Child-custody reform, marital investment in children, and the labor supply of married mothers

Labour Economics 18 (2011) 14–24

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Labour Economics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / l a b e c o

Child-custody reform, marital investment in children, and the labor supply of married mothers John M. Nunley a,1, Richard Alan Seals Jr. a b

b,

⁎

Department of Economics, University of Wisconsin, La Crosse, La Crosse, WI 54601, United States Department of Economics, Auburn University, AL 36849-5049, United States

a r t i c l e

i n f o

Article history: Received 24 May 2009 Received in revised form 26 July 2010 Accepted 11 August 2010 Available online 31 August 2010 JEL classification: D13 J22 K36

a b s t r a c t Research on child custody primarily focuses on the well-being of children following divorce. We extend this literature by examining how the prospect of joint child custody affects within-marriage investment in children through changes in household bargaining power. Variation in the timing of joint-custody reforms across states provides a natural-experiment framework with which to examine within-marriage investment in children. The probability of children's private school attendance declines by 12% in states that adopt jointcustody laws. We also find evidence linking joint-custody reform to higher rates of labor force participation for married mothers, which may indicate less time devoted household production. © 2010 Elsevier B.V. All rights reserved.

Keywords: Child custody Child investment Intrahousehold resource allocation Private school Labor supply Household bargaining

1. Introduction During the first half of the 20th century, courts in the U.S. typically favored mothers in child-custody cases (Brinig and Buckley, 1998; Jacob, 1988, Ch. 8). In the 1960s, states began to remove the explicit preference for mothers so that a parent's gender was no longer the basis for child-custody awards. Even after the move away from maternal preference, most courts continued to award sole custody to mothers (Cancian and Meyer, 1998). However, several states made explicit provisions in their laws favoring joint custody or revealed their preference indirectly by ruling in favor of joint custody during the 1970s and 1980s (Brinig and Buckley, 1998). Citing the best interests of children as the impetus for legislative change, the majority of states followed with legal provisions for joint custody by the mid1980s (Brinig and Buckley, 1998; Cancian and Meyer, 1998). Although child-custody reform became a nation-wide phenomenon, the debate over joint custody's costs and benefits was carried out by a relatively

⁎ Corresponding author. Tel.: +1 615 943 3911. E-mail addresses: [email protected] (J.M. Nunley), [email protected] (R.A. Seals). 1 Tel.: +1 608 785 5145. 0927-5371/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.labeco.2010.08.002

small group of politically active supporters with little empirical evidence to support their claims (Jacob, 1988, Ch. 8). The joint-custody literature primarily focuses on the well-being of children following divorce. We extend this literature by investigating whether joint-custody laws affect within-marriage investment in children. We first use variation in the timing of joint-custody reforms across states, with data from the 1980 and 1990 U.S. Population Censuses, to identify the effect of child-custody laws on married couples' investment in their children's education. Married couples with children who live in states that change their laws to favor joint custody between 1980 and 1990 constitute the treatment group in a natural experiment, while those who live in states that had either instituted joint-custody reform before 1980 or that did not institute joint-custody reform before 1990 represent the comparison group. The dependent variable is children's private school attendance—a verifiable marriage-specific investment in child quality. Although most children in the U.S. attend public school and private school represents only one of the many investments parents can make in child quality, private school has attractive features as a proxy for overall parental investment. Because the financial costs of private school warrant long-run planning by parents, any observed differences in private school attendance resulting from joint-custody reform could be extrapolated to other monetary investments in children.

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Analyzing the effects of child-custody reform on marital investment in children provides an opportunity to study the bargaining behavior of spouses. If we assume the return on child investment is non-rival within marriage but rival outside of marriage, a change in custody regime transfers a portion of the expected return from one parent to the other by altering the time spent with children outside of marriage. The neutrality of an individual family member's non-earned investment returns, with respect to intrahousehold allocation of resources, is a key aspect of the neoclassical model of the family (Becker, 1991). Hence, a unitary model of household behavior predicts no change in child investment following joint-custody reform. However, if child-custody reform alters the distribution of the marital surplus after divorce occurs, cooperative bargaining models of family behavior predict changes in married couples' investment in children. There is ample empirical evidence that changes in family laws and government programs that provide transfers to one spouse shape the bargaining process over the course of marriage (e.g., Attanasio and Lechene, 2002; Chiappori et al., 2002; Genadek et al., 2007; Gitter and Barham, 2008; Gray, 1998; Lundberg et al., 1997; Stevenson, 2007, 2008; Ward-Batts, 2008). States that change the default custodial allocation from maternal preference to shared custody decrease (increase) the expected post-divorce time mothers (fathers) spend with their children. Brinig and Allen (2000) find that women are more likely to file for divorce based on the expectation of sole child custody, an indication that joint-custody reform could raise the costs of divorce for mothers. As a result, joint-custody reform could place mothers in an inferior bargaining position within marriage. The empirical literature on intrahousehold resource allocation documents a higher rate of investment in or spending on children when mothers have greater bargaining power in the household (Attanasio and Lechene, 2002; Bobonis, 2009; Lundberg et al., 1997; Maitra, 2004; Thomas, 1990; Ward-Batts, 2008). If the reform shifts bargaining power away from mothers, who value child quality more on average, child investment may decline. By contrast, the reform could provide additional incentive for fathers to invest in children because they stand to reap a greater portion of the post-divorce benefits from child investment through increased visitation rights. We study the labor supply of married mothers as an alternative household bargaining variable in order to gain a better overall picture joint-custody reform's impact on the allocation of family resources. We use a similar differences-in-differences strategy, as described above, with annual data from the March Current Population Survey (CPS) for the years 1978–1993, to estimate the effect of joint-custody reform on a married mother's decision to participate in market work. Previous research shows a negative relationship between child outcomes and maternal employment (e.g., see Baum, 2003; Ruhm, 2004; Waldfogel et al., 2002). As a result, maternal labor supply could also proxy for non-monetary investment in children. Furthermore, non-monetary investments in children may complement (or substitute for) monetary investments, such that we might expect a positive (negative) co-movement between the two types of investment in response to custody reform. While joint-custody laws were enacted to improve the well-being of children whose parents divorce, we find negative, unintended consequences for children of intact households. The probability of children's private school attendance declines by approximately 12% in states that adopt joint-custody laws. In addition, we find evidence linking jointcustody reform to increases in the labor force participation of married mothers, with much larger increases for married mothers with younger children. The paper proceeds as follows: Section 2 discusses the legal background and economic models of child investment and household bargaining; Section 3 describes the data and econometric methodology; Section 4 presents the results; Section 5 relates our findings to the existing literature; and Section 6 provides concluding remarks.

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2. Theoretical framework 2.1. Legal background The authority of family-court judges to exercise wider discretion and institute joint-custody arrangements is a relatively recent legal innovation. Although child welfare was cited as the primary basis for child-custody reform, the passage of joint custody went against the widely held view among psychologists that sole custody was optimal (Goldstein et al., 1984). However, challenges to the sole-custody standard were issued at this time on the basis that it was an impulsion for post-marital conflict and, therefore, contrary to the best interests of the child (Stack, 1976). As a result, when most states began enacting joint-custody legislation, there was no consensus on the optimal custodial arrangement (Jacob, 1988, Ch. 8). There were many underlying causes of child-custody reform. Women's increasing labor force participation and the more prominent role of men in child rearing were both key demographic changes that helped facilitate joint-custody reform (Jacob, 1988, Ch. 8). The preponderance of “dead-beat” parents (primarily fathers), who were in arrears of child-support payments, also generated political incentives to alter childcustody laws (Jacob, 1988, Ch. 8).2 Contrary to other family-law reforms, expert opinion was relatively absent and personal experiences were more often cited in the legislative discourse on joint custody (Jacob, 1988, Ch. 8). Because it was difficult to show the negative consequences for children and the potential gains came at a low cost to the public, joint-custody reform was discussed by a small group of proponents and passed legislatures in relative obscurity (Jacob, 1988, Ch. 8). A joint-custody provision relegates courts to handle only those custody disputes which cannot be settled privately (Buehler and Gerard, 1995). In the event that child custody must be decided in court, judges have discretion to rule in favor of joint custody if it conforms to the best interests of the child.3 Depending on familyspecific circumstances, joint custody can fall under a protocol of (i) joint legal custody in which parents share in the decisions of child upbringing but the child's primary residence is with one of the parents or (ii) joint physical custody in which both parents share in childrearing decisions and also share physical custody of the child. Under either joint-custody settlement, courts expect divorced parents to maintain a cooperative relationship while raising their children.4 2.2. Economic models of household bargaining and child investment An extensive theoretical literature in economics investigates intrahousehold investment, production and distribution of resources.5 To motivate a discussion of this literature, we broadly group it into two categories: (i) the common preference approach which models the household as a single decision-making unit (e.g., Becker, 1991) and (ii) divorce-threat models in which heterogeneous agents bargain over the marital surplus and utility in the divorced state represents an external 2 Since welfare payments were a federal issue, this political activity included a U.S. Congress mandate that funds would be withheld from paychecks and federal tax returns to pay delinquent child support (Jacob, 1988, pp. 132). By simply granting greater custodial rights, joint custody could also have been a low-cost (for the state) incentive for noncustodial parents to pay child support. In fact, Brinig and Buckley (1998) and Allen et al. (2010) find a positive effect of joint-custody reform on the level and receipt of child support income, respectively. 3 See Buehler and Gerard (1995) for a discussion of the Best Interests of the Child (BIOC) standard and how the standard varies by state. 4 The child-custody-law coding provided by Brinig and Buckley (1998) does not distinguish between joint-legal and joint-physical custody. While we are unable to examine the implications joint-legal and joint-physical custody separately, Kelly (1994) reports that the prevalence of joint-legal and joint-physical custody arrangements occurred concomitant with the passage of joint-custody laws across states. As a result, the child-custody reforms that we examine capture the overall shift to both types of joint-custody arrangements. 5 See Bergstrom (1996, 1997) and Lundberg and Pollak (1996) for excellent surveys of theoretical research on the economics of the family.

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threat point (e.g., Manser and Brown, 1980; McElroy and Horney, 1981).6 Common-preference models predict that changes in the laws governing child custody would have no effect on investment outcomes regardless of which spouse benefits. By contrast, divorce-threat models predict that child-custody reform alters the value of each spouse's options outside of marriage, which could have consequences for withinmarriage investment in children. Because the common-preference model predicts no change in marital investment in children resulting from joint-custody reform, we make some predictions in the context of cooperative bargaining models in the following paragraph. Assume the return on child investment is non-rival within marriage but rival outside of marriage. It follows that changes to laws which govern the allocation of child custody could alter the expected value of divorce by altering divorce costs for mothers and fathers. Joint-custody reform may lower divorce costs for fathers because they expect to lose less of the return from child investment when shared child custody is expected. By contrast, joint-custody reform may increase divorce costs for mothers because they expect to receive less of a return on child investment. Brinig and Allen (2000) find a significant increase (decrease) in the propensity of women to file for divorce when they (do not) expect to receive sole child custody. Their results suggest that the expectation of child custody is the most important factor in mother's decision to file for divorce. In the context of a Nash-bargained outcome, these findings suggest joint-custody reform should unambiguously shift bargaining power to fathers, as the value of divorce decreases for mothers. Hence, post-reform marital investment in children may reflect the preferences of fathers to a greater extent. Cooperative bargaining models fail to take into account some important dynamic features of investment in children. For many families, sending their children to private school is the product of long-term financial planning, which may be independent of changes in custodial rights. Although divorce would increase the financial burden of private school because living expenses increase relative to those in the married household, altruistic parents may still choose to continue private school for their children.7 Furthermore, because of the inherent uncertainty of investing in children over time (e.g., divorce or an uncooperative child), the exact relationship between custody reform and child investment may not be characteristic of Nash-bargaining models which do not integrate risk. While a unitary framework could incorporate the dynamics and uncertainty associated with investment in children (e.g., Becker and Tomes, 1976, 1979, 1986), there remains an implicit assumption that transaction costs are negligible and marital contracts can be fully specified with respect to child investment. Rasul (2006) develops a model of within-family bargaining in which child quality is a public good.8 In Rasul's framework, parents are 6 The collective approach to household behavior pioneered by Chiappori (1992) assumes a Pareto-efficient outcome and incorporates aspects of both the Nash-bargaining and unitary frameworks. The collective model emphasizes the bargaining strength of spouses as a key determinant of household behavior. Child-custody reform, which acts as a “distribution factor” in the collective framework (Browning and Chiappori, 1998; Chiappori et al., 2002), alters the balance of power between spouses by generating opposing income effects, an indication that the household's allocation of resources may reflect to a greater extent the preferences of the spouse with the improved bargaining position. By contrast, Lundberg and Pollak (1993) contend that a within-marriage outcome is more reasonable since the costs associated with divorce are often high. They assume the existence of traditional gender roles that determine internal threat points (e.g., sleeping on the couch, burnt toast, or “silent treatment”) in a Nash-bargaining framework, which have distributional and efficiency consequences. In their separate-spheres model, there is no outside option (i.e. divorce), and they make no assumptions regarding the efficiency of the equilibrium outcome. Since their model has no external threat point, joint-custody reform should have no impact on intrahousehold distribution. 7 Efficient marriage markets could reinforce such persistence in child investment by “assigning” altruistic individuals to “beneficiaries” (Becker, 1991, Ch. 8). 8 Weiss and Willis (1985, 1993) also examine the allocation of child custody in the event of divorce; however, they only consider sole custody as a post-divorce allocation of children. Francesconi and Muthoo (2003) consider joint custody as an option and examine marital investment in children. Their paper differs from Rasul's in several ways. For example, they consider cases in which the allocation of sole child custody to the low-valuation parent is optimal, and divorce cannot occur in their model.

unable to make verifiable (to a third party) child-specific investments, which preclude marriage contracts specifying the amount of investment to be undertaken by each spouse. Instead, married couples contract an ex post allocation of child custody should divorce occur, which affects ex ante incentives to invest. Investment decisions are not only made in the shadow of divorce but also partially determine the outcome of divorce, as the divorce probability is a function of child investment. The inclusion of transaction costs—the inability of couples to specify contractually their contributions to child quality within marriage—provides an element of uncertainty not found in the previously mentioned literature, which generates specific predictions of parental behavior when the post-divorce custodial allocation is variable. Below we formulate some hypotheses concerning jointcustody reform in the context of Rasul's framework. If spouses have homogenous preferences for child quality, joint custody is the optimal post-divorce custody allocation because it maximizes investment in the public good during marriage. However, if spouses have heterogeneous preferences for child quality, sole custody with the high-valuation spouse is the optimal child-custody allocation. If both spouses have an equally high valuation of child quality, we may observe a rise in the probability that a child attends private school when a state adopts joint custody. Alternatively, if one spouse values child quality more on average, we may either observe a positive or negative impact of joint-custody laws on marital investment in child quality. If bargaining power shifts to the highvaluation spouse, the rate at which parents invest in private school for their children could increase. However, if the reform shifts bargaining power to the low-valuation spouse, the probability of children's private school attendance may decline. The empirical literature on intrahousehold bargaining documents an increase in spending on and investment in children when women (primarily mothers) have greater control over household expenditures (Attanasio and Lechene, 2002; Bobonis, 2009; Duflo, 2003; Lundberg et al., 1997; Maitra, 2004; Schultz, 1990; Thomas, 1990; Ward-Batts, 2008). If joint-custody reform shifts bargaining power to fathers, who are, on average, the low-valuation spouse, Rasul's (2006) model predicts an unambiguous decline in marital investment in children.9

2.3. Household bargaining and labor supply According to Becker (1991, Ch. 2), the sexual division of labor in the household is a result of differential investment in task-specific human capital—time spent in market work and/or home production. Becker's framework emphasizes the marriage market as a mechanism to match individuals in such a way that the gains from marriage are maximized through specialization. The process through which decision rules for labor supply are derived is assumed independent of individual bargaining power acquired before or during marriage. Schultz (1990) argues this crucial assumption of the neoclassical model of household labor supply offers a testable hypothesis: the neutrality of individual household member's non-earned income with respect to the intrahousehold allocation of resources. A number of studies investigate the effects of the adoption of unilateral divorce laws on the labor supply of women, which provides a test of the predictions made by unitary models of household behavior and to determine whether the predictions of household bargaining models fit observed behavior. Gray (1998) argues that changes in bargaining power can be identified by allowing the impact of unilateral divorce on married women's labor supply to vary with 9 Blundell et al. (2005) argue that changes in household investment in children resulting from an increase (decrease) in individual resources may not be the result of differences between fathers' and mothers' willingness to pay but rather the responsiveness of mothers' and fathers' willingness to pay to changes in private consumption.

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the underlying property division laws in states. He interprets a positive response in married women's labor supply to passage of unilateral divorce in states with property division laws that favor wives as evidence of a bargaining power shift away from husbands. However, Stevenson (2008) contests Gray's (1998) interpretation by arguing that bargaining power unambiguously shifts to the spouse who places the highest valuation on exiting the marriage. Stevenson (2008) also shows that Gray's (1998) results are sensitive to alternative model specifications, finding that the labor supply of women increases in response to unilateral divorce irrespective of the underlying property division laws. Stevenson (2008) argues that women have incentive to maintain their options outside of marriage when either spouse can dissolve the marital contract. In the context of the collective model, Chiappori et al. (2002) find that women work less when divorce laws benefit them, an indication that bargaining power and labor supply are inversely related. Oreffice (2007) uses a collective model to argue that abortion legalization in the United States shifted bargaining power to married women of childbearing age. She exploits the early adoption of abortion laws as a natural experiment and finds a decrease in wives' labor supply, which is consistent with the predications made by the collective model. The most obvious way custody reform affects maternal labor force participation is through the divorce propensity.10 However, the effect of joint-custody reform on divorce could be ambiguous. For example, mothers may be less likely to file for divorce because they expect to see less of their children—a negative effect on divorce. At the same time, mothers may invest less in their children (i.e. marriage capital) due to a lower expected return because of joint custody—a positive effect on divorce.11 Despite the ambiguous prediction, custody reform can affect the allocation of resources through the intrahousehold balance of power, regardless of whether the reform leads to divorce (Chiappori et al., 2002). Within a bargaining structure, married mothers have an incentive to preserve their options outside of marriage by accumulating labor market skills, as their threat of divorce may not be as credible when shared child custody is expected. It could also be that joint-custody reform causes fathers to increase time in home production as they anticipate a greater role in child rearing following divorce, thereby decreasing both the returns to specialization and/or the mother's bargaining position in the home. Although the process through which mothers lose bargaining power is not clearly defined, based upon our arguments of a bargaining power shift away from mothers in Section 2.2 and previous empirical findings (e.g., Oreffice, 2007), we expect maternal labor supply to increase following joint-custody reform.

3. Data and econometric methodology 3.1. Marital investment in children's education We use data from the 1980 and 1990 five-percent Integrated Public Use Microdata Series (IPUMS) from the U.S. Population Censuses and the child-custody-law coding from Brinig and Buckley (1998) (Table 1) to examine whether the prospect of joint custody affects withinmarriage investment in children's education. The units of observation are children whose biological parents are married at the survey date. We exclude children from blended families because child investment decisions would likely be made by biological parents, one of whom is absent. In addition, examining children whose biological parents are intact allows us to examine how child-custody reform affects the allocation of resources within marriage. 10 Johnson and Skinner (1986) and Sen (2000) find that women increase their labor supply in response to a higher risk of divorce. 11 Halla (in press) uses state-level panel data and finds that joint-custody reform has a positive effect on marriage rates but no effect on divorce rates, which he attributes to countervailing forces.

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Table 1 Year of introduction of joint-custody laws by state. State Alabama Alaska Arizona Arkansas California Colorado Connecticut Delaware Florida Georgia Hawaii Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri

Joint custody 1982 1991 1979 1983 1981 1981 1979 1990 1980 1982 1986 1973 1977 1979 1979 1981 1981 1984 1983 1981 1981 1983 1983

State

Joint custody

Montana Nebraska Nevada New Hampshire New Jersey New Mexico New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming

1981 1983 1981 1974 1981 1982 1981 1979 1993 1981 1990 1987 1981 1992 1989 1986 1987 1988 1992 1987

1979 1993

Notes: The timing of the child-custody reforms are from Brinig and Buckley (1998).

We only include children who are four- to eight-years-old in our analysis, as decisions regarding young children's schooling are likely made by parents. The sample is also restricted by the categorical nature of the education variable provided by the IPUMS, as the survey collapses children who are in kindergarten and those who are not enrolled in school in the same category. As such, we are unable to examine children in grades lower than first. The median marriage duration in which divorce occurs is approximately eight years (U.S. Census Bureau, 2004).12 This is important because spouses who are considering divorce, i.e. those in marginal marriages, are more likely to be aware of how states allocate children in the event of divorce. Although we are unable to determine how long the couples in our sample have been married, the ages of children aid in approximating length of marriage. Because we consider children who are four- to eight-years-old who reside in intact households with both parents present, the sample likely contains children with parents whose marital durations vary widely. For example, consider the oldest children in our sample: those who are eight-years-old at the survey date. Assuming the couple had the child in their first year of marriage, their marriage duration is eight years at the survey date. However, married couples could postpone having children for a few years. This implies marital durations in excess of eight years. As such, the sample likely contains a sufficient number of at-risk marriages—those who would be aware of how the state in which they live allocates child custody in the event of divorce. We use children's private school attendance as a measure of child investment for a number of reasons.13 First, private school enrollment is a verifiable investment in child quality, as the tuition rates for private schools are often substantial.14 Second, children who attend private 12 See http://www.census.gov/population/www/socdemo/marr-div/2004detailed_tables.html. 13 The private school attendance rates across states are presented in Table A1. 14 For the 2008–2009 academic year, the National Association of Independent Schools (NAIS) report that median tuition for member private schools is $17,441, and the tuition rate is substantially higher for private boarding schools. The tuition rates of private schools that are not members of the NAIS are lower, with an average tuition rate of $10,841. Parochial schools are less expensive, with a median tuition rate of $2607. Unfortunately, we are unable to differentiate between the various types of private schools in our analysis. The tuition statistics for the various types of private schools referenced above are from http://www.greatschools.org.

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schools tend to fare better across a number of educational outcomes. For example, minors who attend private schools are less likely to repeat grades (Angrist et al., 2002), more likely to graduate high school (Evans and Schwab, 1995), and more likely to attend college (Altonji et al., 2005). Third, private schools, on average, have smaller class sizes than public schools (National Center for Education Statistics, 2001), and children enrolled in smaller classes have been shown to perform better across a number of educational outcomes than children enrolled in larger classes (Krueger, 1999; Krueger and Whitmore, 2001). For the above reasons, children's private school attendance is commonly used in the literature as a proxy for investment in child quality (Caceres-Delpiano, 2006; Conley and Glauber, 2006). Variation in the timing of joint-custody reforms across states provides a natural-experiment framework with which to examine how the prospect of joint custody affects within-marriage investment in children. Married couples with children who live in states that change their child-custody laws to favor joint custody between 1980 and 1990 are the treatment group, while those who live in states that had either instituted joint-custody reform before 1980 or that did not adopt joint-custody laws by 1990 are the comparison group.15 Approximately 13% of children in our sample attend private school, regardless of the custodial regime in place.16 To justify the difference-in-difference estimator used in our analysis, it is important to establish whether pre-existing differences between treatment and comparison groups are likely to introduce potential confounds to the analysis. First, we examine whether children's private school attendance rates follow similar trends in treatment and comparison states in the years prior to the reforms and whether they return to similar trends following the reforms. Fig. 1 indicates that the private school attendance rates of treatment and comparison states follow similar trends prior to and after the widespread adoption of joint-custody laws. Children's private school attendance rates in treatment and comparison states fall from 1960 to 1970, rise from 1970 to 1980, and follow similar upward trends from 1990 to 2000. However, during the period in which the vast majority of states adopted joint-custody laws, i.e. the 1980s, the trends in children's private school attendance rates in treatment and comparison states diverge. In particular, the share of children attending private school falls substantially in treatment states over this period, while the share of children attending private school remains stable in the comparison states. We also conduct a chi-square test of independence to determine if the distributions of private school attendance differ between states that will be treated between 1980 and 1990 and states that will not be treated between 1980 and 1990. The results from this test reveal that the distribution of private school attendance in treatment states is not statistically different from the distribution of private school attendance in comparison states.17 In addition, Halla (in press) shows that joint-custody reforms occurred uniformly across states over time, implying that early or late adoption of joint-custody laws did not occur systematically by geography or population size. Historical accounts also suggest that joint-custody reform was largely the result

Share of Children Attending Private School

18

0.22 Treatment

Comparison 0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06

1960

1970

1980

1990

Fig. 1. Private school attendance for treatment and comparison states over time.

of routine policy refinements (Jacob, 1988, Ch. 8), which has been an argument used in the literature for unilateral divorce as a natural experiment (e.g., see Wolfers, 2006). Our analysis of preexisting differences in private school attendance between treatment and comparison groups, the arguments and analysis provided by Halla (in press), and Jacob's (1988) historical account support the validity of joint-custody reform as a useful quasi-experimental setting with which to examine how the prospect of joint custody affect withinmarriage investment in child quality. Data from the 1980 and 1990 U.S. Censuses provide a way to control for child and parent characteristics and time-invariant unobserved heterogeneity at the state level. The primary source of omitted variable bias in which we are concerned occurs at the state level (Angrist and Pischke, 2009), as omitted time-varying, state-level variables correlated with the passage of joint custody and children's private school attendance could bias estimates. For example, child custody could be related to legislative agendas in response to increasing welfare recipients attributable to delinquent child-support payments (Jacob, 1988, Ch. 8). The spread of joint-custody reform could also be related to changing societal preferences for child-rearing responsibilities, as rising female labor force participation rates and fathers' increasing role in childrearing provided fathers' rights groups with a political voice to argue for joint custody (Jacob, 1988, Ch. 8). Reforms to the child-support-enforcement (CSE) program, participation in and the benefit levels of the Aid to Families with Dependent Children (AFDC) program, and the female labor force participation rate could be correlated with the passage of joint-custody reform. These variables could also be correlated with children's private school attendance. Failure to account for these state-level covariates could lead to biased estimates.18 The empirical specification takes the probit functional form. We estimate the following equation: Privatei;s;t = β0 + β1 Joints;t + β2 Ci;s;t + β3 Pi;s;t + β4 Ss;t

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Between 1980 and 1990, 30 states adopted a preference for joint-custody arrangements. Twenty-six percent of children in our sample live in states with joint custody as the preferred custodial allocation in 1980, while the percentage of children who live in states with joint custody as the preferred custodial arrangement in 1990 is 87%. 16 According to the 2000 U.S. Census (Table 247) approximately 2.7 million children (9.2% of the total population of elementary school students) attended private elementary school in 1990. Although our sample suggests a higher percentage of children attending private school, the difference likely comes from our sample consisting of only children whose biological parents are married. 17 We cannot reject the hypothesis that observations on children's private school attendance from treatment and control states are drawn from the same distribution: Pearson chi2(1) = 0.8328 (p-value = 0.361), obs = 390,257.

2000

Census Year

ð1Þ

+ ∑s ηs States + λYeart + εi;s;t The terms i, s, and t index children, states, and time, respectively; Private is an indicator variable that equals one if a child attends private

18 We examine the empirical relationship between the adoption of joint-custody reform and the time-varying state-level covariates. A probit regression, using the adoption of joint-custody laws as the dependent variable, reveals that food stamp outlays, female labor force participation, per-capita income, and the adoption of nofault property division laws are positively related to the passage of joint-custody laws.

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school and equals zero if the child attends public school19; Joint is an indicator variable that equals one if a state explicitly codifies or reveals its preference for joint custody by the 1990 Census year and zero otherwise; C is a vector of child-specific controls; P is a vector of parental controls; S is a vector of time-varying, state-level controls; State and Year are state and time fixed effects, respectively; ε is an error term; and the βi are parameters to be estimated. We are primarily interested in the estimate for β1, which measures the difference in the probability of a child attending private school attendance in joint-custody states relative to sole-custody states. The variables in C are the child's age, a squared term of their age, race, and gender, and the variables in P are parents' ages, races, and education levels. The variables in S include the unemployment rate, real per-capita income, the female labor force participation rate, a measure of the extent to which a state's congressional delegation cast liberal votes, an indicator variable for the political party of the governor, an indicator variable for whether the state considers marital fault in the divorce settlement, the maximum AFDC benefit paid to families of four, the value of food-stamp outlays, the level of Supplemental Security Income (SSI) benefits, an indicator variable for whether the state universally withholds child-support payments from father paychecks, and the percentage of the state population who are Catholic. The inclusion of S allows us to minimize the potential bias from a spurious correlation between joint-custody reform and other state-level influences. Summary statistics and formal variable definitions for the controls in C and P are shown in Table A2, and those in S are shown in Table A3. In order to estimate the full effect of joint-custody reform, we omit covariates that may be affected by child-custody reform. For example, household income could be affected by the adoption of joint-custody laws because the reform could affect the labor supplies of parents via changes in household bargaining power. Because child-custody reform may change investment in children, it could also alter fertility decisions. If child-custody reform affects household income and/or fertility, at least a portion of the effect of the joint-custody laws on children's private school attendance would captured in the estimates for these variables (Lee, 2005).20 Examining a sample of children whose biological parents are married could generate sample-selection bias if joint-custody reform alters the composition of the married population.21 To address potential selection issues generated by child-custody reform, we weight the estimates in our regression models by an inverse estimate of the probability that a child lives in a household in which their biological parents are married. This sample-selection-correction technique is commonly referred to as inverse probability weighting (IPW) (Wooldridge, 2002). In our case, the IPW approach uses the predicted values from a reduced-form logistic regression of the probability that a child lives in a biologically intact household on individual and state-level characteristics. The use of IPW allows us to account for the possibility that joint-custody reform affects the composition of the married population, which could lead to substantial bias if left uncorrected.

19 We are unable to distinguish between various religious or parochial private schools, as the IPUMS survey questions on school type are not consistent across the two decennial periods. 20 We checked the sensitivity of the estimates to controls for household income and family size. These models reveal little difference in the estimated effects of jointcustody reform on children's private school attendance. In fact, the inclusion of these covariates tends to strengthen our findings. 21 Stevenson's (2007) research on the effect of divorce laws on marital investment emphasizes the importance of accounting for the potential selection effects generated by divorce-law reforms. In addition, Halla (in press) finds that marriage rates increase in states that adopt joint-custody laws, while Brinig and Allen (2000) find that mothers file for divorce at a higher rate than men due to the expectation of received sole custody.

19

As an additional robustness check, we examine whether our findings are influenced by the long-run planning of parents. In particular, joint-custody reform's impact on children's private school attendance could be confounded by parents who decide to send (or not to send) their children to private school before the adoption of joint-custody laws. We minimize the potential bias stemming from the long-run planning of parents by eliminating observations from states that enact joint-custody laws after 1983. For this sample, the oldest (eight-years-old) and the younger children (four- to sevenyears-olds) in our sample in 1990 were one-year-old and unborn at the time of the last enactment, respectively.22 These restrictions increase the likelihood that the decisions made by parents regarding investment in private schooling for their children occur after the state had adopts joint-custody laws.

3.2. The labor force participation of married mothers A number of studies examine the consequences of higher rates of labor force participation among mothers on child development. While this literature has produced mixed results, maternal employment in the early years of a child's life has recently been shown to have detrimental effects on child development (Baum, 2003; Ruhm, 2004), and the detrimental effects may have lasting consequences (Waldfogel, Han and Brooks-Gunn 2002). Whether maternal employment affects the outcomes of adolescents is another debate that has produced mixed results. Recently, Ruhm (2008) finds evidence of negative effects of maternal employment on the academic outcomes of adolescents. The primary channels through which maternal employment could affect child development are the quantity and quality of time spent mothers with their children. It is not clear whether time spent working necessarily reduces time spent with children, as working mothers could sacrifice leisure time or reduce time allocated to household production by utilizing labor-saving technologies and purchasing household services in the market. In fact, Bianchi (2000) finds little change in time spent with their children by mothers who participate in the labor market at greater rates. However, Ruhm (2008) contends that the negative effects of maternal employment on the academic outcomes of adolescents, especially those from economically advantaged backgrounds, found in his study are likely the result of reductions in the amount of time spent by mothers enriching the home environment. We use mothers' labor force participation as a proxy for nonmonetary investments in children and as a way to examine whether changes in child-custody laws alter the bargaining behavior of parents. We use Brinig and Buckley's (1998) child-custody law coding and annual data from the March CPS from 1978 to 1993 to examine whether joint-custody reform affects the labor force participation of married mothers.23 The analysis used to examine the difference in the probability of participating in the labor force for married mothers in states that adopt joint-custody laws relative to states that do not adopt joint-custody laws is similar to the one described in Section 3.1. One important difference is that we are able to more fully exploit the variation in the timing of joint-custody reforms across states, as annual data are available over the time period in which the majority of child-custody reforms took place.

22 This restriction results in the elimination of observations from Illinois, Maryland, Oregon, South Dakota, Tennessee, Texas, Utah, and Virginia. 23 During the 1980s when most states were establishing joint custody provisions, the labor supply of married women increased substantially (Blau and Kahn, 2007). This period of time is also coincident with a decrease in the sensitivity of married women's labor supply to both their own wages and the earnings of their husbands, which implies a shift in their labor supply function accounts for much of the increase (Blau and Kahn, 2007).

20

J.M. Nunley, R.A. Seals Jr. / Labour Economics 18 (2011) 14–24

Table 2 The effect of joint-custody reform on marital investment in children's private school education. Variable

Unweighted sample

Joint-custody reform

Controls Year and state fixed effects Time-varying state variables Household characteristics Pseudo R-squared

Weighted sample

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

−0.0008 (0.005)

−0.0107** (0.005)

−0.0149*** (0.006)

0.0002 (0.004)

−0.0089* (0.005)

−0.0141 *** (0.005)

X

X X

X

X X

0.0282

0.0285

X X X 0.0597

0.0280

0.0282

X X X 0.0625

Notes: There are 390,257 observations for each model. Estimates are reported as marginal effects. Standard errors clustered at the state-year level are in parentheses. * and ** indicate statistical significance at the ten- and five-percent levels, respectively.

The empirical specification takes the probit functional form. We estimate the following equation: LFPi;s;t = θ0 + θ1 Joints;t + θ2 Xi;s;t + θ3 Ss;t + ∑s ηs States

ð2Þ

+ ∑t λt Yeart + ∑s s States × time trend + εi;s;t : The terms i, s, and t and the variables Joint, S, State, Year, and ε are defined above. The variable LFP equals one if the mother works and zero otherwise; the vector X includes individual-level controls for age, race, and educational attainment; States × time trend is a state-specific linear time trend; and the θi are parameters to be estimated. The vector S includes the same controls as in Eq. (1), except data on the share of the population who are Catholic are not available on an annual basis. However, the inclusion of state-specific linear time trends should capture the influence of any omitted time-varying state-level variables.24 Similar to Eq. (1), we omit control variables that may be affected by joint-custody reform. We are primarily interested in the parameter θ1, which measures the difference in the probability of participating in the labor force for married mothers in states that adopt joint-custody laws relative to those in states that do not adopt joint-custody laws. Similar to the outcome variable discussed in Section 3.1., we examine whether the trends in the labor force participation rates of married mothers in treatment and comparison states differ prior to the passage of joint-custody laws. Fig. A1 shows that married mothers' labor force participation rates in treatment and comparison states follow similar trends prior to the widespread adoption of jointcustody laws in the 1980s. The annual availability of the data also allow us to hold constant permanent and time-varying differences between treatment and comparison states by including state fixed effects and state-specific linear time trends. Our examination of the preexisting trends between treatment and comparison groups prior to child-custody reform and the annual nature of our data deflect concerns that preexisting differences in labor force participation rates between treatment and comparison groups introduce potential confounds to our analysis. 4. Results 4.1. The effect of joint-custody reform on marital investment in children's education Table 2 presents the estimates from Eq. (1) for the full sample of children from all states. Models 1, 2, and 3 show the estimates for the

24 In addition, adding the share of Catholics as a regressor in Eq. (1) has little impact on the estimated effect of joint-custody reform.

unweighted sample, while Models 4, 5, and 6 show the estimates for the sample weighted by an inverse estimate of the probability that the child lives with their biological parents who are married. For each model, we successively add controls to gauge how sensitive the estimated effect of joint-custody reform is to the inclusion of additional covariates. Model 1 shows the simple difference-in-difference estimator, which includes only state and year fixed effects as control variables; Model 2 adds timevarying state-level controls; and Model 3 adds child and parental controls. Models 4, 5, and 6 repeat the same process of adding controls for the weighted sample. In Model 1, joint-custody reform has a negative effect on the probability of attending private school for children, but it is not statistically different from zero. In Model 2, adding the time-varying state-level controls increases the magnitude of the negative effect of joint-custody reform found in Model 1 substantially. Adding the timevarying state-level controls to the model increases the size of the coefficient (in absolute value) such that it becomes statistically significant at the five-percent level, indicating that the probability of attending private school falls by 8.43% (1.1 percentage points) for children who live in states that adopt joint-custody laws. In Model 3, the negative effect of joint-custody reform becomes larger after child and parental controls are added to the model: the adoption of joint-custody laws reduces the probability of attending private school by 12% (1.5 percentage points) for children who live in states that adopt jointcustody laws. This estimated effect is statistically significant at the onepercent level. The estimates presented for Models 4, 5, and 6 are similar to the results for Models 1, 2, and 3. For example, the estimated effect of joint-custody reform on children's private school attendance rates is not statistically significant when state and year fixed effects are the only additional right-hand-side variables included (Model 4). The addition of time-varying state-level controls increases the magnitude of the estimated negative effect, and it becomes statistically significant at the 10-percent level (Model 5). Once additional child and parent controls are added, the effect of joint-custody reform on children's private school attendance becomes larger (Model 6). The marginally statistically significant estimate shown in Model 5 implies a 7.43% (0.9 percentage points) reduction in the probability that a child attends private school in states that adopt joint-custody laws, while the estimate shown in Model 6 translates into a 12% (1.4 percentage points) reduction in the probability that a child attends private school in states that adopt joint-custody laws. The estimated effect of custody reform in Model 6 is statistically significant at the one-percent level. In Table 3, we check the robustness of the results presented in Table 2 by considering whether the long-run planning of parents introduces potential confounds to our estimates. For these models, we repeat the analysis conducted in Table 2 for a restricted sample, which excludes observations from states that pass joint-custody laws after

J.M. Nunley, R.A. Seals Jr. / Labour Economics 18 (2011) 14–24

21

Table 3 The effect of joint-custody reform on marital investment in children's private school education (robustness check—long-run planning of parents). Variable

Joint-custody reform

Controls Year and state fixed effects Time-varying state variables Household-level variables Pseudo R-squared

Unweighted sample

Weighted sample

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

−0.0018 (0.005)

−0.0141*** (0.005)

−0.0170*** (0.005)

−0.0002 (0.004)

−0.0117*** (0.005)

−0.0157*** (0.004)

X

X X

X

X X

0.0237

0.0242

X X X 0.0532

0.0237

0.0241

X X X 0.0560

Notes: There are 307,722 observations for each model. Estimates are reported as marginal effects. Standard errors clustered at the state-year level are in parentheses. *** indicates statistical significance at the one-percent level.

1983. This restriction makes it more likely that joint-custody laws were in place before the private schooling decision is made by parents. Similar to the results presented in Table 2, the effects of jointcustody reform on children's private school attendance are negative, but the statistical significance varies somewhat depending on which controls are included in the model. In particular, in Model 1, jointcustody reform is negative but not statistically significant. The effect remains negative in Model 2, but it becomes statistically significant once time-varying state-level controls are added to the model. This estimated effect is statistically significant at the one-percent level, and it translates into a 10% reduction in the probability that a child attends private school in states that adopt joint-custody laws. The effect of joint-custody reform remains statistically significant at the onepercent level but becomes larger in magnitude when child and parent controls are added to the model (Model 3), and this estimated effect translates into a 13% reduction in the probability that a child attends private school in states that adopt joint-custody laws. The same pattern is borne out by data when estimates are weighted in Models 4, 5, and 6. However, the estimated effects shown in Models 4, 5, and 6 are slightly smaller in magnitude than those presented in Models 1, 2, and 3. In particular, the estimates from Model 5 indicate a nine percent reduction in the probability of attending private school for children who live in states that adopt joint-custody laws, while the estimates from Model 6 indicate a decline in the probability of a child attending private school of 12% in states that adopt joint-custody laws. Overall, the results shown in Tables 2 and 3 indicate less investment in children's private schooling in states that adopt joint-custody laws between 1980 and 1990. The estimated effect of joint-custody reform is largely unaffected by the use of IPW, and the estimates are similar for the full sample and the subsample that excludes observations from states that adopt joint-custody laws after 1983. However, the estimated effect of joint-custody reform is sensitive to the inclusion of additional control variables, especially the inclusion of time-varying state-level variables. Nevertheless, when all controls are included, the estimated effect of joint-custody reform is highly statistically significant. 4.2. The effect of joint-custody reform on the labor force participation of married mothers Table 4 presents the estimated effects of joint-custody reform from Eq. (2) for all married mothers. We present four different model specifications, which differ by the control variables included. Model 1 controls for state and year fixed effects; Model 2 adds a set of timevarying, state-level controls; Model 3 adds state-specific linear trends, which holds constant other state-year specific factors not captured by the set of time-varying state-level controls; and Model 4 adds a set of individual-level controls. Each model is weighted by an estimate of the inverse probability that the mother is married. The statistical significance of the estimated effects of joint-custody reform on

married mothers' labor force participation are robust, but the magnitudes of the estimated effects vary somewhat depending on which controls are included in the model. In Model 1, joint-custody reform raises the probability of participating in the labor force for married mothers by 2% (or 1.2 percentage points). The estimated effect of joint-custody reform is largely unaffected by the inclusion of the time-varying state-level variables (Model 2). However, the inclusion of state-specific time trends reduces the estimated effect of joint-custody reform slightly (Model 3), which translates into a 1.8% (1.1 percentage points) increase in the probability of working for married mothers in states that adopt joint-custody laws. Once individual-level controls are added to the model (Model 4), the estimated effect of jointcustody reform declines somewhat, indicating a 1.4% (0.8 percentage points) reduction in the probability of participating in the labor force for mothers who live in states that adopt joint-custody laws. In Table 5, we investigate further the effects of joint-custody reform on married mothers' labor force participation by examining subsamples selected based on the age of the youngest child. For married women with children eight-years-old or younger, jointcustody reform raises the probability of participating in the labor force by 2.2% (1.1 percentage points). The effect of joint-custody reform is larger for married women with children six-years-old or younger: the probability of working rises by 2.7% (1.3 percentage points) in states that adopt joint-custody laws. Married women with children aged four years or less have a slightly higher probability of working in response to joint-custody reform: the probability of working rises by 3.2% (1.4 percentage points) in states that adopt joint-custody laws. In Model 4, the largest effect of joint-custody reform on labor force participation is identified for married mothers with children who are two-years-old or younger: their probability of participating in the labor force increases by approximately 4% (1.7 percentage points) in response to joint-custody reform.

Table 4 The effect of joint-custody reform on the labor force participation of married mothers. Variable

Model 1

Model 2

Model 3

Model 4

Joint-custody reform

0.0113** (0.005)

0.0120*** (0.004)

0.0108*** (0.004)

0.0084** (0.004)

X

X X

X X X

0.0144

0.0149

0.0150

X X X X 0.0328

Controls State and year fixed effects Time-varying state variables State-year linear trend Household-level variables Pseudo R-squared

Notes: There are 339,991 observations for each model. Estimates are reported as marginal effects. Standard errors clustered at the state-year level are in parentheses. ** and *** indicate statistical significance at the five- and one-percent levels, respectively.

22

J.M. Nunley, R.A. Seals Jr. / Labour Economics 18 (2011) 14–24

Table 5 The effect of joint-custody reform on the labor force participation of married mothers by age of youngest child. Variable

Eight years old Six years old Four years old Two years old or less or less or less or less Model 1

Model 2

Model 3

Model 4

Joint-custody reform Pseudo R-squared Number of Observations

0.0108** (0.005) 0.0362

0.0129** (0.006) 0.0349

0.0140** (0.006) 0.0356

0.0165** (0.007) 0.0374

182,168

155,990

126,054

87,518

Notes: Each model includes state and year fixed effect, state-year linear trends, timevarying state-level variables, and household-level variables. Estimates are reported as marginal effects. Standard errors clustered at the state-year level are in parentheses. ** indicates statistical significance at the five-percent level.

The overall effect of joint-custody reform on married mothers' labor force participation is positive and statistically robust, but the estimated effect is small. However, the reform's impact on married mothers' labor force participation varies substantially by the age of the youngest child. In particular, married mothers with young children, especially those with very young children, are affected to a greater extent than married mothers with older children. 5. Discussion The statistically significant, negative effect of joint-custody reform on marital investment in children's private-school education does not support the restrictions imposed by the unitary model of household behavior (Becker, 1991), but it does support the predictions made by cooperative bargaining models of household behavior (e.g., see Manser and Brown, 1980; McElroy and Horney, 1981). Although we do not conduct explicit tests of the collective model, our finding is also consistent with the predictions made by these models (e.g., see Browning and Chiappori, 1998; Chiappori et al., 2002). For example, a recent test of the collective model shows that increases in the share of household income controlled by mothers result in significant increases in child-specific expenditures (Bobonis, 2009). The model posited by Rasul (2006), which suggests that withinmarriage investment in child quality is driven by parental preferences for child investment and their relative bargaining position within marriage, provides a framework for interpreting our empirical results. Rasul's model makes specific predictions regarding child investment when parents have heterogeneous valuations of child quality. When parents have heterogeneous preferences for child quality, a shift in bargaining power to the low-valuation (high-valuation) parent unambiguously leads to a decline (increase) in within-marriage investment in child quality. Rasul's model also shows that when parents have equally low (high) valuations of investment in child quality, joint custody reduces (increases) investment in child quality. As such, interpreting our findings in the context of Rasul's model suggests that parents have heterogeneous preferences for child quality, and fathers, who are recipients of greater bargaining power following custody reform, appear to have lower valuations of child quality than mothers. This result is in line with the literature on intrahousehold distribution, which documents increases in investment and spending on children when mothers gain bargaining power within households (Attanasio and Lechene, 2002; Bobonis, 2009; Lundberg et al., 1997; Ward-Batts, 2008). The positive effect of joint-custody reform on the labor supply of married mothers reinforces our argument that mothers lose bargaining power in states that adopt joint-custody laws. Recent work by Chiappori et al. (2002) shows that women's labor supply declines when divorce laws benefit them, an indication that bargaining power

within marriage is negatively related to labor supply. Our results are in line with these findings: when child-custody laws benefit fathers, mothers participate in the labor market at greater rates. Custody reform affects married mothers' incentives to participate in the labor force in two ways: (i) increasing one's labor market skills raises their bargaining position within marriage and (ii) preserving one's outside options insures them against increased divorce-threat of fathers based upon their expectation of shared child custody.

6. Conclusions We investigate the effects of joint-child-custody laws on intrahousehold bargaining power and subsequent within-marriage investment in children. Variation in the timing of child-custody reforms across states provides a quasi-experimental setting with which to examine marital investment in children. We use children's private school attendance and the labor force participation of married mothers as outcome variables of the household bargaining process. Our results indicate negative, unintended consequences for children who live in states that adopted joint-custody laws. Their probability of attending private school declines substantially in these states. While private school is only one type of parental investment in child quality, a reduction in the probability of a child attending private school indicates less spending on children's education, as the tuition rates for private school are often substantial. Likewise, lower rates of private school attendance may negatively affect the long-run educational outcomes, as minors who attend private school tend to fare better across a number of different educational outcomes (e.g., see Altonji et al., 2005). In addition, we find a small, positive effect of custody reform on the probability of participating in the labor market for married mothers. However, the effect of custody reform is much larger for married mothers with young children. The probability that a married mother works in the market increases by two percent for the full sample, compared to a 4% increase for a married mother with a child two-years-old or younger. It is unclear whether mothers' participation in the labor market necessarily implies less time spent with children. However, higher rates of participation in the labor market may make it more difficult for these mothers to “enrich” the home environment, which may have negative consequences for child development (e.g., see Ruhm, 2008). We interpret these results in context of recent literature on government programs which target financial transfers to specific family members, primarily women. States that move from a maternalpreference regime to a joint-custody regime decrease (increase) the bargaining power of mothers (fathers) in married households. As a result, marital investment in children may reflect the preferences of fathers to a greater extent. Consistent with previous literature on intrahousehold distribution (e.g., Attanasio and Lechene, 2002; Thomas, 1990; Lundberg et al., 1997; Phipps and Burton, 1998; Maitra, 2004; Ward-Batts, 2008), we find a decrease in child-specific investment after joint-custody reform. The positive effect of jointcustody reform on the probability of participating in the labor force for married mothers could be driven by the incentives created by the reform for mothers to improve their bargaining position within marriage and to preserve their options outside of marriage by accumulating labor market skills. Judges in the U.S. are directed to consider the best interests of the child in the adjudication of child-custody cases. To that end, jointcustody reform may lessen the impact on children of losing regular contact with one of their parents. However, the prospect of postdivorce cooperation under a joint-custody regime may have negative, within-marriage consequences regarding child investment. Further consideration of how joint-custody laws alter child-investment incentives within married households could help avoid negative, albeit unintended, consequences for children.

J.M. Nunley, R.A. Seals Jr. / Labour Economics 18 (2011) 14–24 Table A3 Summary statistics for time-varying state-level controls.

Authors and acknowledgements are listed in alphabetical order. We thank Brandeanna Allen, Charles Baum, Taggert Brooks, Jacob Dearmon, Nabamita Dutta, E. Anthon Eff, Greg Givens, Duane Graddy, Chien-Chung Huang, Chris Klein, Travis Minor, Mark Owens, Adam Rennhoff, Betsey Stevenson, and Joachim Zietz for their assistance and helpful comments.

Appendix A

Table A1 Private school attendance rates by state. State

Mean

Observations

State

Mean

Observations

Alabama Alaska Arizona Arkansas California Colorado Connecticut Delaware Florida Georgia Hawaii Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri

0.1076 0.0532 0.0675 0.0628 0.1281 0.0696 0.1200 0.2324 0.1501 0.0870 0.1607 0.0473 0.1755 0.1110 0.1098 0.0897 0.1201 0.2134 0.0504 0.1613 0.1183 0.1358 0.1337 0.1332 0.1624

6,206 997 5,437 3708 44,632 5133 4,932 964 14,887 8995 1948 2031 19,607 8986 4838 4182 6495 7577 1964 7327 8,991 15,659 7731 4241 7665

Montana Nebraska Nevada New Hampshire New Jersey New Mexico New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming

0.0587 0.1180 0.0569 0.0873 0.1761 0.0683 0.1925 0.0678 0.0659 0.1559 0.0502 0.0835 0.2017 0.1567 0.1048 0.0701 0.0835 0.0681 0.0232 0.0582 0.0917 0.0910 0.0469 0.1969 0.0413

1398 2813 1547 1638 11,845 2781 27,873 9450 1183 17,128 5242 4370 18,921 1512 5353 1227 7266 28,997 4487 1031 9254 6836 3286 8741 945

Table A2 Summary statistics for child, mother, and father variables. Variable description

Mean

Standard deviation

Variable

Variable description

Unemployment Rate

6.3544 1.5056 Percentage of the population unemployed who is searching for employment Average real personal income 14,589.29 5,072.93

= 1 if child In years In years = 1 if child = 1 if child = 1 if child

Mother covariates Age Hispanic Black High School Some College College Graduate

In years 34.0021 5.3416 = 1 if mother is Hispanic 0.0996 0.2994 = 1 if mother is Black 0.0757 0.2644 = 1 if mother graduated from high school 0.4200 0.4935 = 1 if mother completed some college 0.2432 0.4289 = 1 if mother graduated from college 0.1593 0.3659

Father covariates Age Hispanic Black High School Some College College Graduate

In years = 1 if father = 1 if father = 1 if father = 1 if father = 1 if father

attends private school

is male is Hispanic is Black

0.1276 7.4929 56.5609 0.5016 0.1035 0.0779

0.3337 0.6459 9.2422 0.4999 0.3046 0.2680

Standard deviation

0.4773

0.1548

0.5128

0.2442

0.5592 0.3978

0.4965 0.4894

536.4749

220.4399

635.6611

454.4466

12.6381

1.2914

0.5465

0.0458

0.2097

0.4071

0.2177

0.1138

Notes: There are 390,257 observations for all variables. All variables in dollar amounts are adjusted for inflation. The state-level data come from a variety of sources, including the Bureau of Labor Statistics, World Almanacs, American's for Democratic Action, the Census, www.economagic.com, the Department of Health and Human Services, the Association of Religious Data Archives, and Huang (2002).

0.65 0.60 0.55 0.50 0.45

Comparison

Treatment

0.40 0.35 0.30 0.25 0.20 0.15 0.10

Child covariates Private Age Age-squared Male Hispanic Black

Mean

Per Capita Income Liberal The degree to which states' Quotient (House) House of Representatives cast liberal votes Liberal Quotient The degree to which states' (Senate) Senate cast liberal votes Governor = 1 if the governor is a Democrat No-Fault Property = 1 if the state removes marital fault from consideration in the divorce settlement AFDC Benefit Dollar amount of the maximum AFDC benefit paid to families of four Food Stamp Value Dollar amount of Food-Stamp outlays Social Security Log of Supplemental Security Benefits Income Benefits FLFPR Female labor force participation rate Universal = 1 if state withholds childWithholding support awards from nonresidential parents' earnings Percent Catholic Share of the state population who are Catholic

Percentage of Women Participating in the Labor Force

Acknowledgements

Variable name

23

1950

1960

1970

1980

Census Year Fig. A1. Preexisting trends in married mother's labor force participation rates for treatment and comparison states.

References

is Hispanic is Black graduated from high school completed some college graduated from college

Note: There are 390,257 observations for all variables.

36.6446 0.0990 0.0783 0.3409 0.2393 0.2393

6.3753 0.2986 0.2687 0.4740 0.4266 0.4267

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