study: (i) those
parents under 18 in hospitals where interviewing under—18 parents was prohibited; (ii)
fathers who were dead at the time of the child’s birth; (iii) mothers who were not
sufficiently fluent in English or Spanish to complete the interview; (iv) those parents
who intended to give the child up for adoption.

There are implications for the use over-sampling of non-marital births on the
estimation results. Not only will it affect the generality of the findings, but also the
efficiency of the estimators. I have included city indicators in each regression in order
to control for the idiosyncratic differences among cities, upon which over-sampling was
based. Over-sampling is not expected to affect the consistency of the estimators so long
as I have specified the model correctly.

1.5.1. Description of Variables in the Model

The child outcome that will be examined in this study is the revised version of
the Peabody Picture Vocabulary Test (PPVT-R). The PPVT-R has two aims: (1) to test
the respondent’s receptive vocabulary capabilities for standard English and (2) to test
the respondent’s verbal ability7. The PPVT-R is also often used as a measure of
academic readiness for pre-school aged children and hence is salient to examine.

Even though the PPVT-R is useful in measuring English Language proficiency
and can even be usefirl to test respondents with mental and language impediments, one

caveat is that it only serves as a reliable indicator of verbal ability for those living in an

 

7 The PPVT-R is administered by the examiner, selecting a ‘picture plate’ which shows four different
black and white images. The examinee must choose the image that best describes the stimulus word
spoken by the examiner. American Guidance Service, Inc. '

http ://www.state.tn.us/education/c i/cistandardsZOO 1/1a/cik32tssesmentfolder/cik3 rapeabodypicture.htrn

13

environment where English is principally spoken. For instance, the PPVT—R scores of
Hispanic and Latin-American children in the sample may not be reliable indicators of
their cognitive skills. Consequently, the language chiefly spoken in the household must
be controlled for (in some form) if the PPVT-R is to accurately measure the verbal
ability of these childrens.

For the test, the child has to identify the picture that best describes the noun or
the verb spoken by the examiner (Jeruchimowicz et al., (1971)). The PPVT-R is
generally administered to individuals over the age of 2.5 years. The data on the PPVT-R
are provided in the 36-month In-Home Longitudinal Study of Pre-School Aged
Children (a module of the FF CWS). As a result, only a single cross-section of the data
can be used for the purpose of analysis. This immediately reduces the analysis sample
to only 2,368 respondents. The average age of the child at the time the test was
administered was approximately 38 months, underscoring the importance of controlling
for as many factors influencing the child’s cognitive performance as the data will allow.

Table 1 shows the summary statistics of all the variables included in the model.
The outcome measure is the child’s PPVT-R standardized score and the independent
variables include measures of paternal presence, parental attributes, income, family
background, household conditions and proxies for parents’ ability, values and
preferences. The standardized form of the PPVT-R score was chosen because it adjusts
for the mental age-score of each child.

1.5.2. Measures of Paternal Presence

 

8 I include variables indicating whether the mother was interviewed in Spanish as well as parents’ region
of birth as proxy variables for chief language spoken in the child’s household.

14

The analysis sample is restricted to those children who live with their mothers
all (or most of) the timeg. This ensures that any disruptive effect from paternal
movement is not conflated by the disruptive effect that will possibly ensue from
maternal movement into or out of the household. However, this restriction may
introduce bias from sample selection because there are idiosyncratic differences
between mothers who are primary caregivers and mothers who are not. Nevertheless,
the vast majority of mothers in the sample are primary caregivers to the focal child and
so we can argue that any selection bias caused by this restriction would be
inconsequential. The restriction reduces the analysis sample fi‘om 2,368 respondents to
2,202 respondents. The final sample used for analysis is 1,745 respondents due to
missing data for many of the covariates.

The central question needed to derive the family structure types is: “Has the
biological father ever been present in the household? ” From this question, different
measures of paternal presence can be determined (See Figure 1.1). From Figure 1.1, we
get the following measures:

1) Biological father present in the home since child’s birth and married to mother
1) Biological father present in the home since child’s birth and cohabits with

mother

2) Biological father is no longer present in the home and mother is now married to
social father10

2) Biological father is no longer present in the home and mother now cohabits with
social father

3) Biological father is no longer present in the home and mother is now single

X) Social father is present in the home since child’s birth and married to mother

X) Social father is present in the home since child’s birth and cohabits with mother

 

9 Ideally, I would like to restrict the analysis sample to children living with their mothers all the time.
However, in the third-year follow-up interview, the mother is asked if the focal child lives with her “all or
most of the time.” As a result, all primary caregivers are grouped together despite the implications for
instability.

To simplify the various measures of paternal presence, I define “social father” as a man (who is not the
child’s biological father) living and romantically involved with the focal child’s mother.

15

4) Biological father has never been present in the home but the social father is now
married to mother
4) Biological father has never been present in the home but the social father is now
cohabiting with mother
5) Interim relationships
6) Biological father has been completely absent and mother has been single since
child’s birth
Since the FF CWS does not ask the mother about a possible social father in the home at
the baseline, it cannot be observed whether the social father had been present in the
home since the child’s birth. Therefore, the two measures associated with the social
father’s stable presence in the household (X) cannot be directly specified in the model1 1.
I define an interim relationship as a cohabitational relationship that initiated

and/or dissolved between the baseline and third-year follow-up interviews. Interim

relationships could potentially include any of following family transitions:

{father present at birth, absent at one-yearfollow-up and returns by third-yearfollow-
up; father absent at birth, absent at one-year follow-up and enters the home by the
third-year follow-up; father absent at birth, present at one-year follow-up and third-
year follow-up; father present at birth, social father present at one-yearfollow—up and
father returns by third-year follow-up; father absent at birth, social father present at
one-yearfollow-up, he then leaves and father enters the home by third-yearfollow-up;
no father present at child 's birth, social father present at one-year follow-up and

mother is again single by third-yearfollow-up}

 

H These households would likely be captured in measures where the child’s father has never been present
but the social father is currently present -— father’s presence can be determined at the baseline while the
social father’s presence can only be determined in subsequent waves.

16

If we assume that the effects of marriage and cohabitation on early cognitive
development are not statistically different from each other, these numerous measures
can be condensed as follows12 :

1) Biological father has been present in the home since child’s birth (stable
two-parent family structure)
2) Biological father used to be in the home but the social father is now
present (unstable two-parent family structure)
3) Biological father used to be in the home but mother is now single
(unstable single-parent family structure)
4) Biological father has never been present in the home but social father is
now present (unstable two-parent family structure)
5) Interim relationships (unstable family structure)
6) Biological father has been completely absent and mother has been single
since child’s birth (stable single-parent family structure)
Consequently, the number of family structures specified in equation (3), m, is equal to
6. These family structures can be classified as: stable two-parent, stable single-parent,
unstable two-parent and unstable single-parent households.
1.5.3. Descriptive Statistics

Table 1 illustrates that the standardized PPVT-R scores range from 40 to 137
points and the mean for children in the analysis sample is approximately 86 points. This
low mean can be attributed to over-sampling of large cities'3 but should not influence
the regression estimates. 50% of children lived in stable two-parent households while
20% of children lived with their single-mothers since birth. Moreover, over 1% of
children had biological fathers who left but have social fathers present in the household
by the mother’s third-year interview; almost 11% of children had no social father

present after their biological father left. By contrast, 6% of the children in the analysis

 

‘2 The assumption of no statistical difference between marriage and cohabitation fails if the interpretation
of cohabitation varies among the mothers of the sample.

'3 These cities include: Austin, TX; Baltimore, MD; Detroit, MI; Milwaukee, WI; Newark, NJ; New
York, NY; Oakland, CA; Richmond, VA; San Jose, CA (Reichman et al. (2001)).

17

sample never had a biological father living at home but now have a social father
present; 11% experienced numerous disruptions caused by interim relationships of the
mother. These figures reveal that a large percentage of children had their biological
fathers present at least partially; however, a much smaller percentage of children had
social fathers to fill the role of the absentee biological father.

Table 2 gives the mean standardized PPVT-R scores for each family structure
type. The general score means in Panel A show that children of the stable two-parent
family type have higher PPVT-R scores on average than children of stable single-parent
or unstable family structures. This is what we would expect a priori. However, the
means also indicate that children of stable single-mother households have higher scores
on average than children of unstable households. This lends credence to the theory
postulated by Sandefur and Wells (1997), Wu (1996) and McLanahan (1985) that the
stress associated with family disruption creates adverse outcomes for the child. The
means also bolster Fomby and Cherlin’s (2007) instability hypothesis, which posits that
children’s developmental outcomes are worse if they experience multiple family
transitions as opposed to living in a stable environment. The outcome means insinuate
that it is better for a father to be at home all the time than be there intermittently or not
at all; it is also better for a father not to be at home at all than to be there intermittently.

The same pattern of results is also clearly evident in Panels B and C where the
sample is split by gender in order to observe gender differences in the impacts of
patemal presence. The results show that girls have higher average scores in general than

boys as expected (Bomstein and Haynes, (1998)).

18

Table 3 illustrates other independent variables truncated by the following family
types: stable two-parent family, unstable family and the stable single-mother family
structure. The most striking characteristic is that predominantly (over 70%), black
parents and their children represent the stable single-mother household. White and
Hispanic parents largely belong to stable two-parent households, with over 30% of
white parents and about 25% of Hispanic parents comprising this family type. Parents
with at least college education largely constitute the stable two-parent family structure
whereas over 25% of parents who were high school dropouts typify the unstable and
stable single-mother family types.

72% of fathers and 39% of mothers of stable two-parent families report they use
alcohol — more than any other family type. This is not as surprising as it would appear
since most fathers and a large percentage of mothers belonging to other family types
also use alcohol. Also not surprising is that the stable two-parent family structure is
characterized by older parents and higher household income.

Unstable family structures, by contrast, typically display the youngest parents,
the most residential moves since the child’s birth, the shortest dating period before
pregnancy and more mothers with mental or emotional problems compared to any other
family type. For stable single-mother households, only 42% of children were breastfed,
the lowest among all the family types. Parents associated with the stable single-mother
household also have the lowest WAIS-R scores and household incomes.

One caveat in relying on these summary statistics is that they may reflect the use
of over-sampling by the FFCWS. Observing the race averages indicate that about 52%

of mothers and 55% of fathers in the analysis sample are black (47% of mothers and

19

49% of fathers in the total sample are black). The national average of blacks in the US.
population is only about 12%“. Consequently, over-sampling directly increased the
percentage of blacks in the sample. This provides an explanation for why a large
percentage of children lived in stable single-parent households and only a small
percentage had social fathers in the sample. Black children are less likely to have a
father present in the household than any other racial or ethnic group. Subsequently, the
means in Table 1 will be skewed by the use of over-sampling but this should not bias
the regression estimators. In fact, it makes for a policy-relevant sample, where the

results will yield direct implications for social policy.
1.6. Results

Table 4 presents estimates from a specification similar to those in columns (1) and (2)
of Tables 3 and 4 in Lang and Zagorsky (2001). They use the National Longitudinal
Survey of Youth (NLSY) to examine how a parent’s absence during childhood affects
outcomes in adulthood. I define father’s presence as the fraction of time the father has
been living with the child, constructed as the total number of years the biological father
has spent living with the child divided by the child’s age. Column (2) indicates that as
father presence increases from 0 to 1, the child’s standardized PPVT-R score increases
by 5.2 points (about 0.30 standard deviations) when only region-of-birth and interview-
year dummies are incorporated in the model. However, when similar control variables
to Lang and Zagorsky (2001) are included in Column ( 1), the impact of the fraction of
time a father is present in the household is no longer statistically significant, with the

point estimate falling to about 1.2 points. Father’s presence has a larger positive impact

 

‘4 US. Census Bureau, Census (2000).

20

on girls’ than boys’ PPVT-R scores in the simple regression model; however, the effect
dissipates for both boys and girls once the relevant control variables are included,
challenging the statistically significant, albeit modest effects found by Lang and
Zagorsky (2001).

However, if the effect of paternal presence varies by family structure type, then
the small and statistically insignificant results displayed in Table 4 should not be
surprising. Multiple effects subsumed in a single measure become conflated and thus
yield a statistically insignificant estimate.

Table 5 displays the results when the effect of paternal presence is allowed to
vary by family structure. Column set (A) are regressions including only city, region-of-
birth and interview-year dummies. Standardized PPVT-R scores are higher by about 4
points (0.24 standard deviations) for children of stable two-parent families relative to
children of stable single-parent families. In addition, the stable single-parent family
structure generates higher scores than if the father and/or social father were present for
only a portion of the child’s life illustrated by measures (2) and (4). These results
underscore the implications derived from the outcome means in Table 2 and lend
credence to the instability and stress hypotheses posited by Fomby and Cherlin (2007)
and Sandefur and Wells (1997).

When exogenous variables (listed in Table 1) are included in the model in
column set (B), the effect of a father’s stable presence is no longer statistically different
from the effect of his stable absence. The negative effect caused by family disruption is
still apparent, nevertheless. In the instance where the biological father has left and the

social father is now living in the household, the child is at about a 10-point disadvantage

21

(about 0.60 standard deviations); similarly, where the father was never present but the
social father is currently present, the child’s PPVT-R score is about 4 points (0.22
standard deviations) lower than in the stable single-parent case.

Unobserved heterogeneity is expected to upwardly bias the father presence
coefficients. Therefore, column set (D) includes proxy variables (listed in section D of
Table 1) for parental values, preferences and ability. When these proxy variables are
included in the model, the coefficients measuring the father presence effects in general
become larger than the coefficients in column (C), where all independent variables
except the proxy variables for unobserved characteristics are accounted for. Column set -
(D) shows that family disruption lowers the child’s test scores between 2 and 9 points
(between 0.12 and 0.54 standard deviations) relative to the stable single-parent case.

The negative coefficient on father is no longer present but social father is now
present has the largest magnitude ‘across the board’ of any unstable family structure
defined. However, this family type also represents the fewest number of families (27 in
total) compared to the other family types and as such, the large magnitude may just be a
reflection of this small sample. Test scores when the father is completely present
remains statistically similar to test scores when the father is completely absent, and thus
the stability effect holds. What is also interesting is that family structures with two
parents do .not necessarily yield better outcomes than those with one parent. In
particular, unstable two-parent family structures adversely affect child cognitive
performance relative to the stable single-parent household. Consequently, the family

structure effect is not confirmed by these findings.

22

Tables 6 and 7 indicate that in the naive model, girls experience higher scores
than boys when their fathers are completely present as opposed to completely absent.
This is consistent with the outcome means discussed in the previous section. However,
when the full set of variables are incorporated in the model, these gender differences are
not as convincing. Depending on the family type, boys in unstable households score
between 0.12 and 0.40 standard deviations lower than boys in stable single-mother
households and girls in unstable households score between 0.01 and 0.80 standard
deviations lower than girls in stable single-mother households when all variables are
included in these regressions. These estimates are however, largely statistically
insignificant due to small sample sizes.

The only statistically significant estimate belongs to the unstable family
structure in which the child’s biological father has left and the social father has entered
the household. Boys living in this family setting score about 0.35 standard deviations
lower than boys in stable single-mother households; similarly, girls belonging to this
family type score about 0.75 standard deviations lower than girls living in stable single-
mother households. This provides some, albeit weak evidence that during early
childhood years, girls may in fact suffer more due to family disruption than boys. The
stability effect on cognitive ability remains clearly evident since there is no statistical
difference when the child lives in a stable two-parent home as opposed to a stable
single-parent one.

1.6.1. The Resource Effect
An unusual feature of this model is the modest mediating effect of resources in

the child’s household. The resource effect is captured by household income per person

23

and shows that for an increase of $10,000, the child’s PPVT-R standardized score
improves by 1 point (results not shown). This estimate is statistically significant at the
5% level but the magnitude (6% of a standard deviation) suggests that the resource
effect is surprisingly not as important in this model as one would have expected a priori,
particularly because all families in the sample reside in urban areas. Nevertheless, its
inclusion bears a strong implication for consistency of the family structure estimators.
Column set (E) in Table 5 shows that when the resource effect is unaccounted for, the
estimated effect of each family structure type gets smaller (except for the family type in
which the father is no longer present but the social father is)”, indicating upward bias.
This reinforces the importance of controlling for as many factors as possible that
concurrently influence child cognitive ability and family structure, ensuring unbiased
estimators.
1.6.2. Robustness Checks

As stated in section 1.5, twelve large cities were over-sampled. If I have
specified my model correctly, over-sampling should not affect the consistency of the
estimators. As a sensitivity check however, I generate weighted estimators using
national sampling weights from the FFCWS. The results in Table 8 column set (B)
show that the weighted estimators are not statistically different from the un-weighted

estimators in column set (A)'6.

 

'5 This family type includes only 27 observations compared to the other family types, which each have at
least 100 observations.

6 The reason there is a difference in the sample size between the weighted regressions and the un-
weighted regressions is that cities that were not randomly selected into the sample were not assigned
weights. Of the twenty cities in the sample, Detroit, MI; Newark, NJ; Oakland, CA and San Jose, CA
were selected based on special interest to some foundations. As a result, they were not assigned weights
in the study.

24

The identification strategy employed also does not address heterogeneous family
treatment effects. Despite mitigating unobserved heterogeneity, my methodology treats
all families as identical except for time of paternal exit from or entry into the household.
It is salient to note that two families can be identical based on observables at the time of
the test despite one father’s exit from his family. By controlling for conditions
preceding the father’s exit from or social father’s entrance into the household, families
can be distinguished from each other beyond just the look of their present family
structure. I incorporate in the full regression mother’s education since child’s birth,
parents’ alcohol and drug use for all three waves, household income over all three
waves and average number of adults and children in the household over all three waves.

These results, as shown in column set (C), corroborate the main findings of the study.
1.7. Summary

This paper adds to the literature by utilizing rich, policy-relevant data to examine the
various effects of paternal presence and family instability on child cognitive
development. The results show that when an exhaustive set of control and proxy
variables are incorporated in the model, the pre-school aged child is not necessarily
better off when the father is home all the time as opposed to never being home but
he/she is certainly better off when the father is never home as opposed to being home on
a temporary basis. The study was therefore unable to reject the conventional hypothesis
that stable paternal presence yields better cognitive outcomes than stable paternal
absence.

The findings of Cavanagh and Huston (2006), Osborne and McLanahan (2007)

and Fomby and Cherlin (2007) are endorsed by this study since a father’s partial

25

presence in the home stunts cognitive development relative to when he is not living in
the household at all. The study also adds to this literature by reinforcing the stability
effect: there is no statistical difference between the stable single-parent household and
the stable two-parent household when it comes to child cognitive development; for
children of unstable family structures, their PPVT-R scores are lower by 2 to 9 points
(an average of about 1/5 of a standard deviation) relative to children of stable single-
parent households. On the other hand, the family structure effect is not supported by
these results — unstable two-parent households are found to'be worse than stable single-
parent households as it pertains to child cognitive performance.

If the proxy-variable OLS solution and extensive covariates sufficiently
attenuate unobserved heterogeneity, the causal relationship between paternal presence
and child cognitive performance is only apparent in the stability the father generates
within the family setting. Paternal presence improves cognitive development through
the stability of family structure — any type of paternal presence will not necessarily
engender positive results for the child. The stress hypothesis postulated by Sandefur and
Wells (1997), Wu (1996) and McLanahan (1985) gives us some insight as to why this
might be the case: unstable family structures produce negative outcomes due to the
stress and anxiety that accompany each transition. The study was not able to determine
whether more family transitions yielded more adverse effects on early cognitive
development.

Moreover, the findings of Lang and Zagorsky (2001) and Antecol and Bedard
(2007) are not reinforced by this study — the child does not seem to be better off as the

father’s length of residence increases. However, it is important to note that I cannot

26

predict how the child would adjust to his/her family transitions over the course of
his/her life. Since, the subjects of study are pre-school aged children (average age is 38
months), it cannot be determined whether the negative effects of family dissolution are
short-lived or are improved over time. The child may be able to adjust to his/her family
structure as time progresses but this clearly goes beyond the scope of this paper.
Further, these effects may not extend to other child outcomes such as behavioral
problems or substance abuse. Future research may study this in more rigorous detail.
The main policy implication of the findings is the importance of encouraging
family stability, as this should help improve the cognitive development of the children
affected. There may also be implications for children parented by same-sex couples. If
paternal presence only improves child cognitive performance through the stability of the
family structure, it is quite possible that same-sex parents within a stable household may

engender similar positive cognitive outcomes for their children as well.

27

Chapter 2.
Paternal Incarceration, Paternal Absence
and Early Child Development

2.1. Introduction

By 2001, 2.7% of adults in the United States had been incarcerated, indicating a 50%
hike since 1990. More interesting is the fact that 6 out of 10 inmates fi'om 1996 to 2002
were minorities: 40% were black and 19% were Hispanic”. Since statistics show that
over 50% of all inmates grew up in a single-parent household and 46% had a family
member who was previously incarcerated, the increase in incarceration rates could
disproportionately affect minority children as well as their parents. This study will
investigate the extent to which the incarceration of a central family member — the father -—
influences developmental outcomes of young children.

The fundamental identification problem associated with this research question is
the difficulty in isolating the impact on childhood development of paternal incarceration
from the impact of unobserved factors correlated with incarceration. For example, if a
criminal offender lived in unfavorable circumstances ex ante, poor child outcomes may
simply, be another result of the poor pre-existing conditions that also led to the father’s
incarceration. This problem will be addressed using instrumental variables estimation and

a differencing method.

 

'7 Profile of Jail Inmates (2002), Bureau of Justice Statistics.

28

Another pertinent question inextricably linked to the research question is whether
the effect of paternal absence due to incarceration is statistically different from the effect
of his absence in general. The consensus among previous studies is that father absence
has a negative effect on child outcomes (Antecol and Bedard (2007); Corak, (2001); Lang
and Zagorsky (2001); Painter and Levine, (2000)). However, there is evidence that
paternal absence does not always have a negative effect on child development. J afee et a1.
(2003) argue that paternal presence may do more harm than good when the father
exhibits anti-social behavior. In addition, other studies find that it is the instability of
paternal presence (or absence) that engenders negative effects on child wellbeing (Craigie
(2008); Cavanagh and Huston (2006); Fomby and Cherlin, (2007); Osborne and
McLanahan (2007)).

From these studies, the question arises: “Are all absences created equal?” Would
absence due to incarceration be more detrimental because of the circumstances under
which the father became absent? Or, would incarceration induce an improved family
situation due to the timely removal of an anti-social presence from the household? The
study will attempt to distinguish the impact of paternal absence from the impact of
paternal incarceration as they relate to early child development.

The data used to examine this problem is obtained from the Fragile Families and
Child Wellbeing Study (FFCWS), which meticulously measures paternal incarceration as
well as important early child developmental outcomes. Using these data, a prior study by
Wildeman (2008) employed fixed effects estimation to show that paternal incarceration
amplified aggressive behaviors in boys. In my study, paternal incarceration not only

exacerbates aggressive behaviors and ODD symptoms in young children but also lowers

29

their cognitive test scores. However, when the effect of incarceration is effectively
isolated from other factors with which it is correlated, the study finds no statistical
difference between the effect of incarceration on child outcomes and the effect of
paternal absence in general.

The paper is organized as follows. Section 2.2 provides a brief review of past
works that discuss parental incarceration. Section 2.3 gives the data description and
summary statistics of the variables used in the model. Section 2.4 explains the
identification strategies I use to estimate the effect of paternal incarceration. Section 2.5
discusses the results from the differencing and instrumental variables estimation methods.

Section 2.6 includes a summary of the findings and policy implications.
2.2. Background

The most apparent effect of parental incarceration is the strain on economic resources in
the household. It is worth noting however, that the strain caused by incarceration does not
only refer to economic capital, but social capital as well. Clearly, the structure and quality
of family relationships are disrupted by incarceration. Non-resident parents are able to
maintain frequent contact with children if they so choose. In the event of incarceration,
however, children are more at a disadvantage since the avenue for frequent contact is
physically obstructed. Moreover, the incarcerated parent may have been a serious drain
on family resources prior to incarceration. He/She may even become incapacitated if the
stable and supportive environment of the household is disrupted (e.g. due to violence,
abuse or negligence). These hypotheses suggest that paternal incarceration may yield

positive or negative outcomes for the child.

30

It can be strongly argued that criminal offenders and men predisposed to
incarceration possess traits that frustrate family cohesiveness (Western, (2004)).
Subsequently, weak attachment to the family would have occurred even if incarceration
did not. Therefore, the factors and influences that predate paternal incarceration also help
engender incarceration. Put differently, ex-post conditions are merely a continuation of
the pre-incarceration situation. An attempt to simply compare children of incarcerated
parents to children whose parents have never been incarcerated (but have similar
background characteristics), will yield a biased incarceration estimator. This is because
children of criminal offenders are exposed to unobserved factors, which not only increase
the probability of parental incarceration, but also persist to adversely affect child
wellbeing. Conversely, children whose parents have never been incarcerated are arguably
less exposed to these factors and as a consequence, estimates from this simple method of
comparison will not be consistent.

A generally unexplored effect of parental incarceration is its effect on the parent-
child relationship. Incarceration disrupts the attachment mechanism between the
incarcerated parent and the child, especially at early ages. This could possibly lead to
both short-terrn and long-term effects on the child’s well-being. Elicker et al. (1992)
postulate that attachment of the child to the parent, particularly during infancy, increases
social competence among peers. As a result, incarceration is expected to negatively affect
child development due to its inherently disruptive nature.

Despite a priori expectations of an adverse effect, there is still much to be
determined about paternal incarceration and child outcomes. The views presented above

indicate an ambiguous effect of paternal incarceration that could be negative, positive or

31

even zero. Previous works have shown that family instability produces negative
childhood outcomes (Cavanagh and Huston, (2006); Craigie, (2008); Fomby and Cherlin,
(2007); Osborne and McLanahan, (2007)). However, is the effect of instability from
incarceration different from the effect stemming from other sources of disruption such as
divorce or the death of a parent? I examine these differential effects to determine the

influence of incarceration on early child cognitive and behavioral measures.
2.3. Data and Variable Descriptions

The data for this analysis come from The Fragile Families and Child Wellbeing Study
(FFCWS). It follows a sample of approximately 5,000 children born between 1998 and
2000. Parents were interviewed around the time of the child’s birth, with follow-up
interviews occurring at about ages one, three and five years thereafter. Data have been
gathered on not only the child’s developmental outcomes and characteristics, but also on
family relationships and demographics of the parents and focal child. Because both
parents are interviewed on these issues, the roles of both parents and particularly the
father can be examined in detail. This proves to be especially important for the analysis,
as it allows father characteristics possibly linked to his incarceration history to be
incorporated in the model. Both parents report on the father’s past and current
incarceration status in the FFCWS, and the data also include a wide array of child
developmental outcomes useful for this study. (For more information on the FFCWS
data, see chapter 1, section 1.5.)

I will examine cognitive development measured by the Peabody Picture
Vocabulary Test-Revised (PPVT-R) and behavioral problems displayed in the forms of

aggression and oppositional defiant disorder (ODD). These outcome measures are

32

currently only given in the 36-month In-Home Longitudinal Study and as such, only a

single cross-section of data may be used for estimation.

2.3.1. Early Child Development Measures

i. Peabody Picture Vocabulary Test - Revised (standardized)
The Peabody Picture Vocabulary Test-Revised (PPVT-R) is administered to
children over the age of two and a half years old to measure their verbal ability
and English Language proficiency. For the test, the focal child must state the noun
or verb which best describes the image given on a picture plate (J eruchimowicz et
al., ( 1971)). The PPVT-R is also commonly used as a measure of academic
readiness among pre-schoolers and is reliable even for those children with mental
and language impediments. However, for children living in a household where
English is not predominantly spoken, the PPVT-R does not reliably predict verbal
ability. To control for this, I will incorporate in the model parents’ region of birth
as well as an indicator for whether the mother was interviewed in Spanish. PPVT-
R scores are also standardized to adjust for the chronological mental age-score of
the child.
ii. Aggression

Aggressive behavior disorders in a child are shown by acts undeniably intended to
hurt or destroy a person, animal or object (Grusec and Lytton, (1988); Maccoby,
(1980); Shaw and Giovanelli, (2000)). However, to accurately diagnose
aggressive behavior disorders, one must be able to determine intentionality (Shaw
and Giovanelli, (2000)). There are nineteen acts of aggression and defiance listed

in the In-Home Longitudinal Study (see Appendix B) but intentionality of these

33

acts is indistinct. Even though intentionality and thus a conduct disorder cannot be
diagnosed in this instance, it does not negate the importance of examining
aggression in children, since incarceration and criminal propensities are often
preceded by such misguided behaviors during childhood (Robins, (1978);
Sampson and Laub, (1992); Wildeman, (2008)). Thirteen of the acts of aggression
are averaged to create an index, ranging from 0 to about 2, with 0 indicating the
least aggression”.
iii. Oppositional Defiant Disorder (ODD)
Oppositional Defiant Disorder (ODD) can be described as recurrent disobedient,
defiant and aggressive acts, particularly towards those in authority (Greene at al.
(2002)). Unlike the aggression outcome measure, ODD is an actual conduct
disorder. The In-Home Longitudinal Study provides six symptoms of ODD (see
Appendix B) that are requisite for the diagnosis of this type of conduct disorder.
These symptoms are averaged to create the child’s ODD index, which ranges
from 0 to 2, with 2 being the most defiant. Social factors such as poverty and

family disruption are thought to increase the probability of diagnosis and will be

incorporated in the model accordingly (Steiner et al. (2007)).

2.3.2. The Incarceration Measures

The father’s incarceration history and status is inferred from information provided

by both parents in the FFCWS. Mothers are asked about the fathers’ current incarceration

status and whether the father has ever been incarcerated. Fathers are asked about their

current incarceration status and also about their most recent incarceration and release. It

 

'8 Note here that each individual measure ranges from 0 to 2 but averaging all measures creates a
maximum of 1.92.

34

is important to note that mother and father interviews are conducted at different times,
and hence, if one parent declares the father currently incarcerated but the other does not,
this does not necessarily mean that either of the reports is inaccurate. The father could
have been jailed and released prior to the other parent’s interview but this information is
not easily verifiable”.

As a result, a father will be coded as having been incarcerated after the child’s
birth (i.e. incarceration ex post) if either parent reports in any interview that the father is
currently jailed or if the father reports that he was recently incarcerated after the child’s
birth. Father’s incarceration before the child’s birth (i.e. incarceration ex ante) is difficult
to determine from the data. Since follow—up interviews do not occur annually, the jail and
release period could easily have transpired between interviews, so that subtracting the
sub-sample of ex post incarcerated fathers from the total sample of ever-incarcerated
fathers will not yield the precise sample of fathers incarcerated ex ante. The father is
therefore classified as incarcerated ex ante if the year of his incarceration and the year of
his release were before the focal child’s birth year.

2.3.3. Summary Statistics

The summary statistics for all the dependent outcomes and independent variables
are presented in Table 9. The analysis sample is restricted to children living with their
mothers all (or most) of the time due to the concern that mother’s unstable presence in the
household could conflate any disruptive effect that ensues from the father’s incarceration

or partial absence”.

 

19 There are questions on the time the father was jailed and released. However, these data are often missing
in the FF CWS.

20 The analysis sample is further limited to children whose fathers have impulsivity (DDI) scores to ensure
a more accurate picture of the families in the IV sample.

35

The average PPVT-R standardized score for children in the analysis sample is
approximately 86 points. This score seems low but may be attributed to the over-
sampling of large cities in the FFCWS (Reichman et al. (2001))21. Family dissolution,
low education and economic adversity are reality for many children in large cities and
may help explain their low scores.

The child’s aggression measure is an index of thirteen acts of violent and
aggressive behavior”. They are averaged to create an index from 0 to about 2 that
increases with the level of aggression; the mean of this aggression index in the analysis
sample is 0.58. Similarly, the oppositional defiant disorder (ODD) symptoms are
averaged, range from 0 to 2 and increase with the level of defiance. The mean of this
index is 0.63.

Another important pattern displayed in the data is that parents of the focal child
exhibit many characteristics associated with a high-risk environment. Of the fathers in the
analysis sample, 38% were ever-incarcerated with almost 25% of these incarcerated since
the child’s birth. Over 40% of fathers have been absent at least in part while most parents
have a high school degree or less. Household income per person is about $8000 per year
with a standard deviation of over $13,000. With the high probability of single-
parenthood, low education and low household income, the children in the Fragile
Families Study are, in general, at a greater disadvantage.

However, these statistics do not give us a vivid picture of the differences between

the child of an incarcerated father and the child whose father has never been incarcerated.

 

21 These cities include: Austin, TX; Baltimore, MD; Detroit, MI; Milwaukee, WI; Newark, NJ; New York,
NY; Oakland, CA; Richmond, VA; San Jose, CA.

2 The six ODD items are a subset of the nineteen acts of aggression in the FFCWS. These items are
excluded from the aggression index, leaving only thirteen.

36

Table 10 presents comparisons of variable means by father’s incarceration history. The
child of an incarcerated father has a PPVT-R score that is about 4 points lower than the
child whose father has never been incarcerated. Children of incarcerated fathers also
display more aggressive and defiant tendencies as opposed to their counterparts.

In addition to these developmental outcomes, it is evident that other
characteristics of the child’s household vary by the father’s incarceration history.
Incarcerated fathers and their partners are more likely to be black and less educated
relative to non-incarcerated fathers; children of non-incarcerated fathers also live in
households with over $4000 more income per person.

2.4. Econometric Issues and Methods
2.4.1. Omitted Variable Bias

The simple model presented in equation (1) below, controls for exogenous individual

characteristics, X, incarceration, I and absence, A, to explain child outcomes, Y.
YI=B0+BIIi+B2Ai+XiB3+3i (1)
The variable I, is not orthogonal to the error term, 8, since there are unobserved factors in

8 that simultaneously influence child outcomes and the probability of paternal

incarceration. Factors such as innate ability, deviant tendencies, tastes and preferences

may be correlated with both incarceration and child outcomes and constitute time-

invariant unobserved heterogeneity, 9, in equation (2). An identification strategy must be

employed to eliminate unobserved heterogeneity for an unbiased estimator y].

YI=Y0+YIII+72AI+XIY3+9i+Ili (2)

37

To eliminate the time-invariant unobserved factors captured by 9, a differencing
strategy is employed to identify the marginal effect of incarceration ex post on the
outcome measures of early child development. If 9 is interpreted as the father’s “criminal

type” and directly controlled for in the model, the marginal impact of paternal
incarceration may in fact be isolated. Juvenile offenses and incarceration prior to the
child’s birth may well be a strong indicator of father’s criminal tendency as well as other
unobserved characteristics associated with his incarceration ex post. As such, this
indicator will be used, in essence, as a proxy for “criminal type”23. It is important to note
however, that this is an imperfect proxy because “criminal type” may not have been
revealed prior to the child’s birth. Further, the implicit assumption in using this strategy is
that criminal propensities are fixed —- variability stemming from criminality as a response
to events ex post are not considered (e.g. father’s unemployment occurring after child’s
birth could be the cause of incarceration ex post).

We also need to investigate whether absence due to incarceration engenders a
different effect on child outcomes than paternal absence in general. For this reason, the
model will directly control for father absence, to better isolate the marginal impact of

paternal incarceration. Therefore, rewriting equation (1) to include juvenile offenses and

incarceration ex ante, Ia, incarceration ex post, Ip, exogenous variables, X, and other

independent variables, N, we get:

 

23 Grogger (1995) employs a similar differencing strategy to deal with unobserved heterogeneity in
studying the impact of arrests on earnings and employment. For a sample of men arrested between 1972
and 1987, Grogger restricts the analysis sample to data on earnings and employment from 1980 to 1984.
Labor market outcomes of men first arrested after 1984 are compared to a treatment group of men first
arrested before 1985. Subsequently, men initially arrested in or after 1985 are similar in “criminal type” to
those men initially arrested before this period, rendering comparison of their labor market outcomes
unbiased.

38

Yr=(Po+\llIPI+7IIai+<PIAi+Xi<P2+Ni¢3+Vi (3)

The marginal impact of father’s incarceration ex post is [\y — it] from estimation of

equation (3). We can easily estimate this difference via regression by including an “ever-

incarcerated” variable - an indicator for whether the father was jailed before or after the
child’s birth — in lieu of la.

2.4.2. Under-Reporting and Incarceration

An important caveat in using the FFCWS data is that incarceration is likely to be
severely under-reported (Geller at al., (2006); Wildeman, (2008)). In prior studies, it has
been concluded that convicted criminals tend to under-report their crimes by about 35%
(Locander et al. (1976); Witte, (1980)). We can therefore assume that fathers in the
FFCWS also significantly under-report their criminal activity as well as their jail
sentences.

Similarly, it would be erroneous to assume that the mother’s account of the
father’s incarceration status is any more accurate. The mother’s account of father’s
incarceration is likely to be inaccurate due to incomplete information. Even if she
truthfully reports what she knows about the father’s criminal history, how much does she
really know about what happened before she met him? A criminal background bears a
negative stigma not only for the labor market but also for the marriage market (Western,
(2004)). Therefore, the father may not have told his partner about past incarceration or
even current incarceration (if they are no longer in close contact).

There is less convincing evidence to support “over-reporting” (i.e. reporting

incarceration when this is untrue) simply because of the negative stigma associated with

39

event“. From these conjectures, we expect that reported incarceration is either true or
under-stated. For an incarceration indicator equal to 1 if father is incarcerated and 0
otherwise: the true indicator for paternal incarceration is assumed to be equal to 1 when
the father is reported as incarcerated but may also be equal to 1 when he is reported as
non-incarcerated (0 otherwise). In this sense, under-reporting constitutes measurement
error in the incarceration data and may be typified as non-classical measurement error.

Non-classical measurement error implies that OLS estimators will be susceptible
to bias, but not necessarily attenuation bias (Haider and Solon, (2006)). Subsequently, it
is uncertain whether the incarceration effect is over-estimated or under-estimated by
OLS. Freeman (1984) also shows that measurement error in explanatory variables tends
to be more severe in longitudinal data and as a result, under-reported incarceration could
pose a serious problem for estimation using panel data. Wildeman (2008) does not
address the measurement error problem in his use of panel data methods and as such, his
estimated impact of paternal incarceration is likely to be biased. I intend to address this
problem using two-stage least squares or instrumental variables (IV) estimation.
2.4.3. Instrumental Variables (IV) Estimation

A method that can be used to address both unobserved heterogeneity and the
measurement error problem is two-stage least squares or instrumental variables (IV)

estimation. The challenge is finding an exclusion restriction or instrument, i.e., a variable
that is correlated with incarceration but not the error term, 8. One such variable,

formalized by psychologist Scott Dickman, is the Dickrnan’s Dysfunctional Impulsivity

 

24 An extreme case in which the mother may “over-report” father’s incarceration is if she believes he is
such a terrible father/partner that he must have been in jail at some time whether or not she knows this for
sure.

40

(DDI) scale (Dickman, (1990)). Dickman (1990) cites two different types of impulsivity
— functional and dysfunctional. Functional impulsivity is described as “the tendency to
act with little forethought, when such a style is optimal”. Functional impulsivity can be
described as responding to stimuli in ways that reflect enthusiasm and
adventuresomeness or any response in which quick thinking is optimal (Dickman,
( 1990)). A prime example of functional impulsivity is “clutchness” in sports. We could
argue that star athletes such as Roger Federer, Reggie Jackson, Michael Jordan, David
“Big Papi” Ortiz, Tom Brady and Peyton Manning are all famous functional impulsives.

Dysfunctional impulsivity on the other hand, “is the tendency to act with less
forethought than most people of equal ability when this tendency is a source of
difficulty”25. This diagnosis insinuates that if we hold ability constant, dysfunctional
impulsive individuals tend to act with less forethought or self-control when this response
is not optimal. Disorderliness and disregard for facts, for instance, tend to reflect traits of
dysfunctional impulsives (Dickman, (1990)). Alcoholics and excessive gamblers are
sometimes diagnosed as dysfunctional impulsives as a result (Dickman, (1990); Petry,
(2000)).

There are two main questions associated with using dysfunctional impulsivity as
an exclusion restriction: (1) Is dysfunctional impulsivity related to functional
impulsivity? (2) Is dysfunctional impulsivity related to unobserved factors such as innate
ability? Dickman (1990) found no significant relationship between functional and
dysfunctional impulsivity in his study. Therefore, not being able to control for functional

impulsivity in the model should not violate the requirements of a valid instrument. In

 

25 Dickman, Scott J. (1990), page 95.

41

addition, no direct relationship has been found between dysfunctional impulsivity and
intelligence itself. Vigil-Colet and Morales-Vives (2005) found no direct relationship
between impulsivity and intelligence but that impulsivity acts as a moderator variable
between how an individual uses his resources and academic attainment. They find that
the correlations between impulsivity and intelligence measures are largely linked to
absence in planning strategies and lack of forethought in making decisions. Therefore, it
can be deduced that dysfunctional impulsivity influences actions based on the decision to
think rather than the process of how one chooses to think.

It is in this way that criminal behavior might be explained by dysfirnctional
impulsivity, as it is often used as a summary indicator for the capacity for self-control — a
key. determinant of crime (Farrington, (1998); Gottfredson and Hirschi, (1990)).
Criminals (who get caught) are arguably hasty and their lack of planning results in arrest
and eventually incarceration. The F F CWS includes six items from the original twenty-
three item DDI scale; the items are then averaged to create the impulsivity index. The
alpha for these questions using the F FCWS father sample is 0.84, indicating that this
subset is representative of the full scale. Nevertheless, this construct will only be a valid
instrument if it is uncorrelated with ability and other omitted variables while concurrently
not affecting child outcomes other than through incarceration.

However, dysfunctional impulsivity is a heritable trait and as a result may
influence child outcomes other than through incarceration. Irnpulsivity in humans is
linked to serotonin levels in the brain which is in part genetically determined (Hodges,
(2006)). However, if the heritable component of impulsivity can be directly controlled for

in some way, the case can then be made that dysfunctional impulsivity is a valid

42

instrument or exclusion restriction. I will make the stringent assumption that any
impulsivity the child may have genetically inherited from the father would be evidenced
in symptoms of attention deficit and hyperactivity disorder (ADHD) since they
encompass inattentiveness, hyperactivity as well as impulsivity in children (Winkler,
(2006))”.

There are six symptoms that must persist for at least a six month period for
ADHD to be diagnosed (Winkler, (2006)). The 36-month In-Home Longitudinal Study
aptly covers six key symptoms of ADHD and I will average these to create a measure that
should capture the heritable component of dysfunctional impulsivity. The inclusion of
child’s ADHD symptoms in the model should net out any impulsivity the child would
have inherited from the father, rendering the DDI an exogenous instrument.

There is also another instrument I will consider to ensure identification. Racial
profiling (i.e. the targeting of racial minorities by police) makes minorities more likely to
be arrested than other groups due to the mere fact that they are being watched more.

Racial profiling should therefore be positively correlated with incarceration but not
necessarily correlated with 8.

The FFCWS provides data for a suitable measure of racial profiling. The father is
asked in the first-year and third-year follow-up interviews whether he has ever been
stopped by police but not arrested (non-traffic purposes). I argue that a minority father
who has been stopped by police for non-traffic reasons and not arrested may have been a

target of racial profiling. However, if random non-traffic stops are considered standard

 

‘6 The behavioral measures of aggression and ODD may be affected by dysfunctional impulsivity other
than through incarceration if genetically inherited dysfunctional impulsivity is displayed in other forms
beyond the inattentiveness, hyperactivity and impulsivity captured by ADHD.

43

policing procedure in the father’s city, then this event no longer exemplifies racial
profiling since these stops are now independent of race and ethnicity. Therefore, a more
suitable measure of racial profiling is the average non-traffic stops in each father’s city by
his race or ethnicity”. Mean non-traffic stops for incarcerated fathers are 43% while the
average is 39% for non-incarcerated fathers, illustrating an important difference between
the experiences of incarcerated and non-incarcerated fathers in this regard.

Table 11 presents average non-traffic stops by city and race/ethnicity. The means
indicate that among all fathers in the F FCWS sample, 40% have been stopped by police
but not arrested (non-traffic). However, black fathers consistently experience higher rates
of non-traffic stops than any other racial or ethnic group. In fact, for thirteen of the
twenty cities surveyed, black fathers have higher rates of non-traffic stops than the city
average. Similarly, Hispanics have rates higher than the city average in eleven cities;
white fathers experience higher mean non-traffic stops in only three cities. Figure 2.1
depicts the relationship between non-traffic stops and race/ethnicity. It is clearly evident
that non-traffic stops of black fathers are consistently greater than the city averages as
well as non-traffic stops of other racial/ethnic groups. It is important to note that these
rates of non-traffic stops vary significantly from city to city, ensuring that this proxy for
racial profiling is not representing simple racial or ethnic differences. The statistics
suggest that black fathers in the sample are not only most likely to be incarcerated but are
also most likely to be stopped for non-traffic purposes. As such, the argument can be

made that this proxy for racial profiling helps explain paternal incarceration.

 

27 It is important to note that this proxy potentially under-estimates racial profiling events. If a minority
father is stopped by police for non-traffic reasons (i.e. profiled), then arrested for some non-traffic
violation, he would have answered “no” to this question in the FFCWS. Therefore, this proxy arguably only
captures those fathers who have been profiled but “came out clean”.

44

It is also necessary to isolate the incarceration ex post effect from the absence
effect. A father is classified as absent if at any time he is reported as not living with the
focal child. There is reason to be concerned that father absence is correlated with a
number of other household and family circumstances that may influence child outcomes
(Antecol and Bedard, (2007); Corak, (2001); Craigie, (2008); Lang and Zagorsky,
(2001); Painter and Levine, (2001)). The FFCWS includes a large number of variables
that arguably serve to control adequately for these circumstances, allowing paternal
absence to be treated as an exogenous regressor in the model. Still, the use of an
estimation strategy that treats father absence as endogenous is prudent.

For identification of a model with two endogenous variables, there must be at
least two exogenous instruments included in each first-stage regression. In addition to the
two instruments for endogenous incarceration, I propose as instruments for paternal
absence two indicators of father’s paternal attachment. The measures of paternal
attachment are: (i) the steady involvement of the father’s biological father during his

childhood, Z; and (ii) the existence of another male who served as his father-figure

during childhood, 2... Strong connections to his biological father or a steady male role-
model are expected to decrease the likelihood the father is absent from his own child’s
household. These indicators are assumed to be sequentially exogenous and thus
orthogonal to the error term. The reduced-form equations for father absence and
incarceration ex post are given in (4) and (5) below.

Ai :K0+Klzli+KZZZi +K3 Z3I+K424i +ADHDI7~+XIOD+UI (4)

1Pi=§0+€1 ZII+Gzzzi+Qsz3i+€424i+ADHDIT+Xil+GI (5)

45

OLS estimation of (4) and (5) will yield A. and Ipi which will then be introduced into

equation (1) in place of incarceration, I, and absence, A. This second-stage regression

should identify the effect of paternal incarceration ex post on the child outcome, Y.

2.5. Results

The summary statistics presented in section 2.3 imply that children of incarcerated fathers
are at a significant disadvantage as evidenced by their adverse familial circumstances.
However, these results do not clarify whether the outcomes associated with this situation
are largely explained by paternal incarceration itself or the environment to which the
child is exposed.

Table 12 shows estimates of the marginal impact of patemal incarceration using
equation (3). For each child outcome, the regression includes an exhaustive set of
covariates to mitigate unobserved heterogeneity (Craigie, (2008); Antecol and Bedard,
(2007); Lang and Zagorsky, (2001)).The coefficients measuring the impact of a father’s
incarceration ex post are small in magnitude and statistically insignificant for all the child
outcome measures. A father’s absence on the other hand, significantly increases
aggression and ODD indices by 0.03 and 0.05 respectively. Table 13 also illustrates that
the estimated marginal effect of paternal incarceration ex post by his racial or ethnic
group is not statistically different from zero.

These results bolster the perspectives presented in Section 2.2 which suggest that
the effect of incarceration is indeed ambiguous and may not be statistically different from
zero. While the differencing strategy isolates the marginal impact of paternal
incarceration by controlling for bias from unobserved heterogeneity, the estimator still

does not account for bias from measurement error. Moreover, if juvenile offenses and

46

incarceration ex ante, Ia, does not effectively capture father’s “criminal type”, the

estimated marginal impact of incarceration ex post will be imprecise. An arguably more
unbiased estimator would be the IV estimator, as it attempts to correct biases from both
unobserved heterogeneity and measurement error.

OLS and IV regression models are exploited to assess causal arguments on
paternal incarceration and early child development. In addition to incarceration ex post,
OLS regressions in Table 14 control for exogenous variables that influence child
outcomes. These estimated effects of incarceration ex post, like those presented in Table
12, are small in magnitude and are not statistically different from zero, excepting
aggression. Incarceration ex post increases the aggression index by 0.06 and this
coefficient is statistically significant at the 5% level. Similarly, father’s absence increases
both aggression and ODD indices by about 0.05 and 0.06 respectively and these estimates
are statistically significant at the 1% level.

However, after addressing the econometric issues of unobserved heterogeneity
and measurement error using IV estimation, incarceration ex post has a much larger and
statistically significant effect. The IV estimates in Table 14 show that paternal
incarceration ex post exacerbates both aggression and ODD symptoms and lower
cognitive scores of the focal child. The IV estimates in columns (3), (6) and (9) indicate
that cognitive scores fall by approximately 24 points while the aggression and ODD
indices rise by 0.65 and 1.08 respectively and these estimates are all statistically different
from zero. Conversely, the coefficients on father absence are all small and statistically
insignificant in these regressions. The results therefore indicate that incarceration ex post

heightens aggression and ODD symptoms of the child and deteriorates early cognitive

47

development. The magnitudes of these point estimates, when compared to the respective
standard deviations, are quite substantial. In fact, they are all larger than their respective
standard deviations (see Table 9) and consequently, should be treated with caution. IV
estimates that are this large may insinuate a weak instrument problem.

Although these IV regressions control for paternal absence, they do not
instrument for this potentially endogenous variable. The Hausman test for endogeneity
indicates that both paternal incarceration and absence are endogenous in the model. The
Hausman F-statistics provide evidence of endogeneity at the 1% level and as a
consequence, it would be better to instrument for both incarceration and absence in the
IV model (assuming the instruments are valid).

To effectively isolate the effect of paternal incarceration from that of paternal
absence, instrtunents for paternal absence must be included in the first-stage regression.
Columns (2), (5) and (8) present IV estimates for which both incarceration and absence
are instrumented. Once paternal absence is identified in the IV model, the detrimental
impact of a father’s incarceration during the young child’s life is no longer statistically
different from zero and thus bolsters the results fiom the differencing strategy presented
in Table 12. The effect of paternal absence is also not statistically different from zero.
The first-stage F-Statistics for incarceration ex post and absence are 18.75 and 11.44
respectively and they both exceed 10, the simple rule-of-thumb recommended in Staiger
and Stock (1997) to avert the potential bias of weak instruments. From the methods
employed, we can therefore conclude that the effect of a father’s incarceration on early
child development is not statistically different from the effect which ensues from his

subsequent absence.

48

2.6. Summary

This study was unable to reject the hypothesis that the effect of paternal incarceration on
early child outcomes is no different from that of his generic absence. By exploiting
instruments for these endogenous regressors, the results Show the incarceration ex post
effect is not statistically different from zero for measures of cognitive ability, aggression
and ODD of pre-school aged children. Notwithstanding, if we assume generic paternal
absence is exogenous, paternal incarceration reduces child test scores and amplifies their
behavioral problems. Incarceration ex post engenders a 24-point disadvantage for the
affected children relative to those who have never experienced paternal incarceration.

Similarly, aggression and ODD indices rise by 0.65 and 1.08 respectively as a
result of a father’s incarceration. These findings are similar to those of Wildeman (2008)
since he finds that paternal incarceration increases aggressive behavior in boys by about
0.50 standard deviations and between 0.18 and 0.30 standard deviations in girls.

The importance of attending to children of incarcerated parents during the early
developmental years is certainly reinforced here. An important policy recommendation
would be for schools to be notified of the father’s incarceration and the possible effects
that may ensue. In particular, defiant, aggressive and generally disruptive behaviors by
the child can be directly attributed to the father’s incarceration and should be treated as
such by the institution. The implementation of programs that support children of
incarcerated fathers may also help ensure that these deviant and criminogenic tendencies
are not proliferated as the child enters adolescence and even adulthood (Robins, ( 1978);

Sampson and Laub, (1992); Wildeman, (2008)).

49

However, if paternal absence is indeed endogenous as the Hausman test indicates,
the results from the IV regressions that instrument for both incarceration and father
absence are most plausible. Even though the results indicate that there is no statistical
difference between the effect of paternal incarceration and that of paternal absence, they
do not render the study of paternal incarceration irrelevant, as the confidence intervals are
large enough to contain effects of consequential size. For pre-school aged children, the
negative stigma and extemalities of the father’s incarceration may not yet be clearly
understood. These children are possibly unable to discern the difference between types of
paternal absence as well as their implications. At this stage — a father absent is just a
father absent. Future research would therefore do well to examine if older children or

adolescents experience statistically different outcomes due to paternal incarceration.

50

Chapter 3.
An Analysis of the Causes and Correlates
of Family Dissolution

3.1. Introduction

Many prior studies have focused on the consequences of family dissolution,
particularly on child and parental outcomes (Corak, (2001); Lang and Zagorsky, (2001)).
However, also of importance are the factors that cause dissolution in the first place,
especially when children are involved. This study will investigate the time-invariant and
time-varying factors that influence the probability of dissolution among couples with
children and explore whether the hazard of family dissolution is characterized by duration
dependence.

Non-marital cohabitation in the United States has been on the rise and has become
a common phenomenon in recent decades. In fact, almost 5 million households were
headed by cohabiting couples in the year 2000 (Lichter et al., (2006)). Moreover, 41% of
these households had children under 18 living in them”. At the same time, marriage has
been on the decline and divorce has been increasing in recent years. These trends imply
that marriage and family in the United States is becoming in some sense de-

institutionalized (Lichter et al. (2006); Cherlin, (2004); Nock, (2002)). The purpose of

 

28 US. Census Bureau, Families and Living Arrangements, (2000)

51

this study is to therefore observe the factors associated with the risk of union dissolution
— whether this union is bound through marriage or cohabitation.

Previous works have shown that factors such as age, cohabitation, pre-marital
cohabitation, pre—marital conception, out-of—wedlock child-bearing, religious preferences,
education and family background are strong factors affecting the probability a union will
dissolve (Balakrishnan et al. (1987); Menken et al. (1981); Teachman, (1982)).Of these
factors, this study finds that only cohabitation, race, religion and education are strong
predictors of union breakdown. Recent studies have also explored the issue of duration
dependence in unions, finding in general that the longer the union remains intact, the
lower the probability of dissolution (Lichter et al. (2006); Svarer, (2004)). This study
provides strong evidence that this observed duration dependence in unions is due to
unobserved heterogeneity rather than true state dependence. Once relationship quality is
controlled for, and in particular marital status of the couple, there is no statistically
significant relationship between the duration of the union and the hazard of dissolution.

The paper is organized as follows. Section 3.2 provides a brief overview of
previous works that examine the factors influencing the risk of dissolution. Section 3.3
discusses the data used for this analysis as well as the variables and their summary
statistics. Section 3.4 gives the model specification. Section 3.5 discusses in depth the
linear probability and logit estimates and Section 3.6 provides a brief summary of the

findings.
3.2. Literature Review

Previous studies on the factors associated with the stability or dissolution of families have

mainly focused on unions formed through marriage (Balakrishnan et al. (1987); Svarer,

52

(2004) and Teachman, (1982))”. According to this literature, the main factors that
significantly contribute to dissolution include: duration of the union, age at the time of
marriage, difference between the ages of spouses, premarital conception and birth,
cohabitation before marriage, religion, religiosity, employment, educational attainment,
family background and race (Balakrishnan et al., (1987); Larson and Holman, (1994);
O’Connell and Rogers, (1984); Svarer, (2004); Teachman, (1982) and Webster et al.,
( 1995)).

Some studies cite evidence of negative duration dependence on the hazard of
union dissolution, indicating that unions that have lasted a longer period of time have a
lower probability of subsequent dissolution (Lichter et al., (2006) and Svarer, (2004)).
This may be explained by the fact that the couple has a longer period to determine if the
match is a good one and consequently, the longer the union stays intact, the more likely
the union is to be a good match (Svarer, (2004)). An alternative explanation is that over
time, couples accumulate maniage-Specific capital such as assets and children, which
enhance the longevity of the union (Becker et al., (1977) and Svarer, (2004)). Note that
the first explanation of observed negative duration dependence in the hazard of union
dissolution implies that it is due to unobserved heterogeneity in union quality: unions that
are better matches for whatever reason will tend to last longer. The second explanation is
an appeal to a form of state dependence — holding constant the quality of the match, the
longer any union manages to stay intact, the lower will be its probability of dissolving in

the future. This paper will attempt to differentiate between these two explanations of

 

29 One study by Lichter et al. (2006), examines the transitions of cohabiting unions among poor women
into marriage or dissolution. However, they do not discuss per se the factors that lead to either of these
transitions.

53

duration dependence in unions by controlling for a large number of proxies for
relationship quality.

The risk of marital dissolution also tends to be negatively correlated with age at
the time of marriage. This result is reinforced by the theory that younger couples are less
responsible and experienced in dealing with the crucial issues that may affect the stability
of the marriage (Balakrishnan et al. (1987); Menken et al. (1981); Teachman, (1982)).
Menken et al. (1982) provide evidence that marriage before the age of twenty is more
likely to end in divorce relative to first marriages occurring at later years. In addition to
the age of marriage as a determinant of marital dissolution, the age difference between
spouses is expected to be positively correlated with the risk of marital dissolution due to
its effect on relations between spouses, marital satisfaction and even fertility
(Balakrishnan et al., (1987); Casterline et al., (1986)).

Premarital conception and birth are also expected to heighten the risk of family
dissolution. This can be attributed to the immediate effect on the courtship process by
reducing the time in which partners have to determine the quality of the match (Grover et
al. (1985); Larson and Holman, (1994)). As a result, the couple is potentially forced into
a more speedy union. Those who marry after pre-marital conception and birth are
therefore significantly more likely to experience marital instability (Balakrishnan et al.,
(1987); Menken et al., (1982); O’Connell and Rogers, (1984) and Teachman, (1982)).
Balakrishnan et al. (1987) found that women with pre-marital births were twice as likely
to experience marital instability in the first fifteen years of marriage as women who had
post-marital births. Similarly, those who had pre-marital conceptions had about a 30%

chance of separation in the first fifteen years of marriage relative to an 18% chance of

54

separation for women with post-marital births. It is important to note, however, that
marriage after pre-marital conception is on the decline. From the 19508 to early 19703,
about 50% of women who had pre—marital conceptions married prior to their children’s
birth. By the 1980’s, this figure declined to only 32% (O’Connell and Rogers, ( 1984)).

By contrast, cohabitation and cohabitation before marriage have both been on the
rise. Out-of-wedlock births assigned to cohabiting couples increased from 33% to 50%
for whites from the 19803 to the early 19905 (Sigle-Rushton and McLanahan, (2002);
Bumpass and Lu, (2000)). There are conflicting findings, however, as to how
cohabitation status before marriage influences the subsequent risk of dissolution.
Balakrishnan et al. found in their study that women who engaged in pre-marital
cohabitation had a 50% higher risk of dissolution relative to women who did not cohabit
before marriage. By contrast, Svarer (2004) found that couples in the Danish marriage
market who engaged in pre-marital cohabitation had a lower risk of divorce.

Family history is another important factor affecting marital and relationship
stability. Marital or relationship quality serves as the mediating effect between family
history and marital stability. This suggests that marital instability may be directly linked
to low marital quality, particularly among those who have experienced a family history of
marital dissolution. However, not only does family history influence marital quality,
which subsequently affects stability, but also, it affects how marital quality affects marital
stability (Webster et al., (1995)). Studies have shown that being exposed to a single-
parent family structure during childhood is associated with marital instability during
adulthood (Glenn and Kramer, (1987)); Larson and Holman, (1994); McLanahan and

Bumpass, (1988)). Therefore, experiencing parental divorce and a poor quality marriage

55

during childhood could arguably engender an attitude more favorable to dissolution in the
future, especially in the event of marital or relationship discordance (Greenburg and Nay,
(1982); Larson and Holman, (1994)).

However, in addition to the early childhood experience of parental divorce or
family dissolution, I argue that a woman’s relationship with her father or father figure
may influence her future relationship with men. I hypothesize that a strong involvement
of a father during childhood will increase the likelihood that a woman will identify a
positive match and thus decrease the risk of dissolution. A positive paternal influence is
expected to not only increase the spousal quality of the mother herself, but also increase
the likelihood that she will be able to identify high quality males as well. With positive
assortative matching at work, a more stable union can be created.

The data used in this study include detailed information on the incarceration
histories of male spouses, thereby allowing investigation of the impact of incarceration
on the stability of a union. Incarceration interrupts earnings and employment, wage
growth and human capital accumulation — all factors viewed to be important assets of a
male partner. AS a result, incarceration is expected to significantly increase the
probability of divorce and dissolution among incarcerated men, and this expectation has
been confirmed in the one previous study that has examined the topic (Western, (2006)).

Another factor that is believed to lower the risk of divorce is religiosity. Frequent
church attendance has been shown to lower divorce rates in studies by Menken et al.
(1981) and Teachman (1982). Balakrishnan et al. (1987) also reinforced these studies,
finding that women who rarely or never attend church were about 2.5 times more likely

to have their marriage terminated before 25 years than women who went to church at

56

least once a week. Other factors shown to be linked to the risk of marital dissolution

include educational attainment, employment, race and ethnicity.

3.3. Data

The Fragile Families and Child Wellbeing Study (FFCWS) follows a cohort of
approximately 5,000 children, born from 1998 to 2000. Its goal was to capture the
conditions, capabilities and nature of the relationship of parents of these children, and
particularly un-wed parents, during the nascent stages of the focal child’s life
(Reichmann, (2001))”. As a result, rich, detailed and new data are supplied on union
duration and background, demographic and relationship characteristics of both parents.
Follow-up interviews are conducted at one, three and five years thereafter, and so we
have information on the duration of the parents’ marital or cohabitational union prior to
the child’s birth or ex ante and up to the first five years of the child’s life.

Because the focus of the study is the hazard of union dissolution, the sample is
first restricted to only those families that are intact at the time of the focal child’s birth, in
that they report that they are either married or cohabiting. Unlike previous studies, I do
not limit the analysis sample to those couples who are married at the time of the child’s
birth: one purpose of FFCWS is to observe un-wed parents and this is an apt dataset to
look at non-traditional, yet stable family structures. The increasing number of couples
who have chosen to cohabit instead of marry is in fact relevant to the literature on union
dissolution and as such, they are included in the analysis.

Due to the richness of the data, the model will also controls extensively for

background, demographic and relationship characteristics. The response rate for all

 

30 The data are discussed in more detail in chapters 1 and 2 of this dissertation.

57

interviews subsequent to the baseline is over 85%; families for which mothers did not
complete one of the interviews are excluded from the sample. This leaves 2,658 families
in the sample.

A spell is defined as the length of time between two interviews. A spell is only
usable if the biological mother and the biological father of the focal child were either
married or cohabitating at the first interview of the spell. If, at the second interview of the
spell, the mother reports that the couple is no longer married or living together, the
relationship is coded as having dissolved. Since information is not provided as to the
exact date of dissolution, it is assumed that the family was intact up until the day of the
first interview of the spell. Because there are four interviews — a baseline, one-year,
three-year and five-year follow-up interviews — a family can contribute a maximum of
three spells to the sample. However, if a family is observed to have dissolved at the first-
year (third-year) follow-up interview, it is dropped from the sample after contributing
only one (two) spell(s). On average, the duration between interviews is about 20 months
but does vary among the families in the analysis sample. To deal with this problem, I will
control for the interval length or the months between interviews (Rogowski and Karoly,
(2000)).

3.3.1. Summary Statistics and Description of Variables

Table 15 presents the summary statistics for the spells in the analysis sample. Only 16%
of the couples in the analysis sample dissolved by the end of each spell, indicating a
relatively low level of dissolution among couples in the sample within the first five years
of the focal child’s life. One question of interest is duration dependence, i.e. the

relationship between the time the parents have been living together and the probability of

58

dissolution. For that reason, I constructed a variable measuring the length of time the
parents were living together at the time of the interview that begins each spell. Table 15
indicates that the average duration of unions was approximately 5 years at the outset of
each spell. With the duration of unions ranging from 0 to ahnost 28 years, I dissected this
continuous variable into one, two or three year intervals. According to Table 15, only
about 4% of couples had been together less than a year at the beginning of the spell,
while over half of couples were together between one and five years. A little over 25% of
unions had spanned five to ten years and 12% of unions had lasted over 10 years.

According to the literature, demographic characteristics of parents influence the
survival rate of their union. As such, I have included in the model variables measuring
race and ethnicity, age, age difference and education. Fathers are on average
approximately 2.5 years older than mothers in the analysis sample and the mean of
mother’s age at the baseline is 26 years old. The racial composition of mothers in the
analysis sample is also very evenly split among blacks, whites and Hispanics. There are
more mothers who are high school dropouts and high school graduates than those with at
least some college education. Relationship quality and characteristics influence the
probability of dissolution as well, and included in the model are the mother’s relationship
with her father or father figure during her childhood, religious preference and religiosity
as well as both parents’ Dickman’s Dysfunctional Irnpulsivity (DDI) scale.

In the model, the involvement of the mother’s father during her childhood is
included and the summary statistics indicate that most mothers had fathers who were at

least somewhat involved in their lives during childhood. Most mothers are also of the

59

Catholic or Protestant faith but attend church only several times for the year (see
Appendix C for scale).

Scott Dickman defined dysfunctional impulsivity as “the tendency to act with less
forethought than others of equal ability” and the Dickman’s Dysfunctional Impulsivity
(DDI) scale is frequently used as a summary indicator for self-control (Dickman (1990);
Farrington, (1998); Gottfredson and Hirschi, (1990)). Self-control could in several ways
affect the risk of dissolution, particularly with respect to how both partners choose to
handle problems that may arise in their relationship. A sub-scale of the DDI full-scale of
26 questions is provided in the FFCWS and the alpha of 0.84 indicates that this sub-scale
is highly correlative with the full-scale. The scale ranges from 1 to 4 with 1 indicating the
highest level of dysfirnctional impulsivity, the questions are averaged to create a DDI
index (see Appendix B). Both parents scored on average 3 on this scale, indicating little
dysfunctional impulsivity in general.

Child characteristics may also play a role in the stability of a union. It has been
shown that if the child is a boy, family dissolution is less likely (Bedard and Deschenes,
(2004)). Similarly, the birth order of a child is correlated with the stability of a union and
26% of the children in the analysis sample are first-boms for both parents. Child-bearing
outside of wedlock is associated with marital dissolution as well, and 58% of children at
the baseline were borne out of wedlock. In addition, 2% of couples had marriages within
six months prior to the focal child’s birth. This confirms the statistics provided by
O’Connell and Rogers (1984) that these “shot-gun” marriages are in fact declining.

In addition to controlling for time-invariant characteristics that might affect the

probability of dissolution, the model also controls for characteristics that may vary over

60

the observation period. One of these is marital status. Each couple begins a spell in one of
three states: cohabiting, married after an initial period of cohabitation, and married
without cohabitation. At the baseline, about 45% of couples are in the first category; 27%
are in the second, and about 28% in the third. As time progresses, it is possible for
couples to move from cohabiting at the baseline to the pre-marital cohabitation category
in subsequent waves. This happens to 188 couples or 3% of the analysis sample.
Potentially endogenous variables such as residential instability, change in
incarceration status and change in household income are included in the model as lags,
that is, they are measured based on events occurring at the beginning of the previous
spell. This eliminates the potential endogeneity caused when, for example, relationship
dissolution leads to a fall in income or a residential relocation; but this means that spells
beginning with the baseline interview cannot be used in analyses that include these
variables. In the subset of the sample for which these variables can be defined, 37% of
couples have changed residence since the previous interview and only 2% of fathers
changed their incarceration status. The mean household income is about $45,000 and the

mean change in household income between interviews is negligible at ahnost $62.
3.4. Econometric Specification

Consider the linear probability model specification:
Dit=T'iIY+X'itB+8it (1)
where D represents the binary indicator of a dissolved family at the end of each spell. T

is the duration of the union at the time of the interview that begins each spell. T is

divided into intervals ranging from 0 to 12-plus years and these variables are included to

61

test for duration dependence of the length of a union. X is the vector of time-invariant

variables expected to influence family dissolution.

In addition to duration dependence and time-invariant heterogeneity, time-varying
factors also influence the probability of union survival. Cohabitation, pre-marital
cohabitation, child-birth shocks and changes in household size have all been allowed to
vary by spell. A couple is classified as cohabiting in each spell if the mother reports that
both are living together but not married. Similarly, pre-marital cohabitation is recorded as
such if a couple cohabited ex ante or in a spell prior to getting married. A child-birth
shock occurs at the beginning of each spell in which the couple states they have a new-
born or have adopted a child. The number of children and adults in the household is

recorded at the beginning of each spell. These variables are given in the vector Z in
equation (2) below:

DitzT'it'Y'l'X'itB'l'Z'itll+Uit (2)
Some time-varying covariates that potentially influence union survival such as shocks to
family income, are also themselves potentially influenced by union survival. To avoid
this endogeneity problem, a vector of lagged variables A H such as the lagged change in

incarceration status, lagged change in household income and lagged residential moves are

included in (3) below.
DitzT'itY+X'itB+Z'irn+AH'it-IP+Hit (3)

I estimate these models using OLS and Logit specifications.

62

3.5. Results

The linear probability model given in equation (1) is presented in Table 16. Column (1)
presents results from the naive model with no other control variables except the variables
of interest. A union intact for 1 to 5 years does not statistically differ from a union intact
for less than one year, in its probability of dissolving by the next interview. However,
being together for 5 to 10 years significantly decreases the probability of dissolution by
about 14%. In addition, remaining together for over 10 years decreases the likelihood of
separation by about 19% and these estimates are all statistically significant at the 1%
level. Figure 3.1 illustrates the hazard of union dissolution.

As discussed earlier, this observed duration dependence may be due to
heterogeneity in underlying relationship quality. If so, controlling for some of this
heterogeneity should lower the observed duration dependence. Column (2) controls for
the time-invariant variables (except out-of-wedlock childbearing and marriage within 6
months of the focal child’s birth) listed in Table 15. The results indicate that there is no
statistical difference in the effect of being together for up to five years on the probability
of union disruption. However, a union duration over five years positively influences the
probability of a stable union. A union lasting from five to seven years significantly
decreases the probability that a couple has separated at the end of a spell by 8%.
Similarly, a union duration over ten years significantly decreases the risk of dissolution
by 8 — 10%. In summary therefore, this model exhibits duration dependence in that the
longer a couple stays together over the five-year mark, the lower the probability of a
failed union. It also matches the findings reported in studies concerning the vulnerability

of the union to dissolution during the first five years (Lichter et al. (2006) and Smock

63

(2000)). For cohabiting unions especially, this five-year period is where we see couples
dissolve or transition to marriage (Lichter et al., (2006)).

Several time-invariant factors included in this model increase the probability of
union failure. Compared to whites, a mother experiences about a 9% increased risk of
dissolution if she is black and this estimate is statistically significant at the 1% level.
Similarly, being a high school dropout significantly decreases the likelihood of survival
by almost 5% relative to a high school graduate. If a mother reports no religious
affiliation or is Baptist, the likelihood her union will fail rises by approximately 5%.
There is, however, no significant relationship between frequency of church attendance
and the risk of union dissolution.

College education and not being dysfunctional impulsive both significantly
decrease the likelihood of dissolution by 4%. The older a mother is and the larger the age
difference is between the couple, the lower the union failure rate, but by less than 1% per
year. In addition, having a boy significantly decreases the failure rate by 3%.

When variables measuring marital status of the couple at the beginning of the
spell are included in the model (columns (3) and (4) of Table 16), the observed duration
dependence is no longer statistically significant, casting doubt on hypotheses that imply
that time spent together per se will affect the hazard of union dissolution.“ The column
(3) results indicate that other things equal, a cohabiting couple has an 8 — 9% higher risk
of separating than a married couple and this also is statistically significant at the 1%

level.

 

3' The excluded category for the duration intervals is 0 to 3 years in column (4). Since lagged variables are
included in this model, only 18 couples who have been together for less than one year are included in this
regression. Subsequently, using the 0 — 1 year interval as the sole excluded category will induce problems
similar to a dummy variable trap.

64

The column (4) estimates investigate the impact of certain relationship shocks to
the probability of union dissolution, including shocks to place of residence, incarceration
status and household income. The most striking result from this specification is the
magnitude of the coefficient on new incarceration lagged. A father’s incarceration in the
previous wave will increase the likelihood of union dissolution by about 51% and this
estimate is statistically significant at the 1% level. The lagged change in household
income also decreases the union survival rate but by less than 1% for every $10,000
positive shock to household income.

Logit estimates are presented in Table 19. This specification indicates the same
factors significantly affect union disruption as in the linear probability model. However,
in column (3), it is shown that couples together for 10 to 12 years have about 20% lower
risk of union failure than couples together for less than a year and this estimate is
statistically significant at the 10%.

3.5.1. Results for Subgroups

Also interesting is how the results change for various subgroups within the
analysis sample. How do these results differ for low-educated mothers, black mothers,
couples who are cohabiting or married at the baseline? These results are given in Tables
17 and 18. Estimates of the models reported in columns (3) and (4) of Table 16 are now
reported for each subgroup.

Column (1) of Table 17 indicates that in general, the model does not exhibit
duration dependence of union dissolution for low educated mothers after the fifth-year of
the union. However, a slightly counter-intuitive result shown in column (2) is that

couples together three to five years have a 7% higher probability of separation relative to

65

those couples with less experience. This result may be insinuating that the three to five
year period is inherently fragile for low-educated women.

In addition to the implications these samples have for duration dependence, there
are also implications for heterogeneity in the model. Some characteristics shown to be
statistically similar to zero in the full analysis sample are now revealed to be statistically
different from zero for certain sub-groups.

In Table 17 column (1), for low educated mothers, each year her spouse is older
than her engenders about a 1% decrease in the union failure rate. Jewish mothers also
experience a 9% lower risk of dissolution relative to Catholic mothers; by contrast,
mothers with no religious affiliation are 8% more likely to have their union dissolve
compared to Catholic mothers. When lagged endogenous variables are included in the
model in column (2), church attendance improves the probability of union survival by
2%. In column (3) and (4), it is apparent that black mothers have a 12 — 15% higher risk
of disruption when they cohabit. Column (4) of Table 17 shows that for black mothers,
more church attendance decreases the probability of union failure by 3%.

Table 18 also shows results separately for spells involving couples who were
cohabiting at the baseline versus those who were married at the baseline. For these
subgroups, there is no evidence of duration dependence. Duration of the union does not
significantly influence union dissolution for either cohabiting or married couples, once
measures of couple heterogeneity are controlled for.

Columns (1) and (2) show that among spells that involved couples who were
cohabiting at the time of the baseline interview, those that began with the couple being

married are 8% more likely to remain intact than those that began with the couple

66

unmarried. It is also appears that religion plays a role in the risk of union dissolution for
cohabiting couples. For cohabiting couples at the baseline, having no religious affiliation
or being Baptist both raise the probability of union dissolution relative to Catholics.
Irreligiosity and the Baptist faith increase the risk of dissolution by 6% and 7%
respectively compared to Catholicism; when the time-varying lagged factors are included
in the model, the Baptists experience a 12% higher risk of union failure compared to
Catholics. For cohabiting Jewish mothers however, the probability their union will fail is
19% lower than for Catholic mothers. In addition, attending church reduces the
cohabiting union’s likelihood of failure by 1 — 2%. When we compare unions involving
couples married at the baseline, there is no statistical evidence of religion or religiosity
being a vital influence on the risk of dissolution. From these results therefore, religion is
more important to the stability of cohabiting unions relative to marital unions. Column
(4) also reveals that biological father involvement during the mother’s childhood

decreases the risk of dissolution by 5% among married couples.
3.6. Summary

This study seeks to examine the factors, both time-invariant and time-varying, which
influence the probability of union dissolution. In contrast to previous studies, I do not
restrict the analysis to only those unions formed through marriage, but include those
unions formed through cohabitation as well. The inclusion of cohabiting unions in the
study is particularly relevant in an age where some may argue that marriage and the
family are becoming de-institutionalized, as cohabitation becomes more commonplace

(Lichter et al. (2006); Cherlin, (2004); Nock, (2002)).

67

Using the linear probability model and logit specifications, the study finds that
once variables capturing marital status are controlled for, the model no longer exhibits
duration dependence of union dissolution. This sheds a different light on the findings of
Svarer (2004) and Lichter et al. (2006) showing that the longer the union survives, the
lower the probability of dissolution. This result may be due to marital status variables
essentially acting as proxies for unobserved characteristics measuring the couple’s level
of commitment or match quality; however, it casts doubt on explanations of union
stability that cite the importance of the accumulation of union-specific capital to the
persistence of a union (Becker et al., (1977) and Svarer, (2004)).

Nevertheless, there are other crucial factors that do significantly affect a union’s
rate of survival. The model reveals that being black, a high school dropout and
dysfunctional impulsive decrease the likelihood of a stable union. Similarly, having no
religious affiliation or being Baptist positively contributes to union disruption relative to
being Catholic. Positive age difference between partners (i.e. where the man is older) is
not shown to increase the risk of dissolution, thus opposing the findings of Balakrishnan
et al. (1987) and Casterline (1986). Mother’s age and change in household income
significantly lower the union dissolution rate.

The study also does not confirm the findings of Svarer (2004) that cohabiting
couples face a lower risk of dissolution than married couples. In addition, unlike previous
works, the model provides no evidence that out-of-wedlock childbearing, pro-marital
conception or pre-marital cohabitation raises the likelihood of divorce among married
couples (Balakrishnan et al., (1987); Menken et al., (1982); O’Connell and Rogers,

(1984) and Teachman, (1982)).

68

Another striking result from the model is that incarcerated men have over a 50%
higher risk of dissolution compared to non-incarcerated men; this result buttresses the
theory presented in Western (2006) that incarcerated men are indeed less marriageable.
For cohabiting couples, religion seems to be a vital influence in union breakdown relative
to married couples. Unlike studies by Menken et al. (1981), Teachman (1982) and
Balakrishnan et al. (1987), the study does not find that religion or religiosity reduces the
risk of dissolution for married couples. These factors only appear to be important for
unions formed through cohabitation. New births, household size and residential

instability are not shown to significantly influence the survival or failure of a union.

69

 

 

 

 

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Obs. Mean Std. Deviation Min --- Max

(1) (2) (3) (4) (5)
Dependent Outcomes
PPVT-R 1541 86.374 (17.028) 40 137
Aggression 1986 0.579 (0.340) 0 1.923
ODD Symptoms 1999 0.631 (0.429) 0 2
Variables of Interest
Incarcerated Ex Post 2549 0.097 (0.296) 0 1
Ever-Incarcerated 2549 0.377 (0.485) 0 1
Incarcerated Ex Ante 2549 0.076 (0.265) 0 1
Father Absent 2549 0.434 (0.496) 0 1
Exogenous Variables
Male 2549 0.520 (0.500) 0 1
Birth Order 2543 2.092 (1.273) 1 13
Mother's Age 2549 28.351 (6.128) 17 48
Father's Age 2547 30.768 (7.045) 18 66
Mother Black 2549 0.466 (0.499) 0 1
Mother Hispanic 2549 0.235 (0.424) 0 1
Other 2549 0.185 (0.388) 0 1
Father Black 2549 0.485 (0.500) 0 1
Father Hispanic 2549 0.240 (0.427) 0 1
Other 2549 0.275 (0.447) 0 1
Mother Interviewed in Spanish 2549 0.073 (0.261) 0 1
ADHD Symptoms 2549 0.523 (0.574) 0 2
ADHD Symptoms (Missing) 2549 0.424 (0.494) 0 1
Mother was born in US. 2549 0.869 (0.337) 0 1
Father was born in US. 2549 0.804 (0.397) 0 1
Other Independent Variables
Mother < High School Degree 2549 0.255 (0.436) 0 1
Mother has High School Degree 2549 0.313 (0.464) 0 1
Mother < College Degree 2549 0.233 (0.423) 0 1
Mother has at least College Degree 2549 0.136 (0.343) 0 1
Father < High School Degree 2549 0.229 (0.420) 0 1
Father has High School Degree 2549 0.348 (0.476) 0 1
Father < College Degree 2549 0.184 (0.387) 0 1
Father has at least Coll. Degree 2549 0.123 (0.328) 0 1
Household Income per Person (103) 2549 7.85 (13.57) 0 333.33
Household Income per Person (Missing) 2549 0.072 (0.258) 0 1
Father Smokes 2549 0.426 (0.495) 0 1
Father Smokes (Missing) 2549 0.069 (0.254) 0 1
Father Drinks 2549 0.696 (0.460) 0 1

86

Table 9 (cont’d)

 

Father Drinks (Missing) 2549 0.169 (0.375) 0 1
Mother Smokes 2548 0.261 (0.439) 0 1
Mother Drinks 2548 0.344 (0.475) 0 1
Mother has Mental Problems 2549 0.049 (0.215) 0 1
Father has Mental Problems 2549 0.017 (0.130) 0 1
Father Figure Present 2549 0.109 (0.312) 0 1
Number of Residential Moves 2547 1.192 (1.310) 0 11
Child was Breastfed 2549 0.569 (0.495) 0 1
Mother's WAIS—R Score 2543 7.011 (2.572) 0 15
Father's WAIS-R Score 2524 6.664 (2.661) 0 15
Paternal Importance 2530 1.089 (0.158) 1 3
Either Parent Reports Aggravation 2549 0.217 (0.412) 0 1
Religiosity Measure 2549 4.229 (1.564) 0 7
Child will not have Father's Last Name 2549 0.104 (0.305) 0 1
Father's Name is not on Birth Certificate 2549 0.061 (0.239) 0 1
Father did not visit Hospital at Child's Birth 2549 0.099 (0.299) 0 1
Mother considered Abortion 2539 0.249 (0.432) '0 1
Father suggested Abortion 2538 0.080 (0.271) 0 1
Time Mother loiew Father prior to Pregnancy 2549 5.091 (4.791) 0 36
Instruments

Father's Impulsivity 2548 3.019 (0.663) 1 4
Average Non-Traffic Stops 2549 0.406 (0.092) 0.125 0.8
Father's Biological Father Involved 2549 0.312 (0.464) 0 1
Father had Father-Figure 2549 0.668 (0.471) 0 1
Data: FFCWS

87

Table 10. Summgy Statistics by Incarceration Histog .

 

 

 

 

 

 

 

 

 

Ever-Incarcerated Never Incarcerated

Obs. Mean SD Obs. Mean SD
Dependent Outcomes
PPVT-R 677 83.780 (16.084) 864 88.406 (17.474)
Aggression 788 0.639 (0.368) 1198 0.539 (0.314)
ODD Symptoms 796 0.678 (0.454) 1203 0.599 (0.409)
Variables of Interest
Father Absent 960 0.646 (0.479) 1589 0.305 (0.461)
Exogenous Variables
Male 960 0.501 (0.500) 15 89 0.532 (0.499)
Birth Order 956 2.259 (1.434) 1587 1.991 (1.154)
Mother's Age 960 26.316 (5.276) 1589 29.581 (6.280)
Father's Age 959 29.016 (6.384) 1588 31.826 (7.213)
Mother Black 960 0.581 (0.494) 1589 0.396 (0.489)
Mother Hispanic 960 0.204 (0.403) 1589 0.253 (0.435)
Other 960 0.143 (0.350) 1589 0.210 (0.408)
Father Black 960 0.605 (0.489) 1589 0.412 (0.492)
Father Hispanic 960 0.218 (0.413) 1589 0.254 (0.435)
Other 960 0.177 (0.382) 1589 0.335 (0.472)
Mother Interviewed in Spanish 960 0.039 (0.193) 1589 0.094 (0.292)
ADHD Symptoms 960 0.499 (0.565) 1589 0.538 (0.579)
ADHD Symptoms (Missing) 960 0.446 (0.497) 1589 0.410 (0.492)
Mother was born in U.S. 960 0.941 (0.236) 1589 0.826 (0.379)
Father was born in U.S. 960 0.864 (0.343) 1589 0.768 (0.422)
Other Independent Vflbles
Mother< High School Degree 960 0.359 (0.480) 1589 0.193 (0.394)
Mother has High School Degree 960 0.370 (0.483) 1589 0.278 (0.448)
Mother< College Degree 960 0.182 (0.386) 1589 0.263 (0.440)
Mother has at least College Degree 960 0.022 (0.146) 1589 0.205 (0.404)
Father< High School Degree 960 0.334 (0.472) 1589 0.165 (0.371)
Father has High School Degree 960 0.406 (0.491) 1589 0.313 (0.464)
Father< College Degree 960 0.116 (0.320) 1589 0.225 (0.417)
Father has at least College Degree 960 0.009 (0.096) 1589 0.191 (0.393)
Household Income per Person (103) 960 4.38 (6.15) 1589 9.95 (16.16)
Household Income/Person (Missing) 960 0.096 (0.295) 1589 0.057 (0.232)
Father Smokes 960 0.599 (0.490) 1589 0.322 (0.467)
Father Smokes (Missing) 960 0.083 (0.277) 1589 0.060 (0.23 8)
Father Drinks 960 0.675 (0.469) 1589 0.708 (0.455)
Father Drinks (Missing) 960 0.217 (0.412) 1589 0.140 (0.347)
Mother Smokes 960 0.385 (0.487) 1588 0.185 (0.389)

88

Table 10 (cont’d)

 

Mother Drinks 960 0.340 (0.474) 1588 0.347 (0.476)
Mother has Mental Problems 960 0.066 (0.248) 1589 0.038 (0.192)
Father has Mental Problems 960 0.017 (0.128) 1589 0.018 (0.132)
Father Figure Present 960 0.122 (0.327) 1589 0.101 (0.302)
Number of Residential Moves 958 1.531 (1.487) 1589 0.987 (1.144)
Child was Breastfed 960 0.440 (0.497) 1589 0.647 (0.478)
Mother's WAIS-R Score 959 6.766 (2.435) 1584 7.159 (2.640)
Father's WAIS-R Score 950 6.409 (2.524) 1574 6.817 (2.730)
Paternal Importance 955 1.094 (0.177) 1575 1.086 (0.145)
Either Parent Reports Aggravation 960 0.251 (0.434) 1589 0.196 (0.397)
Religiosity 960 4.453 (1.61 1) 1589 4.093 (1.519)
Child will not have Father's Last Name 960 0.157 (0.364) 15 89 0.071 (0.257)
Father's Name not on Birth Certificate 960 0.089 (0.284) 1589 0.044 (0.205)
Father did not visit Hospital at Birth 960 0.172 (0.377) 1589 0.055 (0.229)
Mother considered Abortion 956 0.333 (0.471) 1583 0.198 (0.398)
Father suggested Abortion 956 0.106 (0.308) 1582 0.064 (0.245)
Time knew father prior to Pregnancy 960 4.026 (4.035) 1589 5.735 (5.089)
Instruments

Father's Impulsivity 959 2.838 (0.721) 1589 3.128 (0.599)
Average Non-Traffic Stops 960 0.431 (0.083) 1589 0.391 (0.094)
Father's Biological Father Involved 960 0.371 (0.483) 1589 0.277 (0.448)
Father had Father-Figure 960 0.663 (0.473) 1589 0.672 (0.470)
Data: FFCWS

89

Table 11. Average Non-Traffic Stops by City and Race/Ethnicity

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Average Non-Traffic
Black Hispanic Other Stops per City

0.43

City 1 0.46 0.43 0.29 (0.05)
0.38

City 2 0.39 0.40 0.32 (0.03)
0.43

City 3 0.48 0.21 0.27 (0.10)
0.44

City 4 0.47 0.38 0.30 (0.06)
0.32

City 5 0.34 0.30 0.24 (0.03)
0.34

City 6 0.41 0.36 0.13 (0.12)
0.44

City 7 0.47 0.43 0.37 (0.05)
0.43

City 8 0.38 0.48 0.29 (0.08)
0.47

City 9 0.57 0.54 0.34 (0.11)
0.47

City 10 0.50 0.50 0.38 (0.06)
0.33

City 11 0.33 0.35 0.26 (0.03)
0.36

mg 12 0.36 0.39 0.30 (0.04)
0.38

City 13 0.44 0.31 0.32 (0.06)
0.39

City 14 0.39 0.20 0.42 (0.05)
0.42

City 15 0.50 0.20 0.20 (0.13)
0.46

City 16 0.42 0.8050 0.47 (0.08)
0.48

City 17 0.48 0.55 0.46 (0.03)
0.39

City 18 0.30 0.43 0.21 (0.08)
0.39

City 19 0.42 — 0.37 (0.02)
0.35

City 20 0.31 0.6351 0.38 (0.09)
Average Non-Traffic Stops 0.44 0.40 0.32 0.40

Per Race/Ethnicity (0.07) (0.08) (0.08) (0.09)

 

 

 

 

 

50 There are only 5 observations used for this mean (excluded from Figure 1.1).
51 There are only 8 observations used for this mean (excluded from Figure 1.1).

90

 

Table 1 l (cont’d)

Data: FFCWS

Notes: The table presents mean averages of non-traffic stops in each city by father’s racial or
ethnic group. Due to privacy reasons, the author is unable to identify the cities in the sample by
name. Standard deviations are in parentheses.

91

Table 12. OLS Estimates of the Marginal Impact of Paternal Incarceration on Outcomes

 

 

 

PPVT—R AGGRESSION _O_D_12
(l) (2) (3)
Incarcerated Ex Post -2.057 0.002 0.028
(1 .608) (0.03 9) (0.044)
Ever-Incarcerated52 1 .869 0.050 0.001
(1.397) (0.029) (0.034)
Father Absent -1 .097 0.027 0.046
(0.838) (0.017) (0.020)
Mother Interviewed in Spanish 4087 -0.067 -0.065
(2.571) (0.043) (0.051)
Male -2.033 0.036 0.034
(0.698) (0.014) (0.017)
Birth Order -0.622 0.012 0.003
(0.334) (0.007) (0.008)
ADHD Symptoms 0.362 -0.005 -0.034
(1.027) (0.020) (0.023)
ADI-ID (missing) 0.758 0.003 -0.046
(1.180) (0.023) (0.027)
Mother's Age 0.130 -0.001 -0.001
(0.1 18) (0.002) (0.003)
F ather's Age 0085 -0.002 -0.002
(0.086) (0.002) (0.002)
Mother Black -4.21 5 -0.068 -0. 153
(l .463) (0.032) (0.03 7)
Mother Hispanic -3.598 0.027 -0.035
(1.473) (0.033) (0.03 8)
Father Black -2.137 0.112 0.123
(1.495) (0.030) (0.03 7)
Father Hispanic 0.023 0.035 0.029
(1.570) (0.031) (0.037)
Mother Born in U.S. 3.427 0.170 0.093
(7.148) (0.070) (0.1 19)
Father Born in U.S. 0.332 -0.007 -0.027
(1.615) (0.046) (0.051)
Child was Breastfed 2.140 0.039 0.051
(0.769) (0.01 7) (0.020)
Mother< High School Degree 0.557 0.019 0.027
(0.921) (0.021) (0.024)
Mother< College Degree 3.809 0.018 0.015
(1.027) (0.021) (0.025)
Mother has at least College Degree 9.841 0.014 0.016
(1.83 5) (0.028) (0.03 7)
Mother's WAIS-R Score 0.374 -0.006 -0.001

 

52 This indicator excludes those fathers who though reported as incarcerated at some point, it could not be

determined whether they were incarcerated ex ante or ex post.

92

Table 12 (cont’d)

Father's WAIS-R Score

Father< High School Degree

F ather< College Degree

Father has at least College Degree
Father Smokes

Father Smokes (Missing)

Father Drinks

Father Drinks (Missing)

Mother Smokes

Mother Drinks

Mother has Mental Problems

Father has Mental Problems

Father Figure Present

Household Income per Person/ 10,000
Household Income per Person (Missing)
Number of Residential Moves

Paternal Importance

Either Parent Reports Aggravation
Religiosity

Child will not have Father's Last Name
Father's Name is not on Birth Certificate
Father did not visit Hospital at Child's Birth
Mother considered Abortion

Father suggested Abortion

(0.160)
0.354
(0.149)
-1344
(0.905)
0.178
(1.034)
0.891
(1.787)
0.633
(0.871)
-2215
(1.753)
0.725
(1.212)
2.281
(1.660)
0.504
(0.908)
1.790
(0.797)
0.301
(1.497)
-0.385
(2.082)
0.672
(1.203)
0.892
(0.446)
-0.386
(1.431)
0.288
(0.275)
5.998
(2.216)
-1.629
(0.868)
0.153
(0.238)
0.228
(1.162)
—1.599
(1.492)
0.950
(1.264)
1.946
(0.827)
0.190
(1.230)

93

(0.003)
0.004
(0.003)
0.036
(0.021)
0.039
(0.021)
0.006
(0.028)
0.019
(0.017)
0.026
(0.047)
0.018
(0.021)
0.022
(0.034)
0.072
(0.020)
0.007
(0.016)
0.053
(0.035)
0.082
(0.066)
0.065
(0.026)
-0.006
(0.005)
0.059
(0.029)
0.008
(0.006)
0.013
(0.046)
0.120
(0.018)
0.013
(0.005)
0.021
(0.029)
0.014
(0.036)
0.01 1
(0.029)
0.022
(0.018)
0.069
(0.032)

(0.004)
0.001
(0.004)
0.027
(0.024)
0.015
(0.025)
0.006
(0.034)
0.010
(0.021)
0.043
(0.056)
0.038
(0.026)
0.009
(0.043)
0.066
(0.023)
0.026
(0.019)
0.072
(0.043)
0.168
(0.072)
0.021
(0.030)
0.001
(0.007)
0.097
(0.032)
0.004
(0.007)
0.050
(0.056)
0.1 12
(0.021)
0.020
(0.006)
0.029
(0.036)
0.031
(0.044)
0.001
(0.033)
0.006
(0.022)
0.093
(0.036)

Table 12 (cont’d)

 

Time Mother knew Father prior to Pregnancy 0.148 -0.001 -0.000

(0.089) (0.002) (0.002)
R_Squared 0.23 0.12 0.1 1
Observations 1804 2143 2401
Data: FF CWS.

Notes: All regressions include city, region-of-birth and interview-year dummies. Robust standard
errors are in parentheses.

94

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97

Table 15. Summary Statistics

 

 

 

 

Variables % M20 .39. Min MA
Union Dissolved at the End of Each Spell 5768 0.16 0.37 0 1
Duration of the Union at the Start of Spell 5768 4.90 3.89 0 27.33
0-1 Year Interval 5786 0.04 0.19 0 1
1-3 Year Interval 5768 0.33 0.47 0 1
3-5 Year Interval 5768 0.23 0.42 O 1
5-7 Year Interval 5768 0.14 0.35 0 1
7-10 Year Interval 5768 0.13 0.34 0 1
10-12 Year Interval 5768 0.05 0.22 0 1
12 Plus Year Interval 5768 0.07 0.25 0 1
Time between interviews (Months) 5768 19.53 5.61 3 37
Time-Invariant

Age Difference 2267 2.50 4.76 -15 32
Age Difference Squared 2267 28.84 65.04 0 1024
Mother Black 2450 0.34 0.48 0 1
Mother White 2450 0.30 0.46 0 1
Mother Hispanic 2450 0.31 0.46 0 1
Other 2450 0.05 0.21 0 1
Less than HS 2450 0.34 0.47 0 1
High School 2450 0.23 0.42 O 1
Some College 2450 0.26 0.44 0 1
College 2450 0.17 0.37 0 1
Dad Very Involved 2450 0.40 0.49 0 1
Dad Little Involved 2450 0.35 0.48 0 1
Dad Not Involved 2450 0.23 0.42 0 1
Father Figure Present 2450 0.24 0.42 0 1
No Religion 2450 0.09 0.29 0 1
Catholic 2450 0.35 0.48 0 1
Jewish 2450 0.02 0.12 0 1
Muslim 2450 0.02 0.12 0 1
Baptist 2450 0.20 0.40 0 1
Other Christian 2450 0.32 0.47 0 1
Freq. of Church Attendance 2445 2.88 1.36 1 5
Mother’s Impulsivity Scale 2241 3.01 0.60 1 4
Father’s Impulsivity Scale 1817 3.06 0.65 1 4
Focal Child is a Boy 2450 0.52 0.50 0 1
First Child 2450 0.26 0.44 0 1
Mother's Age at Baseline 2450 26.38 6.08 15 43
Out of Wedlock Childbirth 2450 0.58 0.49 0 1
Marriage within 6 mths prior to birth 2450 0.02 0.14 0 1
Time-Varying

Number of Children in HH 5754 1.78 1.33 0 10
Number of Adults in HH 5753 2.33 0.82 l 9

98

Table 15 (cont’d)

 

 

Cohabit only 5768 0.45 0.50 0 1
Pre-Marital Cohabitation 5768 0.27 0.44 0 1
Married Only 5768 0.28 0.45 0 1

New Birth Shock 5768 0.76 0.43 0 1
Lagged Changes

Residential Move 33 18 0.37 0.48 O 1

New Incarceration 3316 0.02 0.13 0 1

New Release 3316 0.02 0.13 0 1
Household Income (103) 3318 45.35 47.54 0 935.87
Change in Household Income (103) 3316 -O.61 73.73 -906.86 923.70
Data: FFCWS

Note: The time-invariant summary statistics are calculated using the baseline sample only; all
other summary statistics use the entire analysis sample.

99

Table 16. Linear Probability Estimates of the Correlates of Union Dissolution

 

 

(1) (2) (3) (4)
1-3 Year Interval -0.031 -0.021 -0.007
(0.036) (0.035) (0.035) .
3-5 Year Interval -0.049 -0.018 0.013 0.031
(0.03 6) (0.03 6) (0.03 7) (0.022)
5-7 Year Interval -0.144 —0.082 -0.037 -0.015
(0.03 6) (0.03 7) (0.03 8) (0.024)
7-10 Year Interval -0.138 —0.056 -0.013 -0.002
(0.036) (0.03 8) (0.040) (0.026)
10-12 Year Interval —0. 191 -0.099 —0.043 -0.029
(0.03 7) (0.03 8) (0.040) (0.028)
12 Plus Year Interval -0.187 -0.082 -0.024 0.007
(0.03 7) (0.039) (0.041) (0.030)
Interval Length 0.005 0.005 0.007 0.007
(0.001) (0.001) (0.001) (0.003)
Age Difference -0.004 -0.004 -0.001
(0.002) (0.002) (0.002)
Age Difference Squared 0.000 0.000 0.000
(0.000) (0.000) (0.000)
Mother Black 0.086 0.068 0.052
- (0.016) (0.016) (0.020)
Mother Hispanic -0.009 -0.017 0.004
(0.015) (0.016) (0.020)
Other 0.009 0.014 -0.007
(0.021) (0.021) (0.025)
Less than HS 0.044 0.036 0.015
(0.017) (0.017) (0.023)
Some College 0.008 0.016 0.022
(0.016) (0.016) (0.021)
College 0035 -0.006 0.014
(0.016) (0.016) (0.022)
Dad Very Involved —0.009 -0.010 -0.017
(0.018) (0.018) (0.023)
Dad Little Involved -0.018 -0.012 0.004
(0.016) (0.016) (0.022)
Father Figure Present 0.000 -0.003 0.006
(0.016) (0.016) (0.021)
No Religion . 0.047 0.040 0.032
(0.023) (0.023) (0.030)
Jewish -0.002 0.020 0.053
(0.027) (0.027) (0.03 8)
Muslim -0.021 -0.007 0.010
(0.040) (0.03 9) (0.055)
Baptist 0.043 0.039 0.063
(0.019) (0.019) (0.025)
Other Christian 0.008 0.017 0.009
(0.013) (0.013) (0.017)

100

Table 16 (cont’d)

 

Freq. of Church Attendance 0.001 -0.007 -0.008
(0.004) (0.005) (0.006)
Mother Impulsivity Scale -0.040 -0.036 —0.041
(0.010) (0.010) (0.013)
Father Impulsivity Scale -0.041 -0.040 -0.034
(0.009) (0.009) (0.012)
Focal Child is a Boy 0025 -0.024 -0.007
(0.011) (0.011) (0.014)
First Child -0.021 -0.008 -0.000
(0.013) (0.014) (0.019)
Mother's Age at Baseline -0.005 -0.005 -0.004
(0.001) (0.001) (0.002)
Out of Wedlock Childbirth 0.032 0.026
(0.025) (0.027)
Marriage within 6 mths prior to birth -0.020 0.002
(0.032) (0.043)
Number of Children in HH 0.001 -0.001
(0.005) (0.008)
Number of Adults in HH -0.008 -0.010
(0.008) (0.011)
Cohabit only 0.094 0.084
(0.027) (0.030)
Pre-Marital Cohabitation 0.01 1 0.009
(0.012) (0.016)
New Birth Shock 0.016 0.000
(0.017) (0.020)
Residential Move 0.017
(0.015)
New Incarceration 0.508
(0.068)
New Release 0.001
(0.047)
Change in H. Income Def/ 10000 —0.004
(0.001)
Observations 4108 4108 4095 2474
R-squared 0.03 0.09 0.1 1 0.14
Data: FFCWS

Robust standard errors are in parentheses. The excluded category for the duration

intervals is 0 to 3 years in column (4). Since lagged variables are included in this model,

only 18 couples who have been together for less than one year are included in this

regressiOn. Subsequently, using the 0 — 1 year interval as the sole excluded category will

induce problems similar to a dummy variable trap.

101

Table 17. Linear Probability Estimates for Low-Educated and Black Mothers

 

 

 

Mother Low-Educated Mother Black
(1) (2) (3) (4)
1-3 Year Interval -0.009 0.012
(0.043) . (0.067) .
3-5 Year Interval 0.040 0.072 0.012 0.013
(0.047) (0.031) (0.070) (0.043)
5-7 Year Interval -0.036 -0.003 -0.028 0.012
(0.049) (0.03 7) (0.074) (0.052)
7-10 Year Interval 0.031 0.051 0.008 —0.032
(0.05 3) (0.044) (0.078) (0.056)
10-12 Year Interval -0.042 -0.040 -0.041 -0.069
(0.056) (0.043) (0.088) (0.070)
12 Plus Year Interval -0.017 0.047 -0.073 -0.046
(0.056) (0.050) (0.078) (0.059)
Interval Length 0.007 0.009 0.01 1 0.01 1
(0.002) (0.004) (0.003) (0.005)
Age Difference -0.008 -0.004 -0.005 -0.004
(0.003) (0.003) (0.004) (0.005)
Age Difference Squared 0.000 0.000 0.000 0.000
(0.000) (0.000) (0.000) (0.000)
Mother Black 0.076 0.045 0.000 0.000
(0.025) (0.03 3) (0.000) (0.000)
Mother Hispanic -0.027 -0.030 0.000 0.000
(0.025) (0.03 1) (0.000) (0.000)
Other 0.012 -0.055 0.000 0.000
(0.052) (0.05 7) (0.000) (0.000)
Less than HS 0.038 0.019 0.039 0.075
(0.018) (0.024) (0.03 3) (0.044)
Some College 0.000 0.000 0.002 0.061
(0.000) (0.000) (0.03 1) (0.03 9)
College 0.000 0.000 -0.049 0.047
(0.000) (0.000) (0.037) (0.047)
Dad Very Involved -0.018 -0.016 0.013 -0.025
(0.026) (0.034) (0.033) (0.042)
Dad Little Involved -0.016 0.023 -0.016 0.013
(0.023) (0.030) (0.030) (0.039)
Father Figure Present 0009 -0.002 0.009 0.012
(0.023) (0.030) (0.030) (0.039)
No Religion 0.081 0.065 0.072 0.012
(0.035) (0.046) (0.056) (0.074)
Jewish -0.093 -0.085 0.113 0.118
(0.039) (0.05 7) (0.149) (0.174)
Muslim 0.092 0.158 0.056 0.108
(0.122) (0.168) (0.112) (0.145)
Baptist 0.051 0.072 0.097 0.091
(0.029) (0.037) (0.041) (0.052)
Other Christian 0.034 0.021 0.060 -0.008
(0.022) (0.028) (0.041) (0.052)

102

Table 17 (cont’d)

 

Freq. of Church Attendance -0.009 -0.017 -0.017 -0.027
(0.007) (0.009) (0.010) (0.013)
Mother Impulsivity Scale -0.050 -0.058 -0.052 -0.066
(0.014) (0.018) (0.020) (0.027)
Father Impulsivity Scale -0.048 -0.044 -0.042 -0.036
(0.014) (0.018) (0.019) (0.024)
Focal Child is a Boy -0.036 -0.008 -0.029 0.007
(0.017) (0.022) (0.023) (0.029)
First Child 0007 -0.000 -0.018 -0.033
(0.024) (0.033) (0.037) (0.049)
Mother's Age at Baseline -0.005 -0.005 —0.004 -0.004
(0.002) (0.002) (0.003) (0.004)
Out of Wedlock Childbirth 0.051 0.053 0.035 0.026
(0.035) (0.039) (0.051) (0.057)
Marriage within 6 mths prior to birth -0.035 0.046 -0.032 0039
(0.056) (0.083) (0.067) (0.088)
Number of Children in HH 0.002 0.000 -0.008 -0.007
(0.008) (0.011) (0.010) (0.015)
Number of Adults in HH -0.003 0.005 -0.015 -0.015
(0.009) (0.014) (0.020) (0.026)
Cohabit only 0.050 0.015 0.147 0.124
(0.039) (0.045) (0.057) (0.065)
Pre-Marital Cohabitation -0.023 —0.046 0.022 0.006
(0.024) (0.032) (0.03 1) (0.040)
New Birth Shock 0.023 0.001 0.058 0.028
(0.027) (0.030) (0.036) (0.042)
Residential Move 0.015 0.042
(0.023) (0.033)
New Incarceration 0.466 0.442
(0.076) (0.090)
New Release 0.060 0.091
(0.084) (0.1 18)
Change in H. Income Def/ 10000 -0.004 —0.009
(0.002) (0.003)
Observations 2093 1224 l 3 l 6 744
R-squared 0.09 0.14 0.10 0.18
Data: FFCWS

Robust standard errors are in parentheses

* significant at 5%; ** significant at 1%

103

Table 18. Linear Probability Estimates for Couples Cohabiting and Married at Baseline

 

 

Cohabiting Married
(1) (2) (3) (4)
1-3 Year Interval -0.016 -0.001
(0.039) . (0.086) .
3-5 Year Interval 0.003 0.041 0.011 -0.019
(0.043) (0.029) (0.089) (0.035)
5-7 Year Interval -0.054 -0.003 -0.024 -0.054
(0.048) (0.041) (0.090) (0.034)
7-10 Year Interval 0.006 -0.001 -0.022 -0.045
(0.055) (0.050) (0.091) (0.037)
10-12 Year Interval -0.018 -0.038 -0.053 -0.069
(0.089) (0.091) (0.091) (0.037)
12 Plus Year Interval -0.054 -0.008 -0.029 -0.035
(0.076) (0.088) (0.091) (0.039)
Interval Length 0.007 0.008 0.006 0.007
(0.002) (0.004) (0.001) (0.003)
Age Difference -0.007 -0.004 0.001 0.001
(0.003) (0.004) (0.002) (0.002)
Age Difference Squared 0.000 0.000 -0.000 -0.000
(0.000) (0.000) (0.000) (0.000)
Mother Black 0.091 0.061 0.033 0.029
(0.026) (0.035) (0.01 8) (0.024)
Mother Hispanic -0.012 0.008 0.004 0.010
(0.027) (0.035) (0.018) (0.026)
Other 0.108 0.046 -0.019 -0.011
(0.063) (0.074) (0.014) (0.022)
Less than HS 0.044 0.021 0.000 -0.013
(0.023) (0.031) (0.025) (0.034)
Some College 0.034 0.059 -0.008 -0.012
(0.024) (0.032) (0.019) (0.026)
College -0.024 0.034 -0.026 -0.018
(0.051) (0.063) (0.018) (0.025)
Dad Very Involved -0.007 0.011 -0.009 -0.051
(0.028) (0.036) (0.021) (0.030)
Dad Little Involved -0.013 0.035 —0.011 -0.033
(0.024) (0.032) (0.021) (0.029)
Father Figure Present -0.025 -0.004 0.034 0.018
(0.024) (0.03 1) (0.020) (0.027)
No Religion 0.056 0.039 0.038 0.042
(0.034) (0.044) (0.028) (0.03 8)
Jewish -0.189 -0.193 0.009 0.044
(0.053) (0.076) (0.028) (0.041)
Muslim 0.014 0.123 -0.023 -0.027
(0.116) (0.161) (0.031) (0.049)
Baptist 0.074 0.1 17 0.006 0.01 1
(0.032) (0.042) (0.020) (0.027)
Other Christian 0.046 0.030 -0.001 -0.006
(0.027) (0.034) (0.012) (0.017)

104

Table 18 (cont’d)

 

Freq. of Church Attendance -0.014 -0.019 0.001 0.000
(0.007) (0.010) (0.005) (0.006)
Mother Impulsivity Scale 0054 —0.062 -0.021 -0.023
(0.017) (0.022) (0.01 1) (0.015)
Father Impulsivity Scale 0054 -0.052 —0.020 -0.015
(0.014) (0.019) (0.011) (0.015)
Focal Child is a Boy -0.023 0.016 -0.024 -0.023
(0.018) (0.024) (0.01 1) (0.015)
First Child 0019 -0.003 -0.004 -0.007
(0.024) (0.033) (0.015) (0.021)
Mother's Age at Baseline -0.005 -0.003 -0.003 -0.004
(0.002) (0.003) (0.002) (0.002)
Out of Wedlock Childbirth 0.000 0.000 0.000 0.000
(0.000) (0.000) (0.000) (0.000)
Marriage within 6 mths prior to birth 0.000 0.000 -0.011 -0.011
(0.000) (0.000) (0.035) (0.046)
Number of Children in H 0.004 0.007 0.000 -0.005
(0.009) (0.013) (0.005) (0.007)
Number of Adults in H -0.006 -0.007 .0009 -0.012
(0.009) (0.014) (0.011) (0.017)
Cohabit only 0.078 0.078 0.000 0.000
(0.025) (0.026) (0.000) (0.000)
Pre-Marital Cohabitation 0.000 0.000 0.008 0.007
(0.000) (0.000) (0.012) (0.016)
New Birth Shock 0.015 -0.014 0.010 0.006
(0.029) (0.032) (0.018) (0.021)
Residential Move 0.044 -0.014
(0.025) (0.016)
New Incarceration 0.491 0.562
(0.074) (0.183)
New Release 0.055 -0.030
(0.100) (0.03 7)
Change in H. Income Def/ 10000 -0.007 -0.003
(0.002) (0.001)
Observations 2102 1 192 1993 1282
R-squared 0.06 0.12 0.07 0.09
Data: FFCWS

Robust standard errors are in parentheses
* significant at 5%; ** significant at 1%

105

Table 19. Logit Estimates of Union Dissolution

 

 

(1) (2) (3) (4)
1-3 Year Interval -0.223 —0.124 -0.062
(0.213) (0.232) (0.230)
3-5 Year Interval -0.346 -0.113 0.050 0.209
(0.220) (0.245) (0.246) (0.155)
5-7 Year Interval -l .169 -0.684 -0.389 -0.200
(0.249) (0.278) (0.280) (0.224)
7-10 Year Interval -1.097 -0.404 -0.125 -0.083
(0.250) (0.285) (0.295) (0.246)
10-12 Year Interval -1.914 -1.179 -0.803 -0.683
(0.383) (0.413) (0.425) (0.459)
12 Plus Year Interval -1.825 —0.976 -0.515 -0.140
(0.350) (0.389) (0.399) (0.371)
Interval Length 0.040 0.047 0.056 0.063
(0.008) (0.009) (0.012) (0.021)
Age Difference -0.038 -0.034 -0.011
(0.015) (0.015) (0.020)
Age Difference Squared 0.002 0.001 0.001
(0.001) (0.001) (0.001)
Mother Black 0.686 0.552 0.476
(0.123) (0.128) (0.171)
Mother Hispanic 0.049 -0.013 0.171
(0.151) (0.158) (0.202)
Other 0.119 0.187 -0.225
(0.290) (0.288) (0.452)
Less than HS 0.264 0.205 0.087
(0.121) (0.124) (0.168)
Some College 0.071 0.118 0.235
(0.128) (0.131) (0.172)
College -0.862 -0.576 -0.218
(0.222) (0.236) (0.283)
Dad Very Involved -0.085 -0.101 -0.212
(0.140) (0.141) (0.191)
Dad Little Involved -0.162 -0.127 0.021
(0.124) (0.124) (0.163)
F athcr Figure Present 0.029 -0.003 0.048
(0.122) (0.123) (0.159)
No Religion 0.352 0.342 0.285
(0.180) (0.186) (0.25 8)
Jewish -0.242 0.075 0.505
(0.553) (0.556) (0.556)
Muslim -0.156 -0.053 0.296
(0.532) (0.541) (0.608)
Baptist 0.383 0.369 0.570
(0.160) (0.164) (0.212)
Other Christian 0.121 0.222 0.131
(0.138) (0.144) (0.187)
Freq. of Church Attendance 0.007 -0.064 -0.079

106

Table 19 (cont’d)

(0.037)

Mother Impulsivity Scale 0312
(0.081)

Father Impulsivity Scale 0310
(0.071)

Focal Child is a Boy 0199
(0.093)

First Child 0163
(0.118)

Mother's Age at Baseline 0046
(0.012)

Out of Wedlock Childbirth

Marriage within 6 months prior to child’s birth

Number of Children in HH

Number of Adults in HH

Cohabit only

Pre-Marital Cohabitation

New Birth Shock

Residential Move

New Incarceration

New Release

Change in H. Income Def/ 10000

Observations 4108 4108

(0.039)
0.294
(0.084)
0.314
(0.072)
0.209
(0.095)
-0.063
(0.129)
0.039
(0.012)
0.324
(0.227)
0.1 19
(0.379)
0.014
(0.043)
0.041
(0.059)
0.792
(0.262)
0.221
(0.199)
0.068
(0.142)

4095

(0.051)
-O.346
(0.109)
0.274
(0.097)
0.032
(0.125)
0.020
(0.172)
0.036

' (0.016)

0.289
(0.255)
0.060
(0.451)
0.008
(0.063)
0.062
(0.088)
0.593
(0.296)
0.086
(0.233)
0.044
(0.166)
0.150
(0.128)
2.416
(0.414)
0.020
(0.451)
0.042
(0.010)

2474

 

Data: FFCWS
Robust standard errors are in parentheses
* significant at 5%; ** significant at 1%

107

 

 

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Figure 3.1. The Hazard of Union Dissolution

 

 

IO
N.“
O
O
my
O
E
OF‘
> u
(0
F— . .
O
0
ID
0‘
' I I I I
O 5 10 15
ttdum

avgfail — Probability of Failure
ttdum — Duration of the Union at a start of a Spell

111

Appendix A.
Constructed Variables

1) Fraction of time Father is Present

2) Household Income/Person

3) Paternal Importance

4) Mental/Emotional problems

5) Other father figures present

6) Parents’ Drug Use

7) Parent Reports Parental Aggravation

8) Residential Instability

Definition

The total number of years father has spent
living with the child divided by age of the
chfld.

Household income divided by household
Size.

Average of the questions reflecting the
mother’s evaluation of the importance of the
father’s involvement in the upbringing of the
chfld.

Likert scale: {(1) Very important, (2)
somewhat important and (3) not important}

How important is it for father to teach child
about life?

How important is it for father to provide
direct care to child?

How important is it for father to show love
and affection to the child?

How important is it for father to provide
protection for child?

How important is it for father to serve as
authority figure and to discipline the child?

The parent is characterized as having mental
or emotional problems if he/she is taking
medications for mental illnesses such as
anxiety, depression or ADD.

Defined as all men over the age of eighteen,
living in the child’s household aside from
the male spouse/partner.

Parents’ level of smoking, alcohol
consumption and illegal drug use over the
all three waves.

Both parents answer four questions on
aggravation on a scale of 1 to 4 (1 being the
most aggravated). He/She is classified as
aggravated if he/she rates his/her
aggravation as 1 or 2 on the aggravation
scale.

The total number of residential moves the
child has experienced since birth.

112

Appendix A (cont’d)

9) Father Absent The child’s biological father is reported as
absent from the child’s household in any
wave.

10) Religiosity The number of times per week mother
attends church.

11) Ever-Incarcerated This indicator excludes those fathers who

are reported as incarcerated, but it could not
be determined whether they were
incarcerated ex ante or ex post.

113

Appendix B.

Scales Documentation

 

 

 

Aggression ODD ADHD DDI — Fafler’s Impulsivity
Can’t wait turn Defiant Cannot concentrate I often say whatever comes
into my head without thinking
Demanding Disobedient Cannot sit still Often I don‘t think enough
before I act

Breaks others’ things Angry moods Quickly shifts actions I often say/do things without
considering the consequences

Easily frustrated Temper tantrums Demanding My plans fail because I fail to
think them through first
Gets in fights Uncooperative Gets into everything I often make up my mind

w/o considering the situation

No guilt after misbeh. Stubborn Can’t wait turn I get into trouble because I
don't think before I act

Hits others

Hurts animals/people unintentionally
Attacks people

Punishment doesn’t change behavior
Screams a lot

Selfish/won’t share

Wants a lot of attention

Likert Scale:

O-Not True O-Not True O—Not True l-Strongly Agree
2-Very True 2-Very True 2-Very True 4-Strongly Disagree
Alpha on Full Sample:

0.88 0.77 0.72 0.84

 

Notes: The items are averaged to create each scale.

114

Appendix C.

Religiosity — How often do you attend religious services?

Likert Scale:
1 — Once a week
2 — Several times per month
3 — Several times per year
4 — Hardly
5 — Never

115

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