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The Journal of Socio-Economics 45 (2013) 1– 9

Contents lists available at SciVerse ScienceDirect

The Journal of Socio-Economics

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n the causes and consequences of divorce�

lessandro Balestrinoa,∗, Cinzia Ciardib,c, Claudio Mamminia

Università di Pisa, ItalyAzienda USL3, Pistoia, ItalyUniversità di Firenze, Italy

a r t i c l e i n f o

rticle history:eceived 12 January 2012eceived in revised form 30 January 2013ccepted 2 February 2013

EL classification:

a b s t r a c t

In most Western economies, the flourishing of the Welfare State has coincided with a decline of the role ofthe family: divorce has been introduced, and the number of married couples has decreased relative to thatof cohabiting ones. We argue that divorce is a costly process and that its likelihood may be overestimatedby limitedly rational agents; hence, it may act as a reason for the reduction of the number of marriagesand the increase of cohabitation. We also show that the model’s predictions are more in line with the

12

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stylised facts than those coming from a standard model with full rationality.© 2013 Elsevier Inc. All rights reserved.

vailability heuristics

. Introduction

Isabel Archer, the heroine of Henry James’ novel The portrait of lady,1 is a young American heiress living in Europe. She refuses aarriage offer by a fascinating English gentleman and another by a

rilliant American industrialist, and ends up marrying an Americanxpatriate in Italy. He is a superficially charming person who turnsut to be instead rather dull, and, predictably, only interested in heroney. Although she comes soon to realise the harshness of her

ituation, and to suffer from it, she endures her plight and in factanages, with a flourish of brinkmanship, to strike out a uneasy

lliance with her otherwise estranged husband in defending theppearance of a happy marriage. At the end of the story, we leave

er in the middle of an inner fight, slowly building up the strengtho go against her husband’s will. Divorce never crosses her mind: inact, at the very end of the book, she refuses an offer to elope with

� An early and somewhat longer version of this paper was presented at the 2008ESifo Employment and Social Protection Area Conference, May, Munich, Germany:e are grateful to the audience for their comments. We also benefited from an

nsightful referee report that helped us to focus the paper on its main theme. Sections and 4 have been written jointly; Section 2 by C. Ciardi: Section 3.1 by C. Mammini,nd Sections 3.2–3.4 by A. Balestrino.∗ Corresponding author. Tel.: +39 0502212437.

E-mail address: balestrino@sp.unipi.it (A. Balestrino).1 Henry James (1843–1916), brother of the philosopher and psychologist William,

s one of the greatest figures in the English literature (he himself was American, butived in England for almost his entire adult life). He is credited with establishing theovel as a recognized literary genre, as opposed to a form of entertainment.

053-5357/$ – see front matter © 2013 Elsevier Inc. All rights reserved.ttp://dx.doi.org/10.1016/j.socec.2013.02.006

her former American suitor, still in love with her, and goes back toher husband.

In the novel, the action is set in the late XIX century. However,until not many years ago most women would have fully subscribedto Isabel’s behaviour, and, given similar circumstances, would haveperformed the same precarious balancing act. Today, we can under-stand Isabel only if we put her in historical perspective. That theauthor portraits her as having the means to decide for herself andall the same not finding the strength to do it, is actually a power-ful testimony of how strong was at the time (and later as well) thesocial stigma attached to divorce.2

The issue of divorce is of course a multi-faceted one, and it isimpossible to deal with it in all its complexity in a single arti-cle. We therefore focus on a specific question, one we believe isof some interest and also somewhat overlooked in the literature.

We start by reviewing the process whereby divorce has become, inthe Western world, socially acceptable and legally permissible inrecent decades after centuries of stigmatisation3; then, we move on

2 In the 1996 film taken from James’ book, directed by Jane Campion, the storyends before Isabel decides whether to go back to his husband or not – in the 20thcentury, it was permissible to imagine an open ending.

3 Divorce was not common, but not always explicitly forbidden in the ancientWestern cultures; restrictions against it began roughly with Constantine (who wasRoman Emperor from 306 to 337 and famously initiated the evolution of the empireinto a Christian state) and became stronger over the centuries as the church tookjurisdiction over all the issues pertaining to marriage. The restrictions have lastedfor centuries. For example, in Italy, divorce was illegal until the 1970s; in the UK, it

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o our main task, that is to investigate the impact that the availabilityf divorce has had on marriage. This point is of some interest, wergue, because one might think that the introduction of divorce is aotential deterrent to the reduction of the number of marriages: tohe extent that divorce offers a way out of a mismatched marriage,t should decrease the costs of marrying. However, the evidenceoes not support this line of reasoning, as marriages in the Westernountries have continued to fall in number despite the large popu-arity of divorce (for a confirmation of this trend, see e.g. Stevensonnd Wolfers, 2007). We offer an argument in the opposite direction,asting divorce as a further reason for not marrying.4

To accomplish the preliminary part of our task, we suggest at aeneral level that the deep transformation of the Western societiesn the last forty years has favoured both the introduction of divorcend the reduction of marriages; while in the past the family washe sole provider of many services (basic education and health-are, insurance, old-age support, etc.) today both the State and thearket offer important alternatives (public and private education

nd health-care, public and private insurance and pensions, etc.). As consequence, the role of the family has declined, and less peoplehoose to marry; at the same time, the taboo against divorce haseen dropped, as there is no need to protect the family at all costs.

As far as our core argument is concerned, we suggest that theery possibility of divorce may act as an additional and independenteterrent to marriage. The simple reason for that is that divorce isostly. It is true that in recent years, certain costs of divorce haveecreased substantially; legal fees are less than they used to be,he time required for finalising the process is shorter, the socialtigma has been removed at least partially, etc. This relative reduc-ion should however not blind us to the fact that divorce remains,n absolute terms, extremely costly on the psychological side; itenerates a painful condition from which one may in fact be neverree (Beck and Beck-Gernsheim, 1995). Once people anticipate thatheir marriage may end up in a divorce, they may be less prone to

arry, and prefer a form of union (say, cohabitation) in which lessommitment is needed.

To develop our argument, we employ a limited rationalitypproach, based on the notion of “availability heuristics”. Peoplere said to rely on availability heuristics when they “assess. . . therobability of an event by the ease with which instances or occur-ences can be brought to mind” (Tversky and Kahneman, 1982b,. 11). Now, the availability of the facts stored in our memory isot necessarily related to the frequency with which they actuallyappened; we remember more easily facts that have somehowolicited an emotional response or are especially out of the ordi-ary. Hence, the use of availability heuristics implies a tendencyo overestimate certain probabilities – in our case, that of divorce.his would mean that deterring effect that divorce might have onarriage is compounded by a perception error, a “bias”. We will

ee that this hypothesis fits the stylized facts better than the moretandard assumption of perfect rationality.

The paper is organised as follows. The next section illustrateshe wider context within which our analysis takes place, illustrat-ng the historical changes in the Western world that have modified

he role of the family and made marriage less indispensable overhe decades; it also includes the main references to the economic,istorical and sociological literature on which we rely for our study.

as legally possible since the 1930s, although it was clearly frowned upon, and aajor liberalisation was realised in the early 70s; in the US divorce has never been

eally prohibited, but became a relevant phenomenon only starting from the 70s,hen unilateral divorce was introduced. Other countries have made divorce legal

ither immediately earlier (Canada in the 1960s) or later (e.g. Spain in the 1980s).4 In the economic literature this point is made, from different perspectives, also

y Cigno (2008) and Konrad and Lommerud (2008).

Socio-Economics 45 (2013) 1– 9

Then, Section 3 presents our methodological position, develops themodel and shows that it is more consistent with stylised facts thana model with fully rational agents, thereby defending our choice ofmodelling marriage and divorce decisions using a limited rational-ity framework. Section 4 summarises.

2. The family and the State as providers of social protection

The first step of our narrative is a brief sketch of the evolu-tion of the family as society has moved from its agricultural pastthrough a transitional phase of industrialisation to its contem-porary post-industrial structure. Our aim is to show that, sincethe State has progressively taken over most responsibilities thatwere once the province of the family, particularly in the field ofsocial protection, the advantages of marrying have correspond-ingly declined; this has motivated a reduction in the number ofmarriages as well as a change in the nature of marriage itself. Ofcourse, we simplify the story as much as we can, taking some-what extreme views in order to save space and time; we willrefer the reader to the existing literature on the subject whenappropriate. We also ask the reader to keep in mind that our sweep-ing generalisations may obscure across-countries differences (weremark however the cases in which this may matter most); but,our intention is exactly that of capturing the similarities more thanemphasising the differences, so our strategy is consistent with thataim.

The economic literature on divorce has been heavily influencedby Becker’s pioneering work on family economics. According toBecker (1991) the main determinants of divorce are to be foundin the couple’s earnings differentials. For example, high-earningwomen gain relatively little from a marriage, since the small incomedifferential implies that there is less scope for an efficient sexualdivision of labour; moreover, they have a stronger fall-back posi-tion in case of divorce. On the whole, then, Becker’s perspectivesuggest that high-income, well-educated women are more proneto divorce – which is in fact in line with the evidence he refersto. We take here a complementary perspective, as we look at whydivorce has become permissible at a certain point in history, ratherthan focusing on the nature of divorce once it has been established.To put it differently, the Beckerian focus is on the motivations andthe costs of divorce in our contemporary society; we look mostlyat how changes in the structure of society have made divorce pos-sible. To this end, we rely mostly on the sociological literature onthe transformation of marriage: our emphasis lies in particular onhow the societal changes over the past few decades impact on therelative position of men and women within a couple (Beck andBeck-Gernsheim, 1995; Giddens, 1992), focusing more on the dif-ference, or lack thereof, in the source of earning than in the level –although clearly variations in sources will normally reflect them-selves into variations in level.

The historical background (see e.g. Landes, 2003) is as follows.As is well-known, until the late XVIII century, the agricultural sectorin the Western world was dominant; non-agricultural productionwas carried out at the artisanal level. That may be referred to as a“pre-industrial society”. Starting from the 1760 onwards, new man-ufacturing processes started to emerge (such as the use of steampower and machines in iron production) and slowly the “industrialsociety” began to take shape. In particular, the period from 1870 to1914 sees what is usually called the “Second Industrial Revolution”during which deep technological transformations changed dramat-ically the nature of production (steel being a prime example) and

of infrastructures for civil and industrial use (electricity, railroads,radio, etc.). This process has continued with the advent of massproduction in the 20th century. However, in the last 50 years or so,the industrial sector has been progressively replaced by the service

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not eliminated), and, most importantly from our point of view, thesymmetry is re-established in terms of the source of purchasingpower. This generates a different scenario than in the industrial

5 Caucutt et al. (2007) present a model in which families progressively emigratefrom the countryside to the city, and social security emerges from a political processin which the city dwellers vote in its favour against the farmers. They also show thata calibrated version of their model fits with the historical transformation of theeconomy in the US roughly between the 1880 and the 1950 – from the beginning ofthe second industrial revolution to the maturity of the industrial system.

6 The exact figure is 46.5% for 2011, as compared to 67.5% for men (the age intervalfor both genders is 15–64). It is noteworthy that the gap was 31 percentage pointsin 1993. This means that although women are still not very active in the labour

A. Balestrino et al. / The Jour

ector as the dominant one in all the advanced countries: corre-pondingly, we are commonly said to be living in a “post-industrialociety” (Bell, 1973). Our plan is then to trace briefly the evolutionf the family over this period (our main reference is to the work ofeck and Beck-Gernsheim, 1995 and Giddens, 1992).

We start from observing that, in the course of this evolution, theamily working arrangements (who works at home and who worksutside) have changed. We will then try to spell the implication ofhis process of change for the pattern of entitlements to the goodsnd the services that enter the consumption bundle of the partners.pecial attention needs to be paid to the nature of these services.ome of them, like love or companionship, are intangible and cannly be found within a family. Others, mainly material services likehild care, mutual insurance, old-age security, have been for cen-uries provided within the family, but are today, and have beenor the last five or six decades, provided also by the Welfare State:hese are mostly insurance services, for which markets are knowno be typically incomplete. We will see that the working arrange-

ent has implications not only for the goods consumed within theamily and the services provided therein, but also for the access tohe State-provided services.

In a pre-industrial society, the market has a very limited role.oth men and women are engaged in self-production, and the divi-ion of labor across genders does not necessarily reflect the insideome/outside home cleavage. The family is in fact very much a busi-ess organisation running, e.g. a farm. It is important to notice thaten and women, although they fulfill different tasks, contribute

o the prosperity of the family in a symmetric fashion, in the sensehat they all work within the family itself: for example, the husband

ay tend the fields, and the wife may take care of the house. Theirlaim on the commodities entering the family consumption basketomes from the same source. It is difficult here to speak of disparityn earning levels, as there is no money metric through which thealue of production can be assessed.

In this situation, marriage is a very desirable arrangement. Onef its more important functions is that of providing social insur-nce. In the pre-industrial society this service was provided withinhe family like everything else and its availability was the maineason for marrying. Only later, as we shall see, people will begino appreciate the opportunity of obtaining love, companionshipnd mutual emotional support from the partner. Indeed, it is onlyfter the end of the pre-industrial age, roughly starting from theIX century, that romantic love entered the cultural climate andegun for example to surface in novels (think e.g. of Jane Austen’sooks, published in the early XIX century). Until then, women anden needed reciprocal support against the possible misfortunes of

ife: it was quite hard to obtain that kind of support outside theamily. Only affluent people could afford to live alone and attempthe risky process of replacing their partners. As is well-known, theing of England Henry VIII had had six wives: but he needed themnly to produce an heir. Or, to continue with our literary refer-nces, think of Goethe’s The Elective Affinities, published in 1809,hose main characters (who form a couple) are both in their sec-

nd marriage: of course, they came from the aristocracy, becauset the time, for ordinary people divorce simply did not exist as anption.

Later, the advent of the industrialised society helped to raise theeneral standard of living by increasing the level and improving theistribution of wealth, and at the same time, induced a change in thetructure of the family. The man starts working for the market whilehe woman attends to the household chores, and the consumptionoods are acquired through the market (as opposed to self-

roduction). In this case, we do have an evident earning disparity,ue to the fact that market production is rewarded in money units,hereas home production is not. Following a standard Beckerian-

ype argument, we want to focus however on a particular

Socio-Economics 45 (2013) 1– 9 3

aspect of this disparity. While it is obvious that the sexual divisionof labour reflects in principle an efficient task allocation routine, it isalso obvious that it implies an asymmetry in the power relationship,should any dispute arise between the partners. As the consump-tion basket is no longer self-produced, but only accessible via themarket, and given that only the man has a direct claim on moneyincome (the instrument needed to access the commodity market),the fall-back position of the two partners in case of disagreementis extremely unequal, despite the fact that the home production ofthe women is just as important as the market production of theman as far as the well-being of the family is concerned. Moreover,with the passage to industrialisation, also insurance services can beprovided by the State; a relevant example is the pension system,that entitles anybody who works in the market to a pension onceretired.5 Note again the asymmetry: the State crowds out the fam-ily as the provider of old-age security, but the claim to this service isreserved to those who work outside the family, that is men. Womencan access the survivors pension scheme, but only if married to themen originally entitled to the pension. Men have easier access tooutside services than women – which again reinforces a tendencyto differentiate across genders the fall-back positions in case of adispute.

Hence, while for women it remains crucial to find a man whowants to marry them, for men it becomes relatively costly to find awoman to marry and to take care of. When these costs more thancompensate the gains in term of goods and services not available onthe market, a man will need something else to become willing: theintangible services like love and companionship become crucial, asthey are the only ones that can readdress the balance in favour ofthe decision to marry. To reprise our literary references, it is notby chance that romantic love became the mainstay of the novel-istic production of the industrial era: the Bronte sisters publishedin 1847 Jane Eyre (Charlotte) and Wuthering Heights(Emily), thusestablishing a template for all subsequent Romantic novels.

The situation depicted above was probably a reasonably good fitfor the reality of the Western world until, say, the 1970s. The next,dramatic step, is when we arrive, during that decade, at the so-called post-industrial society, in which the service sector becomesquantitatively the most important. The key point here is that in apost-industrial society both partners commonly work outside thehome, and share the household work or hire on the market a per-son to do it. There are of course large variations across countries inthis respect, but even relatively backward countries such as Italyhave a female participation rate to the labour market of almost 50%(one of the lowest in the EU).6 In this case, there is less scope for asexual division of labour, because comparative advantages tend tobe modest in as much as marketable skills are more homogenousacross genders. The difference in terms of the level of money incomethat the two genders may obtain is reduced (although certainly

force, they are closing the gap with men even in Italy. These data can recovered online at http://www.bancaditalia.it/pubblicazioni/relann/rel11/rel11it, or simply byconsulting the printed version of the annual relation of the Bank of Italy (the 2012edition in this case). At the date in which we accessed the data (January 2013), onlythe Italian language version was available.

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do use availability heuristics in real life. Casual observation suggestsit: for example, it is at least as likely to die in car accidents as inplane crashes, possibly more likely, but since the latter are muchmore spectacular and as such heavily emphasized by the media,

8 That would be true of Western countries; in Muslim countries, the children arenormally assigned to the father.

9 This rules out several possible explanations for the costly nature of divorce.

A. Balestrino et al. / The Jour

ociety. In the latter, the shadow value of home-production mightave been greater than the value of the market production, stillhe woman would have had less power in any dispute. In theost-industrial society, for both genders power comes from marketarnings, whose levels can be compared to determine the relativeall-back positions, as is usually emphasized in Beckerian analysesf divorce.

Moreover, marriage in the post industrial society is almostntirely replaced by the Welfare State and the market as the mainrovider of insurance and other commodities previously availablexclusively inside the family. When both the partners work outsideome you can find on the market goods and services that replacehose produced inside the household: not only domestic helps orake-away food, but also child-care services, health assistance, careor the elderly, and so on and so forth. All this is available to personsf both genders. This of course makes marriage entirely redundantn material terms. If you have enough financial resources, you canuy all these commodities and services, and thus avoid marriage: itll becomes a matter of choice. The only thing that may still makeorthwhile to marry someone is the possibility to enjoy romantic

ove or at least an affectionate relationship.7

As a consequence, mismatches are not tolerated: if your firstim in getting married is to find someone who does the laundryor you, you can bear a clash of personalities, but when only loveounts, the match has to be perfect (LeVine et al., 1995). Divorces seemingly a solution, but since, as we shall argue, it is a costlyolution, loose forms of union such as cohabitation might becomereferable to marriage as they require much less commitment (at

east from a legal point of view). It is a matter of fact, indeed, thativorce first and cohabitation later have become more commonnd socially acceptable: it is presumably no coincidence that, as weoted in footnote 3, during the 1970s in several Western countriesivorce became legal were it was not or was made easier where itas already. Or to make just one example out of many concerning

ohabitation (evidence on which can be found in Kiernan, 2001),n Great Britain the percentage of women aged 20–24 in living-n partnerships who were cohabitating without legal marriage hasone from 11% to 55% in the years between 1980 and 1995 (Ermishnd Francesconi, 2000).

Our claim then is that the availability of social protection ser-ices from the Welfare State has made divorce possible, first byaking it socially acceptable, and then legally permissible. In due

ourse, this has paved the way for the practice of cohabitation,ecause the possibility of divorce has made marriage less attractive.et us follow this argument a bit more closely.

As we moved from the traditional through the industrial to theost-industrial family, the attitude towards divorce has changed,ecoming progressively more favourable. From being a threat tohe social protection network, which was constituted exclusivelyy the families in a traditional society, divorce becomes for the

ndustrial and especially post-industrial families, an option that,otentially, makes people better-off by allowing an avenue ofscape from mismatched marriages. So, people have modified theirreferred option (have become supporters, rather than opponents,f divorce) as the circumstances have changed over the years. How-ver, as we already noticed, it is true that divorce constitutes apotentially” useful option, but, of course, it is also true that it is

costly option, especially in psychological terms (Beck and Beck-ernsheim, 1995). When a person divorces, the connection with

ne’s former partner will take a long time to be really severed, ifver. To see this, it is sufficient to consider that the main sourcef divorce costs is the fact that during the years of marriage the

7 Stutzer and Frey (2006) study the link between marriage and subjective well-eing using data for Germany for the 1984–2000 period.

Socio-Economics 45 (2013) 1– 9

couple has established rights over a number of household publicgoods, and as long as these goods still exist after the divorce, newrules have to be found for letting the former spouses continue toexercise their rights, or for compensating one of them if he or sheforfeits them. So, divorcees have to agree on what to do with jointproperties, such as houses or cars, and in case of children, theyhave to agree on how to share custody, parental responsibilities,etc. The conflict that may, and normally will, arise between thespouses at the time of divorce is extremely painful. The “agree-ments” have often to be imposed by a judge. Divorce law providesseveral pre-ordained solutions to the conflict (varying from countryto country, although there are common features such as assigningthe children to the mother,8 etc.), and this may help insofar as itreduces the duration of the conflict. However, it is clear for exam-ple that divorced parents will always retain some sort of link withthe each other (they will remain the parents of their children, nomatter what); fresh opportunities to rekindle the conflict, and theattendant costs, may arise for a long time. A divorced person doesnot revert to single status: he or she is forever an ex-spouse.

Moreover, we should not forget that also a marriage entails costsof different nature (ranging from the monetary outlay for the cere-mony to the psychological adjustment to the habits of the partner);when divorce is not an option, those costs, to be faced up-front, canbe weighed against a safe future return, but once divorce becomespossible, the return from marriage becomes uncertain.

Given all this, it is possible to argue that the very possibility ofdivorce may in fact make marriage a less, rather than a more, popu-lar option. If a person estimates a sufficiently high probability thathis or her marriage ends up in a divorce, the costs to be faced in thatcase are so high that it makes sense to choose an alternative living-in option (say cohabitation). And we will see that the availabilityheuristics induces people to overestimate events whose occurrenceis particularly easy to remember – among them, one might argue,divorces.

3. Marriage and divorce in a post-industrial society

3.1. Methodological assumptions

Before entering into our formal analysis, we clarify our method-ological approach. We see the agents as endowed with a form oflimited rationality.9 That is, they try to assess the benefits andcosts of marrying, and are intent on deciding to marry only if ben-efits exceed costs: in this sense, they are “rational”. However, weallow for the possibility that they make mistakes, in particular weassume that the agents use what is called an “availability heuristics”(Tversky and Kahneman, 1982b): in this sense, their rationality is“limited”.

There are several empirical confirmations of the fact that people

For example, Zoja (2000), from a Jungian perspective, suggests the following. Aslong as marriage was indissoluble, entering into it could be construed as a rite ofpassage; now that marriage can be terminated, relatively easily, with a divorce act, itcannot be any longer interpreted in this way. Hence, marriage becomes less desirablebecause it cannot satisfy the archetypal need of initiation that men and women arebelieved to possess within their collective unconscious. This argument is not easilyamenable to a modelisation within our framework, that is based on methodologicalindividualism – i.e. on the presumption that all actions are consciously oriented toan end.

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hey are more easily called to mind: as a consequence, many of usre afraid of boarding a plane, but not of driving a car. Heuristicsllow us to cut on decision-making costs (which is why are oftenmployed), but they may, and often will, induce judgment errors:everal experiments illustrating the mistakes descending from thevailability heuristics and other judgment biases are discussed inhe literature.10

Our contention is that family formation and dissolution is aarticularly fruitful area for applying the notion of availabilityeuristics.11 It would be too much to contend that availabilityeuristics has a general plausibility as a decision rule. It has beenonvincingly argued that heuristics and biases can be overcome byrequent players in private markets (List, 2004), due to a repeatednteraction effect – people can be expected to learn quickly how toehave efficiently. But the occasional nature of the act of marry-

ng implies that the players in the marriage market do not repeathe “transaction” often enough to become “frequent players”. True,t has also been argued that the family, like the market, is a placen which economic decisions are taken repeatedly through inter-ctions between two (or more) agents, and therefore it is justs possible to assume that such agents learn over time to makefficient choices. However, this argument, which is at the heartf the so-called collective models of the family (Chiappori, 1988;rowning and Chiappori, 1998; Apps and Rees, 1999), refers tohe management of an existing family, not to the formation of aew one. To be sure, its validity, within its field of application, haseen challenged from many sides: for example Lundberg and Pollak2003) have noticed how the repeated interaction argument failso cover important and difficult decisions with long-term, largelynforeseeable, consequences and a high degree of irreversibility

say when one of the partners is considering whether to moveo another city or to switch to another job.12 By the same logic,t seems even less plausible to apply the argument to family for-

ation: there are indeed significant costs to be faced in case oneould wish to reverse the decision to marry, and more generally

here clearly is limited scope for repeated interaction.In a nutshell, then, the idea is that divorce is a good instance of

fact that generates an emotional response and thus tends to fig-re prominently in our memory – exactly what it takes to activatehe availability heuristics. When we hear that someone we know isetting a divorce, we feel sorry for her; a kid who sees his parentsivorcing will probably suffer long-term negative consequences;elebrity divorces, and the tabloids feasting on them, hit our imag-nation. On the other hand, lots of marriages are happy; but, since

happy marriage is not breaking news, this goes largely unno-iced. As a consequence, agents would tend to overestimate thectual occurrence of divorces, and, relatedly, also to overestimatehe probability that they themselves will divorce.

.2. The model

We now consider the formal model, and try to assess how itsredictions are compatible with a few stylised facts about marriagend divorces that have been established in the empirical literature.

10 For in-depth accounts of the pervasiveness of cognitive fallacies, see e.g.ahneman et al. (1982), Todd and Gigerenzer (2003), Gilovich et al. (2002), andahneman (2011).11 In fact, Tversky and Kahneman’s (1982a, p. 164) first example of availabilityeuristics is as follows: “. . .one may assess the divorce rate in a given communityy recalling divorces among one’s acquaintances”.12 To model these issues, Lundberg and Pollak (2003) advocate a non-stationary,ulti-stage game in which the absence of a commitment mechanism makes inef-

cient outcomes possible. Simpler alternatives to the collective approach callor non-cooperative models assuming Cournot behaviour – see e.g. Konrad andommerud (1995) and Anderberg and Balestrino (2007).

Socio-Economics 45 (2013) 1– 9 5

We will focus on what happens as generations succeed each other,in particular what happens to the marriage rate when divorce isintroduced in a post-industrial society. To this end, we employ anoverlapping generations (OLG) model. The element that connectsthe various generations is the information that members of thepresent generations can collect on the behaviour of the past ones.The behaviour we are interested in is of course the one concerningdivorce, and the information comes from the actual rate of divorceof past generations.

Initially, the formal model does not include the option of cohab-itation. The model tries to explain a phenomenon which hasoccurred prior to the insurgence of this practice, namely the impactof divorce on marriage in the early years of its availability. However,since we argued that this impact has paved the way for cohabitationto become socially accepted, we will later consider in an extensionhow this can accommodated in the model.

Agents live for two periods. In the first, agents decide whetherto marry or stay single; in the second whether to stay marriedor divorce. Decisions are taken on the basis of lifetime utility.In general, the per-period utility function includes three items:a consumption (net income) flow (y), a material services flow(x), and an immaterial services flow (Z). Flows do not depend onperiods, and we ignore discounting. The population comprises Nmen and N women; then, there will be at most N couples. Allagents have the same utility function; all men earn the same, andso do all women, but we allow for gender-specific differences inearnings/consumption levels, as well as in the flows of both kindsof services. We do not explicitly model search and matching; wesimply assume that, in the first period, each agent has a once-in-a-lifetime opportunity to meet another agent of the opposite gender:if they are willing to marry each other, the marriage will take place,otherwise they will stay single. Incidentally, this prevents us fromexploring one of the possible roles of cohabitation, namely that ofallowing the partners to know each other and establishing whethermarriage is a reasonable option or not. This is of course an interest-ing question, but it lies outside the scope of the model.

An important element for the analysis is the extent to whichagents have compatible personalities and enjoy each other’s com-pany or not. In our simplified setting, the only chance they haveto get to know each other is during the first period; if a man mar-ries a compatible-type woman the flow of immaterial services Ztakes a positive value, Z = � > 0, otherwise, it takes a negative valueZ = − � < 0. In this latter case, if divorce is available, they might wantto contemplate its feasibility in the second period.13 The probabil-ity, for each agent, to end up in a good or in a bad match will bekey for the subsequent analysis. A realistic, and at the same timesimple, way of modelling this probability is to assume that it isidiosyncratic to the couple. There are so many possible personalityvariants, so many diverse circumstances under which people meetand marry, so many different senses in which two people may becompatible with each other, that it seems reasonable to assume thateach couple has a different chance of forming a successful union.Hence, letting �ij denote the probability of a successful marriage fora generic couple formed by agents i and j, the expected value of theimmaterial service flow for agent i is

E(Zi) = �ij� + (1 − �ij)� = (2�ij − 1)�. (1)

13 In a more complete model, we would have added a period in which the agentssearch for their preferred partner, thereby limiting the risk of a subsequent divorce.However, this would not have altered the qualitative results in any way. Studieswhich explicitly focus on search processes and divorce are provided, e.g. by Cameron(2003). For search models in the presence of bounded rationality, see Todd andGigerenzer (2003); for marriage search and cognitive limitations, see Balestrino andCiardi (2008).

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The true probability is, plausibly, not known to the agents. So,hey have to guess it, and compute the expected value of the imma-erial services flow on this basis. For now, we do not specify the

echanics of the guess; we only notice that each agent will makehe guess in his or her own way, using different procedures for col-ecting information and elaborating it, etc. Later, we will study theormation of this estimated probability in a more detailed way; forow, we proceed by taking it as given. Hence, denoting the subjec-ive probability by pij, we have that the perceived expected values

2pij − 1)�. (2)

We now have all the elements to write the per-period utilityunction; if we take x and z to measure the income equivalents of theervice flows, and assume risk-neutrality, we write, for a marriederson:

i = yi + xi + (2pij − 1)�; (3)

ssuming that the material services flow can be replaced with anquivalent one available on the market, for a single person we willave instead.i = yi + xi (4)

We take it that in a post-industrial society, both genders have theame utility functions: as we saw, their position within the familynd towards the State and the market is the same.

Suppose first that divorce is not allowed. So, agents i and j, whoeet in their first period of life, will marry if

(yi + xi) + (2pij − 1)2� ≥ 2(yi + xi) (5)

nd

(yj + xj) + (2pji − 1)2� ≥ 2(yj + xj). (6)

here will be a critical probability level p̌, such that only agentshose actual p exceeds that value will be willing to marry: only

hose who expect a reasonably successful marriage will accept it.o find the critical value, just solve

i + xi + (2pij − 1)� = yi + xi, (7)

o arrive at

ˇ ij = 12

, ∀i, j. (8)

his follows because in that case the expected value of z will beero, and thus the equality (7) will hold. We state:

laim 1. In a post-industrial society in which divorce is not allowed,nly agents for whom pi ≥ 1/2 are willing to marry; actual marriagesill take place when two agents, both willing to marry, meet.

The only difference between being married or not is the qualityf the relationship with the partner; if one expects it to be good, her she will marry, otherwise stays single.

Suppose now that, for unspecified reasons, divorce is allowed,nd that � represent its costs (all reduced to their monetary equiv-lent). Would this alter the incentives to marry? Lifetime utilityrom marriage when divorce is possible is

i = pij2(yi + xi + �) + (1 − pij)((yi + xi − �) + (yi + xi − �)). (9)

herefore, once divorce is allowed, a person marries if

ij2(yi + xi + �) + (1 − pij)((yi + xi − �) + (yi + xi − �)) ≥ 2(yi + xi).

(10)

ence, the cut-off probability is:

ˇ ij = � + �

2� + �, ∀i, j. (11)

Socio-Economics 45 (2013) 1– 9

Then, we have:

Claim 2. In a post-industrial society in which divorce is allowed,only agents for whom pi ≥ (� + �)/(2� + �) are willing to marry; actualmarriages will take place when two agents, both willing to marry, meet.

The possibility of divorce changes the behaviour of the agents inthat it makes marriage less likely – the more so, the larger is � . Infact, if � is approximately zero, then the critical probability level isapproximately 1/2, i.e. the same as without divorce law. If divorceis extremely accessible, then marriage behaviour does not change.We have actually argued that this is not the case – � is likely to belarge; so, in order for agents to be willing to marry under divorcelaw, the perceived probability of a good marriage must be strictlylarger than 1/2 (whereas in the absence of divorce law 1/2 wasenough). If we order all agents from the one with the lowest to theone with the highest subjective probability pi, then we can view thethreshold value p̌ as partitioning the society into two groups, onecomprising all those who are willing to marry (pi > p̌) and the otherall those who stay single; the introduction of divorce law reducesthe number of those belonging to the former group.

3.3. Availability heuristics vs. perfect foresight

So far, we have taken the subjective evaluation of the probabilityof a successful marriage as given. Now, we will compare the case ofagents who are able to perfectly forecast this probability (perfectforesight) with the one in which they use availability heuristics. Ofcourse, the perfect foresight framework needs no presentation: it isthe standard assumption in economic theory. As for the recourse toan availability heuristic in the present context, we have defendedit previously, arguing that, with specific reference to the marriagemarket, this latter assumption is at least as plausible, possibly moreplausible, than that of full rationality. We will try to reinforce thatargument here.

A perfectly rational agent i, when he or she meets a prospectivepartner j a time t, predicts accurately the probability �ij

t that the

eventual marriage is a “good” match: so, we have pit = �ij

t . At theopposite extreme, there is an agent who relies entirely on availabil-ity heuristics. In our setting, he will use a perception of the divorcerate of the previous generation to assess the probability of his or herown marriage ending in a divorce. Such perception will err in thesense of overestimating the actual occurrence of divorces. Assum-ing that at time t − 1 there are M couples, the actual rate of divorcewill be zero without divorce law, and will equal

dMt−1 =

�Mm=1(1 − �m

t−1)

M(12)

with divorce law. The perceived divorce rate might be expressed as

ıt = f (dMt−1) (13)

with f(0) = 0, f (dMt−1) > dM

t−1 for dMt−1 > 0. Then, a totally biased agent

i, when he or she meets a prospective partner j a time t, pre-dicts inaccurately the probability the eventual marriage is a “good”match by setting pi

t = 1 − ıt .In fact, it might be more realistic to assume that most agents

lie between these two extremes, and that their assessment of theprobability is governed by the following rule:

pit = ki�ij

t + (1 − ki)(1 − ıt), (14)

where ki ∈ [0, 1]. As k approaches unity, the agent qualifies as

prevalently rational; as k approaches zero, the agent qualifies asprevalently biased. The parameter k is in principle agent-specific,and as such indexed by the superscript i; it may be taken to reflectthe degree of what is called “self-efficacy” (Bandura, 1997) or

A. Balestrino et al. / The Journal of

Table 1Willingness to marry by category of divorce risk.

Agent Rational Biased

Period � − 1 � � + 1 � − 1 � � + 1High risk (� < 1/2) nw nw nw w w nw

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Medium risk (1/2 < � < (� + �)/(2� + �)) w nw nw w w nwLow risk (� > (� + �)/(2� + �)) w w w w w nw

perceived behavioural control” (Ajzen, 2005), that is the subjec-ively held probability than one is capable of executing a certainourse of action (in this case, stay married). The higher the degreef self-efficacy or perceived behavioural control, the more accurates the perception of what one can actually do or not, and thereforehe more precise is the estimate of one’s chances.

Suppose that in our post-industrial society divorce has just beenntroduced at time �. The actual rate of divorce was zero at � − 1,nd according to our formulation of the availability heuristic, theerceived rate at period � will be zero too – see (13). This seemslausible: no divorce has ever occurred and therefore the biasedgents overestimate the frequency of the only type of marriage theyan remember – that is, stable marriages. Since however divorceso occur at time �, the perceived risk of divorce for agents who formheir expectations exactly at � will be positive and larger than thectual rate of divorce.

Let us now investigate what happens in each of the periods � − 1, and � + 114 for agents facing different divorce risks, consideringhe polar cases of perfect foresight (ki = 1) and perfect bias (ki = 0)

the intermediate cases can be understood as a mix of these twoxtreme situations. Agents are classified as having high, mediumnd low risk of divorce; the exact definition and the outcomes areresented compactly in Table 1.

Consider rational agents first. The behaviour changes as the riskf divorce decreases – as we move down from one line to the nextrecall that � is the true probability of having a good marriage). Therst category includes agents who are very prone to divorce: beingational, they clearly are not willing to marry in any of the threeeriods under consideration because of (8). The second category

ncludes agents for whom the risk of divorce takes an intermediatealue: they are willing to marry at � − 1, but unwilling once divorces introduced – see (8) and (11). Finally, the third category includesgents with low risk of divorce: under rationality, they are alwaysilling to marry – the couples formed at � will divorce at � + 1 with

probability 1 − �ijt < 1/2, but this will not alter the incentives to

arry at � + 1.Under bias, several combinations are possible. We focus here on

ne which has, in our view, interesting features – all the others cane analysed in a similar way. We have chosen the following case:

ijt >

� + �

2� + �at t = � − 1, �; (15a)

ijt <

� + �

2� + �at t = � + 1. (15b)

his combination may be interpreted as follows. We know thathen divorce is not allowed, the availability heuristic induces the

gent to overestimate the incidence of stable marriages; this is15a). Then, at � − 1 and � they all should be willing to marry, irre-pective of their actual divorce risk, as we report in Table 1. As

consequence, there will be many marriages, and among them a

izeable share will be unstable, as also all agents with medium-o-high divorce risk have married. Therefore, there will be a largectual rate of divorce at �; this in turn, will generate a low perceived

14 The period � + 1 is representative of all subsequent periods.

Socio-Economics 45 (2013) 1– 9 7

rate of successful marriages at � + 1 – which is (15b). Then, thebiased agents will not marry at � + 1, again irrespective of theirdivorce rate (see the last column of Table 1). Incidentally, noticethat at � + 1 biased agents with high and medium divorce risk followthe same course of action that they would take as rational agents,whereas those with low divorce risk follow the opposite path.

We see a clear pattern emerging from Table 1. In a rational world,changes are more nuanced: the agents use all the available infor-mation and take a course of action that reflects their actual divorcerisk (they become more willing to marry as the risk declines). Biasedagents act on the basis of a misinterpretation of the evidence theyhave access to, and do not rely on their actual divorce risk. Theintroduction of divorce thus generates a sharp change of behaviourfor the biased agents – all jump from being willing to being unwill-ing to marry. Instead, in the case of rational agents only those withintermediate risk change their attitude. Recall however that thisis an extreme characterisation producing extreme outcomes; if allagents were fully biased, nobody would marry from � + 1 onward.Of course, there must be partially biased agents who remain willingto marry after the introduction of divorce: to be precise, these willbe those for whom

pijt ≥ � + �

2� + �at t = � + 1, (16)

that is, those whose estimated rate of successful marriages is stilllarge enough to be above the threshold identified in Claim 2.

Comparing the outcomes of Table 1, and accounting for the likelybehaviour of intermediate types (neither fully rational nor fullybiased), it is possible to argue that, depending on whether thereis a prevalence of rational or biased agents, we expect differingimpacts of divorce on marriage decisions. Under rationality, onlythe medium-risk agents change their attitude towards marriagewhen divorce is introduced at �; so, the model predicts a moder-ate reduction in the number of marriages. Instead under bias allagents change their attitude, so the prediction is that the pres-ence of divorce reduces the number of marriages sharply. Indeed,we know that virtually all developed countries have experienceda continuing and significant reduction in the number of marriagesin the last decades, and that the fall in the marriage rates beginsroughly at the same time as the spread of divorce (see below for afew examples).

A further look at Table 1 indicates also that, as we move towardsa prevalence of biased agents, we expect a larger rate of divorceat �, but not necessarily from � + 1 onwards. Indeed, at � biasedagents are all willing to marry no matter how risky is their mar-riage, whereas rational agents only marry if their divorce risk islow; instead, from � + 1 onwards the only difference in behaviourbetween rational and biased agents concerns the low-risk type,which should affect the overall divorce rate minimally anyway. So,in the rationality case, the divorce rate should be stable over time,whereas in the availability heuristics case should first rise and thenslow down.

The stylised facts do not appear to contradict the availabilityheuristic assumption. It is often the case in the Western countriesthat the divorce rate has jumped up after the introduction of divorcelaw or after some drastic procedural simplification, and then hasslowed down to lower levels (accompanied by a reduction of thenumber of marriages). This is for example the pattern followed inall three countries that we mentioned in footnote 3 (Italy, UK, US),where divorce rates went very high in the 70s and have since sta-bilised at lower levels (see e.g. Smith, 1997 for an in-depth analysisof the UK case, and Rasul, 2006 for a theoretical discussion that

sheds light on many empirical findings for the US and elsewhere).Recall that divorces occur early on in marriage (Becker, 1991), sothat it takes relatively little time for the divorce rates to adjust inresponse to changes in the environment.

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A competing explanation would be that when divorce law isntroduced or divorce is made easier, there is a backlog of unsuc-essful marriages that determines the initial jump upwards of theivorce rate; once this first wave has vanished, a trend settles inthis is for example what Smith, 1997 argues). This argument maye valid or not, but, mostly, it is difficult to reconcile it with theiew of the agent as rational and capable of perfect foresight. First,t would imply that many agents with poor prospects of a good

arriage had actually married – but in a rational world this shouldot have happened on a large scale. Second, it would imply that thegents underestimated the cost of divorce, again something thathould not happen in a rational world; couples who have had tondure a difficult marriage due to the impossibility of divorce mustave found a way of coping with the situation over the years, and

t is doubtful that the vast majority of them might want to embarkn a divorce at this stage if they are aware of the high costs of therocess.

.4. Allowing for cohabitation

As we have mentioned more than once in the text, cohabitations nowadays common in the post-industrial society. Historically,he phenomenon is clearly linked to the introduction of divorce:he data we showed above indicate that in the 1970s divorce wasntroduced or made easier in several Western countries, and thatince the 1980s the number of cohabiting couples has increasedteadily. Our next question is therefore, what happens in our formalodel, if we allow for cohabitation as an option?To see this, we must imagine that when two agents meet in

he first period and want to live together they can choose betweenarrying and cohabiting. In the second period, marriage can be

issolved through divorce: cohabitation through a much simplereparation process. Let us posit that the cost of leaving one’s partnerfter the period of cohabitation is ı (just as for divorce, also in thisase all the cost components are converted into their monetaryquivalent). Suppose also that cohabiting may carry a social stigma

≥ 0 per period. Then the lifetime utility from cohabiting is

i = pij2(yi + xi + � − �) + (1 − pij)((yi + xi − � − �) + (yi + xi − ı)).

(17)

f we compare (17) with the lifetime utility from marrying whenivorce is allowed (9), we see that the model we have developed soar can then be rationalised as one in which vi > wi, and thereforehe option of cohabitation was always dominated by that of marry-ng (with the possibility of divorce). A few computations will showhat vi > wi occurs if

1 + p

1 − p� + ı > �, (18)

here � , it will be remembered, is the cost of divorcing. It is ofourse likely that ı < �: the costs of separating after cohabiting doot include for example all the legal expenditures (there are nei-her monetary outlays such as the lawyer’s fees nor opportunityosts due to all the time lost in court, etc.), and even emotionallyhey might be inferior because cohabitation presupposes less com-

itment than marriage. The term (1 + p)/(1 − p), however, exceedsnity, and as long as � is large enough, i.e. as long as the optionf cohabitation is sufficiently stigmatised, it is quite possible forohabitation to be the costlier option.

Still, over the years social habits change: it is a fact that thetigma of cohabitation has been progressively reduced until it has

een entirely removed, at least in the Western countries. If � is closeo zero, then the fact that ı < � implies that it will be marriage withhe possibility of divorce to be always dominated by cohabitation.hen, nobody will marry, and divorce will necessarily disappear.

Socio-Economics 45 (2013) 1– 9

This result is of course very sharp, but it would be easy to make itmore nuanced; it is for example perfectly plausible to assume that�, � and ı are agent-specific (or vary across social groups), and thenwe will have that for some individuals marrying is always prefer-able to cohabiting while for others the opposite is true. We couldalso have those parameters varying over time. But the sharp versionis enough for our purposes, inasmuch as it is shows how the modelcan be made consistent with yet another stylised fact, namely theincreasing importance of cohabitation as a living-in option in ourcontemporary post-industrial society.

4. A concluding summary

In this paper, we have began by reviewing the question why inthe past 40 years or so, divorce has become an increasing popularoption in our Western civilization after centuries of stigmatisation.We have argued that this is to be understood in the more generalcontext of the changes brought about by the replacement of infor-mal social protection networks with the formal safety net suppliedby the Welfare State. Since the family has lost its previous place asthe main provider of social services, marriages have decreased innumber, and divorce has become legally possible as well as sociallyaccepted.

Our main contribution has been that of investigating the reasonswhy the introduction of divorce has not limited the decrease of thenumber of marriages, rather has acted as an additional reason for itsreduction. We argued that this is due to the extremely costly natureof the divorce process (both in monetary and psychological terms):the expected benefit from a marriage appears very small to manyagents. Divorce can then be argued to have favoured cohabitation,more than marriage.

In order to study this issue, we have relied on a limited rational-ity assumption, and compared it with the more standard perfectrationality assumption. To be more precise, we compared a casein which individuals were able to predict exactly the probabilityof divorce with another in which, due to the use of availabilityheuristics, they overestimated the actual risk of divorce – therebycomputing an exceedingly low expected benefit from marriage. Wenoticed that the predictions of the two versions of the model onhow the marriage rate as well as the divorce rate should move overtime are somewhat different, and discuss their compatibility withthe main stylised facts, concluding that the latter do not contradictthe availability heuristics hypothesis. In particular, the fact that thedivorce rate is higher in the first periods of divorce law than insubsequent ones is indeed compatible with this hypothesis. An ini-tial tendency to overestimate the incidence of successful marriagefavours the presence of unstable marriages, that necessarily endup, in most cases, with a divorce. In subsequent periods, this ten-dency vanishes, and is replaced by a tendency to overestimate therisk of divorce; therefore all marriages are discouraged, includingin particular the unstable ones, and the rate of divorce goes down.

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