marriage, specialization, and the gender division of...

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[ Journal of Labor Economics, 2007, vol. 25, no. 4]� 2007 by The University of Chicago. All rights reserved.0734-306X/2007/2504-0004$10.00

Marriage, Specialization, and theGender Division of Labor

Matthew J. Baker, Hunter College, City University

of New York

Joyce P. Jacobsen, Wesleyan University

We consider why the gender division of labor is so often enforcedby custom and why customary gender divisions of labor generallyinvolve both direction and prohibition. In our formal model, agentsfirst learn skills and then enter the marriage market. We show thatwasteful behavior may emerge due to strategic incentives in special-ization choice and human capital acquisition and that both problemsmay be mitigated through a customary gender division of labor. Thisdivision is not Pareto improving. Both the distributional effects andwelfare gains of a customary gender division of labor decrease asopportunities for market exchange increase.

I. Introduction

Gary Becker’s (1991) work(s) on the economics of marriage began thestudy of marriage and its relationship to the gender division of labor andhuman capital acquisition. Becker’s theory began with the observationthat spouses could specialize in specific tasks and then engage in trade at

Early versions of this article were presented in seminars at the U.S. NavalAcademy, Hunter College, and Wesleyan University and at the 2003 InternationalAssociation for Feminist Economics session at the Allied Social Science Associ-ations meeting entitled “Feminism Meets New Institutionalism.” We would liketo thank Nancy Folbre, Oded Galor, Victor Li, Padma Rao Sahib, Gil Skillman,and session participants for valuable comments and suggestions. Contact the cor-responding author, Joyce Jacobsen, at [email protected].

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minimal transactions costs within a marriage. Specialization within mar-riage created the added benefit of allowing increasing returns to scale inhuman capital as specialization allows human capital to be used moreintensively.

While Becker’s work provides an explanation for why a gender divisionof labor exists, it does not explain why, throughout history, we have sooften observed a customary gender division of labor under which womenand/or men are prohibited from performing certain activities by customand are encouraged to engage in others. In Becker’s model(s), there is noexplicit reason for society to sanction a gender division of labor for agentsas agents should always find it in their best interests to specialize whengains to doing so are present.

So why is the gender division of labor so often dictated and rigidlyenforced by custom? Why are both women and men so often prohibitedfrom engaging in specific tasks by prevailing social norms? Hadfield (1999)explains customary gender divisions of labor as mechanisms that mitigatea coordination problem in the marriage market. As specialization requiressome coordination, if agents must decide which tasks to learn withoutfull knowledge of the characteristics of potential spouses, a well-specifiedgender division of labor prevents the possibility that men and womenwill fail to coordinate on different tasks.

In this article, we develop a complementary explanation for why agender division of labor might occur. In addition to considering how acustomary gender division of labor can reduce coordination problems inthe marriage market, our theory also considers how it might mitigate themarital hold-up problem. Thus, for both reasons, a customary genderdivision of labor affects educational decisions made prior to the searchfor a spouse and subsequent intrafamilial bargaining over the marriagesurplus. We also discuss the resulting distributional aspects of a customarygender division of labor.

The initial work on division of marital surplus produced the observationthat treatment within marriage generally depends on the opportunitiesavailable outside of marriage.1 Subsequent work has focused on how thedivision of surplus arising from marriage influences spouses’ prior humancapital investment decisions. As spouses foresee that investments mayinfluence the share of marital surplus obtained in bargaining, premaritaleducational investments generally turn out to be suboptimal. This maritalhold-up problem appears to be robust to a variety of different modelspecifications. Konrad and Lommerud (2000) develop a model in whichintramarital time allocation decisions are made with varying degrees ofcooperation. They find that educational decisions made in anticipation of

1 See Manser and Brown (1980), McElroy and Horney (1981), and Lundbergand Pollak (1993, 1994). Lundberg and Pollak (1996) reviews the literature.

Gender Division of Labor 765

marital time allocation are influenced by how cooperatively time allo-cation decisions are made but are generally inefficient because of strategicoverinvestment by agents. Vagstad (2001) studies educational decisions ina framework in which spouses must learn how to perform both domesticand market tasks and finds that, because of the resulting disadvantage insurplus bargaining, agents invest too heavily in learning market tasks andtoo little in learning domestic tasks.2

Other work has focused on the interaction between educational deci-sions and marriage markets. Echevarria and Merlo (1999) present a modelin which marriage partners bargain simultaneously over consumption,numbers of children, and childrens’ education; while marriage marketconsiderations affect educational decisions, decisions remain inefficient.Peters and Siow (2002) study human capital accumulation with assortativematching and nontransferable utility using a model with only public goodswithin marriage. They find that investments are efficient in a large fric-tionless matching market but not generally otherwise.3 Iyigun and Walsh(2004) extend Peters and Siow (2002) to allow for production of privategoods within marriage and endogenous sharing of output based on bar-gaining. Iyigun and Walsh also find that investments are efficient only ina large frictionless matching market. Felli and Roberts (2002) investigatethe degree to which investment inefficiencies depend on market frictions,and they find both efficient and inefficient equilibria educational decisions;as competition reaches its peak and coordination failures disappear, in-vestments become efficient. In a similar framework, Cole, Mailath, andPostlewaite (2001a, 2001b) describe how varying degrees of specificityaffect the nature of prior investments made in anticipation of bargainingover marital surplus. They find that, while there exist bargaining rulesthat support efficient investments, there is no guarantee that the “right”bargaining rule will be implemented. One of the chief lessons of thisliterature, then, is that the hold-up problem is robust to different modelspecifications, although its exact nature and importance depend on mar-riage market characteristics, how outside-marriage options are specified,and how outside options and the marriage market interact. In settings inwhich the marriage market does not function perfectly, participants in amarriage bargaining game have some bargaining power. The anticipationof this bargaining power provides agents with an incentive to behave

2 Lundberg (2002) develops a similar model in which spouses anticipate jointdecisions over the allocation of familial time and asks whether or not crediblecompensatory rules can be set up within marriage that encourage optimal decisionsprior to marriage.

3 Peters (2004) studies education and assortative matching problems more gen-erally. See also Clark and Kanbur (2004), who delve more deeply into whetheror not assortative matching in fact obtains in matching markets.

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strategically in choosing premarital investments in anticipation of theirbargaining power.

In the broader literature on the hold-up problem, a variety of differentsolutions to hold-up problems have been explored, including shiftingproperty rights (Williamson 1985; Hart and Moore 1990), legal remediesfor breach of contract (MacLeod and Malcomson 1993), and wage-postingand directed search (Acemoglu and Shimer 1999).4 Our work suggeststhat a gender division of labor or, more generally, institutions that prohibitagents from performing certain tasks and encourage them to engage inothers, may also mitigate the hold-up problem. Our theory combineselements of the standard model of education, time allocation, and surplusdivision (as in Lommerud [1989] and Konrad and Lommerud [2000]),with a framework in which spouses may learn multiple tasks (as in Vagstad[2001]). Agents then search for complementary partners in a marriagemarket, match, and bargain over marriage surplus, subject to an exogenousprobability of marriage dissolution.

Our model contains some notable innovations. One innovation is theway in which we model the returns agents expect to receive outside ofmarriage. We allow agents limited opportunity for exchange and spe-cialization outside of marriage. This generalizes the approach of Vagstad(2001) and Lundberg (2002), who describe tasks as “market” or “do-mestic” work; we allow each potential task performed to be, to varyingdegrees, market work or domestic work. Further, our model characterizesthe marriage market differently from the assortative matching frameworksemployed by Cole et al. (2001a, 2001b), Felli and Roberts (2002), Petersand Siow (2002), Iyigun and Walsh (2004), and Peters (2004) and explicitlybuilds in marriage market frictions. In our model, agents engage in searchfor a complementary partner subject to frictions, where we use a matchingprocess to characterize frictions in the marriage market, as in Diamond(1982), Mortensen (1982), and Pissarides (2000). Like other models withfrictions in the marriage market, this results in some bargaining powerover the marital surplus and thus generates an opportunity for agents tobehave strategically. Our method allows the difficulty or ease with whichan alternative spouse may be found to enter into the determination anddivision of marital surplus and also allows us to assess the interactionbetween marriage market factors and the incentives to acquire differenttypes of skills.5

We describe the two types of social problems that may arise in the

4 See Williamson (1985) or Grossman and Hart (1986) for a description of thegeneral hold-up problem.

5 In some respects, our work carries out an agenda outlined by Vagstad (2001),who notes the need for careful consideration of the impact of the functioning ofthe marriage market on the incentives spouses have to learn market and domestictasks.


model as the career choice problem and the jack-of-all-trades problem;these two problems can be thought of as dimensions of the incentiveproblem described by Vagstad (2001) that arise when agents have to choosebetween learning market and domestic tasks. The career choice problemarises because agents of both genders prefer to learn tasks that are moremarketable. When equipped with more marketable skills, agents commanda larger share of the surplus created when married. However, this effectmay lead to relative scarcity in the marriage market for those who spe-cialize in less marketable skills, which increases their bargaining power.We show that this problem has the potential to generate fewer marriagesthan are socially desirable and too many specialists in marketable tasks.

The jack-of-all-trades problem is the standard hold-up problem cap-tured by much of the literature on education and bargaining within mar-riage and is similar to the basic incentive problems discussed by Konradand Lommerud (2000), Vagstad (2001), and Lundberg (2002). It is theresult of what can be called an underspecialization incentive. In our model,agents learn a variety of tasks to ensure a reasonable living when notmarried, but they also face a strategic incentive to learn a variety of tasks.To the extent that one is better off when not married if one is self-sufficient, this affects the bargaining within marriage over surplus, andself-sufficient agents are able to command a larger share of the marriagesurplus. We show that this problem may generate less productive mar-riages, which a gender division of labor may alleviate at cost: those agentswho are not married and who are currently searching for partners are lessable to subsist. The formalization of this trade-off allows one to assessthe circumstances under which a gender division of labor increases societalwelfare.

One usefulness of bargaining models of marital surplus division is theinsight they lend into the forces behind the relative treatment of spouseswithin marriage. This body of theory, is, for example, able to explain theobserved positive correlation between the treatment of women withinmarriage and women’s opportunities outside of marriage. This relation-ship has borne itself out in a variety of settings, as described in Heer(1958, 1963), Blood and Wolfe (1960), Buric and Zecevic (1967), Rodman(1967), Safilios-Rothschild (1967, 1970), Bahr (1972), Scanzoni (1972),Saltzman-Chafetz (1995), Lundberg, Pollak, and Wales (1997), and Chiap-pori, Fortin, and Lacroix (2002). The positive correlation between treat-ment within marriage and the ability to function outside of it also appliesin less developed countries (Blumberg 1988) and emerges across culturesof very different levels of sophistication (Rodman 1967).

In practice, it seems that, throughout history, the gender division oflabor has been somewhat arbitrary. Consider table 1, taken from Jacobsen(1998, 217); it uses data from Murdock (1967). This table uses data from863 past and present societies to create a simple breakdown for 11 activity

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Table 1Distribution of Tasks across 863 Nonindustrial Societies

Activity Only/Mostly Men Both Only/Mostly Women Societies

Hunting 100 0 0 738Metal working 100 0 0 360Boat building 96 3 1 215Fishing 79 15 6 562House building 75 10 15 457Animal husbandry 64 22 14 412Leather working 46 5 49 280Weaving 30 12 58 265Pottery making 9 5 86 328Gathering 8 14 78 396Agriculture 32 32 36 639

Source.—Jacobsen (1998, 217), adapted from Murdock (1967).

groups by whether only or mostly men, both genders equally, or onlyor mostly women perform chores in the activity group. While some tasks,such as hunting, are almost exclusively men’s activities, many tasks arenot consistently allocated to one gender or the other, even though in amajority of cases only one gender performs the task; agriculture, appearingat the bottom of the table, is perhaps the best example of this phenom-enon.6 This is in contrast to Becker’s assertion that the gender divisionof labor is driven by biological differences between men and women andtherefore should be relatively consistent across societies.7 In considerationof this evidence, Hadfield (1999) notes that the basic coordination problemin skill acquisition does not imply that particular tasks need to be doneby either men or women, just that some gender division of labor needsto be specified. Our theory has similar implications; an important featureof task segregation is not that specific tasks are allocated to a specificgender but instead that some task segregation be specified to coordinatein the marriage market. Unlike Hadfield (1999), we focus on distributionof gains to specialization and hold-up problems: in our model, given thetask segregation specified by a gender division of labor, agents may stillchoose to learn their specified tasks inefficiently. Therefore, we also in-

6 In a more detailed array of 46 subactivities compiled for a set of 224 non-industrial societies, Murdock (1937) finds these same general patterns, namely,the prevalence of assignment to one or the other gender rather than nongendertyping of activities and the variation across societies for most activities regardingwhich gender actually performs the task. See Jacobsen (1998, 218) for a reprintingof these data.

7 This patterning also contrasts with another biological-difference-based theoryof the gender division of labor posited by Galor and Weil (1996). They suggestthat men have comparative advantage in physical tasks and women have it inmental tasks and thus gendered labor divisions would be comparable for societiesat the same level of development.


vestigate how a gender division of labor may influence learning, given apattern of task segregation.

We show that a customary gender division of labor may mitigate boththe jack-of-all-trades problem and the career choice problem by forcingone segment of the population to learn specific tasks.8 We also show thatsuch rules have distributional consequences: the relative position of onespouse within marriage may be worsened, resulting in poorer treatmentboth within marriage and outside of it. Thus, a gender division of labormay increase welfare, but this increase in overall welfare may not be Paretoimproving for both genders. These arguments together are suggestive asto why customary gender divisions of labor have proven to be so enduring,even when seemingly anachronistic. Our results indicate that a customarygender division of labor might have social value in some circumstancesbut to some degree occurs at the expense of the disadvantaged genderand may harm the ability of individuals to function outside of marriage.Further, one gender may have a vested interest in maintaining the cus-tomary gender division of labor because of the distributional consequencesof the rule.

II. The Model

A. Basic Framework

Becker (1991, chap. 2) models human capital acquisition, marriage, andtime devoted to production as a simultaneous choice. Matching and bar-gaining models of marriage typically modify this framework so that de-cisions are made sequentially: educational investments are made first, thenmatching in the marriage market occurs, marriage terms are negotiated,and time allocation decisions are made. We follow this conventional se-quence of events.

The population consists of type m and type f agents; the number ofeach type of agent is normalized to one.9 All agents gain utility from

8 In this sense, our theory, like Lundberg (2002), focuses on ways in whichmarital hold-up and coordination problems might be solved rather than discussingthe details of the problem. Lundberg’s focus is primarily on family policy, whileours is on the role of custom.

9 Like most models of marriage, our model posits only two types of agents. It isinteresting that a number of societies feature what is, in effect, a third gender role.These roles have been found in a number of societies, including a number of Amer-ican Indian tribes, where such roles appear to be inextricably tied to homosexualbehavior, as well as the xanith in Oman, the mahu of Tahiti, and the hijra in India(Jacobsen 1998, 401). There is some debate over whether these third-gender personstook on cross-gender roles or truly filled a third position within societies withdifferent associated tasks. This second possibility posits an interesting additionalmodeling problem for future research.

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consuming two consumption goods, a and b, according to a utility func-tion:

u p u(a, b).

The quasi-concave utility function has the standard shape: u 1 0, u 1a b

, and both goods are essential:0, u ! 0, u ! 0, u 1 0 u (0, b) paa bb ba a

.u (a, 0) p �b

Agents have one unit of labor time to allocate to production of eithergood. The amount of time devoted to production of good a is t, so theamount of time devoted to production of good b is .1 � t

The total amount of output that an agent can produce depends on hisor her skill set. As is also typical in the literature, we assume that pro-duction occurs according to a linear technology. The amount of good aan agent can produce is given by

a p at,

where t is the time allocated to production of good a and the total amountof good b that an agent is capable of producing is

b p b(1 � t).

Agents’ skill sets are captured by the parameters a and b. Agents arenot endowed with skills naturally but must engage in costly learning toacquire skills. We denote these costs as

c p c (a, b); i p f, m.i i

The subscripts on the costs-of-learning function allow for potentialdifferences in the costs of learning across genders but do not precludethe possibility that women and men are identical in their capacity to learntasks. In fact, we focus primarily on the case in which ; thus, wec p cf m

posit that there are no biological differences in the capacity to learn dif-ferent tasks. However, by allowing for cost functions to vary, one couldstudy the impact of biological differences between men and women onthe gender division of labor. We postpone for the time being making anyparticular assumptions about the shape of the cost function; below, weshall consider cost functions tailored to our examples.

In the first phase of the game, agents learn skills, which amounts tochoices of a and b given the costs of acquiring skills given by ci.10 In fact,analyzing this decision can be quite complex. Agents’ choices of a andb depend upon the choices of other agents, as the choices of other agentsinfluence the potential for specialization. While it is true that a type fagent, for example, will prefer to invest more in learning to produce good

10 In this regard, our model is similar to Vagstad (2001) and Lundberg (2002),which also model multidimensional educational choices.


a if it is expected that type m agents invest more in learning to producegood b, it is also true that specialization patterns within marriage can bequite sensitive to both the absolute and comparative advantages of spouses.Moreover, it is possible that agents’ objective functions are not concave,creating the possibility for corner solutions.11 For this reason, we shallrely on two specialized versions of the model that yield clear analyticalsolutions for investment decisions and result in one spouse in every mar-riage having a comparative advantage in one of the two skills, with someability to perform the other skill if need be. When matched with an agentof the opposite gender in marriage, an agent may then apply his or herspecialty skill and rely on the spouse for the other good but otherwisemust produce the second good on his or her own if there is no otheropportunity to specialize. After agents have simultaneously decided onspecialties and learning, the second stage of the game commences.

In the second phase of the game, agents enter a marriage market inwhich they match with a complementary partner of the opposite genderand specialty. Those women who have elected to specialize in producinggood a enter a marriage market in which they search for men who havespecialized in producing good b, and vice versa. The marriage market isassumed to be segmented, so that type f agents who have specialized inproduction of good a face no possibility of encountering a type m agentwho is also specialized in production of good a. There are potentiallytwo marriage markets, one in which type f agents specializing in a pro-duction are matched with type m agents specializing in production of band one in which type f agents specialized in production of good b arematched with type m agents specializing in production of good a. Withineach market, agents randomly encounter complementary agents of theopposite type.12 Note that, in the case in which all women specialize inone task and all men in the other, there is effectively only one marketsegment.

As in other models of marriage and production, marriage generatesreturns to its participants by creating a low-transactions-costs environ-

11 This is a typical result in many models of specialization within the family; see,e.g., Becker (1991).

12 This is a model of segmented market search; see Acemoglu (1997). In mostother ways, our model closely mirrors the classic search-and-matching model dueto Diamond (1982), Mortensen (1982), and Pissarides (2000). While we assume thatthe marriage market is segmented, our modeling results go through in virtuallyidentical fashion under the assumption that the marriage market is not segmented,so that agents match with agents of the opposite gender and then observe thepotential partner’s characteristics. In our specialized versions of the model, if agentswith the same specialty are matched, there is no surplus to be gained from marriagebetween two agents with identical skills, so each agent is better off continuing tosearch for a complementary partner rather than marrying a partner who does nothave complementary skills.

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ment within which two agents with complementary skills can engage inspecialization, production, and exchange. A clear statement of the valuecreated by the marriage environment requires description of the returnsagents can achieve outside of marriage. Thus, we first describe agents’autarkic “outside marriage” returns.

B. Autarkic Utilities and Potential for Exchange

Autarkic utility forms an important part of an agent’s leverage in bar-gaining over the gains to marriage, and it also describes the well-being ofagents when they are not married and are engaged in a search for acomplementary partner. For these two reasons, autarkic returns occupyan important place in our model and warrant a detailed discussion.

We begin by noting that, if an agent is not matched with a marriagepartner and has no other opportunities for exchange, he or she mustallocate time to the production of both goods. That is, the agent earnsreturns

h(a, b) p max u(at, b(1 � t)). (1)0 ≤ t ≤ 1

Marriage is one such opportunity for specialization and exchange, but,generally speaking, agents may have some opportunity for specializationand exchange even if not married, for instance, through access to laborand/or goods markets or some alternative institution. For utmost sim-plicity, we imagine that the relative price of good a is one; thus, if anagent were able to find such an exchange opportunity, the agent couldearn utility

e(a) p max u(a(1 � x), ax). (2)0 ≤ x ≤ 1

Expression (2) is similar to expression (1) with one notable exception. Asstressed by our notation, the function depends only on the agent’se(a)ability to perform his or her specialty task, while h depends upon theagent’s ability to perform both tasks. The possibility of exchange allowsthe agent to replace his or her autarkic opportunity cost trade-off withthat in the market, as in any model of comparative advantage.

To reflect the idea that the agent may not always have an exchange andspecialization opportunity, we adopt a simplistic framework in which theagent encounters an exchange opportunity with some exogenous prob-ability p. Thus, an agent who has specialized in production of good aearns expected utility

a a a a au p 1 � p h (a, b) � p e (a). (3)( )


The same chain of logic applies to an agent who has specialized in pro-duction of good b:

b b b b bu p 1 � p h (a, b) � p e (b). (4)( )

The probabilities and are natural, if simplistic, measures of the degreea bp pto which exchange opportunities exist outside of marriage. The inclusionof the probability of encountering an exchange opportunity outside ofmarriage is our way of measuring the specificity of investments, whichemerges as a crucial factor in analyzing investment decisions in different,yet related, models such Cole et al. (2001a, 2001b). Further, this modelingtechnique generalizes the approach of other work that focuses on thedistribution of effort among spouses between “market” work and “do-mestic” work, as in Konrad and Lommerud (2000), Vagstad (2001), andLundberg (2002).13 In our model, each task is potentially domestic and/or market work, depending on the probability of encountering an outsideexchange opportunity. This will allow us to see how the potential rolefor a gender division of labor changes as tasks vary in the degree to whichthey are domestic or market work. A final point worth establishing isthat, as long as an agent is not equally gifted at the two tasks, autarkicutility is strictly increasing in the degree to which an outside exchangeopportunity is present.

C. Marriage Returns and Marriage Surplus

Following Becker (1991), in our model the gains to marriage stem fromthe fact that marriage is a zero-transactions-costs environment and agentscan therefore specialize and exchange within marriage to maximum jointadvantage.14 With a slight abuse of notation, let a and b also denote theamount of goods a and b that marriage partners are able to produce.Within marriage, they may costlessly negotiate agreements that result ina Pareto-optimal distribution of these quantities within the marriage. Sinceagents are assumed to have identical preferences, a Pareto-optimal dis-tribution of goods within marriage gives each agent an equal consumptionbundle. Then, assuming u to be homogenous of degree one in its argu-

13 While our approach generalizes that taken in previous literature, we still haveavoided explicitly modeling outside-marriage exchange institutions; however, weshall discuss some related issues at further length below.

14 This framework is similar to Becker’s original formulation, and it is also similarto that employed in Hadfield (1999). Contrast this with “public goods” models ofmarriage, in which marital surplus arises through provision of public goods withinmarriage, as in Lommerud (1989), Vagstad (2001), and Lundberg (2002).

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ments, the total utility generated by marriage in this case can be writtenas

1 1W(a, b) p 2u a, b p u(a, b). (5)( )2 2

If the couple must produce all goods itself and neither marriage partnerhas any opportunity for exchange outside of marriage, time allocationsare chosen to maximize (5) given the skills of the spouses. In what follows,we focus on the case in which the type f agent is an a specialist, whilethe type m agent is a b specialist. Substituting production functions into(5) gives

W p u(a t � a t , b (1 � t ) � b (1 � t )). (6)f f m m f f m m

In this context Becker (1991, 33) shows that it is optimal for at least oneagent to specialize completely in production of one good. Like Hadfield(1999), we also find it easier to work with a stronger case of Becker’sresult and assume that full specialization is optimal, so that within mar-riage each agent fully allocates all of his or her time to his or her specialty.15

Thus, in the event that there is no potential to enter into exchange agree-ments outside of marriage, we may write total marriage returns as

H p H(a , b ).f m

So far, we have assumed that married agents have no potential to engagein exchange outside of marriage in a labor market. What if the couplehad an opportunity to trade a for b? In this case, the married coupleachieves utility

aE p u a 1 � x* , x*a � b ,( ( ) )f f f f m

where is the optimal quantity of good a that the couple exchanges inx*fthe market at the assumed 1 : 1 trade ratio. We might also consider thecase in which the type m agent is able to exchange b for a:

bE p u a � 1 � x* b , x*b .( ( ) )f m m m m

How does the presence of exchange opportunities influence marriage re-turns? Since we assumed that the two goods entered into the utility func-tion in the same way, the marginal gains from engaging in market exchangefor one good can be studied by differentiating the utility function with

15 We thus sidestep some of the complexities involved in choosing marital allo-cations of time for reasons of tractability. Our chief purpose is describing in simplefashion gains to specialization. The time allocation has been studied extensively in,e.g., Lommerud (1989) and Konrad and Lommerud (2000). Still, in the currentarticle, agents do spend some amount of their lifetime executing both tasks as aresult of search frictions.


respect to or and evaluating the result at or . Forx x x p 0 x p 0f m f m

example,

a�E �u(a , b ) �u(a , b )f m f mp � � .F�x �a �bf x p0f

The above expression may be either positive or negative, and that dependson the marginal utilities of the two goods at the productivity levels/outputlevels . Since the two goods enter the utility function in exactly thea , bf m

same fashion, we have the following:a�E

! 0 if a ! b ,f m�xf

a�Ep 0 if a p b ,f m

�xf

a�E1 0 if a 1 b .f m

�xf

This indicates that there are gains to engaging in an exchange opportunityonly if, for example, the type f agent has an absolute advantage in pro-ducing good a so that . A similar argument would illustrate thata 1 bf m

this is also true when an opportunity to exchange good b presents itself.We thus have the following form of marriage returns, taking into theaccount the probabilities with which exchange opportunities presentthemselves:

a a aW a , b p H 1 � p � p E , a 1 b ,( ) ( )f m f m

H, a p b , (7)f m

b b bH 1 � p � p E , a ! b .( ) f m

A similar function can be developed for the case in which theW(b , a )f m

agents have chosen alternative specialties. As in the case of individualagents’ returns, note further that marriage returns never depend on eitheragents’ ability to perform their nonspecialty task. If married, agents fullyspecialize, regardless of whether or not an outside exchange opportunitypresents itself.

D. Matching and the Search for a Marriage Partner

Once agents have made skill acquisition decisions, agents enter a match-ing game in which they may be matched to an agent with a complementaryskill set, by which we mean an agent of the opposite type who has acomparative advantage in production of the other good. When matched

776 Baker/Jacobsen

with a complementary partner, agents of opposite types and skill setsimmediately strike a Nash bargain over division of the marriage surplus,and then they engage in joint production and distribution. If agents arenot matched, they produce alone for a period and then reenter the match-ing process in the next period. Married agents are separated from theirspouses by exogenous forces at the rate s. When separation occurs, agentsreenter the matching game and search for a new spouse.16 Agents thereforemove in and out of marriage according to a two-state Markov processover an infinite horizon, which allows us to focus on the long-run be-havior of the system.17

There are potentially four types of agents in the model: type f agents,who specialize in production of good a; type f agents, who specialize inproduction of good b; type m agents, who specialize in production ofgood a; and type m agents, who specialize in production of good b. Sincewe have normalized the size of each population of agents to be of measureone, we can denote the population frequency of each type of agent as

, , , and , respectively. We shall also use this notation to refer toa b a bf f m meach type of agent.

We denote the percentage of agents of each type who are unmarriedby including a “U” subscript, so the fraction of unmarried is . Thea af fUmatching technology describing the process by which unmarried agentsifare matched with unmarried agents is given by, at any time t, asjm

ij ij i jw p w ( f , m ),U U

where either , denoting the case in which type f agents specializingij p abin production of good a are matched to type m agents with specialty b,or , denoting the opposite case. We assume that w is continuousij p baand homogenous of degree one.

Using the matching technology, we can explicitly describe the solutionfor lifetime utilities, matching probabilities, and the fraction of the lifetimethe typical agent spends married. The matching technology can be usedto describe the flow of agents into and out of marriage. For example, the

16 We assume that there is an exogenous separation rate for largely technicalreasons. We do, however, expound on the role of the separation rate in ensuingsections. A good discussion of time allocation under the threat of divorce is Lom-merud (1989).

17 This methodology does have some shortcomings. For example, it is difficultto analyze the lasting effects of marriage (e.g., due to having children), as thisintroduces nonstationarity into the model. Of course, this criticism could beleveled at virtually every search-and-matching model of employment or part-nership formation.


fraction of agents and agents who are unmarried at any given timei jf mobey the following laws of motion:

˙ i ij i j i if p �w ( f , m ) � s( f � f ),U U U U

j ij i j j jm p �w ( f , m ) � s(m � m ). (8)U U U U

The first expression on the right-hand side of each of the equations in(8) describes the number of unmarried agents who match, marry, and thusexit the unmarried state, while the second term on the right-hand side ofthe two equations in (8) describes the number of married agents who areseparated from their current match and who thus enter into the pool ofunmatched agents; in writing these expressions, we have exploited thefact that . This simply means that the fraction of married andi i if p f � fM U

unmarried agents must add up to the total number of type f agents spe-cialized in production of good i.

In steady-state equilibrium, it must be the case that and˙ i j˙f p 0 m pU U

. This relationship implies that, in a steady state, the following must be0true:

i i ij i j j j¯ ¯s f � f p w f , m p s m � m . (9)( ) ( ) ( )U U U U

The equalities in (9) mean that the flow of unmarried agents whoifmatch in the marriage market must equal the flow of agents who matchjmin the marriage market. Equation (9) implies that

i i j j¯ ¯f p f � m � m . (10)U U

Equation (10) indicates that the number of unmatched agents on one sideof the market is generally equal to the number of unmatched agents on theother side of the marriage market only when the number of participantson each side of the market is equal. If it should be the case, for example,that there are more agents than agents, the result would be that therei jf mare, at any given time, more unmatched agents than agents. This hasi jf mimportant ramifications for the probability that any type of agent finds amatch when searching for a marriage partner, and it also affects bargainingover marriage surplus. The steady-state probability that an unmarried type

agent finds a match (a type agent) at any particular time isi jf m

ij i j¯ ¯w ( f , m )U Uiq p , (11)f ifU

778 Baker/Jacobsen

while the probability that an unmarried agent finds an agent isj im fU

ij i j¯ ¯w ( f , m )U Ujq p . (12)m jmU

Note that the equilibrium match probability (11) for a type agent isifincreasing in the number of agents in the market and decreasing injmthe number of agents in the market. Equation (10) indicates that andi i¯f qf

will only be equal when there are equal numbers of agents andj iq fm

agents in the marriage market.jmLet V denote the (steady-state) lifetime utility of a married agent, R

denote the lifetime utility of an unmarried agent, and S denote the shareof marriage surplus obtained by the agent. In a steady state, the lifetimeutility of a type agent specializing in production of goodk p f, m i p

is described bya, bi i i irV p S � s(R � V ), (13)k k k k

while the steady-state lifetime utility of a type k agent specializing in iproduction who is unmarried is

i i i i i¯rR p u � q V � R . (14)( )k k k k k

Solving equations (13) and (14) gives the following equations:i i i¯su � (q � r)Sk k kiV p , (15)k i¯r (r � s � q )k

i i i¯(r � s)u � q Sk k kiR p . (16)k i¯r (r � s � q )k

Describing the division of the marriage surplus closes the model. Wefollow convention and suppose that surplus is divided according to aninstantaneous symmetric Nash bargain. Surplus shares and are de-i jS Sf m

termined by the solution toi i j jV � R p V � R . (17)m m f f

Applying (15) and (16) to (17), we havei i i j j iS p D W � D u � D u . (18)k k k l l k

The share coefficients are given byiDk

i¯r � s � qkiD p . (19)k i j¯ ¯2r � 2s � q � qk l


To aid in keeping the subscripts and superscripts straight, if we chose, we could take or to examine the case in whichk p m, l p f i p a j p b

type m agents specialize in production of a and type f agents specializein production of b, for example.

The shares in (19) reflect the idea that bargaining power depends onthe proportion of each type of agent in the population. Note that theshare equations described by (19) imply that when there areD p 1/2equal proportions of type f and type m agents participating in a marriagemarket, as in this case the equilibrium matching probabilities (11) and(12) are equal (recall further the discussion of steady-state fractions ofeach type of agent searching for a marriage partner at eqq. [9] and [10]).If there are not equal proportions of complementary agents in the marriagemarket, the relatively scarce side of the marriage market enjoys a bar-gaining advantage, which is reflected by a larger value of D. This is becausethe scarcer side of the market matches more easily, as reflected by a largervalue of q, which, in turn, implies a larger value of D.

Since agents move in and out of marriage according to a two-stateMarkov process in equilibrium, in the long run, an agent of any type andspecialty spends the following fraction of time married (omitting sub-scripts for brevity),

q,

¯s � q

and a fraction of time unmarried,

s.

¯s � q

Weighting each value function by the fraction of time spent in marriageand the the fraction of time spent away from marriage allows for thefollowing representation of lifetime utilities:

qS � suU p . (20)

¯r q � s( )Lifetime utility depends on the fraction of time spent in each state (marriedor unmarried) and the division of the marriage returns. Our primaryinstrument in analyzing specialty selection and human capital acquisition,any resulting impacts on the relative welfare of the sexes, and optimaldecisions with and without a customary gender division of labor is U in(20), coupled with the shares of surplus described in (19).

E. Strategic Specialty Choice

There are two potential types of social problems that occur in ourmodel, both of which may be mitigated by a customary gender division

780 Baker/Jacobsen

of labor. The first problem, which is the focus of this section, blendselements of a coordination problem with strategic choice of specialty. Onemight describe this section of this article as developing the marriage marketramifications of the results described in Vagstad (2001) and Lundberg(2002) pertaining to agents’ choices in learning market and domestic work.As Vagstad showed, agents prefer to learn market tasks because of theleverage gained in marital surplus bargaining. The exposition of our modelin this subsection develops some of the nuances of this picture and alsosupplements understanding of the coordination model of Hadfield (1999).

We begin by describing career choice in the absence of a customarygender division of labor. To isolate the career choice aspect of the problem,suppose that there is no inherent difference between type f agents andtype m agents and that the costs of learning to produce good a or goodb as a specialty are equal. Further, suppose that career choice is discrete,so an individual chooses a career at a fixed cost c and thereby gains abundle of skills, denoted by for an agent specializing in a pro-a a(a , b )duction, and for an agent specializing in b production. To reiterate,b b(a , b )we assume that

a a a b b bc a , b p c a , b p c( ) ( )and also that

a b b a a ba p b , a p b ; a 1 a .

These assumptions imply that the acquired skill bundles are mirror imagesof one another. Since agents are identical, there is no difference in theaggregate returns created by either type of marriage (i.e., either an a tob type marriage or a b to a type marriage), so regardless of which genderperforms which task in marriage, we write returns achieved by a marriedcouple as W, where . The neglect of whether or nota bW p 2u(a /2, b /2)an exchange opportunity for either good is present is made possible byour assumptions that neither agent has an absolute advantage in produc-tion and that the goods receive equal weight in the utility function, asdescribed in Section II.C, equation (7).

The specialty choice game has an easily characterizable set of equilibria.There are two pure-strategy equilibria in which all agents of each typespecialize in production of the same good and a mixed-strategy equilib-rium in which positive fractions of agents specialize in both tasks. Thetwo pure-strategy equilibria cannot in general be Pareto ranked, as theyboth generate equal social welfare. However, each gender strictly prefersthe equilibrium in which he or she is more specialized in the relativelymore marketable task.

To be more explicit, consider the pure-strategy equilibrium in whichall type f agents specialize in production of good a, while all type m agents


specialize in production of good b. In this case, the probability of findinga mate when unmarried is equal for both types of agents (indeed, themeasure of participants in the only existing side of the marriage marketis one) and collapses to . The lifetime utilities described byi j ¯q p q p qk l

(20) and the surplus division equations (18) and (19) simplify to

a b a¯1 q(W � u � u ) � 2suf m faU p ,f,ps ¯2 r (q � s)b a b¯1 q(W � u � u ) � 2sum f mbU p . (21)m,ps ¯2 r (q � s)

In this case, recall that the shares of the surplus described by (19) reduceto 1/2.

Social welfare is the sum of utility obtained by both types, weightedby the fraction of the population of each type (which in this case is unity):

a bqW � su � suf mSW p . (22)¯r q � s( )

Suppose now that there is a difference in the returns individuals earndue to differences in the likelihood that agents of different specialties areable to find outside exchange opportunities. In particular, suppose that

, from which it follows that (see eqq. [3] and [4]). Thus,a b a bp ! p u ! uf m

ceteris paribus, agents prefer the equilibrium in which they specialize inthe task for which there are more exchange opportunities outside of mar-riage; note how the difference enters into the utility functions inb au � um f

(21).These results imply that each gender prefers the pure-strategy equilib-

rium in which they are specialized in the relatively more marketable task.How might one measure the gains that accrue to society from this effectmore generally? As a benchmark for the no-coordination case, considerthe mixed-strategy equilibrium in which some fraction of agents of bothtypes specialize in both tasks.18 In the mixed-strategy equilibrium, agentsof both types must receive equal utility from either career choice:

a b b aU p U ; U p U .f f m m

Since , it follows that (see eqq. [3] and [4]). This leadsa b a bp ! p u ! u

18 There remains the difficult conceptual question as to whether or not themixed-strategy equilibrium is the appropriate baseline for describing outcomesin a completely uncoordinated environment. In this game, there is no natural focalpoint, and neither pure-strategy equilibrium is a natural choice over the other, sothe mixed-strategy equilibrium is a reasonable yardstick for the case in whichcoordination is absent.

782 Baker/Jacobsen

to the implication that, at the mixed-strategy equilibrium, there are un-equal numbers of each type of agent in the market. Specifically, b af 1 fand , so that more agents of each gender specialize in the relativelyb am 1 mmore marketable task. This is because, when when there are equala bu ! unumbers of each type of agent in the marriage market, , indicatinga bU ! Uthat some agents specializing in production of a could switch to b pro-duction and earn strictly greater utility.

This argument renders clear how utilities are equilibrated across spe-cialties. As agents move toward more marketable tasks, those that arespecialized in unmarketable tasks grow scarcer. Because they are relativelyscarce in the marriage market, they are able to obtain a share of surplusin marriage bargaining that offsets the disadvantage due to specializationin the nonmarketable task. One may employ these results to show that,even though one of the pure-strategy equilibria increases social welfare,it may not necessarily generate a Pareto improvement for each type ofagent. Consider the utility of f agents specialized in a at the pure-strategyequilibrium; this utility is given by the first part of (21). At the mixed-strategy equilibrium, this agent earns instead

a a aq S � suf faU p , (23)f,ms a¯r (q � s)f

where is to be determined. Let and denote the equilibrium sharea a b¯ ¯S D Df f m

of surplus obtained at the mixed-strategy equilibrium. Since ata bf ! mthe mixed-strategy equilibrium, we have , which, in turn, im-a b¯ ¯ ¯q 1 q 1 qf m

plies that . Lifetime utility (23) at the mixed-strategy equi-a b¯ ¯D 1 1/2 1 Df m

librium can now be written as

a a b b a a¯ ¯q [D (W � u ) � D u ] � suf f m m f faU p . (24)f,ms a¯r (q � s)f

For utility at the pure-strategy equilibrium to be greater than utility atthe mixed-strategy equilibrium, the following inequality must hold, using(21) and (24) to form :a aU 1 Uf,ps f,ms

b a a a¯ ¯m W � u � m u ! s q � q u . (25)( ) ( )f m m f f f

The weights and are defined by the following expressions:m mm f

1 1a a a a¯ ¯¯ ¯ ¯ ¯m p q q D � � s q D � q ,f f f f f( ) ( )2 2

1 1a b a b¯ ¯¯ ¯ ¯ ¯m p q q D � � s q D � q . (26)m f m f m( ) ( )2 2

The sign of (25) is ambiguous. The term on the right-hand side of theinequality in (25) is positive, as , meaning that those specialized ina¯ ¯q 1 qf


nonmarketable tasks are more likely to find matches at the mixed-strategyequilibrium relative to the pure-strategy equilibrium. Since ,aD 1 1/2 mf f

is greater than zero, and since , is less than zero. Thus, onebD ! 1/2 mm m

may conclude that a switch from a mixed-strategy equilibrium, in whichboth genders perform both tasks, to a pure-strategy equilibrium, in whicheach gender performs a specific task, produces ambiguous results on theutility of the gender that is forced to specialize in the less marketable task.Consider inequality (25) as the term gets very small; this may happen,auf

for example, because an individual specialized in production of good acannot produce b well and/or has almost no opportunity to engage inexchange outside of marriage; in short, this agent’s skills are relativelyspecific to marriage. As the term goes to zero, the inequality in (25)auf

cannot be satisfied, as the right-hand side goes to zero while the left-handside remains strictly positive. This happens because, at the coordinatedequilibrium, agents specialized in the relatively marriage-specific task nolonger have the twin advantages gained through relative scarcity: easiermatching and the resulting increase in bargaining power.

Thus, in the circumstance in which one gender learns a highly marriage-specific task, the gender division of labor may be welfare improving butnot Pareto improving. This result reinforces explanations for several fea-tures of a customary gender division of labor. For example, the fact thatthe gender division of labor might be welfare increasing in circumstancesin which there are limited opportunities to engage in exchange and spe-cialization outside of marriage and when agents do not or must not spenda large fraction of their lives unmarried makes strong intuitive sense.Further, the idea that a customary gender division of labor puts the partywith relatively less marketable skills at a disadvantage in bargaining overthe marriage surplus and therefore leaves this party with a smaller shareof the marriage surplus, and in some sense treated relatively less wellwithin marriage, also coincides with empirical observation.

The flip side of the result that the gender division of labor reduces theutility of one party relative to the mixed-strategy equilibrium is that itincreases the utility of the other relative to the mixed-strategy equilibrium.Thus, a motive for the party in relative power to maintain the genderdivision of labor even after it has outlived its welfare-enhancing propertiesis suggested by this work.

F. Customary Gender Division of Labor and the Hold-Up Problem

We began this section by illustrating the incentive problem that occurswhen there is no customary gender division of labor, but we now focuson reasons why one agent type may be explicitly prohibited, possibly bysocial sanction, from performing one task or the other. We show thatrelative to the social optimum, agents invest too much in learning tasks

784 Baker/Jacobsen

that they do not perform when married, and they invest too little in tasksthat they do perform. This investment strategy renders agents less relianton marriage and thus better positioned to bargain over marriage terms.In some circumstances, a customary gender division of labor, by prohib-iting agents from engaging in certain tasks, may reduce agents’ incentivesto learn tasks that they will not specialize in during marriage. Not sur-prisingly, the rule has distributional consequences that may cause a re-duction in lifetime utility for one party relative to a regime in which thereis no customary gender division of labor, though this effect may be neu-tralized if both groups are restricted in the tasks that they may perform.This latter possibility amounts to a case in which the gender division oflabor forces both parties to marriage away from a noncooperative in-vestment equilibrium and closer to a cooperative one, though a two-sidedgender division of labor is an imperfect means of accomplishing this.

To keep things simple, we focus on one pure-strategy equilibrium: onein which all type f agents specialize in production of good a when marriedand all type m agents specialize in production of good b when married.We also now model learning choices as continuous rather than discrete.This isolates our study of incentives from our investigation of specialtychoice in the previous section. It also allows us to illustrate clearly anadditional motive as to why a society might wish to prohibit membersof one group from engaging in certain tasks, beyond simply directingthem toward a certain specialty.

Consider the human capital investment decision of one type f agent,, given the behavior of all other type f agents and all type m agents.f

(Indeed, throughout this section we shall treat the decisions of type magents as fixed.) Whenever matched with a type m agent (adopting theconvention that all variables pertaining to are marked with a hat),ˆ ˆf freceives a share of the marriage surplus determined by

b b a aˆ ˆ ˆV � R p V � R . (27)m m f f

Equation (27) indicates that the division of the surplus receives dependsfon the population characteristics of agents of both types. If any type magent were to refuse marriage with , in the next period he would befmatched with the “typical” type f agent, as the probability of seeing fagain is zero. If we first solve for the standard division of the surplusdescribed by (17), substitute the result into (27), and solve for , we getaSf

f m f mˆ ˆ¯ ¯(q � r)W � r(u � u ) � q(1/2)(W � u � u )a b a baS p . (28)f ¯(2r � q)


Substituting from (28) into (20) yieldsaSf

f m f m fˆ ˆ ˆ¯ ¯ ¯q[(q � r)W � r(u � u ) � q(1/2)(W � u � u )] sua b a b aaU p � . (29)f ¯ ¯ ¯r (2r � q)(q � s) r (q � s)Social welfare can be written in the same form as previously described

in (22):a bqW � su � suf mSW p . (30)

¯r q � s( )Consider now the individual type agent’s incentive to invest in learn-ˆaf

ing the two tasks. The agent’s first-order conditions for maximizing (29)are

f ¯�U q �W �u s �u �ca a a¯p q � r � r � � p 0, (31)( )[ ]¯ ¯ ¯�a r(2r � q)(q � s) �a �a r(q � s) �a �a

f ¯�U q �u s �u �ca a ap � � p 0. (32)

¯ ¯ ¯�b (2r � q)(q � s) �b r(q � s) �b �b

By contrast, maximization of social welfare with respect to the type fagents choices of a and b yields the following two first-order conditions:

�SW 1 �W �u �ca¯p q � s � p 0, (33)( )¯�a r (q � s) �a �a �a

�SW s �u �cap � p 0. (34)

¯�b q(r � s) �b �b

Comparing social welfare and individual returns allows one to see thesources of the incentive problem in human capital acquisition decisions.19

19 One must be careful with the second-order conditions for this problem be-cause of the potential nonconcavity of the indirect utility function. Let

2 2 2 2 2� W � u � c � u � ca aF p g � g � ! 0, F p g � ! 0,11 1 2 22 22 2 2 2 2�a �a �a �b �b

2 2� u � caF p g � ,12 2�a�b �a�b

where and . The assumption that¯ ¯ ¯ ¯ ¯g p q(q � r)/[r(2r � q)(q � s)] g p s/[q(r � s)]1 2

utility functions are quasi-concave and homogenous of degree one, coupled withthe assumption that the human capital of male agents is fixed, is sufficient toensure a unique maximizing value so long as the cost of investment function

satisfies , and the cross partial of the cost functionc 2 c 2c(a, b) � /�a 1 0 � /�b 1 0is not too large. This will guarantee that and that2� c/�a�b F , F ≤ 0 F F ≥11 22 11 22

.2F12

786 Baker/Jacobsen

Agents excessively weight outside-marriage returns and weight too littlewithin-marriage returns, as evidenced by the presence of additional

and terms in expressions (31) and (32) relative to (33) and�u /�a �u /�ba a

(34).20 The basic incentive problem is essentially that described by Vagstad(2001). Agents maximize the share of the surplus that they are able toobtain through bargaining and not the surplus itself. From the perspectiveof society, this agent invests too little in learning the task that will beperformed in marriage and too much in learning the task that will not beperformed in marriage. However, note that the socially optimal investmentin the nonspecialty task described by (34) does imply that the agent shouldinvest some effort in learning how to produce good b. If it is hard to finda match in the marriage market or if the rate of separation is high, equation(34) implies that the marginal social benefits from agents learning howafto produce b increase. This is because, under these circumstances, theyare likely to spend a sizable fraction of their lifetimes unmarried, and theymay need to be able to perform task b to subsist.

A customary gender division of labor may, under some circumstances,mitigate the incentive problem, but, in light of (34), it may go too far. Agender division of labor takes the form of a restriction on the set ofactivities that a type f agent may perform. If the agent is prohibited fromperforming task b, for example, the result is that the agent simply chooses

; there is no reason to learn how to do something that the agentb p 0will never be allowed to do. If b is restricted to be zero, the result mayeither increase or decrease social welfare; welfare increases because stra-tegic investment incentives are eliminated, but welfare decreases becausetype agents are now more helpless when not married.af

Consider the following discrete choice example, in which type f agentsspecialize in production of good a but must decide whether or not tolearn to perform task b. In the event that an agent has learned the task,we normalize their skill level to one, so . The agent must decidea p 1whether or not to choose . Take the utility function to beb p 1 u p

. It then follows that the agent will choose if no market1/2 1/2a b t* p 1/2is available and if a market is available. Then, from (1) and (2),x* p 1/2we obtain the following expression for autarkic utility when the agenthas chosen to learn how to produce good b ( ):b p 1

1 1au (b p 1) p (1 � p ) � p .f a a2 2

20 There is, in fact, another incentive problem at work, one which emergesbecause agents do not consider the impact of human capital investments on thebargaining opportunities of others. We do not discuss this externality here; seeAcemoglu (1997).


Fig. 1.—The marginal private and marginal social gains to learning a nonspecialty taskas functions of . The region between the two vertical dashed lines is the region in whichpa

a customary gender division of labor increases welfare.

If the agent chooses not to learn how to produce good b, the agent earnsautarkic utility

1au (b p 0) p p . (35)f a2

Expression (35) reflects the fact that the agent is not self-sufficient if thereis no potential for accessing outside markets. Using (29), we can computethe change in lifetime utility due to learning how to produce b as

¯ ¯1 (1 � p ){[qr/(2r � q)] � s}aaDU p � c .f b¯2 r (q � s)

By applying (30), we can compute the gain in social welfare due due tothe agent learning how to produce b as

1 (1 � p )saDSW p � c .b¯2 r (q � s)

Figure 1 graphs and as functions of , the probability thataDU DSW pf a

the individual is able to access a labor market. The social returns to learn-ing the task are generally less than the private returns as social returns

788 Baker/Jacobsen

do not consider the distributional impact of learning additional tasks. Infigure 1, the gap between the two causes a social problem only in theregion between the dashed lines, when is of moderate size. Why doespa

this happen? When is very small, it may be both socially and individuallypa

desirable for type f agents to learn how to produce good b, as there islittle chance of self-sufficiency outside of marriage if agents are completelyspecialized. However, when is very large, it is both socially and indi-pa

vidually desirable that agents not learn how to produce b. This is becausethe high implies ample specialization opportunities outside of marriage,pa

and the agent is more often than not able to rely on her primary skilland thus not need task b. In between the dashed lines of the figure, theprivate gains to learning how to produce good b are positive, while thesocial gains are negative. In this region, society would be better off if fagents did not learn how to produce good b, but type f agents wouldchoose to learn it. In this environment, prohibiting type f agents fromperforming task b may be socially desirable, even though it has a negativeimpact on type f agents’ utility.

III. Discussion

There are several interesting ways in which the model presented in thisarticle might be extended. One potentially fruitful modification would beto allow for different circumstances surrounding the bargaining game. Inour approach, the threat points in the bargaining game are influenced byprior human capital investment decisions, and these decisions can be al-tered by social norms. Thus, a useful extension might be to include morecomplex notions of the potential threat points, which might offer insightsinto more complex patterns of task segregation—for example, why itmight be the case that married women are prohibited from doing certaintasks but unmarried women are not. In our model, preventing marriedwomen from doing a task but allowing unmarried women to perform thetask does not change the basic bargaining problem, because the unmarriedstate of the world is what determines womens’ threat points in bargainingover the marital surplus. However, if threat points were specified differ-ently, distinctions like this would matter. For example, Lundberg andPollak (1996) describe a bargaining game where breakdowns in bargainingover marital surplus do not necessarily result in separation but insteadresult in spouses pursuing some sort of noncooperative action within thehousehold. Under these circumstances, prohibiting women from doingcertain tasks within marriage would matter for the division of surplus.

A further extension that we believe to be fruitful would be to introducea more detailed matching process that allows for endogenous search effort,matching technology, separation costs, and/or endogenous separation


from marriage.21 Allowing for endogenous search effort in finding aspouse and introduction of endogenous separation from marriage mightallow one to explore in more detail the dynamic relationship betweenmarket work, divorce, rates of marriage, and the gender division of laborover time. One might conjecture, for example, that the gender divisionof labor would encourage agents to exert greater effort in finding a spouse,while the decline of the gender division of labor might result in fewermatches and more separations. In turn, this process might continue toundermine the gender division of labor. Further, one might roughly anal-ogize a separation cost with a social stigma attached to divorce and studyhow a divorce stigma interacts with the gender division of labor and thegrowth of the market over time.

The search process described in the model could also be modified toallow for uneven sex ratios so as to relate this line of work explicitly tothose papers that consider aggregate sex ratio effects on both premaritalhuman capital investment and marital surplus division (see, in particular,Iyigun and Walsh [2007]). One might expect that an excess supply of menrelative to women would increase the incentives, absent any gender di-vision of labor, for women to learn nonmarketable skills and men to learnmarketable ones, as on average women would spend less time unmarriedthan men. It is plausible, however, that the gender division of labor inthis case may then act to restore some of the bargaining power men lostdue to the uneven sex ratio.

While our model is not a model of the evolution of the gender divisionof labor, it is suggestive as to why a gender division of labor originallyarose and may explain its impact on the relative well-being of men andwomen once adopted. Our model also suggests a link between the decliningimportance of the gender division of labor over the past century in moderneconomies. The literature relating family economics, fertility, and growthdraws an explicit link from the opportunities for market participation pro-vided by growth to changes in family structure. For example, Greenwoodand Seshadri (2002) describe how industrialization reduces the need forchildren, as goods traditionally provided by children may be more cheaplypurchased in the market. Hazan and Maoz (2002), who consider explicitlythe potential dynamics of formal labor force participation over time, predicta nonlinear (S-curve) path in which changing social norms, which are af-fected by a change in women’s formal labor force participation, reinforcethe rise in women’s labor force participation that is precipitated by therising value of women’s labor outside the home. This would tend to coun-teract the tendency of the gender with the distributional advantage to resistchange. Galor and Weil (1996) argue that higher wages for women raise

21 Such models have been developed in the search-and-matching literature; seePissarides (2000).

790 Baker/Jacobsen

the costs of children relatively more than they raise household income. Ourmodel suggests that one aspect of this transition is that it may decrease theimportance of having a specialist in what was traditionally viewed as non-market work in the family. Thus, as market opportunities increase, genderroles break down, fertility declines, and the relative treatment of womenwithin marriage improves.

IV. Conclusions

We have developed a theoretical model of the gender division of laborthat relies on the importance of the ultimate distribution of marriagesurplus for human capital acquisition. The role of a gender division oflabor is to limit possibilities for strategic acquisition of human capital;human capital accumulated for the purposes of gaining better treatmentwithin marriage. Our model is capable of explaining several phenomenathat typically coexist with the gender division of labor, such as these:

1. The gender with the distributional advantage tends to have the moremarketable form of labor or the form of labor that provides the moreeasily traded output (outside of marriage).

2. The gender with the distributional advantage would more stronglyresist changes in labor markets that would make labor of the other gendermore marketable.

3. The gender with the distributional advantage would more stronglyresist changes in marriage patterns that would increase the probability ofseparation, such as less stringent standards for receiving a divorce.

4. The more restricted gender is treated more poorly within marriage.

More broadly construed, our work offers an explanation for the cus-tomary gender division of labor that matches well aspects of the insti-tutional evolution of societies as they move through different phases ofdevelopment. It also suggests why a customary gender division of laboris most conspicuous at those stages of development in which labor marketsare somewhat, but not completely, developed. One might also add thatour theory suggests that, in societies with low levels of technologicalsophistication, such as hunter gatherers, and in modern societies, there islittle need for a gender division of labor.22 In the former case, this isbecause human capital acquisition is not as important, and there is greaterneed for individuals to be self-sufficient. In the latter case, individuals,even when highly specialized in certain tasks, may sustain themselves

22 This nonlinear progression is in partial contrast to that suggested by Galorand Weil (1996), whose theory predicts that the degree of specialization woulddecline over time as the reward to physical labor declines during the process ofdevelopment.


through market exchange. Thus, they face little incentive to strategicallyacquire skills they will not use.

While this article provides several reasons for why the gender divisionof labor might exist, it has not presented an explicitly dynamic theorythat explains the interplay among human capital accumulation, the de-velopment and decline of customs, task segregation, and economic growth.Constructing such a model and studying its correspondence with changesover time for a broad sample of societies constitutes an interesting avenuefor further research.

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