1. society
2. social institution
3. marriage

The effect of child support laws on marital formation∗
Daniel I. Tannenbaum†
March 27, 2015
Abstract
This paper studies the effect of child support laws on selection into marriage. I develop
a simple model of dating, fertility, and marriage, showing that because there are utility gains
to having children within marriage, some couples with low match quality marry in the event
of a pregnancy who would not otherwise – these are shotgun marriages. A child support law
introduces an intermediate contract between no-relationship and marriage, which establishes
custody rights for the father in exchange for transfers to the mother. The model implies that
following the introduction of child support, shotgun marriages decline and the match quality of
remaining shotgun marriages are higher on average. I show evidence that these predictions are
consistent with marital patterns in the U.S. since the 1970s, when child support enforcement first
became effective: shotgun marriages have fallen dramatically, and while shotgun marriages are
low quality relative to non-shotgun marriages in terms of divorce probability and self-reported
measures of marital happiness, their relative quality has been increasing since the 1970s. I
present direct evidence of the effect of child support laws on marriage, marriage quality, and
fertility, using variation within state-year cells in populations differentially affected by child
support enactments. The estimates suggest that child support laws account for a large fraction
of the observed decline of shotgun marriages, and part of the recent decline in divorce.
JEL No. J12, J13, K36
Keywords: child support, family, marriage, divorce
∗
I thank Enghin Atalay, Marianne Bertrand, Pietro Biroli, Pierre-Andr´e Chiappori, Matthew Gentzkow, William
Hubbard, Joaquin Lopez, Kevin Murphy, Sebastian Sotelo, Adriaan Ten Kate, and seminar participants at the
University of Memphis and Chicago Harris for helpful comments and suggestions. Special thanks to Jane Waldfogel
for sharing the child support enforcement expenditure data, to Anne Case and Sara McLanahan for sharing their
child support statute data, and to Hannah Lazar for invaluable research assistance. Funding from a University of
Chicago Social Sciences grant is gratefully acknowledged. All errors are my own.
†
Becker Friedman Institute, The University of Chicago, [email protected].
1
1
Introduction
In the last forty years the U.S. has dramatically strengthened the enforcement and collection of
child support from non-resident parents. Beginning in 1975 with Part D of the Social Security
Act, and continuing with major legislation in the 1980s and 1990s, these statutes were enacted to
protect children and ensure that non-resident parents, the majority of whom are male, share in the
burden of child rearing.1
Child support laws also have the potential to affect individual decisions regarding marriage and
fertility. Child support laws ensure that mothers can receive support without having to marry
the father; they also allow fathers to have a legal relationship with their child without marriage.
Child support laws also increase the cost of fathering a child, particularly an unwanted child, and
males may respond by increasing their use of contraceptives. Understanding the impact of child
support laws on family structure is of critical importance, not least because dramatic changes in
marital patterns, including selection into marriage and divorce, have coincided with a period of
rapid child support expansion (Stevenson and Wolfers, 2007). To the extent that child support
laws affect marital formation, they also affect the family structure in which children are reared,
which may have consequences for their long-term chances of success (Case et al., 2002; McLanahan
and Sandefur, 1994).
This paper develops a simple model of dating, fertility, and marriage to illustrate the effects
of a child support law. Because there are gains to having children in marriage relative to outside
marriage, some couples with low match quality marry in the event of a pregnancy who would not
otherwise – these are shotgun marriages. A child support law introduces an intermediate contract
between no-relationship and marriage, which establishes custody rights for the father in exchange
for transfers to the mother. Following the introduction of a child support law, marriage becomes
less attractive to females since they receive additional transfers outside of marriage, while marriage
becomes more attractive to males who must pay these transfers. Because men gain additional
custodial rights outside of marriage, in equilibrium, low match quality couples who would have
a shotgun marriage absent the child support law choose this intermediate contract and no longer
marry. The model delivers key predictions about marriage: under child support, fewer shotgun
marriages form and the match quality of shotgun marriages that do form are higher on average.
The theoretical framework also predicts that an increase in child support enforcement will
increase contraceptive use among men who have a distaste for children and will reduce total births
from these men. Child support enforcement puts downward pressure on total out of wedlock births
because men who are least likely to marry following a pregnancy increase their contraceptive use
the most. Nevertheless, the fraction of births that are out of wedlock may increase, because a lower
fraction of parents marry following a pregnancy.
1
To provide a benchmark sense of child support enforcement, its reach and expansion, in the fiscal year 2013
there were 15.6 million child support cases and $31.6 billion of total distributed child support collections, compared
to 4.1 million cases and $3.6 billion in the fiscal year 1978, valued at 2013 USD (source: Office of Child Support
Enforcement, FY2013 Preliminary Report - Table P-52 and Carmen Solomon-Fears, 2005).
2
I present descriptive evidence that the marriage patterns in the U.S. since the 1970s are consistent with the predictions of the model. Using data from the Survey of Income and Program
Participation (SIPP) and the National Survey of Families and Households (NSFH), I define the
empirical counterpart of shotgun marriages as marriages that occur between the first pregnancy
and birth, as in Akerlof et al. (1996). I first show that shotgun marriages have lower match quality
on average than other marriages, in terms of divorce hazard rates and self-reported measures of marital stability. Second, I show that since the advent of child support legislation, shotgun marriages
have declined dramatically and the match quality of shotgun marriages relative to non-shotgun
marriages has increased.
I then consider direct evidence for the effect of child support laws on marriage, marital quality,
and fertility, using two primary sources of data on child support enforcement. The first is a stateyear database of child support legislative enactments, used in prior studies by Plotnick et al. (2007)
and Case et al. (2000). These laws are classified by type, and include provisions that require genetic
tests in disputed cases, facilitate paternity establishment, impose penalties for failure to pay, or
implement wage withholding procedures. The second dataset consists of state-year child support
enforcement expenditures, based on annual reports from the Office of Child Support Enforcement,
and used in previous work by Freeman and Waldfogel (2001).
To identify the effect of child support enforcement on the shotgun marriage decision, I estimate
the differential impact of child support laws on single women who experience a pregnancy compared
to those who do not, within a state-year cell. This strategy has the advantage of holding fixed timevarying determinants of marriage trends that may be correlated with the timing of child support
enactments. A crucial part of identifying a causal impact in this setting is showing that child
support enforcement does not affect female fertility differentially based on her underlying likelihood
of having a shotgun marriage. Concretely, we might worry that child support discourages fertility
for women who are most likely to have a shotgun marriage. To explore this possibility, I estimate
the direct effect of child support on fertility and find the estimates small and insignificant, too small
by an order of magnitude to explain the estimated effects on marriage.2 The results taken as a
whole suggest that the full set of child support laws adopted by U.S. states reduced the shotgun
marriage rate – the fraction of out of wedlock pregnancies resolved in a marriage before birth –
by 6-8 percent, relative to its total decline of approximately 20 percent over the 1976-1992 sample
period for which the child support legislative data is available.
To consider the direct effect of child support laws on marital match quality, I estimate the effect
of child support laws at the time of marriage on the probability of divorce, for shotgun marriages
compared to non-shotgun marriages. The estimates suggest that child support laws at the time of
marriage reduce the probability of divorce for shotgun marriages relative to non-shotgun marriages
2
Aizer and McLanahan (2006) finds a negative effect on fertility for those with a high school degree or less, and
slightly positive effects for those with some college or more. But low-educated women are less likely to have a shotgun
marriage than high-educated women. The theoretical model in this paper corroborates their finding: those who are
least likely to marry following a pregnancy reduce their fertility the most. Both pieces of evidence suggest that the
estimates presented in this paper on the effect of child support laws on shotgun marriages are a lower bound of the
true effect, in absolute value.
3
– the magnitude is 3-4 percent over a 3-year horizon, and 6-7 percent overall. This result supports
the prediction that child support laws affect selection into marriage, particularly for the lowest
match quality couples who would marry only as a result of the pregnancy. By contrast, child
support laws adopted during the marriage have no statistically significant effect on the probability
of divorce, both for shotgun and non-shotgun marriages. Hence, the primary channel through which
child support laws affect divorce appears to be selection at the time of pregnancy, rather than one
that affects couples conditional on marriage.
The empirical analysis emphasizes shotgun marriages because these are the marginal marriages
most likely to be affected by child support laws. Prior to the advent of child support, a child
born out of wedlock had no legal father and, following the precedent set by English common law,
was considered filius nullius, the child of no one. If the couple was married at the time of a birth,
however, the husband was (and still is) granted the presumption of paternity (Edlund, 2013), which
was accompanied by visitation rights, the right to sue for custody, and even the right to pick up
the child from school; but it also included financial obligations to support the child. A marriage
after the birth of the child would have established the father as a step-father only, and if he desired
to establish legal parental rights he would have had to go through legal proceedings to formally
adopt the child. Hence a shotgun marriage was an important means for establishing paternity and
guaranteeing legal rights to the father while at the same time securing financial support to the
mother. Couples facing out of wedlock pregnancies face a direct and immediate tradeoff between
transferring custodial rights and marital match quality.
This paper contributes to the literature studying long-term marital trends, including the decline
of shotgun marriages (Akerlof et al., 1996; Alesina and Giuliano, 2006) and the rise of out of wedlock
births (Willis, 1999). Akerlof et al. (1996) document that the shotgun marriage rate declined
between 1965 and 1990, and argue that this decline accounts for the majority of the increase
in out of wedlock fertility over this period. To understand the economic mechanism behind the
decline of shotgun marriages, Akerlof et al. (1996) present a model in which the availability of
contraceptives and abortion can reduce shotgun marriages. This paper is complementary to their
work, presenting both theoretical and empirical evidence that child support is a key factor behind
the dramatic decline of shotgun marriages.3
Several studies find that child support laws have led to a decline in total out of wedlock births
(Plotnick et al., 2007; Case, 1998; Aizer and McLanahan, 2006), although Rossin-Slater (2013)
finds that the adoption of in-hospital paternity establishment programs reduces parental marriage,
and hence increases out of wedlock births. The theoretical model of this paper rationalizes these
findings. I show that a decline in total out of wedlock births can occur, due to an increase in
contraceptive use to avoid costly unwanted births. However, conditional on an out of wedlock
pregnancy, marriage rates decline and the fraction of births that are out of wedlock increases. The
empirical evidence presented in this paper is consistent with this unified interpretation.
3
An important distinction between the Akerlof et al. (1996) model and the one in this paper is that Akerlof et al.
(1996) present out of wedlock fertility as welfare-diminishing for women, while here it is welfare-enhancing for women,
because mothers no longer marry dads with whom they have poor match quality.
4
A further contribution of this paper is to emphasize the empirical implications of child support
policies for marital match quality. Prior research has considered marital happiness or divorce as
a function of income or unemployment shocks within households (Weiss and Willis, 1997; Hellerstein and Morrill, 2011; Bertrand et al., 2013). Others have looked at the implications of divorce
laws for investment in marriage-specific capital (Stevenson, 2007), bargaining within the marriage
(Stevenson and Wolfers, 2006), and marital dissolution (Wolfers, 2006). This paper is the first to
my knowledge to study the effect of child support laws on divorce, through its effect on selection
into marriage. Moreover, while several authors have pointed out the decline in divorce rates after
the 1980s (Stevenson, 2007; Rotz, 2011; Goldin and Katz, 2000), emphasizing the importance of
age-at-marriage and the availability of contraceptives as potential causes, none have considered the
role of child support.
The rest of the paper is organized as follows. Section 2 presents a brief overview of the child
support process and how statutes affecting non-married parents have evolved historically; Section 3
presents the theoretical model; Section 4 presents evidence on marital patterns that are consistent
with the model’s predictions; Section 5 provides the regression framework and estimates the direct
effect of child support legislation; and Section 6 concludes.
2
An overview of the child support process and enforcement data
Federal child support legislation was first introduced as a response to the growing number of single
mothers receiving Aid to Families with Dependent Children (AFDC). While child support cases are
adjudicated under state law, beginning in 1975 the U.S. federal government has placed requirements
on states as a condition for receiving federal funds. The first major federal policy affecting child
support was the creation in 1975 of part D of Title IV of the Social Security Act, which created
the federal Office of Child Support Enforcement (OCSE). The OCSE was required to establish
a parent locator service and to set operational standards for state-level program enforcement, to
audit state program operations, and to certify cases to federal courts and to the IRS for enforcement
and support collections. Several key federal laws followed in the 1980s and 1990s, including the
1984 Child Support Enforcement Amendments, the 1988 Family Support Act, and the 1996 welfare
reform bill – all of which compelled states to usher in major changes in paternity establishment,
and the enforcement and collection of child support payments.4
The primary purpose cited in these laws is twofold: to promote the best interests of the child
by promoting financial stability within families, and to decrease dependence on public assistance.
Pursuant to the federal laws enacted over the last four decades, every state now provides for
expedited and automatic processes for establishing child support cases, affecting both families who
receive federal assistance (IV-D cases) and those who do not. Figure 4 plots trends in child support
4
Lerman and Sorensen (2001) provides a useful overview of child support enforcement. See also http://greenbook.
waysandmeans.house.gov/2012-green-book/child-support-enforcement-cover-page/legislative-history,
which has a concise legislative history of Federal laws regarding child support.
5
income receipt, revealing extremely low rates of child support income in the 1970s and rapid growth
throughout the 80s and 90s.
At the individual level, the child support process begins with paternity establishment. If the
mother is married at the time of birth, the husband is presumed to be the father. If the mother
is unmarried at the time of birth, the state or child support agency will attempt to determine
paternity, pursuant to the state laws in effect. There have been significant changes in the procedure for establishing paternity since the 1970s. For example, most states now have in-hospital
Voluntary Acknowledgement of Paternity programs, which present acknowledgement forms to the
man accompanying the mother in the hospital at the time of birth (Rossin-Slater, 2013). Beginning
with the Family Support Act of 1988, states now require all parties in a contested paternity case to
take a genetic test upon the request of any party, at the states up-front expense. Federal laws also
began imposing minimum paternity establishment rates upon states: initially set at 50 percent by
the 1988 law, it has been incrementally increased to 90 percent, as mandated by the 1996 welfare
reform law.
If paternity is not established or presumed, a biological father has no rights or obligations to
his child. From a legal perspective, the child and biological father are strangers. For centuries,
governments and church parishes have attempted to reduce their welfare rolls by locating absent
fathers and getting them to financially contribute, notably in the 1576 Poor Law in England; but
the difficulty of determining paternity in an age before blood typing or genetic testing proved too
great of a burden, and often led to denials of paternity and mud-slinging allegations of the mother’s
promiscuity (Hemholz, 1977). Famously sordid trials no doubt had a chilling effect on women who
wished to bring action against their child’s father but feared having their reputation slandered in
open court. In practice, paternity establishment was revolutionized by late-20th century developments in technologies that assist in identifying, or ruling out, a potential father (U.S. Department
of Health and Human Services, 2002).
For divorced couples – that is, cases in which paternity is not legally in doubt – child support
orders have been a component of alimony since well before the 1975 federal law (Bromley, 1971),
although data on the frequency of payments or compliance with these orders prior to the creation
of the OCSE are difficult to find.
Once paternity is established, the next stage of the child support process is to obtain a child
support order. The process for obtaining a child support order has been transformed and streamlined since 1975. If the mother is a recipient of public aid (IV-D cases), the IV-D agency will
initiate child support proceedings against the person alleged to be the father, beginning with paternity establishment and through securing a child support order. In public aid cases there are
administrative determinations that can circumvent even having to get a court involved. A mother
who is not a recipient of public aid has to bring a child support action to court herself, beginning
with a paternity action and followed by a petition for child support. The child support order itself
specifies the monthly child support amount, after consideration of the father’s income sources and
the state guidelines for child support payments. Most states have an “income shares” model in
6
place, which takes into account the incomes of both parents, in order to more accurately reflect
the standard of living of the child and the percent of responsibility each parent has traditionally
held. The child support order will also specify the method of payment, which now may include
wage garnishment or automatic withholding from public assistance such as unemployment benefits,
Social Security Income, or tax returns.
2.1
Child support enforcement data
Child support laws can be broadly classified into four types: those that promote or require higher
rates of paternity establishment, those that increase the ease with which non-custodial parents can
be tracked, those that change the financial penalties or even jail time faced by non-custodial parents
who fail to meet their child support obligations, and those that reform the technology or method
of payment of child support, such as income withholding provisions.
In this paper I rely on two state-year datasets of child support enforcement. The first is used
by Plotnick et al. (2007) and Case (1998), which is a database of child support legal enactments,
from 1976-1992, classified by type. (For the remainder of the paper I refer to this data as the CaseMcLanahan data.) I construct a state-year legislative index, denoted CS st , which is an average of
9 indicator variables, each of which represents a different child support law and takes a value of 1
if the associated law is in effect in that state and year. Hence, the index is a continuous variable
ranging from 0 to 1, where 0 reflects that the state has none of the 9 laws in effect and 1 reflects
that the state has all 9 laws in effect. By using this index in the empirical analysis that follows, I
implicitly assume each law has the same marginal effect, even though there might be substantial
heterogeneity in their impact.
The legislative index includes laws at each stage of the child support enforcement process,
and, to enumerate these laws they are: a law requiring immediate income withholding for new or
modified child support cases, deducting child support obligations from the obligor’s paycheck; a law
allowing the custodial parent to place a lien on the non-custodial parent’s property; a law permitting
genetic tests to be used to resolve disputed cases; a law allowing paternity to be established while
the child is below 18 years of age; a law requiring the provision of local child support collection and
enforcement services to non-recipients of AFDC; a law requiring withholding of arrearages from
parents who are delinquent on their payment; a law creating criminal penalties for failure to pay
child support; a law establishing the right to bring a child support action against a parent residing
in another state; a law creating a central registry for child support payments.
Figure 3 plots the mean adoption rate across states of each of the 9 different child support
statutes used in the analysis. The figure shows a dramatic increase in adoption of statutes, and
considerable variation in the timing and abruptness of enactments across states. While incremental
changes to child support collection and enforcement have taken place since the 1970s, with the
gradual trend being toward greater enforcement and stronger measures to promote collection, certain federal laws brought abrupt changes, which can account for the dramatic rise in certain types
of laws. For example, in 1984, Congress enacted Public Law 98-378, which required states to imple7
ment income withholding procedures for parents delinquent on payments, and hence in Figure 3 we
see a big jump in state laws withholding for delinquency between 1984 and 1985.5 Similarly, Public
Law 100-485, was enacted in October of 1988 and implemented income withholding procedures that
would take effect immediately, unless the parties were able to come to an alternate arrangement;
Figure 3 shows a spike in state laws introducing immediate withholding between 1988 and 1990.
The second state-year dataset is the log average expenditures on child support enforcement
per single mother family, which comes from the annual reports of the Office of Child Support
Enforcement (OCSE), 1977-2009. This data was used in Freeman and Waldfogel (2001) and, as
of this writing, is available through the NBER website as “Work-Family Policies and Other Data.”
Trends in log expenditures are illustrated in the right panel of Figure 3. The figure shows that mean
child support enforcement expenditures roughly tripled over the period 1980 to 2000: the median
state spent approximately $200 per single mother family on enforcement in 1980 and increased it
to approximately $600 per single mother family in 2000 (both numbers in constant 2000 USD).
3
A marriage model with child support
The model presented here shows how a child support policy affects both marriage and fertility. The
main result is that child support eliminates the lowest quality marriages that would form absent
the policy, by introducing a contract that grants fathers limited custodial rights in exchange for
a transfer. Child support also affects contraceptive use; men who dislike children take action to
reduce the probability of an unwanted birth when it becomes more costly. A child support policy
puts downward pressure on total out of wedlock births because men who are least likely to marry
following a pregnancy increase their contraceptive use the most. However, the fraction of births
that are out of wedlock may increase because those parents who want children are less likely to
marry following a pregnancy.
The model presented here builds on earlier models of child support in Aizer and McLanahan
(2006) and Rossin-Slater (2013). The approach taken here differs in that both marriage and fertility
are endogenously determined, permitting child support to affect both pregnancy rates and marital
choices conditional on pregnancy. The model more closely resembles Chiappori and Oreffice (2008),
which considers the effect of contraceptive availability on intrahousehold allocations. The model
here differs in that marital matches are random, and fertility is endogenous.
3.1
The environment
There is a continuum of men and women of equal size who live for a single period and receive utility
from consumption, children, and companionship. At the beginning of the period men and women
are matched randomly into couples. All couples have premarital sex which can lead to a pregnancy,
5
Prior to this law, only Federal employees were subject to wage garnishment, which began in 1975. In 1981, the
IRS was authorized to withhold Federal income tax returns and States were mandated to withhold unemployment
benefits from absent parents delinquent in their child support payments.
8
but either partner can use contraceptives, denoted by ei , to reduce the likelihood. Denote the
probability of a pregnancy δ(eW , eM ).
At the end of the period two pieces of information are revealed: first, couples find out whether
there is a pregnancy; second, regardless of whether there is a pregnancy, they receive a marital
quality shock, denoted θ, which represents a match-specific companionship factor. I assume that θ
is random and independent across couples and has distribution F (θ) that is symmetric with mean
zero.6
Upon receiving these two pieces of information, couples decide their consumption and whether
to marry. Men earn wages wh . Women earn wh unless they become pregnant, in which case they
earn w` , assumed to be strictly less than wh . This assumption reflects the earnings losses due to
time away from work.
3.2
Preferences
Men have linear preferences over consumption and children. Their utility in marriage is given by
UM (aM , k) = aM + θ + v · k, where aM denotes male consumption of the private good, normalized
to have unit price; θ denotes the marital match quality; k is a dummy variable indicating the
presence of children; and v is the individual-specific preference parameter for children, assumed to
be distributed over a connected support [−V, V ]. Some males may derive a negative utility from
the presence of children; for the purposes of illustrating the model, I assume there is a positive mass
of males who enjoy children (v > 0) as well as a positive mass who derive disutility from children
(v < 0).
To sharpen the analysis, men are assumed to derive no utility from children outside a marriage.7
This assumption is intended to capture the lessened custodial rights of fathers outside of marriage,
but it may also reflect the father’s emotional distance from living away from the child (Browning
et al., 2014; Edlund, 2013; Chiappori and Oreffice, 2008). The utility of men when single is thus
written UM (aM , k) = aM .
Female utility takes the linear form U (aW , k) = aW + θ + u · k, where u is an individual-specific
taste for children distributed over the interval [−U, U ]. Like men, women receive the match quality
component θ only if they marry. Unlike men, however, women’s utility from children does not
depend on her marital status, reflecting her role as the default custodian of the child. Her utility
when single is written U (aW , k) = aW + u · k.
Taste for children is assumed to be perfectly observable to both partners. Note that the gains
from marriage are asymmetric in the presence of children: fathers gain custodial rights, while both
partners enjoy the match quality component θ.
Utility in this model is transferable; partners can reduce their private consumption to persuade
their partner to marry. Since the purpose of this model is to study marital formation and not
6
The mean-zero assumption is without loss of generality, but simplifies the exposition.
7
What is necessary for the results to hold is that outside of marriage v is diminished by some factor.
9
intrahousehold allocations, I assume the partners split evenly any surplus generated by marriage.8
3.3
Marriage equilibrium
Since utility is transferrable, we need only look at the total marital surplus to know the set of
marriages that form in equilibrium. The surplus of marriage relative to being single is given by
S(θ, v) = 2θ + v · k, which includes the match quality enjoyed by both partners and the male utility
from children, v, if there is a child. The surplus function is not a function of u because women
do not need to be married to enjoy children. Couples will marry if S(θ, v) ≥ 0, or, equivalently, if
θ ≥ − v·k
2 . The minimum match quality needed to marry depends on the event of a pregnancy: if
there is no pregnancy, couples will marry if θ ≥ 0, while if there is a pregnancy couples will marry
if θ ≥ − v2 .
In couples whose male enjoys children (v > 0), there is a set of θ ∈ [− v2 , 0] who will marry in the
event of a pregnancy who would not otherwise: these are shotgun marriages. Shotgun marriages
have low match quality compared to non-shotgun marriages that have θ ≥ 0. Shotgun marriages
form because the utility gains from having children within marriage offset the losses of a poor
match.
There are no shotgun marriages if the male gets disutility from children (v < 0) because there are
no utility gains to having children within marriage; in fact, there are utility losses. Put differently,
no couples with v < 0 will marry who will not in the absence of children.9
To determine consumption levels we must determine the willingness of each partner to make
transfers to marry. Let τM be the man’s maximum willingness to pay to enter a marriage, and τW
be the minimum transfer a woman is willing to accept in order to marry. There is no restriction
on the sign of τM or τW , which may be positive or negative depending on the male or female’s
willingness to marry.
The male’s willingness to pay is pinned down by his indifference between marriage and remaining
single, given by τM = θ + v · k, and is increasing in match quality θ and his taste for children v.
Similarly, the woman’s willingness to accept a transfer is given by τW = −θ, decreasing in θ because
she requires less persuasion to marry when she is in a good match. The equilibrium in the marriage
market is depicted in Figure 1.
Since the gains to marriage are split evenly, the equilibrium transfer is given by the midpoint
between τM and τW , which is
w` · (1 − k) + (wh + u +
v
2)
v·k
2 .
Utility in marriage for the woman is thus given by U (aW , k) =
· k + θ, and for the man, UM (aM , k) = wh + θ +
v
2
· k. If the couple
chooses not to marry, the woman receives utility U (aW , k) = w` + u · k, while the man receives
utility UM (aM , k) = wh .
8
This assumption does not change the match quality nor the set of marriages that form. It does mean, however,
that this model is ill-suited to study important questions such as the effect of child support laws on intrahousehold
allocations. I leave these questions for future study.
9
For these couples there will be a set of couples [0, v2 ] who would have gotten married had it not been for the
pregnancy. These couples would rather remain single than face the utility losses of establishing parenthood with a
dad who dislikes children.
10
Figure 1: Marriage equilibrium
The figure illustrates the supply and demand for marriages in period 2, for a couple in which the man enjoys
children (v > 0). The lowest quality marriages, between [− v2 , 0], only form because of the pregnancy and
hence are labelled shotgun marriages.
3.4
Contraceptive use
Both men and women can purchase a positive amount of contraceptives at unit cost pe . This cost
can be interpreted either as a pecuniary or non-pecuniary cost, and may include the effort from
visiting a pharmacy or from remembering to take the pill or to use a condom. Contraceptive use e
affects the probability of a pregnancy, δ(eW , eM ), assumed to be decreasing in each argument and
convex, so that the marginal product of contraceptives is decreasing in contraceptive use. I also
assume eM and eW are imperfect substitutes. The equilibrium concept used here is Nash, so that
each partner takes the other’s choice of contraceptive use as given when deciding her own level.
When choosing the optimal level of e, the woman must weigh the expected utility gains of having
a child, which includes the direct gain u as well as the gains from marriage (i.e. extracting part of
the surplus generated by having children in marriage), against the cost, which includes her reduced
wages and the price of contraceptives. The female’s decision is given by the following maximization
problem:
max −pe eW + δ(eW , eM )[w` + u + π1 θ1 ] + (1 − δ(eW , eM ))[wh + π0 θ0 ]
{ef }
(3.1)
In Equation 3.1 I use the following notation to simplify the expression: π1 = 1 − F (− v2 ), which
is the probability of drawing a θ high enough to generate a marriage when there is a pregnancy;
θ1 = E[θ + v2 |θ ≥ − v2 ], which is her expected share of the marital surplus conditional on a marriage
11
when there is a pregnancy. Similarly, π0 = 1 − F (0), the probability of marriage when there is no
pregnancy, and θ0 = E[θ|θ ≥ 0], her expected gain from marriage when there is no pregnancy.
The benefits of using contraceptives are higher when the wage losses from pregnancy (wh − w` )
are large, when women have a negative taste for children (u < 0), and when the utility gains from
marriage with children, v, are lower.
The man’s problem is similar:
max wh − pe eM + δ(eW , eM )π1 θ1 + (1 − δ(eW , eM ))π0 θ0
{ef }
Proposition 1. (a) Only males with v ∈ [−V, −¯
v ] use contraceptives, where −¯
v < 0; contraceptive
use is decreasing in v over this range. (b) Female contraceptive use is strictly decreasing in her
partner’s taste for children, v. (c) If either partner uses contraceptives in their relationship, the
female partner will use strictly more iff wh − w` > u.
Proof. See Appendix I.1.
The intuition for Proposition 1(a) is straightforward. Men who dislike children are unlikely to
draw a θ high enough to marry if their partner gets pregnant. In order to increase the chance of
enjoying the benefits of marriage without children, they prefer to use contraceptives.
Proposition 1(b) reflects the fact that women enjoy a larger surplus from marriage the larger is
their partner’s v; in addition, the likelihood of drawing a θ high enough to marry and enjoying the
larger surplus is also increasing in v. Hence, the greater is their partner’s taste for children, the
more women will want to have children. Proposition 1(c) reflects the fact that if the wage losses
from the pregnancy exceed her utility gain from a child, she will use more contraceptives than her
male partner. This result holds regardless of her partner’s v.
Note there is an externality in contraceptive use: a male who uses contraceptives will affect the
probability that a woman gets pregnant, while a woman who uses contraceptives will affect the
probability that a man fathers a child. This externality, along with an additional assumption that
male and female contraceptives are substitutes, leads to underutilization and a greater number of
total births than a social planner would choose.
3.5
Child support: marriage and fertility
Consider a child support policy that affects couples who choose not to marry. Specifically, the law
requires a fixed transfer amount τ ` to the mother from the non-custodial father in exchange for
custodial rights.10 The increased custodial rights are modeled as a term α` v in the father’s utility
in the case of non-marriage, where 0 < α` < 1, to reflect the fact that fathers gain legal rights as
10
As can be seen from Figure 4, even though child support laws have strengthened considerably, enforcement is
still less than perfect. In this model I assume all fathers must pay child support if the couple does not marry, but
the implications of the model are the same if we instead assume an exogenous fraction ζ of fathers are caught by
enforcement are forced to comply with the law.
12
the established father.11 Since some fathers have negative v, they may suffer utility losses from this
increased relationship.
The main objective of the model is to understand how such a policy affects the range of θs for
which marriages form, and equilibrium fertility rates δ(eW , eM ).
Let us return to the marriage market equilibrium. Male utility outside of marriage is now given
by UM (aM , k) = aM +(α` v−τ ` )·k, while for women it is given by U (aW , k) = aW +(u+τ ` )·k. Total
marital surplus is now S cs (θ, v) = 2θ + (1 − α` )v · k, and hence couples will marry if θ ≥ − (1−α)v
.
2
∗ = − (1−α)v , below which
The child support equilibrium has a new threshold match quality, θcs
2
marriages will not form, and this equilibrium match quality is defined by the intersection of the
new supply and demand curves, illustrated in Figure 2. Thus we have the following result.
Proposition 2. Shotgun marriages decline and match quality of shotgun marriages increases relative to non-shotgun marriages with children.
Proof. See Appendix I.2.
The intuition is simple. Shotgun marriages occur only for couples with v > 0. Mothers gain a
fixed transfer τ ` by not marrying; hence the minimum transfer they require to accept a marriage
shifts up by exactly τ ` . Fathers have to pay the transfer τ ` outside of marriage, hence their
willingness to pay curve shifts up. But it shifts up less than the full amount τ ` because of α` , the
increase in custodial rights outside of marriage.
It is important to emphasize that the custodial rights term, represented by α` , is the key driver
of Proposition 2. By contrast, the size of the child support payment τ ` is irrelevant for the marriage
decision. The size of the child support payment τ ` is irrelevant because couples decide to marry
based on the total marital surplus; the size of τ ` does not matter for the total surplus because it
is a transfer from the male to the female and contributes zero in net. This point is important for
understanding whether the large amount of delinquency in child support payments is relevant for
the child support effect on marriage to operate. Proposition 2 shows that it is not: a father failing
to pay all or part of τ ` will not impact the marriage decision, as long as the α` is granted.12 The
size of the transfer τ ` and the father’s compliance is important for the mother’s welfare, however.
A second point of emphasis is that child support is welfare-enhancing for the marginal women
who no longer marry. This is in contrast to the shotgun marriage model of Akerlof et al. (1996), in
which a decline in shotgun marriages is welfare-diminishing for these marginal women. The decline
in shotgun marriages in the Akerlof et al. (1996) model arises as a result of a new technology,
contraceptives and abortion, which is adopted by an exogenous fraction of women. The adoption of
this technology by a large enough fraction of women will induce the shotgun marriage equilibrium
11
This assumption reflects that prior to child support, if the father was not married to the mother he had no
presumption of paternity by the state, and hence no rights or obligations to the child. This modeling assumption has
been used in theoretical models of marriage including Rossin-Slater (2013); Edlund (2013); Chiappori and Oreffice
(2008).
12
Paternity establishment is a prerequisite for a court to order child support payments. Hence the α` must be in
effect before the transfer τ ` is, or is not, made.
13
Figure 2: Child support
The figure illustrates how child support changes the supply and demand for marriages (for the case with
v > 0). Child support eliminates the lowest quality (shotgun) marriages.
to switch to a second equilibrium in which men no longer have to promise to marry as a means for
obtaining premarital sex. The exogenous fraction of women who fail to adopt the new technology
are worse off because they can no longer extract a shotgun marriage promise, and no longer marry.
In the model presented here, by contrast, marriages are facilitated by transfers that are determined
endogenously. The marginal women here are better off because they no longer marry men they
have poor match quality with, and they get additional transfers from these men by not marrying
them.13
The woman’s contraceptive use decision under child support is based on the following maximization problem.
13
In the model presented here, men do not willingly make transfers if they decide not to marry. A simple extension
would allow for investments in children, in which case men may make transfers outside of marriage to increase the
mother’s investments in the child (see, e.g., the model of Willis, 1999). Child support transfers may crowd out these
private transfers, as found empirically in Lerman and Sorensen (2001).
14
max −pe eW + δ(eW , eM )[w` + u + π1 θ1 + (1 − π1 )τ ` ] + (1 − δ(eW , eM ))[wh + π0 θ0 ]
{ef }
(3.2)
The only difference from Equation 3.1 is the positive term (1−π1 )τ ` , the transfer she will receive
if she and the father choose not to marry, which makes having a child relatively more attractive.
Women will choose an equilibrium level of ef weakly less than prior to child support.
The man’s decision problem under child support is the following.
max wh − pe eM + δ(eW , eM )[π1 θ1 + (1 − π1 )(α` v − τ ` )] + (1 − δ(eW , eM ))π0 θ0
{ef }
The second term in brackets, (1 − π1 )(α` v − τ ` ), reflects the custodial rights transfer if the
couple does not marry. This term is positive if v >
τ`
α`
and negative otherwise. Men with a high
taste for children will desire them more under child support because now they can even enjoy them
outside of marriage. Men with v <
τ`
,
α`
however, desire them less.
Proposition 3. (a) Following the adoption of a child support law, more men use contraceptives,
and men who used contraceptives prior to the law use a strictly greater amount. (b) Child support
leads to weakly fewer births in couples with a male who has v ∈ [−V, −¯
v ]. (c) Child support leads
to weakly more births for couples with v >
τ`
.
α`
Proof. See Appendix I.3.
The intuition for Proposition 3 is that child support has a higher cost for men the higher is their
distaste for children. The reason is that child support forces them to have a legal relationship with
their child, represented by the term α` v, which is more costly for more negative v. Proposition 3(b)
establishes that the effect of child support on men’s contraceptive use is stronger than the effect on
women’s, for a range of negative v. In this range total births decline. The reason is that males with
negative taste for children pay the price of interacting with their child in addition to the transfer
that affects both partners.
Proposition 3(b) also makes clear that child support laws have the potential to affect unwanted
births: they reduce both the number and fraction of births that are unwanted to the male.
Discussion: out of wedlock births
Of considerable interest to policymakers is what happens to total births out of wedlock, and to the
fraction of all births that are out of wedlock.
There are several forces acting on birth rates. First, men with sufficient distaste for children
have fewer children. These men are least likely to marry following a pregnancy (because they
require a high θ to marry) putting downward pressure on total out of wedlock births. Second, men
with sufficient taste for children have more children, putting upward pressure on all births, but
especially in-wedlock births.
15
Because fewer births occur to men with low v (unlikely to marry) and more births occur to men
with high v (likely to marry), there is downward pressure on the out of wedlock fraction. However,
because the marriage decision is affected as well – couples are less likely to marry conditional on
an out of wedlock pregnancy – there is upward pressure on the fraction of births that are out of
wedlock.
More sharply drawn conclusions about total births and the out of wedlock fraction require
further assumptions about the distribution of v, the properties of δ(·), and the cost of contraceptives
relative to the wage losses to the woman. A special case of interest occurs when v > 0 for all men,
that is, if no man bears a cost of interacting with his child. In this case the out of wedlock fraction
will unambiguously rise.
To provide some empirical context for the discussion, Figure 7 plots birth rates to married and
unmarried couples between 1970 and 2000, as well as the fraction out of wedlock. The striking and
well-documented increase in the out of wedlock fraction over this period has been accompanied by
relatively flat trends in total births, both for married and unmarried couples. The rise in out of
wedlock births appears to reflect a transformation in the marital decision of parents, rather than a
change in total fertility among married versus non-married couples.
In any policy discussion it is critical to distinguish between the policy’s effect on pregnancy, and
its effect on marriage conditional on pregnancy. The model above shows that a child support law
has ambiguous predictions for total fertility – some couples are more likely to have children while
others are less likely – but unambiguous predictions for shotgun marriages: marriage conditional
on pregnancy goes down.
Discussion: contracting over α
The result that child support laws cause poor match quality couples to decide to remain single
in the event of a pregnancy hinges on the assumption that parents cannot bargain over custodial
rights. It is important to consider whether such an assumption is a reasonable one.
Previous authors have argued that parents cannot bargain over custodial rights because such
transactions amount to contracting over children and such promises will not be enforceable in a court
of law (Edlund, 2013). Perhaps more important is that private individuals lack the technology of
enforcement available to the state; for example, the ability to track the non-custodial parent across
state lines, or to garnish wages. In the context of the model, we can think of the technology of
enforcement as any technology that facilitates the exchange of custodial rights α for the transfer
τ `.
In addition to any legal or technological barriers to enforcing private contracts, there is an
economic argument why such private contracts may break down. The key distinction between a
private contract and a marriage contract is that an individual can only have one marital contract
at a time. By contrast, a woman could conceivably have many private contracts with several men
at a time. In the absence of child support, the only assurance the male has that he is the sole male
custodial rights-holder is if the child is born within marriage. Under child support, this changes:
16
there is only one legally established father and these rights and obligations are enforced outside of
marriage.
Discussion: divorce
The model above does not explicitly include a divorce decision. A trivial extension would add a
second time period, with a match quality shock that is correlated with the couple’s first period
match quality; for example, θ˜ = θ + ξ. The divorce decision would be determined by where θ˜
lies relative to the marriage threshold. One clear implication is that as long as match quality is
positively correlated over time, couples with a higher match quality in period 1 will be less likely
to divorce in period 2. Based on this observation, the empirical analysis of this paper uses divorce
probability as a reasonable proxy for θ.
Child support laws, by affecting selection into marriage, will have an affect on divorce. An
equally important question is whether a child support law affects the divorce decision for alreadymarried couples. The answer hinges on whether α` , the custodial rights the father would receive
upon divorce, changes as a result of the child support law. Note that paternity is presumed for
couples who have children within wedlock, and hence child support laws may not necessarily increase
a divorced man’s custodial rights, as it would for a never-married man. A change in the transfer
amount, τ ` , or the probability of collecting τ ` through better enforcement technology, would not
affect affect the divorce decision conditional on marriage because the total marital surplus would
remain unchanged.
4
Empirical trends in shotgun marriages
In this section I explore empirical trends in shotgun marriages to lend support to the model and to
highlight aggregate empirical patterns. I stress at the outset that the tables and figures presented
in this section do not establish a causal link to child support laws, which is the focus of Section 5.
The model has empirical predictions for shotgun marriages that are directly testable in the
data. First, shotgun marriages have lower match quality on average than other marriages. Second,
after the advent of child support legislation, shotgun marriages decline and the match quality of
shotgun marriages relative to other marriages increases.
To investigate these empirical trends in marriage, I use two data sources. The first is the
Survey of Income and Program Participation (SIPP), from 1991, 1992, 1993 and 1996, which has
marital and fertility histories in Topic Module 2. The second is the National Survey of Families and
Households (NSFH), Wave 1, which also includes marriage and fertility histories, with surveys of
respondents in 1987-88. SIPP has the advantage of a much larger sample size and more recent data,
while the NSFH has the advantage of including self-reported measures of marital happiness and
stability, which I use to measure match quality. I measure match quality in the SIPP using divorce
hazard rates over 3-year, 5-year, and any-year time horizons, which is possible because SIPP asks
respondents the year, if any, their marriage was terminated in a divorce.
17
I restrict the analysis of shotgun marriages to first marriages and first births. Both SIPP and
NSFH data have the month and year of first marriages and first births.14 I use these dates to define
shotgun marriages as a marriage occurring between 0 months and 8 months prior to the birth.15
It is important to note that while the model precisely defines a shotgun marriage as a marriage
that would not have occurred had it not been for the pregnancy, empirically it is a challenge to
construct a corresponding measure that is equivalent to this definition. The empirical measure I
adopt is inexact for two reasons: it is possible that some marriages occurring between month 0
and month 8 prior to the birth would have occurred anyway, in absence of the child; similarly, it
is plausible that many marriages that occur prior to the pregnancy only occur for the purposes of
having a child within wedlock and would not have occurred otherwise.
Figure 6 shows the trend in the shotgun marriage rate in the U.S., using data from SIPP. The
shotgun marriage rate is defined as the fraction of out of wedlock pregnancies that are resolved in
a marriage before birth. The shotgun marriage rate in year t is constructed as the fraction of out
of wedlock (first) pregnancies in year t that have a marriage between 0 months and 8 months prior
to the birth. Figure 6 plots a three-year moving average of the shotgun marriage rate.
In 1960 about 60 percent of out of wedlock pregnancies were resolved in a marriage before
birth, declining to roughly 20 percent in 1995. The decline in shotgun marriages presented here
is consistent with the evidence in Akerlof et al. (1996) and complements the empirical finding in
the sociology literature that since the 1970s, out of wedlock pregnancies are far more likely to be
resolved in cohabitation rather than marriage (Lichter et al., 2014).
It is important to stress that the decline in shotgun marriages preceded the strengthening of child
support laws by 5-10 years, thus the decline cannot be explained completely by the advent of child
support laws. Child support represents but one important factor in the marriage decision, of which
there are likely to be multiple. Moreover, child support was introduced in part as a response to
the increase in the number of single-mother families on welfare. It may have succeeded in reducing
welfare receipt among these women (Huang et al., 2004), but, based on the evidence that will
be presented in Section 5, this paper argues that child support had the unintended consequence of
actually increasing the number of single-mother families, through its effect on the marriage decision.
Figure 6 also plots the fraction of total first marriages in year t that are shotgun marriages,
showing a decline throughout 1960-1995 period, from about 9 percent to about 4 percent.
14
I use SIPP from 1991-1996 and not other years because in other years the months of first birth and first marriage
are suppressed for confidentiality purposes. In the 1996 SIPP, of 26,370 mothers 79.5% report their first child’s month
and year of birth, while in the 1993 SIPP, of 14,708 mothers the corresponding number is 40.5%. (The 1992 and
1991 SIPP are similar to 1993 in the fraction missing.) Table 13 explores the missing data problem, revealing that
certain subpopulations are more likely to have non-missing dates, including higher educated respondents, married
respondents, and older respondents.
15
Neither SIPP nor NSFH includes data on miscarriages or abortions. I therefore restrict the analysis to the first
live birth reported by the respondent.
18
4.1
Shotgun marriage quality
Now I turn to evidence that shotgun marriages are lower quality than all other marriages, and show
that their quality relative to other marriages has been increasing over time. I measure marriage
quality in two ways. The first measure uses self-reports of marital stability and happiness from the
NSFH, and the second uses divorce hazard rates constructed from SIPP.
The NSFH asks about marital happiness and stability at the time of the interview (1987-1988).
I follow the work of Bertrand et al. (2013) and define three marital quality variables based on three
survey questions in the NSFH data. The first question asks “Taking things all together, how would
you describe your marriage?” Respondents can choose answers from a scale of 1 (very unhappy)
to 7 (very happy). I define a binary variable “very happy” as answering 7 to this question.16 The
second question asks if, during the past year, either the husband or wife has discussed the idea of
separating. I define “discuss separation” as a binary variable taking the value of 1 if the respondent
answers yes that either partner has discussed separation. The third question asks about trouble
in the marriage: “During the past year, have you ever thought that your marriage might be in
trouble?” and I define a variable “marriage trouble” equal to 1 if the respondent answers yes.
Since I only observe marital stability variables for still-existing marriages, there is a selection
bias because the lowest quality marriages will not be in the sample. Hence I impute values for
marriages that ended in separation or divorce: I code “very happy” equal to 0, “discuss separation”
equal to 1, and “marriage trouble” for these marriages.17 Using the imputed data, 34 percent
of respondents report their marriage as “very happy”; 46 percent of the sample answers yes to
discussing separation with their spouse; and 28 percent of the sample reports that in the past year
they thought their marriage might be in trouble.
In the regressions that follow, I include only one respondent per household. The NSFH selects
one adult per household as the primary respondent, which is chosen at random at the time of
sampling. I restrict the sample to primary respondents who are either married, separated, or
divorced, and aged 18 or over at the time of the survey. I then estimate the following regression
0
qit = β0 + β1 shotgunit + γ xit + it
(4.1)
The dependent variable qit represents marital quality using one of the measures discussed above.
The shotgunit variable indicates if the marriage was a shotgun marriage. The vector of controls xit
includes dummies for the year of marriage, gender, race, completed years of schooling, number of
children, and census region (geographic identifiers finer than census region are suppressed by the
NSFH for confidentiality purposes). The vector xit also includes a variable for household income
and respondent’s age at the time of the interview. Note that because the shotgunit variable is
an imperfect empirical approximation to the theoretical definition given within the model, there is
16
About 46 percent of survey respondents answer “very happy” and hence this represents a natural division of
responses into a binary variable; the results are not sensitive to this choice of definition.
17
I report estimates without imputation as well, i.e. using the selected sample of marriages that remain as of the
NSFH survey date. (See Table 2.)
19
potential for measurement error to attenuate the estimate of β1 .
Table 1 reports estimates of estimation of Equation 4.1 using NSFH data. First marriages
that are shotgun marriages are 7.2 percent less likely to be reported by the respondents as “very
happy”. In addition, shotgun marriage respondents are 6.2 percent more likely to discuss the idea
of separating with their partner, and 4.2 percent more likely to report having thought the marriage
might be in trouble in the last year. I estimate Equation 4.1 using only the selected sample of
marriages that remain intact as of the time of sampling (i.e. without any imputation for divorced
couples), and report the results in Table 2. The results are similar: shotgun-married couples are
less likely to report being very happy, more likely to discuss separation, and more likely to report
their marriage being in trouble.
Table 3 reports the results from estimating Equation 4.1 using SIPP and the divorce hazard as
the dependent variable. The 3-year divorce hazard is defined as a binary variable taking a value of
1 if the respondent was divorced within 3 years of her first marriage. The 5-year hazard is defined
similarly for the 5-year period. The divorce (any) variable takes a value of 1 if the respondent and
her first spouse divorced at all. Table 3 shows that there is no significant increase in the probability
of divorce within the first three years of marriage for a shotgun marriage relative to a non-shotgun
marriage. However, there is a 1.6 to 1.7 percent increase in the probability of divorce within the
first 5 years (off of a baseline of 10 percent), and a 3.4 to 3.6 percent increase in the probability
of divorce over the lifetime (off of a baseline of 28 percent), for shotgun marriages compared to
non-shotgun marriages.
Table 4 reports estimates of the same regression but now including dummies for the decade of
marriage – 1970s, 1980s, and 1990s (where marriages in the 1960s are the omitted category) – and
interactions between decade of marriage and the shotgun marriage indicator. The results show that
there has been a steady decline in divorce probability in each decade relative to the 1960s. The
table also shows that shotgun marriages in the 1990s were significantly less likely to end in divorce
compared to shotgun marriages in earlier decades. Note the large and negative coefficients on the
1990s marriage indicator. This is in part a mechanical effect: all women in the SIPP sample are
asked for retrospective marital histories at the time of the survey, and hence, a 1990s marriage has
had only a few years in which it could have ended in divorce before the data collection, compared
to marriages in earlier decades.
The empirical trend that more recent shotgun marriages are less likely to divorce compared to
other marriages is anticipated by the model: following child support enforcement, shotgun marriages
are less likely to form, and the marital quality of shotgun marriages that do form increases.
I turn now to estimating the direct effect of child support laws on marriage, fertility, and
divorce.
20
5
Regression framework: the direct effect of child support enforcement
I use child support enforcement data from two sources: the Case-McLanahan child support statute
data, and the Freeman and Waldfogel (2001) NBER Work-Family child support enforcement expenditure data. The key empirical specification uses variation within state-year cells to estimate
the effect of child support enforcement on marital formation, marital dissolution, and fertility.
5.1
First stage: child support income
Over the period 1976-1992, there was striking growth in child support enactments across states,
as illustrated by Figure 3. There was also a nearly three-fold increase in OCSE expenditures on
child support enforcement. Before examining the effect of these changes on marriage and fertility,
I provide first-stage evidence that increases in enforcement actually led to greater child support
income receipt of mothers.
Figure 4 presents preliminary evidence that child support income receipt has increased substantially over this period. This figure plots the fraction of never-married mothers who report receiving
any child support income in the March CPS, 1968-2013.
To consider the direct effect of state child support enactments on child support income receipt,
I adopt a regression framework using the March CPS. I restrict the sample to the population of
never-married mothers who report having a custodial child in the household under 18 years of age,
and who also report the father living outside the household.
Each mother in the CPS is matched with the child support regime in place in her state of
residence s, in the year of her child’s birth, t − a, where t is the survey year and a is the age of
her youngest child. The state of residence at the time of the survey is assumed to be the state
of residence at the time of the youngest child’s birth. Let CS st−a represent a child support law
index representing the strength of the child support regime in place at time t − a.18 CS s,t−a is a
continuous variable ranging from 0 to 1, where 0 indicates state s has none of the child support
laws in place at time t − a, and 1 indicates state s has all laws in place at time t − a. Let Incist be
an indicator taking a value of 1 if person i receives any child support income in year t.
0
Incist = β0 + β1 CS s,t−a + γ xist + ist
(5.1)
where xist is a vector of individual controls, including age, age-squared, age at the time of first
birth, race indicators, dummies for the four education categories, and state-year fixed effects. The
variable ist is an error term representing the unobserved determinants of child support receipt.
In this regression we expect the sign of β1 to be positive, indicating that the adoption of a child
support law has a positive effect on the fraction of women reporting child support income receipt.
18
I use child support laws in place at time t − a rather than those in place at time t because child support orders
are infrequently renegotiated, and there may be selective renegotiation in that mothers most likely to benefit from
renegotiation are those likeliest to do so.
21
Table 5 indicates that this is indeed the case. Since the child support index is constructed with
9 laws, we can interpret the coefficient as representing the effect of moving from a regime with
none of the laws in place to all 9 laws, on the probability of receiving child support income. Here
these laws increase the probability of child support receipt by 5.2 percent, in the specification with
state and year fixed effects (column 3). Given that the total fraction of the sample receiving child
support is under 25 percent, the magnitude of the laws’ cumulative effect is quite large.
We might be concerned that states that adopt stronger child support laws have a population
of individuals more likely to comply with such laws; in this case β1 may reflect state-year specific
attitudes toward the legal system or child support laws rather than the effect of the laws per se.
Because there is variation within state-year cells in the age of the youngest child it is possible to
include state-year (s × t) fixed effects, hence controlling for state-year attitudes that might lead to
greater compliance. These estimates are reported in column (4) of Table 5, revealing a coefficient
of .052 on the child support index. The inclusion of state-year fixed effects means the identifying
variation is variation in laws at the time of birth of the youngest child, within a state-year cell, and
the result is qualitatively similar.
Other coefficients may be of interest as well. From Table 5 we see that older, higher educated,
and non-minority mothers are more likely to report having received child support income.
Table 6 reports a similar regression using the OCSE data on child support enforcement expenditures, a regression that was also reported in Freeman and Waldfogel (2001) but over a smaller
sample period. In the specification with state and year fixed effects, the results show that a one
percent increase in average enforcement expenditures per single mother family corresponds to a
2.0% increase in the probability of a mother receiving any child support income.
5.2
Marriage
Because SIPP contains retrospective marital and fertility histories, we can construct an individuallevel panel data set, which we can use to identify the effect of child support laws on the probability
of never-married individuals getting married.
In each year I define an age cohort of women between 18 and 40, a range chosen so that these
women are old enough to make their marital choices without parental consent, and young enough to
be likely to marry or become pregnant for the first time. Restricting the sample to this population,
I run the following regression:
0
marry1stist = β0 + β1 owpregist + β2 owpregist × CS st + γ xist + ist
(5.2)
The variable owpregist is an indicator for never-married woman i becoming pregnant for the
first time in year t. The variable marry1stist is an indicator for person i becoming married for
the first time in either year t or year t + 1. The variable CS st represents the child support enforcement measure for state s in year t.19 The vector of individual controls xist includes a high
19
The respondent’s state of residence at the time of the survey is assumed to be her state of residence in each year
22
school completion dummy, race dummies, age dummies, and SIPP survey year dummies. I omit
higher education categories from the regression controls because the decision to get married may
affect educational attainment, and their inclusion would hence introduce a simultaneity bias. The
preferred specification includes interacted state-year fixed effects, although I also present the results
from a regression that includes state and year fixed effects separately, with additional state-year
controls.
The coefficient β1 in Equation 5.2 represents the effect of having an out of wedlock pregnancy
in year t on the individual’s decision to get married in year t or t + 1, compared to those who do
not have an out of wedlock pregnancy in t. The coefficient of interest is β2 , which represents the
differential effect of child support enforcement on marriage for those single women who become
pregnant, compared to those who do not.
The inclusion of interacted state-year fixed effects is critical because it does not require the usual
“common trends” assumption needed for a differences-in-differences regression. In the specification
with separate state and year fixed effects, the identifying assumption is that women in states affected
by a child support law would make the same marital decisions as women in states unaffected by the
law, if the law had not been implemented. This assumption is quite strong since common trends
in attitudes toward single-parenthood and child support enforcement may be jointly determined.
With state-year fixed effects, the identification compares women who become pregnant to those
who do not within state-year cells; these women are therefore exposed to the same statewide legal
regime and the same state-year attitudes about single parenthood. Any state-level time trends in
attitudes toward fertility, marriage, or child support enforcement will be absorbed in the interacted
fixed effect.
Of course, pregnancy is a choice, and the selection concern that arises from this observation
requires careful consideration. I defer this discussion until Section 5.4, after presenting estimates
of the direct effect of child support enforcement on fertility. For now, it is worth emphasizing
that in order to give the estimates of Equation 5.2 a causal interpretation, we must assume that
child support laws do not cause differential selection into pregnancy based on propensity to marry.
In the context of the model, there is differential selection based on propensity to marry, but the
selection works against finding a negative coefficient β2 : men who are least likely to marry decrease
their fertility the most, implying that selection would make child support appear to increase the
propensity to marry. To the extent that this effect is operating in the data, our estimate of β2
would underestimate the true effect of child support laws on marriage.
Table 7 reports the results from the estimation of Equation 5.2. Columns (1) and (2) report
estimates using state and year fixed effects separately; column (3) reports estimates using interacted
state-year fixed effects. The results are similar. The coefficient on the interaction term pregist ×CS st
is negative and significant, estimated at −6.7 percent, to −7.2 percent in the preferred specification.
This coefficient indicates that a person with a pregnancy in year t under a stricter child support
of the panel. This assumption requires there to be no migration by women who have an out of wedlock pregnancy to
states based on their child support regime.
23
regime is 7.2 percent less likely to marry than someone who does not become pregnant in the same
state-year cell, relative to zero child support enforcement.
This result confirms a key prediction of the model, which is that child support laws disproportionately affect the marriage decision of women who become pregnant out of wedlock compared to
those who do not. Column (4) restricts the sample to women who experience an out of wedlock
pregnancy. This column reflects that, of the population of women who experience an out of wedlock
pregnancy, those who become pregnant under a stricter child support regime are 8.4 percent less
likely to marry. Column (4) permits the following back-of-the-envelope calculation: moving from a
regime with 0 of the child support laws in place to one with all of them in place, leads to 8.6 percent
reduction in the shotgun marriage rate, out of the observed 20 point decline in the shotgun marriage
rate over the 1976-1992 sample period. This represents roughly 43%, a substantial fraction of the
decline.
The magnitude of the estimated effect may appear striking given that such a small percentage
of never-married mothers with children report the receipt of child support income, as is shown in
Figure 4. The model offers some guidance into this question: specifically, that the dollar amount of
the payments transfer is not what alters the marriage decision (i.e. the size of τ ` in the model), but
rather the establishment of paternity and the increase in custodial rights (i.e. the shift in α` ). If
paternity establishment rates for out of wedlock births increase, marriage decisions will be affected,
even if a large fraction of established fathers are delinquent on payments.20
Table 8 estimates the same regression, with state-year log average child support enforcement
expenditures per single mother replacing the child support law index on the right-hand side of
Equation 5.2. Following Aizer and McLanahan (2006) I use a three-year average of log expenditures
that includes years t, t − 1, and t − 2.21 The qualitative results are the same as those reported
in Table 8: an increase in child support enforcement expenditures has a negative effect on the
decision to get married, for pregnant women compared to non-pregnant women. An increase in
enforcement expenditures by 10 percent leads to a .35 percent decrease in the propensity to marry,
in the preferred specification with state-year fixed effects. Column (4) presents the effect of child
support enforcement on the sample of women with out of wedlock pregnancies. We can use this
column to extrapolate the effect of child support on shotgun marriages over the entire sample
period 1982-1996. Log enforcement expenditures increased by .754 over this period, and hence we
estimate the effect of child support enforcement over this period to account for a decline in shotgun
marriages of 2.6 percent (.035*.754*100) out of a total decline in the shotgun marriage rate of 14
percent over the sample period.
20
Paternity establishment has increased substantially over the sample period: in 1978, 111 thousand paternities
were established, increasing to 1.6 million in 1999 (U.S. House U.S. House of Representatives, 2014). The Family
Support Act of 1988 required 50% of children born out of wedlock and receiving cash benefits or IV-D child support
services to have paternity established, and this requirement has been incrementally increased to 90% as part of the
1996 welfare reform bill.
21
The results are not sensitive to the inclusion of 0, 1, or 2 lags, and results from these alternative specifications
are available upon request.
24
5.3
Fertility
Consider now the effect of child support on the probability of having an out of wedlock pregnancy.
Let owpregist denote an indicator for never-married individual i becoming pregnant for the first
time in time t. I estimate the following regression, on the population of never-married women:
0
owpreg ist = β0 + β1 CS st + γt xist + ist
(5.3)
In Equation 5.3, the coefficient of interest is β1 , which represents the effect of child support
enforcement on a pregnancy, for never-married women. Note that the coefficient β1 may capture
both a displacement effect (i.e. delaying children until the woman is older), or a reduction in total
births. Equation 5.3 is estimated with state and year fixed effects, and with controls for state-year
demographics and their interaction with year fixed effects, to control for state-specific trends that
may be correlated with the adoption of child support statutes.
Table 9 reports estimates using the child support index on the right hand side. The main
result is that child support laws have a negative effect on the probability of never-married women
becoming pregnant, but the effect is not statistically significant. Moving from a regime with 0
of the child support laws in place to one with all 9 decreases the probability of pregnancy by 0.6
percent. This result, while not significant, supports a finding in the literature that child support
laws reduce out of wedlock fertility (Plotnick et al., 2007; Case, 1998; Aizer and McLanahan, 2006).
Table 9 does not find heterogeneity by education, unlike Aizer and McLanahan (2006).
Table 10 estimates Equation 5.3 using log enforcement expenditures as the CS st variable. Here
we find that increasing child support enforcement leads to insignificant effects on fertility ranging
from 0 to 0.01 percent increase on fertility.
The small fertility effects estimated here may reflect the model’s ambiguous predictions for
fertility: while men who dislike children will father fewer of them, those who like children will
father more of them.
5.4
Selection
Let us now return to the discussion of selection into fertility raised in Section 5.2. To restate the
selection issue, it is plausible that child support only affects fertility and not marriage; under this
interpretation, the effects on marriage observed in Section 5.2 are because individuals who are most
affected in their fertility also happen to be the most likely to marry following a pregnancy. There
are two reasons why the selection story cannot account for the estimated effects on marriage.
First, it should be noted that the literature has found that young and low-educated men and
women reduce their fertility the most in response to child support legislation, while older and moreeducated individuals have little response (Aizer and McLanahan, 2006; Plotnick et al., 2007). But
older and higher educated men and women have far higher rates of shotgun marriage than younger
and less-educated, contradicting the selection story. The theoretical model in this paper supports
the prior literature: those who are least likely to marry reduce their fertility the most, and again,
25
suggests that the empirical effects estimated on marriage in Section 5.2 are a lower bound on its
true effect.
Second, the magnitudes of the response in fertility are far too small to explain the estimated
effects on marriage. A back-of-the-envelope calculation, with numbers chosen to be as generous as
possible to the selection story, illustrates the point. Suppose there are two groups, called “low” and
“high” educated for expositional purposes, each having 1/2 of total pregnancies. And suppose that
the high educated group decreases fertility by 0.6 percent once the full set of child support laws is
in place, while the low education group does not change their fertility at all. Suppose further that
the highest education category are 20 percent more likely to have a shotgun marriage compared
to the low educated women, a generous estimate based on the data. In this example the change
in fertility will affect the overall shotgun marriage rate by less than one-quarter of one percent, a
tiny fraction of the 6-8 percent estimate found in Section 5.2. For these two reasons, selection into
fertility can play only a minor role in the estimates found in Section 5.2.
5.5
Marital match quality
One prediction of the model presented in Section 3 is that once child support is enforced fewer
shotgun marriages form and those that do form are higher quality on average. The key mechanism
is that child support laws affect selection into marriage, with worse matches preferring to remain
single once child support laws are in effect. To test the prediction on marital quality, I estimate
the following regression on the sample of women who marry.
0
divorcei,t+h = β0 + β1 shotgunist + β2 shotgunist × CS s,t−1 + γ xist + ist
(5.4)
Each woman in the sample marries for the first time in year t. The variable shotgunist takes
a value of 1 if the marriage was a shotgun marriage and 0 otherwise, divorcei,t+h is an indicator
for the woman’s first marriage ending in divorce within h years of the marriage date. I report the
results for h ∈ {3, 5, ∞}.
Each woman is linked to the child support regime in her state s one year prior to her marriage,
denoted by CS s,t−1 , so that for shotgun marriages this corresponds to the year of pregnancy,
ensuring consistency with the regression framework of Section 5.2. In Equation 5.4, the coefficient
of interest is β2 , which reports the differential effect of child support enforcement on the quality
of shotgun marriages compared to non-shotgun marriages. The vector xist is the standard vector
of individual controls, and I report two specifications of ist , one that includes both state and year
fixed effects, and a second that includes interacted state-year fixed effects.
In Equation 5.4, the probability of divorce is used as a proxy for marital match quality. The
model predicts that child support laws affect marital match quality through selection into marriage,
and that the selection effect is strongest for shotgun marriages. Hence we would expect β2 to be
negative: in state-year cells with stronger child support laws, shotgun marriages will be less likely
to divorce relative to non-shotgun marriages.
26
If state and year fixed effects are included separately, the identification of β2 requires that the
timing of child support enactments are uncorrelated with attitudes toward divorce. A natural concern is that individuals who make divorce decisions based on their attitudes about family structure
and child-rearing also make up the electorate determining state policies regarding child support.22
To address this concern I report results from a specification that includes interacted state-year fixed
effects. This specification is identified by comparing the divorce decision of shotgun marriages to
non-shotgun marriages within a state-year cell, in which time-varying attitudes toward divorce and
child support are held fixed.
Table 11 reports the results, which are notably consistent across the two specifications. The
coefficient on shotgunist reflects what was shown in Section 4.1, that shotgun marriages are more
likely to end in divorce. In the preferred, interacted state-year specification, shotgun marriages are
1.4 percent more likely to divorce within 3 years (though we cannot reject a hypothesis that there
is no difference); 3.2 percent more likely to divorce within 5 years (significant at p = .10), and 5.2
percent more likely to divorce overall (significant at p = .05). Note that Table 11 has a smaller
sample size compared to Table 4 because it uses a shorter time horizon, 1976-1992, which are the
years for which the child support legal database is available.
The coefficient on shotgunist ×CS s,t−1 strongly supports the prediction of the model for marriage
quality. Increasing the child support index from 0 to 1 leads to a reduction in divorce probability by
4.4 percent within 3 years, 5.3 percent within 5 years, and 6.8 percent overall for shotgun marriages
compared to non-shotgun marriages.
Do child support laws affect divorce directly?
It is plausible that child support laws at the time of marriage affect a couple’s divorce decision
directly, separate from the selection effect. For example, if child support laws were to affect the
custodial rights the husband would receive if the couple were to divorce, then it would have a direct
effect on the divorce decision. Note, however, that having been married, the husband has already
been granted the presumption of paternity, and its associated rights and financial responsibilities,
which appear to have remained relatively stable over time (Bromley, 1971): the paternity rights
increase has been for unmarried dads not divorced dads.
The estimates of β1 in columns (1), (3), and (5) of Table 11 suggest that there is no effect
of child support laws at the time of marriage on non-shotgun marriages. Child support laws
at the time of marriage appear to affect shotgun marriages only. The interpretation of β2 as the
selection effect is unlikely to differ even if there is a direct effect of child support on divorce, because
it is identified from the differential impact on shotgun marriages compared to other marriages.
Unless child support laws at the time of marriage have a direct effect on divorce that differentially
22
The direction of bias is ambiguous, however. If the electorate takes a negative view of divorce, and this is
correlated with a desire for harsher punishment of deadbeat dads (i.e. greater child support enforcement), then β 2
will be biased upward and we will understate the negative effect of child support on divorce. On the other hand,
if negative views of divorce are correlated with a desire to have less state support for single moms (i.e. less child
support enforcement), then β2 will be biased downward and we will overstate the effect of child support.
27
affects shotgun marriages compared to other marriages, our estimate is interpreted as capturing
the selection effect.
In order to investigate any direct effect of child support laws on divorce, I construct a variable
∆CSs,t+h = CSs,t+h − CSs,t , which represents a change in child support laws between the year
of marriage and h years later. The goal is to uncover whether child support laws adopted since
marriage have any effect on an individual’s divorce status h years from the marriage year. The
estimation equation is
0
divorcei,t+h = β0 + β1 shotgunist + β2 shotgunist × ∆CSs,t+h + γ xist + ist
(5.5)
and the results are reported in Table 12. Note that by including 3-year or 5-year lead terms for
child support adoption, the regression mechanically loses years 1989-1992 or 1987-1992, a period
of considerable child support statute adoption. Moreover, the interpretation of the coefficient on
∆CSs,t+h is different than that of the CSs,t variable estimated earlier because different types of
laws are adopted at different times. And the regression also loses power due to fewer observations.
These caveats aside, Table 12 shows that child support statutes adopted since marriage do not have
a clear effect on divorce rates.
6
Conclusion
This paper introduces a theoretical framework for understanding the effects of child support laws on
marriage and fertility, and then provides direct evidence in the data: first, by testing the model’s
predictions for trends in shotgun marriage rates, and shotgun marriage quality, and second, by
estimating the direct effect of child support enforcement on marital formation, fertility, and marital
quality.
The theoretical framework shows that a child support law eliminates the lowest quality marriages
that would form absent the policy, by introducing a contract that grants fathers limited custodial
rights in exchange for transfers to the mother. The model also predicts that a child support law will
increase contraceptive use among men with distaste for children and reduce births from these men.
A child support law puts downward pressure on total out of wedlock births because men who are
least likely to marry following a pregnancy increase their contraceptive use the most. Nonetheless,
the fraction of births that are out of wedlock may increase, because a lower fraction of parents
marry following a pregnancy.
The empirical evidence is remarkably consistent with these predictions. First, I show that while
shotgun marriages are low quality relative to non-shotgun marriages, in terms of divorce hazard and
self-reported measures of marital happiness, their relative quality has been improving over time.
Divorce hazard rates among shotgun marriages have fallen relative to non-shotgun marriages since
the 1990s. Second, I show direct evidence that child support laws have reduced the propensity to
marry following an out of wedlock pregnancy, and have reduced the likelihood of having an out of
wedlock pregnancy.
28
The main takeaway is that child support laws, which are intended to ensure that the noncustodial parent contributes to child rearing, have important consequences for fertility and marriage.
The magnitudes estimated in this paper suggest that the increase in child support enforcement can
account for a substantial part of the long-run decline in shotgun marriage, and part of the recent fall
in the divorce rate. Child support laws are thus central to understanding major trends in marriage
and fertility in the second half of the 20th century, during which child support enforcement went
from virtual non-existence to automatic and near-universal. Future research may shed light on
whether child support affects other dimensions of behavior, including father’s labor supply (see e.g.
Cancian et al., 2013, and Rich et al., 2007), or participation in informal employment.
29
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32
Appendix I: Model
I.1
Proof. Proposition 1(a).
The first order necessary condition (F.O.C.) for eM is given by
pe ≥ −δeM (eW , e∗M )[π0 θ0 − π1 θ1 ]
with equality if e∗M > 0.
Note that when v = 0, π1 = π0 and θ1 = θ0 , and the term in brackets is equal to 0. This, plus
the assumption that δeM (·) < 0 and δeM eM (·) > 0, means that e∗M = 0 for a man with v = 0. We
now show that the term in brackets is decreasing in v, so that e∗M = 0 for any v ≥ 0.´
Since π0 θ0 does not depend on v, we turn our attention to the second term, π1 θ1 =
´∞
F (− v2 )] = − v (θ + v2 )f (θ)dθ. Taking a partial derivative with respect to v, we have
∞
−v
2
(θ+ v2 )f (θ)dθ
1−F (− v2 )
[1−
2
ˆ∞
1
v
v
(θ + )f (θ)dθ = (1 − F (− )) > 0
2
2
2
∂(π1 θ1 )
∂
=
∂v
∂v
− v2
Hence we have e∗M = 0 for v ≥ 0.
Let −¯
v denote the male who is indifferent between using an infinitesimal amount of contraceptives and none, given the female’s contraceptive choice. This −¯
v is defined implicitly by the
following equation.
pe = −δeM (ef , 0)[π0 θ0 − π1 θ1 ]
Now we show that male contraceptive use is decreasing in v over the region −v ∈ [−V, −¯
v ]. We
can see this by taking a total differential of the F.O.C.:
1 θ1 )
δeM (eW , e∗M ) ∂(π∂v
deM
=
dv
δeM eM (eW , e∗M )[π0 θ0 − π1 θ1 ]
(6.1)
The numerator is always strictly less than zero because δeM (eW , eM ) < 0 and we have shown
above that
∂(π1 θ1 )
∂v
> 0. The denominator term in brackets is equal to zero if v = 0, and is decreasing
in v. Hence we have the result that
de
dv
< 0 over the region for which we have an interior solution.
Proposition 1(b) and 1(c).
The woman’s first order condition for eW is given by
pe ≥ −δeW (e∗W , eM )[(wh − w` ) − u + π0 θ0 − π1 θ1 ]
(6.2)
with equality if e∗W > 0. As before, the term in brackets is decreasing in v and hence female
33
contraceptive use is decreasing in v as well.
Let κ = (wh − w` ) − u, which is the woman’s wage losses from pregnancy minus the utility from
having a child. If κ > 0 we can see from the first order condition, that the female will use weakly
more contraceptives than the male v she is matched with, while if κ ≤ 0 she will use weakly less.
If κ > 0, and the male’s F.O.C. holds with equality (and e∗M > 0), the female will use strictly more
contraceptives. If κ > 0 and the female’s F.O.C. holds with equality (and e∗W > 0), the male will
use strictly less.
I.2
Proof. Shotgun marriages only form when there is a pregnancy and in couples with men who have
v > 0. Prior to child support shotgun marriages are the region θ ∈ [− v2 , 0]. Following the law,
shotgun marriages are the region θ ∈ [− (1−α)v
, 0]. Hence, average marital quality is higher under
2
child support: E[θ|θ ∈ [− (1−α)v
, 0]] > E[θ|θ ∈ [− v2 , 0]] so long as θ has positive mass in the region
2
[− v2 , − (1−α)v
] for some v > 0.
2
Now consider non-shotgun marriages with a pregnancy. Couples whose men have v > 0 are
just as likely to form after child support as before: they form when θ > 0. Couples with v < 0 are
more likely to marry, and for these couples average quality is lower: E[θ|θ ∈ [− (1−α)v
, 0]] < E[θ|θ ∈
2
[− v2 , 0]]. Thus, average marital quality of non-shotgun marriages with children decreases.
I.3
Proof. Proposition 3(a).
The first order condition for eM is given by
pe ≥ −δeM (eW , e∗M )[π0 θ0 − π1 θ1 − (1 − π1 )(α` v − τ ` )]
(6.3)
with equality if e∗M > 0.
Suppose v ≥
τ`
α`
. For this range of v, there is an extra negative term in brackets, and hence
these men choose weakly less contraceptives after the law compared to before. But recall that men
with v > 0 used no contraceptives before child support, so they continue to choose e∗M = 0.
Suppose now v <
τ`
α`
. For this range of v, the term in brackets has an additional positive term,
−(1 − π1 )(α` v − τ ` ), which is absent without the law. For this range of v, men will use weakly more
contraceptives.
The threshold v for which a man is indifferent between using an infinitesimal amount of contraceptives is denoted by v¯` , implicitly defined
pe = −δeM (eW , 0)[π0 θ0 − π1 θ1 − (1 − π1 )(α` v¯` − τ ` )]
The range of v for which men will use contraceptives will expand, from [−V, −¯
v ] to [−V, v¯` ],
where −¯
v < v¯` , and v¯` may be positive or negative. And for the range of v for which we had an
interior solution prior to child support, [−V, −¯
v ] men will use strictly more contraceptives.
34
Now we prove Proposition 3(b) and 3(c).
Consider the female’s first order condition:
pe ≥ −δeW (e∗W , eM )[(wh − w` ) − u + π0 θ0 − π1 θ1 + (1 − π1 )τ ` ]
with equality if e∗W > 0. Note that she will choose weakly less contraceptives than before because
of an additional positive term (1 − π1 )τ ` , at all levels of v. Since males with v >
no contraceptives, there will be a weakly greater fertility rate for v >
τ`
.
α`
τ`
α`
continue to use
This proves 3(c).
Now consider couples with v < −¯
v . In these couples, if women chose eW = 0 prior to child
support, equilibrium births will go down for these couples after child support, since women will
continue to choose eW = 0 but men will use positive amounts of eM .
Now consider couples with v < −¯
v in which both partners choose positive e. Taking the ratio
of female-to-male F.O.C.s we have
1=
δeW (e∗W , e∗M )
π0 θ0 − π1 θ1 + (1 − π1 )τ ` + κ
·
δeM (e∗W , e∗M ) π0 θ0 − π1 θ1 + (1 − π1 )τ ` − (1 − π1 )α` v
(6.4)
where κ = (wh − w` ) − u. Here, κ > 0 by the assumption that women use positive amounts of
contraceptives.
Consider the fraction on the right first. The denominator has an additional term −(1 − π1 )α` v
which is positive for v < 0. Thus, moving to a child support policy, in couples with v < −¯
v , the
denominator of the right fraction is larger than the numerator. And thus, e∗M must increase more
than e∗W decreases, to maintain equality. Thus, men will have a larger increase in contraceptive use
compared to females, and the birth rate will go down for these couples.
Appendix II: Tables and Figures
35
Figure 3: Child support statute adoption
The figure on the left plots the mean rate of adoption across states of four types of child support
statutes including those requiring genetic tests, paternity establishment, penalties for failure to
pay, and wage withholding (source: Case-McLanahan data). The figure on the right plots trends in
percentiles of mean state child support enforcement expenditures per single-mother family in 2000
USD (source: OCSE annual reports).
Figure 4: Child support income receipt
The figure plots the fraction of never-married mothers with the child’s father absent from the
household receiving any child support income. Source: March CPS. The lines are presented in
three different colors to reflect three different CPS variables that were needed to construct the
series.
36
Figure 5: First marriage month relative to first birth month
This figure plots a histogram of the difference in months between first marriage and first birth.
Source: 1991, 1992, 1993 and 1996 SIPP
Figure 6: Shotgun marriage rates by year
The left panel uses data from SIPP and plots three-year moving averages of the following two series:
(1) the fraction of out-of-wedlock first pregnancies that are resolved in a marriage before birth, and
(2) the fraction of first marriages that are shotgun marriages.
37
Table 1: Match quality of shotgun marriages relative to other marriages
Very happy
Discuss Separation
Marriage trouble
(1)
(2)
(3)
Shotgun marriage
∗∗∗
-0.072
(0.017)
0.062
(0.022)
0.042∗∗∗
(0.015)
Female
-0.041∗∗∗
(0.011)
-0.017
(0.015)
0.042∗∗∗
(0.010)
African-American
-0.115∗∗∗
(0.019)
0.131∗∗∗
(0.022)
0.110∗∗∗
(0.018)
Other
race/ethnicity
-0.006
(0.021)
0.057∗∗
(0.027)
-0.042∗∗
(0.019)
No children
0.007
(0.018)
0.028
(0.023)
0.002
(0.016)
Number of
children
0.007∗∗
(0.004)
-0.017∗∗∗
(0.005)
-0.011∗∗∗
(0.003)
Age at survey
-0.006
(0.017)
-0.092∗∗∗
(0.023)
-0.023
(0.016)
North Central
-0.010
(0.016)
0.025
(0.021)
0.002
(0.014)
South
0.048∗∗∗
(0.015)
0.025
(0.020)
-0.008
(0.013)
West
0.001
(0.017)
0.041∗
(0.022)
0.044∗∗∗
(0.015)
Log Household
Inc.
0.050∗∗∗
(0.005)
-0.064∗∗∗
(0.007)
-0.064∗∗∗
(0.005)
HS Degree
-0.026∗
(0.015)
0.010
(0.019)
0.004
(0.014)
Some college
-0.085∗∗∗
(0.018)
0.053∗∗
(0.023)
0.041∗∗
(0.016)
College degree
-0.088∗∗∗
(0.019)
0.093∗∗∗
(0.025)
0.048∗∗∗
(0.017)
Yes
8,343
0.045
0.34
Yes
4,508
0.195
0.46
Yes
8,343
0.099
0.28
Marriage yr. dummies
Observations
R2
Mean of dep. var.
∗∗∗
Results from the estimation of Equation 4.1. Data is from 1987-1988 NSFH, and the sample consists
of married respondents age 18 and over. Each column has as its dependent variable one of the three
marital happiness variables defined in the text. Standard errors in parentheses. ∗ p < 0.10 , ∗∗ p < 0.05
,
∗∗∗
p < 0.01
38
Table 2: Match quality of shotgun marriages relative to other marriages conditional on staying
married
Very happy
Discuss Separation
Marriage trouble
(1)
(2)
(3)
-0.099
(0.025)
∗∗
0.090
(0.042)
0.039∗∗
(0.019)
Female
0.029∗
(0.016)
-0.019
(0.028)
0.017
(0.012)
African-American
-0.060∗
(0.031)
0.071
(0.049)
-0.005
(0.024)
Other
race/ethnicity
-0.022
(0.029)
0.036
(0.052)
-0.052∗∗
(0.023)
No children
0.055∗∗
(0.027)
-0.015
(0.048)
-0.065∗∗∗
(0.021)
Number of
children
0.004
(0.006)
-0.011
(0.011)
-0.001
(0.004)
Age at survey
-0.027
(0.026)
-0.031
(0.046)
0.011
(0.020)
North Central
-0.031
(0.022)
0.026
(0.041)
0.014
(0.017)
South
0.032
(0.021)
0.068∗
(0.039)
0.029∗
(0.016)
West
-0.008
(0.024)
0.088∗∗
(0.043)
0.045∗∗
(0.019)
Log Household
Inc.
-0.002
(0.009)
-0.021
(0.015)
-0.003
(0.007)
HS Degree
-0.039∗
(0.023)
0.025
(0.042)
0.010
(0.018)
Some college
-0.090∗∗∗
(0.027)
0.023
(0.048)
0.022
(0.021)
College degree
-0.093∗∗∗
(0.027)
0.110∗∗
(0.051)
0.027
(0.021)
Yes
4,288
0.057
0.43
Yes
1,281
0.124
0.31
Yes
4,288
0.071
0.17
Shotgun marriage
Marriage yr. dummies
Observations
R2
Mean of dep. var.
∗∗∗
Results from the estimation of Equation 4.1. Data is from 1987-1988 NSFH. Each column has as
its dependent variable one of the three marital happiness variables defined in the text. The sample
consists of respondents 18 and over whose first marriage is intact at the survey date. Standard
errors in parentheses. ∗ p < 0.10 , ∗∗ p < 0.05 , ∗∗∗ p < 0.01
39
Table 3: Shotgun marriages and the likelihood of divorce
Divorce (3yr)
Divorce (5yr)
Divorce (any)
(1)
(2)
(3)
(4)
(5)
(6)
Shotgun marriage
0.004
(0.004)
0.004
(0.005)
0.016∗∗
(0.006)
0.017∗∗
(0.007)
0.035∗∗∗
(0.010)
0.038∗∗∗
(0.010)
African-American
-0.003
(0.005)
-0.005
(0.005)
0.017∗∗∗
(0.006)
0.017∗∗
(0.007)
0.062∗∗∗
(0.009)
0.039∗∗∗
(0.010)
Other
race/ethnicity
-0.022∗∗∗
(0.007)
-0.022∗∗∗
(0.006)
-0.026∗∗∗
(0.005)
-0.024∗∗∗
(0.006)
-0.053∗∗∗
(0.010)
-0.068∗∗∗
(0.012)
Age at first
birth
0.001∗∗∗
(0.000)
0.002∗∗
(0.001)
0.003∗∗∗
(0.001)
0.003∗∗∗
(0.001)
0.001∗
(0.001)
-0.005∗∗∗
(0.001)
HS Degree
0.001
(0.005)
0.002
(0.009)
0.006
(0.014)
0.007
(0.014)
0.016
(0.019)
0.018
(0.020)
Some college
0.005
(0.005)
0.006
(0.011)
0.020
(0.017)
0.021
(0.017)
0.059∗∗
(0.023)
0.066∗∗∗
(0.022)
College degree
-0.028∗∗∗
(0.006)
-0.026∗∗∗
(0.010)
-0.031∗∗
(0.015)
-0.029∗
(0.015)
-0.021
(0.021)
-0.019
(0.022)
Age in 2001
-0.007∗∗∗
(0.000)
-0.007∗∗∗
(0.001)
-0.013∗∗∗
(0.001)
-0.012∗∗∗
(0.001)
-0.018∗∗∗
(0.001)
-0.005∗∗∗
(0.001)
Yes
No
30,697
0.020
0.08
Yes
Yes
30,697
0.024
0.08
Yes
No
30,697
0.035
0.13
Yes
Yes
30,697
0.041
0.13
Yes
No
30,697
0.102
0.31
Yes
Yes
30,697
0.086
0.31
Marriage yr. dummies
State f.e.
Observations
R2
Mean of dep. var
Results from the estimation of Equation 4.1. Data is from 1991, 1992, 1993 and 1996 SIPP. The
dependent variables are divorce hazard in the first 3 years, first 5 years, and any divorce. Standard
errors are clustered at the state level. ∗ p < 0.10 , ∗∗ p < 0.05 , ∗∗∗ p < 0.01
40
Table 4: Shotgun marriages and the likelihood of divorce, over time
Divorce (3yr)
(1)
Divorce (5yr)
(2)
(3)
Divorce (any)
(4)
(5)
∗∗
∗∗∗
(6)
Shotgun marriage
0.014
(0.011)
0.017
(0.011)
0.027
(0.012)
0.030
(0.013)
0.066
(0.019)
0.069∗∗∗
(0.019)
Shotgun * 1970s
marriage
-0.001
(0.013)
-0.003
(0.017)
0.001
(0.021)
-0.001
(0.021)
-0.027
(0.024)
-0.028
(0.024)
Shotgun * 1980s
marriage
-0.009
(0.013)
-0.011
(0.014)
-0.005
(0.016)
-0.007
(0.016)
-0.028
(0.020)
-0.031
(0.020)
Shotgun * 1990s
marriage
-0.057∗∗∗
(0.016)
-0.060∗∗∗
(0.016)
-0.076∗∗∗
(0.016)
-0.080∗∗∗
(0.016)
-0.104∗∗∗
(0.019)
-0.110∗∗∗
(0.020)
1970s marriage
-0.012∗∗
(0.006)
-0.010∗∗
(0.005)
-0.024∗∗∗
(0.007)
-0.022∗∗∗
(0.008)
-0.058∗∗∗
(0.009)
-0.055∗∗∗
(0.010)
1980s marriage
-0.061∗∗∗
(0.008)
-0.056∗∗∗
(0.007)
-0.110∗∗∗
(0.011)
-0.105∗∗∗
(0.012)
-0.266∗∗∗
(0.015)
-0.259∗∗∗
(0.015)
1990s marriage
-0.113∗∗∗
(0.011)
-0.106∗∗∗
(0.013)
-0.218∗∗∗
(0.016)
-0.210∗∗∗
(0.017)
-0.471∗∗∗
(0.019)
-0.461∗∗∗
(0.021)
Yes
No
30,697
0.017
0.08
Yes
Yes
30,697
0.022
0.08
Yes
No
30,697
0.028
0.13
Yes
Yes
30,697
0.035
0.13
Yes
No
30,697
0.083
0.31
Yes
Yes
30,697
0.089
0.31
Baseline controls
State f.e.
Observations
R2
Mean of dep. var
∗∗
Results from the estimation of Equation 4.1. Data is from 1991, 1992, 1993 and 1996 SIPP. The
dependent variables are divorce hazard in the first 3 years, first 5 years, and any divorce. Baseline
controls included but not reported are: education dummies, race dummies, year of first marriage,
age in the year of first birth, age at the time of the survey. Standard errors are clustered at the
state level. ∗ p < 0.10 , ∗∗ p < 0.05 , ∗∗∗ p < 0.01
41
Table 5: Child support laws’ effect on child support receipt, 1976-1992
Any child support income
(1)
(2)
∗∗∗
(3)
∗∗∗
(4)
Child support
law index
0.127
(0.017)
0.139
(0.014)
0.052
(0.017)
0.051∗∗
(0.020)
Age at survey
0.028∗∗∗
(0.003)
0.028∗∗∗
(0.003)
0.021∗∗∗
(0.002)
0.020∗∗∗
(0.003)
Age squared
-0.000∗∗∗
(0.000)
-0.000∗∗∗
(0.000)
-0.000∗∗∗
(0.000)
-0.000∗∗∗
(0.000)
Age at first
birth
-0.005∗∗∗
(0.001)
-0.005∗∗∗
(0.001)
-0.000
(0.001)
-0.000
(0.001)
African-American
-0.051∗∗∗
(0.013)
-0.068∗∗∗
(0.011)
-0.065∗∗∗
(0.011)
-0.065∗∗∗
(0.011)
Other
race/ethnicity
-0.040∗
(0.020)
-0.032
(0.020)
-0.034∗
(0.019)
-0.028
(0.020)
HS Degree
0.058∗∗∗
(0.008)
0.052∗∗∗
(0.007)
0.050∗∗∗
(0.007)
0.049∗∗∗
(0.008)
Some college
0.080∗∗∗
(0.010)
0.081∗∗∗
(0.011)
0.075∗∗∗
(0.011)
0.077∗∗∗
(0.011)
College degree
0.100∗∗∗
(0.013)
0.099∗∗∗
(0.013)
0.095∗∗∗
(0.014)
0.091∗∗∗
(0.014)
More than 1
child
-0.003
(0.009)
0.002
(0.009)
0.025∗∗∗
(0.008)
0.022∗∗
(0.009)
No
No
Yes
No
Yes
Yes
24,627
0.036
24,627
0.053
24,627
0.058
State f.e.
Year f.e.
State-year f.e.
Observations
R2
∗∗∗
Yes
24,627
0.116
The sample is restricted to never married mothers between 17 and 60 with a child 18 years or less
in the household whose father is reported absent from the household. The dependent variable is an
indicator for whether the mother receives any child support income at time t, where child support
income data is from March CPS. The right-hand side variable of interest is an index of child support
laws in the mother’s state in the year of birth of the child, where the index is constructed using
the Case-McLanahan data, 1976-1992. Standard errors are clustered at the state level. ∗ p < 0.10 ,
∗∗
p < 0.05 ,
∗∗∗
p < 0.01
42
Figure 7: Fertility trends in the U.S.
Birth rates for U.S. women aged 15-34 with no prior children, and percent of total births to unmarried mothers, 1970-2000. Birth rates are plotted separately for married and un-married women
and are represented per 1000 women in each marital group, age 15-34.
43
Table 6: Child support enforcement and its effect on child support receipt, 1982-1996
Any child support income
(1)
(2)
∗∗∗
(3)
Log Avg. C.S.
Expend
0.046
(0.013)
0.077
(0.007)
0.020∗
(0.012)
Age at survey
0.001∗∗∗
(0.000)
0.001∗∗∗
(0.000)
0.001∗∗∗
(0.000)
African-American
-0.045∗∗∗
(0.013)
-0.062∗∗∗
(0.010)
-0.060∗∗∗
(0.010)
Other
race/ethnicity
-0.050∗∗
(0.019)
-0.034
(0.020)
-0.036∗
(0.019)
HS Degree
0.067∗∗∗
(0.007)
0.060∗∗∗
(0.006)
0.059∗∗∗
(0.006)
Some college
0.103∗∗∗
(0.007)
0.098∗∗∗
(0.007)
0.096∗∗∗
(0.007)
College degree
0.109∗∗∗
(0.011)
0.103∗∗∗
(0.010)
0.102∗∗∗
(0.010)
Number of own
children in household
0.022∗∗∗
(0.004)
0.023∗∗∗
(0.004)
0.023∗∗∗
(0.004)
No
No
47,625
0.024
Yes
No
47,625
0.041
Yes
Yes
47,625
0.044
State f.e.
Year f.e.
Observations
R2
∗∗∗
The sample is restricted to never married mothers between 17 and 60 with a child 18 years or less
in the household whose father is reported absent from the household. The dependent variable is an
indicator for whether the mother received any child support income in year t, where child support
income data is from March CPS. The right-hand side variable of interest is the log average OCSE
expenditures per single mother family in year t, for the years available, 1977-2009. Standard errors
are clustered at the state-year level. ∗ p < 0.10 , ∗∗ p < 0.05 , ∗∗∗ p < 0.01
44
Table 7: Child support laws’ effect on marriage
Marriage cohort
(1)
(2)
∗∗
(3)
∗∗
∗∗
O.W. Pregnancy
No O.W. Pregnancy
(4)
(5)
∗∗∗
Pregnant X C.S.
Index
-0.068
(0.028)
-0.072
(0.031)
-0.067
(0.028)
-0.084
(0.028)
Pregnant
0.362∗∗∗
(0.015)
0.367∗∗∗
(0.017)
0.362∗∗∗
(0.015)
0.386∗∗∗
(0.015)
Child support
law index
-0.000
(0.003)
0.001
(0.004)
0.003
(0.004)
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
62,946
0.064
0.06
62,946
0.063
0.06
State
Year
Demographic*year effects
State-year f.e.
Number of individuals
R2
Mean of dep. var.
Yes
62,946
0.065
0.06
Yes
12,452
0.113
0.07
50,494
0.050
0.06
Data is from 1991, 1992, 1993 and 1996 SIPP, and the sample is restricted to females in the 18-40 age
cohort. The dependent variable is an indicator for the mother getting married for the first time in
year t or t+1. Controls used in all regressions include a high school degree indicator, race dummies,
age dummies, SIPP sample year dummies. Columns (2) and (5) include the following state-level
demographics and their interaction with year fixed effects: percent black in the population, share
of people under 18 below 100% of the federal poverty line, the male unemployment rate, and the
maximum AFDC monthly benefit for a family of 3 with no income (in 2000 USD). Column (4)
restricts the sample to women whose first pregnancy was out of wedlock, and column (5) restricts
the sample to all other women. Standard errors are clustered at the state-year level. ∗ p < 0.10 ,
∗∗
p < 0.05 ,
∗∗∗
p < 0.01
45
Table 8: Child support enforcement and its effect on marriage
Marriage cohort
(1)
(2)
∗∗
(3)
∗∗
∗∗
O.W. Pregnancy
No O.W. Pregnancy
(4)
(5)
∗∗
Pregnant X C.S.
Expend.
-0.034
(0.015)
-0.035
(0.015)
-0.035
(0.015)
-0.036
(0.015)
Pregnant
0.512∗∗∗
(0.079)
0.513∗∗∗
(0.079)
0.512∗∗∗
(0.079)
0.520∗∗∗
(0.081)
Log Avg. C.S.
Expend.
0.003∗∗∗
(0.001)
0.002
(0.002)
0.003∗
(0.002)
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
63,111
0.062
0.05
63,111
0.062
0.05
State
Year
Demographic*year effects
State-year f.e.
Number of individuals
R2
Mean of dep. var.
Yes
63,111
0.064
0.05
Yes
12,525
0.110
0.06
50,586
0.047
0.04
Individual-level data is from 1991, 1992, 1993 and 1996 SIPP; state-year child support enforcement
expenditures data is from the OCSE annual reports. Sample is restricted to females in the 18-40 age
cohort. The dependent variable is an indicator for the mother getting married for the first time in
year t or t+1. Controls used in all regressions include a high school degree indicator, race dummies,
age dummies, SIPP sample year dummies. Columns (2) and (5) include the following state-level
demographics and their interaction with year fixed effects: percent black in the population, share
of people under 18 below 100% of the federal poverty line, the male unemployment rate, and the
maximum AFDC monthly benefit for a family of 3 with no income (in 2000 USD). Column (4)
restricts the sample to women whose first pregnancy was out of wedlock, and column (5) restricts
the sample to all other women. Standard errors are clustered at the state-year level. ∗ p < 0.10 ,
∗∗
p < 0.05 ,
∗∗∗
p < 0.01
46
Table 9: Child support laws’ effect on fertility
Female age cohort
Less than H.S.
H.S. Degree
(1)
(2)
(3)
(4)
-0.003
(0.004)
-0.005
(0.004)
-0.001
(0.018)
-0.005
(0.005)
H.S. Degree
-0.012∗∗∗
(0.002)
-0.012∗∗∗
(0.002)
African-American
0.012∗∗∗
(0.001)
0.012∗∗∗
(0.001)
-0.012∗∗∗
(0.003)
0.016∗∗∗
(0.001)
Other
race/ethnicity
-0.002
(0.002)
-0.002
(0.002)
-0.005
(0.006)
-0.001
(0.002)
Yes
Yes
Yes
Yes
Yes
37,976
0.008
0.02
Yes
Yes
Yes
4,552
0.029
0.02
Yes
Yes
Yes
33,205
0.007
0.02
Child support
law index
State
Year
Demographic*year effects
Number of individuals
R2
Mean of dep. var.
37,976
0.008
0.02
Data is from 1991, 1992, 1993 and 1996 SIPP. Sample is restricted to never-married women without
children who are in the marital age cohort 18-40. The dependent variable is an indicator for the
mother having an out-of-wedlock pregnancy for the first time in year t. All columns include the
following state-level demographics, and columns (2), (3), and (4) add their interaction with year
fixed effects: percent black in the population, share of people under 18 below 100% of the federal
poverty line, the male unemployment rate, and the maximum AFDC monthly benefit for a family
of 3 with no income (in 2000 USD). Standard errors clustered at the state-year level. ∗ p < 0.10 ,
∗∗
p < 0.05 ,
∗∗∗
p < 0.01
47
Table 10: Child support laws’ effect on fertility
Female age cohort
Less than H.S.
H.S. Degree
(1)
(2)
(3)
(4)
Log Avg. C.S.
Expend.
0.001
(0.001)
0.001
(0.002)
0.001
(0.006)
0.001
(0.002)
H.S. Degree
-0.002∗∗
(0.001)
-0.002∗∗
(0.001)
African-American
0.008∗∗∗
(0.001)
0.008∗∗∗
(0.001)
-0.007∗∗∗
(0.002)
0.011∗∗∗
(0.001)
Other
race/ethnicity
-0.003∗
(0.001)
-0.003∗
(0.001)
-0.007∗∗
(0.003)
-0.002
(0.001)
Yes
Yes
Yes
Yes
Yes
31,989
0.012
0.02
Yes
Yes
Yes
4,441
0.035
0.02
Yes
Yes
Yes
27,267
0.010
0.02
State
Year
Demographic*year effects
Number of individuals
R2
Mean of dep. var.
31,989
0.011
0.02
Data is from 1991, 1992, 1993 and 1996 SIPP. Sample is restricted to never-married women without
children who are in the marital age cohort 18-40. The dependent variable is an indicator for the
mother having an out-of-wedlock pregnancy for the first time in year t. All columns include the
following state-level demographics, and columns (2), (3), and (4) add their interaction with year
fixed effects: percent black in the population, share of people under 18 below 100% of the federal
poverty line, the male unemployment rate, and the maximum AFDC monthly benefit for a family
of 3 with no income (in 2000 USD). Standard errors clustered at the state-year level. ∗ p < 0.10 ,
∗∗
p < 0.05 ,
∗∗∗
p < 0.01
48
Table 11: Child support enforcement and the probability of divorce
Divorce (3yr)
(1)
Divorce (5yr)
(2)
(3)
Divorce (any)
(4)
(5)
Shotgun X C.S.
Index
-0.036
(0.021)
∗∗
-0.044
(0.021)
∗∗
-0.056
(0.027)
Shotgun
0.006
(0.013)
0.014
(0.013)
0.032∗
(0.017)
Child support
law index
0.005
(0.026)
0.025
(0.029)
0.046
(0.037)
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
State
Year
Demographic*year effects
State-year f.e.
Number of individuals
R2
Mean of dep. var.
18,499
0.038
0.06
Yes
20,903
0.068
0.06
18,499
0.063
0.11
∗∗
(6)
∗
-0.053
(0.026)
∗∗
-0.071
(0.030)
-0.069∗∗
(0.030)
0.032∗∗
(0.016)
0.053∗∗∗
(0.019)
0.052∗∗∗
(0.019)
Yes
20,903
0.090
0.11
18,499
0.129
0.28
Yes
20,903
0.163
0.28
Individual-level data is from 1991, 1992, 1993 and 1996 SIPP. Sample is restricted to women who
were married one or more times. The dependent variable is an indicator for the woman’s first
marriage ending in divorce within 3 years, 5 years, or any year from the marriage year. The child
support law index is from Case-McLanahan and is matched with the year prior to the woman’s
first marriage year. Controls included in all regressions: dummies for number of children (including
zero), age at the first child’s birth, a dummy for the SIPP sample year. Columns (1), (3), and (5)
include the following state-level demographics and their interaction with year fixed effects: percent
black in the population, share of people under 18 below 100% of the federal poverty line, the male
unemployment rate, and the maximum AFDC monthly benefit for a family of 3 with no income (in
2000 USD). Standard errors clustered at the state-year level. ∗ p < 0.10 , ∗∗ p < 0.05 , ∗∗∗ p < 0.01
49
Table 12: Child support laws adopted since marriage and the probability of divorce
Divorce (3yr)
Divorce (5yr)
(1)
(2)
(3)
(4)
Shotgun
-0.009
(0.010)
-0.002
(0.010)
0.031
(0.021)
0.021
(0.019)
Shotgun×∆CSt+3
0.051
(0.044)
0.045
(0.044)
∆CSt+3
0.013
(0.028)
Shotgun×∆CSt+5
-0.017
(0.055)
0.020
(0.053)
∆CSt+5
0.003
(0.035)
State
Year
Demographic*year effects
State-year f.e.
Number of individuals
R2
Mean of dep. var.
Yes
Yes
Yes
14,503
0.038
0.06
Yes
Yes
Yes
Yes
16,907
0.065
0.06
11,901
0.059
0.11
Yes
14,305
0.084
0.11
Individual-level data is from 1991, 1992, 1993 and 1996 SIPP. Sample is restricted to women who
were married one or more times. The dependent variable is an indicator for the woman’s first
marriage ending in divorce within 3 years, 5 years, or any year from the marriage year. The child
support law index is from Case-McLanahan and is matched with the year prior to the woman’s
first marriage year. Controls included in all regressions: dummies for number of children (including
zero), age at the first child’s birth, a dummy for the SIPP sample year. Columns (1) and (3)
include the following state-level demographics and their interaction with year fixed effects: percent
black in the population, share of people under 18 below 100% of the federal poverty line, the male
unemployment rate, and the maximum AFDC monthly benefit for a family of 3 with no income (in
2000 USD). Standard errors clustered at the state-year level. ∗ p < 0.10 , ∗∗ p < 0.05 , ∗∗∗ p < 0.01
50
Table 13: Analysis of missing pregnancy dates in SIPP
Pregnancy date missing
(1)
Single/Never
Married
-0.144∗∗∗
(0.01)
Number of
children
0.027∗∗∗
(0.00)
Age at SIPP
survey
0.013∗∗∗
(0.00)
African-American
0.019∗∗∗
(0.00)
Other
race/ethnicity
-0.027∗∗∗
(0.01)
HS Degree
0.000
(0.00)
Some college
-0.034∗∗∗
(0.00)
College degree
-0.078∗∗∗
(0.00)
Education
missing
-0.018
(0.02)
SIPP 1992
0.004
(0.00)
SIPP 1993
0.008∗∗
(0.00)
SIPP 1996
-0.373∗∗∗
(0.00)
Married in 1970s
-0.306∗∗∗
(0.00)
Married in 1980s
-0.281∗∗∗
(0.01)
Married in 1990s
-0.110∗∗∗
(0.01)
Observations
R2
Mean of dep. var.
65,812
0.597
0.23
Individual-level data is from 1991, 1992, 1993 and 1996 SIPP. The dependent variable is an indicator
for the woman having a missing pregnancy date. Standard errors in parentheses. ∗ p < 0.10 , ∗∗ p < 0.05
,
∗∗∗
p < 0.01
51