Property division on divorce with inequity aversion

International Review of Law and Economics 27 (2007) 111–128

Property division on divorce with inequity aversion Ian Smith School Economics and Finance, University of St. Andrews, St. Andrews, Fife KY16 9AL, United Kingdom

Abstract In the absence of transaction costs, the divorce decision is invariant to legal rules on post-divorce asset allocation. This article introduces a one-sided inequity aversion model to show that property division laws can have efficiency as well as distributive consequences. When divorce is a credible threat, aversion to inequity may prevent spouses renegotiating their marriage to avoid an inefficient marital dissolution. Contemporary trends towards greater equality in property division can be interpreted in terms of their beneficial efficiency effects in addition to standard distributive concerns. © 2007 Elsevier Inc. All rights reserved. JEL classification: D1; K0 Keywords: Property settlement; Divorce; Inequity aversion

1. Introduction Since the 1970s, unilateral (no-fault) divorce rules have been introduced in nearly all common and civil law jurisdictions across the United States and Europe. Although some fault laws persist, the trend is overwhelmingly in the direction of excluding fault both from the grounds for divorce and from property settlement and alimony. This wave of legal innovation continues to generate a great deal of theoretical and empirical interest.1 Although the trend towards easier divorce and its consequences dominates the literature, a parallel development receiving less attention in the law and economics literature is the E-mail address: [email protected]. Recent discussions consider the effect of no-fault divorce on the divorce rate (Clark, 1999; Wolfers, 2006), marriage formation (Rasul, 2006a), the economic welfare of divorcees and their children (Gruber, 2004), domestic violence (Dee, 2003), suicide rates (Stevenson & Wolfers, 2006), labor supply (Chiappori, Fortin, & Lacroix, 2002; Gray, 1998) and marital investment and household bargaining power (Stevenson, 2007). 1

0144-8188/$ – see front matter © 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.irle.2007.06.006

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evolution of property settlement rules. This relative neglect has occurred despite the fact that the financial consequences of marital dissolution, rather than the grounds for divorce, preoccupy the family justice system in many countries. It is well known that over the past 40 years judicial decisions on the division of family assets on divorce in common law jurisdictions have moved towards greater equality of outcome. All 15 American states with rules allocating property according to title in 1973 had switched to equitable distribution by 1985 (Allen, 1990). This stylized fact is reinforced by statutory changes that have expanded the scope of marital wealth available for division to include, for example, pensions and, in some regimes, earning capacity.2 Since these trends favor a more even split of total household assets, they have functioned to improve the divorce payoffs of wives relative to their husbands (Frantz & Dagan, 2004). Theoretically, legal rules on marital property distribution should not matter for the divorce decision if parties can make Coasean bargains. In the absence of prohibitive transaction costs, marriage partners can always make utility transfers to ensure the continuation of an efficient marriage whatever the legal rules for dividing finances on divorce. A marriage dissolves only when a shock reduces the value of the marriage below the joint utility payoffs from divorce (Becker, Landes, & Michael, 1977). This is the definition of efficient divorce. By contrast, divorce would be inefficient if, at best, only one partner is better off and their individual gain does not exceed the welfare loss incurred by the other party.3 Such an inefficient marital dissolution can arise if transaction costs are high enough to prevent spouses preserving an efficient marriage through private bargaining (Allen, 1998). Under these conditions, settlement laws can matter for marital dissolution. For whatever reason, when parties are unable to contract on all allocations within marriage, property settlement rules may have efficiency consequences. In the model of Peters (1986), for example, spouses agree ex ante to a fixed sharing rule within marriage which cannot be renegotiated. The absence of even partially transferable utility induces some inefficient divorces under unilateral dissolution rules. However, Peters’ exclusion by assumption of ex post bargaining over marital shares is difficult to justify. Alternatively, Zelder (1993a, 1993b, 2002) shows that under unilateral divorce rules one party may be unable to compensate a spouse with a credible divorce threat to remain in an efficient marriage due to the presence of household public goods. As a married couple usually already shares the full benefits of the family home and children, these cannot be readily transferred between spouses renegotiating the terms of their marriage. 2 In the case of England and Wales, for example, divorce courts were permitted for the first time to make lump sum capital orders in addition to standard income maintenance awards following the Matrimonial Causes Act 1963. Judicial authority to make property transfers between divorcing spouses was only introduced in 1970 by the Matrimonial Proceedings and Property Act. And it was not until the Welfare Reform and Pensions Act 1999 that courts were empowered to make pension sharing orders for divorcees (Cretney, 2003). 3 Divorce may be privately inefficient (efficient) but socially efficient (inefficient) if the interests of third parties, primarily children, are considered. For simplicity, it will be assumed that parents fully internalize the welfare of their children in their decision-making. This assumption ensures that private and social efficiency are equated. In practice, of course, not all parents will be sufficiently altruistic in the sense that they may still divorce (or stay married) even when their gain from doing so is exceeded by the loss to the children. Both Becker and Murphy (1988) and Weiss and Willis (1985) address these theoretical issues. For present purposes, since family law places considerable emphasis on the best interests of the children in the divorce settlement, this will be reflected in the property division outcome for most households.

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This paper abstracts from both fixed sharing rules and public goods and shows that an inefficiency problem can emerge if spouses are concerned about fairness. A general result from the relatively recent literature on social preferences is that when parties care about equitable outcomes, an unfair allocation of resources not only affects distributive shares but also the total utility generated (Fehr & Fischbacher, 2002). In terms of the family, one demonstrable implication is that the distribution of the gains from divorce can have efficiency consequences. In particular, to the extent that property settlement laws are important in determining the distribution of utility on marital dissolution, they can influence the divorce decision itself. It is the effect of property division rules on the efficiency of the divorce decision that is the focus of this study. The frequently discussed shift from mutual consent to unilateral divorce and the role of fault in property settlements will not be considered. Alimony will also be ignored as it is rare and difficult to enforce and typically constitutes only a very minor part of any divorce settlement (Weiss & Willis, 1993). While it is the needs of dependent children, if any, which are typically given judicial priority, the paper abstracts from explicit consideration of issues concerning optimal child residence, access and support. These topics are addressed in recent theoretical work by Bowles and Garoupa (2003), Francesconi and Muthoo (2003), and Rasul (2006b) among others. Of course, while the concern here is primarily with the division of assets, it is acknowledged that property settlements will reflect the needs of children. In what follows, a model will be developed that demonstrates how, with a given set of property division rules, inefficient divorce may arise due to the fact that fairness concerns constrain the allocation of resources within marriage itself. It will then be argued that this model provides insights into developments in property division settlement rules on divorce over the past 40 years. In particular, it is proposed that, in the context of easier divorce, growing average levels of marital wealth and shifts in perceptions of fairness within marriage, property division laws have evolved, in effect, to reduce the incidence of inefficient divorce. Consider an example that has attracted significant recent attention in England and Wales (Barton & Hibbs, 2002). It refers to those divorce cases where household wealth exceeds the financial needs of the family. An important long-standing legal precedent applied in such instances is the doctrine of “reasonable requirements”. This rule of thumb was formulated by Lord Justice Ormrod in O’D v O’D 1976 to determine a wife’s award in divorce cases with surplus wealth. It used a wife’s accustomed standard of living and the needs of any children as a reasonable basis for calculating her slice of the financial cake. An award to the wife would usually only exceed her reasonable requirements in the event that she had been involved directly in the generation of the marital assets, say as a business partner. So although the statutory framework offers wide discretion to judges, Ormrod’s rule provided some degree of predictability in terms of a gendered pattern of allocating surplus marital wealth. In Dart v Dart 1996, for example, following the end of a 14 year marriage, and having made no exceptional contribution, Mrs. Dart recouped a mere £9m (less than 2.5%) of her husband’s immense £400m fortune. Although the most well-known reported cases are those involving the super rich, the same judicial approach was also applied to less wealthy households with surplus assets to distribute. Insofar as this legal regime provided incentives for wealthy husbands to dissolve their marriages, it is unlikely that their wives

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would be able to renegotiate terms to preserve an efficient marriage without violating fairness norms. Recently, however, a landmark House of Lords ruling in White v White (October 2000) is widely interpreted as introducing a new yardstick of equality for those cases where wealth exceeds needs. The “reasonable requirements” doctrine was dismissed as violating both gender equality and the modern view of marriage as a partnership in which spouses share equally in its fruits. By explicitly bringing post-divorce asset redistribution into line with contemporary views on the nature of fairness within marriage, the argument in this paper is that such changes in property settlement rules serve to reduce the likelihood of inefficient divorce.4 Prior to formal and detailed examination of how this mechanism operates, it is appropriate to discuss briefly a large body of related literature.

2. Related literature The possible effects of property division rules on divorce have primarily been studied in the context of the potential inefficiencies that arise if settlements do not fully compensate women for post-divorce losses in their expected lifestyle. In particular, many authors argue that the failure of distribution rules adequately to protect specialized homemakers reduces ex ante incentives for socially optimal levels of marital investments that are less valuable if the marriage is discontinued (Bolin, 1994; Brinig & Crafton, 1994; Cigno, 1991; Dnes, 1999; Grossbard-Shechtman, Ekert-Jaffe, & Lemennicier, 2002; Laferr`erre, 2001; Landes, 1978; Rainer, 2007; Rea, 1993). In the absence of contractual protection, sinking a marriage specific investment enhances the marital surplus but, in so far as a wife’s earning capacity is sacrificed, also asymmetrically limits her outside option. Given his greater ex post bargaining power, a husband could expropriate his wife’s specific investment by threatening either divorce or prolonged domestic discord of “harsh words and burnt toast” (Bergstrom, 1996, 1997) unless marital terms are renegotiated to his advantage. The risk is especially severe for wives locked-in to a heavy marital investment at an early stage in the relationship. For in addition to the negative effect on their earning capacity, first mover investment makes wives vulnerable to strategic bargaining as both their fecundity (Siow, 1998) and value in the remarriage market decline with age relative to that of their husbands (Cohen, 1987). The consequence is that resources will be expended to defend against ex post opportunism. In particular, anticipating the financial risks from divorce, married women face an incentive to insure themselves by allocating time away from household production to participation in paid employment (Johnson & Skinner, 1986; Parkman, 1992; Sen, 2000). This is the classic underinvestment result of contract theory. Its social cost is possibly lower quality marriages, inducing a positive feedback on the divorce risk itself (Rowthorn, 1999). However, three recent experimental studies, which all apply their results directly to the marital context, suggest caution regarding this widely accepted economic logic. Oosterbeek, 4 This move towards equal division is consistent with trends in other common law jurisdictions without an explicit community of property. However, it requires appropriate procedural safeguards to prevent other inequities arising. An example is that of strategic wedding vows, in which entry into (a short) marriage is pursued primarily to obtain half of joint goods through a subsequent opportunistic “divorce into money”.

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Sonnemans, and van Velzen (2003) investigate the effects of disagreement payoffs on investment choices in an alternating offers bargaining game in which contracting is efficient. They present subjects, later interpreted as “wives”, with a choice between either a large surplus and disagreement payoffs that are very unequal (equivalent to high marital specialization) or a smaller surplus with equal outside options (no specialization). They find that almost all “wives” prefer the former efficient choice. Similarly, in joint venture bargaining experiments, G¨uth, Ivanova-Stenzel, Sutter, and Weck-Hannemann (2004) and G¨uth, Ivanova-Stenzel, and Tjøtta (2003) find that individuals are willing to make high relationship specific investments in order to generate a larger surplus even if it risks exploitation in ex post bargaining. This outcome is independent of the share of the pie exogenously allocated to partners if the relationship failed. Applying these results to the divorce context, the authors suggest that legal rules do not affect marital specific investment and the distribution of marital gains within marriage. Partners displayed a strong drive to pursue the most efficient outcomes and to distribute the gains relatively evenly. The powerful implication is that decision-making within families may not be very sensitive to legal rules or judicial norms governing the distribution of wealth following divorce.5 The least that can be said is that the debate on the strength of the links from divorce compensation to ex ante marital investment and marriage quality remains unresolved. Appealing to these recent experimental results, the model developed here abstracts from the dynamics of investment considerations and instead focuses narrowly on the fairness issue. 2.1. Empirical studies There are several empirical studies that investigate the impact on divorce rates of the inclusion by courts of marital fault in property settlement (Brinig & Buckley, 1998; Friedberg, 1998; Gray, 1998; Weiss & Willis, 1997). However, there are few that attempt formal tests for the effects of alternative property division rules (title, equitable, community) under a no-fault regime. An exception is Allen (1990) who finds that divorce rates rose in title states that adopted unilateral divorce in the 1970s but did not immediately change their property distribution laws. He interprets his result as showing that some titled spouses made opportunistic use of the low cost exit from marriage now offered by no-fault rules. Since they did not require inter-spousal compensation to be paid to secure consent for divorce, wealth-owning partners could unilaterally dissolve the marriage and retain their assets. Allen, however, does not explicitly spell out the nature of the transaction costs that prevented spouses disadvantaged by divorce from compensating their partner to stay in an efficient marriage. The argument here is that fairness considerations can play such a role.

5 Ellingsen and Johannesson (2004) examine the effect of permitting a proposer in an anonymous one shot ultimatum game to communicate a promise not to exploit bargaining power. They find that this promise induces a larger proportion of players to make a relationship specific investment and results in a greater share of even splits of the net surplus than in the absence of communication. Although the study is not explicitly applied to marriage, it clearly has relevance to an institution based on mutual promises to care.

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3. A divorce model with inequity aversion Consider a husband (h) and wife (w) who each choose whether to divorce or continue in a marriage. Marital utility is given by mi = σi M − Max{0, ci M(φi − σi )},

for i ∈ {h, w}

(1)

where mi : the marital utility of spouse i; M: value of the marriage to be shared; σ i : i’s share of M; φi : share of M that i considers fair (fairness preferences); ci : degree of aversion to inequity. Eq. (1) is a modified one-sided application of the inequality aversion model developed by Fehr and Schmidt (1999).6 For simplicity, the model only permits spouses to care about disadvantageous inequity and so is a special case of two-sided models that also allow an individual to be averse to benefiting from inequity (when φi − σ i < 0). Typically, individuals care much more about experiencing unfavorable inequity than they do about benefiting from unfairness. Of course, within marriages spouses internalize one another’s welfare to some extent and so are typically concerned not to exploit their partner. However, introducing advantageous inequity into the model can be readily shown simply to reinforce the impact of fairness on the risk of inefficient divorce, strengthening the results reported below (Smith, 2005). Given that complicating the analysis with two-sided inequity would yield little in the way of additional insight, the greater realism that it offers is forfeited for the sake of clarity. The one-sided unfavorable inequity aversion term, ci M(φi − σ i ), is introduced to capture the cost of deviation for a spouse from perceived fair shares in marriage. The magnitude of the loss depends on the extent of the deviation (φi − σ i ) and the sensitivity of marital dissatisfaction to unfairness, captured by the weight ci ≥ 0. In principle, both the degree of inequity aversion ci as well as the marital shares considered fair φi can differ between the parties. Notice that unlike under standard inequality aversion theory, the fairness comparison is not directly between one individual’s payoff and that of another person. Rather than spousal payoff differences, the comparison is between the share of marital gains a person considers fair and their actual share. In a non-egalitarian marriage in which shares are distributed unequally, for example, this will not induce any unfairness cost if both parties consider such unequal sharing equitable. The model imposes minimal structure on preferences for equity. It is simply assumed that upon marriage, the husband and wife agree on a fair division of the marital gains. These shares are assumed, at least initially, to be consistent rather than conflictual such that φw + φh ≤ 1. When φw + φh < 1 then fair shares do not exhaust the available gains. Whatever the agreed division, it is unenforceable in the sense that either party is free to seek to renegotiate the shares. Indeed, later changes in marital circumstances may induce fairness preferences that generate conflicting equity claims such that φw + φh > 1. The bargaining game that determines actual marital shares is not modelled explicitly. Rather the focus will 6 Bar-Gill and Ferhstman (2004) also build a one-sided inequity aversion model in a buyer–seller incomplete contracting context.

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be on the existence or otherwise of a contracting zone that permits a mutually agreeable marital bargain. 3.1. Divorce payoffs Divorce utility for a spouse, di = δi A + ni , is defined as linear in wealth and additively separable in its financial and non-monetary components, where δi A: utility of assets allocated to spouse i; δi : share of the assets allocated to i, where δh + δw = 1; ni : non-asset utility from divorce. The parameter δi is the legal policy variable. A change in δi can be interpreted as both a policy shift with respect to the distribution of assets across former spouses or, equivalently, a change in the scope of marital property designated as matrimonial rather than separate. The expected value of δi will also be affected by the needs of children. Given that child welfare generally takes priority in the divorce settlement, the spouse with primary responsibility for childcare, for example, may anticipate the award of the family home, typically the most valuable component of marital property.7 Non-asset utility from divorce ni refers to the value of divorce independent of the property settlement. It is determined by such factors as opportunities in the remarriage and labor markets as well as possible psychic benefits. The analysis makes a number of further simplifying assumptions. First, there are no inequity aversion costs on divorce. In so far as such costs exist, they will affect the ease with which private negotiations can reach a settlement (Farmer & Pecorino, 2002). Second, all parameter values are known by all parties. In particular, spouses are assumed to have correct expectations over their asset share on divorce, δi , regardless of whether this is court determined or negotiated in private bargaining in the shadow of the law. Third, the trade-offs between child residence, support, access and property division are not modelled explicitly since specifying the preferences and bargaining considerations that determine the composition of the divorce settlement are well beyond the scope of the paper.8 Fourth, although some attention is paid to the distinction between different types of property regime in common law countries (title and equitable), different forms of community regime (acquests and universal) are not considered. Fifth, define D as joint utility from divorce where D = dh + dw . Finally, it is assumed throughout that divorce is inefficient, namely, D < M.

7 In English law, the court uses its powers to ensure adequate housing for the children of the marriage. This can result in rather complex settlements which may, for example, allocate occupation of the house to the wife, as typically the custodial parent, until the children cease to be dependent or until she remarries at which point the property may be sold and the proceeds shared equally with her former husband. 8 To address this issue, the model would need to introduce a settlement bargaining game that included a specification of spousal preferences over children and household assets as well as modelling the fairness of divorce outcomes. However, this would be a very different objective from the present project which is to draw attention to the role of fairness in marriage, explaining how equity constraints on intra-marital resource distribution can affect the incidence of divorce and to demonstrate the sensitivity of this result to property settlement rules. For recent discussions of settlement bargaining, see Farmer and Tiefenthaler (2003), Fella, Manzini, and Mariotti (2004), Rainer (2007) and Weiss and Willis (1993).

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3.2. Marital reservation shares Marital reservation shares ri give the minimum share of the marital pie M required by each spouse to stay married. It is defined as the share that equates marriage and divorce utilities, mi = di . If a spouse’s actual share falls below the marital reservation level then divorce is a credible threat. There are two cases to consider, corresponding to whether or not the reservation share is affected by fairness concerns. (i) The reservation share of marital utility is independent of fairness concerns. The important threshold is the relationship between a spouse’s divorce payoff di and fair marital utility φi M. If di ≥ φi M then marital utility must exceed that given by the fair share by a sufficient amount for the spouse to prefer marriage over divorce. Specifically, the reservation share is that which makes the spouse as well off as when divorced, namely ri = di /M. In this case, the reservation share is independent of disadvantageous inequity aversion. Whether the inequality di ≥ φi M holds for a spouse, and so whether ci affects ri , will clearly be influenced by the components of the divorce payoff. Of particular interest for present purposes is the effect of variations in the legal policy parameter δi . Define δ¯ i as the threshold value of δi that is sufficiently high to equate δi = φi M and ensure that equity concerns are irrelevant to a spouse’s reservation utility all else equal. Assuming A > 0, δ¯ i can be written as δ¯ i = (φi M − ni )/A. The higher the level of marital financial wealth, the lower the share of assets on divorce that makes the reservation share independent of fairness concerns ceteris paribus. (ii) The reservation share of marital utility is related to fairness concerns. For δi = φi M, the reservation marital share that equates mi = di is given by ri =

ci φi di + . 1 + ci M(1 + ci )

(2)

If the divorce payoff is less than fair marital utility for spouse i then the reservation utility required to stay in the marriage depends on the strength of fairness concerns, ci . If a spouse does not care about inequity then ci = 0 and ri = di /M as in case (i). However, for ci > 0 the reservation marital utility will be inflated above the divorce payoff (ri M/di ) because a spouse requires compensation for any inequitable distribution of marital utility. If a spouse’s actual marital share is less than the reservation share, σ i < ri , then the compensation is insufficient and the spouse prefers to divorce rather than remain in an unfairly organized marriage, even if actual marital utility exceeds the divorce payoff, σ i M > d. As ci → ∞, ri → φi and a spouse will only accept a fair marital share. For intermediate values of ci ,   1 di ∂ri φi − . = ∂ci M (1 + ci )2

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This partial derivative is positive under the maintained assumption that di < φi M so stronger fairness concerns increase the reservation marital share.9 This can be understood using Eq. (2). As the intensity of inequity aversion increases, the weight given to fairness in the reservation share rises while that applied to di /M declines at the same rate. But given di /M < φi the net effect is to raise ri . 3.3. The contracting zone Ignoring other forms of bargaining cost except unfavorable inequity concerns, the magnitude of the contract zone is given by z = 1 − rh − rw . To anticipate the main finding, even though M > D, if the effect of fairness concerns on reservation shares is sufficiently strong such that rw + rh > 1, inefficient divorce will result. For values of z < 0, the contract zone has been eliminated and divorce occurs. In other words, the minimum shares required by each spouse to stay in the marriage cannot be simultaneously satisfied. The transaction costs arising from inequity aversion have induced mutually inconsistent reservation utilities and marital dissolution follows. Of course, if rw + rh ≤ 1 then it is always possible to renegotiate marital shares to preserve the marriage. The issue of interest is the effect of matrimonial property law δi on the bargaining zone and the divorce decision. For marital partners, there are three possible combinations of cases (i) and (ii) described above. (a) The inequality di ≥ φi M is satisfied for both spouses. Corresponding to case (i) in which fairness concerns are irrelevant to reservation shares of marital utility, ri = di /M and the size of the contracting zone is given by dh dw A + n w + nh D − =1− =1− (3) M M M M As long as M > D, z is necessarily positive and no efficient marriage dissolves. Inequity aversion plays no role. Spouses are always able to strike a self-enforcing Coasean bargain to preserve an efficient marriage. Empirically, this is perhaps an unlikely configuration since to maintain the validity of the assumption that M > D, when di ≥ φi M for both spouses, requires that φh + φw ≤ D/M < 1. In words, fairness preferences need to be sufficiently deferential. With respect to the legal policy parameter, it is clear from Eq. (3) that under the specified conditions δi is irrelevant to the determination of z and to the divorce decision. However, settlement rules are important in determining whether the weak inequality di ≥ φi M holds for both spouses. If a spouse’s share of assets on divorce is sufficiently small such that δi < δ¯ i then di < φi M and there is a possible influence for δi and fairness concerns on divorce behavior. This is examined in the following section. (b) The strict inequality di < φi M is satisfied for one spouse only. z=1−

9

At a decreasing rate as the second partial derivative ∂2 ri ∂ci2

=

−2 (1 + ci )3

is negative for di < φi M.



φi −

di M



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Assume without loss of generality that for a wife dw < φw M as in case (ii) so her reservation marital share is given by rw =

c w φw δw A + nw , + M(1 + cw ) 1 + cw

where cw > 0

whereas for the husband dh ≥ φh M so rh = dh /M. Under these conditions, the size of the bargaining zone z = 1 − rw − rh is given by z=1−

cw φw (1 − δw )A + nh δw A + nw − . − 1 + cw M(1 + cw ) M

(4)

Notice that

   ∂rh  ∂rw A = A  = < ∂δw M(1 + cw )  ∂δw  M

for A > 0 and cw > 0.

As the marginal effect of a change in δw on rw is smaller in absolute terms than that on rh , a decrease (increase) in δw reduces (enlarges) the contract zone all else equal even though there is no change in the joint divorce payoff, D = dw + dh . Intuitively, since rh = dh /M, a change in the husband’s divorce utility fully feeds through into his reservation marital share. But the minimum utility the wife requires to remain in the marriage is less responsive to the corresponding change in her divorce payoff because she cares about the inequity implied by a given marital share. Differentiating Eq. (4) with respect to δw gives ∂z A cw = > 0. ∂δw M 1 + cw

(5)

From the partial derivative in (5), it is clear that the marginal effect of a change in δw on the contracting zone is more powerful the greater the proportion of assets in the value of the marriage (A/M) and the larger the wife’s fairness concern. The model implies that when the marital reservation share is sensitive to inequity aversion for only one spouse (in this case the wife), increasing the other spouse’s share of marital assets on divorce (decreasing δw ) will shrink the contract zone, inducing inefficient divorce if z < 0. Divorce arises because the required minimum increase in the husband’s share of marital utility, when he has a credible divorce threat, exceeds the maximum she is willing to forego. The rise in rh is sufficiently greater than the fall in rw such that rw + rh > 1 and divorce ensues. Following a shock to divorce payoffs, in the form of a decrease in δw , it may be impossible to renegotiate terms to save an efficient marriage if inequity aversion is sufficiently strong and the share of financial assets in the value of the marriage sufficiently high. Importantly, this outcome can occur even if initially neither spouse is incurring any inequity cost, σ i = φi . Fair distribution within marriage does not necessarily prevent inefficient divorce. If the fairness costs of inter-spousal transfers required to sustain a marriage following a pure redistribution of divorce utilities are too high, divorce is induced. Note from Eq. (4) that a contracting zone could be re-established and the marriage saved following a disadvantageous change in δw if the wife reduces her desired fair share φw or relaxes her fairness concern cw sufficiently.

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Empirically, of course, it is the case that δw has increased rather than declined over the past few decades with the shift from title to equitable property regimes. Under the stated assumptions, this legal trend serves to enlarge the contract zone and reduce the likelihood of inefficient divorce all else equal, especially in higher wealth marriages. (c) The inequality di < φi M is satisfied for both spouses. Under this condition, the contracting zone is given by z=1−

(1 − δw )A + nh c h φh δw A + nw cw φw − . − − M(1 + ch ) 1 + cw 1 + ch M(1 + cw )

(6)

For the specific case of ch = cw , we have z=1−

cw (φw + φh ) A + (nw + nh ) − . 1 + cw M(1 + cw )

As in case (a), the size of the bargaining zone is independent of the legal parameter. For spouses who share the same degree of inequity aversion, the positive effect of increase in δw on rw is exactly offset by the decrease in rh , leaving z unchanged. When ch = cw the legal variable δw only has an effect on z if it becomes sufficiently large such that δw > δ¯ w ⇒ dw ≥ φw M or sufficiently small such that (1 − δw ) > δ¯ h ⇒ dh ≥ φh M as given by the parameter configuration studied in case (b). The limits δ¯ w and δ¯ h define the range of values within which the legal parameter can vary without affecting the contracting zone. Between these limits the value of z is both constant and at its maximum value. The size of the range is given by (φw + φh )M − (nw + nh ) − A . δ¯ w + δ¯ h − 1 = A The smaller the difference between M and D, the more vulnerable the marriage and so the more likely that a change in the legal parameter will induce δi > δ¯ i and affect the magnitude of z. In addition, the independence result needs to be modified when ch = cw since then variations in δw affect the contracting zone. The larger the difference between the fairness costs, the greater the impact. 3.4. Specific parameter values for the model With the exception of Allen (1998), very little is known empirically about the extent to which divorce is efficient or inefficient. What is clear, however, is that the past 40 years have witnessed an intensification of a longer term trend both to expand the scope of matrimonial property and also to split it more evenly on divorce. These twin factors serve together to increase the magnitude of the δw parameter beyond the historically common value of onethird of the husband’s estate (Geddes & Zak, 2001). In terms of stylized facts, the legal reforms have occurred during a period of rising prosperity in which the value of average family wealth has grown. These changes all function to increase the utility from divorce for women relative to the value of remaining married. In terms of the model, take the case of a traditional marriage between a male breadwinner and a female homemaker in the 1950s or 1960s prior to most of the changes in divorce law on marital finances. Assume as a benchmark that the prevailing sexual ideology systematically

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Table 1 Alternative parameter values for the model

M φh φw mh mw δh δw A nh nw ch cw dh dw D rh rw z δ¯ h 1 − δ¯ w Divorce?

(1)

(2)

(3)

(4)

(5)

100 0.6 0.4 60 40 0.9 0.1 40 20 5 1.5 1.5 56 9 65 0.584 0.276 0.14 1 0.125 No

100 0.6 0.4 60 40 0.9 0.1 60 20 5 1.5 1.5 74 11 85 0.74 0.284 −0.024 0.667 0.417 Yes

100 0.6 0.4 60 40 0.6 0.4 60 20 5 1.5 1.5 56 29 85 0.584 0.356 0.06 0.667 0.417 No

100 0.4 0.6 40 60 0.6 0.4 60 20 5 1.5 1.5 56 29 85 0.56 0.476 −0.036 0.333 0.083 Yes

100 0.5 0.5 50 50 0.6 0.4 60 20 5 1.5 1.5 56 29 85 0.56 0.416 0.024 0.5 0.25 No

Italicized numbers indicate changes from the previous column. Note that the size of the contracting zone, z, is maximized for all values of δh within the range [δ¯ h , 1 − δ¯ w ]. Marriage is assumed to be efficient in each case in that M > D.

granted husbands a 60% share of the gains from marriage and this was widely accepted as the equitable norm by both sexes (φh = 0.6, φw = 0.4). Note that inequality does not necessarily imply perceived inequity if unequal shares are, for whatever reason, the normal marital expectation.10 Suppose further that matrimonial property law allocated assets (A = 40) by title to property giving on average 90% of the marital wealth to the husband on divorce, δh = 0.9. This case is illustrated in column (1) of Table 1 together with specific values assigned to the other parameters of the model. Although the share of property in the total divorce payoff is not small, A/D = 0.615, the property rules and non-asset utilities imply that the wife would suffer considerable hardship on marital dissolution compared to her husband (dw = 9, dh = 56). Since both parties are enjoying levels of marital utility exceeding their reservation levels, the marriage survives. As di < φi M for both spouses, the analysis developed above in case (c) applies. Notice that the legal parameter can vary within a wide range δh ∈ [0.125, 1] with no effect on the contracting zone. Martial reservation shares are insensitive to most plausible legal rules on property settlement. 10 Even today, observations that wives enjoy a disproportionately small share of household leisure time or private consumption relative to their husbands may at least in minor part arise from an agreed principle of unequal sharing. Of course, there are other factors such as gender ideology and bargaining power differences that may account for the “double shift” of labor market and household work that many wives bear (Dempsey, 1997; Parkman, 2004).

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Consider a marriage with a higher value of assets of A = 60 as shown in column (2). This can be conceived as akin to the property settlement case discussed in the introduction and that has attracted considerable recent interest in England and Wales where household wealth exceeds the financial needs of the parties. Notice that M is held fixed so this is likely a marriage with lower levels of non-asset marital utility compared to the first case. The precise form of the relation between wealth within marriage and marital utility is left unspecified as nothing substantive is lost from ignoring this complication. The effect of the change is to raise the divorce payoffs and reservation shares for both parties. While the marriage remains efficient as M > D, the bargaining zone has been eliminated (z = −0.024) and inefficient divorce would follow all else equal. To understand this outcome, note that the husband now has a credible divorce threat since he is better off divorced dh = 74 than married mh = 60. He requires a transfer of 14 to induce him to remain in the union. Although the wife’s marital payoff of mw = 40 greatly exceeds her divorce utility dw = 11, fairness concerns entail that her reservation marriage utility is rw M = 28.4. Since the maximum transfer she is willing to offer is only mw − rw M = 40 − 28.4 = 11.6, the fairness cost of reducing the wife’s share of the value of the marriage by 14 units is too great to permit a marriage saving bargain. Note that this outcome is not an artefact of defining an unequal split as fair. The same inefficient divorce result would arise in this example even if φh = φw = 0.5. This illustrates the proposition stated in case (b) above that inequity aversion can generate inefficient divorce even if both spouses believe the actual distribution of utility within marriage is fair. The source of the problem with this constellation of parameter values is that fairness concerns prohibit a marriage preserving renegotiation of marital shares when one partner has a credible divorce threat. It is possible to restore a positive contracting range by shading the value of the legal parameter. Column (3) illustrates the consequences of reducing the husband’s share of marital property on divorce from 0.9 to 0.6. This adjustment reduces his divorce payoff to the original level of 56. Although his wife’s divorce payoff is now much larger, given her greater share of marital property, her marital utility remains above her reservation level so the marriage continues.11 A comparison of columns (1) and (2) suggests an efficiency explanation as having a role in the evolution of recent trends in property division laws. In the context of increasing marital wealth and highly unequal matrimonial property distribution on divorce, statutory revision of legal rules to favor women can be interpreted as preserving efficient marriages. Particularly during the 1970s when unilateral divorce laws and procedural changes reduced the costs of exit from marriage, parallel shifts in settlement rules from title to equitable statutes can be viewed not only as mitigating potential hardship for divorced women but also as serving to reduce the likelihood of inefficient divorce. Specifically, the probability that property-owning husbands have a credible threat to dissolve an efficient marriage diminished as the price of divorce for such men increased. Of course, none of this analysis of property settlement rules would have applicability to families with few assets to distribute.

11

For this example, it can be shown that any dh within the range 0.25 ≤ δh ≤ 0.833 would be marriage preserving.

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3.5. Fairness preferences In standard models of household behavior and bargaining, events such as the birth of children, the need to care for an ageing relative, unemployment or ill health can affect both the magnitude of the gains from marriage and the intra-household allocation of resources. A potentially important effect within the context of an inequity aversion framework is for a marital shock to induce a change in fairness preferences. This can make a marriage vulnerable to inefficient divorce because a change in the φi ’s affects reservation shares, ri , and so the contracting zone z when di < φi M for one spouse. Following the birth of a baby, for example, the mother may expect her husband to share the additional burdens evenly whereas an inflexible father may consider it unfair to change his lifestyle to accommodate the new arrival. Notice that, for given fairness preferences, renegotiation of actual marriage shares has no effect on the efficiency of divorce since while variations in σ i determine marital utility, the size of the contracting zone remains unaffected. It is the φi ’s that matter. Suppose that following some shock to the marriage the spouses both consider it fair that the 60:40 split should now favor the wife. The consequences are enumerated in column (4). Given the husband’s marital utility is only 40, whereas his divorce payoff is 56, he requires a transfer (of at least 16) to stay in the marriage. However, due to the strong positive effect of the new fairness preferences on the wife’s marital reservation share, her maximum willingness to compensate (60 − 47.6 = 12.4) is insufficient. As a result, z < 0 and the agreed fairness parameters could not sustain the marriage given that the husband gains so much from divorce. Several models suggest that preferences for fairness are selected by evolutionary processes (Bar-Gill & Ferhstman, 2004; Huck & Oechssler, 1999) and in particular that an equal split is the evolutionary stable bargaining convention (Young, 1998). In addition, the norm of equal shares in a pseudo-marital context has some degree of experimental support as reported earlier. Indeed, it is quite commonly assumed in theoretical work that marriage is an equal sharing arrangement (Allen, 1992; Bowles & Garoupa, 2003; Farrell & Schotchmer, 1988). Suppose then that both partners aspire to and practice equal sharing as fair such that φw = φh = 0.5. This generates the parameter values listed in column (5). Although the husband can gain slightly from divorce, the wife is now able to compensate him without violating her reservation marital share. Notice that the size of the bargaining zone would be maximized and no transfer required if policy makers changed the value of the legal parameter δh so as to favor the wife within the range δh ∈ [0.25, 0.5]. Again, this efficient marriage preserving parameter configuration is consistent with legal trends in the distribution of marital property on divorce.

4. Conclusion The main contribution of this paper is to provide an efficiency-based proposal for the trend in the evolution of property settlement law on divorce over the past 40 years in common law jurisdictions. The explanation relies on an application of recent theoretical developments in our understanding of how social preferences affect decision-making, especially the role of

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fairness concerns. In particular, it is shown that the rules on the distribution of matrimonial property on divorce can lead to inefficient dissolution when spouses are averse to an unfair division of utility within marriage. Under unilateral divorce laws, this outcome occurs when only one spouse gains from divorce and the price of renegotiating terms to preserve the marriage is too high with respect to the intra-marital inequity it would generate. In other words, when there are fairness constraints on the way marital resources and roles can be allocated, property settlement laws can have a significant influence on divorce outcomes, especially in marriages with non-negligible financial assets and a high degree of aversion to inequity. By contrast, for highly efficient marriages with low divorce payoffs, or for those with only a relatively small amount of matrimonial property, wide variation in settlement rules need have no impact whatsoever on the divorce decision. Using this model, significant contemporary trends towards greater equality in marital property division can be interpreted in terms of their beneficial efficiency consequences in addition to the traditional justification based on distributive concerns. Under traditional title laws that systematically disadvantaged non-property-owning wives on divorce, the introduction of unilateral divorce rules and growing levels of household wealth entailed that some women were unable to compensate their husbands to remain in an efficient marriage without generating excessive unfairness in the distribution of marital resources. The subsequent shift to equitable property regimes over the past 40 years in American states and other common law jurisdictions has served to mitigate the incentives such husbands faced to initiate inefficient divorce. Moreover, insofar as fairness preferences within marriage have become more egalitarian, the evolution of property settlement rules that mirror this development again functions to protect marriages that would otherwise have inefficiently dissolved. Notice that this approach differs from, though is complementary to, the view that legal reform of marital property rules has simply arisen due to concern over financial hardship of disadvantaged divorcees and children and the resulting implications for public spending. In other words, the model provides a new theoretical interpretation of developments in property division rules. The model has a simple normative implication regarding legal reforms with respect to the division of matrimonial property on divorce. Namely, to minimize the incidence of inefficient divorce, property settlement laws should reflect prevailing norms on fair distribution within marriage sufficiently closely. The point is that this will reduce the likelihood that marital property considerations provide one party with a credible divorce threat. To the extent that a norm for equity within marriage exists and is widespread within a society, there is an efficiency case for the legal regulation of the financial consequences of divorce to mirror this norm. For if there is a large enough wedge between legal standards of fairness in post-divorce asset distribution and intra-marital sharing conventions, this may induce credible divorce threats that cannot be compensated with a side payment due to resistance to the required violation of fairness within marriage that such payments imply. Of course, in common law jurisdictions, couples and their lawyers negotiating privately over property distribution have discretion to depart from the statutory standards to take into account the particular circumstances of marriages that do not conform to the social norm. This is likewise true with respect to judicial decision-making in the event of a contested settlement. Nevertheless, the shadow of the matrimonial property law remains significant

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in determining both the efficiency of the divorce decision and the equity of distributive outcomes. There are various ways in which the analysis could be extended. An obvious development of inequity aversion theories would be to endogenize the unfairness cost. More specifically, it would be of interest to investigate the factors that determine the intensity of inequity aversion within marriage and its variation across spouses. There is also scope for a comparison of the relative effects, if any, of equitable and community division rules on the efficiency of divorce. The impact of alternative settlement rules on the incidence of divorce for alternative distributions of marital gains and financial assets across married couples could also be investigated. Finally, the model could be extended in a number of directions to incorporate marital investment decisions, household bargaining, uncertainty over the divorce settlement as well as aversion to unfair outcomes on divorce.

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