Can adequate child support be legislated? Responses to guidelines and enforcement.

Argys, Laura M. ; Peters, H. Elizabeth

I. INTRODUCTION

In response to the high levels of poverty faced by children of divorced parents, federal and state governments adopted a number of policies during the 1980s aimed at increasing child support awards and payments. These laws required all states to have numerical child support guidelines to be used by parents who could not agree on their own and to increase state enforcement of delinquent child support awards. Implicit in much of the policy discussion about divorce is the assumption that within marriage parents will jointly act in the best interest of their children, but that after divorce children may not be adequately provided for, and legislative action is required. In the extreme, this view is represented by the stereotype of the deadbeat dad, a term that describes a father who doesn't care enough about his children to continue any involvement with them either in terms of time or money. Similarly, economic models often assume a noncooperative outcome in which the non-custodial father will not provide what he did during marriage (e.g., Weiss and Willis, 1985).

Our article makes several contributions to the literature on the determinants of child support by absent fathers. In contrast to almost all of the work on this topic that has been based on noncooperative models, we develop a theoretical model in which some families may be able to achieve a cooperative outcome, which increases the total resources available to children. In particular, our model identifies three different types of outcomes: (1) cooperative and self-enforcing; (2) noncooperative and self-enforcing; and (3) noncooperative and state-enforced. Each of these outcomes has different implications for the well-being of children and for the level of government involvement in divorce settlements. We then derive the conditions under which families can achieve each of these outcomes, and we specifically model how policy variables affect whether or not a particular outcome is achieved, the levels of payments, and levels of compliance (conditional on the type of outcome). Our empirical work provides reduced-fo rm evidence that is consistent with a model that distinguishes these different types of outcomes, and we find that policies can affect the type of outcome, as well as the level of child support awards and payments.

Section II of this article provides background and motivations for our topic. We develop a general theoretical framework in section III and compare outcomes under assumptions of symmetric versus asymmetric information. Section IV incorporates the legal environment by modeling the impact of guidelines and state enforcement efforts on the probability the custodial parent (CP) will impose the guidelines, the level of child support awards, and the noncustodial parent's (NCP's) compliance. In section V we interpret comparative statics. Section VI examines the determinants of reduced-form models of the probability of a court-ordered child support award and shows that the predictions of the model are consistent with data on the characteristics of divorce settlements and parental behavior for those with voluntary versus court-ordered settlements. A summary of the findings and policy implications concludes.

II. BACKGROUND AND MOTIVATION

In contrast to the marriage literature, which predominately uses cooperative bargaining models, the literature on divorce generally assumes that divorcing parents are unable to reach cooperative agreements. For example, Weiss and Willis (1985) model parental expenditures on children after divorce as a principal-agent problem in which the absent father cannot verify the child expenditures made by the mother. This problem of asymmetric information leads to an inefficient, noncooperative outcome. Del Boca and Flinn (1995) also use a noncooperative model to examine the government's choice of compliance outcomes. Others have analyzed compliance with child support awards using an economics of crime framework (Beron, 1988; Beller and Graham, 1991; Chambers, 1979).

Although the noncooperative case cannot be ignored, it is also important to recognize the existence of another kind of divorce in which the father pays the full amount of child support owed, maintains contact with his children, and cooperates with the mother in the upbringing of the children. The fact that one-third of children with divorced parents in the National Longitudinal Survey of Youth (NLSY, 1997) characterized their parents' relationship as friendly (as opposed to neutral, hostile, or having no contact) suggests that the elements to achieve a cooperative settlement may be present in a substantial fraction of cases (Argys and Peters, 2001). In addition, Maccoby and Mnookin (1992) report that a substantial majority of parents experience little conflict over the terms of the divorce.

Another type of distinction that is not often made in empirical studies of child support agreements is the difference between self-enforced and state-enforced agreements. But data show that more than half of fathers who are required to pay child support pay the full amount owed. This substantial degree of compliance is striking given that the probability of being forced to pay by the state has been fairly low (Office of Child Support Enforcement, 1997). Data from the Child Support and Alimony Supplement to the Current Population Survey show that one-third of respondents classify their divorce settlements as voluntary, and award levels and compliance are higher in voluntary divorce settlements than in settlements that are court ordered (Current Population Reports, various years). Consistent with the central role of information in enabling cooperative outcomes, previous research has also found that fathers who maintain regular contact with their children pay higher amounts of child support and are more likely to comply with awards (Furstenberg et al., 1983; Peters et al., 1993). (1)

Given that a cooperative outcome is believed to be what is best for children, it is surprising that the economic and policy literature on divorce has so little to say about how to achieve this ideal outcome. In this article we build on Weiss and Willis (1985) by incorporating the actions of the state and contrasting the implications of cooperative and noncooperative models. We derive hypotheses about the factors that would lead families to choose cooperative versus noncooperative outcomes, and we test our hypotheses using data on child support awards from the NLSY. In our model, an NCP's willingness to pay child support will depend on the level of altruism toward his (or her) children and the possibility of enforcing an agreement with the CP regarding the total expenditures on the children. Child support awards and compliance will also depend on the level of child support guidelines and on state efforts to enforce child support agreements.

III. RESOURCE ALLOCATION IN DIVORCED FAMILIES

In this article we view child support awards and payments over time as part of a dynamic long-term contract between the CP and the NCP. Because of the presence of children, parents maintain a continuing relationship after divorce. The divorce settlement spells out the financial obligation of the NCP over time. As an implicit part of the contract, the CP has the responsibility for making child expenditures and also has control over access to the child. If child expenditures are observable (e.g., if the NCP has some regular contact with the children and can observe their well-being), parents may be able to reach Pare to efficient outcomes. We model this as a Nash cooperative bargaining game. If child expenditures are not observable, the game can be characterized by the Weiss and Willis (1985) noncooperative principal agent solution. Both of these outcomes are self-enforcing, although child support payments would be higher for cooperative divorce settlements. Recognition of the role of the state leads to a third possible outcome. The CP will choose to impose the child support guideline when utility from that choice exceeds the alternative. The choice will depend on the guideline amount, state enforcement efforts, parental altruism toward their children, and the parents' ability to enforce a cooperative outcome.

In this section we model of the determinants of the NCP's willingness to pay child support under assumptions of asymmetric versus symmetric information. The concept of a repeated game is used to capture the idea that child support payments (made by the NCP) and expenditures on children (made by the CP) are part of an ongoing process that continues until the children are adults. We begin by modeling these parental decisions in the absence of child support guidelines (or any court-imposed award) and zero enforcement of child support awards.

Although the emotional and financial relationships between the husband and wife are altered on separation, we assume that both parents retain an emotional attachment to their children. The following equation specifies the ex-wife's (w) and ex-husband's (h) payoff functions as discounted time-separable utility functions whose arguments are own consumption, [X.sub.w] and [X.sub.h], and the consumption or expenditures on their children, [X.sub.c] in each month (t) until child support ends (t = T):

(1) [U.sub.i] = [summation over (T/t=0)] [U.sub.i][[X.sub.i](t),[X.sub.c](t)]/[(1 + r).sup.t]

i = w, h

where r denotes the individual's rate of time preference. In this model child welfare is measured simply by the resources allocated to the child. (2) The fact that [X.sub.c] enters each parent's utility function illustrates our assumption that child well-being is a public good for parents (see Weiss and Willis [1985] for the initial development of this idea). (3) One factor that does change at divorce is that decisions (even those involving children) are assumed to be made by each parent separately. However, each parent is affected by the other's decisions, and coordination or cooperation is a possible outcome. To capture this idea, for each time period we specify a separate budget constraint for each parent, assuming for convenience that the ex-wife is the CP and the ex-husband is the NCP: (4)

(2) [Y.sub.w](t) + S(t) = [X.sub.c](t) + [X.sub.w](t)

(3) [Y.sub.h](t) - S(t) = [X.sub.h](t)

where [Y.sub.w](t) and [Y.sub.h)(t) are the exogenously determined incomes of the each parent, and S(t) is child support paid by the NCP in month t. (5) Evidence shows that borrowing constraints are likely to be important for low-income families and especially families headed by single mothers (Zeldes, 1989; Peters, 1993). Thus, we assume that capital markets are imperfect and that the budget constraints must be satisfied in each time period. (6)

In our model the NCP makes a transfer, S(t), at the beginning of each month. The CP receives this transfer and then makes expenditures, [X.sub.c](t), on behalf of the child. (7) These actions are repeated each month. Because of the assumption of imperfect capital markets, each parent has a continuous strategy set at each time period that is bounded by their income constraint such that 0 [less than or equal to] S(t) [less than or equal to] [Y.sub.h](t) and 0 [less than or equal to] [X.sub.c](t) [less than or equal to] [Y.sub.w](t) + S(t). Given these two conditions, the model simplifies to a repeated game with the payoffs represented by the utility function evaluated only in the current month. (8)

The game has been described except for the information assumptions. It is clear that the CP's information set is a singleton, because she receives a transfer from the NCP and knows the amount with certainty. This may or may not be true for the NCP.

Asymmetric Information

If the NCP has little or no contact with his children, information about the GP's expenditures on the child, [X.sub.c], is asymmetric (see Weiss and Willis, 1985). In this case, the repeated nature of the game cannot help produce a Pareto efficient outcome because the NCP cannot react to the CP's choice of [X.sub.c]. Thus, the CP is free to choose the levels of [X.sub.c] and [X.sub.w] that maximize her own utility without fear of retaliation. The problem unravels into a one-shot game played over and over, and each parent will maximize his or her individual utility in each month.

Maximizing the CP's utility (Equation [1]) subject to her household budget constraint (Equation [2]), we obtain the usual condition that the marginal utilities per dollar are equalized across consumption alternatives. The CP will treat the child support transfer as additional income and will increase [X.sub.c] according to her marginal propensity to spend on the children. In other words her spending on children does not depend on the source of the additional income but only on the total amount of income.

The CP's reaction function is:

(4) [X.sub.c] = [X.sub.c][\.sub.S=0] + [[micro].sub.w]S

where [X.sub.c][\.sub.S=0] is the amount of [X.sub.c] that would be provided by the wife if S = 0, and [[micro].sub.w] = [partial][X.sub.c]9 [partial] [Y.sub.w], the wife's marginal propensity to spend on the children. We can also think of [[micro].sub.w] as a parameter of the utility function that reflects the mother's altruism toward her children. If [X.sub.c] and [X.sub.w] are both normal goods, then 0 [less than or equal to] [[micro].sub.w] [less than or equal to] 1. (9)

In a one-shot game, a rational NCP will choose S in each month to maximize his utility subject to the CP's reaction function. Substituting Equation (4) into the NCP's utility function (Equation [1]) and maximizing subject to the NGP's budget constraint yields the following first-order condition for an interior solution:

(5) ([partial] [U.sub.h]/[partial][X.sub.c])/([partial][U.sub.h]/[partial][X.sub.h]) = 1/[[micro].sub.w].

Given a specific utility function, we can use Equation (5) and the NCP's budget constraint (Equation [3]) to solve explicitly for [X.sub.h] and [S.sup.min], where we define [S.sup.min] as the NCP's willingness to pay child support under asymmetric information. More generally,

(6) [S.sup.min] = f([Y.sub.w], [Y.sub.h], [[micro].sub.w], [[micro].sub.h]),

where [[micro].sub.h] is a utility function parameter that measures the NCP's altruism toward his children.

Equation (5) illustrates the principal-agent outcome: To obtain an additional dollar of [X.sub.c], the NCP has to transfer more than one dollar to the CP. The price of [X.sub.c], to the NCP is the reciprocal of the fraction of income that is spent on the child, 1/[[micro].sub.w]. In effect, this raises the price of [X.sub.c], to the NCP and decreases the amount that he would desire to transfer. We assume that the NCP knows the CP's utility function (and thus [[micro].sub.w]) from his experience in the marriage. The outcome will be the same every month, unless there is a change in parents' incomes or utility parameters. (10)

This game can be thought of as a kind of self-enforcing contract; because it is a CournotNash equilibrium, neither parent has any incentive to change his or her behavior. However, because asymmetric information creates a distortion in the perceived price ratio of [X.sub.h], to [X.sub.c], the sum of the CP and NCP's utilities is less than what could be obtained with a Pareto optimal outcome. As noted by Weiss and Willis (1985), child expenditures are also less. In the next section we explore the conditions under which a Pareto improving outcome could be achieved.

Symmetric Information

NCPs who have regular contact (e.g., visitation) with their children can observe the wellbeing of those children and can verify [X.sub.c]. With symmetric information, each party observes the other's behavior and can motivate cooperation through threat of retaliation or promise of reward (e.g., altering [X.sub.c], or S). Compared to the asymmetric information equilibrium, symmetric information could enable an agreement between the CP and NCP to provide greater [X.sub.c], and S. Because the game is repeated over multiple periods, the two parents can specify an implicit contract that ties child support payments in period t + 1 to a given level of [X.sub.c] in period t. Once reached, this agreement is potentially self-enforcing, because both parent's utilities are improved over the asymmetric information case and any defection from the agreement can be punished in the future. (11)

Using the assumptions of the Nash (1950) cooperative bargaining model, (12) the specific bargaining outcome, [X.sup.po.sub.c] and [S.sup.po], can be obtained from maximizing the product of the gains to each parent:

(7) max[[U.sub.h]([X.sub.c], [X.sub.h]) - [[U.sup.min.sub.h]]

x [[U.sub.w]([X.sub.c], [X.sub.w]) - [U.sup.min.sub.w]]

subject to the joint budget constraint:

(8) [Y.sub.h] + [Y.sub.w] = [X.sub.h] + [X.sub.w] + [X.sub.c].

The first-order conditions from this maximization problem yield the familiar Samuelson (1954) condition for the optimal provision of a public good: Choose [X.sub.c] such that the sum of the parents' marginal rates of substitution between child and own consumption is equal to the price ratio.

(9) ([partial][U.sub.w]/[partial][X.sub.c])/([partial][U.sub.w]/[partial] [X.sub.w])

+ ([partial][U.sub.h]/[partial][X.sub.c])/([partial][U.sub.h]/[partial] [X.sub.h]) = 1

Specifying the utility functions for the two parents, this maximization problem could be solved explicitly for [S.sup.po]. More generally, we specify the Pareto optimal transfer that the parents can agree to as follows:

(10) [S.sup.po] = g([Y.sub.w], [Y.sub.h], [[micro].sub.w], [[micro].sub.h]).

In summary, in the absence of state-imposed child support guidelines and enforcement, divorce settlements will be in one of two regimes: (1) If there is no contact between the NCP and his children, information about child expenditures is asymmetric, and child support payments (and awards) will be [S.sup.min]; (2) if frequent visitation allows the NCP to observe the children's well-being, information about child expenditures is symmetric, and child support payments (and awards) will be

[S.sup.po]. (13) Note than in both cases divorce settlements are self-enforcing, and full compliance is expected.

When the role of the state is ignored, cooperative or noncooperative outcomes are determined solely by whether information is symmetric or asymmetric. In the next section we show that when child support guidelines (or any court-imposed awards) are incorporated into the model, some parents who might have voluntarily reached cooperative outcomes (because of symmetric information) may instead choose a noncooperative outcome, especially when the guideline level is high relative to parental altruism toward children. Noncooperative agreements made under these circumstances will not be self-enforcing.

IV. THE ROLE OF THE STATE IN FAMILY RESOURCE ALLOCATION AFTER DIVORCE

During the 1980s federal and state governments in the United States passed a number of laws aimed at increasing child support awards and payments. The federal Child Support Enforcement Amendments of 1984 required all states to adopt advisory child support guidelines by 1987, and the Family Support Act of 1988 mandated that states adopt guidelines with rebuttable presumption by 1989. Guidelines specify the amount of child support to be paid as a function of the number of children, the NCP's income, and sometimes the CP's income. These federal laws also required that states use more vigorous enforcement measures, such as automatic wage withholding and garnishment of tax refunds and lottery winnings. The probability that a delinquent parent will be caught and forced to pay, however, is still fairly low. (14) Even with automatic wage withholding, a NCP who wants to avoid paying can change jobs or become self-employed.

In this section we introduce the possibility that the legal environment may affect child support outcomes. Because the child support guideline amount will be imposed when the parents cannot come to an alternative agreement, a model of child support awards must incorporate both willingness to pay and the state guidelines and enforcement efforts already described. Child support guidelines provide divorcing parents with exact information regarding the default position of the courts if the parents fail to reach an alternative agreement. Guidelines can also alter the subset of feasible settlement outcomes as parents "bargain in the shadow of the law" (Mnookin and Kornhauser, 1979) by bestowing greater bargaining power to one parent or the other.

Guidelines will be ineffective if there is no enforcement by the state. If the award exceeds self-enforcing levels, NCPs would not voluntarily comply with the orders, and third-party enforcement is required to ensure full compliance. We define p as the probability that a delinquent NCP will be forced to pay his child support obligation in a particular month. For example, an employed individual whose order was established in a state with automatic wage withholding and who still resides in that state faces p = 1. Moving out of state, changing jobs, or less than complete enforcement by the state will result in 0[less than or equal to][rho] < 1. (15)

When the two parents cannot agree, the court will impose the guideline, [S.sup.g]. The child support award, [S.sup.a], is then equal to the guideline amount. The CP will decide to accept the NCPs voluntary payment or cause the guideline to be imposed. Her decision depends on the NCP's response when [S.sup.g] is imposed. In each month he will choose to make payments (S) that maximize

(11) E([U.sub.h])

= [rho][U.sub.h][[Y.sub.h] - [S.sup.g], [[micro].sub.w] ([Y.sub.w] + [S.sup.g])]

+ (1 - [rho])[U.sub.h][[Y.sub.h] - S,[[micro].sub.w] ([Y.sub.w] + S)]

This expression is the husband's utility from paying the full amount, weighted by the probability of getting caught, plus his utility from paying an amount S, weighted by the probability of not getting caught. (16) If CPs are unable to smooth expenditures through borrowing and saving, the first-order condition from maximizing this utility is identical to the asymmetric case defined by Equation (5), and the solution for S is [S.sup.min]. An NCP who is forced to pay more than he desires in a month in which he is caught will not respond by reducing voluntary payments below the desired amount in other months. (17) The NCP pays [S.sup.min] if full payment is not enforced and [S.sup.g] if the state enforces the child support award in that month. (18) Under this scenario, the voluntary compliance rate (i.e., compliance in a month of nonenforcement) will simply be the ratio [S.sup.min]/[S.sup.g], but, if p > 0, the lifetime compliance rate will be greater than [S.sup.min]/[S.sup.g]. The collection of past due child s upport would increase the compliance rate further, but we don't model this explicitly because child support agencies have had little success in collecting arrears. (19) These results suggest that increases in the default award and improvements in state enforcement efforts will improve the financial well-being of children (and custodial mothers) for parents who cannot come to an agreement.

Negotiations over the divorce settlement will result in one of three outcomes. Parents will agree to a cooperative self-enforcing settlement ([S.sup.po]), a noncooperative self-enforcing settlement ([S.sup.min]), or the CP will insist on [S.sup.g], the guideline amount, and the NCP will respond by paying [S.sup.min] if he is not caught or [S.sup.g] if he is caught. (20) Note that full information is necessary but not sufficient to achieve a cooperative outcome. When state guidelines are high relative to parental altruism and enforcement is efficient, some mothers may achieve higher utility by having the guidelines imposed and taking the chance that the father will be forced to pay [S.sup.g]. In the following paragraphs we describe the conditions under which different outcomes will occur. To examine compliance outcomes, we focus on the factors that affect the determination of the award: (1) symmetric versus asymmetric information, and (2) negotiated versus imposed awards.

Case 1: Asymmetric Information and [S.sup.min] Is Negotiated

As discussed, if the NCP cannot observe the CP's expenditures on children, then [S.sup.min] is the only self-enforcing child support amount. The NCP would agree to [S.sup.min] even if the guideline amount were lower because he cares about his children, and [S.sup.min] is the best that he can do under asymmetric information. In this case we will observe full compliance. The CP would agree to [S.sup.min] if her utility from that agreement, [U.sup.min.sub.w] were greater than her expected utility from imposing [S.sup.g], [U.sup.g.sub.w] defined by the right-hand side of Equation (12):

(12) [U.sup.min.sub.w]

[greater than or equal to] [rho][U.sub.w][(1 - [[micro].sub.w])([Y.sub.w] + [S.sup.g]), [[micro].sub.w]([Y.sub.w] + [S.sup.g])

+ (1 - p) [U.sub.w] [(1 - [[micro].sub.w])([Y.sub.w] + [S.sup.min]), [[micro].sub.w] ([Y.sub.w] + [S.sup.min])].

The higher the guideline and the larger p, the [rho] less likely it is that this condition will be met. (21) The condition is more likely to be met if either the father or the mother has a high degree of altruism toward the children. A high degree of mother's altruism would reduce the price distortion that the father faces due to asymmetric information and would increase his demand for child expenditures. A high degree of father's altruism would also increase his demand for [X.sub.c] and his willingness to pay child support.

Case 2: Asymmetric Information and [S.sup.g] Is Imposed

The CP will insist on [S.sup.g] if the inequality in Equation (12) is reversed. In this case we observe [S.sup.min] with probability (1 - [rho]) and [S.sup.g] with probability p. Case 2 will be more likely to occur for parents living in states with higher guidelines and enforcement efforts and less likely to occur if either parent is highly altruistic toward the children. We will observe partial or zero compliance when the award is not enforced.

Case 3: Symmetric Information and [S.sup.po] Is Negotiated

As discussed, if frequent contact between the NCP and his children provides information about [X.sub.c], a Pareto optimal outcome can be sustained. As before, the wife will agree to [S.sub.po], if her utility from that agreement is greater than her expected utility from imposing [S.sup.g], [U.sup.g.sub.w]:

(13) [U.sup.po.sub.w] [greater than or equal to] p[U.sub.w][(1 - [[micro].sub.w]) ([Y.sub.w] + [S.sup.g]),

[[micro].sub.w]([Y.sub.w] + [S.sup.g])] + (1 - [rho])[U.sub.w][(1 - [[micro].sub.w])([Y.sub.w] + [S.sup.po]), [[micro].sub.w]([Y.sub.w] + [S.sup.min])].

The factors that will affect the likelihood of this outcome are the same as those described in case 1 except that an increase in the mother's altruism will not affect the father's demand for child expenditures, because there is no price effect when information is symmetric.

Case 4: Symmetric Information and [S.sup.g] Is Imposed

The CP will insist on [S.sup.g] if the inequality in Equation (13) is reversed. In this case we observe [S.sup.po] with probability (1 - [rho]) and [S.sup.g] with probability [rho]. Case 4 will be more likely to occur for parents living in states with higher guidelines and enforcement efforts and less likely to occur if the father is highly altruistic toward the children. Again, full compliance will occur only when enforced by the state.

These four cases illustrate the impact of child support policies. Increases in [S.sup.g] and [rho] will increase awards and lifetime child support payments for those in groups 2 and 4. In addition, increases in [S.sup.g] will increase the likelihood that parents will move from case 1 (self-enforcing) to case 2 (guidelines imposed) or from case 3 to case 4. With asymmetric information, an increase in guidelines that moves parents from case 1 to case 2 will have an unambiguously positive effect on child expenditures. With symmetric information, if guidelines are so high as to cause mothers who would have bargained cooperatively to impose guidelines instead (i.e., moving from case 3 to case 4), child expenditures may fall, as the family changes from a cooperative to a noncooperative allocation model. This situation is likely to occur only for mothers who put a low weight on child expenditures.

V. COMPARATIVE STATICS AND EMPIRICAL IMPLICATIONS

We denote the probability of observing case 1 as (1 - [gamma])P1 where (1 - [gamma]) is the probability that information is asymmetric. To facilitate the comparative statics analysis, we adopt a random utility specification (Maddala, 1983; McFadden, 1973). Given this framework, the condition in Equation (12) can be written as

(14) P1 = prob([U.sup.min.sub.w] + [[member of].sup.po.sub.w] [greater than or equal to] [U.sup.g.sub.w] + [[member of].sup.g])

= prob([[member of].sup.po.sub.w] [greater than or equal to] [U.sup.g.sub.w] + [[member of].sup.g] - [U.sup.min.sub.w])

where [[member of].sup.min] and [[member of].sup.g] are residuals that capture errors in optimization. Similarly, the probability of observing case 3 is [gamma]P3, where the condition in Equation (13) can be written as

(15) P3 = prob([U.sup.po.sub.w] + [[member of].sup.po] [greater than or equal to] [U.sup.g.sub.w] + [[member of].sup.g])

= prob([[member of].sup.po] [greater than or equal to] [U.sup.g.sub.w] + [[member o].sup.g] - [U.sup.po.sub.w]).

We can now write an expression for the expected child support award for a random member of the population:

(16) E([S.sup.a]) = (1 - [gamma])P1[S.sup.min] + (1 - [gamma])(1 - P1)[S.sup.g] + [gamma]P3[S.sup.po] + [gamma](1 - P3)[S.sup.g]

or, more generally,

(17) E([S.sup.a]) = [S.sup.a]([Y.sub.w], [Y.sub.h]. [[micro].sub.w], [[micro].sub.h], [rho], [S.sup.g], [gamma]).

By calculating the partial derivatives of Equation (16) with respect to the independent variables, we can determine the expected effects of these variables on the actual award, [S.sup.a]. Each derivative consists of two basic components: (1) the effects of the independent variable on the probabilities of cases 1-4 weighted by the differences in the average court award in each of the four cases, and (2) the effects of the independent variable on the average award in each case, weighted by the probability of that case. The expressions from this exercise are cumbersome and are provided in an appendix available from the authors on request. Here we briefly summarize the results and explain the intuition behind the results.

1. In general, increases in father's income will increase the child support award, because [S.sup.min] [S.sup.po] and [S.sup.g] are all increasing in father's income, whereas increases in mother's income will reduce the award. As mother's income rises, [X.sub.c][\.sub.S=0] increases. This increase in the father's purchasing power will cause a decrease in his desired transfers to the mother to accommodate an increase in his own consumption.

2. The effect of mother's altruism, [[micro].sub.w], on the child support award is ambiguous, because the effects of [[micro].sub.w] on [S.sup.min] and [S.sup.po] are theoretically ambiguous. The outcome depends on the relative impact of the income and substitution effects as the father alters his consumption choices (in the noncooperative case) due to a change in the price of child consumption. We expect that award levels will rise with increases in father's altruism, because voluntary payments are higher.

3. The effect of the guideline amount on awards is unambiguously positive. Higher guidelines will raise awards for all who cannot reach self-enforcing agreements and will also increase the probability that the guideline will be imposed. The same effect is expected for an increase in state enforcement efforts.

4. The expected award is greater when information is symmetric, because [S.sup.po] [greater than or equal to] [S.sup.min].

In a similar fashion, the probability of guideline use is defined as

(18) prob([S.sup.a] = [S.sup.g]) - (1 - [gamma])(1 - P1) + [gamma](1 - P3).

Taking partial derivatives of Equation (18) and assuming risk neutrality and that [X.sub.c] is a normal good, we find that an increase in [Y.sub.h] will decrease the use of guidelines when the resulting increase in [S.sup.min] is greater than the increase in [S.sup.g]. In other words, an increase in [Y.sub.h] will decrease the use of guidelines for highly altruistic fathers (or if the demand for child expenditures is highly income elastic), and an increase in [Y.sub.h] will increase the use of guidelines for fathers with less than average levels of altruism.

The effect of mother's income is more complex. It depends on the altruism levels of both the mother and the father. Fathers with high levels of altruism are less likely to use the guidelines, but the effect of mother's altruism is ambiguous, because of the ambiguous effect of on [S.sup.min]. Increases in [S.sup.g] and p will increase the probability that the default will be imposed, because these variables increase the value to the mother of that option. Families with symmetric information will rely less on the guidelines, because [S.sup.po] [greater than or equal to] [S.sup.min], and the wife will be less likely to insist on [S.sup.g] when [S.sup.po] can be achieved.

VI. EMPIRICAL ANALYSIS

The preceding discussion suggests that the characteristics of self-enforcing settlements will be different from those associated with court-imposed settlements. In addition, our theory suggests that greater default awards and more intense state enforcement efforts at the time of the settlement will increase the use of guidelines and the level of child support awards. To test these hypotheses we extract a sample of divorced or separated women with children from the NLSY 1979 cohort, and we merge this sample with state- and year-specific information on child support policies by the date of the original child support award. The NLSY 1979 data are well suited to our analysis because an expanded battery of child support questions was added as part of the 1993 interview. To examine the nature of child support awards we select a sample of 229 mothers who indicated that they were owed child support in 1993 and responded to detailed questions regarding their child support awards. (22) In addition to reporting award and payment information, these women were asked about the method of reaching their child support agreement. The longitudinal nature of the data allows us to append child support guideline and enforcement policies in place in the woman's state of residence at the time of her child support award. (23)

Table 1 reports the characteristics of these divorced or separated mothers by the three methods by which they could have reached their child support agreement. Twenty-one percent reported that they reached an agreement without assistance, and 44% said that the award was court-ordered; the remainder used lawyers to reach an agreement. Compared to women with court-ordered settlements, we see that women who settled without assistance have characteristics that are associated with self-enforcing outcomes. They have higher child support awards, payments, and compliance rates. For example, women who settled without assistance received almost 80% of the child support that was owed. In contrast, women with court-ordered awards received only about half of what was owed. Women who settled without assistance are also more likely to reach a different settlement than what is mandated by the state: Only 20% reported using guidelines versus 71% for women with court-ordered settlements. In addition, women who settled without assistance are more likely to have modified their initial divorce settlement as circumstances changed over time: 31% of these women have modified their award compared to less than 24% of women with court-ordered awards. This difference may reflect lower costs of negotiation. Finally, we expect that parents with asymmetric information are less likely to settle on their own, because awards that are self-enforcing with asymmetric information ([S.sup.min]) are lower than cooperative awards ([S.sup.po]) The fact that only 13% of fathers who settled without assistance have no contact with their children, compared to 24% of fathers with court-ordered settlements is consistent with this expectation.

Note that the third category, "Reached Agreement Using Lawyers," is likely to be somewhat heterogeneous with respect to the likelihood that parents reach a self-enforcing agreement. Parents with high income and assets who might agree on child support may use lawyers because of the complexity of the settlement. In contrast, other parents who cannot agree may use lawyers as a means to obtain a more favorable settlement. (24) Consistent with the notion of this type of within-group heterogeneity, Table 1 shows that families who used lawyers have rates of father-child contact, compliance, and guideline use that are in between the rates reported for those who settled without assistance and the court-ordered group.

Some of the differences in these child support outcomes are likely to be related to differences in fathers' characteristics across the three groups. Specifically, lower awards, receipt, and compliance among those who have court-ordered awards may result from fathers in this group earning over $5,000 less per year than fathers in either of the other two categories. The bottom panel of Table 1 reports the means characteristics for the three groups holding income constant at the average income level of fathers in the group that Reach Agreement Without Assistance ($25,666). The calculations in Table 1 illustrate that when we control for income differences, awards are higher for the court-ordered group, but payments are lower resulting in substantially lower compliance rates for those with court-ordered awards compared to those who settled voluntarily.

The differences noted highlight the importance of understanding the method by which parents reach a settlement. To examine the determinants of the wife imposing a default settlement versus the parents reaching a self-enforcing settlement, we estimate reduced-form logit regressions of Equation (18). The results are reported in Table 2. We use two alternative indicators of imposing a default settlement. In the second column the dependent variable is a dichotomous variable indicating that the child support award was court-ordered rather than the result of an agreement reached without assistance or with the aid of lawyers. In the third column the dependent variable is equal to one if the mother reported that child-support guidelines were used to determine the award amount and equal to zero otherwise. (25) We report marginal probabilities from the logit regressions.

These reduced-form models include characteristics of parents (i.e., incomes and education levels) and measures of interactions between family members, such as the duration of the marriage and frequency of father-child contact after separation or divorce. To examine the impact that child support policies at the time of the award have on the method of settlement we include measures of state- and time-specific child support enforcement efforts and default award levels. We define two measures of state enforcement efforts: (1) to measure the intensity of effort we use the annual enforcement expenditures per case reported to the state child support enforcement (IV-D) agency for collection; and (2) to measure the effectiveness of enforcement measures we use the annual IV-D child support collections per dollar of administrative expenditures. (26)

Variation across states and over time in these two measures of child support enforcement are illustrated in Figures 1 and 2. Figure 1 depicts the level of annual expenditures (in constant 1990 dollars) per child support enforcement case for the median state and the states with the highest and lowest expenditures in each year from 1980 through 1992. With the exception of one state reporting extremely high expenditures in 1981, (27) expenditures on child support enforcement have risen over time. The median expenditure per case increased from $50 to $153 by 1992. There are also substantial differences in child support enforcement expenditures across states. In 1992, the maximum expenditure was $309 per case, compared with a minimum expenditure of only $36. For our sample, the mean administrative expenditure per case is $124.

The degree to which these expenditures translated into additional child support collections also varied substantially across states during this time period, as shown in Figure 2. Though the mean collection ratio for our sample is just over 3, some states collected more than $10 for each $1 in enforcement expenditures; however, in the early 1980s, some states were not able to break even.

In addition to state enforcement measures, we are able to observe variation in the level of the default award across states when statewide guidelines were in effect. (28) Applying the guideline formulas to the characteristics of a representative family we can calculate the default award for each state in every year. (29) The variable included in the regressions measures the deviation of the default award in the respondent's state from the sample mean default award. Because this variable cannot be created for women whose awards were established prior to the adoption of statewide child support guidelines, we also include a dichotomous variable indicating that guidelines had been adopted in the woman's state of residence at the time of the child support award. (30)

Our model predicts that as greater enforcement of child support awards increases payments by unwilling NCPs, the likelihood that the default award is imposed will increase. The results in Table 2 confirm this hypothesis. Both enforcement measures demonstrate the expected relationship. For example, in the second column, a $100 per case increase in enforcement expenditures increases the probability of a court-ordered child support award by just over 21 percentage points. Similarly, an increase by $1 in collections per dollar of child support enforcement expenditures increases the probability of a court-ordered award by 7 percentage points. The estimates presented in the last column suggest a similar effect of enforcement expenditures on the probability that guidelines are used to determine the award. (31) To address the possibility that court-ordered awards and enforcement efforts are simply moving together over time, we include a linear trend variable. There is no identifiable trend for either method of award determination.

Our theory also suggests that as the default award rises, choosing this option becomes more attractive. We find no evidence, however, that court-ordered awards are more likely for women living in states that set higher default award levels. The absence of an effect of guideline levels on the type of child support settlement may not capture the whole effect of higher default awards on settlement type, because we can only measure differences in default levels while guidelines were in effect.

Some measures of the father's ability to pay child support also affect the method of settlement. In Table 2 we see that the greater the father's income was during the marriage, the less likely a court-ordered award is, perhaps because there are greater gains to be made by negotiating a mutually beneficial agreement. Better educated fathers are somewhat less likely to have court-ordered settlements; however, guideline use is more prevalent among this group. (32)

Finally, we try to capture the degree to which the mother and father are able to cooperate. Because this is not easily observable, we include proxy variables, such as the duration of the marriage, and contact between the father and child in the first survey after separation. (33) We find evidence that contact between the father and child decreases the probability of using guidelines to determine the amount of child support. Surprisingly, father--child contact is not significantly associated with a reduction in the probability of a court-ordered award. (34) One possible explanation for this finding is that some court-mediated disputes may be over custody or visitation rather than over money.

From the analysis we find that better enforcement of child support awards reduces the probability of self-enforcing child support agreements. This has potentially important implications for child support outcomes. Does this shift toward court-ordered awards improve the financial situation for children whose parents divorce? According to our theory changes in child support policies at the time of the award have predictable effects on child support award and receipt levels and compliance rates through their effect on the type of award. Specifically, better state enforcement of child support awards should increase the amount of awards and receipt. In the absence of effective enforcement, some women might have agreed to lower voluntary awards because they could expect full payment. As enforcement of child support awards improves, the proportion choosing court-ordered awards increases, as evidenced by the previous results. Those who now expect greater payments will opt for the higher default award amounts. The eff ect of better enforcement efforts on compliance, however, is ambiguous, because there are offsetting effects: Better enforcement efforts increase compliance ratios for those with court-ordered awards, but better enforcement also decreases the proportion that have self-enforcing awards. Similar logic suggests that increasing the default award will cause the amounts awarded and received to increase. However, because higher default awards do not improve the collection of child support but do increase the number of court-ordered awards, we expect the compliance ratio to fall.

In Table 3 we report estimates from ordinary least squares regressions of the monthly child support award amount at the time of the original award (second column) and the average monthly amount of child support received in 1992 (third column). In the last column we report estimates from a two-limit Tobit regression of the ratio of child support received to child support owed in 1992. (35)

The results from these reduced-form models indicate that better state enforcement at the time of the award has no significant positive effect on these child support outcomes. These policies are expected to affect later child support payments and compliance through their effect on the choice of voluntary versus court-orders settlements. (36)

One possible explanation for the lack of any impact of enforcement on subsequent child support payments is that improved enforcement may result in fathers offsetting enforcement by lowering voluntary payments in response to ill-will created by collection efforts. More generous child-support guideline formulas do, however, increase both awards and receipt for women in states with guidelines. Each $100 increase in the default award increases actual awards by $96, although receipt increases by only $53. Higher default award levels do not significantly reduce compliance with child support awards.

In addition to the effect of these policies, the ability of fathers to pay child support also determines child support awards and payments. Not surprisingly, women whose ex-husbands had higher earnings at the time of separation can expect greater child support awards and payments. Compliance rates are also higher for fathers with higher income perhaps because it is difficult or more costly to avoid enforcement by changing jobs or moving to the underground economy. A similar relationship between income and compliance was found by Garfinkel and Robins (1994) and Sonenstein and Calhoun (1990). Both awards and receipt are higher for women whose ex-husband was well educated and those who were married for a longer time.

VII. CONCLUSIONS AND DISCUSSION

The theoretical model presented in this article provides a wealth of predictions about the allocation of family resources in the aftermath of divorce as well as an evaluation of the role of various child support policies in determining the type of child support award and therefore determining child support payments. With verifiability, parents may be able to reach Pareto optimal self-enforcing settlements that unambiguously increase the well-being of both parents and children. Contact between the NCP and his children results in greater child support payments and child expenditures, if not offset by high levels of conflict between parents. Thus, policies encouraging involvement of NCPs and reducing antagonism during the divorce process can simultaneously increase the well-being of children and their divorced parents. Although child support policies may not be necessary in cases in which altruistic parents can reach cooperative settlements, these policies can improve financial support for many children. State actions can affect both child support awards and subsequent payments, but policies combining increased guideline awards and enforcement efforts must be coordinated. Payments by true deadbeat dads (i.e., those for whom [S.sup.min] = 0) will be determined solely by state default award levels and enforcement efforts.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

TABLE 1

Sample Characteristics by Method of Determining Child Support Award

 Reached Agreeement
 without Assistance

A. Mean sample characteristics

No father-child contact (a) 0.133
Annual child support owed (b) $3,290
 (1,803)
Annual child support recieved (b) $2,536
 (1,605)
Compliance ratio (b) 0.786
 (0.346)
Used guidelines to determine award 0.204
(d)
Modified original child support 0.306
award (b)
Father's annual income (c) $25,666
 (19,289)
Sample size 49

B. Mean child support
characteristics controlling for
differences in father's income (e)

No father-child contact 0.133
Annual child support owed (b) $3,290
Annual child support recieved (b) $2,536
Compliance ratio (b) 0.786
Used guidelines to determine 0.204
award (d)
Modified original child support 0.306
award (b)
Sample size 49

 Reached Agreeement
 Using Lawyers

A. Mean sample characteristics

No father-child contact (a) 0.234
Annual child support owed (b) $3,952
 (2,653)
Annual child support recieved (b) $2,597
 (2,892)
Compliance ratio (b) 0.605
 (0.440)
Used guidelines to determine award 0.557
(d)
Modified original child support 0.215
award (b)
Father's annual income (c) $24,773
 (13,492)
Sample size 79

B. Mean child support
characteristics controlling for
differences in father's income (e)

No father-child contact 0.163
Annual child support owed (b) $3,887
Annual child support recieved (b) $2,693
Compliance ratio (b) 0.577
Used guidelines to determine 0.567
award (d)
Modified original child support 0.250
award (b)
Sample size 79

 Court-Ordered Child
 Support Agreement

A. Mean sample characteristics

No father-child contact (a) 0.243
Annual child support owed (b) $3,211
 (1,900)
Annual child support recieved (b) $1,808
 (2,117)
Compliance ratio (b) 0.511
 (0.455)
Used guidelines to determine award 0.713
(d)
Modified original child support 0.238
award (b)
Father's annual income (c) $19,370
 (9,530)
Sample size 101

B. Mean child support
characteristics controlling for
differences in father's income (e)

No father-child contact 0.103
Annual child support owed (b) $3,692
Annual child support recieved (b) $2,231
Compliance ratio (b) 0.613
Used guidelines to determine 0.722
award (d)
Modified original child support 0.281
award (b)
Sample size 101

(a) Measured in the first survey after separation.

(b) Measured in 1992.

(c) Averaged during the parents' marriage.

(d) Measured at the time of the child support award.

(e) Father's annual income is held constant at $25,666.

TABLE 2

Logit Regressions of the Method of Determining Child Support Award

 Court-Ordered Award Used Guidelines

State child support enforcement 0.214 ** 0.190 ***
expenditures per case ($100s)
 (2.31) (2.99)
Ratio of state child support 0.073 *** 0.049 **
collections to expenditures
 (2.55) (2.28)
Guidelines adopted in state -0.040 --
 (0.27)
Guideline award amount in states -0.128 --
with guidelines ($100s)
 (1.55)
Father's annual earnings ($1,000s) -0.009 ** -0.001
 (2.79) (0.60)
Mother's annual earnings ($1,000s) -0.004 -0.006
 (0.58) (1.05)
Number of children -0.004 0.062
 (0.07) (1.18)
Any father-child contact -0.111 -0.417 *
 (0.64) (1.70)
Mother is black 0.248 ** 0.011
 (2.44) (0.13)
Mother is Hispanic 0.100 0.070
 (0.79) (1.12)
Mother's education (years) -0.018 0.026
 (0.85) (1.43)
Father's education (years) -0.031 * 0.029 *
 (1.75) (1.81)
Duration of marriage (years) -0.002 -0.007
 (0.12) (0.55)
Trend 0.020 0.002
 (0.75) (0.14)
Intercept yes yes
Chi-square (df) 131.92 *** 57.45 ***
 (16) (14)
Sample size 229 229

Notes: The estimates reported are [partial]P/[partial]X = [beta] (P[1 -
P]) from the logit P = 1/(1 + exp[-X[beta]). t-Statistics, calculated
from robust standard errors that are adjusted for clustering within
states, are in parentheses. All models include a dichotomous variable
equal to one if father's income is missing, and a dichotomous variable
equal to one if child support was awarded prior to 1984 because
information on father-child contact was not obtained prior to to the
1984 interview.

* p < 0.10.

** p < 0.05.

*** p < 0.01.

TABLE 3

Regressions of Child Support Outcomes

 Ordinary Least Squares
 Monthly Child
 Support Award (b)

Intercept -186.49
 (1.67)
State child support enforcement -10.51
expenditures per case ($100s) (0.39)
Ratio of state child support -10.11 *
collections to expenditures (1.73)
Guidelines adopted in state -2.28
 (0.04)
Guideline award amount in states 96.18 ***
with guidelines ($100s) (3.82)
Father's annual earnings ($1,000s) 4.02 *
 (2.02)
Mother's annual earnings ($1,000s) 0.08
 (0.05)
Number of children 82.01 ***
 (6.05)
Any father-child contact 58.53
 (1.40)
Mother is black -0.06
 (0.00)
Mother is Hispanic 13.81
 (0.32)
Mother's education (years) -1.25
 (0.12)
Father's education (years) 11.93 **
 (2.28)
Duration of marriage (years) 7.68 *
 (1.95)
Year of child support award 7.00
 (0.74)
[R.sup.2] 0.357
Chi-square (df) --

Sample size 229

 Ordinary Least Tobit (a)
 Squares
 1992 Monthly Child 1992 Compliance
 Support Receipt (c) Ratio (c)

Intercept -134.93 yes
 (1.34)
State child support enforcement -14.79 -0.016
expenditures per case ($100s) (0.58) (0.23)
Ratio of state child support -11.23 0.003
collections to expenditures (1.45) (0.14)
Guidelines adopted in state -50.29 -0.170
 (0.94) (1.52)
Guideline award amount in states 53.32 * 0.087
with guidelines ($100s) (1.73) (1.23)
Father's annual earnings ($1,000s) 4.94 *** 0.008 ***
 (3.20) (2.85)
Mother's annual earnings ($1,000s) -0.11 0.002
 (0.06) (0.44)
Number of children 11.39 -0.144 ***
 (0.58) (2.95)
Any father-child contact 32.35 0.135
 (0.89) (1.07)
Mother is black -64.44 * -0.159 *
 (1.84) (1.95)
Mother is Hispanic -20.67 -0.037
 (0.65) (0.46)
Mother's education (years) 0.58 -0.016
 (0.06) (0.80)
Father's education (years) 16.03 ** -0.003
 (2.04) (0.15)
Duration of marriage (years) 7.49 ** 0.015
 (2.04) (1.41)
Year of child support award 3.13 0.019
 (0.31) (0.97)
[R.sup.2] 0.298 --
Chi-square (df) -- -50.99 ***
 (16)
Sample size 229 229

Notes: t-statistics, calculated from robust standard errors that are
adjusted for clustering within states, are in parentheses. All models
include a dichotomous variable equal to one if father's income is
missing, and a dichotomous variable equal to one if child support was
awarded prior to 1984 because information on father-child contact was
not obtained prior to the 1984 interview.

(a) The estimates reported are [partial]y/[partial]x = [beta]
([[PI].sub.2] - [[PI].sub.1]) where [[PI].sub.1] and [[PI].sub.2]
represent the cumulative density function evaluated at (-X[beta]) and (1
- X[beta]) respectively. This calculation is derived from the likelihood
function for the two-limit Tobit because the dependent variable is
bounded by 0 and 1. See Maddala (1983) for detailed derivation.

(b) Measured at the time of the initial award agreement.

(c) Measured in 1992.

* p < 0.10.

** p < 0.05.

*** p < 0.01.

(1.) Note that this correlation could also be due to a selection effect in which more altruistic fathers spent both more time and money on their children.

(2.) The model could be made more realistic (and more complicated) by replacing [X.sub.c] (i.e., inputs to child rearing) with a variable which represents child quality or well-being (i.e., child outcomes). In such a model we would need to specify a production function for child well-being where inputs include parent-child contact, parental conflict as well as expenditures on the child. This extension is similar to the model specified in Peters (1992).

(3.) It is somewhat problematic to model utility as a function of actual expenditures or child well-being if they are not observed by the NCP. Without changing any of the results we derive, we could think of NCP utility as a function of expected expenditures or child well-being.

(4.) Throughout this paper we use the words CP and wife and NCP and husband interchangeably.

(5.) In other work (Peters, 1992), income is treated as endogenous to estimate the role of differential time costs in determining the child custody/visitation arrangements. These results show that time costs do not play a very large role in decisions about custody and visitation. To focus more directly on the issue of compliance and the determinants of child support awards, in this article we assume that labor supply and earnings are exogenous. The prices of [X.sub.c], [X.sub.w], and [X.sub.h] are normalized to one.

(6. ) We have examined the implications of perfect capital markets in an earlier version of the article and most of the predictions of the model remain the same (Argys and Peters, 1996). See note 17 for the main exception.

(7.) National data from the CPS (Current Population Report, 1991) show that only 7.3% of the sample of women with children from absent fathers had a joint custody agreement. In this theoretical development we ignore cases of joint custody and assume that the CP makes all the expenditures on children and the NCP contributes to the children's well-being only through the child support transfers to the CP's household. In general, child expenditures made directly by the NCP would not alter the model unless they exceed the amount the total amount that the CP would spend on the child after the child support transfer.

(8.) The solutions to this repeated one-shot game are the same in all periods. For convenience we drop the time notation in the subsequent presentation.

(9.) To simplify the exposition, we assume [[micro].sub.w] is a constant, and [X.sub.c] = [[micro].sub.w] ([Y.sub.w] + S). The assumption that the expansion path is nonlinear ([[micro].sub.w] = [Florin][[Y.sub.w]+ S]) + would complicate the notation but would not change any of the substantive results. Hoffman (1989) develops a similar presentation of the principal agent model.

(10.) Although [[micro].sub.w] may change over time, such a change will not alter [S.sup.min] because the NCP cannot observe its value in the case of asymmetric information after divorce.

(11.) The general framework outlined is sometimes referred to as the Folk theorem (Kreps, 1990). Technically, the game must have an infinite horizon (or, equivalently, an uncertain endpoint), or it will unravel back to the self-enforcing asymmetric information outcome. Although our time horizon is not infinite, for most divorces it extends very far into the future, especially for cases involving younger children. Therefore, at the beginning of the game, it is reasonable to expect that cooperation is possible for some time periods, if there is some possibility that one player will adopt a strategy to punish the other. See Kreps et al. (1982) for a derivation of the maximum number of noncooperative time periods in a finitely repeated prison s dilemma. This proof assumes that there is some probability that one's opponent is a tit-for-tat player.

(12.) See Manser and Brown (1980) and McElroy and Homey (1981) for some of the earliest applications of this type of bargaining model to family decision making.

(13.) The degree of trust or animosity between the parents is another factor that could affect whether or not they are able to achieve a cooperative Pareto optimal settlement.

(14.) For example, in 1996, only 27.9% of all nonwelfare cases that were reported to the Child Support Enforcement offices resulted in a child support collection (Office of Child Support Enforcement, 1997).

(15.) We model [rho] as a constant, that is, unaffected by the compliance behavior of the NCP. It is also possible that [rho] is an increasing function of the delinquent amount (e.g., states put more effort into collecting large delinquencies). We do not incorporate this possibility into our model.

(16.) Note that the specification of [X.sub.c] in both states illustrates that the CP will spend only the fraction, [[micro].sub.w], of any transfer on the child. This behavior mirrors the asymmetric case, because if the court imposed [S.sup.g], then by definition, the parents have failed to reach a cooperative settlement.

(17.) Under an assumption of perfect capital markets, an NCP can undermine the effectiveness of child support guidelines by reducing voluntary payments when not forced to pay the full amount so that the expected total transfers are closer to the NCP's optimum.

(18). It has been suggested that voluntary payments could be increased by implementing a system of penalties for noncompliance similar to that used by the Internal Revenue Service (Hoffman, 1992). Imposing a penalty provides an incentive for the NCP to increase payment even if he is not caught. By 1986 all states had criminal penalties, such as jail time, for nonpayment of child support, but NCPs are rarely thrown in jail because caseworkers realize that incarcerated fathers are not earning money to pay child support. In theory, monthly voluntary payments are an increasing functions of the severity of the penalty, but because of infrequent use we ignore penalties in our model.

(19.) Data from the Office of Child Support Enforcement (1997) shows that in 1996, 52% of current support obligations but only 8% of arrearages were collected by state IV-D agencies.

(20.) It might seem that the guideline would serve as a threat point from which cooperative agreements may be negotiated; however, a threat point may not be an "expected" value but rather must be fully externally enforced or self-enforcing, like in the case of the voluntary noncooperative solution.

(21.) Under risk neutrality and if p > 0, the inequality in (13) would be met whenever [S.sup.min] [greater than or equal to] [S.sup.g].

(22.) See Argys et al. (2001) for a more detailed description of this sample.

(23.) Other data sets with information on the nature of the child support award cannot be used to assess the effects of child support policies because they do not indicate the state of residence at the time of the award.

(24.) In national data from the Child Support and Alimony supplement to the Current Population Survey, women were asked to characterize their divorce settlement as either voluntary or court-ordered. In those data, about two-thirds of women report that the divorce settlement was court-ordered. In the NLSY data it is likely that some of the women who reported using lawyers would have chosen the category court-ordered under the Current Population Survey classification scheme.

(25.) We also estimated a multinomial logit model (not shown here, but available from the authors on request), in which the dependent variable includes the three categories separately. The effect of all independent variables on the probabilities of voluntary settlement and using lawyers are so similar that we combine these two categories in the results reported here.

(26.) In addition, we examined the impact of various child support enforcement tools. We created a variable counting the number of enforcement tools states have available, such as use of mandatory wage withholding, immediate wage withholding, liens against property, and criminal penalties in cases of noncompliance. A similar variable indicating the total number of enforcement tools is used by Freeman and Waldfogel (1998) in their analysis of child support receipt among never married mothers. This variable is never significant in our analyses and is not included in reported regressions.

(27.) Noticeably higher than its report in all other years, in 1981 Arizona reported expenditures in excess of $650 per case. No one in our data set settled their child support award in Arizona that year, so this extreme value is not included in our analysis.

(28.) Before the widespread use of guidelines, the state still played a role in providing a default settlement when parents could not agree to any alternative. However, the expected default settlement had a large variance and was highly dependent on which judge presided over the divorce case (White and Stone, 1976).

(29.) This representative family has two children, the father earns $20,000 per year, and the mother earns $10,000. In 1991 monthly guideline amounts for this family varied from a low of $321 in Utah to a high of $560 per month in Connecticut.

(30.) Documentation of state-by-state variation in the presence of child support guidelines and default level during this time period can be found in Argys et al. (2001).

(31.) The positive relationship between state enforcement efforts and the probability of court-ordered awards or guideline use could also be the result of endogeneity. That is, states with many court-ordered awards must spend more on enforcement. We estimated the models in Table 2 using one-year lags of the two enforcement variables and find the same results. State fixed effects models produce similar but slightly less significant enforcement effects.

(32.) The puzzling effects of father's education on court-ordered awards and guideline use appear to result from the fact that fathers who use lawyers to settle their child-support cases (and by our definition do not have court-ordered awards) are typically better educated and more likely to use guidelines. We reestimated the two models in Table 2 excluding those who use lawyers from our sample, and the significant positive relationship between father's education and guideline use disappears.

(33.) There are two possible explanations for a positive relationship between father--child contact and voluntary awards. First, as noted in our theory, it may allow verification of expenditures and facilitate cooperative agreements and increased child support payments. On the other hand, it may simply capture unobservable characteristics of fathers that lead to improved child support outcomes. In our empirical work, the effects of contact must be interpreted with caution. We reestimated both equations without the father-child contact variables and the other coefficients were unaffected.

(34.) The data also allow us to measure the frequency of father--child contact. However, there are no significant differences between the coefficients on separate measures of frequent and infrequent contact.

(35.) Because this ratio takes values between zero and one inclusive, we estimate this model using a two-limit Tobit. See Maddala (1983) for details.

(36.) Later child support enforcement efforts would also be expected to alter child support payments and compliance, but our sample size is insufficient to allow us to disentangle the effects of policies both at the time of the award and payment.

REFERENCES

Argys, L. M., and H. E. Peters. "Can Adequate Child Support Be Legislated? A Theoretical Model of Responses to Child Support Guidelines and Enforcement Efforts." Unpublished manuscript, University of Colorado, Denver, 1996.

-----. "Interactions between Unmarried Fathers and Their Children: The Role of Paternity Establishment and Child-Support Policies." American Economic Review, 91(2), 2001, 125-29.

Argys, L. M., H. E. Peters, and D. Waldman. "Can the Family Support Act Put Some Life Back into Dead Beat Dads? An Analysis of Child Support Guidelines, Award Rates and Levels." Journal of Human Resources, 36(2), 2001, 226-52.

Beller, A. H., and J. W. Graham. "The Effect of Child Support Enforcement on Child Support Payments." Population Research and Policy Review, 10(2), 1991, 91-116.

Beron, K. J. "Applying the Economic Model of Crime to Child Support Enforcement: A Theoretical and Empirical Analysis." Review of Economics and Statistics, 70(3), 1988, 382-90.

Chambers, D. L. Making Fathers Pay: The Enforcement of Child Support. Chicago: University of Chicago Press, 1979.

Current Population Reports. "Child Support and Alimony: 1978." Series P-23, no. 112, U.S. Department of Commerce, Bureau of the Census, September 1981.

-----. "Child Support and Alimony: 1985." Series P-23, no. 152, U.S. Department of Commerce, Bureau of the Census, August 1987.

-----. "Child Support and Alimony: 1989." Series P-60, no. 173, U.S. Department of Commerce, Bureau of the Census, September 1991.

Del Boca, D., and C. J. Flinn. "Rationalizing ChildSupport Decisions." American Economic Review, 85(5), 1995, 1241-62.

Freeman, R. M., and J. Waldfogel. "Does Child Support Enforcement Policy Affect Male Labor Supply?," in Fathers under Fire: The Revolution in Child Support Enforcement, edited by I. Garfinkel, S. McLanahan, D. Meyer, and J. Seltzer. New York: Russell Sage, 1998, chap. 5.

Furstenberg F. R. Jr., C. Winquist Nord, J. L. Peterson, and N. Zill. "The Life Course of Children of Divorce: Marital Disruption and Parental Conflict." American Sociological Review, 48, 1983, 656-68.

Garfinkel, I., and P. K. Robins. "The Relationship between Child Support Enforcement Tools and Child Support Outcomes," in Child Support and Child Well-Being, edited by I. Garfinkel, S. S. McLanahan, and Philip K. Robins. Washington, DC: Urban Institute Press, 1994.

Hoffman, R. C. "Crack Down on Deadbeat Dads." New York Times, 5 December 1992, p. 15.

Hoffman, S. D. "Failing to Pay Child Support: Altruism, Antagonism, and AFDC." Unpublished manuscript, October 1989.

Kreps, D. M. A Course in Microeconomic Theory. Princeton, NJ: Princeton University Press, 1990.

Kreps, D. M., P. Milgrom, J. Roberts, and R. Wilson, "Rational Cooperation in the Finitely Repeated Prisoner's Dilemma." Journal of Economic Theory, 27, 1982, 245-52.

Maccoby, E. E., and R. H. Mnookin. Dividing the Child: Social and Legal Dilemmas of Custody. Cambridge, MA: Harvard University Press, 1992.

Maddala, G. S. Limited Dependent and Qualitative Variables in Econometrics. Cambridge: Cambridge University Press, 1983.

Manser, M., and M. Brown. "Marriage and Household Decision Making: A Bargaining Analysis." International Economic Review, 21(1), 1980, 31-44.

McElroy, M. B., and M. J. Homey. "Nash-Bargained Household Decisions: Toward a Generalization of the Theory of Demand." International Economic Review, 22, 1981, 333-47.

McFadden, D. "Conditional Logit Analysis of Qualitative Choice Behavior," in Frontiers in Econometrics, edited by P. Zaremba. New York: Academic, 1973.

Mnookin, R. H., and L. Kornhauser. "Bargaining in the Shadow of the Law: The Case of Divorce." Yale Law Journal, 88(5), 1979, 950-77.

Nash, J. "The Bargaining Problem." Econometrica, 18(2), 1950, 155-62.

Office of Child Support Enforcement. Child Support Enforcement: Twenty-first Annual Report to Congress. U.S. Department of Health and Human Services, Administration for Children and Families, 1997.

Peters, H. E. "Child Custody and Monetary Transfers in Divorce Negotiation." Presented at the annual meeting of the Econometrics Society, New Orleans, LA, 1992.

-----. "The Importance of Financial Considerations in Divorce Decisions." Economic Inquiry, 31, 1993, 71-86.

Samuelson, P. A. "The Pure Theory of Public Expenditure." Review of Economics and Statistics, 36, 1954, 386-89.

Sonenstein, F. L., and C. A. Calhoun. "Determinants of Child Support: A Pilot Survey of Absent Parents." Contemporary Policy Issues, 8(1), 1990, 75-94.

Weiss, Y., and R. J. Willis. "Children as Collective Goods in Divorce Settlements." Journal of Labor Economics, 3(3), 1985, 268-92.

White, D. R., and R. T. Stone. "A Study of Alimony and Child Support Rulings with Some Recommendations." Family Law Quarterly, 10(1), 1954, 75-91.

Zeldes, S. P. "Consumption and Liquidity Constraints: An Empirical Investigation." Journal of Political Economy, 79(2), 1989, 305-46.

RELATED ARTICLE: ABBREVIATIONS

CP: Custodial Parent

NCP: Noncustodial Parent

NLSY: National Longitudinal Survey of Youth

LAURA M. ARGYS and H. ELIZABETH PETERS *

* This research was supported by NICHD grant #HD26555. We are grateful for comments from Mark Cronshaw, Ramana Polavarapu, Paul Schultz, William Schulze, and Robert Willis.

Argys: Associate Professor, Department of Economics, University of Colorado at Denver, Denver, CO 80217-3364. Phone 1-303-556-3949, Fax 1-303-556-3547, E-mail laura.argys@cudenver.edu

Peters: Professor, Department of Policy Analysis and Management, Cornell University, Ithaca, NY 148534401. Phone 1-607-255-2595, Fax 1-607-255-0799, E-mail ep22@cornell.edu