Toward resolving the puzzle of the household division of labor:
The role of trust in specifying neoclassical economic, powerdependency, and sex-role attitude explanations1
(Word Count: 14,210)
Yoosik Youm and Edward O. Laumann
The University of Chicago
Yoosik Youm
The University of Chicago
Ogburn-Stouffer Center #357
1155.E.60th.Street.
Chicago, IL, 60637
yyoum@midway.uchicago.edu
(Voice) 773-256-6338
(Fax) 773-256-6313
Edward O. Laumann
Department of Sociology
The University of Chicago
5848.S.University Avenue
Chicago, IL, 60637
ob01@midway.uchicago.edu
(Voice) 773-702-8691
(Fax) 773-702-4607
1
Some of the results in this article were presented at meetings of the Sunbelt XIX International Social
Network Conference, Charleston, SC, February 1999 and the Population Association of America, New
York, NY, March 1999. The research presented in this paper was supported by the Ford Foundation (Grant
No. 940-1417-2) and the National Institute for Child Health and Human Development (5 RO1 HD2835603). We want to gratefully acknowledge the helpful comments and suggestions from Pierre-Andre
Chiappori, Michael Chwe, Jenna Mahay, Kazuo Yamaguchi, and Ezra Zuckerman.
1
Toward resolving the puzzle of the household division of labor:
The role of trust in specifying neoclassical economic, powerdependency, and sex-role attitude explanations
Three competing paradigms (Becker's neoclassical economic model, powerdependency theory, and the sex-role attitude explanation) have attempted to
solve the puzzle of persistent gender inequality in the division of housework,
but with mixed results. We propose ‘trust’ between the couple as the basis for
resolving this puzzle. We develop a game model adapted from the more general
form of trust games, where the trust between partners is the key contingency
specifying the relevance of neoclassical economics and power-dependency theory.
Under the condition of high trust, partners behave as if they share a unitary
utility function because they can safely assume their partners’ gain will be
their own gain. This corresponds to the argument of neoclassical economics.
Under the condition of low trust, however, partners can no longer assume a flow
of future fair rewards and thus try to decrease their share of housework by
using their resources (options outside marriage) as a threat in their
bargaining with their partners. This corresponds to the power-dependency model.
After measuring the level of trust by the social networks of the couple, we
suggest the mechanisms through which trust plays once again the key role in
specifying the relevance of the sex-role attitude explanation. High trust
increases the couple’s ability to create their own behavioral script without
relying on institutionally given gender ideology. These three hypotheses are
consistently supported by empirical data from the Chicago Health and Social
Life Survey, a cross-section representative survey of Chicago residents in
1995. In sum, neoclassical economics only has explanatory power under the
condition of high trust, while power-dependency and sex-role attitude
explanation only increase their explanatory power under the condition of low
trust.
Why don't you stay the evening kick back and watch the TV
and I'll fix a little something to eat.
Oh I know your back hurts from working on the tractor
How do you take your coffee, my sweet?
I will raise the children if you pay all the bills
...
I will wash the dishes while you go have a beer.
Where is my Marlboro man?
Where is his shiny gun?
Where is my lonely ranger?
Where have all the cowboys gone?
--- From Paula Cole’s song, ‘Where Have All The Cowboys Gone’ ---
2
INTRODUCTION
Three approaches to the household division of labor
Research drawing from three theoretical perspectives has tried to
solve the persistent puzzle posed by the division of housework between
men and women: why do women still do most of the housework even when
they are employed? Numerous studies have found that employed married
women do about twice as much housework as employed married men do,
although exact estimations vary somewhat (Geerken and Gove 1983;
Goldscheider and Waite 1991; Lennon and Rosenfield 1994; Pleck 1985;
Ross 1987). None of the three approaches, however, has provided a
compelling resolution of the puzzle and different empirical studies
have supported different approaches (Shelton and John 1996). First, we
shall critically review and compare these three perspectives
(neoclassical economics, power-dependency theory, and the sex-role
attitude explanation). Then we shall introduce the notions of
structural embeddedness and noncooperative game theory to define the
concept of trust that is the specifying condition under which these
three theories have explanatory power.
Neoclassical economic theory, especially as exemplified by Gary
Becker’s work, argues that the partner with the greater comparative
advantage in the market (for example, the higher wage rate) will
specialize in paid work and the other partner will specialize in
housework in order to maximize their shared unitary utility. This
division of labor maximizes the joint utility function of the couple
due to the greater resulting efficiency in the division of labor: the
joint payoff of a couple who adopt a division of labor based on
comparative advantage is more than the couple’s joint payoff when they
both specialize in paid work (Becker 1991). This ‘common preference’
3
(unitary utility of the couple) is guaranteed by consensus (Samuelson
1956) or altruism (Becker 1991).
The assumption of a single joint utility function, however, has been
challenged. In economics, a Nash bargaining model assuming a
cooperative game between two persons has been proposed for the
intrahousehold division of labor (Manser and Brown 1980; McElroy and
Horney 1981). In this account, the division of household labor is the
result of bargaining between two persons with separate utility
functions. According to the Nash bargaining model, a higher threat
point (i.e., the minimum welfare level if no agreement can be reached
between the players, divorce being the payoff in this case) always
decreases housework and increases paid work. Elaborating these models,
Lundberg and Pollak developed a cooperative model that replaces an
external threat point with an internal one and introduces transaction
costs (1993) and a repeated noncooperative game (1994; 1996) to explain
intrahousehold decisions. Chiappori and his co-authors have also
developed ‘collective models’ that only assume that allocations are
Pareto optimal without specifying any explicit solution process
(Alderman et al. 1995; Bourguignon and Chiappori 1992; Chiappori 1992).
All these are efforts to explain intrahousehold decisions without
relying on a single household utility function.
In sociology, power-dependency theory (also akin to exchange theory
or a resource dependence explanation), built on Blood and Wolfe’s work
(1960), corresponds to Nash bargaining models in economics. It holds
that partners bring their own resources or options as a threat in the
bargaining to increase their own power and thus, to negotiate their own
ways out of housework. The partner with more resources is less likely
to do housework and less likely to perceive a given division as fair
(Blair and Lichter 1991; Brayfield 1992; Lennon and Rosenfield 1994;
4
Presser 1994; Ross 1987). Hereafter, by power-dependency theory we will
mean both power-dependency theory in sociology and Nash bargaining
models in economics.
Providing a third perspective on the issue in contrast to
neoclassical economics and power-dependency theory, gender theory
criticizes not only neoclassical economics and power-dependency theory
but even with the sex-role attitude explanation as well. In
contradistinction to Becker’s neoclassical economics, it recognizes the
diverging and sometimes conflicting interests of family members and
stresses the need to recognize issues of distributive justice even in
caring families (Ferree 1990; Thompson 1991). Against neoclassical
economics and power-dependency theory, it also argues that the division
of housework is not just the result of economic reasoning but also the
result of ‘gender display.’ By doing housework, women display and
maintain their femininity; by avoiding housework, men display and
maintain their masculinity. Criticizing a sex-role attitude explanation
that stress only processes of gender-identity socialization as a
catchall mechanism (Lopata and Thorne 1978), gender theory emphasizes
the actual societal processes that construct and maintain gender (West
and Zimmerman 1987). Thus, according to gender theory, housework is one
of the processes whereby gender is constructed and maintained (Berk
1985; McCrate 1988; Hochschild and Machung 1990). In line with this
recent development, this paper will show specific conditions under
which individual-level sex-role attitudes and socialization become
salient for the household division of labor. A sex-role attitude
approach has explanatory power only among the couples with no trust.
New key to the puzzle: trust
5
An important lesson to be drawn from these diverse approaches is
that we must conceptualize the family as the place where both love and
bargaining (or care and struggle) coexist (Stark 1984). We must
identify the conditions under which reciprocity and altruism emerge,
rather than assume that they are always or never characteristic of
families (Ferree 1990, p. 879). Following this dictum, we shall show
that the three perspectives are not mutually incompatible but depend
for their applicability on the level of the trust between the couples.
We hypothesize that when the level of trust is high, altruism and joint
unitary utility dominates the couple’s interaction, and the reliance on
sex-role attitude decreases. But when trust is low, bargaining and
negotiation dominate their interaction and the realization or
expression of sex-role attitude increases.
We first propose to measure structural embeddedness of the couples
by their social networks. Next, we examine a game in which trust
emerges from strong structural embeddedness and becomes the contingent
factor upon which the validity of neoclassical economics and powerdependency theory depends. In the following section, we suggest the
mechanisms through which trust serves as a contingent factor specifying
the relevance of the sex-role attitude explanation. These hypotheses
about the relationship between trust level and the validity of the
three explanations are consistently supported by empirical data
presented in a later section.
STRUCTURAL EMBEDDEDNESS OF COUPLES
We measure structural embeddedness as a network characteristic of
the couple. Let’s compare the two networks in figure 1A and 1B.
----------------------------------------------
6
Figure 1A and 1B about here
---------------------------------------------In figure 1A, ego and spouse each has two friends but each partner
does not know the other partner’s friends (i.e., the two sets of
friends do not overlap). In figure 1B, in contrast, ego’s friends are
also the spouse’s friends. Couples with this kind of overlapping social
network are strongly structurally embedded. Strong structural
embeddedness facilitates trust by four mechanisms (cf. Coleman 1988;
Laumann 1973: 83-130; Sandefur and Laumann 1998). First, overlapping
networks increase monitoring efficiency. In figure 1B, the spouse can
easily check what ego did last night by asking mutual friends. Second,
an overlapping network also increases the effect of reputation (Frank
1988). If ego betrays his or her spouse, he or she will lose his/her
“face” with mutual friends. Third, an overlapping network is more
likely to elicit coordinated and shared attitudes or opinions that will
facilitate trust through mutual social support and shared activities.
Finally, because there is more mutual reinforcement and sharing of
attitudes and activities due to overlapping networks, the couple’s own
emotional commitment to one another is increased.
Through these mechanisms, strong embeddedness provides a couple with
the network capacity to build trust within the dyadic relationship
itself2. We examine how trust emerges from strong structural
embeddedness after considering the relevance of differentials in wage
rates within partnership pairs in the next game theoretic model
section. In this sense, then, we are more interested in the network
We will use ‘embeddedness’ without specifying ‘structural’ for the rest of the paper. Temporal
embeddedness (frequent and long-duration relationship) can produce the same results as structural
embeddedness as exemplified in various iterative game-theoretic models. We do not consider temporal
embeddedness in this paper.
2
7
capacity to facilitate trust than in the actual subjective levels of
trust within partnership pairs.
A TRUST GAME OF THE DIVISION OF HOUSEWORK
We use a noncooperative game model to examine the division of
housework because of two considerations. First, we believe that most
family settings that must divide housework between the partners are
tightly interdependent and thus game-theoretic in nature. A gametheoretic situation is one in which each individual’s reward depends
not only on his or her own actions but also on the actions of the other
(Elster 1983). Second, among game models, we prefer a noncooperative
rather than a cooperative game model customarily employed in economic
research on the division of housework. A cooperative model assumes
enforceable agreements as a given and is thus unable to examine the
conditions under which reciprocity and altruism (or opportunism or
betrayal) emerge in the family.3
This game is to decide between the husband and wife (or cohabiters)
who will specialize in housework and who will specialize in paid work.
Specializing in housework has two disadvantages. First, it means the
interruption of one’s career and decreased earning capacity and career
prospects. Second, it also poses another risk: the couple-specific
capital resulting from the investment of time and energy in securing
household-specific knowledge and skills is not easily transferred to
another couple. In other words, if there is a separation, he or she
3
In this connection, it is interesting that Lundberg and Pollak proposed two different views regarding
cooperative and noncooperative models. In a 1993 paper, they argued that a cooperative game model was
appropriate for studying families because families contain complex, loosely structured social interaction.
However they suggested an alternative view in papers published in 1994 and 1996 in which they contend
that noncooperative game models provide a better fit for family study for the same reasons we propose
(1993; 1994; 1996).
8
cannot readily transfer that capital to a new household that has
different eating preferences, different children, etc. In contrast to
this situation, specializing in paid work increases earning capacity
and career prospects and produces a much more general form of human
capital that can be easily transferred to another family unit. Thus
nobody has any incentive to invest in housework unless he or she can be
sure there will be a fair reward from his or her partner’s future gains
from paid work.
In this sense, we can call a person who chooses housework a
‘trustor’ and the act of choosing housework as ‘placing trust.’ In the
same vein, we shall call a person a ‘trustee’ if he or she chooses paid
work based on his or her partner’s choice of housework. A trustee has
two subsequent options. He or she can give fair rewards to his or her
partner since his or her successful career is based on his or her
partner’s sacrifice of having foregone paid work. Or, he or she can
deny fair rewards by cheating or leaving for a more attractive partner
or providing poor care for the partner. We shall call the former
behavior ‘honoring trust’ and the latter ‘betraying trust.’
We will examine two different games in the succeeding sections: a
game with weak embeddedness and a game with strong embeddedness. Before
discussing each game, let us introduce five common assumptions
applicable to both games. First, honoring trust means the equal
distribution of payoff (i.e., the utility from wages and housework)
from the division of labor between the spouses. Second, the wife and
husband are identical except that the husband has a comparative
advantage in the marketplace rather than in the household (for example,
a higher wage rate4). Third, there are gains from the division of labor
4
Even though we use a higher wage rate as an example of the comparative advantage in the market sector
here, comparative advantage defines a broader situation. Husband has a comparative advantage in the
9
in the sense that the joint payoff of the couple from a division of
labor based on the comparative advantage between the spouses is greater
than the joint payoff from the situation in which both specialize in
paid work. This assumption follows Becker’s theorem about the division
of household labor: all but possibly one member would completely
specialize based on their comparative advantage. Moreover, with
constant or increasing returns to scale of the production function, all
members must completely specialize based on comparative advantage
(Becker 1991: 33-37). Fourth, being betrayed is the worst for the
person who is betrayed. Fifth, doing housework is worse than doing paid
work, other things being equal, because of the two disadvantages
described above.
Also, note that actual decisions are continuous between pure
housework and pure paid work even though we present them, for brevity,
as dichotomous in our game model. Thus, specialization must be
interpreted with relative terms in our game models. Furthermore, no
sex-role attitude is assumed. We will examine it in a later section of
the paper.
In the next section, we examine the game assuming weak embeddedness
by adding additional assumptions and show that the equilibrium of the
game corresponds to the predictions of power-dependency theory. Next,
we develop the game with strong embeddedness and show that trust
emerges due to this strong embeddedness and thus the equilibrium of the
game corresponds to the neoclassical economic argument. Although we
shall consider some additional assumptions in subsequent sections of
market sector if the marginal product ratio of wife (vs. husband) in market sector is less than the marginal
product ratio of the wife (vs. husband) in the household sector. Thus, even if wife has a higher wage rate,
the wife has a comparative advantage in the household sector if she does better than the husband in both the
market sector and the household sector and the gap between her hourly household product and her
husband’s hourly household product is greater than the gap between her wage rate and her husband’s wage
rate.
10
the paper to generate all the possible concrete payoffs for purposes of
illustration, we shall only need the five previously defined
assumptions plus a specific assumption about a couple’s embeddedness to
identify the equilibrium for each game (please see the appendix for the
full proof).
A game with weak embeddedness: predicting the applicability
of the power-dependency model
Figure 2 shows an extensive form of the game for the household
division of labor with weak embeddedness between spouses, being adapted
from the more general form of trust games (Weesie and Raub 1996). This
model assumes that there is only negligible cost from the dissolution
of the marriage (or cohabitation) because spouses are weakly
structurally embedded5 in addition to the five assumptions specified in
the previous section6.
---------------------------------------------Figure 2 about here
---------------------------------------------Let us now examine the payoffs at the six end nodes in figure 2. The
first value before the comma in the parenthesis refers to the wife’s
payoff and the value after the comma refers to the husband’s payoff.
Table 1 summarizes the six situations.
---------------------------------------------Table 1 about here
5
Or, alternatively, we can assume that both players believe that there is only a slim probability for
‘honoring trust’ while almost certain probability for ‘betraying trust’ because they know they are only
weakly embedded: there is no monitoring mechanism, no reputation to lose, no coordinated beliefs, etc.
This alternative game theoretic modeling produces basically same output throughout the paper.
6
However, the people who are betrayed have the worst payoff because they sacrifice their career and get
nothing for doing so.
11
---------------------------------------------The wife and husband produce both paid work and housework and get
utility from both of them even though the decisions about who will
specialize in paid work and the distribution of the resultant payoff
have not yet been made. The best scenario is ‘betraying trust,’ meaning
that ego chooses paid work based on the partner’s housework (sacrifice)
and subsequently betrays the trust (note that we assume there is only
negligible embeddedness and thus there are no costs incurred from guilt
or bad reputation). We assume that if the wife betrays trust, this
brings a payoff of 12 to her and if ego is the husband, then this means
a payoff of 17 to him because we assume the husband has the higher wage
rate.7 The worst scenario is ‘spouse betrays trust’, the opposite case
to the best: ego specializes in housework and is betrayed later by the
spouse who specializes in paid work. In this case, according to
community property law, the couple splits the value of the gain from
the division of labor (the betrayer gets to take his or her wage rate
with him or her).8 For illustrative purpose, we assume 15% of the total
payoff will go to the person who is betrayed. ‘Husband honors trust’ is
the second best followed by ‘wife honors trust’. We assume that
honoring implies an equal distribution of resulting payoff from wages
and housework based on one spouse’s sacrifice (housework). Thus, if the
husband honors trust, then both spouses get 10 (20 divided by two) and
if the wife honors trust, then both get 7 (14 divided by two).
Now, we have two situations left: ‘both specialize in housework’ and
‘both specialize in paid work’. Between these two, ‘both specialize in
7
We do not, however, attempt any comparison of the payoff between husband and wife since comparison
of interpersonal well-being is not possible. Although the numbers representing payoffs are chosen
arbitrarily, the equilibrium to every game described in the paper does not change so long as the ordering
between several essential payoffs does not change (see the appendix for proof).
8
We thank one of the anonymous reviewers for this point.
12
paid work’ is better than ‘both specialize in housework’ because the
former does not entail the loss of career prospects even though both
scenarios suffer from no gain derived from the division of household
labor. Both are assumed to be better than the worst case (‘spouse
betrays ego’) but worse than ‘wife honors trust’ because there are no
gains from the division of labor in either situation.9 Thus, we assign a
payoff of 5 for ‘both specialize in paid work’ and a payoff of 4 for
‘both specialize in housework’ to the wife. For the husband, it will be
6 and 4 respectively (see table 1). The husband’s payoff from ‘both
specialize in paid work’ is assumed to be 6 instead of 5 because of his
higher wage rate.
Under this payoff structure, what will they choose? Or, in other
words, what is the solution of this game? From the wife’s point of
view, it is natural to ask ‘what will happen if I choose housework’ (or
paid work) in order to decide between housework and paid work.10 Let’s
examine the outcome when she chooses housework, the first upper branch
depicted in figure 2. Once she selects housework, her husband can
choose between paid work and housework. If he decides to do paid work,
he can honor her trust or he can subsequently betray her trust.
However, once he chooses paid work, he will betray her trust because
payoff 17 is greater than payoff 10. Knowing this, the husband will
choose paid work instead of housework once his wife chooses housework
because 17 is greater than 4. All these strategic moves are common
knowledge in the sense that both the wife and the husband know them.
That is, both the wife and husband are certain that if the wife selects
housework, the husband will choose paid work and will subsequently
9
Again this is not a necessary assumption. We make this assumption to simplify the illustration. See the
appendix for the full proof.
10
Figure 1 assumes the wife decides first. Even if husband chooses first, the equilibria of the games are not
changed for any of the games discussed in this paper, including the appendix.
13
betray her trust (the bold solid line in the upper half of the figure
2). The wife now knows that when she chooses housework, she will get 3
since her husband will betray her trust.
What if she chooses paid work? Then, the husband can decide between
paid work and housework. If he chooses housework, the wife can either
honor his trust or subsequently betray it. She will betray his trust
because payoff 12 is greater than payoff 7. Given this knowledge, the
husband will avoid housework and choose paid work because payoff 6 is
greater than payoff 4. Now the wife knows if she chooses paid work, she
will get 5 since her husband will also choose paid work (the bold
dotted line in the lower half of the figure 2).
The wife is now ready to decide. She knows that if she chooses
housework, she will get a payoff 3 because her husband will betray her
trust (the bold solid line). Also she knows that if she takes paid
work, she will get payoff 5 because her husband will choose paid work
instead of housework, knowing that she will betray his trust if he were
to take housework (the bold dotted line). Thus, the wife will choose
paid work because payoff 5 is greater than payoff 3. Once she chooses
paid work, then her husband will also choose paid work and get payoff 6
(thus the bold dotted line shows the equilibrium path in this game).
This is equilibrium11 in the sense that as long as the other person does
not change strategy, ego has no incentive to change strategy. That is,
once both players end up in this situation, both will stick to it. As
long as the spouse specializes in paid work, ego must also specialize
in paid work to maximize his or her interest. Let us emphasize once
again that even though we used all the possible payoffs for
This kind of equilibrium is called a ‘subgame-perfect equilibrium’ in game theory (Friedman 1986;
Selten 1975). It is one of the possible equilibria when decisions are made over time in the game. In our
model, the spouse can honor or betray in subsequent moves.
11
14
illustration, only the order between payoffs matters in determining
equilibrium and we need only six assumptions (the five commons
assumptions plus the assumption of weak embeddedness) to obtain the
same equilibrium of the game (see the appendix for the proof).
This solution is the result when each partner cannot trust the other
because there is no cost incurred from betrayal (or there is only a
slim chance of honoring trust) and thus, each must specialize in paid
work as much as possible in order to maximize his or her own interest.
Both partners try to maximize paid work hours (and thus, minimize
housework hours) and have to negotiate the actual hours of paid work
and housework because a minimum amount of housework must be done in
order to maintain the union.12 In other words, it is a bargaining
situation without placing trust or taking turns. In this bargaining
situation, we can assume that both will try to increase their own paid
work hours by using their options outside marriage as a threat, as many
economic bargaining models argue. As a result of such bargaining,
having more options (or resources) outside marriage means higher
bargaining power, and thus always decreases housework and increases
paid work.13 Therefore, the solution of the game with weak embeddedness
corresponds to power-dependency theory in sociology (or various
bargaining models in economics), where having more options outside
marriage decreases housework hours. Even though we assume that the
payoff will be 5 and 6 for the wife and husband, respectively, when
‘both specialize absolutely in paid work,’ the actual payoffs will be
12
Note that actual decisions are continuous between pure housework and pure paid work even though we
present them, for brevity, as dichotomous in our game model.
13
Most economic models are adapted from the Nash bargaining model. The Nash bargaining outcome is
the solution to the maximization problem: Max (u1 - d1)(u2 - d2), under the condition that u1 + u2 = u, where
u1 and u2 are the payoffs to the two individuals respectively and d 1 and d2 are the threat points or options
outside bargaining (Friedman 1986; Nash 1953). The solution can easily be derived as u1 = ½ (d1 - d2) + ½
u and u2 = ½ (d2- d1) + ½ u. It can be easily confirmed from this solution that higher threat points always
increase payoffs (or hours of paid work, here) once the other partner’s threat point is given.
15
determined by the options outside of marriage for each spouse, which
are not specified in this model.14 In the next section, we shall examine
the changed solution that arises under the condition of strong
embeddedness.
A game with strong embeddedness: predicting the
applicability of the neoclassical economic model
Figure 2 depicts a game that modifies the previous model by taking
into account the costs incurred from strong embeddedness.15 We will show
that the solution to this game corresponds to the neoclassical economic
argument.
---------------------------------------------Figure 3 about here
---------------------------------------------Let’s assume there is a cost of 816 incurred from strong embeddedness
whenever there is a betrayal. This cost includes loss of affection,
love, companionship, children, reputation, etc. We also assume that the
amount of embeddedness is symmetric, that is, the wife and her husband
share the same amount of embeddedness and, also, the same amount of
cost is incurred by the betrayer and the betrayed. Thus, whenever there
is a betrayal, there is cost of 8 to both players. The payoffs of the
game are the same as those of the previous game except in the cases
where betrayal occurs. The second node payoff changes from (3,17) to (-
14
Thus, the actual solution would contain continuous choices rather than dichotomous choices such as 98%
paid work and 2% housework, as specified in footnote 12.
15
Or alternatively, we can assume that players believe there is almost certain probability of being honored
while there is only slight chance of being betrayed. This alternative game-theoretic modeling produces the
same result.
16
The actual number representing costs does not matter so long as it is greater than 7 (the difference of the
husband’s payoffs between betrayal and honoring) so that husband prefers honoring trust to betraying trust.
See the appendix.
16
5,9) and the last node payoff changes from (12,2) to (4,-6). What is
the solution of the new game?
Again, the wife is wondering what happens if she chooses housework.
Once her husband picks paid work, he has two options: to betray or to
honor her trust. However, now he will honor her trust because honoring
trust is better than betraying trust due to the high betrayal cost of
8. In other words, the net benefit of the betrayal becomes negative,
thus there is no incentive to betray: the net benefit of betrayal in
the previous game was 7 (= 17-10), while it now is -1 (= 9-10). Thus,
the husband will get 10 by honoring her trust if he chooses paid work,
given his wife’s choice of housework. Otherwise he will get 4 by
choosing housework, given his wife’s housework. Now both partners know
that if the wife chooses housework, her husband will choose paid work
and subsequently honor her trust. This will give a payoff of 10 to both
of them (the bold solid line in figure 2).
What if she chooses paid work? Her husband can choose between paid
work and housework and if he takes housework, she can then betray his
trust or honor his trust. However, both know she will honor his trust
because now she will get only 4 instead of 12 from betraying his trust
due to the betrayal cost of 8. Given the fact that she will honor his
trust, her husband will get 7 if he chooses housework and he will get 6
if he chooses paid work. Thus, if the wife chooses paid work, her
husband chooses housework to get 7 (the bold dotted line in the figure
2).
Now the wife is in a position to decide. She will choose housework
instead of paid work because the former brings her payoff 10 (the bold
solid line) while the latter brings her only 7 (the bold dotted line).
In the game with strong embeddedness, the wife can trust her husband
since she knows her husband will not betray her because of the high
17
cost of betrayal, and this allows the wife to specialize safely in
housework (thus, the bold solid line shows the equilibrium of the
game). Again, this is the equilibrium solution in the sense that no one
has an incentive to change his or her strategy as long as the spouse
does not change his or her strategy. As long as the wife specializes in
housework, the best strategy for the husband is to specialize in paid
work and honor the trust. Also, as long as the husband specializes in
paid work and honors the trust, the best choice for the wife is to
specialize in housework. Again, please note that we only need the six
assumptions we specified to get a unique equilibrium that corresponds
to neoclassical economics even though we examined all the possible
payoffs for purposes of demonstration (see the appendix for the full
proof).
The game shows how trust emerges from strong embeddedness. The
couple behaves as though they share one utility function because they
are strongly structurally embedded: the husband’s gain is the wife’s
gain. This equilibrium is identical to the prediction of neoclassical
economics: the person with the higher wage rate will specialize in paid
work while the other will specialize in housework to maximize the
unitary utility function of the couple.
The emergence of trust from embeddedness
In the first game with weak embeddedness, neither partner can place
trust in the other because each knows the other partner will
subsequently betray their trust. In the second game with strong
embeddedness, however, each partner knows that the other partner will
not betray his/her trust because of the costs incurred, and therefore,
18
that each can trust the other.17 The trust emerging from this strong
embeddedness permits each player to assume that their partner’s gain is
their own gain and thus that they can act as though they share a
unitary utility function and fulfill the prediction of neoclassical
economics.
How much embeddedness is necessary to produce trust in these games?
In the game with weak embeddedness, the net benefit from betrayal is 7
(= 17-10) for the husband and 5 (= 12-7) for the wife. If the cost of
betrayal from embeddedness is less than 5, then the net benefit from
betrayal is still positive for both partners, and neither can trust the
other. If it is more than 7, then the net benefit from betrayal is
negative for both partners, and both will trust each other. If the cost
ranges between 5 and 7, only the husband can trust the wife because the
net benefit from betrayal is negative for the wife while it is still
positive for the husband. Thus, as long as the cost from embeddedness
is less than 5, neither partner will trust each other and the
equilibrium of the game is the same as the one in the game with weak
embeddedness (figure 1). As long as the cost is more than 7, both will
trust each other and the equilibrium is the same as the one in the game
with strong embeddedness (figure 2).18
Emergence of trust thus depends on the amount of comparative
advantage in the market (the wage rate in our example) for each spouse
in addition to the embeddedness level of the couple. Identical levels
of embeddedness can produce different results (trust or no trust),
depending on the wage of each spouse. Thus, embeddedness and trust are
Here we are not talking about ‘blind trust.’ Somebody can place trust in another only if he or she can
expect that the other will keep his or her promises based on the available options and their consequences
(Dasgupta 1988). In other words, trust is not defined in situations in which the potential loss is greater than
the potential gain (Coleman 1990).
18
Middle-range embeddedness case in which betrayal cost ranges between 5 and 7 is examined in the
appendix.
17
19
distinct concepts. Because it is a practical impossibility to obtain
for the actual costs from embeddedness and the potential wage rates for
each spouse from extant data sets, we propose to measure trust with the
level of embeddedness characterized by a couple’s social network. This
simplification, however, is not overly problematic in later OLS
analyses because most demographic factors including wage rates are
controlled for and thus stronger embeddedness entails higher trust in
general (cf. Sandefur and Laumann 1998). We also defer to the appendix
the discussion of the case where only one spouse can have trust in the
other (an instance of the middle-range embeddedness discussed above).
MEASURING SEX-ROLE ATTITUDES
In line with the recent development in gender theory, we argue that
individual-level sex-role attitudes are not self-evident, comprehensive
operationalization of gender theory itself. That is, gender theory is
concerned with probing more deeply into the actual societal processes
upon which the realization of attitudes is contingent. We contend that
the effects of sex-role attitudes on the division of housework are also
contingent on the level of trust. Strong embeddedness that facilitates
trust decreases the effects of sex-role attitudes. As the trust level
goes up, couples are more likely to share coordinated attitudes and
thus to establish couples’ own specific behavioral scripts regarding
the division of housework. Without trust, there is no option but to
rely upon institutionally given sex-role attitudes to solve the issue
of the division of housework. If there is trust, however, couples can
20
discuss and negotiate the issue and, by trial and error, establish a
behavioral script appropriate to their particular situation.19
Table 2 summarizes our hypotheses that trust plays the key role in
specifying the validity of three major paradigms in accounting for the
household division of labor. Under high trust, only neoclassical
economics is valid in predicting the division of housework. Powerdependency theory and sex-role attitude explanation gain significance
only as the level of the couple’s trust goes down.
---------------------------------------------Table 2 about here
----------------------------------------------
DATA AND MEASURES
Before presenting the regression results, let us briefly describe
the data and measures.
Data
19
A similar line of argument can be found in network research revolving around the concept of role. In her
seminal work, Bott (1957) showed that the highly interconnected couples produced less specialized
division of labor (one of the criteria for highly interconnected couples is sharing the same friends and
leisure activities so that spouses less connected to their respective cliques of same-gender friends and
consanguine friends). Burt (1992: 254-60) refined it by contending that such couples (or high trust couples
in our paper) have more structural autonomy that enables them to be more responsive to each other than to
any external influences and thus to have lower sex-role segregation. Even though our argument produces
the same prediction regarding the division of household labor, there is a basic difference: a role explanation
implicates the process through which role identity is shaped and maintained while the trust argument
underscores the social mechanism through which sex-role attitudes are actually realized or expressed in a
relationship, even after sex-role attitudes (or sex role identities) are given. We believe that, based on two
facts, the trust mechanism is effective independently of the role-identity process. First, there is no
attitudinal difference regarding the breadwinner question between the high trust and low trust people: 39%
of the low trust respondents agreed or strongly agreed with the breadwinner statement while 31% of the
high trust people did. Second, sex-role attitudes are significant only among the low trust people, as table 5
will reveal. Among the high trust couples, even though they may believe in a strong gendered division of
labor, the sex-role attitude is not expressed in the couple’s actual division of household labor.
21
The Chicago Health and Social Life Survey (CHSLS) provides a unique
data set for exploring these issues. While the CHSLS consists of a
total sample of 2,114 in Chicago and its environs, including a
representative sample of Cook County plus cross-section samples of four
selected neighborhoods, we shall use only the Cook County cross-section
sample of 890 collected in 1995 by face-to-face interviews averaging
90-minutes in duration.20 From these 890 respondents, we selected only
those who were heterosexual and living with their sexual partner at the
time of the interview, and excluded students, resulting in a final
sample of 396 respondents. While the final sample is modest in size,
the data set is unique in containing both detailed housework questions
and social network questions that are essential for measuring the level
of trust for each respondent.
Dependent Variable: natural log of housework hours per week
The respondent was asked: “Please tell me how many hours a week you
spend and how many hours a week your partner spends doing each of the
following tasks?” The question included eight tasks: preparing meals,
washing dishes, cleaning house, outdoor tasks, shopping,
washing/ironing, paying bills, and childcare. We summed the hours for
all eight tasks, truncated at a maximum of 120 hours per week, in order
to calculate the total number of housework hours per week spent by
respondents. This truncation was also used by Lennon and Rosenfield to
reduce overestimation (1994). We then, took the natural log of the
total number of hours of housework as the dependent variable since the
20
We dropped the data from the four neighborhoods because they are heavily over-sampled relative to the
cross-section sample and would thus contribute, with appropriate weighting, only 3 or 4 cases to the crosssection count if we want to preserve the cross-section’s representativeness.
22
distribution is highly skewed to the right (logging is applicable to
every respondent since the minimum hours of housework is set at two).
Unlike many studies that exclude childcare hours (Blair and Lichter
1991; Brines 1994; Ferree 1991; Lennon and Rosenfield 1994), we include
them in the total number of housework hours, following other research
(Coverman 1983; Shelton and Firestone 1989). Although we readily
acknowledge that including childcare hours overestimates total
housework hours to some unknown extent because of the substantial
overlap likely between childcare and other housework, we include them
because it is non-discretionary and thus a more specialized household
activity. While people can often arrange their other household chores
to suit their convenience, people providing childcare must be ready to
do so at any time. Although it may require the same amount of hours as
other chores, it does not allow people arrange their life according to
their own needs but to their children’s needs. Due to this special
property of childcare, the person providing childcare is more
specialized in housework than the person who isn’t. Thus, instead of
excluding childcare hours, we limited housework hours to 120 hours per
week to minimize overestimation.
Table 3 shows that the estimations from the CHSLS are generally
consistent with other data sets. There are no significant differences
in any of the comparisons between the National Survey of Families and
Households (or Quality of Employment Survey) and the CHSLS.
---------------------------------------------Table 3 about here
----------------------------------------------
23
We could not run regressions by using both spouses’ housework hours
because we do not have matched-pair data. Even though we asked the
respondent about their spouses’ housework hours, there is a great
discrepancy between the reported housework hours for each gender. For
example, male respondent answered that their spouses were doing 46
hours a week on average while female respondents reported they were
doing 66 hours of housework a week. As a result of such big
discrepancies, we could not get consistent results. We do not, however,
think our alternative regressions using only respondents’ self-reported
housework hours are seriously problematic for two reasons. First, our
model applies across couples in the sense that more wage gap or the
greater the resource gap means the greater the specialization for all
couples. Second, our regressions do contain couples’ information as
independent variables, including the wage gap and the options outside
marriage. Respondent-only housework hours were used in several research
studies without serious measurement problems (for example, Brines,
1994)
Natural log of weekly wage ratio
While we directly asked the respondents about their own wage rates,
we must estimate the partner’s wage rate because we had not directly
asked about it. We first ran an OLS regression of the natural log of
the wage rate per week of the respondent by using the respondents’
years of schooling, years of job experience, gender, and race as
predictors.21 Based on the result of this OLS equation, we estimated
each partner’s natural log of their weekly wage rate based on his or
Years of schooling were estimated from the respondent’s highest academic degree, such as high school
graduation, bachelor’s degree, etc. Years of experience is calculated by using a formula of (age - years of
schooling - 6) as is conventionally done in economic research (Murphy and Welch 1992; Murphy and
Welch 1993).
21
24
her years of schooling, estimated years of job experience, gender, and
race.22 The wage gap is calculated as the gap between: “natural log of
respondent’s wage rate” minus “natural log of partner’s wage rate”.
This becomes the natural log of the wage ratio.
Options outside marriage/cohabitation
Following Lennon and Rosenfield’s measure of perceived options
outside marriage (1994), we asked the following question: “Even though
it may be very unlikely, think for a moment about how various areas of
your life might be different if you and (PARTNER) separated. For each
of the following areas, how do you think things would change?” Response
categories ranged from 1 (= much worse) through 5 (= much better). We
selected two areas: expectations of change in the standard of living
and in overall happiness23. Treating these variables as continuous fits
the data better than other options, such as treating them as
categorical measures or combining them into a single measure.
We only measure perceived options rather than measuring objective
indices for options outside marriage, such as education level or income
level. Even though earning gap (Blair and Lichter 1991, Presser 1994)
or education level (Bergen 1991; Coverman 1985; Ishii-Kuntz and
Coltrane 1992; Kamo 1994; Ross 1987; Spitz 1986) has often been
proposed as a proxy for options, it suffers from many problems. First,
higher education does not always lead to a higher threat point because
the spouse is also likely to have higher education due to homogamy.
22
The equation is as follows: log(weekly wage rate) = -3.575 +1.017*(years of schooling) -0.025*(years of
schooling)2 + 0.063* (years of job experience) - 0.001*(years of job experience)2 - 1.011*women 0.515*African American
23
Questions were also asked about ‘social life’, ‘sex life’, and ‘parenting’. But we only include ‘standard of
living’ and ‘happiness’ areas because everybody places different priorities on ‘parenting’ and overall
happiness seems to subsume ‘social life’ and ‘sex life’ conceptually. Preliminary OLS regressions confirm
the notion that social life and sex life are strongly related empirically to the measure of overall happiness.
25
Second, even resource gap between spouses does not measure options
outside marriage. Threat in bargaining comes not directly from
bargainers’ resource gap but from potential alternative options in the
case of dissolution. Even though a woman has much lower education (or
wage) than her husband, if she can find a better husband with higher
wage (than the current husband’s wage) who will spend more time on
household chores, she can demand more housework from the current
husband. Simple measures of resource level (either in absolute or
relative) cannot gauge the potential welfare in the case of
dissolution. Potential welfare depends on critical parameters of
marriage market such as age, physical attractiveness, earning capacity,
and occupational prestige that will work for each gender in a different
way. Third, earning gap or education is also closely correlated with
other alternative explanations. Earning gap measures comparative
advantage in market sector in neoclassical economics an education is
highly correlated with sex-role attitudes (also with comparative
advantage in market sector). For example, higher education leads to
more housework for men with contrast to power-dependency argument
(Bergen 1991; Brayfiled 1992; Presser 1994) and even though higher
education leads to less housework for women, it can be also interpreted
as sex-role attitude effect rather than power-dependency (Huber and
Spitze 1983). Fourth, objective options are not effective unless they
are perceived and thus, used as threats in bargaining. All these
problems are applicable to most objective measures of options outside
marriage (or cohabitation).
For these reasons, we decided to include only subjectively perceived
options in our analysis at the risk of under-specification of options
outside marriage. In particular, under-specification is not so serious
a problem in our analysis because our primary goal is not to check if
26
an effect is significant or not but to examine systematic change in
significance across different trust levels.
Sex-role attitudes
Two items were used to measure sex-role attitudes. One item asked
respondents how much they agreed (on a 1 - 4 scale) with the following
statement: “It is much better for everyone if the man earns the main
living and the woman takes care of the home and family”. We reversed
the score for this item to measure liberalness of a respondent’s
attitude, treating it as continuous after examining several options.
The second item measured the extent of emotional closeness the
respondent felt toward the same-sex parent when he or she was a child.
This is coded 1 if there was no same-sex parent or no same-sex parent
substitute present. It has value of 3 if the respondent reported
feeling ‘very close’ to the same-sex parent. Otherwise, the respondent
received a “2” for reporting feeling ‘somewhat close’ to ‘not at all
close’ to the same-sex parent. The use of this item was suggested by
the work of Hochschild and Machung (1990), who found that men who
expressed less affiliation with a detached, absent, or overbearing
father spent more hours on housework than those who reported feeling
close to their fathers, suggesting a differential internalization of
the male role model. Again this variable is treated as continuous after
testing other options.
Trust of the couples
As suggested in figure 1A and figure 1B, trust is a function of two
components. First, we measure the overlap of the couple’s respective
networks of friends. To do this, we asked respondents to enumerate up
to six of their friends, including up to three free-time partners and
27
up to three discussion partners, and to specify the relationship
between each of these social network intimates and the respondent’s
cohabitor/spouse. Second, we wanted to measure the relative exclusivity
of the couple’s free time together as an indicator of the strength of
the dyadic tie. The raw values referring to shared free time come from
responses to the following question: “During your relationship with
(PARTNER), about how much of your free time did you spend with
(PARTNER)?” Responses include: all, most, about half, some, very
little, none. We coded trust as high only if ‘all’ or ‘most’ of the
respondent’s free time is shared with his/her spouse/cohabitor and all
the respondent’s friends know the spouse/cohabitor. (If, however, the
social intimates know the spouse/cohabitor but do not get along with
him/her, we coded the relationship as low trust.) Any other pattern of
ties between social intimates and the spouse/cohabitor are coded as low
trust.24 Thus, trust is a dichotomous variable: high and low. Treating
the variable as dichotomous fits the data better than other options,
such as treating them as continuous or as a categorical variable with
more than 2 categories.
Other control variables
Gender, race/ethnicity, age, family income, cohabiting, living with
children under 18 or younger, and education are included as control
variables. Square terms of age and family income were also included in
all the regressions to identify curvilinear effects, but none was
found. Also, we examined the interaction terms between gender and
race/ethnicity, but none was significant. Accordingly, we eliminated
24
As a result of this calculation, we had to drop 37 people who had no friends in addition to their spouses.
28
the square and interaction terms from the regressions to get more
accurate estimates.
Table 4 shows summary statistics for all the variables included in
the final regressions. We present means with standard deviations for
the continuous variables and the percentage distributions for the
categorical variables.
---------------------------------------------Table 4 about here
----------------------------------------------
RESULTS
In order to test our hypotheses that claim the level of the trust as
a contingent factor in specifying the validity of each of three
approaches, we ran OLS regressions to examine if the size and
statistical significance of coefficients representing each approach
change as trust level varies, as summarized in the table 2. Table 5
presents the OLS regression results for the neoclassical economic,
power-dependency, and sex-role attitude models as well as all-combined
models. Every model has three versions: for all the respondents, for
those with low trust only, and for those with high trust only. We ran
regressions separately by trust level instead of treating the trust
level as a variable because the trust variable interacts with many
variables, as shown in table 5. Since the dependent variable is logged,
coefficients must be interpreted as the percent change in housework
hours per one unit increase in the independent variables.
---------------------------------------------Table 5 about here
----------------------------------------------
29
Evaluating the three approaches
The explanation advanced by neoclassical economics is evaluated by
the variable, ‘the log of the wage ratio between the respondent and
his/her spouse.’ Model 1, which includes only control variables and the
log of the wage ratio, shows that the wage gap is significant at 1%
alpha level. A one percent increase in the wage ratio decreases
housework by 8%. This exactly follows the neoclassical economic
prediction. Spouses with the higher wage rates are more likely to
specialize in paid work. However, the strength of the wage gap effect
in predicting the division of housework changes as the trust level
changes. As the trust level goes up from model 1L to model 1H, both the
size and statistical significance (measured by absolute t-values in
parentheses) of the coefficient increases by about 100%. As people have
more trust, they are more likely to conceive their spouses’ gain as
their own gain and thus, they act as though they share one utility
function. This makes the neoclassical economics argument more powerful
in predicting the division of housework among couples with high trust.
This relationship is maintained even in models that take all the
variables into account (all-combined models), which will be examined in
the next section.
To evaluate the power-dependency explanation in model 2, we used two
variables: expectation for change in the standard of living and in
overall happiness. As the power-dependency theory argues, expectation
of an improvement in the standard of living if the partnership should
fail decreases housework hours: one unit more option decreases
housework by 10% (see table 4 for details about the measurement unit).
A change in expectations for overall happiness, however, has no
significant impact on housework hours once expectation of living
30
standard is taken into account. Even though both options lose
significance when they are included in model 2L and model 2H due to
decreased small sample size, our hypothesis that the strength of the
option effect in predicting housework hours will decrease as trust
level goes up is partly confirmed. As trust level increases from model
2L to model 2H, the option for improved living standard loses its
statistical significance by 65% (from 1.4 to 0.5 in absolute t-values)
and also loses its effect size by 60% (from -0.1 to -0.04). Couples
with lower trust are more likely to be in a bargaining situation (when
compared to high trust couples) to decide the division of housework and
options outside marriage become more important in deciding the
household division of labor. The option for improved happiness does not
change its significance based on trust level from model 2L to model 2H
but both options follow our prediction in the all-combined models to be
discussed below that has much better specification due to the
simultaneous inclusion of all the variables.
The sex-role attitudes explanation is represented by two indicators,
the liberal attitude toward the ‘breadwinner’ question and ‘closeness
to the same-sex parent’ when the respondent was a child. In model 3,
liberal males are likely to do 11% more housework than males who are
one unit more conservative (see table 4 for the measurement unit). On
the other hand, liberal women are likely to do 15 % less housework
(0.11-0.26=-0.15) than women who are one unit more conservative. Thus,
liberalness increases the equal division of housework. Closeness to
same-sex parent is not significant in model 3. However, all four
variables (including interaction terms with women) follow our
prediction as we move from model 3L to model 3H. As trust level goes up
from model 3L to model 3H, all variables lose their statistical
significance and the size of the effect by more than 60% except ‘close
31
to same-sex parent’. However, ‘close to same-sex parent’ changes its
signs and also its interaction term with women loses its statistical
significance in model 3H. Thus, regardless of sex, people who were
closer to their same-sex parent are more likely doing housework. This
result challenges our initial interpretation of the variable and
requires some re-interpretation of the variable. This variable may
serve as a proxy for a family-oriented ideology in model 3H while it
stands for a version of sex-role attitude in model 3L. We will discuss
this in detail in the next section.
All-combined Models
The model 4 is the same model we have seen in previous research: the
all-combined model but without specification of trust level. The
conclusion might be drawn that neoclassical economics and sex-role
attitude toward the breadwinner are valid even when all the variables
are taken into account, while power-dependency theory and closeness to
same-sex parent possesses no explanatory power. Once we add trust as a
contingent factor, however, the equations tell a very different story.
With respect to the expectations of neoclassical economics, the wage
gap is not significant, even at the 10% level among those who are in
low trust partnerships (model 4L). Among those in high trust
relationship, however, the wage gap becomes significant even at the 1%
level (model 4H). Moreover, the size of the effect grows from 4% to
11%. Among those in low trust partnerships, the wage gap makes no
difference in determining housework hours. Even when persons have lower
wage rates than their partners, they must maximize their own paid work
because they cannot safely assume that their sacrifice of job careers
for spouses’ careers will be repaid in the future. Figure 4A shows how
32
the significance level of the wage gap, which is represented by the
absolute t-value, increases as trust level goes from low to high.
---------------------------------------------Figure 4A about here
---------------------------------------------Although options outside marriage/cohabitation are not significant
in either model because of under-specification and small sample size as
we mentioned earlier, the absolute t-values do move in the direction
predicted by our hypothesis. The absolute t-values (values in the
parentheses) are decreased at least by 90% when the level of trust goes
up (from 1 to 0.1 or from 0.7 to 0.0). Also, the size of the effect is
decreased to almost zero when the trust level is high. This confirms
our argument that when the trust level is high, people stop behaving as
if they have separate interests and act more in accord with a shared
unitary utility function. Options outside marriage/cohabitation gain
significance when people have lower trust. This is summarized in figure
4A via the absolute t-values. We believe the fact that both do not
obtain statistical significance in both models reflects the inadequacy
of our measure rather than the failure of power-dependency theory. The
relative level of options outside marriage/cohabitation is not easily
measured since it requires subjective judgments responding to many
complex factors such as potentially available new partners, new jobs,
etc. We believe, however, these two variables are sensitive enough to
indicate how the validity of power-dependency theory changes as the
level of trust changes.
Under conditions of low trust, both items for the sex-role attitude
explanation (‘attitude toward breadwinner’ and ‘closeness to same-sex
parent’) attain statistical significance (even though the breadwinner
item is not statistically significant, its interaction term with women
33
is significant, which means we need both for proper interpretation).
Liberal males do housework 8% more than males who are one unit more
conservative while liberal women do 19% (0.08-0.27=-0.19) less
housework than women who are one unit more conservative. If males were
close to their father, then do 23% less housework than males who were
less close to their fathers by one unit (see table 4 for detailed
information about the unit measure). However, if women were close to
their mother, they do 5% (0.28-0.23=0.05) more housework than women who
were less close to their mother. We can interpret this as differential
sex-role internalization. For men, being closer to their fathers means
stronger internalization of masculinity norms and for women, being
closer to their mothers means internalization of stronger femininity
norms. This confirms Hochschild and Machung’s argument that the only
recurring theme they could discover had to do with the son’s
disaffiliation from a detached, absent, or overbearing father for
explaining who does housework chores (1990).
Under the condition of high trust, however, the story changes.
First, the attitude toward the breadwinner, including an interaction
term with women, becomes insignificant even at the 10% level. Thus,
attitude about who must be the breadwinner becomes insignificant in
deciding the division of household labor. The interaction term between
women and closeness to same-sex parent also becomes insignificant.
Thus, regardless of sex, people who were one unit closer to their samesex parent are doing 30% more housework. The interpretation of this
unexpected result follows below.
Figure 4B shows how the significance of sex-role attitude’s effect
changes, depending upon the level of the trust. Attitude toward the
breadwinner declines in statistical significance by about 86% (0.7 to
0.1). The interaction between women and the attitude toward the
34
breadwinner also loses its statistical significance by 70% (from 2 to
0.6). Closeness to same-sex parent does not lose its significance, but
its interaction term with women becomes insignificant and the direction
of effect changes from negative to positive. We can suspect that under
the condition of high trust, the effect reflects a more family-oriented
ideology rather than sex-role attitude per se. This family-oriented
ideology increases housework hours regardless of sex. As the level of
trust goes up, the odds couples can establish rules for the division of
household labor specific to their own situation increases. If the level
of trust is low, couples have no option but to rely upon
institutionally given sex-role attitude.
---------------------------------------------Figure 4B about here
----------------------------------------------
Interpretation of control variables
Let’s consider the results pertaining to the control variables now.
The result of model 4 (the all-combined model that includes everyone
without specifying trust level) will be discussed to exemplify this
interpretation. African Americans are likely to do 17% more housework
than whites regardless of gender. Also, being a year older means 2%
less housework. If people live with children (18 years or younger),
they are likely to do 57% more housework.
Cohabiting interacts with gender. Cohabiting increases housework by
20% for male (even though the main effect of cohabiting itself is not
significant, we include it for interpretation because the interaction
effect is significant). Thus, if a man is cohabiting, he is likely to
do 20% more housework than a married man. However, if a woman cohabits,
then she is likely to do 33% less than a married woman (0.2-0.53=-
35
0.33). This shows that people do housework more equally when they are
cohabiting than when they are married. On average, however, women are
likely to do 150% more housework than men.
The education effect also depends on gender. For example, college
graduated men are likely to do 50% more housework than men with less
than a high school education (less than high school education is the
reference group). However, women with a college education are likely to
do only 7% (0.5-0.43=0.07) more housework than women with less than a
high school education. This suggests that people who have more
education have a more equal division of housework.
In addition to the new interpretation of the three major approaches,
partitioning people by trust level gives us better insight into the
effects of cohabiting and education. Cohabiting makes a difference in
models that do not specify trust level such as model 1, model 2, model
3, and model 4 (interaction between sex and cohabiting is significant
at 1% or 5% level). Once we run regressions separately for the people
at different levels of trust with all the variables taken into account
as in model 4L and model 4H, however, the effect is greatly decreased
(significant at 10% in model 4L and not significant even at the 10%
level in model 4H). Cohabiting leads to a more equal household division
of labor in models that do not partition people by trust level, even
after controlling for other factors such as age, attitudes, and
education. Cohabiting makes a difference because cohabiting couples’
embeddedness level is lower than married couples’ embeddedness in
general and thus the cohabiting couples lack the trust that makes a
strong division of labor possible (only 36% of cohabiting people have
high trust when compared to 46% of married people in our data set).
However, if a cohabiting couple has high trust, then they should behave
just like married couples. This is confirmed in our regressions. Once
36
trust level is controlled in model 4L and model 4H by partitioning, the
difference between cohabiting couples and married couples is greatly
decreased because the difference derives from the level of trust, not
from marriage per se.
The effect of education is also greatly decreased in models that
applied only for people with the same level of trust (such as model 1L,
1H, 2L, 2H, 3L, 3H, 4L, and 4H), as the specifications for other
variables are improved. The education effect might operate through the
wage gap, options outside marriage/cohabitation, and especially through
gender attitudes in models 1 through 4. As our specifications for the
wage gap, options outside marriage/cohabitation, and sex-role attitudes
are improved in models that partition people by the level of trust, the
education effect is decomposed into these three effects as well, and
thus loses much of its significance. Education has statistically
significant effects in all models that do not partition people (such as
model 1, model 2, model3, and model 4) while it loses most of its
significance in other models that apply only for the people with the
same trust level. We also improved R-square by about 10% with the same
set of variables by introducing the level of trust in all-combined
models (from 0.48 to 0.53 or 0.52)25.
DISCUSSION AND CONCLUSION
Why do women do most of the housework? This seemingly simple puzzle
has provoked numerous research efforts drawn primarily from three
theoretical perspectives, but without consistent answers. Instead of
25
Various diagnostic measures show that model 4L and model 4H are free from heteroscedasticity, nonnormality, and collinearity, which are common problems of linear regressions. Nine regressions for models
1 through 3H suffer from one or another of these problems even though they are not so serious as to vitiate
the results.
37
treating them as inherently incompatible, we have argued that the
relative levels of trust between spouses can be used to specify the
conditions under which the several approaches have explanatory power.
The level of a couple’s trust is assessed sociologically as measured by
the characteristics of the social network in which the couple is
structurally embedded. The divergent paths taken by neoclassical
economics and power-dependency theory are elaborated by our gametheoretic model operating under the constraints imposed by different
levels of structural embeddedness. In addition, we try to show how
structural embeddedness works as a direct mechanism to facilitate trust
and then as a conditional factor upon which the realization of
individual-level sex-role attitudes depends.
OLS regressions, as summarized in Figures 4A and 4B, reveal that the
neoclassical economic approach prevails under conditions of high trust
while power-dependency theory and the sex-role attitude explanation
prevail under conditions of low trust, as our hypotheses predicted.
Partitioning couples by the level of trust also improves model fit and
thus provides new insights into the effects of cohabitation and
education. Different mechanisms are operative as a function of the
level of trust. Failure to specify the level of trust confounds
different mechanisms and produces mixed results.
But there are also some important limitations of our analysis that
suggest promising directions for future work. First, our measurement of
housework hours is unsatisfactory because we lack matched-pair data on
the couples. Future work needs to gather such data for a more
convincing estimation of the division of household labor. But even with
such data, we must be alert to the possibility that self-reported
housework may also be subject to systematic biases between the genders
that produce inconsistent results. Second, although we avoided the
38
pitfalls of using education and the couple’s earning gap as proxies for
the couple’s power-dependencies, we must acknowledge that our measure
of perceived options is also inadequate in specifying fully the power
dependencies within the couple. Future work must develop more
appropriate questions to quantify perceived options outside the
relationship.
Third, while this study treated the division of household labor as a
consequence of the gender wage gap, power-dependency, and sex-role
attitudes, the causal order could be the reverse. For example,
subjecting women first entering the labor market to gender-linked wage
differentials due to work-place discrimination may subsequently widen
the wage gap and create greater power dependencies over time, thus
leading to a self-fulfilling process of enhanced gender disparity after
several years of labor force participation.26 Our paper, being limited
to cross-section data, thus can cast no light in sorting out the causal
directions of the several processes we have featured in our analysis.
Only longitudinal data can do this, and gathering such data should be a
priority in future research.
As a final comment, we believe that valuable insights into the
empirical world have been gleaned by exploiting the analytic rigor and
clarity of game theory in helping us discern the divergent implications
of different levels of trust and cooperation on individual behavior in
non-zero sum, noncooperative games. We were led to a close
consideration of how systematic differences in the equilibria of
different games might translate into diverging empirical trajectories
for couples differently circumstanced with respect to their levels of
mutual trust. In the real world, the logic of the games is not
26
For example, Shelton and Firestone showed that part of the gender gap in earnings directly attributable to
women’s greater household labor time (Shelton and Firestone 1989).
39
transparent in the sense that everyone can accurately perceive his/her
own and his/her partner’s payoffs from the very outset. If that were
the case, many would never have married or decided to live together in
the first place. Only time can fully disclose the underlying payoff
matrix. It is for this reason that not every couple in a cross-section
survey occupies the equilibrium point for its respective game. Many may
be in process toward their equilibrium end point. In short, the
analytic deductions implied by the different games are not
deterministically set but only stochastically approximated in the real
world. In addition, of course, lack of fit of the empirical data with
the analytic deductions of game theory arises because of the many
imperfections in the measurement of the key variables driving the
models that were noted above.
40
Friend1
Friend1
Ego
Spouse
Ego
Friend 2
Spouse
Friend 2
Figure 1A. Weak structural embeddedness
Figure 1B. Strong structural embeddedness
41
(10 , 10)
Assumptions
Honoring Trust
Husband
1. The couple is weakly embedded
: if betrayal occurs, there is
no cost incurred by either
partner.
Betraying Trust
Paid Work
Husband
(3 , 17)
Housework
Housework
(placing trust)
2. Honoring trust means equal
distribution of joint payoff.
3. The wage rate is higher for
the husband.
(4 , 4)
Wife
(5 , 6)
4. There are positive gains from
the division of labor.
Paid Work
5. Being betrayed is the worst.
Paid Work
(7 , 7)
Husband
6. Specializing in housework has
disadvantages.
Housework
(placing trust)
Honoring Trust
Wife
Betraying Trust
(12, 2)
Figure 2. A noncooperative game with weak embeddedness implying the predictions of power-dependency theory
42
(10 , 10)
Assumptions
Honoring Trust
Husand
1. The couple is strongly embedded
: if betrayal occurs, both
partners incur a cost of 8.
Betraying Trust
Paid Work
Husband
(-5 , 9)
2. Honoring trust means equal
distribution of joint payoff.
Housework
Housework
(placing trust)
3. The wage rate is higher for
the husband.
(4 , 4)
Wife
4. There are positive gains from
the division of labor.
(5, 6)
Paid Work
5. Being betrayed is the worst.
Paid Work
Husband
(7 , 7 )
6. Specializing in housework has
disadvantages.
Housework
(placing trust)
Honoring Trust
Wife
Betraying Trust
(4 , -6 )
Figure 3. A noncooperative game with strong embeddedness implying the predictions of the neoclassical economic model
43
Figure 4A. Changes across levels of trust
in absolute t-values of the wage rates
and options outside relationship
Figure 4B. Changes across levels of trust in
absolute t-values of gender attitude
and closeness to same-sex parent
:’*W’ means interaction term with women.
44
Honoring Trust
Husand
t=1
Betraying Trust
Paid Work
Husband
t=2
Housework
Housework
(placing trust)
Wife t=5
Paid Work
Paid Work
t=4
Husband
Housework
(placing trust)
Honoring Trust
Wife
t=3
Betraying Trust
Figure A1. A non-cooperatitve game of the division of household labor
45
Table 1. The summary of payoffs for the game with weak embeddedness
Strategy
Husband betrays wife
Wife betrays husband
Husband honors wife’s trust
Wife honors husband’s trust
Both specialize in paid work
Both specialize in housework
46
Wife
3
12
10
7
5
4
Husband
17
2
10
7
6
4
Table 2. Hypotheses on the relationship between the level of trust and the import of each paradigm
Trust level
The significance of
effects in predicting the
division of housework
Low trust
High trust
Low
High
Power-dependency theory
High
Low
Sex-role attitude theory
High
Low
Neoclassical economics
47
Table 3. The comparison of mean housework hours
NSFH*
CHSLS
Males
Females
Males
Females
Meal preparation
2.3 (3.2**)
9.5 (6.3)
3.7 (4.8)
9.9 (8.6)
Washing dishes
1.7 (2.4)
5.7 (4.3)
2.3 (2.9)
5.0 (5.5)
Cleaning house
1.5 (2.3)
7.6 (6.1)
3.3 (5.0)
8.1 (7.3)
Work Outdoor
4.5 (5.0)
1.7 (2.9)
3.5 (4.9)
2.4 (3.3)
Shopping
1.3 (1.6)
2.9 (2.1)
2.7 (3.0)
4.5 (5.4)
Laundry
0.6 (1.3)
4.1 (3.2)
1.7 (3.5)
5.6 (4.9)
Paying bills
1.2 (1.6)
1.6 (1.9)
1.7 (5.3)
1.3 (1.5)
Childcare***
12.1 (16.6)
33.0 (35.2)
13.3 (19.4)
28.2 (32.8)
Total
25.2
66.1
32.2
65
* 1988 National Survey of Families and Households (Blair and Lichter
1991).
** All the values in the parentheses are standard deviations.
*** For this item only, the reference data are the 1977 Quality of
Employment Survey (QES) for employed white people (Coverman 1983).
Values are based on the estimation for spouses by respondents. We used
these values because Coverman only provides the standard deviations for
these estimations.
48
Table 4. Summary statistics of variables for regressions
Mean
housework per week
race
gender
age
family income
(thousand dollars)
living with children
(18 or younger)
cohabiting
education
log (wage ratio)
option: standard of
living
option: overall
happiness
attitude:
breadwinner
close to same-sex
parent
trust
50.88
White (65%), African Americans (22%), Hispanics (14%)
men (43%), women (57%)
38.86
58.21
Standard
Deviation
38.40
- - - - 9.64
42.36
Number of
observations
386
388
388
388
368
yes (55%), no (45%)
- - -
388
married (85%), cohabiting (15%)
less than HS* (16%), HS (34%), more than HS (50%)
-0.11 (or 0.9 as wage ratio)
2.18
1:much worse, 2:worse, 3:same, 4:better, 5:much better
1.87
1:much worse, 2:worse, 3:same, 4:better, 5:much better
2.68
1:stronlgy agree, 2:agree, 3:disagree, 4:stronlgy disagree
2.55
1:no same-sex parent, 2:somewhat close/not close, 3:very close
low (56%), high (44%)
- - - - 2.35
0.89
388
388
376
381
0.88
378
0.90
385
0.69
388
- - -
351
*: high school
49
Table 5. OLS results on housework hours (absolute t-values are in parentheses)
Neo-classical economic models
Power dependency models
Model 1
Model 1L
Model 1H
Model 2
Model 2L
Model 2H
All people
Low trust
people
High trust
people
All people
Low trust
people
High trust
people
African Americans
Hispanics
Age
Family income
Living with Children
Cohabiting
Women
Cohabiting*Women
HS graduates
College graduates
HS*Women
College*Women
0.18*
0.14
-0.02***
-0.00
0.58***
0.20
1.05***
-0.56***
0.36**
0.53***
-0.30
-0.58***
0.18
0.23
-0.02***
-0.00
0.62***
0.24
1.06***
-0.63**
0.28
0.46*
-0.16
-0.26
0.25
0.13
-0.02**
-0.00
0.57***
0.25
0.79***
-0.47
0.47*
0.53**
-0.18
-0.61*
0.17*
0.11
-0.02***
+0.00
0.59***
0.21
1.31***
-0.59***
0.37**
0.52***
-0.41*
-0.71***
0.16
0.16
-0.02***
+0.00
0.63***
0.25
1.3***
-0.66**
0.28
0.5*
-0.27
-0.47
0.38*
0.26
-0.02**
-0.00
0.54***
0.28
1.12***
-0.59*
0.52*
0.52*
-0.2
-0.67*
Log(wage ratio)
Option: Living standard
Option: Happiness
-0.08***
-0.1**
0.07
-0.1(1.4)
0.05(0.8)
-0.04(0.5)
0.1(0.9)
358
0.43
182
0.47
143
0.44
-0.06**(2.2) -0.12***(4.5)
Liberal Attitude: Breadwinner
Breadwinner*Women
Close to same-sex parent
Closeness*Women
N
R2
362
0.46
183
0.49
146
0.51
*: 0.05<P-value<0.1
**: 0.01<P-value<0.05
***: P-value<0.01
50
Table 5. continued (absolute t-values are in parentheses)
Sex-role attitude models
African Americans
Hispanics
Age
Family income
Living with Children
Cohabiting
Women
Cohabiting*Women
HS graduates
College graduates
HS*Women
College*Women
Model 3
Model 3L
Model 3H
Model 4
Model 4L
Model 4H
All people
Low trust
people
High trust
people
All people
Low trust
people
High trust
people
0.11
0.11
-0.02***
-0.00
0.60***
0.23
1.77***
-0.58***
0.28
0.47**
-0.24
-0.53**
0.1
0.12
-0.03***
0.00
0.64***
0.12
1.26**
-0.49
0.19
0.33
-0.06
-0.15
0.33*
0.13
-0.02**
-0.00
0.57***
0.32
1.64**
-0.64*
0.28
0.39
-0.03
-0.5
0.17*
0.12
-0.02***
-0.00
0.57***
0.20
1.50***
-0.53**
0.35*
0.50***
-0.23
-0.43**
0.19
0.08
-0.03***
-0.00
0.62***
0.17
1.03*
-0.58*
0.23
0.35
-0.08
-0.07
0.32*
0.13
-0.02***
-0.00
0.56***
0.15
1.52**
-0.38
0.46*
0.47*
-0.15
-0.53
-0.07***
-0.07
0.05
-0.04 (1.4)
-0.07 (1.0)
0.05 (0.7)
-0.11***
(3.8)
-0.00
(0.1)
+0.00 (0.0)
Log(wage ratio)
Option: Living standard
Option: Happiness
Liberal Attitude: Breadwinner
Breadwinner*Women
Close to same-sex parent
Closeness*Women
N
R2
All-combined models
0.11*
-0.26***
0.03
0.06
0.15(1.4)
-0.34**(2.6)
-0.23**(2.1)
0.31**(2.1)
0.03(0.4)
-0.13(1.0)
0.27*(2.0)
-0.11(0.6)
0.08
-0.22***
0.04
0.01
367
0.45
187
0.5
148
0.47
351
0.48
*: 0.05<P-value<0.1
**: 0.01<P-value<0.05
***: P-value<0.01
51
0.08 (0.7)
0.01 (0.1)
-0.27** (2.0) -0.08 (0.6)
-0.23** (2.0) 0.30** (2.5)
0.28* (1.9)
-0.23 (1.3)
178
0.53
141
0.52
Appendix: Proof of the equilibria of noncooperative games
over the household division of labor
For brevity in the text, we examined equilibria of the two games by
using illustrative payoffs. Here, we shall give formal proofs for the
equilibria of these games. In addition to the two games analyzed in the
text, a game with middle-range embeddedness is also examined.
----------------------------------------------Figure A1 about here
----------------------------------------------Each game has five subgames (including the game itself), as shown in
figure A1 at t=1, 2 ,3, 4, and 5.
We can express this game involving five successive games as:

t
 [ I , {S
t
t
i }, {u i (  )}]
where I refers to the players (husband and wife), Sti is the strategy of
person i at subgame t, uti is a payoff for player i at subgame t, and
t=1,2,3,4, and 5 for the different subgames. Specifically, we use the
format, uh(sw, sh) to indicate the payoff for the husband and uw(sw, sh)
for the wife. Please note that the wife’s strategy is always presented
before the husband’s strategy.
According to the subgame perfect equilibrium theorem (Selten 1975),
the equilibrium of the whole game can be derived by tracing back each
Nash equilibrium for the five subgames, using backward induction.
Before getting into each game, let’s clarify our assumptions and
propositions that are common for every game.
1. Assumptions
Assumption 1: Honoring trust means equal distribution of the payoff
(i.e., the utility from wage and housework) from the division of labor
between spouses.
Assumption 2: The husband and wife are identical except the husband has
a higher wage rate.
Assumption 3: There are positive gains from the division of labor in
the sense that the joint payoff from the division of labor based on
comparative advantage is greater than the joint payoff when both
specialize in paid work.
Assumption 4: Being betrayed is the worst outcome for the person who is
betrayed.
Assumption 5: Housework is worse than paid work, other things being
equal, because of the disadvantages described in the text.
2. Propositions
52
Proposition 1.
u1h(housework, honoring) > u2h(housework, housework)
Proof
Let’s suppose that u1h(housework, honoring) = u1w(housework,
honoring) = a, according to Assumption 1. Assumption 3 ensures
2a > u4h(paid work, paid work) + u4w(paid work, paid work)
(equation 1)
Let’s also suppose u2h(housework, housework) = u2w(housework, housework)
= m (we assume that the husband and wife produce the same payoff from
housework according to Assumption 2). Then, according to Assumption 5,
we can conclude
u4h(paid work, paid work) + u4w(paid work, paid work) > 2m
(equation 2)
From equations 1 and 2, we can conclude that 2a > 2m, which means that
a > m. Thus, u1h(housework, honoring) > u2h(housework, housework).
Proposition 2.
u1h(housework, honoring) > u3h(honoring, housework)
u1w(housework, honoring) > u3w(honoring, housework)
Proof
If we suppose that the joint payoff from (housework, honoring) at
t=1 is A and the joint payoff from (honoring, housework) at t=3 is B,
then Assumption 2 ensures that A > B and thus A/2 > B/2. According to
Assumption 1,
u1h(housework, honoring) = u1w(housework, honoring) = A/2 and
u3h(honoring, housework) = u3w(honoring, housework) = B/2.
Since A/2 must be greater than B/2, Proposition 2 is proved.
Proposition 3.
u1w(housework, honoring) > u4w(paid work, paid work)
Proof
Let’s suppose the joint payoff from (housework, honoring) at t=1 is
2a. Also let’s assume that u4w(paid work, paid work) = b and u4h(paid
work, paid work) = b + c (c > 0 because of Assumption 2). Then, we can
conclude that 2a > b + (b + c) because of Assumption 3. If we add the
term, d as the amount of gains from the division of labor, then
2a = b + (b + c) + d, (a, b, c, d >0).
This leads to the equation that a = b + (c + d)/2
(equation 3)
Now u1w(housework, honoring) - u4w(paid work, paid work)
= a - b = [b + (c + d)/2] - b (by equation 3)
= (c + d)/2 > 0 ( c, d >0)
Thus, u1w(housework, honoring) > u4w(paid work, paid work).
Proposition 4.
u3h(betraying, housework) < uth(sw, sh) at any t  3 or sw  betraying
u1w(housework, betraying) < utw(sw, sh) at any t  1 or sh  betraying
These are true by Assumption 4.
53
Now let us turn to proving the equilibrium of each game. We adopt a
three-stage proof for ease of presentation. We will first consider the
equilibrium of the upper half game (the case of the wife selecting
housework) and then the equilibrium of the lower half game (the case of
the wife choosing paid work) and, finally, the equilibrium of the whole
game by comparing the two half game solutions.
3. Proof for the equilibrium of the game with weak
embeddedness
Weak embeddedness leads to the following additional assumption and
proposition.
Assumption 5.1: Embeddedness is so weak that everybody is better off by
betraying trust rather than honoring it.
Proposition 5.1
u1h(housework, betraying) > u1h(housework, honoring)
u3w(betraying, housework) > u3w(honoring, housework)
These are true by Assumption 5.1.
Equilibrium of the upper half game
At  1, according to Proposition 5.1., the husband will betray. Given
this, at  2 , the husband will choose paid work instead of housework
because u1h(housework, betraying) > u2h(housework, housework) from two
equations: (1) u1h(housework, betraying) > u1h(housework, honoring)
according to Proposition 5.1 ,and (2) u1h(housework, honoring) >
u2h(housework, housework) according to Proposition 1. Thus, once the
wife selects housework, she will get u1w(housework, betraying), which is
the worst outcome for her, according to Proposition 4.
Equilibrium of the lower half game
The same logic applies to  3 : the wife will betray the trust
according to Proposition 5.1. Given this equilibrium at  3 , the husband
chooses paid work to avoid housework because it leads to the worst
outcome for him according to Proposition 4. Thus, once the wife chooses
paid work, she will get u4w(paid work, paid work).
Thus, at  5 , the wife chooses paid work to avoid housework because
work, paid work) > u1w(housework, betraying) due to Proposition
4. ‘Both specialize in paid work’ is the unique equilibrium under the
assumption of weak embeddedness. This equilibrium holds even if the
husband is the first to decide.
u4w(paid
4. Proof for the equilibrium of the game with strong
embeddedness
Strong embeddedness entails the following assumption and proposition.
Assumption 5.2: Embeddedness is so strong that everybody is better off
by honoring trust rather than betraying it.
Proposition 5.2
u1h(housework, honoring) > u1h(housework, betraying)
54
u3w(honoring, housework) > u3w(betraying, housework)
These are true by Assumption 5.2.
Equilibrium of the upper half game
At  1, according to Proposition 5.2, the husband will honor the
trust. Also at  2 , the husband will choose paid work instead of
housework according to Proposition 1. Given this equilibrium at t=2 (or
under the assumption that the husband will honor trust), the wife is
sure that once she chooses housework, the husband will honor her trust.
Thus, the wife knows that she will get u1w(housework, honoring) if she
selects housework.
Equilibrium of the lower half game
At  3 , the wife will honor trust (proposition 5.2). Thus, if the
wife chooses paid work, the equilibrium will be either (paid work, paid
work) or (honoring, housework). Therefore, once the wife takes paid
work, she will get either u4w(paid work, paid work) or u3w(honoring,
housework).
However, u1w(housework, honoring) > u4w(paid work, paid work) as
stated in Proposition 3 and also u1w(housework, honoring) > u3w(honoring,
housework) according to Proposition 2. Thus, whatever the wife will get
from the lower half game (paid work) is less than the payoff she will
get from the upper half game (housework): the wife will select
housework instead of paid work.
Thus, the unique equilibrium of the game is that the wife
specializes in housework while the husband specializes in paid work and
honors her trust. This equilibrium holds even if the husband is the
first to decide.
5. Proof for the equilibrium of the game with middle-range
embeddedness
Middle-range embeddedness defines the following assumption and
proposition.
Assumption 5.3: Embeddedness is strong enough to make honoring better
than betraying for the wife but not sufficiently strong for the
husband. (It is not possible that honoring is better than betrayal only
for the husband because the net benefit from betrayal is greater for
the husband than for the wife, as discussed in the text)
Proposition 5.3
u1h(housework, honoring) < u1h(housework, betraying)
u3w(honoring, housework) > u3w(betraying, housework)
Both are true by Assumption 5.3.
Equilibrium of the upper half game
At  1, according to Proposition 5.3, the husband will betray trust.
Also at  2 , the husband will choose paid work instead of housework
because u1h(housework, betraying) > u2h(housework, housework) from two
equations: (1) u1h(housework, betraying) > u1h(housework, honoring)
according to Proposition 5.3, and (2) u1h(housework, honoring) >
55
u2h(housework, housework) according to Proposition 1. Thus, once the
wife selects housework, she will get u1w(housework, betraying), which is
the worst outcome for her, according to Proposition 4.
In order to get a unique equilibrium, we need an additional
assumption to specify if ‘both specialize in paid work’ is better (or
worse) than ‘being honored’ for the husband. We examine both cases and
draw a unique equilibrium for each.
Assumption 5.3.1: ‘Both specialize in paid work’ is better than
‘being honored’ for the husband.
Proposition 5.3.1
u4h(paid work, paid work) > u3h(honoring, housework)
This is true by Assumption 5.3.1.
Equilibrium of the lower half game
Even though the wife will choose honoring trust (proposition 5.3) at
t=3, the husband will choose paid work at t=4 because of Proposition
5.3.1. Thus, choosing paid work at t=5 leads to both doing paid work
and the wife getting u4w(paid work, paid work).
In the final stage at  5 , the wife will choose paid work because
work, paid work)> u1w(housework, betraying) according to
Proposition 4. Thus, both specialize in paid work is the equilibrium of
the game, which corresponds to the argument derived from powerdependency theory. This equilibrium holds even if the husband is the
first to decide.
u4w(paid
We have another unique equilibrium if we have the following
assumption instead of Assumption 5.3.1.
Assumption 5.3.2: ‘Both specialize in paid work’ is worse than
‘being honored’ for the husband.
Proposition 5.3.2
u4h(paid work, paid work) < u3h(honoring, housework)
This is true by Assumption 5.3.2.
Equilibrium of the lower half game
At t=3, the wife will choose honoring trust (proposition 5.3); and
given this, the husband will choose housework at t=4 because of
Proposition 5.3.2. Thus, selecting paid work at t=5 leads to (honoring,
housework) and the wife will get u3w(honoring, housework).
5
In the final stage at  , the wife will choose paid work because
housework) > u1w(housework, betraying) according to
Proposition 4. Thus, the husband specializes in housework and the wife
honors his trust is the equilibrium of the game. This equilibrium holds
even if the husband is the first to decide. However, this equilibrium
is anomalous in the sense that the husband with the higher wage rate
specializes in housework while the wife with the lower wage rate
specializes in paid work even if the couple is identical in every other
respect. This odd result comes from the fact that the husband gets a
higher benefit from betrayal than the wife due to his higher wage rate.
Because of this, there exist a form of middle-range embeddedness that
u3w(honoring,
56
ensures only the wife’s loyalty but not the husband’s loyalty. This
equilibrium is unstable in two senses. First, once we take conventional
gender attitudes into account, this equilibrium cannot be maintained.
Second, the husband may want to increase the level of embeddedness so
that the wife can trust him and thus, he can specialize in paid work in
order to maximize his payoff. This, of course, changes the game to the
one with strong embeddedness. Or, he may want to find another woman
with whom he can build strong embeddedness. We can thus conclude that
the power-dependency explanation prevails in most cases of middle-range
embeddedness.
In general, then, only under the condition of strong embeddedness
does neoclassical economic theory hold. Power-dependency theory
prevails in all the other game circumstances.
57
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