1"Better the devil you know than the devil you don't." English proverb For many individuals, divorce is a high stakes gamble. The gains they will receive by remaining married are far from certain, given that future income, asset values, and nonpecuniary rewards (including love) are susceptible to random shocks. Nonetheless, the value of a current marriage can appear to be a "sure bet" compared to the highly uncertain payoff associated with divorce. The financial well being of divorced women in particular often depends on the generosity of property settlements, the availability of post divorce transfers, growth of their own labor market earnings, and luck in the remarriage market all of which are subject to considerable randomness. While the inherently risky nature of divorce is widely acknowledged in the policy arena and social science literature, this article is the first to address the following question: How important are individual levels of risk aversion in determining who divorces? We begin our analysis by recasting a simple model of divorce to highlight the role of individual risk preference. Following the seminal work of Becker, Landes and Michael (1977), we assume individuals compare the expected utilities associated with marriage and divorce on an ongoing basis in response to new information about current match quality, expected divorce costs, prospects for remarriage, and other factors. In contrast to existing studies, we assume individuals are risk averse. If divorce were the only alternative to involve risk, then an individual would not divorce unless the expected consumption associated with divorce exceeded the known consumption associated with marriage by an amount at least as large as her risk premium. In fact, we assume both alternatives involve risk, and that divorce is location independent riskier (Jewitt 1989) than marriage. This particular definition of "riskier" ensures that the risk premium that an individual must receive in order to choose divorce over marriage increases monotonically in her Arrow Pratt index of risk aversion. Simply put, a risk averse individual is predicted to be less likely to divorce than is her more risk tolerant counterpart. To assess this prediction empirically, we use data from the 1979 National Longitudinal Survey of Youth (NLSY79) to estimate discrete choice models of married women's and men's divorce decisions. Our key regressor is a measure of each
2individual's relative risk tolerance, which is derived from responses to questions about the willingness to accept alternative lifetime income gambles. We also control for an array of variables intended to measure the economic gains to marriage and divorce, including characteristics of marriage markets and state laws governing divorce. Our estimates reveal that risk preference plays an important role in the decision to divorce, especially for women. For example, among representative women in their fourth year of marriage, a one point (1.8 standard deviation) increase in risk tolerance raises the predicted probability of divorce by 11.4%. Among representative men with the same marriage duration, an identical one point increase in risk tolerance (which equals one standard deviation in the men's distribution) is associated with a 4.3% increase in the predicted probability of divorce. When we consider identical men and women (for whom all characteristics equal grand means rather than gender specific means), the marginal effects just described change to 16.7% for women and 4.0% for men. This gender comparison is consistent with the notion that risk aversion deters divorce, and that divorce entails a greater income gamble for women than for men. Although risk and uncertainty are central to many analyses of marriage and divorce, surprisingly little attention has been paid to individual heterogeneity in risk preference. The role of risk aversion is featured prominently in studies that view marriage as a mechanism for insuring against income risk (Chiappori and Reny 2006; Chiappori and Weiss 2007; Hess 2004; Kotlikoff and Spivak 1981; Rosenzweig and Stark 1989). However, Chiappori and Reny (2006) are the first contributors to this literature to consider how individual variation in risk aversion comes into play; they argue that risk sharing motives lead to negative assortative matching on risk preference. Studies that take a search theoretic approach to marital matching (Burdett and Coles 1999; Mortensen 1988) are, by their very nature, concerned with decision making under uncertainty. Despite this focus, the assumption of risk aversion let alone heterogeneity in risk preference has been introduced into search models only recently. Sahib and Gu (2002) argue that unmarried, risk averse individuals establish a higher reservation level for marital partners than for cohabiting partners if marriage is the riskier of the two alternatives. In the only empirical studies to use a measure of individual risk preference as a determinant of marital transitions, Schmidt (2008) and Spivey (forthcoming) find
3that the waiting time to marriage decreases with risk aversion, presumably because risk averse individuals attach less value to continued search and/or place more value on the risk pooling gains to marriage. A lack of data can be blamed for the relative inattention paid to the influence of individual risk preference on marital transitions. The NLSY79 is the only large scale, U.S. survey to elicit information on all respondents' risk preferences while also supporting detailed analyses of transitions into and out of marriage. During three of the 22 interviews conducted through 2006, NLSY79 respondents were asked whether they would accept two hypothetical, lifetime income gambles of varying riskiness. 1 We use multiple responses to these questions to estimate an Arrow Pratt index of relative risk tolerance that accounts for both measurement error and aging effects. While identical income gamble questions were included in multiple rounds of the Health and Retirement Study, that survey's focus on older individuals makes it less appropriate for an analysis of divorce. The questions were also included in the Panel Study of Income Dynamics, but were only asked of employed respondents in a single interview year. In 2004, the German Socio Economic Panel Study (SOEP) asked respondents to rate their willingness to take risks in a number of specific contexts, while also asking about their willingness to participate in a particular, hypothetical lottery. Because the SOEP has followed a large, representative sample of individuals for over 20 years and collected detailed information on labor market activities and family formation it is a viable non U.S. alternative to the NLSY79 for an analysis of the effects of risk preference on marital dissolution. 2 THE DECISION TO DIVORCE We rely on the simple, canonical discrete choice model that is often used to identify determinants of divorce (Becker et al. 1977; Charles and Stephens 2004; Hoffman and Duncan 1995; Weiss and Willis 1997). The model is based on the assumption that couples marry because they expect marriage to bring them higher utility than the 1 Details on the income gamble questions are provided in the data section. The design and validity of these questions which originated in the Health and Retirement Study are discussed in Barsky et al. (1997) and Kimball, Sahm and Shapiro (2008). 2 Other sources of data on individual risk preferences include the Surveys of Consumers, Italy's Survey of Household Income and Wealth, the Dutch Brabant Survey, and the Dutch DNB Household Survey.
4alternative states, and subsequently divorce when new information causes them to change their assessment of the relative gains to marriage. This view of the decision process leads to the estimation of a sequential, discrete choice model with proxies for the expected gains to marriage and divorce as regressors. While analysts have relied on a range of theoretical ideas (e.g., intra household specialization, consumption smoothing, bargaining, and marital search) to justify their choice of covariates, they have only considered the case where decision makers are risk neutral. 3 In this section, we demonstrate how risk aversion is likely to affect the divorce decision. In the unrealistic case where the value of continued marriage is known with certainty and only divorce entails a risk, well known principles of utility theory apply: whereas risk neutral individuals divorce whenever the expected utility of divorce exceeds the known utility of continued marriage, risk averse individuals require the expected utility of divorce to exceed the utility of marriage by "enough" to compensate for the risk (Pratt 1964). We devote the first subsection to formalizing the choice model and showing that this well known risk premium argument also applies to the case where marriage is risky, but divorce is riskier. While the risk premium argument provides an intuitive interpretation of the effect of risk tolerance on the decision to divorce, in the second subsection we consider alternative interpretations. Specifically, we discuss ways in which an individual's level of risk tolerance might be determined by or otherwise related to her expected gains to marriage and divorce. If we fail to control fully for these gains, then a positive link between risk tolerance and divorce could reflect the fact that highly risk tolerant individuals gain relatively less from marriage than do their more risk averse counterparts. Effects of Risk Tolerance on the Choice Between Two Risky Options Let ),,,( citcithititit XXXMM be the lifetime consumption that individual i receives if she remains married from time t to the end of her horizon. The woman's gain to marriage depends on current and future values of her own characteristics )( it X, her husband's 3 Becker et al. (1977:1143) implicitly acknowledge that marriage is risky when they claim that "(t)he probability of divorce is smaller the greater the expected gain from marriage, and the smaller the variance of the distribution of unanticipated gains from marriage." However, they do not explicitly consider the risky nature of divorce and, in fact, appear to assume agents are risk neutral.
5characteristics ),( hit X tangible factors such as joint financial assets that characterize the couple ),( cit X and intangible characteristics of the marriage such as love ).( cit The lifetime consumption the woman receives if she instead divorces at time t is ),,,,( itcithititit ZXXXDD where it Z represents current and future divorce costs and characteristics of the marriage market. The value of divorce includes hit X and cit X insofar as financial components of these vectors affect property settlements, alimony, and child support, while components such as children affect the indirect costs of divorce. Each individual has an increasing, concave utility function )( it CU defined over consumption that implies an Arrow Pratt measure of relative risk tolerance UCU itit /. We assume that relative risk tolerance (which is the inverse of relative risk aversion) varies across individuals and ranges from zero to infinity. While we assume everyone is risk averse, the limiting case is an individual who is neutral toward risk and would need no premium to accept the riskier of two options with equal expected payoffs. Before turning to the case where both marriage and divorce involve risk, we consider the decision rules that maximize (expected) utility under two simpler scenarios. If the lifetime consumption associated with marriage and divorce are both known with certainty, the woman chooses to divorce whenever );()( itit MUDU empirical implementation of this model simply requires that we have data for the determinants of it Mand it D. Alternatively, if it Mis known with certainty but divorce is risky, the woman divorces whenever )()( itit MUDEU that is, whenever ),(])([ ititit MUDEU S where 0 it is the risk premium the woman is willing to pay to receive itit DE)( with certainty rather than face the uncertain outcome of divorce. Pratt (1964) establishes that under this scenario, it decreases monotonically with the index of relative risk tolerance . it Because this particular model predicts that the probability of divorce increases in , it its empirical analog should include a control for it in addition to controls for the determinants of it Mand it D.
6Having established the role of risk preference when divorce is the only risky option, we turn to the scenario that more accurately describes the divorce decision: marriage is risky, and divorce is even riskier. We assume divorce is the riskier option for two reasons. First, the woman's consumption while married )( it Mdepends on the evolution of her current husband's characteristics, while her consumption while divorced )( it Ddepends on the current and future attributes of a potential new husband; thus, it Dis riskier than it Mbecause its depends on which second husband (if any) is selected as well as realizations of his characteristics over time. Second, while hit X and cit X are determinants of both it Mand , it Dtheir contribution to it D depends on how they will change over time and how they will be distributed after the divorce. Women are typically more dependent than men on spousal income, alimony, child support, and other income sources that become more uncertain upon divorce (Bianchi, Subaiya and Kahn 1999; Cancian, Danziger and Gottschalk 1993; Light 2004). Thus, the arguments in the preceding paragraph imply that divorce entails a greater income gamble for women than for men. 4 While it seems noncontroversial to assume divorce is riskier for women than for men on average, we expect the risk to differ among individuals of a given gender. For example, women with high earnings potential, no children, and/or explicit prenuptial agreements are likely to face relatively little uncertainty about their consumption if they divorce. Our empirical model identifies the effects of itit DM,and it on the probability of divorce at the mean level of unobserved risk. To demonstrate that the risk premium argument continues to apply when both options are risky, we must be explicit about the sense in which divorce is riskier than marriage. Rather than describe a stochastic process by which ,,,, itcithitit XXX and it Z evolve over time, we simply assume both it Mand it D are random variables with cumulative distribution functions M Fand , D F respectively. We further assume D Fis location independent riskier than M Fas defined by Jewitt (1989). This condition holds if 4 We do not attempt to measure the riskiness of divorce by comparing actual pre and post divorce income because risk is based on ex ante assessments and not ex post realizations. Stated differently, whether a woman ultimately "wins" or "loses" the income gamble inherent in divorce is not an indication of the risk she faced.
7and only if (1) .)1,0( )()( )()( 11 pF MpF D MD pdccFdccF As Chateauneuf, Cohen and Meilijson (2004) demonstrate, an alternative definition is that D Fsingle crosses M Fsuch that the (negative) horizontal distance )()( 11 cFcF MD is nondecreasing in every interval below the crossing point. Location independent risk is the most general stochastic order to guarantee that the premium a risk averse individual will pay for partial insurance is monotonically decreasing in her Arrow Pratt coefficient of risk tolerance (Chateauneuf et al. 2004; Jewitt 1989; Landsberger and Meilijson 1994). 5 While location independence is a plausible distributional assumption, it does not have to hold for the risk premium argument to apply. Alternative definitions of "riskier" might entail deviations from monotonicity but still yield a negative correlation between it and . it When both divorce and marriage are risky, the woman divorces whenever ),()( itMitD MUEDUE where the expectations are formed over D Fand. M F This condition is met whenever )()( itMititM MUEDUE S, where 0 it is now the risk premium the woman is willing to pay to draw itit D from the less risky distribution M F rather than face the riskier divorce outcome. Because the assumption of location independent risk assures that it decreases monotonically in , it we continue to predict that, all else equal, the probability of divorce rises with a woman's level of relative risk tolerance. Effects of Risk Tolerance on the Gains to Marriage and Divorce The preceding discussion provides a familiar rationale for including a measure of relative risk tolerance among the determinants of divorce: it is inversely related to the risk premium needed to compensate women for the extra risk associated with divorce. A 5 Ross (1981) demonstrates that a mean preserving spread does not guarantee that the risk premium is monotonic in the Arrow Pratt index unless additional distributional assumptions are made. The distributional assumption of location independent risk guarantees the monotonicity of the risk premium for every nondecreasing and concave utility function. In order to include risk lovers (for whom utility functions are nonconcave), we would have to assume the definition of riskiness proposed by Bickel and Lehmann (1979).
8woman's risk preference can also affect (or be correlated with) her search for a husband both before and after her current marriage, the extent to which she engages in within household risk sharing, and her bargaining power. Matching, risk sharing, and bargaining contribute to the relative gain associated with marriage which, in turn, affects the probability of divorce. In this subsection, we consider how risk preference might affect the probability of divorce through these additional channels. Consider a situation where single women search for marriage partners; for now, we set aside the option to cohabit rather than marry, as well as the ability to engage in assortative matching on risk preference. Given this simple scenario, we expect the value of search and, therefore, the reservation level for an acceptable husband to increase with the woman's degree of relative risk tolerance. This argument, which originates in the job search literature (Pissarides 1974) and is applied to marital search by Schmidt (2008) and Spivey (forthcoming), suggests that components of it M increase in it . In contrast to the prediction emerging from the risk premium framework, we might find that the probability of divorce decreases in it to the extent that it is positively correlated with unmeasured components of . it M This na ve prediction does not necessarily hold once we acknowledge that cohabitation is another option available to single women. As shown by Sahib and Gu (2002), a risk averse woman can mitigate the risk inherent in marriage by forming a cohabiting union with her potential mate. Thus, match quality might be higher among relatively low women who cohabit before marriage than among relatively high women who transition directly from single to married. Moreover, because women can expect to re launch the search process after a divorce, any relationship between risk preference and it M can also exist between risk preference and . it D In short, search models suggest ways in which it might be correlated with it M and , it D but do not yield an unambiguous prediction about the effect of risk tolerance on divorce. Risk sharing provides another mechanism by which a woman's risk preference can affect the gains associated with marriage and divorce and, in turn, the probability of divorce. Given the consumption smoothing opportunities inherent in a two adult household (Weiss 1997), one prediction is that a highly risk averse woman derives a
9higher level of expected utility from marriage than does a more risk tolerant woman (Schmidt 2008, Spivey forthcoming). However, Chiappori and Reny (2006) argue that the desire to share risk leads to negative assortative matching on risk preference. If high women are matched with low husbands and vice versa, then the additional marital consumption accruing to the couple as a result of risk sharing behavior is unlikely to be tied to the woman's risk preference. Only to the extent that couples fail to sort on risk preference would we expect unobserved elements of it Mthat represent intra household risk sharing to be correlated with . it 6 More generally, any factor that (i) affects the probability of divorce; (ii) is left unmeasured in our empirical choice model; and (iii) is correlated with it can affect our inferences about the relationship between risk tolerance and divorce decisions. Many "errors in variables" interpretations are immediately undermined by the fact that we estimate markedly different relationships for women than for men; while this is consistent with the risk premium argument, an alternative interpretation requires a gender difference in the omitted variable's effect on divorce decisions and/or correlation with risk tolerance. By invoking bargaining models of marriage (Lundberg and Pollak 1994 1996; Manser and Brown 1980; McElroy and Horney 1981), for example, we could argue that highly risk tolerant women (but not men) succeed in allocating marital gains toward themselves. Although we have no a priori reason to believe that bargaining power is systematically related to risk preference, it is a prime example of a factor that affects divorce decisions and is controlled for imperfectly. ESTIMATION OF THE DIVORCE MODEL To implement our model empirically, we assume )()( itMitDit MUEDUESis linear in factors that determine the gains to marriage and divorce. That is, (2) , 654321ititc itc ith itititit ZXXXS where it continues to represent the Arrow Pratt coefficient of relative risk tolerance and c itc ith itit XXX,,, and it Zrepresent the factors described above. The risk premium argument 6 If women self insure against a potential divorce by increasing their labor supply (Greene and Quester 1982, Johnson and Skinner 1986, Stevenson 2007), relatively risk averse women may contribute a relatively high share of total household income but this factor is readily measured.