Breen Cooke

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The Persistence of the Gendered Division of Domestic Labour

Richard Breen Lynn Prince Cooke Nuffield College Nuffield College

Oxford OX1 1NF, UK Oxford OX1 1NF, UK

+44 (0) 1865 278 538 phone +44 (0) 1865 280 370 phone

+44 (0) 1865 278 621 fax

[email protected] [email protected]

Total word count (excluding this page): 9,385

December 2004


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Abstract

Why has the gendered division of domestic labour proved so resistant to change

despite the growth in married womens labour force participation? We develop a

game theoretic model of marriage to show that womens individual levels of relative

economic autonomy are not in themselves sufficient to bring about an aggregate shift

in the division of domestic labour. Using data for 22 countries from the 1994

International Social Survey Programme, we show that what is required is that there

be a greater proportion of economically autonomous women within the society as a

whole, together with a sufficiently large proportion of men who, if faced with an

economically autonomous woman, would rather participate in domestic tasks than

endure marital breakdown. These results suggest that until we see greater gender

material equality for the majority of women in a society and an evolution in mens

gender ideology, the gendered division of domestic labour will persist.


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Introduction

Womens increasing labour force participation was expected to lead to a

revolution in the gendered division of labour under which men are breadwinners and

women spend their time in unpaid domestic activities, depending on their husband

for economic support. Social exchange, bargaining and contract models predicted

that womens greater labour force participation would enable them to negotiate more

equal sharing of unpaid work (Blau, 1960; Blood and Wolfe, 1960; England and

Farkas, 1986). The revolution in the gendered division of labour, however, stalled at

the door of most households (Hochschild, 1989): while womens labour force

participation continues to rise across countries, the increase in mens share of

domestic work and childcare has been modest, remaining about one third of the time

contribution of women (Blossfeld and Drobnic, 2001; Gershuny, 2000).

Berk (1985) suggests that the persistence of womens responsibility for the

domestic sphere arises because couples do gender. Couples do gender to

legitimate social arrangements based on gender category (West and Zimmerman,

1987). Hochschild (1989) argues that where mens beliefs about relative gender

power are threatened by wives earning power, couples seek a balance by having the

breadwinning wife do more domestic tasks regardless of the logic of the

pocketbook. Empirical support for this conjecture has been found in the United

States (Brines, 1994) and Australia (Bittman et al., 2003): as wives become the

primary breadwinners, they do more of the domestic tasks to reinforce traditional

gender identities.


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The division of labour is part of the on-going negotiation process of marriage

and can affect marital outcomes. Some models of the family contend that increases

in womens labour force participation result in greater marital instability because of

womens decreasing need for mens economic production (Becker, 1981, 1985) or

increasing competition for occupational status (Parsons, 1953). Empirical evidence

of the direct relationship between womens employment and marital instability,

however, is mixed (Brines and Joyner, 1999; Bumpass, Martin, and Sweet, 1991;

Hoffman and Duncan, 1995; Ruggles, 1997; South, 2001), or effects are contingent

on other factors (Aberg, 2003; Schoen et al., 2002; South and Lloyd, 1995).

In contrast, Oppenheimer (1988, 1997) argues that womens employment is

now desirable for family economic flexibility. Sweeney (2002) found evidence that

employed women in the U.S. are more likely to marry than unemployed women.

Similarly, Moffitt (2000) reports that U.S. marriage rates have been declining at a

faster rate among the least-educated women. In contrast, the greater income

associated with more highly-educated, dual-career couples appears to off-set any

negative effects of more educated womens economic independence (Moffitt, 2000).

An oversight in these analyses of the effects of the changing division of paid

labour on marriage is that none of them controls for possible effects of shifts in the

division of unpaid, domestic labour. More than two decades ago, Huber and Spitze

(1980) found that employed wives thoughts of divorce decrease with husbands

increasing housework contribution. More recent evidence reveals that husbands

greater domestic contribution increases the likelihood of second births in Germany

(Cooke, 2004) and Hungary and Sweden (Olh, 2003). Yet if husbands greater


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domestic participation is beneficial for family outcomes, the question remains of why

we do not see a greater shift in the division of domestic labour.

In this paper we use game theory to model the conditions under which the

aggregate gendered division of domestic labour is expected to change through a

process of marriage selection and differential marital stability. To the best of our

knowledge this is the first sociological application of game theory to family

bargaining, although several economists have applied it in this way (Chen and

Wooley, 2001; Lundberg and Pollak, 1993, 1994; Manser and Brown, 1980;

McElroy and Horney, 1981). While most of the paper is devoted to development of

the model, we also include a preliminary empirical test of it using data from the 1994

International Social Survey Programme.

Game Theory and the Family

Although applications of formal game theory to the family are absent from

sociology, there is a sociological tradition of viewing family outcomes as a function

of relative bargaining power. Relative bargaining power is determined by resources

that individuals can call upon within marriage and the attractiveness of possible

alternatives to the marriage. Economic resources are a primary source of bargaining

power (Blood and Wolfe, 1960; Weber, 1958), so the gendered division of labour

reinforces superior male bargaining power within the family (England, 1993).

Because of persistent gender wage differentials (Blau and Kahn, 1996; Blau et al.,

2002), mens relative economic strength is likely to be maintained even when women

are employed. Confining womens activities to the sphere of the home also reduces

their bargaining strength because it increases their investment in marriage-specific


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capital, such as children, that is not readily transportable to a new relationship

(England and Farkas, 1986; England and Kilbourne, 1990). Consequently, the more

extreme the gendered division of labour, the more important maintaining the

marriage is for women than men. This enables men to negotiate solutions more

favorable to themselves in terms of family expenditures, leisure time, and their

assistance with the amount or type of domestic tasks (Blau et al., 2002).

Game theory makes explicit the interdependency of the players in negotiating

the division of labour. Each player has a set of possible strategies, the payoffs to

which depend on the actions taken by all players. The first economic applications of

game theory to the family modeled marriage as a cooperative game in which binding,

costlessly enforceable agreements are possible (Manser and Brown, 1980; McElroy

and Horney, 1981). In these models the threat point is divorce and it is assumed that

an individuals threat point can change as exogenous factors change (Manser and

Brown, 1980). The family instability resulting from womens labour force

participation predicted by the neoclassical economic and functionalist sociological

models is one solution within this game: as womens economic independence

increases, they are more likely to quit a marriage. Yet this quit only occurs if a

woman is unable to negotiate her own personal best outcome in the family, a process

not modeled within the neoclassical and functionalist theories.

Lundberg and Pollak (1993, 1994) argue that, because there are mutual

benefits, such as shared living economies and enjoyment of children, the threat point

in non-cooperative games is not divorce but a reversion to traditional gender roles.

Men will focus on the breadwinner role, while women will assume responsibility for

the domestic sphere. Without help from her partner, however, this results in an


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under-production of the family goodeither children or a well-maintained home

since women will only take on what they can manage on their own (Lundberg and

Pollak, 1993). This non-cooperative model accounts for the observed decline in

hours spent in housework (Gershuny, 2000) and in fertility as women increase their

labour force participation (see Lehrer and Nerlove, 1986 for a review).

Applications of game theory to the family have for the most part been

theoretical. Empirical tests have assessed the effect of laws (Gray, 1998) or policies

(Phipps and Burton, 1995) on womens labour force participation, and the effect of

transfers on family expenditures (Lundberg et al., 1997). None of these models or

evidence sheds light on why the gendered division of domestic labour is so resistant

to change as womens labour force participation increases over time. To do so, we

apply game theory to the consequences of partner selection for marital decision-

making.

Courtship and the Marriage Game

The marriage market requires decision-making under uncertainty (Beckeret

al., 1977). The greater diversity of possible female (and to a lesser extent, male)

roles has increased the uncertainty, and new characteristics of men and women

become important in determining the quality of a marriage. Until World War II, the

gendered division of labour was the norm, although at best it was an ideal applicable

to white, middle-class households during specific historical periods. Married black

women in the United States and working class women more generally have

historically had high labour force participation rates (Blau et al., 2002; Goldin,

1990). But these transgressions from the norm did not alter widely held beliefs about


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mens and womens ideal-typical roles. Under the male breadwinner norm a mans

potential earnings were a primary consideration in a womans marriage decision.

There is evidence that the rise in wages following World War II induced

more middle-class married women to enter the labour market, but subsequent

generations of women increasingly expect to work as a matter of right (Goldin,

1990). Oppenheimer (1988, 1997) argues that as mens employment has become

more precarious, the desirability of female employment increases. The increasing

desirability of womens employment should in turn increase the likelihood that men

assume more domestic tasks to facilitate this employment, and that women prefer

men who do. Thus, mens willingness to participate in domestic tasks becomes a

new aspect that needs to be ascertained prior to committing to a marriage. Not only

is this information important to women intending to work throughout marriage and

desiring more egalitarian marital roles, but it now also needs to be explicit among

those women and men desiring the traditional gendered division of labour.

We model this uncertainty by assuming that there are three types of men and

of women, defined by their preferences over outcomes shaped by the actions taken

by each in determining the domestic division of labour. The assumption of three

types is surely a simplification, but it accords with Hochschilds (1989) qualitative

groupings and womens relative distribution of preferences for paid versus domestic

work suggested by Hakim (2000). A players type is private information: each

player knows his or her own type and also the distribution in the population of types

of the other gender, but needs to rely on information provided by the potential

partner to determine that persons type. This greater uncertainty means that there is


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more information to be gleaned during the courtship process, but in the game that we

present it is only aftermarriage that a partners true type is revealed.

Figure 1 illustrates the extended form of the game, which shows the choices

facing each player at each move of the game (represented by squares) and the

outcomes of their actions (represented by nodes). Each outcome has a perceived

payoff for the woman and the man. The woman makes the initial decision of whether

to marry (Yes) or not (No). If the woman chooses not to marry she receives payoff

S, for remaining single, and the man receives payoff B, for remaining a bachelor. If

she marries, it is then the husbands move, in that he can participate in domestic tasks

(cooperate), in which case the couple receives the payoff (C,C), or he chooses not to

participate (defect). If the husband defects, then the woman must decide whether to

remain in the marriage (Remain) and accept payoff R, or Divorce and receive payoff

D. The husbands payoffs here are M and P, respectively.

[Figure 1 about here]

The game is an extension of the trust game (e.g. Gibbons, 1997) in which

women take the role of truster. This reflects the fact that women still retain the

primary responsibility for childcare and domestic work in marriage if the man

decides not to participate. In other words, marriage requires that the woman trusts her

husband to cooperate and this, in turn, gives him (the trustee) the option to defect.

Types differ in their ranking of the payoffs. Female types differ in the

relative traditionalism of their gender ideology and their ability to be economically

autonomous. Economic autonomy is shaped by policies affecting womens access to

education and employment, her relative earnings within waged work, public and

private transfers in the event of divorce, and other policies that affect womens


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ability to establish autonomous households (Orloff, 1993). Because of mens

historical high level of labour market participation, their types differ mainly in

gender ideology, although they are also responsive to variations in the costs of

divorce, as shown by Nixons (1997) evidence for the United States that stronger

child support enforcement reduces the incidence of marital breakup.

The first type of woman, Traditional, has the most traditional gender

ideology and would expect to assume the majority of domestic tasks even under

those economic circumstances when she might have to work. She has not invested

heavily in human capital and thus has poor economic alternatives to marriage. Her

payoffs are ranked C>R>S>D: that is, she prefers to remain married to being

divorced or to not marrying regardless of her husbands participation in domestic

tasks.1

The second type of woman, Transitional, has payoffs ordered C>S>R>D. She

has an alternative to marriage but has no outside option once in one. The typical

example of the Transitionaltype, represented by the majority of women since World

War II, is someone who works full-time when single, but after marriage stays at

home with pre-school children, returning to employment, often on a part-time basis,

as the children grow up (Blau et al., 2002; England and Farkas, 1986; Hakim, 2000).

Part-time employment allows a woman to balance family and economic demands

(Blossfeld and Hakim, 1997; Hakim, 2000), but this entails lower investment in

human capital, leaving a woman economically vulnerable in the event of a divorce.

Consequently, once married, if she is employed, she will work the double-shift of

paid and unpaid labour if her husband chooses not to participate because the

alternative of divorce is not economically feasible.


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The third type of woman,Autonomous, has payoffs ranked C>S>D>R. She

has both an alternative to marriage and viable outside options after she marries. She

has the most egalitarian gender ideology and either a career or access to other means

of support that minimize the importance of her partners relative earnings. In

economic termsAutonomous women have the greatest bargaining power among the

three types of women.

Considered as players in an extended trust game, Traditionalwomen must

always trust; Transitionalwomen have the option of not trusting; andAutonomous

women have both this option and an outside option, which can force two of the three

male types discussed below to honour her trust.

The three male types are as follows.Hardliners have preferences ordered

M>B>P>C. They would prefer to see their marriage end in divorce or separation

rather than contribute in any substantive way to domestic work and childcare,

although they prefer not to marry than to marry and separate. They prefer the

traditional division of labour in terms of their own role as sole breadwinner and will

not alter their behaviour even if their female partners find it necessary to work.

Adjusterspreferences are ordered M>C>B>P. They prefer not to do unpaid

domestic work but would rather do so than lose the marital family through divorce.

Thus they will contribute to domestic tasks if the womans outside alternatives to

marriage are sufficiently attractive to threaten divorce. But, as withHardliners, they

prefer not to marry than to marry and ultimately divorce. The third male type,

Cooperator, is comprised of that small proportion whom Hochschild (1989) found

willingly participate fully in unpaid domestic tasks; their preferences are C>M>B>P.


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Given the three types of each gender, if couples knew each others type

before marrying, there would be nine possible subgame perfect equilibria of the

game (shown in Table 1). Traditionalwomen would always marry and remain

married regardless of the mans type; Transitionalwomen would marry

Cooperators, but decline to marryHardliners orAdjusters because both these types

of men defect when paired with a Transitionalwoman; andAutonomous women

have sufficient bargaining power to have cooperative marriages with eitherAdjusters

orCooperators and would never marry aHardliner, because no matter who a

Hardlinermarries, he will always defect.

[Table 1 about here]

Under these subgame perfect equilibria, becauseAutonomous women always

enjoy marriages in which the husband cooperates, an increase in the proportion of

women of this type should lead to an increase in the proportion of all marriages that

are cooperative. This is what the bargaining models predict because they implicitly

assume womens greater economic autonomy results in mens greater participation in

domestic tasks. As the proportion of employed married women continues to

increase, male Cooperators,being preferred by both Transitionaland Autonomous

women, would be more likely to marry than any other type. As noted by Hochschild

(1989), the first child creates a crisis in the division of domestic labour, so it could be

expected that TransitionalandAutonomous women married to Cooperators would

be willing to have more children. If we were to assume that a mans type is inherited

or modeled by his male children (see Chodorow, 1978 or Cunningham, 2001), then

the proportion ofCooperators should be steadily increasing over generations as all

female types would marry and have more children with such men, assuming no other


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differences in fertility among the different pairings. Recent evidence from several

countries suggests that mens greater participation in domestic tasks increases the

likelihood of higher parity births (Cooke, 2004; Olh, 2003). In contrast, as women

gain more economic autonomy and more non-traditional gender ideology, marital

probabilities are lower in pairings with the first two types of men:Hardliners would

marry only Traditionalwomen, who, as Hakim (2000) reports, are only a small

proportion of women in modern industrialized societies, andAdjusters would marry

only TraditionalandAutonomous women.

These outcomes can only occur, however, if there is complete information

about each partners type during courtship. The assumption of complete information

also rules out any possibility of divorce (shown by the absence of any equilibria in

which the womans second move is Quit in response to a mans move of Defect)

because women and men would know which pairings led to divorce and so avoid

them. Consequently, it is more plausible to proceed under the supposition that

information about the other is incomplete at the time of marriage. Thus, the

equilibrium outcomes of the game with incomplete information will depend on the

players mutual beliefs about the others type and the actions they take in the light of

these.

One might argue that couples can discern their partners true type during

courtship, but evidence suggests that considerations of social desirability lead people

to claim a more non-traditional gender ideology that does not translate into more

non-traditional behaviour once married (Press and Townsley, 1998).2 In addition,

Hochschild (1989) noted that the crisis in the family division of labour occurs after

the birth of the first child, regardless of what each partner believed about the extent


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of the others egalitarian gender ideology beforehand. Cohabitation also does not

appear to provide reliable information as to true types: evidence suggests that the

division of domestic tasks is different among cohabitors than among married couples

(Brines and Joyner, 1999), and that persons who cohabit prior to marriage are more

likely to divorce (Berrington and Diamond, 1999; Lillard et al., 1995; Santow and

Bracher, 1994). Consequently, the model we develop assumes that neither men nor

women know the true type of the person they are playing against at the time of the

decision to marry. 3

The distribution of male types,Hardliner, Adjusterand Cooperator, in the

population is indexed by 1, 2, 3 and female types (Traditional, Transitionaland

Autonomous) by 1, 2, 3. These distributions, and, are known to individuals

because they reflect the normative gender role behaviours within the culture,

reinforced through media representations and the shared experiences of others.

Consequently, when a woman meets a man, she assigns an initial probability of

1that he is aHardliner, 2 that he is anAdjusterand 3 (=112) that he is a

Cooperator. The man similarly assigns initial probabilities 1, 2, 3 as to which type

of woman he is facing.

To find the games equilibria we make two assumptions: the first is that the

probability of a Transitionalwoman marrying is never greater than the probability

for anAutonomous woman. A Transitionalwoman will prefer to marry (play Yes

rather than No) given thatAdjustermen Cooperate rather than Defect, and that the

expected payoff from Yes exceeds the payoff from No: that is,

SCR >++ )( 321 . (1a)


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Likewise, anAutonomous woman will prefer Yes to No given thatAdjustermen

Cooperate rather than Defect and that

SCD >++ )( 321 . (1b)

So our first assumption could be interpreted as saying that the payoff to an

Autonomous woman from divorce is as big or bigger than the payoff to a

Transitionalwoman from remaining in an uncooperative marriage, given that all

other payoffs do not differ between them.

The second assumption is that, as reported by Hochschild (1989), the

proportion ofCooperatormen is sufficiently small so that neitherTransitionalnor

Autonomous women will marry if noAdjustermen will cooperate. The assumption is

that the equivalent conditions to 1a and 1b that arise when allAdjusters defect are

never met. For example, forAutonomous women this means that the expected payoff

to Yes when anAdjusterdefects is less than the payoff to No:

SCD .


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The actions ofTransitionalandAutonomous women will depend upon the

actions of the maleAdjusters and their share in the male population, while the actions

ofAdjusters depend on the proportion ofAutonomous women and on the actions of

Autonomous and Transitionalwomen. AnAdjusterwill prefer to cooperate when

faced with anAutonomous woman but defect when faced by any other female type,

but his beliefs about the distribution of possible types he is facing will depend on the

initial belief distribution, , and on the actions taken by women, in the light of which

he updates his beliefs using Bayess rule. These updated beliefs concern the

probability distribution of female types who have played Yes in other words, the

distribution of possible types a man has married (we denote this distribution Y).

AnAdjusterwill cooperate ifY3 is sufficiently large and defect otherwise.

But given that, in equilibrium, men know the actions taken by all types of woman, Y

is wholly determined by the initial distribution, . In particular, Y

3 > 3 when

Autonomous women marry but Transitionals do not; Y3 = 3 when both marry; and

Y3 =0 when neither marry. Thus when onlyAutonomous (and Traditional) women

marry, anAdjusterwill prefer to cooperate if ~

3 . If all women marry he will

prefer to cooperate if 3 . If only Traditionalwomen marry thenAdjustermen

will always defect. The two threshold beliefs forAdjusters are thus~

, the minimum

proportion ofAutonomous women in the population sufficient to makeAdjustermen

cooperate when onlyAutonomous (and Traditional) women marry; and , the

minimum proportion ofAutonomous women in the population sufficient to make

Adjustermen cooperate whenAutonomous and Transitional(and Traditional)

women marry. It follows that ~ > .


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The resulting equilibria of the marriage game are shown in Figure 2. Which

equilibria can be reached depends on the initial distributions ofAdjustermen and

Autonomous women.

(1) For all combinations of and there is an equilibrium in which only

Traditionalwomen will marry andAdjustermen will defect (this is the N,N;d

equilibrium shown in Figure 2).

(2) Given a share ofAdjustermen,TA

222


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ofAutonomous women for which anAdjusteris indifferent between cooperating and

defecting, and, given an initial belief ~

3


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An increasing proportion of Autonomous women will be associated withgreater male participation in domestic tasks only given a sufficiently large

proportion of Adjuster men. This implies a significant interaction effectbetween the proportion of Autonomous women and the proportion of Adjuster

men in a society.

This hypothesis will be tested using data from the 1994 International Social

Survey Programme (ISSP).4

Data and Measures

We use data from the module on Family and Changing Gender Roles that

was fielded in the 1994 ISSP.5 Because our hypothesis concerns observed country

differences in the division of domestic tasks, the individual data reported by married

or cohabiting6

women and men in each of 22 countries are used to construct national

aggregated measures. A scale of who in the household is responsible for domestic

tasks is regressed on the distribution of gender types within the country using

ordinary least squares regression.

Dependent Variable: A Scale of Domestic Responsibility

The scale measuring couples relative responsibility for domestic tasks is

derived from questions on who is normally responsible for: 1) caring for the sick, 2)

doing laundry, 3) doing the grocery shopping, 4) deciding what to have for dinner,

and 5) doing small repairs (reverse coded). In a traditional division of domestic

labour, the women would always do the first four tasks and the man would always do

small repairs.7

Factor analysis (results available from authors) reveals high loadings

on a single factor for all but the fifth item. Consequently, the domestic responsibility

scale is created by summing responses across the four dominantly female tasks and


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dividing by four, resulting in a scale ranging from 1, a traditional division of unpaid

labour where the woman is always responsible for the tasks, to 5, a non-traditional

division where the man is always responsible. Cronbachs (1951) alpha is between

0.50 and 0.59 in Bulgaria, East Germany, Hungary, Israel, Russia and Slovenia;

between 0.60 and 0.69 in Austria, the Czech Republic, Italy, Japan, Norway, Poland,

Sweden and West Germany; and 0.70 and above in Australia, Canada, Great Britain,

Ireland and Northern Ireland, the Netherlands, New Zealand and the United States.

Womens rather than mens, reports of the division of domestic responsibility are

used because they have been found to be more accurate given that women tend to

perform most of the tasks (Berk and Shih, 1980; Press and Townsley, 1998).

Independent Variables

The ISSP survey contains numerous questions on gender and family attitudes

with which to construct female and male types based on ideology (see Table 2). We

first attempted to construct a factor score for gender types, but the same questions did

not always load on the same factors across the countries. Further, as argued in detail

by Braun et al. (1994), the interpretation of individual questions pertaining to

children also varies across cultural contexts. One question, however, assesses the

extent to which respondents support a normative notion of a gendered division of

labour: A mans job is to earn money; a womans job is to look after the home and

family. Possible responses are on a five-point Likert scale, ranging from 1, strongly

agree, reflecting the most traditional gender ideology, to 5, strongly disagree.



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We categorize individuals based on their responses to this question.

Hardlinermen and Traditionalwomen either agree or strongly agree with the

statement;Adjustermen and Transitionalwomen are either neutral or somewhat

disagree; andAutonomous women and Cooperatormen strongly disagree with the

statement. The grouping of disagreement with traditional norms together with neutral

responses reflects that reported attitudes might shift ahead of behaviour (Press and

Townsley, 1998). An interaction term is computed by multiplying the percentage of

Autonomous women in a country by the percentage ofAdjustermen. This

interaction is expected to predict the greatest shift in the division of domestic

responsibility.

The marriage game dynamics are predicted to hold across capitalist countries,

but there is ambiguity as to whether they hold within transitional economies. In

formerly state socialist economies all adults were expected to be part of the labour

force, yet the wage structure was such that it is doubtful whether either gender could

be economically autonomous. This could affect marital bargaining and so we include

a control variable for formerly state socialist countries.

Results

The distribution of gender types by country is presented in Table 3. On

average, in each country a third of men areHardliners, less than a third of women

are Traditional; roughly half areAdjustermen orTransitionalwomen; and the mean

percentage ofCooperatormen is just 17 percent, similar to Hochschilds (1989)

estimate based on her qualitative data. The mean proportion ofAutonomous women

is one-quarter.


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Regression results are presented in Table 4. The top panel presents results of

the tests of our hypothesis; the bottom panel presents the same analyses but replacing

Adjusters with Cooperatormen. According to our model, the size of this group

should be unrelated to the distribution of the division of domestic responsibility. The

first model predicts womens reports of the division of domestic labour as a function

of the control variable for former state socialist economies and the percentage of

Autonomous women. It explains very little variance in the reported division of

domestic tasks and the coefficient for the percentage ofAutonomous women, while

statistically significant, is substantively quite small, with a single percentage point

change predicting just a 0.01 shift along the five-point scale of domestic

responsibility.

The second model in the top panel includes the percentage ofAdjustermen

and explains substantially more variation in mens domestic responsibility. As

expected, increases in both the percentage ofAutonomous women and ofAdjuster

men are associated with a more equal division of domestic work, though the

coefficient for the former is now even smaller and does not reach statistical

significance.


The interaction term ofAdjuster*Autonomous in the third model in the top

half of the table predicts a significant shift in the division of domestic responsibility,

providing clear support for our hypothesis. Furthermore, once the interaction term is

included, the main effect of the percentage ofAutonomous women becomes

significantly negative. The results imply that if the share ofAdjustermen is greater


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than about 47 percent (slightly below the mean for our sample), an increase in the

percentage ofAutonomous women will lead to a more egalitarian domestic division

of labour, but below this threshold an increase in the percentage ofAutonomous

women results in a reporting of a more traditional division of domestic labour. By

contrast, the models reported in the lower part of Table 4, in which the share of

Cooperatormen is used in place of the share ofAdjusters, fare very poorly, with

none of the explanatory variables reaching statistical significance.

Conclusion

We have proposed a game theoretic model of marriage to explain the slow

observed reduction in the gendered division of domestic labour despite womens

rising labour force participation. As argued by Oppenheimer (1988, 1997), gender

specialization is no longer an optimal family strategy in an era of flexible labour

markets. As a result, employment, not domesticity, is an increasingly desired female

attribute in the marriage market (Sweeney, 2002). But the shift away from a rigid

gendered division of labour adds additional uncertainty into the marriage market

because women and men no longer possess common knowledge about expected roles

in marriage. We capture this new uncertainty in the marriage game by mens and

womens lack of knowledge about the type of partner they are facing during

courtship.

Under the resulting model, the proportion of marriages in which men

contribute to domestic work may increase as the proportion ofAutonomous women

increases, but this effect is contingent on the share of maleAdjusters in the

population. Thus, to realize an aggregate change in the division of domestic labour,


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both a greater proportion of women within a society must beAutonomous so that

they can credibly threaten divorce in the face of a non-cooperating man, and a greater

proportion of men must have a sufficiently non-traditional gender ideology to prefer

domestic participation over divorce.

We have not investigated the mechanisms by which the distributions of types

of men and women in a country change, or whether individuals change their type

during their lifetime, although these are both areas worthy of future investigation. It

is reasonable to assume that an increase inAutonomous women is driven by

exogenous processes that will be reflected in their gender ideology. This is evident

here in that women in all countries, on average, report more non-traditional gender

attitudes than men. But possible mechanisms for change among men is less obvious,

particularly since the opportunities and constraints on mens labour force

participation have changed much less than those on womens. Bianchi and her

colleagues (2000) found that womens declining time contribution to domestic tasks

since the 1960s was in large part due to compositional changes brought on by

employment outside the home, delayed marriage and reduced fertility. In contrast,

only a small proportion of mens modest increase in domestic time contribution can

be attributed to similar factors.

Future research might also explore under what circumstances Lundberg and

Pollaks (1993) assertion holds regarding reduced fertility as the initial threat point in

family bargaining. It is possible that policy shapes whether divorce or fertility is the

viable threat point for women. When faced with a non-cooperating partner, women

in countries with strong policy support for the male breadwinner model can only

reduce fertility within marriage, compared with women in countries with better


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24

access to market or state resources that enable greater economic autonomy and give

credibility to a threat of divorce. Analyzing these dynamics requires having panel

data for a wide range of countries representing a range of policy contexts.

Appendix

Here we discuss other equilibria that arise when some degree of separation of

signals of type is possible. We assume that men and women try to signal their type

(truthfully or not) to their potential partner before the marriage game begins and we

model their attempts to do so by simultaneous signaling, after which they update

their beliefs and the woman then makes the decision of whether to marry or not.

Which types have an incentive to signal falsely? Among men, Cooperators

have no such incentive. They have a dominant strategy of always cooperating in the

marriage game and so women of all three types would play Yes when faced with a

Cooperator.Adjusters always have an incentive to try to appear to be Cooperators

because this will induce Transitionalwomen (who would not knowingly marry an

Adjuster) to marry them.Hardliners will have an incentive to pose as Cooperators

(though not asAdjusters) under certain conditions. They always defect, and this will

yield them their most-preferred outcome ifTraditionalorTransitionalwomen play

Yes, but, when faced with anAutonomous woman, they would do better if she played

No. TransitionalandAutonomous women will not marry aHardlinerbut will marry

a Cooperator, and so aHardlinershould signal that he is a Cooperatorif

BM

PB

>

)(32

In words, he should signal that he is a Cooperatorprovided that the share of

Transitionalwomen is large enough to induce him to take the risk of sending the


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25

wrong signal to anAutonomous woman. Among women, Transitionals have an

incentive to appear to beAutonomous, since this would yield them cooperative

marriages withAdjustermen (which they otherwise would not have). Traditional

women also have an incentive to signal that they areAutonomous for the same

reason, provided that we take their payoffs as C>R>S>D. However if, as noted in an

earlier footnote, their payoffs were R>C>S>D then they would have no such

incentive.

Fortunately, whether or not Traditionalwomen andHardlinermen signal

that they are, respectively,Autonomous and Cooperators, makes no difference to the

qualitative features of the equilibria of the marriage game. If men can discern

Traditionalwomen and women can spotHardlinermen, this simply shifts downward

the threshold initial beliefs shown in Figure 2 which determine the actions of the

other four types. Since beliefs are updated after signaling using Bayess rule, a signal

that distinguishes Traditionalwomen (but not the other types) will lead a man to the

belief that the non-Traditionalwoman he is facing isAutonomous with probability

3/(2+3), compared with 3 in the absence of signaling. Likewise, a womans belief

about the probability that she is facing anAdjusterwill be higher than her initial

belief if, after signaling, she knows for certain that she is not facing aHardliner.8

The upshot of this is that the thresholds shown in Figure 2 can be reached with lower

initial beliefs, 2 and 3.

In the text we showed the equilibria of the game under two assumptions

about signaling: mutual separation (MS) in which everyone knows the type of the

person they face (the results of which are shown in Table 1) and mutual pooling


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26

(MP) in which there are no reliable signals of type. Now we turn to equilibria of the

game under two other assumptions about signaling.

(i) Male Pooling Female Separating (MPFS). Here the man knows the womans type

but not vice versa (with the possible exception thatHardlinermen can be identified).

In this case, a Transitionalwoman will always play No and anAutonomous woman

will play Yes ifA

22 . So in this case there are two equilibria: in one (which

holds for any values ofand) only Traditionalwomen marry,Hardliners and

Adjusters defect and Cooperators cooperate; in the other equilibrium, (which can

occur when A22 ) TraditionalandAutonomous women marry,Hardliners

always defect, Cooperators always cooperate andAdjusters defect or cooperate

depending on whether they marry a Traditionalor anAutonomous woman.

(ii) Female Pooling Male Separating (FPMS). Here the woman knows the mans type

but not vice versa (with the possible exception that Traditionalwomen can be

identified). The equilibria here are those shown on the top row of Figure 2. They

depend on mens beliefs about the proportion ofAutonomous women because this

determines the actions ofAdjustermen.

These different signaling scenarios carry consequences for the proportion of

cooperative marriages and the trend in the domestic division of labor that differ from

those arising from our preferred scenario, MP. Under MPFS the proportion of

cooperative marriages is increasing in the share ofAdjustermen, while under FPMS

it is increasing in the share ofAutonomous women. But in our analyses we saw that

there is a significant interaction effect between these two which is not predicted by

either MPFS or FPMS but which does follow from MP.


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27

Notes

1. A Traditionalwomans preferences might be ordered R ~C>S>D or even

R>C>S>D inasmuch as she actively prefers to have greater responsibility for

domestic duties as shown by Greensteins (1996) evidence that women with the most

traditional gender ideology perform more domestic tasks regardless of their

husbands gender ideology, and Allen and Hawkinss (1999) evidence that a

proportion of women act as gatekeepers to their husbands involvement in domestic

tasks.

2. One might also argue that it is easier for men to assess a womans type since

policies and her education and employment are known early in courtship, whereas a

woman can only infer a mans ideology. Yet as Hakim (2000) has argued, highly

educated women with the potential for high earnings may in fact prefer to remain at

home. In this circumstance, the man may incorrectly conclude that a highly-

educated woman isAutonomous when she is in fact Traditionalin her preferences.

3. But in the appendix we investigate the equilibria of the game under the

assumptions that one sex knows the type of members of the other.

4. Given the multiple equilibria in some of the cells of Figure 2 it is possible that, in

a given country, we would observe no change in the proportion of marriages in

which men co-operate, even if the shares ofAdjusters andAutonomous women

increased: but provided that this does not hold true of all countries, then a cross-

sectional comparison of the type we perform here should demonstrate the

relationships described in the hypothesis.


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28

5. More information on the ISSP, including codebooks, is available at

http://www.issp.org. A module on this same topic was also fielded in the 1988 ISSP

but it did not include questions about responsibility for domestic tasks.

6. The ISSP does not distinguish between whether people are legally married or

living as married.

7. One response category was tasks done by third person, although it was unclear

if this was hired assistance or other family members. Further, only 1 percent of

respondents answered in this way, so this category was recoded as missing.

8. By Bayess rule we have that the probability that the man is anAdjuster(adj for

short) given that he does not signal that he is aHardliner(ns for short) is equal to:

2

32

2

)(~)|~()()|(

)()|(

>

+=

+

adjpradjnspradjpradjnspr

adjpradjnspr

Acknowledgements

Thanks to Hans-Peter Blossfeld, Diego Gambetta, Shelly Lundberg, Valerie Kincaid

Oppenheimer, Daniel Verdier, participants at a seminar at the Centro de Estudios

Avanzados en Ciencias Sociales, Instituto Juan March, Madrid on October 30, 2002,

and, particularly, Margaret Meyer for comments on earlier drafts of this paper.


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Figure 1

The Marriage Game

marry?W

(S,B)

H

(C,C)

W

(D,P)

(R,M)W= wife's moveH= husband's move

Cooperate

Defect Divorce

No

Yes

Remain

Male Types:

1:Hardliner: M > B > P > C -- always defects

2:Adjuster: M > C > B > P

3: Cooperator: C > M > B > P -- always cooperates

Female Types:

1: Traditional: C > R > S >D -- always plays Yes; remains in marriage

2: Transitional: C > S > R >D -- always remains in marriage

3:Autonomous: C > S > D >R -- always plays Yes


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Table 1

Subgame Perfect Equilibrium, with Complete Information

Player Movesa

(Wifes First/Wifes Second; Husbands)

Male types and probabilitiesFemale types and

probabilities Hardliner1 Adjuster2 Cooperator3

Traditional1 YS;d YS;d YS;c

Transitional2 NS;d NS;d YS;c

Autonomous 3 NQ;d YQ;c YQ;c

Notation:

Womens Possible Moves:Move 1 Move 2Y= Marry S=Stay in the marriage N= Not Marry Q=Quit the marriage

Mens Possible Moves:d= Defect (no help)

c=Cooperate (help)

a. The notation includes both the expected moves and moves off the equilibrium path. For example,

anAutonomous

woman is not expected to marry aHardliner

man (N). Were she to go off theequilibrium path, however, and do so, he would defect (d) and she would subsequently quit (Q)

the marriage.


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35

A2 = minimum proportion ofAdjustermen in the population sufficient to make

Autonomous women prefer to marry, when allAdjusters cooperate

T2 = minimum proportion ofAdjustermen in the population sufficient to makeTransitionalwomen prefer to marry, when allAdjusters cooperate

~

= The minimum proportion ofAutonomous women in the population sufficient

tomakeAdjusters cooperate when just TraditionalandAutonomous women

marry.^

= The minimum proportion ofAutonomous women in the population sufficient

tomakeAdjusters cooperate when all three female types marry.

Figure 2

Equilibria of the Marriage Game

For Transitional and Autonomous Women and Adjuster Men

N,N;d

N,N,:d

p,Y;r

N,q:r

N,N,d

Y,Y;c

N,q;r

N,N;dN,N;d

N,Y;c

N,q:r

N,N;d

N,Y;c

N,q;r

N,N;d N,N;d N,N;d

~

^

Womans

initial belief

about

proportion

of

Adjuster

men

Mans initial belief

about proportion of

Autonomous women

Note: The equilibria are Transitionalwomans First Move,Autonomous WomansFirst Move;AdjusterMans Move.

The moves ofTraditionalWomen and ofHardlinerand Cooperatormen arenot reported (these are always Y, d, c, respectively).

In the mixed strategy equilibrium, p is the probability than a Transitionalwoman plays Y, q is the probability that anAutonomous woman plays Y, and

r is the probability than anAdjusterplays c.

2

2


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Table 2

1994 ISSP Attitude Questions Pertaining to the Gendered Division of Labour

1. A working mother can establish just as warm and secure a relationship withher children as a mother who does not work. (R)2. A pre-school child is likely to suffer if his or her mother works.3. All in all, family life suffers when the woman has a full-time job.4. A job is all right, but what most women really want is a home and children.5. Being a housewife is just as fulfilling as working for pay.6. Most women have to work these days to support their families. (R)7. Both the man and woman should contribute to the household income. (R)8. A mans job is to earn money; a womans job is to look after the home and

family.

9. It is not good if the man stays at home and cares for and the woman goes outto work.

10.Women should stay at home full-time when there is a child under school age(3-point scale: home full-time, work part-time, work full-time).

11.Work is best for womens independence. (R)Note: (R) indicates reverse coding so that a higher score reflects more non-traditional

attitudes.


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37

Table3

PercentageDistrib

utionofGenderTypesAcrossCountries

MarriedorC

ohabitingIndividuals,Age1

8-65

WOMENSTYPES

MENSTYPES

Traditional

Transitional

Autonomous

Hardliner

Adjuster

Cooperator

Australia

17%

51%

31%

25%

57%

18%

Austria

35

37

27

39

45

16

Bulgaria

62

26

11

62

27

11

Canada

7

48

45

9

55

36

CzechRepublic

48

42

9

54

40

6

EastGermany

8

52

40

9

63

28

GreatBritain

17

59

23

22

61

17

Hungary

47

44

9

55

38

7

Ireland

23

52

25

31

51

17

Israel

19

54

27

27

54

20

Italy

25

50

25

34

50

16

Japan

29

36

35

40

35

26

Netherlands

12

62

26

17

63

20

NewZealand

16

55

28

20

60

20

NorthernIreland

20

57

23

16

67

16

Norway

10

49

41

13

61

26

Poland

55

42

3

69

28

2

Russia

64

34

2

68

30

1

Slovenia

33

53

14

39

54

8

Sweden

8

46

46

10

59

30

USA

12

58

29

23

58

17

WestGermany

25

48

26

36

50

14

Note:Percentagesmay

nottotalto100duetorounding.


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Table4

OLSUnsta

ndardizedCoefficientsPredicting(WomensReportsof)M

ensParticipationinDomes

ticTasks

(1,womanalway

sresponsible,to5,manalwaysresponsible)

22Countries1994

MODEL1

MODE

L2

MODE

L3

b

SE

b

SE

b

SE

Constant

1.673***0.147

1.267***

0.216

2.302***

0.318

Formersocialistcountry

0.185

0.119

0.253*

0.111

0.061

0.098

PercentAutonom

ouswomen

0.010*

0.005

0.005

0.005

-0.044**

0.013

PercentAdjustermen

0.010*

0.004

-0.011

0.006

Autonomous*Ad

juster

0.094***

0.025

Fchange

2.3

1

5.6

0*

14.3

4***

AdjustedR2

0.1

1

0.2

8

0.5

9

MODE

L2

MODE

L3

b

SE

b

SE

Constant

1.662***

0.153

1.818***

0.257

Formersocialistcountry

0.194

0.124

0.130

0.152

PercentAutonom

ouswomen

0.015

0.015

0.011

0.017

PercentCooperatormen

-0.007

0.020

-0.019

0.026

Autonomous*Cooperator

0.032

0.043

Fchange

1.5

1

1.2

5

AdjustedR2

0.0

7

0.0

5

*p

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