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dissertation entitled

The Strategic Use of Child Support Payments
and Visitation Rights

presented by

Donna M. Anderson

has been accepted towards fulfillment
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—_fi.fi__ 7 7-

THE STRATEGIC USE OF CHILD SUPPORT PAYMENTS AND
VISITATION RIGHTS

BY

Donna Marie Anderson

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

DOCTOR OF PHILOSOPHY

Department of Economics

1993

ABSTRACT

THE STRATEGIC USE OF CHILD SUPPORT PAYMENTS AND VISITATION
RIGHTS

BY

Donna Marie Anderson

This thesis deals with the determination of child
support and noncustodial parent-child visitation in the
post-divorce environment. A strategic bargaining model of
negotiations over child support and visitation rights is
proposed that emphasizes the influence of the custodial
parent's control of visitation rights and the noncustodial
parent's control of child support on the process and
outcome: the custodial parent uses his or her control over
the time the child spends with the noncustodial parent to
elicit certain behavior from the noncustodial parent, namely
payment of child support, while the noncustodial parent uses
his or her control of child support to obtain the agreed
upon amount of visitation. The model incorporates the
child's welfare into the utility function of each parent.
The one-period Nash equilibrium leads to lower support
payments and visitation than the efficient outcome. The
optimal outcome can be supported in a repeated game, a
better approximation of the post-divorce environment, with
the use of trigger strategies: as long as both parties care
enough about the future, the threat of noncooperation in the
future makes the agreement self-enforcing.

Data from the National Survey of Children are used to

test the interdependence of the visitation and child support
decisions. The analysis suggests that child support is
being used strategically based on the significance of the
simultaneous equation specification and the significance of
various strategic factors important to the theory such as
the pre-divorce negotiation costs, the post-divorce
relationship between the parents, and the preferences of the
child and parents. The evidence of the strategic use of
visitation is less compelling. The significance of the
parents' relationship indicates the importance of family
dynamics in child support determination and the need for
more research and better data in this area. These results
suggest that legally allowing child support and visitation
to be linked, and stricter enforcement of visitation awards
would help alleviate the child support noncompliance

problem.

To my husband,
John D. Hibshman,
for his patience, love,

and support.

iv

ACKNOWLEDGMENTS

I would like to thank the members of my committee for
their guidance in this project. Daniel S. Hamermesh
provided encouragement throughout the entire process, from
the first inception of the idea in my second year to the
final thesis two years later. I would like to particularly
acknowledge his help on the empirical section of this
thesis. I would also like to thank his wife, Francis
Hamermesh, for the information she furnished me on the legal
aspects of the divorce process, and suggestions she made
early in the process on various sources of data. Carl
Davidson was especially instrumental in the early stages,
supplying not only important suggestions to the theory, but
encouragement as well. Jeff Wooldridge's help in guiding me
through the econometrics is much appreciated. I thank him
for the time he devoted in helping resolve the problems I
encountered in the simultaneous equation system and his
patience working through the process with me. All committee
members were always available to read my material and prompt
in returning drafts with valuable comments. I thank them
all for these courtesies.

Special thanks go to the administrative staff in the

economics department, and to Ann Feldman, whose help and
counsel throughout these last few years was unmeasurable.
In addition, I would like to thank my friends at the
Institute for Public Policy and Social Research for
providing an interesting (in so many ways) and enjoyable
place to work. I would like to give special thanks to the
members of the Policy Analysis Division at the time, Kel
Utendorf, Andrea Ranval, and Daniel Kashawlic. Their sense
of humor provided much needed relief during those often
stressful years.

Finally, I give thanks to a very special person in my
life, my daughter, Madison. She has helped me keep life’s

problems in perspective.

vi

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . .

CHAPTER I. INTRODUCTION . . . . . . .

A. Statistics on Child Support and Visitation

Rights . . . . . . . . . . . . .

B. Literature on Child Support and Visitation

C. Private Ordering . . . . . .
D. Purpose of this Thesis . . .
CHAPTER II. THE SINGLE PERIOD MODEL

A. The Strategic Case . . . . .

1. The Custodial Parent's Problem

2. Comparative Statics . .

3. Noncustodial Parent’s Problem

4. Comparative Statics . .
5. Equilibrium . . . . . .
B. The Pareto Optimal Case . . .

C. The Competitive Case . . . .
1. Comparative Statics . .
CHAPTER III. REPEATED GAME MODEL . .

A. Equilibrium in a Dynamic Game

B. Balanced Temptation Equilibrium

C. Conclusion . . . . . . . . .

CHAPTER IV.
MODEL 0 O O O O O O O O O O O O

A. Data and Sample . . . . . . .
8. Empirical Methodology . . . .

vii

A CROSS-SECTION, SIMULTANEOUS EQUATIONS

O O O O O 0

ix

12
16
19
19
20
23
24
26
27
27

30
32

33
33
36

37

38
38

43

B.

Estimation . . . . . . . . . . .
1. Estimation of Child Support Equation
2. Estimation of Visitation Equation .

Empirical Results . . . . . . .
1. The Amount of Child Support Received
2. ViSitation O O O O O O O O O C I O O

conCIuSion O O O O O O O O O O O O O O O

V. A DYNAMIC MODEL . . . . . . . . . . .

Empirical Methodology . . . . . . . . . .

Estimation . . . . . . . . . . . . . . .

Empirical Results . . . . . . . . . . . .

Conclusion . . . . . . . . . . . . . . .

VI. CONCLUSION . . . . . . . . . . . . .

Possible Extensions of the Model . . . .

The Current System of Child Support and

Visitation in the United States and Michigan

C.

D.

Policy Implications . . . . . . . . . . .

Future Directions . . . . . . . . . . . .

APPENDIX 1 O C O O O O O O O O O O O O 0 O O O 0

APPENDIX

APPENDIX 3 . . . . . . . . . . . . . . . . . . .

APPENDIX
APPENDIX

APPENDIX

6 O O O O O O O O O O O O O O O O O O O

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . .

viii

48
49
51
52
52
58
63
66
68
69
70
72
74

75

78

82

87

89

9O

91

92

96

97

98

LIST OF TABLES

Table 4.1 Means and Standard Deviations of Sample
Characteristics in Cross Section Analysis

Table 4.2
Received in Period 2 . . . .

Table 4.3

Year 0 O O O O O O O O O O 0

Table 5.1 Means and Standard Deviations of Sample
Characteristics in Dynamic Analysis

Table 5.2 Tobit Estimates of the Amount of Child

Support Received in Period 3

ix

Estimates of the Amount of Child Support

Estimates of the Number of Days the Child
Spent with the Noncustodial Parent in the Past

53

59

64

67

71

CHAPTER I. INTRODUCTION

A child support order in a divorce is a remedy to
enforce the obligation of support which parents owe their
children. Unfortunately, lack of compliance with court-
ordered payments is pervasive. A large percentage of
custodial parents living alone with children never receive
support from the absent noncustodial parent. Custodial
parents who do receive child support often receive this in
insufficient amounts and at irregular intervals. According
to the 0.8. Bureau of the Census, only 51 percent of women
awarded child support payments received the full amount of
the child support award in 1989K

Otherwise law-abiding citizens with the ability to pay
are exhibiting a complete disregard for the law.
Satisfactory data do not exist on the noncustodial parent's
reasons for inadequate payments, or nonpayments. One
possible motive for noncompliance that has not been
adequately developed in the economic literature is that the
payments are being used strategically by the noncustodial
parent in order to influence the behavior of the custodial
parent. At the same time, however, the custodial parent is
using his or her control over the time the child spends with

the noncustodial parent to elicit certain behavior from the

 

1All 1989 and 1990 descriptive statistics are from the
0.8. Bureau of the Census, Current Population Reports, Series

P-60, #173, Child Support and Alimony; 198 .
1

2
noncustodial parent. Thus, actions taken by each parent
affect the outcome, or well-being of the other parent,
suggesting a gaming situation.

This thesis develops a dynamic game-theoretic model of
strategic child support payments in which the parents engage
in a gaming strategy that results in an equilibrium
distribution of child support payments and visitation
rights. A divorced parent controlling payments (the
noncustodial parent) strategically interacts with the ex-
spouse who has custody of the child (the custodial parent)
and control over visits. Even though each parent is
altruistic towards the child, they are also affected by

actions taken by the other parent.

A. Statistics on Child Support and Visitation Rights

Census data show that as of spring 1990, 58 percent of
divorced or separated women age 15 and over with children
under 21 years of age had a legally binding child support
agreement. This is down from 1986 when the figure was 61
percent, and 1979 when the percentage was 59 percentfl.
Among those with an award and due payment in 1989, only
about one-half received full payment, about one-quarter
received partial payment, while one-quarter received no

payment at all. These particular statistics have not

 

2U.S. Bureau of the Census, Current Population Reports,

Series P-23, #52 (106), Child Suppppt apg All'mpny: 1985
1.1.91.1).-

3

changed since 1979, when 23 percent of women due child
support received less than they were due, 28 percent
received no payment, and around one-half received full
payment. Health care benefits were included in the child
support awards of 40 percent of mothers, though only two-
thirds of the absent fathers required to do so actually
provided them, while 7 percent who were not required to do
as part of a child support award provided the benefits.

Two-thirds of the women due child support payments in
1989 were awarded payments through the court system, while
an additional 29 percent had voluntary agreements, which may
also be approved by a court. Only 4 percent of women had
some other type of agreement. Court-ordered payments
usually take place when a mutually acceptable agreement
cannot be worked out between the parties. Voluntary written
agreements between the parties are not ordered by the courts
and may or may not have been recognized by the courts as
part of the divorce proceedings. Interestingly, the mean
amount of child support received by women with voluntary
child support awards was $2,929 in 1989, 48 percent higher
than the mean amount received by women with court-ordered
agreements. Women with voluntary agreements also received a
higher percentage of payments due (83 percent) than women
with court-ordered payments (61 percent).

Of those women who were never awarded child support
payments in 1989, 64 percent wanted an award but did not

obtain it for various reasons such as the father was unable

4
to pay, paternity could not be established, the father could
not be located, or the mothers did not pursue an award. 6
percent had a final agreement pending, meaning a child
support agreement was awaiting final legal action before
becoming final, or a voluntary written agreement was not yet
final. 9 percent had another settlement, and the remaining
22 percent did not want a child support award.

55 percent of absent fathers had visitation privileges
with their children in 1990, another 7 percent had joint
custody, and 38 percent had neither. Moreover, 63 percent
of absent fathers lived in the same state as their children
in 1990. An additional 26 percent of absent fathers lived
in another state and the remaining 11 percent of absent
fathers either lived overseas or had an unknown residence.
Absent fathers who lived in the same state as their children
had a payment rate of 81 percent while fathers who resided
in a different state had a rate of 66 percent. Those
fathers with residences overseas or unknown had a payment
rate of 47 percent.

A higher percentage of mothers of children whose
fathers had visitation privileges were awarded child support
(78 percent) as compared to those who had neither visitation
privileges nor joint custody (27 percent). The award rate
for mothers of children whose fathers had joint custody was
65 percent, less than the rate for fathers with visitation
only. This is understandable because in such situations the

father provides support functions in lieu of cash payments.

5

A higher percentage of fathers with joint custody pay the
child support due (90 percent) than fathers who have
visitation privileges (79 percent) and those without
visitation or joint custody provisions (44.5 percent).

These statistics underscore three primary points
explored in this thesis: the low rate of full compliance
with child support awards and the fact that this rate has
not changed over the past decade; the link between
visitation and child support; and the importance of the
relationship between the ex-spouses as evidenced by the
significance of voluntary agreements in the receipt of
higher amounts of child support. Delving into the latter
two points hopefully will promote a better understanding of

the first point and appropriate enforcement initiatives.

B. Literature on Child Support and Visitation

Many papers that concentrate on the child support
compliance issue empirically, focus on the effects of
noncompliance on the post-divorce economic status of
custodial and noncustodial families, including Nichols-
Casebolt (1986), Weitzman (1981), and Garfinkel and
Oellerich (1989). These studies found, for example, that
divorce has a more negative economic impact on women than it
does men, resulting in financial difficulties and often
poverty for the custodial parent.

A recent paper by Del Boca and Flinn (1990) focused on

the effects of a divorce settlement on the post-divorce

6
welfare levels of the parents and the children by first
theoretically modelling the preferences of each parent
within the legal environment, and then empirically
estimating the behavioral parameters that characterize these
preferences. Similar to my thesis, each parents' utility is
a function of own consumption, and child ”quality" as
measured by expenditures on the child and time spent with
each parent. They use their estimates, derived from
Wisconsin Child Support Experiments data, to determine the
optimal custody arrangements and child support orders within
a Nash equilibrium framework. These divorce outcomes are
then compared to those observed in the data and found to be
markedly differenfih They conclude that more information is
needed on the objectives of the judges and lawyers involved
in determining settlements.

Other papers focus on the determinants of child support
awards and receipt, most notably Beller and Graham (1985).
Using 1979 Census data, they found that the likelihood of
being awarded child support depended upon the needs of the
mother and her children as measured by the number and ages
of the children, education of the mother, mother’s age at
divorce, and upon the absent father’s long-term ability to
pay as measured by education, value of property settlement

at divorce, and age at divorce. In contrast, the likelihood

 

3Thejprimary limitation of their one-period model is that
the interactions they seek to model are1almost surely dynamic,
not static.

7
of receiving child support due depended less upon the
circumstances of the woman and more upon the current
financial well-being of the ex-husband. His income was
found to affect whether or not any child support was
actually paid, but not how much was paid. Fathers with low
current incomes evaded payment altogether, instead of
partially cutting back on payments, a result supported in
Peters et al (1992). Because of the different types of
noncompliers, Beron's (1990) research emphasized the
important policy implications of distinguishing between
those who pay no support at all from those who pay some
support.

Other reasons for noncompliance examined in the
literature include remarriage by the noncustodial parent
(Garasky, 1990), and lack of enforcement of awards. This
latter issue is the primary focus of one of the most
exhaustive studies done on the collection of child support
by Chambers (1979). It was based on 13,000 case files in
twenty-eight Michigan counties, as well as interviews with
fathers, ex-wives, court personnel, judges and jail keepers.
Chambers found that the counties with the highest rates of
compliance shared two characteristics: a self-starting
system of collecting child support, where child support
payments are made directly to the court so that court
personnel can monitor compliance, and a high incarceration
rate.

More recently, Robins' (1986) empirical analysis of the

8
effectiveness of child support enforcement policies on the
receipt of child support disclosed that the state's child
support enforcement programs have a significant positive
effect on receiving child support for all families who
reported receiving help from the child support agency. He
also found that the program had significant effects on
whether an AFDC family had a support obligation, but no
effect for non-AFDC families.

These results lend support to the neoclassical theory
of low child support in which differences in child support
payments between households are attributed to differences in
relative prices (e.g., the price of noncompliance as
measured by the state’s enforcement efforts), demographic
factors, and income. Economists therefore emphasize the
effect of policy changes, such as increasing enforcement, on
the receipt of child support payments.

One problem with this model, as noted by Folbre (1984),
is that neoclassical theory assumes random variation in
family utility functions. (A divorced couple with children
is considered a family, albeit a binuclear one as opposed to
a nuclear one). However, if systematic differences in
unobservable family utility functions exist, the
interpretation of observed relationships between changes in
household behavior and changes in relative prices would be
wrong. If, for example, income has an effect on the
relative bargaining power of the two parents, families where

one parent controls substantial wealth may make very

9

different decisions than those in other, similar families.
Likewise, control of visitation can be a very powerful
bargaining tool, and its effect on the outcome depends upon
the noncustodial parent’s attachment to his children and his
own bargaining tools. The use of income or visitation as
sources of bargaining power may therefore render the utility
functions endogenous to the particular family. Ignoring the
strategic effect of these factors confounds the empirical
estimates of the effects of relative prices on outcomesi.

The estimates of the positive effect of visitation on
child support receipt promotes the possibility that these
two factors are being used strategically. Wallerstein and
Huntington (1983) studied the link between payments and
visits. They found that visitation and the post-divorce
relationship with the children were among factors correlated
with nonsupport. At eighteen months post-divorce, children
who were fully supported were visited more frequently than
other children. Frequency of contact was a less significant
measure of the father’s interest than the pattern of the
visit and the duration of each visit. For example, weekend
visits and overnight visits were highly correlated with
child support. Additionally, the relationship between child

support and visiting, while of little consequence at the

 

‘Several economists, including Manser and Brown (1980),
McElroy and Horney (1981, 1990), and McElroy (1990) examine
this issue as it relates to a nuclear family. They derive
Nash-bargaining models of household decision-making which
allow for different family member utility functions and derive
a joint utility function within a bargaining framework.

10
time of the separation, grew increasingly important over the
years that followed.

Furstenburg et a1 (1983), in their study of the
patterns of contact maintained by the noncustodial parent
and the child, also found a positive relationship between
compliance with a child support award and contact between
the noncustodial parent and child. Using data from the
National Study on the Well-Being of Children, they
established that the fact of support rather than the amount
of support seemed to be related to the maintenance of ties
between father and child.

Weiss and Willis (1985) developed a model of optimal
marriage contracts to explain this linkage. Their reason
for nonpayment of support is the existence of a monitoring
problem: the noncustodial parent suffers a loss of control
over the allocative decisions of the custodial parent and
cannot be sure the custodial parent is spending the award on
the child. This results in a nonoptimal allocation of their
joint resources. In Weiss and Willis' 1989 paper, they
estimated that ex-wives spend up to three-fourths of a child
support transfer on their own consumption. The authors
proposed an enforcing arrangement solution in the form of a
sequential bargaining process in which the noncustodial
parent pays support only after receiving child visitation
rights and insuring the payments are being spent on the
child.

Recent work by Peters et al (1992) utilize an implicit

ll

contracting framework to understand how child support
compliance is affected by the dynamic nature of the parents'
relationship and the relationship between the non-custodial
parent and the children. They test their theory using
longitudinal data collected by the Stanford Child Custody
Project of over 1,000 California families who filed for
divorce in 1984 and 1985. They found that the level of
contact between the noncustodial parent and his children was
a strong predictor of compliance to support awards.
Significantly, they recognized that child support agreements
can be voluntarily modified after divorce if the original
agreement becomes inefficient in the face of changing
circumstances such as remarriage of one parent, or change in
employment status. Frequently, these changes are not
negotiated legally into a new formal contract due to high
legal costs, so that an unwritten or implicit contract is
the result. In other words, the couple engages in private
ordering, discussed in the next section. Consequently, one
or both parties may be legally noncompliers, though they are
full compliers with respect to the new informal contract.
The emphasis of their empirical analysis is on the extent
informal modifications of initial divorce agreements occur
and compliance with the new implicit agreements.

These latter papers allude to the importance of the
relationship between former spouses in the post-divorce
environment. Rather than ending a family with children,

divorce changes the relationships within the family. The

12
particular aspect of this post-divorce relationship my
thesis deals with is the informal post-divorce process over
the determination of child support and noncustodial
visitation. This process can be handled formally through
the legal system, or informally. My thesis deals with the

informal process, legally termed "private ordering".

0. Private Ordering

Private ordering is defined as "‘law’ that parties
bring into existence by agreement"5. ‘Under private
ordering, two parties are given considerable leeway to
negotiate the outcome of their dispute within the framework
of the law. The current legal system has varying degrees of
private ordering at divorce. The foremost situation is when
the divorcing couple negotiates custody, visitation, child
support, and property division at the time of divorce. When
a divorcing couple has no children, the law generally
recognizes the power of the parties upon separation or
divorce to make their own arrangements concerning marital
property and alimony, subject to no or little subsequent
court modification.

However, when minor children are involved, parents lack
any formal power to make their own law. Private agreements
concerning custody, child support, and property division are

possible and common, but agreements cannot bind the court,

 

’Mnookin, R.H. and L. Kornhauser, "Bargaining in the
Shadow of the Law", 1979, p. 951, fnl.

13

primarily because it is the ultimate responsibility of the
state to determine what arrangement is best for the child.
Further, even if the parties' initial agreement is accepted
by the court, it lacks finality. A court may at any time
during the child’s minority reopen and modify the initial
decree in light of any subsequent change in circumstances.

Nevertheless, available evidence suggests that parents
actually have broad powers to make their own deals at this
time. In a recent study, Mnookin et al (1990), using data
from the Stanford Child Custody Study, found that in the
overwhelming majority of cases, it is the parents, often
with the involvement of lawyers, who resolve issues
concerning custody and visitation following divorce.
As noted in Mnookin and Kornhauser (1979), advantages exist
to these private order contracts. Time and financial costs
involved with legal adjudication can be minimized. The
parties can avoid the risks and uncertainties of litigation,
which may involve all-or-nothing consequences. The
negotiated outcome is more likely to be consistent with the
preferences of each spouse, and thus more likely to be
obeyed, than would a court-imposed solution. Most
importantly, the child benefits because the parents know
more about the child's circumstances than does the judge and
are thus in a better position to decide what is best for the
child and for themselves. Finally, a child's future
relationship with each of his or her parents is more secure

with a negotiated settlement than by one imposed by a court

14
after an adversary proceeding. For these reasons, some
legal scholars conclude that the state has an interest in
facilitating parental agreement outside the court and "see
the primary function of contemporary divorce law not as
imposing order from above, but rather as providing a
framework within which divorcing couples can themselves
determine their post-dissolution rights and
responsibilities"°.

Another situation where private ordering is evident is
in the post-divorce situation when, due to changing tastes
and economic and personal circumstances over the family's
life cycle, the parties wish to renegotiate the initial
agreement (see Peters et al, 1992). However, as just
described, it can be costly and risky to go to court. In
Michigan, for example, certain divorce orders concerning
custody, visitation, support, and domicile can be modified
only if one of the following time-consuming and costly
procedures occur: both parties have signed an agreement
which, if approved by the court is entered as an order; or
one party files a motion for a change, a hearing is held,
and the court enters an order granting a change. The
chance for legal alterations is further inhibited by the
restriction that requests for order modifications cannot be
made more than once every two years.

Wallerstein and Kelly (1980) inquired about post-

 

‘Mnookin, R.H. and L. Kornhauser, "Bargaining in the
Shadow of the Law", 1979, p. 1.

15
divorce litigation to change original financial agreements.
They found that one-fifth of the women, and a slightly lower
percentage of the men had initiated litigation to terminate
alimony or reduce child support, to increase child support
or recover payments in arrears, or to link payment of child
support directly to visiting rights. Visitation was more
likely to be litigated among families where child support
was higher, while litigation over money occurred more often
among the poorly supported families. Since litigation is
costly, it was most often initiated by those who could
afford it, who were still angry, and who felt they had a
good chance of winning.

Because of these transactions costs, parents engage in
private ordering to arrive at an outcome that is optimal in
the face of changing circumstances. A divorcing couple
attempts through bargaining to divide money and child-
rearing responsibilities to reflect personal preference.
However, another potential linkage between support payments
and visitation rights is within the context of enforcement.
Since it is often time-consuming and expensive to enforce
promises in court, linking these two matters can serve to
secure delivery of the promise. If a father fails to pay
support, his spouse may reciprocate by cutting off the
father's visitation or making it more difficult. Even
though this tactic is illegal in most states since there is
no legal connection between these two matters, it is

nevertheless likely to be more effective than court

16
enforcement if the father cares about his visitation rights.
Likewise, a father may believe that his ability to cut off
support will ensure that the mother will keep her end of the
bargain concerning visitation.

As Mnookin and Kornhauser note, it is not so
distasteful in terms of its effect on the child as it may
seem.

If withholding support payments is an effective
way of ensuring that the custodial spouse will not
interfere with court-ordered visitation, it is
certainly not as potentially damaging to the child
as the legally sanctioned alternatives of calling
out officials to force surrender of the child, or
moving for a contempt order that would put the

custodial parent in jail until a promise to
comply. (p. 965, fn 56).

D. Purpose of this Thesis

No game-theoretic model exists to predict and evaluate
alternative outcomes in this strategic game situation.
This thesis addresses this deficiency within a sequential
bargaining framework, and solves for visitation rights and
child support resulting from divorced parents’ bargaining.
It attempts to develop more fully the theory that child
support payments and visitation rights are instruments in a
strategic repeated game between the two parents. Rather
than focussing on the demographic determinants of
noncompliance, this thesis concentrates on explaining the
behavior of the two parties involved in bargaining for their
individual welfare maximization and the resulting outcome.

It makes use of the theory of noncooperative games where

17
cooperation can emerge as a noncooperative equilibrium in
repeated games.

In noncooperative games, attention is focused on the
actions that each player is able to take, and how these
actions jointly determine each player's payoff. Just how
players achieve their outcomes, the strategies and
bargaining levers they use, the institutional and legal
framework within which bargaining takes place, is very
important in determining what they achieve. The appropriate
strategy depends on just how an offer will be received and
responded to by the other side. Since many situations
involve explicit or implicit bargaining, noncooperative
games have dominated the literature over the past few years
and is a particularly viable methodology in explaining the
divorce and post-divorce environments.

This thesis is organized as follows. Chapter II
formalizes a single-period model of the post-divorce
situation. An important feature of the model is that the
welfare of each parent depends directly upon the welfare of
the child. When divorcing parents bargain over economic and
custody issues, they make decisions that protect their
children's interests as well as their own. Analysis shows
that payment of child support by the noncustodial parent
depends upon whether payment of child support will lead to
the desired amount of visitation, and explains how
underpayment of child support can result. Chapter III

provides a repeated game model of the post-divorce

18
bargaining process. I show that the interactions can result
in a Pareto improving outcome for both parents.

The theory suggests that the parents' and child's
preferences, one parent’s knowledge of the other's
preferences, the state of the current relationship between
the former spouses, and the costs of negotiating a divorce
settlement affect the outcome as much as standard economic
variables such as the noncustodial parent's ability to pay
and the custodial parent's need, examined in previous
papers. The single period and dynamic empirical analyses,
presented in Chapters IV and V, respectively, use the
National Survey of Children (NSC) data set. NSC is a
longitudinal study of 0.8. children that comprises three
waves conducted in 1976, 1981, and 1987. Since this data
set is national, it is broader than many of the sets used in
previous analyses, such as Peters' et al (1992) data set
which is restricted to families in two California counties.
Most importantly, NSC contains data on visitation and
preferences that allow the model to be tested.

The empirical analysis suggests that the proposed model
is consistent with key features of the post-divorce
situation, most importantly the strategic role of child
support in the post-divorce environment. The thesis
concludes with comments about policy implications and future

research possibilities.

CHAPTER II. THE SINGLE PERIOD MODEL

In order to simplify the analysis, the female parent
(f) is assumed to be the custodial parent, and the male
parent (m) is assumed to be the noncustodial parent. The
two players, the divorced parents, are assumed to operate
with complete information. The non-custodial parent is

assumed to move first.

A. The Strategic Case

Since the noncustodial parent does not directly decide
the time he will spend with the child, or the child’s
consumption, a model in which the noncustodial parent takes
the consumption of the child and his visitation with the
child as fixed by the custodial parent appears appropriate.
However, optimal behavior then results in a child support
level of zero. If child support is not seen by the
noncustodial parent as being directly related to the child's
consumption (if the noncustodial parent feels the custodial
parent is spending the support on herself) or visits with
the child, the effect of support is the standard income
effect and the optimal response is to pay nothing. Though
this consequence is certainly the outcome in a large number
of cases, it is only one of a number of outcomes in
strategic bargaining.

A model in which the noncustodial parent anticipates

the effect his payments have on the child's consumption and

19

20

on time spent with the child is thought more appropriate.
If this parent acts first, the noncustodial parent takes
into account the custodian’s reactional choice of the
child's time allocation to his choice of support payments
when optimizing with respect to the payments.

1. The Custodial Parent's Problem

As standard in solving sequential problems, the second
stage of the bargain is considered first. Taking the amount
of child support, s, as given, the female’s optimization
problem is to maximize the following utility function:
(2.1) U’(x,t,,tm,l,) = u'(x,t,,l,) + a'U°(x,t,,tm)

subject to the following budget and time constraints:

(2.2) wgn-+Ifl + s = x
(2.3) t,+h,+1,=H
(2.4) t, + t_ = T‘.

The elements of the model are:

u‘(x,t,, 1,) = female's self-interested utility
function

If(x,tnt5) = child's utility function

x = goods consumed by the female and child

s = child support payments

'Hr‘ time the child spends with the custodial
parent

tIn = time the child spends with the noncustodial
parent

If a total time the child has to spend with

parents

21
H = total available hours

time the female spends in the labor market

£7
u

SE = female’s leisure time

H
no
II

female's non-support income
wf = female's wage
af==weight the female parent attaches to the
child's utility.

Each parent maximizes a weighted utility function in
which the utility of the child is given some weight, Itr by
the female parent, and all. by the male parent. If the
parents are altruistic, as they are assumed to be in this
model, a'>10, i = f,m. If a‘= 1, the utility function
maximized by a parent would be U‘4-If, in which case the
parent is indifferent between receiving utility directly, or
indirectly through enjoyment of the child’s consumption. If
a‘> 1, the parent attaches more weight to the child’s
welfare than to his or her own.

According to the budget constraint, the custodial
parent chooses goods for herself and the child, represented
by 1. Thus, x is modelled as a public good in the female’s
household. No distinction is made between goods consumed by
the mother and goods consumed by the child in order to
simplify the analysis. It is also a realistic assumption in
that the mother and child usually have the same standard of
living. The price of x is normalized to one.

The second constraint represents the mother's time

constraint while the third constraint represents the child's

22
time constraint. The time the child spends with his or her
parents is assumed fixed at T2 again to simplify the
analysis. This time is to be divided between time spent
with the custodial parent, t" or the noncustodial parent,
t_. Since the custodian has control over the amount of time
the child spends with his or her father, t. and t, become
the other choice variables for the female.

The utility functions of the female and child are
assumed to be positive and concave in their arguments. The
following partials have the usual signs:

U‘,>0, U°2>0, U°3>0, u',>0, u'2>0,u‘,>0,
where the subscripts on U represent partial derivatives.

The general form of the custodial parent's optimization
problem becomes:

(2 . 5) Max £'=U‘(x, t,, tn, 1,) +11 [w,(H-t,-1,) +I'+s-x)

(2 . 5a) Max £‘=u'(x , t,, 1,) +a'U° (x, t,, T‘-t,) +1: [w,(H-t,-l,) +I'+s-x)
where n represents the Lagrange multiplier, and x, tn and l,
are the choice variables.

First order conditions necessary for a maximum are:

(2.6) £fl==if,+-afiF,-1u = 0

(2.7) $2 = u'z + a‘(U°2 - U°3) - wry = 0

(2.8) $2, = u', - wfu = 0

(2.9) £‘,=w,(n-t,-1,)+I‘+s-x=o.

Combining equations (2.7) - (2.8) gives
(2.10) u'z + affflfz - [13) = 1 or

u3

23

(2.103) M = 1.
U‘.

The private MRS between t, and l, is set equal to the ratio
of the price of time spent with the child over the price of
leisure, both equalling w“ resulting in a ratio of one.
Under the assumption that U'is quasiconcave and that the
implicit function theorem holds, equations (2.6) - (2.9)

define the following set of implicit (or reaction)

functions:

(2.11) x(I‘,s,w,;a’)
(2. 12) t,(I',s,w,;a')
(2.13) 1,(I',s,w,;a')
(2.14) u(I',s,wf;a')

2. Comparative Statics
Comparative static results for x, 1,, and t,, assuming

an interior solution, are:

d; > 0, (pl, > 0, gp,>'or < 0
ds ds ds

The amount of time allocated to the noncustodial parent will
be affected in an undeterminable way by a change in support
payments unless restrictions are placed on the utility
functionh If t,is a normal good for the female, then
dt,/ds > 0. Given time spent with the child is fixed, this
means that t. is an inferior good and the noncustodial
parent is unable to "buy" more time with the child.

However, the opposite could result if t, is an inferior

 

7See Appendix 1 for a detailed derivation.

lWSU’

24

good. There are times over the family's life-cycle when the

._- a--c-rance for leisure, such

at a "difficult"

= 0, and t. a 0
'e is less to say
2 marginal
Lion unchanged.

infer what

18h the solution
5e. For example,
a the custodial
and have a lot of
3e low (given
marginal utility
is now scarce),

Thus, t. could

.zation problem is

).tr(sl.tn(8))

 

25
The choice variables for this parent are s, 1., and x.
where:
xi = goods consumed by the male
I'II = male's income
hIn a time the male spends in the labor market
lIII = male's leisure time
w; = male's wage
a“ = weight the male parent attaches to the
preferences of the child.
The price of x. is also normalized to one. The partials for
the male are u", > 0, u'“2 > 0, and u""3 > 0. Since t. and x
can be expressed in terms of child support payments, the
male will incorporate this information into his utility
maximization problem and choose s accordingly.
The noncustodial parent's optimization problem, after
constraint substitution, becomes:
(2.19) Max E‘“ = U“(xm,t,(s),tm(s),lm,x(s))
+ o[wm(H-(T°-t,(s))-lm)+I"‘-s-x,]
(2.19a) Max ii" = u'“[xm,T°-t,(s) ,lm] + a“U°[x(s),t,(s),T°-
t.(s)1 + atw.<H-<T°-t.<s> )-1..) +Im-s-x..1
where c is the Lagrange multiplier, and s, 8., and 1. are
the choice variables.
The first order conditions with respect to 1)x,, 2)s,
3)1_, and 4)o necessary for a maximum are:
(2.20) s, = U“: - a = o

(2 e 2 1) E2: -U"2dtf/ds+amU°ldX/ds+am (Uc2-Uc3) dtf/dS+WmOdtf/ds-O=O

26
(2.22) E, = u“"3 - wmo = 0
(2.23) E, = w_(H - (T°-t,) - 1m) + I“ - s - x. = 0.
The inclusion of dtnlds and dx/ds in these equations
represents the female's reactions to his choice of s.
Combining equations (2.20)-(2.21) results in the strategic

efficiency condition:
(2.24) -p"2gp,[ds + amyjldxzds + a‘“(§£2-E3)gt,j_g§ = 1-wmdtf/ds
um1
(2.24a) (Umz-Um3)dt,Ld_s + Umsdx/s = 1 - wmdtf/ds.
U“:
The private MRS between s and x, is set equal to
(1 - wmdtf/ds) .
Under the assumption that U1“ is quasiconcave and that
the implicit function theorem holds, (2.20) - (2.23) emerge

as implicit functions.

(2.25) s(wm,I'“; a”)
(2.26) lm(wh,I"; a“)
(2.27) xm(wh,I"; a“)
(2.28) 0(wh,I“; a“)

4. Comparative Statics
The effect of the custodial parent’s income on support
payments is given in equation (2.29) where B, is the
determinant of the bordered Hessiani.
(2.29) ds/dI'“ == 1/H, {dtf/ds[u“2,u“‘33+u“23u“'3,+wm(u“,,u“33-u"‘,,um23-
uml3um3l+uml3um21) 1 ’umnumsa‘i'umisz} -

The sign of this comparative static depends upon the sign of

 

“See Appendix 2 for a detailed derivation.

27

dt,/ds, or how the custodial parent reacts to an increase in
support payments. In other words, as explained previously,
whether or not time spent with the child is a normal good
for the custodial parent determines how an increase in s
will affect time the noncustodial parent spends with the
child and thus whether he will increase support payments as
his income increases.

5. Equilibrium

After eliminating x and x, from the female and male
utility functions using the budget constraints, and 1. and
1, using the time constraints, (s', t,‘) is a Nash
noncooperative equilibrium for this model, or a Stackelberg
equilibrium, if:
(2.30) U’(t,°, s') = max U'[t,, s'] and

(2.31) U“(t,‘, s') = max 0°[t,'(s), s]

B. The Pareto Optimal Case

The previous allocation is not optimal since Pareto-
superior allocations exist. The Pareto optimal allocations
of T‘ and s are found by first solving the individuals'
private optimization problems given t" t_, and s are fixed.
This results in the choice variables x_, 1., x, and 1, as
functions of t" t_, and s as shown below. The custodial
parent's optimization problem is:
(2.32) Max cf = U‘(x,t,,t.,,1,) +t[w,(H-t,-l,) + If + s - x]
The first order conditions define the following implicit

functions:

28

(2-33) X°(8. tn t... W“ I'; a')
{2-34) IRIS. tn t... w" I‘; a‘)
(2.35) r°(s, t,, tan, w,, I'; a')

The noncustodial parent's optimization problem is:
(2.36) Max E“ = U"(xm,t,,tm,lm,x(s))+f[w_(H-tm-ln)+I"+s-xm]

which results in:

(2.37) x..°(s. tr: t... w.. I"; a")
(2.38) lm°(s, t,, tn, w,, I“; a“)
(2-39) f°(8. tn t... w“ I"; a“)

The second part of this solution process involves the
social planner solving the following problem to arrive at
the Pareto optimal distribution of tn th, and s.

(2.40) Max U‘(x, t,, tm, 1,)

subject to:

(2.41) U“(xn,t,(s),tm(s),lm,x(s)) 2 Umo
(2.42) t, + tn = T“

(2.43) x“, = x,°(t,,tm,s)
(2.44) x = x°(t,,tm,s)
(2.45) 1,, -- lm°(t,,tm,s)
(2.46) 1, = l,°(t,,tm,s)

where Ufl,is some arbitrary fixed utility level for the
male.
The lagrangian for this problem is:
(2.47) s = U‘(x°(t,,tm,s), t,, Tc-t" l,°(t,,tm,s)) +
I‘[U"'(xm°(tf,tm,s) ,tf,T°-tf,1m°(tf,tm,s) ,x°(tf,tm,s)-U"o] .

Differentiating with respect to 1) s, 2) t" and 3) r

29

yields:

(2.48) s, = U‘,dx°/ds + U',dl,°/ds + a[u°,dx./as + mung/as +
[mar/as] = o

(2 . 49) 2, = o',dx°/ dt,+U'2-U‘3+U‘,dl,°/ dtf+a (U“,dx_/dt,+U‘“2-
U“3+U“,dlm°/dt,+U“,dx°/dtf) = o

(2.50) £3 = U‘“(xm°(t,,tm,s), t,, T°-t,, 1m°(t,,tm,s),

x°(t,,tm,s) - um0 = o.

In comparing these first order conditions with those of
the individual’s strategic conditions, it is seen that their
allocations of time and support payments are not optimal.
After making the substitution H "hr' hf for lf in equation
(2.49), it can be rewritten as
(2.51) c, = U‘2 - U‘, - u', + a(U°,dxm/dt,+U‘“2-

U‘“3+U“‘,dlm°/dt,+U‘“,dx°/dt,) = 0
The custodial parent's private strategic first order
condition with respect to tfis.found in equation (2.7),
rewritten in a form below in which the lagrangian multiplier
is substituted out.
(2.7a) 2', = U'2 - U‘3 - U‘, = o
In comparing (2.51) and (2.7a), note that the female does
not consider the effect of‘q10n the male's utility, which
results in an overallocation of T‘ to herself, and an
underallocation of t. to the father, since t, enters her
utility function only indirectly through afif. A consumption
externality is present since her consumption of t, affects

the father's consumption of tm. The amount of the

30
externality equals the latter half of equation (2.51), or
(2.52) Externalityf = a(U"',dx_,/dt,+U"2-
U'3+U",d lm°/ dt,+U",dx°/ dt,)

The same result follows in the allocation of support
payments. After substituting H - tn - h, for l, in
equation (2.48), it can be rewritten as
(2.53) s, = u‘,dx°/ds + U‘,d1,°/ds + a[U"2dt,/ds + U“,dx°/ds]=0
When compared to the noncustodial parent's private strategic
first order condition with respect to 3, equation (2.21),
rewritten below in a slightly different form without the
lagrangian multiplier, underallocation of support payments
results because the noncustodial parent does not consider
the effect of his actions on the custodial parent’s utility.
(2.21a) £2 = U“,dt,/ds + Umsdx/ds - (1/w)U"‘3 = 0.

The amount of the externality is equal to
(2.54) Externality,ll = 1/a (U‘,dx°/ds + U‘,dl,°/ds) + (1/w)U"‘3

Let (s', t!) represent the Pareto optimal allocation of
these two goods. This can result with constant communication
the two parents and/or if the two parents see each other
frequently. Section III shows that this can also result in

a dynamic model through the use of trigger strategies.

C. The Competitive Case

For sake of comparison with the strategic case, the
competitive equilibrium is derived here. In the competitive
equilibrium case, each partner takes the other's decision as

given when making their own decision. In this case, the

31

custodial parent's optimization problem is the same as in
the strategic case, found in equations (2.1) - (2.4). The
noncustodial parent's problem changes in that his choice of
s is not a function of how the custodial parent reacts to
his choice in her choice of t_. However, the noncustodial
parent still does consider how the support payments affect
consumption in the custodial parent's household in making
his decision on s9. His objective function becomes:
(2.55) U'“(xm,t,,tm, 1m,x(s) )=u“‘(xm,tm, 1m)+a“‘U°(x(s) ,t,,tm)
subject to the constraints found in equations (2.16) -
(2.18), rewritten below.
(2.16’) wmhn + II“ - s = xIn
(2.17') tn + hm + lIn = H
(2.18’) t, + 1:m = T‘.

The first order conditions with respect to 1)x., 2)s,

3)1_, and 4)B, the lagrangian multiplier are:

(2e56) E! = ““1 " B = O

(2.57) £2 = amlfidX/ds - B = 0.

(2.58) £3 = 1.1"“3 " WmB = O

(2e59, £4 = Wm(H - (Tc-tf) " 1m) + In - S - X“, = 0

Combining equations (2.56) - (2.57) results in the

competitive efficiency condition:

 

9The assumption that the noncustodial parent acknowledges
the linkage between support payments and custodial household
spending is necessary to insure that the amount of support
payments is positive in cases where the noncustodial parent
cares about the child. This condition also incorporates those
cases where the noncustodial parent is sensitive to how much
of his support is being spent on the child.

32

(2-60) smallish = 1 or
u“,
(2.60a) W = 1 .
U")

1. Comparative Statics

The effect of the noncustodial parent's income on
support payments is given below, wherezflh is the determinant
of the bordered hessianw.
(2.61) ds/dI" = 1m, (-u'“uu'“33+u“'132) .
In comparing this with the same comparative static in the
strategic case found in equation (2.29), it is seen that s
does not depend upon dtf/ds, or the custodial parent's
visitation decision reaction to the amount of support. The
sign of this comparative static in the current scenario is
also ambiguous, though the sign depends solely upon the
relative size of -u9nufin versus uPnz rather than on this and
the custodial parent's reaction to the amount of support
payments as in the strategic case. This comparison
underscores the advantage of examining the strategic case,
which emphasizes the interdependence of the decision makers.

This interdependence is tested in Chapter IV.

 

10See Appendix 3 for a detailed derivation.

CHAPTER III. REPEATED GAME MODEL

The primary limitation of the one-period model is that
in reality the game continues for a long period of time.
The parents will want to consider some other objective
besides maximizing current utility. A dynamic, or repeated
game, in which the players face the same game for a long
period of time better represents the post-divorce situation.
Further, since the static Nash equilibrium determined above
is not Pareto optimal, there exists an incentive to
cooperate which implies that cooperation rather than
noncooperation may best characterize the post-divorce
situation for many couples. It will be shown in this
chapter that the cooperative outcome can be supported in a
subgame perfect Nash equilibrium in the repeated game, given

that each party cares enough about the future.

A. Equilibrium in a Dynamic Game

Let U‘,(tm,s) be parent i’s utility as defined by
equations (2.1) and (2.15) in the single period model at
date t (t=0,1,...T), where T is infinite. Each parent
wishes to maximize the present discounted value of his or
her utility; that is:
(3.1) in 6‘U‘,(tm,s) ,

where 8 is the discount factor (6=1/(1+r), where r is the

rate of time preference, and 6<1.) 6 close to 1 means the

33

34
future is valued more than when 6 is close to zero.

The two parents operate with common knowledge and
complete information. The play of the game is sequential,
i.e., at each date t, the male chooses the amount of support
first and then the female chooses the amount of visitation.
Because the players move one at a time, and each player
knows all previous moves when making his or her decision,
the game is one of perfect information.

The game is an infinite sequence of the single period
game played at each iteration". Though the static Nash
equilibrium of the previous single-period model played
repeatedly is an equilibrium of this game, it is not the
only equilibrium. Consider the following strategies: The
noncustodial parent pays the Pareto optimal level of support
in period t if the custodial parent delivered the Pareto
optimal level of visits. Likewise, the custodial parent
delivers t." if s" was paid in the previous period. If ever
one of the players cheats, the game reverts to the static
Nash equilibrium played repeatedly. Given hl represents the
history of the game's actions, this can be stated formally
for the custodial parent:

(3.2) tm(h,) = to," if h, = (th,sP;...;tn',sP) and

tm(h,)=tm' otherwise for the current and all

 

"This is equivalent to a finite game in which the number
of periods is a random variable. Although most child support
legally ends when a child turns 18, children often require
financial support for further education and/or in getting
started in a new life after high school.

35
previous t.
For the noncustodial parent:
(3.3) s,(h,) = s" if h, = (tn’,s';...;tm’,s") and
s,(h,)=s' otherwise for all previous t.

These are the classic "trigger" strategies formalized
in Friedman (1971). These form an equilibrium as long as
both parties care enough about future utilities so that the
threat of noncooperation in the future is sufficient to
convince players to play the Pareto efficient strategy. Let
U‘(tm°,s") represent the utility to parent 1' when the female
cheats, U‘(tm",s°) the utility when the male cheats,
U‘(tu’,s') the utility when each play the static Nash
outcome, and U‘(tm",s") the utility when each play the
efficient outcome. If

(3.4) 6' 2 g‘(tm°,s") - Q'(tm9,s')
U'(t...°.sP) - U‘(t..’.8')

and

(3.5) 6‘“ z. g2(tm",s‘) - U‘“(tm",s")
[10(tmp'SC) - Um(tm.ls.)

then the Pareto optimal equilibrium can be sustained. In
other words, as long as both parents’ discount factors are
high enough, this cooperative outcome is subgame perfect.

If, however, at least one parent's discount factor is
sufficiently low, the agreement is destroyed. Consider the
cases where fathers have no interest in maintaining contact
with their children over the long run. Their discount
factor is low and their incentive to pay support is

diminished. This also extends to the cases where mothers

36
strategically forgo child support forever in order to
absolve themselves from the obligation of granting

visitation with the ex-spouse.

B. Balanced Temptation Equilibrium

Bargaining power can be introduced in this model using
the discount factor. One component of bargaining power is
the players’ relative concern for the future. The parent
who is less patient and is thus more likely to cheat on the
agreement has more control over the situation. This
player's relative indifference to the long run arrangement
means the opponent must make concessions in order to
maintain the relationship. For example, if the father is
more likely to withdraw from the bargain (lower 6), he
forces the mother to accept a lower level of support
payments, resulting in a new equilibrium.

This equilibrium, (s",tm") , formally the balanced
temptation equilibrium (Friedman, 1971), is the highest
supported level of tI and s at which the two players'
temptation to cheat, expressed in equation (3.6), is
equalized. The one period gain from cheating for each
player is given in the numerator and the per period loss

following cheating is depicted in the denominator.

(3.6) Qf(tm°,s') - U‘Itg'.s_")_ = 92(tm',s°) - E(§m’,s')
Uf(tmptsp) '- U'(tm°,s°) I’m‘tmptsp) '- Um(tm.os.)

 

37

C. Conclusion

In this chapter I show how the repeated game developed
by Friedman (1971), in which the players use a "tit-for-tat"
strategy, can be applied to post-divorce bargaining. Each
player is deterred from breaking an agreement, not by a
legally binding contract, but by the credible fear that the
opponent will cheat. This informal bargaining and an
informal agreement outside the realm of the courts is the
consequence of the transactions costs involved with going to
court to revise the legal visitation and support payments
agreement, mentioned in the introduction. Factors
facilitating the cooperative agreement in this game include
the fact that only two parties are involved in the game, and
that the time it takes to detect a cheater and thus
retaliate is short since payments are usually made monthly
and visits are customarily made weekly. Since retaliation
can be immediate, the cost of deviating is increased. Tacit
collusion is thus easier to sustain.

One type of test of the empirical implications of the
repeated game requires data proxying the parents' discount
rates, which is not available in the National Survey of
Children. Another test involves the relationship between
visitation and child support in different periods. This is

performed in Chapter V.

CHAPTER IV. A CROSS-SECTION, SIMULTANEOUS EQUATIONS MODEL

The previous theoretical chapters indicate how
visitation can be treated as a variable in the decision
about child support payments and how the amount of child
support received can affect the amount of visitation between
the child and the noncustodial parent. They also reveal the
importance of pre-divorce and current negotiating costs, the
preferences of all involved participants, information, and
time preference, to the outcome. Despite the intuitive
appeal of these models of strategic behavior, it is
important to test their validity. The model gives rise to
certain testable hypotheses described below. This chapter
and the next develop a set of estimating procedures that
incorporate these issues and present the results of these

tests.

A. Data and Sample

Most past economic studies have made extensive use of
data from a special supplement to the 0.3. Bureau of Census’
Current Population Survey, Chllg Suppopt apd Alimony, that
provides information about child support arrangements of a
nationally representative sample of women with children
(Beller and Graham, 1985; Robins, 1986; Garfinkel and
Oellerich, 1989; Beron, 1990). Though this data set
contains much demographic and economic information for each

family, there is little information on the noncustodial

38

39
parent and none on visitation. The Michigan Panel Study of
Income Dynamics (PSID), a national longitudinal study that
began in 1968, contains information on both parents if the
parents were part of a nuclear family at some point during
the survey period selected (Nichols-Casebolt, 1986). Another
nationally representative sample that examines marital
stability and divorce settlements is The National
Longitudinal Study of the High School Class of 1972. Used
by Weiss and Willis (1989), it contains data on the use of
lawyers and the legal costs of divorce, and subjective
measures of marital happiness and the bitterness of divorce,
as well as standard sociodemographic variables available for
both ex-spouses.

Richer data sets that contain more information on the
noncustodial parent and procedures taken by the legal system
to enforce court orders tend to be geographically limited
(Del Boca and Flinn, 1990, use court data from 18 Wisconsin
counties; Chambers', 1979, data is limited to 28 counties in
Michigan.) This is also true of data sets that contain
visitation details (Wallerstein and Kelly's, 1980, and
Wallerstein and Huntington's, 1983, data on sixty divorced
California families; and Peters' et a1, 1990, data on 1,000
California families).

The data set used in this study is the National Survey
of Children, a longitudinal study of U.S. children that
comprises three waves. It was conducted in 1976, 1981, and

1987, and used by Furstenburg et al (1983) to study the

W1

HI

In

40
incidence of marital disruption in children's lives, and the
amount of contact children maintain with the noncustodial
parent. In 1976, the Foundation for Child Development
sponsored a survey in which the purpose was to study the
well-being of children. The specific purpose of the first
wave was to assess the physical, social, and psychological
well-being of different groups of American children. For
Wave 1, the original sample was a multi-stage stratified
probability sample of households in the continental United
States containing at least one child aged 7-11 and producing
2,193 households. Data were eventually gathered for 2,301
children in 1,747 households. Black households were
oversampled in order to yield interviews with approximately
500 black children. The sample was weighted to adjust for
the oversampling of black children, and to correct for
differences between the Census and sample figures for
several demographic characteristics.

Interviews were conducted with the children and with
the parent most knowledgeable about the child (usually the
mother) in 1976, and with the child's main teacher in 1977.
Topics of the questions included family characteristics,
including financial status; location; the parents' marital
history, childbearing and childrearing patterns; the state
of their relationship and their relationship with the child;
the parents’ employment history and education; and the
child's friends, social activities, physical and mental

health, personality, and academic performance.

41

In this survey, the child, rather than the family, is
the primary unit of analysis. Up to two children from each
family were eligible to be interviewed, along with the most
knowledgeable parent. The researchers determined the number
of eligible children by their birthdate. If more than two
children were eligible, only two were selected at random to
be interviewed. Since two children from one family and one
set of parents were included in the sample, the information
pertaining to these families was weighted by one-half in all
analyses in order to avoid double-counting.

The specific purpose of the second wave was to
determine the effects of marital disruption and conflict on
children. To that end, the 1981 survey followed up all
those children who were in a high conflict (as reported by
the parents in the first wave) or disrupted family in Wave 1
plus a subsample of the others. 90 percent of the children
were relocated and interviews were conducted with 1,423
children and the more knowledgeable parent. School
information was also collected using a mailed questionnaire.
The sample was weighted to adjust for the differentials
between the Census and the sample populations. In addition
to the information gathered in the first wave, Wave 2
contained considerable information for dissolved marriages
on details of the marital dissolution, including components
of the divorce/separation settlement and the divorce
process; the relationship between the respondent and the

former spouse; contact between the child and each parent;

42
and the child’s feelings about his parents' break-up.

The purpose of the third wave was to examine the
social, psychological and economic well-being of sample
members as they became young adults, with particular
emphasis on sexual and fertility behavior. A total of 1,147
children and the primary parent from Wave 2 were
interviewed. Wave 3 respondents were asked about
contraceptive use and family planning; receipt of child
support and welfare; establishment of paternity; and
attitudes regarding marriage, child support, and welfare.

The sample for my study is restricted to ever-divorced
or currently separated families with an outside, or
noncustodial, parent identified by the custodial parent.
Since information relevant to the theory is available for
the former spouse of the custodial parent which was not
available for the outside parent in general, such as the
former spouse’s location, communication between the former
spouses, and various aspects of the divorce or separation
process, the sample was further restricted to those families
in which the outside parent was a former spouse of the
custodial parent. This provides a sample that consists of
228 children in 174 families”. For the single-period
simultaneous relationship analysis, Wave 2 data are used.
The longitudinal analysis in Chapter V utilizes Waves 2 and

3.

 

”The sample changes slightly from one test to the next
because of missing information.

43

B. Empirical Methodology

In the single-period model, the amount of the child’s
time the custodial parent allocates to the noncustodial
parent is affected by the amount of child support received,
though the sign of the effect is indeterminate: an increase
in child support payments could result in an increase or
decrease in the child’s time allocated to the noncustodial
parent, depending upon whether the child’s time is a normal
good for the custodial parent or not. Additionally, the
amgppt of child support paid by the noncustodial parent is
indirectly affected by how the support affects visitation.
Therefore, an important test of the theory is whether a
significant relationship exists between child support
payments and visitation in the two equations in which child
support and visitation are dependent variables. If a
relationship exists, the issue then to be examined is the
direction of the relationship.

However, a significant relationship between these two
variables alone does not prove this thesis’ strategic
theory. A positive relationship supports other primary
theories linking visitation and child support. One such
theory is Weiss and Willis’ (1985) monitoring theory where
fathers who pay support want more contact with their child
to assure that their payments are being spent on the child.
Another possibility is that fathers who see their child
regularly are more aware of the child’s needs and so pay

support regularly. However, one feature that separates the

44
strategic threat theory from these theories is the
interdependence of the child support and visitation
decisions. According to the theory, the noncustodial parent
takes into account the custodial parent’s reaction in terms
of visitation granted when deciding how much support to pay.
Likewise, the custodial parent considers how her decision
will affect the noncustodial parent’s decision. If both
parents are determining child support and visitation, the
ordinary least squares estimation procedure would not
provide unbiased or consistent coefficient estimates and a
simultaneous equation estimation procedure would be
appropriate.

Another factor that separates this theory from the
others is the significance of various strategic variables.
Theoretically, the higher the negotiating costs, the less
likely a child support/visitation agreement is reached and
kept. If the divorce process was marked by conflict, it
could indicate an unwillingness to cooperate post-divorce.
Two dummy variables are used to estimate pre-divorce
negotiation costs. If the custodial parent reported that
the former spouses argued a lot before separation, or if
this same parent asserted that child support was a difficult
issue to work out at separation, the less child support paid
or visitation will be granted”. Likewise, if the current,

post-divorce relationship is one of conflict, it is less

 

13Complete definitions of the variables are given in
Appendix 4.

45
likely that any agreement is upheld. Conflict in the
current relationship is represented by a dummy variable
equalling one if the conflict level between the custodial
parent and the former spouse increased after separation
according to the custodial parent.

The theory also showed that the parents’ and child’s
preferences affect the outcome. The child’s preferences
with respect to time spent with each parent are incorporated
into the decisionmakers’ (his or her parents’) utility
functions and positively affect the parents’ utility under
the assumption of altruism. To test whether the child’s
desires are considered in making decisions, the significance
of the variable measuring the child’s closeness to the
outside parent, as reported by the child, is tested. This
dummy variable equals one if the child contends the
relationship is extremely close or quite close, and zero
otherwise. The custodial parent’s preferences are taken
into account with two dummy variables measuring preference
for time spent with the child. The first measures the
custodial parent’s satisfaction with the current custody
arrangements which equals one if the custodial parent is
very satisfied with the arrangements, and zero otherwise.
The second evaluates the child’s relationship with the
custodial parent, equalling one if the relationship is
reported by the custodial parent to be extremely close or
quite close, and zero otherwise.

As shown in Chapter II, Section B, the optimal

46
allocation of child support and visitation rights can result
when each parent takes into account the effect of his or her
decision on the other parent’s utility. This occurs the
more information one parent has about the other’s
preferences, or the shorter the time since the marriage
ended, represented by the number of years since the divorce
or separation.

The variables just mentioned are the primary ones in
this strategic model. In addition, control variables are
added that have been shown in other studies to affect child
support and visitation. These include a dummy variable for
race, equalling one if the respondent is black, and zero
otherwise; a dummy variable signalling whether or not the
custodial parent remarried“; and a dummy variable for the
distance the outside parent lives from the child, equalling
one if the noncustodial parent lives within a one hour drive
from the child, and zero otherwise. Variables representing
the custodial parent’s need are also incorporated into the
analysis. These are the total number of children, family
income, and a dummy variable indicating whether the
custodial parent received any post-high school education.

As is the case in most past studies, a good measure of
the noncustodial parent’s ability to pay is not available.

Previous analyses used the custodial parent’s age to proxy

 

“The marital status of the noncustodial parent is highly
correlated with several of the explanatory variables, such as
his or her closeness to the child, and so it was not included
in the analysis.

47
this influence. Though considered a poor approximation, it
is included here to conform with past work.

Information from the Office of Child Support
Enforcement (1981) was used to classify the custodial
parent’s state of residence using a parameter measuring the
effectiveness of the state’s child support enforcement
procedures. This parameter is the number of child support
enforcement techniques available in the individual states’
child support enforcement programs. These include: (1) wage
garnishment - in response to a judicial proceeding, the
employer of a noncustodial parent withholds wages only if
child support payments are in arrears; (2) criminal contempt
- nonpayment of child support is seen as an offense or
injury against the court, as opposed to another party in the
lesser charge of civil contempt, and a fine or imprisonment
is imposed; (3) attachment - taking, apprehending or seizing
property for the purpose of securing satisfaction of the
child support judgement; (4) debt set-off - provides for the
set-off of state or federal income tax refunds against child
support debts; (5) liens - an encumbrance on real and
personal property for the amount of overdue support; and (6)
income withholding - a provision for the employer to
withhold wages from an employee for current child support
payment or arrearages and forward the sum to the family or
the public assistance agency.

Since the theory is concerned with upholding an

agreement, the ideal measure of child support is a

48
proportion of the child support due that is actually
received. However, the amount due is available for only a
limited subsample of the population, so the child support

measurement used is the amount of child support that was

 

--‘ Iva-‘1 . *—
..-—e

received in the past year as reported by the custodial
parent. Similarly, the amount of visitation agreed upon in
the initial divorce settlement is not available, so
visitation is measured as the number of days the child spent
with the noncustodial parent in the past year, also as

reported by the custodial parent.

C. Estimation

Past studies have investigated separately the affect of
visitation on child support payments, and the affect of
child support on visitation. This approach, however,
ignores the complex interdependence between these two
factors. A simultaneous equations approach is thus
necessary to account for this situation in which two parties
are jointly determining child support and visitation.

This section sets up the general simultaneous equations

models. I have:

(4.1) c‘ = my + B,'x, + r,'z, + u,
(4.2) v = a,c‘ + B,'x, + r,'z, + u,
(4.3) c = max (0, c‘)

where 0* is the latent child support variable, C is the
observed child support variable, V represents visitation and

equals the number of days the child spent with the

49

noncustodial parent in the past year, the a’s and B’s are
coefficients, the X’s are the control variables, and the P’s
are the strategic factors. The u’s are the bivariate normal
error terms with zero mean and independent of X'and z . The
reduced forms of equations (4.1) - (4.2) are:
(4.4) c‘ = «xx + v,
(4.5) V = «3’1: + v,
where (Vu"h) are also bivariate normal with zero mean, and
independent of.x.

1. Estimation of Child Support Equation

The estimation technique used here to estimate the
child support equation in this simultaneous equation tobit
model is one introduced by Smith and Blundell (1986).
First, reduced form coefficients of (4.5) are estimated.
Note that a reduced form of V can be estimated if what is
included in the system is the latent variable C" rather than
the observed variable C. That is, because the system is
linear in (C?,‘V), the reduced form of V'can be determined
and this specific estimation technique can be used. The
advantage of using C' is that it makes the simultaneous
aspects of the problem solvable. The disadvantage arises in
the interpretation of the coefficients: they no longer
represent the partial effects of the individual variables on
observed child support, but rather on the latent variable.
Since the major tenet of the theory is the decision-makers’
interdependence in arriving at equilibrium child support and

visitation, a simultaneous equations solution to the model

50

will take precedence.

To continue, following Smith and Blundell I write u,
conditional on v, as
(4.6) u, =- p,v, + e,
where eg is normally distributed with zero mean and.is
independent of V, X“ and v,. Substituting (4.6) into (4.1),
I get the conditional model
(4.7) c‘ -= (2,17 + mm, + r,'z, + p,v, + 45,
(4.7a) c‘ = W's + e,

and the following conditional censoring rule

(4.8) c = c’ if e, > was
and
(4.8a) C = 0 otherwise.

Note that the parameters 112 enter C’s conditional density
through v3. I use the estimates for i} from (4.5) to obtain
an estimator for p“ then estimate (4.7a) - (4.8a) using
tobit estimation procedure”.

The noncustodial parent’s driving distance from the
child is assumed not to affect the amount of child support
received given support does not have to be delivered in
person, but can be sent through the mail. Additionally,

though child support is assumed to be affected by the

 

15Because of the two-step estimation procedure,
technically the standard errors in the second step should be
adjusted. Here, computations were carried out using the
statistical program STATA, which reports incorrect standard
errors. Previous applications have shown this to make little
difference (see Vella, 1993) so the uncorrected standard
errors are reported.

51
noncustodial parent’s relationship with the child, it is
assumed not to be affected by the child’s relationship with
the custodial parent. These two variables, therefore, serve
as identifiers for the child support equation.

2. Estimation of Visitation Equation

Nelson and Olson (1978) provide a computationally
tractable method for computing visitation that is similar to
two-stage least squares“. First I estimate II, of equation
(4.4) using a tobit estimation procedure and form the
instrument 5'. The structural coefficient estimates (2,, 8,,
and z, are obtained using OLS, after replacing C’ by C“ on
the right hand side of equation (4.2). If the model were
linear in (C, V), this would produce the two stage least
squares estimator.

Variables representing the financial need of the
custodial family and the financial well-being of the
noncustodial parent are assumed not to affect visitation.
These variables, which include the custodial parent’s age,
education, number of dependents, and family income, serve as
identifying variables of the visitation equation. The
enforcement variable is also included in this group since
the enforcement programs apply to child support rather than

visitation awards.

 

16The reason this method was not used in the estimation of
child support is that, as noted by Smith and Blundell (1986),
Nelson and Olson’s procedure inconsistent in the presence of
censoring.

52

D. Empirical Results

After excluding observations with missing values, the
samples for each of the analyses in this section contain 204
or 207 observations. Means and standard deviations of
variables are presented in Table 4.1.

1. The Amount of Child Support Received

The tobit and the simultaneous equation results are
presented in Table 4.2 in columns 1 and 2, respectively. A
test for endogeneity of the independent variables is whether
the residual 5} is significantly different from zero. It is
at the 1% level, leading to the conclusion that this
simultaneous equation system is the correct specification of
child support receipt. It is this endogeneity and the
interdependence of both the child support and visitation
decisions that separates the strategic theory from other
theories that link these two variables. The high
significance of the strategic variables as a group in the
model, evidenced by an F-statistic of 2.90 indicating
significance at the 1% level, further supports the strategic
aspect of the theory.

The outcome of the simultaneous equation system differs
from the single equation model in that the coefficient on
the number of visits is larger in the former and more
significant, indicating that child support is more
responsive to the number of visits than estimated in the
single equation model. This is as expected given the

positive relationship between the two variables and the

53

Table 4.1 Means and Standard Deviations of Sample
Characteristics in Cross Section Analysis

 

 

 

 

 

 

 

 

 

 

 

 

 

VARIABLE lWEAN' Eflfl)DEV
Family/Demographic Characteristics:
CP’s Age 38.344 5.672
CP’s Education .210 .408
CP’s Family Income 17419.590 11975.610
# of CP’s Dependents 4.161 1.505
CP Remarried .474 .500
NCP’s Driving Distance From Child .671 .471
Legal Climate:
# of State Enforcement Techniques 5.195 1.609
Negotiating Costs:
Argued Before Separation .592 .493
Child Support Was a Difficult Issue to Work Out at .106 .309
Squafimn
Divorce Settlement Obtained .853 .354
inuenus: J
Child’s Closeness to NCP .525 .500
Child’s Closeness to CP .842 .366
Settlement Has Changed Since Separation .225 .419
CP’s Satisfaction with Custody .724 .448
Current Relationship:
Conflict Between CP and NCP .058 .235
Information:
Years Since Divorced/Separated 5.782 3.879
Child Support:
Child Support per Year 1163.344 1776.047
Visitation:

.. . MiflflL. 151:1“

 

 

 

SOURCE: National Survey of Children, Wave 2, 1981. Divorced or separated families in which the outside patent is the
custodial parent's former apouae. CP-Cuatodial Parent. NCPn Noncustodial Parent

54
feedback relationship: child support is dependent upon
visitation, but also affects the value of visitation.
Within the context of the theory, the noncustodial parent’s
child support decision affects the custodial parent’s
visitation decision, which in turn affects the child support
amount. The noncustodial parent’s action in response to the
custodial parent’s reaction to his decision implies that
child support is being used strategically by the
noncustodial parent.

Both of the variables representing pre-separation
negotiating costs are significant, though the results
initially appear conflicting. The amount of arguing the
couple did before separation is negative, meaning that the
less the couple argued before the separation, the more child
support paid. This supports the hypothesis that negotiating
costs are important in upholding the outcome of a pre-
separation agreement, and that the lower the costs, the more
likely the agreement will be kept.

On the other hand, whether child support was a
difficult issue to work out at separation suggests the
opposite. However, rather than representing negotiating
costs, the amount of time a couple spent hammering out a
settlement could indicate the degree of commitment to making
the arrangement work. If this were the case, it would lend
additional support to the theory.

One possible explanation for the significance of these

two variables is that they could be measuring the ability to

55
obtain a divorce settlement, and that whether or not a
settlement was negotiated is what affects child support. To
test this possibility, a dummy variable indicating whether
or not a divorce settlement was obtained was included in the
estimation. The results are reported in column 3 in Table
4.2. The positive sign on this variable is as predicted
based on past studies, meaning that families with divorce
settlements receive more child support. This could indicate
something about the effectiveness of the enforcement -
enforcement is more effective when an award exists - or
about the state of the parent’s pre-divorce relationship -
similar to the argument in the previous paragraph, parents’
who obtain a settlement are committed to making the
arrangement work. The addition of this variable did not
noticeably affect the estimated coefficients or standard
errors on the two pre-divorce variables, nor of the other
variables. I conclude that the state of the pre-divorce
relationship influences bargaining in the post-divorce
environment beyond their influence on the probability of
obtaining a divorce award.

The state of the current relationship is also important
in child support determination. If the level of conflict
increased after separation, less child support is received.
Under the negotiating cost premise, a harmonious
relationship leads to lower negotiating costs, which
facilitates compliance. Since high conflict relationships

are more likely to use strategic weapons and threats, this

56
suggests that child support is being used as a strategic
threat.

The significance of the variable representing the
child’s relationship with the noncustodial parent indicates
that the child’s preferences are being considered in the
support decision. The negative sign on this variable means
that the closer their relationship, the lower the child
support. After controlling for visits, what may be
happening is that the noncustodial parent is using money to
compensate the child for a less-than-ideal relationship, or
to relieve his or her own guilt about any emotional distance
from the child.

The significance of the variable representing the
custodial parent’s satisfaction with the custody
arrangements also indicates that the custodial parent’s
preferences are considered in the support decision, though
this was not explicitly modelled in the theory. The results
indicate that the less satisfied the custodial parent is
with the current custody arrangements, the more child
support paid. One explanation is that the noncustodial
parent is compensating the custodial parent for his or her
unhappiness with the custody situation.

The variable representing whether a change in the
initial settlement occurred is significant but negative
meaning that a settlement change brings about lower, rather
than higher, child support. Either the optimal amount of

child support was already being received, implying that a

57
change was not in the best interests of the custodial
parent, or that a new settlement was not being enforced.
Information on which parent initiated the settlement change
would clarify whether child support or visitation was
modified and which premise is supported.

The results on the demographic characteristics conform
to past studies. African American families receive less
child support per year than similar white families,
estimated here at $1,093, though the coefficient is not
significant. The significance and positive sign on the
family income variable and the negative significance of the
number of dependents imply that the custodial parent’s need
is not a factor in the receipt of child support, supporting
Beller and Graham (1985). The income result, along with the
positive sign on the education variable, could mean that
families with the knowledge and legal resources to get a
child support award enforced receive higher amounts of
support. Or, as hypothesized by Beller and Graham (1985),
it could represent the fact that the standard of living to
which the family is accustomed has increased, raising,
rather than diminishing need.

The sign of the state’s enforcement variable is the
opposite of what I expected. It suggests that the more
enforcement techniques used by a state, the less support
received by the custodial parent. However, the coefficient
on this variable is weakly significant, suggesting either

that this is a poor measure of the state’s enforcement of

58
child support laws, or that the enforcement mechanisms were
in place, but were ineffective.

2. Visitation

The current relationship between each parent and the
child can affect visitation. As discussed previously,
visitation/intimacy will vary at different times in the
parent’s life (e.g., if the parent is dating, he or she
might prefer less time with the child), and the child’s life
(e.g., younger children might enjoy their parents’ company
more than teenagers would). Therefore, visitation is
expected to be higher the closer the child is to the outside
parent and the less intimate the child’s relationship with
the custodial parent. It is also expected to be higher if
the noncustodial parent is within one hour’s drive from the
child due to the lower cost of contact.

OLS and the Nelson and Olson (1978) two-step estimates
of the number of days per year the child spends with the
noncustodial parent are reported in columns 1 and 2,
respectively, in Table 4.3. A Wu-Hausman [Wu (1973);
Hausman (1978)] test of the appropriateness of the
simultaneous equation specification involved arguments
similar to those used to derive equation (4.7). First I
define for C>0
(4.9) 6, = c - 6'
where C" is obtained from estimating equation (4.4). Then I

estimate equation (4.10) using OLS for the observations for

which C>0.

59

 

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61
(4.10) V = a,(: + B,'x, + r,'z, + “I + u,
The significance of 1, is a test of endogeneity. The results
are presented in Appendix 5. The insignificance of the
residual term means I cannot reject the hypothesis that no
endogeneity of the independent variables exists. OLS was
thus determined to be the correct estimation procedure.

As shown in column 1, child support is positively and
significantly related to visitation, as each additional
dollar of child support results in approximately one-tenth
of an additional day in visitation. The positive sign
indicates that an increase in child support is an increase
in the custodial parent's income, causing her to decrease
the consumption of this particular good. This leaves more
time for the child to spend with the noncustodial parent,
meaning that the noncustodial parent is able to "buy" more
time with the child.

As in the analysis of the receipt of child support, the
positive relationship between visitation and child support
by itself does not prove that visitation is being used as a
strategic weapon by the custodial parent. Unfortunately,
there is not much in these results that differentiates the
thesis' strategic model from other theories that link these
two variables. Though the vector of strategic variables is
significant as a group at the 5% level (F-statistic = 2.58),
few of the variables are significant individually. Neither
the relationship between the child and the noncustodial

parent, nor the custodial parent's relationship with the

62
child are significant. The custodial parent appears to have
little control over visitation, discrediting the strategic
game theory. Additionally, the level of conflict in the
current relationship, and the number of years since
separation do not appear to affect visitation.

If the custodial parent is satisfied with the custody
arrangements, the more contact there is between the
noncustodial parent and the child. This advances the
original hypothesis that the closer the arrangement to the
parents’ preferences, the more likely the agreement is
upheld, meaning higher visitation. This hypothesis is also
supported by the significant, positive sign on the variable
representing a change in the initial settlement. If I
assume that a modification in the settlement occurs to
correspond more closely with the preferences of the parties
involved, and that more visits are optimal, a positive sign
on this variable signifies that a modification in the
initial settlement moves the couple closer to the optimal
outcome for visitation.

One of the variables representing negotiating costs,
whether child support was a difficult issue to work out, is
weakly significant while the other one, the amount of pre-
separation arguing, is insignificant". This provides very

little support for the theory as it relates to visitation.

 

"The addition of the dummy variable indicating whether a
divorce award was obtained had no significant affect on the
coefficient estimates.

63
The other variables are insignificant. Notably, if the
noncustodial parent is within an hour's drive of the child,
he or she spends more time with the child, though the

coefficient is insignificant.

3. Conclusion

I hypothesize that the equations I seek to estimate are
interrelated in a more complete model. In the child support
case, a single equation tobit estimation procedure no longer
provides unbiased or consistent estimators of all the
coefficients because the endogenous variable used as a
regressor, visitation, is contemporaneously correlated with
the disturbance term. Due to the simultaneous equation
bias, I use a two step procedure to arrive at consistent
estimates of the parameters in the child support equation.

By including such strategic factors as the costs of
negotiating a pre- and post-divorce settlement, the
information one parent has about the other, the preferences
of both parents and the child, and visitation in the child
support equation, this empirical study expands previous
models that include only estimates of the custodial parent’s
need and the noncustodial parent’s ability to pay. The
strategic variables are significant as a group and
individually, supporting the theory.

Not much in the theory concerning the visitation
decision is supported. First of all, the decision is not

interdependent with the decision about child support, as

64

Table 4.3 Estimates of the Number of Days the Child Spent with the Noncustodial Parent in the Past

 

 

 

 

 

 

 

Year‘
(1) (2)
OLS Nelson-Olson
Child Support .009 *" -.001
(2.352) (-.065)
R800 -6.923 -18.524
(-.437) (-.488)
CP Remarried -17.485 -27.248
(-1.309) (-1.288)
NCP’s Driving Distance from Children 3.471 15.848
(.278) (1.198)
Years Since Divorced/Separated .075 -.645
(.045) (-.421)
Argued Before Separation 5.477 -4.788
(.460) (—.265)
Child Support was A Difficult Issue to Work Out at -33.179 * -28.653 **
Separation (-1.856) (-2.041)
Child’s Closeness to NCP 17.773 26.500 “W
(1.538) (2.935)
CP’s Satisfaction w/ Custody Arrangements 23.456 * 13.349
(1.795) (.697)
Child’s Closeness to CF 9.137 12.114
(.559) (.400)
Conflict Between CP and NCP 20.167 17.667
(.833) (.863)
Settle-sat Has Changed Since Separation 40.314 *** 29.398 ***
(2.841) (2.650)
Constant -3.153 15.526
(-. 135) (.741)
F-statistic F(12,195)=2.24 F(12,192)=2.87
N 208 205
R2 .121 .152 I

 

 

 

SOURCE: National Survey of Children, Wave 2, 1981. Sample consists of divorced or separated families in which the outside
pared is the cuuodial parem’s former sparse.

'T-Iatisties are in parentheses.

”‘ Indicates significance at the 1% level for a two-tailed test.

“ Indicates significance at the 5% level for a two-tailed test.

‘ Indicates significance at the 10% level for a two-tailed test.

65
evidenced by the rejection of the simultaneous equation
specification. Further, the only strategic variables that
matter are those representing preferences, and child
support. The significance of the preference variables in a
single equation model, however, also supports other theories
of visitation, such as Peters et al (1992) and Weiss and
Willis' (1985) efficient contract theories. Therefore the
evidence on the strategic use of visitation by the custodial
parent is less compelling than the evidence of the strategic

use of child support by the noncustodial parent.

CHAPTER V. A DYNAMIC MODEL

As indicated in Chapters 2 and 3, the parents interact
with each other for a long period of time, so a dynamic
empirical model is a better representation of the post-
divorce situation. In this gaming model, each player is
assumed to move sequentially, so the player knows all
previous moves when making his or her move. That is, the
noncustodial parent has the opportunity to pay or not to pay
child support in one period, while the custodial parent
responds by granting or not granting a certain amount of
visits. The noncustodial parent reciprocates with child
support after observing the visits bestowed by the other
parent, and so on. Each player has the opportunity to
establish a reputation for cooperation which might encourage
the other player to do the same. The strategy used by both
parties in their decisionmaking is the "tit-for-tat"
strategy. This means that each player cooperates in the
first round, then either cooperates on each round thereafter
if the opponent cooperated, or abandons cooperation if the
opponent did not cooperate. The tit-for-tat hypothesis
suggests that a relationship exists between one player's
actions in the previous period and the other player's
actions in the current period.

To explore this possibility, I examine the relationship
between current child support and past visitation. Data

from the last two waves are used to observe the interactions

66

67

of child support and visitation decisions over time. The

sample consists of those custodial families that report a

child support amount in the third period equalling O or

higher“, and visitation in the second period, resulting in

119 observations. Table 5.1 provides the means and standard

deviations of variables used in this chapter's analysis.

Table 5.1 Means and Standard Deviations of Sample Characteristics in Dynamic Analysis

 

 

 

 

 

 

 

I VARIABLE MEAN SI'D DEV
I Family/Danographic Characteristics:
Child’s Age in 1987 19.578 1.530
CP’s Family Income in 1987 3.360 1.669
I of CP’s Dependents in 1987 3.043 1.269
Legal Climate:
Total Enforcement Expenditure/Average Annual Child 40.437 26.697
Support Enforcement Caseload
Enhance:
Settlement Has Changed Since 1981 .084 .278 |
Child Support Variables:
Child Support per Year in 1981 1163.344 1776.047 J
Child Support per Year in 1987 326.153 1207.592 '

 

 

Visitation:

 

 

 

49;;

SOURCE: National Survey of Children, Waves 2 and 3, 1981 and 1987. Divorced or separated families in which the outside
pared is the custodial parem’s former spouse. CPI-Custodial Parent. NCP-Noncustodial Parent.

 

18That is, missing observations and those reporting "not

applicable" were excluded.

68

3. Empirical Methodology

If the tit-for-tat strategy is employed, then child
support in Wave 3 should rise with past visitation in Wave
2, all other factors held constant. Though the data set is
not particularly well-suited to studying this connection
since the six year hiatus between Waves 2 and 3 is so large,
some of the findings are suggestive. The amount of child
support received in Wave 2 is included in order distinguish
between the dynamics of the tit-for-tat theory and the
possibility that child support in period 3 is highly
correlated with child support in period 2.

The control variables in Wave 3 are limited in
comparison to Wave 2. For example, the visitation variable
and variables representing the current relationships between
the child and each parent are not available in Wave 3.
However, other explanatory variables important in explaining
child support in Wave 2 that are constant across time are
thought important in explaining support in Wave 3. These
include the pre-divorce "negotiating costs" variables, and
the demographic variables of race, custodial parent’s age,
and custodial parent's education. Child support in Wave 2,
included in the regression, captures these effects, so they
are not included separately. The number of the custodial
parent's dependents and family income in Wave 3 is included
since they have changed since Wave 2 for many families.

A proxy for the effectiveness of a state's child

support enforcement in Wave 3 is included, equalling the

69
total dollars spent on enforcement per child support
enforcement case, according to the Office of Child Support
Enforcement (1988). The child’s current age is also
included in this analysis. The children's ages in this wave
range from 17 to 22, meaning some of these children are now
self-sufficient and the custodial parent is no longer
eligible for support. I expect, therefore, that families
with children at the lower end of this age spectrum will
receive more child support.

The explanatory variable of greatest interest is
visitation in the previous wave, though whether the child
support agreement has changed since the previous wave is
also importantt. I hypothesize that a negotiated change in
the agreement brings the two parties closer to their true
preferences and an optimal outcome, which is assumed to be

higher child support payments.

3. Estimation

Estimation techniques available for pooled cross-
section and time series data such as random effects and
fixed effects models are not an option here due to the data
set's deficiencies. Specifically, the data set does not
contain child support and visitation for all three time
periods. I use an alternative test that examines the link
between visitation in Wave 2 with child support in Wave 3.
This test involves estimating the following system using a

tobit approach

70
(5.1) c‘, =- a,v, + to, + B,'x, + r,'z, + u,
(5.2) c, .. w (a, c")
where c‘, is child support in Wave 3, and c, and V, are child

support and visitation in Wave 2, respectively.

C. Empirical Results

Because of the possibility of sample selection bias, I
use Heckman's (1979) two-step procedure to test for
selectivity. This bias would exist if the fact that child
support is reported in the third wave also determines how
much the custodial parent receives. I find no evidence of
sample selection bias: the coefficient on A, the inverse
Mills ratio, is insignificant”. No correction was made,
therefore, for selectivity.

Table 5.2 presents the results of the tobit analysis
regressing child support in Wave 3 on visitation in Wave 2
and other control variables. Lagged visitation is
significant and positive at the 5% level, providing support
for the hypothesis that a tit-for-tat game is being played.
A change in the settlement is strongly significant and
positive, indicating that those who obtain a change receive
higher payments. This variable could be picking up
something about the relationship of those parents who can
get along well enough to negotiate a new settlement that

results in higher child support. Or it could mean that the

 

1"The coefficients of the probit equation used to estimate
A are given in Appendix 6.

71
bargaining gets them closer to their true preferences so
they pay (or receive) higher amounts of child support.
Variables on the current state of the relationship are
necessary to investigate which of these explanations apply
here. The child's age is significant and negative, as
hypothesized. The rest of the variables are not

significant.

Table 5.2 Tobit Estimates of the Amount of Child Support Received in

 

 

 

   
 

 

 

 

Period 3'
I
l of Visits Between Child & NCP in Wave 2 (V_,) 8.391 **
(2.061)
Child Support Received in Wave 2 (C,,) .122
(.478)
Number of CPS Dependents 465.649 ll
(1.312)
CP’s Family Income -.048
(-1.51 1)
Enforcement Techniques 12.511
(.634)
Settlement Has Changed Since Wave 2 3927.054 ***
(3.171)
Child’s Age -804.483 **
(-2.229)
Constant 5863.733
(1.126)
Chi-Square 29.43
N 1 19
Log Likelihood Function -250. 022
: attona urvey o l ren, mp e comma tn

which the outside parent is the custodial parent’ a former spouse. CP= Custodial Pareru. NCP=Noncustodial Parent.
'T-mics are in parentheses.

‘“ Indicates significance at the 1% level for a two-tailed test.

” Indicates significance at the 5% level for a two-tailed test.

‘ Indicates significance at the 10% level for a two-tailed test.

72

D. Conclusion

While the findings are suggestive, they do not clearly
establish the causal role visitation plays in the child
support decision, much less the tit-for-tat theory. Monthly
data along with panel data estimation techniques are
necessary to evaluate this theory of child support receipt
more convincingly.

The fact that a settlement change positively and
significantly affects child support receipt raises
interesting lines of inquiry about the extent of private
ordering. As advanced previously, this relationship could
mean the parents are moving closer towards their true
preferences, which are assumed to be higher child support
payments. Peters et a1 (1992) analyze factors associated
with informal changes and formal, or legal, changes in a
divorce agreement about child support payments. As they
hypothesize, changes in circumstances such as the employment
situation, and the custodial arrangements lead to
modifications in the agreement. They then look at the
affect these changes in circumstances have on compliance and
find that these same factors that lead to modifications
significantly affect compliance with the formal agreement
but not the informal agreement. What they conclude is that
changing circumstances and preferences lead to modifications
in the initial agreement, which lead to full compliance,
albeit with an informal agreement, supporting the belief

that a fair amount of private ordering is occurring.

73

It is unclear from the NSC data used in this thesis
whether the settlement change was legally altered, or
whether the change was merely an informal agreement between
the two parties. If most of the changes were informal
arrangements”, the positive relationship between settlement
change and child support receipt lends support to the
private ordering theory. A settlement change could also
divulge information about the parents' current relationship
and ability to bargain. Better data on the parties’
preferences, such as their preferred amount of contact with
the child and the preferred amount of child support at a
certain point in time; the parents' current relationship;
and who initiated the change are necessary to distinguish

these possible explanations.

 

20Peters et a1 (1992) estimate that 80% of modifications
in their study were informal rather than formal changes in the
initial divorce settlement.

CHAPTER VI. CONCLUSION

This thesis deals with the issue of child support and
noncustodial parent-child visitation in the post-divorce
environment. The goal is to understand the dynamics of this
situation in order to formulate intelligent policies. I
propose a strategic bargaining model of post-divorce
negotiations over child support and child visitation rights
and emphasize the influence of the decision-makers' control
of resources, which in this situation are child support and
visitation rights, on the bargaining process and outcomes.
Data from the National Survey of Children are used to test
the theory.

The one-period Nash equilibrium leads to lower support
payments and visitation than the efficient outcome. The
optimal outcome can be supported in a repeated game with the
use of trigger strategies. A repeated game is a better
approximation of the post-divorce relationship where
informal agreements are often used to enforce mutually
beneficial trades due to the often excessive transaction
costs of legally binding contracts. The repeated game leads
to equilibrium outcomes that do not arise when the game is
played only once, including the Pareto optimal and balanced
temptation equilibria. The parents cooperate because they
hope that cooperation will induce further cooperation in the
future. As long as both parties care enough about future

utility, the threat of noncooperation in the future makes

74

75
the informal agreement self-enforcing. Various ways exist
to enrich the basic theoretical model, discussed in the next
section.

The empirical cross-section analysis considers the
interrelationship of the child support and visitation
decisions made by each parent by specifying a pair of
simultaneous equations. Applying the theory to the data
presents many difficulties, specifically how to determine
whether the relationship is strategic or not. One crucial
test of this analysis focuses on whether these decisions are
interrelated. This is shown to be true for child support
where child support is best specified in a simultaneous
equation system. The amount of child support affects the
custodial parent's visitation decision, which in turn
affects the noncustodial parent's child support decision.
This empirical analysis provides support for the strategic
theory as it relates to child support. This suggests
certain policy implications, discussed shortly, beginning
with a brief review of the current child support system in
the United States and how these laws are implemented in the

state of Michigan.

A. Possible Extensions of the Model

It is likely that the noncustodial parent's decision on
child support is a function of whether his payments are
being spent on the child. A distinction could be made in

the model between the consumption of the child and mother,

76
1, versus 8,. This allows for consideration of the cases
where the custodial parent banks the support payments, while
the noncustodial parent legitimately prefers his payments to
used immediately.

Additionally, it is likely that each parent is more
concerned over non-market issues, such as values the child
is developing while in the company of the other parent, and
less concerned about pecuniary matters. This can be
incorporated into the model by having the child's utility
function develop over time via a taste parameter that is
constantly evolving. This extension of the basic model then
permits analysis of situations where payment of child
support or visitation allowance is conditional on the giving
parent's perception of the other parent’s behavior while in
the company of the child. For example, the custodial parent
might withhold visits because she disapproves of the places
the noncustodial parent frequents while the child is in his
company. Or she disapproves of the way the noncustodial
parent disciplines the child while in his company.

This model assumes no informational disparities exist,
though in reality one parent could have private information
about the opponent's risk-aversion, or his or her ability to
deliver the promised goods, as in the case where the
noncustodial parent knows more about his own ability to pay
child support than the custodial parent. Suppose, for
example, that the noncustodial parent is pleading poverty

but the custodial parent does not believe him. She

77
withholds visits until she becomes convinced that he is
telling the truth or he pays up. From a policy perspective,
legal intervention whereby the court has the right to all
income sources of the noncustodial parent, would lead to
substantial gains in the efficiency of the bargaining
process. [See the following for examples of games of
incomplete, or private, information: Bebchuk (1984); Spier
(1992); Reinganum and Wilde (1986); Nalebuff (1987); Shavell
(1989); and Rubinstein (1985)].

The existence of private information can lead to
bargaining power disparities. Bargaining power was modelled
here using the parties' discount rate, though this was not
tested empirically due to the difficulty in measuring it.
The idea is that the more impatient player will accept a
smaller share. Finding a proxy for this variable leads to a
test of this idea. Other measurements of bargaining power
that are empirically easier to measure are also possible.
One is each party’s ability to handle transaction costs
whereby the party better able to handle costs has an
advantage. Another is the degree of uncertainty concerning
the legal outcome if the parties go to court, which is
linked to the parties’ attitudes towards risk. Substantial
variance among the possible court-imposed outcomes is more
of a disadvantage to the more risk-averse party. Uncertainty
about the outcome could increase transaction costs.

The possibility of forgiveness once an opponent cheats

is a plausible outcome in this highly emotional game. It is

78
very likely that the efficient outcome can be achieved once
the agreement has been broken, if the cheater "repente" and
adequately compensates the opponent (Segerstrom, 1988).
If, for example, a noncustodial parent who has cheated in
the past, can repent by paying back child support,
cooperation can resume. The introduction of a "repentance"

strategy in this game would make for a richer model.

B. The Current system of Child Support and Visitation

in the United States and Michigan

Aid to Families with Dependent Children (AFDC) was
enacted as part of the Social Security Act of 1935 to
provide for the needs of poor fatherless children, most of
whose fathers had died (Garfinkel, 1988). However, as
welfare costs mounted, enthusiasm for public support of
children who had able-bodied fathers diminished as
congressional interest in private child support payments
grew.

Between 1950 and 1988, Congress enacted a series of
bills to strengthen public enforcement of private child
support. The most significant legislation was passed in
1975, when Congress added Part D to Title IV of the Social
Security Act, thereby establishing the Child Support
Enforcement (IV-D) program. States, which are responsible
for running this program under federal guidelines, are
reimbursed by the federal government for about 70% of the

cost of establishing paternity, locating noncustodial

79
parents, and collecting child support.

In 1984, Congress voted unanimously to require all
states to automatically withhold child support from the
wages of noncustodial parents who are delinquent in their
child support payments for one month, under the Child
Support Enforcement Amendments of 1984. It also requires
the states to extend the period during which paternity suits
can be initiated to the child's eighteenth birthday, to
expedite the process for enforcing support orders, and to
establish statewide child support guidelines. The Family
Support Act of 1988 requires all states to impose immediate
wage withholding at the time a child support order is
established by 1994, whether the absent parent is delinquent
or not. Currently, federal lawmakers are calling for a
federalized system to enforce child support payments and
remove the burden from the states. The reasons include
standardizing the child support collection and enforcement
system across states, and instituting a method of enforcing
child support awards when the noncustodial parent moves out
of state. To this end, the lawmakers are calling for making
use of the IRS to withhold wages across state lines”.

In Michigan, one of the top states in terms of
collection, a public agency called the "Friend of the Court"

is responsible for all official matters relating to divorce

 

2"'Federal Plan to Enforce Child Support is Pushed by
Liberals and Conservatives", Wall Street Journal, May 10,
1992.

80
and paternity for nonwelfare as well as welfare cases. Its
duties include investigating, reporting and making
recommendations to the court on child custody, visitation,
and support; providing mediation as a way of settling
disputes over custody and visitation; collecting, recording,
and releasing all support payments ordered by the court to
the parent, guardian or welfare department; and enforcing
all custody, visitation, and support orders. (See Friend of
the Court Act, Michigan Compiled Laws (MCL) 552.501-
552.535). Michigan's Friend of the Court was founded in
1917 because the private system of support enforcement had
proven ineffectual (Chambers, 1979). "Friend of the Court"
is the title for both the person heading the agency in each
county and for the agency itself. The Friends of the Court
themselves are appointed by the governor at the
recommendation of the local circuit judges.

State and federal law require that a child support
guideline be used by Friends of the Court, prosecuting
attorneys and judges when recommending or ordering
appropriate child support amounts (MCL 552.519; Federal
Child Support Enforcement Amendment of 1984). Deviation is
possible if a judge or the Friend of the Court determines
that use of the guideline would result in an unjust or
inappropriate order. Reasons for deviation must be set
forth in a report and recommendation by the Friend of the
Court and on the record or in writing by the court. In

Michigan, the child support guidelines consider both the

81
noncustodial and custodial parent's income. As to
visitation, if the parents agree on visitation terms, the
court shall order the visitation terms unless the court
determines on the record that the visitation terms are not
in the best interests of the child (Child Custody Act, MCL
722.21-722.29).

In Michigan, the Friend of the Court does not wait for
a complaint from the custodial parent to begin enforcement
efforts if the noncustodial parent misses one month of
support. The agency can issue an income withholding order,
a lien on a payer’s property, civil contempt proceedings,
and if necessary, jail (Support and Visitation Enforcement
Act, MCL 552.601-552.650). Effective January 1, 1991, all
new and current support orders that have been modified must
provide for immediate income withholding similar to the
deductions for income taxes. A delinquency does not have to
occur before income withholding takes place.

If the parent required to pay support leaves the State
of Michigan, he or she must continue to pay support through
the Friend of the Court. If child support payments stop,
the parent receiving support has the right to request that
an action under the Revised Uniform Reciprocal Enforcement
of Support Act (RURESA) be filed. A RURESA order
establishes a support order in the state where the
noncustodial parent lives and this state then has the
responsibility for enforcement.

Contrary to child support delinquency, the Friend of

82
the Court begins enforcement proceedings of visitation
orders only after it receives a written complaint stating
specific facts including dates, times and reasons given
about an alleged denial of visitation, and when the Friend
of the Court determines that there is reason to believe the
court's order has been violated. The Friend of the Court
can schedule a meeting with the parties and attempt to
reconcile differences, or refer the parties to a mediator.
If these fail, the Friend of the Court can begin a civil
contempt proceeding, or petition the court for a change in

the existing visitation order.

C. Policy Implications

The theory and empirical analysis emphasize the
importance of the parents' relationship, both in the pre-
divorce negotiation process, and in the post-divorce use of
child support as a strategic weapon. These are found to be
more important than many of the economic and demographic
factors. This suggests that policies addressing family
dynamics must be examined along with the implications of
enforcing the current laws outlined above in order to
alleviate the child support problem.

Specifically, this thesis has shown that child support
is an instrument in a strategic game between the two
parents. It can be used to punish, threaten, signal, or
enforce a bargain. If perfect enforcement of child support

awards and visitation awards existed, these strategic uses

83
would not be possible, and the Pareto optimal amount of both
would be realized. However, perfect enforcement does not
exist, especially in the case of visitation.

Legal enforcement of child support awards such as
programs that automatically withhold support from
noncustodial parents’ paychecks are expected to lessen the
strategic function of support payments as they diminish the
parents' ability to negotiate private contracts and enforce
agreements. However, given that this enforcement will still
be imperfect, and given the weakness of visitation awards'
enforcement relative to that of child support awards, these
policies might serve to increase bargaining costs
unnecessarily, increase the custodial parent’s bargaining
power, and lead to a demand by the noncustodial parent for
higher visitation rights. The benefits of a nonvoluntary
system of child support in terms of increased collection
must be weighed against the costs”, primarily the spillover
effects of decreasing the strategic functions of child
support just mentioned, and the reduction in individual

responsibility as the government not only handles the

 

”Whether child support withholding from paychecks will
increase the amount collected is questionable. It is
speculated by David L. Levy, President of the National Council
for Children's Rights, Washington, D.C. that the majority of
those affected by the law are those who pay close to the full
amount of child support anyways. A third party is introduced
unnecessarily, resulting in an increase in the child support
bureaucracy. (Testimony before the Committee on Finance,
United States Senate, One Hundredth Congress, Second Session
(February 4, 1988) , on welfare reform and the problem of child
support and ways to improve the current system).

84
collection and distribution of support, but also starts
guaranteeing minimum payments for those due child support.

What this thesis implies for policy in the absence of
perfect enforcement is that allowing a link between
visitation and child support would move the amount of both
commodities received by both parties towards the efficient
level. This occurs because an informal, relatively low cost
enforcement mechanism is now at the disposal of each parent.
This link can be explicitly written into the divorce
settlement, stating in the legal record that child support
does not have to be paid if visitation is withheld. Or
states could allow judges to consider frustrated visitation
rights in cases where the noncustodial parent has been
accused of child support nonpayment.

These recommendations are controversial as most state
statutes do not accept a guardian’s refusal to allow a
noncustodial parent to visit his children as an excuse for
the noncustodial parent to stop or reduce child support
payments. The reason is that society's first objective is
to protect the child”. A child should not lack support
because of harmful actions taken by the parent. However,
though it has become illegal to stop support payments if the
custodial parent does not deliver visitation, in exchange
the courts do not enforce visitation orders to the same

extent they do support awards. The system appears to be

 

”W by Joseph Lieberman. p- 54-

85
working against itself when it should be working to bring
these areas together under one coherent policy.

A less controversial recommendation is to institute
policies encouraging visitation. These include granting
visitation awards to noncustodial parents, stricter
enforcement of these awards to insure compliance on the part
of the custodial parent, and joint custody in custody
disputes. Concerning the latter recommendation, the effect
of joint custody on children has been explored in much
detail elsewhere and so is not discussed here. (See Qgint
Qugtng_ang_§hargg_£a;gntigg, edited by Jay Folberg, for a
collection of diverse views on this subject.) My study
underscores the benefits of joint custody, as it maximizes
the contact the child has with the noncustodial parent.

The imbalance in the enforcement of visitation awards
as compared to child support awards has generated the
creation of fathers’ rights groups, dedicated to helping
fathers gain equal rights in divorce matters. These groups
argue that the system is biased against them, with evidence
to support them. As cited in the previous section, many
laws have been enacted at the federal level to enforce child
support payment, but none concerning visitation. Michigan
is considering a bill that would confiscate the driver’s
license of a noncustodial parent who is delinquent for one
month or $1,000 in support and who repeatedly ignores
collection efforts, but is doing nothing to punish custodial

parents who renege on a visitation agreement. Additionally,

86
enforcement in Michigan is quicker and therefore less costly
for a custodial parent with a support complaint than for a
noncustodial parent with a visitation complaint. A
noncustodial parent just has to miss one month of payments
before enforcement proceedings begin, while enforcement
proceedings of visitation orders begin only after the
noncustodial parent files a complaint with the Friend of the
Court stating specific details of the visitation denial.

One reason fathers’ rights groups give for the
imbalance in the post-divorce debate is the sexism of the
court system which reflects society's view that women need
to be protected, while men do not, and that men are the ones
who provide for the family’s financial needs while women
provide for the family's emotional needs”. The idea that
fathers have nurturing relationships with their children and
want to continue that after divorce is counter to society's
view of the traditional roles of men and women. Whether
this is true is speculation at this point, but is a
possibility that should be investigated in the future.

To determine whether this or the other allegations are
true, and whether policies encouraging visitation
recommended in this thesis would insure higher child support
payments requires better data. Statistics on the current
status of visitation in particular, and on the noncustodial

parent in general, are in short supply. The Current

 

2"Al Lebow, Executive Director of Fathers for Equal Rights
of America, Southfield, MI in an interview July 15, 1993.

87
Population Reports, cited in the introduction, provide some
data concerning the percentage of noncustodial parents with
visitation awards, though nothing on compliance with these
awards, and enforcement of awards. Further, this
information is provided by the custodial, rather than the
noncustodial parent. This information is necessary in order
to assess just how big a problem this is, and to have a
benchmark to compare any policies that seek to remedy this
situation. Therefore, a related recommendation is to devote

more resources to the collection of this information.

D. Future Directions

Estimates of how many families experience this
situation is necessary before appropriate policies are
implemented. This requires a more extensive and detailed
survey. Longitudinal data are necessary to test many
aspects of the repeated game, including whether a repeated
game leads to a Pareto optimal solution. Better data are
needed on each parent's discount rate, their preferences at
different points in their child's life, and other
circumstances surrounding and following separation and
divorce over a period of time. The use of panel data allows
for a richer dynamic specification so that an individual's
past behavior can affect current behavior. Documentation
on the absent parent such as ability to pay, employment
status, and education for which inadequate proxies are

substituted, is particularly needed in order to obtain a

88
more accurate picture of the child support and visitation
situation. The same care that is used in collecting child
support award and receipt information should be used to
collect equally important but ignored information on
visitation for noncustodial parents, such as how many
parents are covered by a visitation award, and the
compliance rate. These data and more sophisticated
longitudinal analysis will lead to additional valuable
insights into the actual dynamics of the post-divorce
situation.

Noncustodial parents’ child support behavior has not
changed much over the past decade despite strict laws
designed to enforce payment: only about 50 percent of
noncustodial parents paid the full amount of support in
1989, the same as in 1979. This thesis suggests it is time
to examine reasons for this noncompliance rooted in family
dynamics, particularly related to the link between child

support and visitation.

APPENDIX 1

89

APPENDIX 1

Differentiating the custodian's first order conditions,

equations (2.6) - (2.9), results in:

 

 

 

 

 

 

- O -1 -w, -w, W pduq P-l -
'1 “in +ancu 0’12-3'01°n-U°u) “fts d" 0
"W “ftz'afmcaruczfl uf22+af e22"2U°23+U°33) “f2: dtr — 0 ds
_ "W “‘31 uf32 uf33 _ _dlr_ L 0 A

The system implies the following equations:
dx/ds = 1/ HI: (“‘23) 2 ' “fawn + u'nu'33w, ' ufnufflwf ' “rial-1‘32“: +
u'nu'nwfj
(“it/‘38 = 1/H[uf21uf33 " ufzaufst + ufnufnwr ' ‘ilfuufzswf " (“ftslzwr +
“ftaufziwrl
where H is the determinant of the bordered Hessian. dx/ds =
dx/dI' since s is nonwage income for the female. Thus,
dx/ds > 0 and dl,/ds > 0, assuming normality. This also
applies to dtrlds; that is, dtrlds > 0 if time spent with the

child is a normal good.

APPENDIX 2

90

APPENDIX 2

Differentiating the noncustodian’s first order

conditions, equations (2.20) - (2.23), results in:

 

 

 

 

 

r '1 r- - -
0 -l wmdt/ds-l -wIn tip -1
'1 11"“ -U",2dt,/dS Um” d 0
= (11“I
w_dt/ds-1 -u‘“2,dt,/ds A -u'“23dt,/ds ds 0
“Wm “m3: -um32dt,/ds “mss dlm L 0

 

where A = dx/ds [a"’(U°l + U°ndxlds + dtfls (U°,2-IJ‘,3+U°2,-U°3,))]

+dtf/ds [-u'“2 + a'“(U°2-U°3, + dt,/s (umn-Wn+U°232+U°33) + awn] .
0 measures the sensitivity of the constrained objective
function to changes in the constraint, which, in this case
is income. The system implies the following equation:
ds/dI“ = 1/H.{dtr/d5 [umztum33+um23um3t+wm (umttumn‘umnumza'

(unis) 2""1m13‘1m21) ] ’umuum33+ (nun) 2}

where H, is the determinant of the bordered Hessian. The
sign of this comparative static depends upon the sign of
dt,/ds, or how the custodial parent reacts to an increase in

support payments.

APPENDIX 3

91

APPENDIX 3

Differentiating the noncustodian's first order

conditions, equations (2.56) - (2.59), results in:

 

 

 

 

 

0 -1 -1 -wIII dB -1
-1 um” 0 um” d 0
= dP'
-1 0 a“dx/ds(U°+U°,,) 0 ds 0
-w,,I u“,, 0 u“,, J (ll,In 0

 

The system implies the following equation:
dsldlIll = 1/Hc['umuum33 + (“"13)2]

where Hc is the determinant of the bordered Hessian.

APPENDIX 4

92

APPENDIX 4

DEFINITION OP VARIABLES

VARIABLE

Race

Custodial Parent's Education

Custodial Parent's Age
Child's Age

Custodial Parent’s Family Income
in Wave 2

DESCRIPTION

Dichotomous variable is
equal to 1 if respondent
is black, 0 otherwise.

Education of custodial
parent equalling 1 if
post-high school
education was achieved,
and 0 otherwise.

Custodial parent's age.
Child's age.

Categorical variable of
the custodial parent's
total family income. If
income fell between $0-
$5,000, variable equals
$2,500; if between $5,000
and $10,000, variable
equals $7,500; if between
$10,000 and $15,000,
variable equals $12,500;
if between $15,000 and
$20,000, variable equals
17,500; if between
$20,000 and $25,000,
variable equals 22,500;
if between $25,000 and
$35,000, variable equals
$30,000; if between
$35,000 and $50,000,
variable equals 42,500;
if over $50,000, variable
equals $65,000.

93

Custodial Parent's Family Income
in Wave 3

Number of Custodial Parent’s
Dependents

Custodial Parent Remarried

NCP’s Driving Distance From Child

State Enforcement Variable
in Wave 2

State Enforcement Variable
in Wave 3

Categorical variable of
the custodial parent's
total family income. If
income fell between $0-
$10,000, variable equals
$5,000; if between
$10,000 and $20,000,
variable equals $15,000;
if between $20,000 and
$30,000, variable equals
$25,000; if between
$30,000 and $40,000,
variable equals 35,000;
if between $40,000 and
$50,000, variable equals
45,000; if between
$50,000 and $60,000,
variable equals $55,000;
if between $60,000 and
$70,000, variable equals
65,000.

Number of people
depending on custodial
parent’s family income.

Whether respondent has
remarried or living with
partner of opposite sex
(1), or otherwise (0).

Dichotomous variable is
equal to 1 if former
spouse lives an within an
hours drive away, 0
otherwise.

Number of child support
enforcement techniques
used by custodial
parent’s state in 1981.

Total enforcement
expenditures per child
support enforcement
caseload in 1987.

94

Argued Before Separation

Child Support was a Difficult
Issue to Work Out at Separation

Divorce Settlement Obtained

Child's Closeness to Noncustodial
Parent

Child's Closeness to Custodial
Parent

Dichotomous variable is
equal to 1 if the former
spouses argued often
before separation
according to the
custodial parent, 0 if
they argued occasionally
or not at all.

Dichotomous variable is
equal to 1 if child
support was a difficult
issue to work out at
separation according to
the custodial parent, 0
otherwise.

Dichotomous variable is
equal to 1 if a
settlement over custody,
visitation, and finances
was obtained at divorce
or separation, 0
otherwise.

Dichotomous variable is
equal to 1 if the child
is extremely close or
quite close to the
noncustodial parent
according to the child, 0
if the child is fairly
close or not very close
to the noncustodial
parent.

Dichotomous variable is
equal to 1 if the child
is extremely close or
quite close to the
custodial parent
according to the
custodial parent, 0 if
the child is fairly close
or not very close to the
custodial parent.

95

Custodial Parent's Satisfaction
With Custody Arrangements

Conflict Between Custodial and
Noncustodial Parents

Settlement Has Changed Since
Divorce

Settlement Has Changed Since
Wave 2

Years Since Divorce/Separation

Child Support in Wave 2

Child Support in Wave 3

f of Visits Between Child & NCP

Dichotomous variable is
equal to 1 if the
custodial parent is very
satisfied with current
custody arrangements, 0
if the custodial parent
is somewhat satisfied or
not at all satisfied with
current custody
arrangements.

Dichotomous variable is
equal to 1 if the
conflict level between
the custodial parent and
former spouse increased
after separation
according to the
custodial parent, 0
otherwise.

Dichotomous variable is

equal to 1 if settlement
changed since divorce, 0
otherwise.

Dichotomous variable is
equal to 1 if settlement
changed since Wave 2, 0
otherwise.

Years since divorce or
separation.

Current child support per
year in 1981 as reported
by the custodial parent.

Current child support per
year in 1987 as reported
by the custodial parent.

The number of days the
child spent with the
noncustodial parent in
the past year as reported
by the custodial parent.

APPENDIX 5

96

APPENDIX 5

ENDOGENEITY TEST ON VISITATION EQUATION

 

 

OLS Estimates of the Number of Days the Child Spent with the Noncustodial Parent in the Past Year‘

 

 

 

 

Child Support
(-.942)
Race -66.441
(-.996)
NCP’s Driving Distance from Children 54.355 **
(2.006)
Years Since Divorced/Separated 1.786
(.694)
Argued Before Separation -22.036
(-.640)
Child Support was A Difficult Issue to Work Out at -51.290 **
Separation (-2.366)
. Child’s Closeness to NCP 19.582
x (1.303)
. CP’s Satisfaction w/ Custody Arrangements -8.157
‘ (-.223)
‘ Child’s Closeness to CP 80.938
p (1.399)
; Conflict Between CP and NCP -8.629
(-.282)
Settlement Has Changed Since Separation 46.205 **
‘ (2.614)
, E .027
(.912)
i Constant -12.283
(-.31 1)
F-statistic F(13,89)= 1.66
t N 103
‘ R2 .195

 

SOURCE: National Survey of Children, Wave 2, 1981. Sample consists of divorced or separated families

in which the outside parent is the custodial parent’s former spouse.
'T-statistics are in parentheses.

“‘ Indicates significance at the 1% level for a two-tailed test.
“ Indicates significance at the 5 % level for a two-tailed test.

' Indicates significance at the 10% level for a two-tailed test.

APPENDIX 6

97

APPENDIX 6

Probit Estimates for Receipt of Child Support in Period 3 used to Estimate A and Determine Selectivity

 

 

 

 

I of Visits Between Child & NCP in Previous Period 2 .002
(1.318)
Child Support Received in Previous Period 2 -.000
(-.196)
Number of CP’s Dependents .127
(1.061)
CP’s Family Income -.000
(-.555)
Enforcement Techniques .001
(.097)
Settlement Has Changed Since Wave 2 1.459 ***
(3.153)
Child’s Age -.409 ***
(-3.314)
Constant 3.961 s4: 1
(2.151) .
Chi-Square 34.76 1
N 1 19
Log Likelihood Function -42.351 :
_ ._ _ -_ _____m________ ___ ____________ _ __ 4
A = flBX/a)/F(BX/a)” -397.493 ’
(-1.337) J

 

 

SOURCE: National Survey of Children, Waves 2 and 3, 1981 and 1987. Sample consists of divorced or
separated families in which the outside parent is the custodial parent’s former spouse. CPB Custodial
Parem. NCP=Noncustodial Parent.

'T-statistics are in parentheses.

Vand F are the standard normal density and standard normal cumulative distribution functions,
respectively. B represents the probit maximum likelihood estimates, reported in this table. X is the vector

of independerl variables.
”‘ Indicates significance at the 1% level for a two-tailed test.
” Indicates significance at the 5 % level for a two-tailed test.

‘ Indicates significance at the 10% level for a two-tailed ten.

BIBILIOGRAPHY

BIBLIOGRAPHY

Bebchuk, Lucien A., "Litigation and Settlement Under

Imperfect Information". BAN2_leurnal_2f_Essn2mis.
Autumn 1984, 15(3): 404-415.

Beller, A., and J. Graham, "Variations in the Economic Well-
Being of Divorced Women and Their Children: The Role of
Child Support Income", in M. David and T. Smeeding,
Eds., o ' on a uit U e t c o 'c
Well-Being, NBER and University of Chicago Press,
Chicago, 1985, 471-506.

Beron, K.J., "Policy Issues and Child Support Payment
Behavior: Empirical Findings", antempgragy Policy
Issues, January 1990, 8(1), 124-134.

Chambers, D., Mgking Eathegs Egg, University of Chicago
Press, Chicago, 1979.

Cooter, Robert, Stephen Marks, and Robert Mnookin,
"Bargaining in the Shadow of the Law: A Testable Model

of Strategic Behavior", Jgurnai of Legal Studies, June
1982, 11: 235-247.

Del Boca, D., and C. Flinn, "The Effect of Child Custody and
Support Arrangements on the Welfare of Children and
Parents", Economic Research Reports, R.R.#90-16, C.V.
Starr Center for Applied Economics, New York
University, April, 1990.

Erlanger, Howard 8., Elizabeth Chambliss, and Marygold S.
Melli, ” Cooperation or Coercion? Informal Settlement
in the Divorce Context", Disputes Eggcessing Reseaggn
Ezggggm, Working Papers Series 7, Institute for Legal
Studies, University of Wisconsin-Madison Law School,
Madison, WI, March 1986.

Fethke, Carol C, "An Economic Model of Asset Division in the

Dissolution of Marriage", Americgn Egongmig Review, May
1984, 74(2): 267-270.

98

99

, "Division of Marital Property in a Sequential-
Game Framework", 7 ce
no 8 s ' h e ‘c

Statistical_e__osia_1on 15- -21-

, ”How the Law Structures the Non-Cooperative Game
of Property Division in Divorce", Draft 1990.

J2int_Quatedx_and_§hared_£arenting. J- Folberg. Ed-. The

Bureau of National Affairs, Inc., Association of Family
Conciliation Courts, 1984.

 

 

Folbre, Nancy, "Household Production in the Philippines: A

Nonneoclaesical Approach". £22n2m12_2exelonnent_and
Cultural_§hange. 1984. 32(2): 303-330.

Friedman, J., "A Non-Cooperative Equilibrium for

Supergames", Review pf Economic Studips, 1971, 38, 1-
12.

Furstenberg, Jr., F.F., C.W. Nord, J.L. Peterson, and N.
Zill, "The Life Course of Children of Divorce: Marital
Disruption and Parental Conflict”, Apprippp

Spgiplpgigal Revieg, 1983,48, 656-668.

Garasky, 8., "Child Support and Second Families with
Children: Which Children Come First?", Draft, 1990.

Garfinkel, I., and D. Oellerich, "Noncustodial Father’s
Ability to Pay Child Support", Qpppgrpppy, May, 1989,
26(2), 219-233.

Hausman, J.A., "Specification Tests in Econometrics",

Econometrics. 1978. 46. 1251-1271-

Heckman, J.J., "Sample Selection Bias as a Specification

Error", Epppppprripp, 1979, 47, 153-161.

Lieberman, J.I., Spiig Suppprr in America, Yale University
Press, New Haven, CT, 1986.

Manser, M. and M. Brown, "Marriage and Household Decision
Making: A Bargaining Analysis", te t' a

Egyigfl, 1980, 21(1), 31- 44.

McElroy, M.B., "The Empirical Content of Nash-Bargained

Household Behavior". Ihe_lournal_ef_numan_Bessurses.
Fall 1990, 25(4), 559-583.

McElroy, M.B. amd M.J. Horney, "Nash-Bargained Household
Decisions: Toward a Generalization of the Theory of

Demand", Interpprippai Economic prieg, June 1981,
22(2), 333-349.

100

, "Nash-Bargained Household Decisions: Reply",

In1ernational_Econom12_Bexiem. Feb 1990. 31(1). 237-
242.

 

Mnookin, R.H., "Divorce Bargaining: The Limits on Private
Ordering”,
Egfigzm, Summer, 1985, 18(4), 1015-1037.

Mnookin, R.H., E.E. Maccoby, C.R. Albiston, and C.E. Depner,
"Private Ordering Revisited: What Custodial
Arrangements Are Parents Negotiating?", in S.D.

Sugarman and H H- Kay- EdS-. Dixorce_Beforn_at_1he
grppprpggg, Yale University Press, New Haven, CT, 1990.

Mnookin, R.H, and L. Kornhauser, "Bargaining in the Shadow

of the Law: The Case of Divorce”, xg1g_Lag_ggurnal.
1979, 88, 950-997.

Nalebuff, Barry, "Credible Pretrial Negotiation", BARR
Spurpai pf Economicg, Summer 1987, 18(2):198-210.

Nelson, Forrest, and Lawrence Olson, "Specification and
Estimation of a Simultaneous-Equation Model with
Limited Dependent Variables", t t Eco
pripg, October, 1978, 19(3): 695-709.

Nicols-Casebolt, A., "The Economic Impact of Child Support
Reform on the Poverty Status of Custodial and
Noncustodial Families", Jo n e
Egpily, November, 1986,48, 875-880.

Peters, H.E., L.M. Argys, E.E. Maccoby, and R.H. Mnookin
"Cooperative and Non-cooperative Contracting at
Divorce: Evidence from Child Support Compliance and
Award Modifications", Draft, 1992.

Pollack, E.J., "Court Lifts Rule on Tuition in Divorce

Suite". Eall_§treet_gournal. January 19. 1992. pp- Bl-
82.

Reinganum, Jennifer F. and Louis L. Wilde, "Settlement,
Litigation, and the Allocation of Litigation Costs",

Rgpd Spprpal pf Ecopomicg, 17(4): 557-566.

Robins, Philip K., Child Support, Welfare Dependency and

Poverty, Apgricap chnopic Reviey, September 1986,
76(4): 768-788.

Roth, Alvin E., Keith Murnighan, and Francoise Schoumaker,
"The Deadline Effect in Bargaining: Some Experimental

Evidence”. Anerican.£22n2m12_zexieu. September 1988.
78(4): 806-823.

101

Rubinstein, Ariel, "A Bargaining Model with Incomplete
Information About Time Preferences”, Eppppmprripp,
September 1985, 53(5): 1151- 1172

Segerstrom, Paul S., "Demons and Repentance", Spprppi_pr
Economic_1heorx. 1988. 45: 32-52-

Shavell, Steven, "Sharing of Information Prior to Settlement

or Litigation". Band_iournal_of_zson2m12§. Summer 1989.
20(2):183-195.

Spier, Kathryn E., "The Dynamics of Pretrial Negotiation",
Bexiex_of_fic_n2mis_§12dies 1992. 59=-108-

Smith, Richard J., and Richard W. Blundell, "An Exogeneity
Test for a Simultaneous Equation Tobit Model with an
Application to Labor Supply", Ecopopepripg, May, 1986,
54(3): 679-685.

U.S. Bureau of the Census, Current Population Reports,

Series P-23, #106, cpiid Supporr and Aiimppy; 122g,

U.S. Government Printing Office, Washington, D.C.,

1980.

U.S. Bureau of the Census, Current Population Reports,
Series P-23, #152, Spilg Supporr apg Alimony; 19SS,
U.S. Government Printing Office, Washington, D.C.,
1987.

U.S. Bureau of the Census, Current Population Reports,
Series P-60, #173, C ' o 98
U. S. Government Printing Office, Washington, D. C.,
1991.

U.S. Department of Health and Human Services, Office of
Child Support Enforcement, Child Suppprt Enforcement;
x h n e o n ress t e 'od '

Qpppmppr_11r_12S1, U.S. Government Printing Office,
Washington, D.C., December 1981.

102

U.S. Department of Health and Human Services, Office of

Child Support Enforcement. Qhila_§upport_nnforc_men11

ess

Dgg_mhgr_11r_12S1, U. S. Government Printing Office,
Washington, D.C., December 1984.

U.S. Department of Health and Human Services, Office of

Child Support Enforcement, Shiig Supporp Epforcemeprg

te nth A nua e t P i
Epgipg September 30l 128 S, U.S. Government Printing

Office, Washington, D. C., 1988.

U.S. Department of Health and Human Services, Office of

Child Support Enforcement, Child Support Epforcepepr;

tee t nnua e o e s

Ending_§ept_nb_r_3_1_1229. U 8 Government Printing
Office, Washington, D. C., 1990

Vella, F., "A Simple Estimator for Simultaneous Models with
Censored Endogenous Regressors", t' a c m
vaiew, May 1993, 34(2), 441-457.

Wallerstein, J.S., and D.S. Huntington, "Bread and Roses:
Nonfinancial Issues Related to Fathers’ Economic
Support of Their Children Following Divorce", in J.

Cassetty, Ed., e ta - O ' ,
Lexington, MA, 1983, 135-156.
Wallerstein, J. S., and J. B. Kelly, Suryiv ipg rhe Breahup;

Rpw Shiigrpp ppd Rgrents gope with inprcg, Basic

Books, Inc., New York, 1980.

Weiss, Y., and R.J. Willis, "Children as Collective Goods
and Divorce Settlements", ou o abo EC 0 ,
1985, 3(3), 268-292.

Weiss Y., and R.J. Willis, "An Economic Analysis of Divorce
Settlements", Economics Research Center/NORC Working
Paper No. 89-5, University of Chicago, April, 1989.

Weitzman, L.J., "The Economics of Divorce: Social and
Economic Consequences of Property, Alimony and Child

Support Awards", SQLA Lap Reyipw, 1981, 28, 1181-1268.

Wu, D., "Alternative Tests of Independence Between
Stochastic Regressors and Disturbances”, co r a,
1973, 41, 733-750.

      

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