2500+ words Essay

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Polygamy

28th October 2019

SESS 0042

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Two kinds of polygamy  Polygyny = one husband, many wives  Polyandry = one wife, many husbands  Polyandry much rarer than polygyny  Serial monogamy will not be considered

polygamy in this lecture  Not all societies monogamous in law are

also monogamous in fact (concubinage, extra-marital relationships…)

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Summary of theory  Exchange theory = voluntary trade benefits both  Specialization = focusing on what each is good at  Public goods = same thing is “enjoyed twice”  Joint production = two can do what one cannot  Insurance/diversification = back-up plans are

useful

 If it’s so great, why do we form couples instead of triples, quadruples, whole teams?

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Assumptions about polygyny

 One man can have more than one wife but all women have only one husband

 Men propose (marriage and division of spoils), women respond

 Shapley-Shubik transferable utility

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Distribution of spoils under monogamy and under polygyny

Abby Barbar a

Carrie Dana

Jake 15 11 12 3

Kyle 10 14 2 4

Len 8 11 9 10

Martin 12 8 10 13 12:1

12:2

9:0

15:03:12

3:11

3:10

Following Shapley-Shubik, stable matches max Σu.

2:10

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Results of going poly  Jake has two wives: he lures Carrie away from Len

 He offers her more than Len can  Len remains single

 For every woman, there exists some other man who makes a better husband to her than Len

 All women have seen their payoffs increase relative to monogamy  This is a result of increased competition among men  (So: why are women NOT lobbying for polygyny?)

 BEWARE! We have assumed the gains from matches to be mutually independent (not realistic)

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How is women’s reservation utility determined?

Married to A Married to B Married to C Married to D

Being a wife #x1 2 3 4 5

Woman’s reservation utility U0

Conclusion: A woman would agree to be someone’s second wife if and only if that yields her higher overall utility than the best of all other alternatives which include being the first wife of other potential husbands.

Marginal contributio n

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Utility generated in marriage:

Men’s situation

Number of wives0 1 2 3 4

U0

Conclusion: A man will get a second (and higher-order) wife if and only if her marginal contribution to the marriage is at least as high as the portion of the overall gain she consumes herself.

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A study aid: analogy  How is marriage market like a labor

market  If marriage is a like a firm, then under our

assumptions  The husband is like the owner (= residual claimant)  The wife is like an employee (gets fixed wage)

 In equilibrium, MP = w, i.e. each employee is paid his/her marginal product

 The same happens with optimal number of wives: they’re taken on until MB = MC

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Marginal contributions by extra wives

 Assume

 Output of each marital link

θF = 5 Jake (θM = 7) Kyle (θM = 5)

Len (θM = 3) Martin (θM = 2)

Only wife

34 24 14 9

One of 2 33 23 13 8 One of 3 32 22 12 7 One of 4 31 21 11 6

   

 n

i FiM

n

i FiM nnU

1

2

1



 nU FiMFi  

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Gains from marriage with one wife, with two wives, with three wives…

Abby 5

Barbara 4

Carrie 3

Dana 2

Jake 7 34, 33, 32, 31

27, 26, 25, 24

20, 19, 18, 17

13, 12, 11, 10

Kyle 5 24, 23, 22, 21

19, 18, 17, 16

14, 13, 12, 11

9, 8, 7, 6

Len 3 14, 13, 12, 11

11, 10, 9, 8 8, 7, 6, 5 5, 4, 3, 2

Martin 2

9, 8, 7, 6 7, 6, 5, 4 5, 4, 3, 2 3, 2, 1, 0

3:0

Following Shapley-Shubik, stable matches max Σu.

6:2

14:5

24:10

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Gains from marriage with one wife, with two wives, with three wives…

Abby 5

Barbara 4

Carrie 3

Dana 2

Jake 7 34, 33, 32, 31

27, 26, 25, 24

20, 19, 18, 17

13, 12, 11, 10

Kyle 5 24, 23, 22, 21

19, 18, 17, 16

14, 13, 12, 11

9, 8, 7, 6

Len 3 14, 13, 12, 11

11, 10, 9, 8 8, 7, 6, 5 5, 4, 3, 2

Martin 2

9, 8, 7, 6 7, 6, 5, 4 5, 4, 3, 2 3, 2, 1, 0

3:0

Following Shapley-Shubik, stable matches max Σu.

6:2

14:5

24:10 10:22 8:17 6:12

2:7

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Marginal contributions by extra wives

 Assume

 Output of each marital link

θF = 5 Jake (θM = 7) Kyle (θM = 5)

Len (θM = 3) Martin (θM = 2)

Only wife

34 24 14 9

One of 2 31 21 11 6 One of 3 26 16 6 1 One of 4 19 9 -1 -6

   

 n

i FiM

n

i FiM nnU

1

3

1

2 

 2nU FiMFi  

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Gains from marriage with one wife, with two wives, with three wives…

Abby 5

Barbara 4

Carrie 3

Dana 2

Jake 7 34, 31, 26, 19

27, 24, 19, 12

20, 17, 12, 5 13, 10, 5, -2

Kyle 5 24, 21, 16, 9 19, 16, 11, 4 14, 11, 6, -1 9, 6, 1, -6

Len 3 14, 11, 6, -1 11, 8, 3, -4 8, 5, 0, -7 5, 2, -3, -10

Martin 2

9, 6, 1, -6 7, 4, -1, -8 5, 2, -3, -10 3, 0, -5, -12

3:0

Following Shapley-Shubik, stable matches max Σu.

6:2

14:5

24:10 13:18 11:13

8:6

2:3

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Gains from marriage with one wife, with two wives, with three wives…

Abby 5

Barbara 4

Carrie 3

Dana 2

Jake 7 34, 27, 8, -29 27, 20, 1, -36 20, 13, -6, - 43

13, 6, -13, -50

Kyle 5 24, 17, -2, - 39

19, 12, -7, - 44

14, 7, -12, - 49

9, 2, -17, --54

Len 3 14, 7, -12, - 49

11, 4, -15, - 52

8, 1, -18, -55 5, -2, -21, -58

Martin 2

9, 2, -17, -54 7, 0, -19, -56 5, -2, -21, -58 3, -4, -23, -60

3:0

Following Shapley-Shubik, stable matches max Σu.

6:2

14:5

24:10 11:16 9:11

8:6

2:3

 3nU FiMFi  

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Some observations  The steeper is the decline in MP, the stronger

is the case against polygamy  If men and women are complements, the

high-θ persons will be polygamous  PAM is sustained  The extent of polygamy will depend on how

dispersed θ is among men (most men will likely have 1 wife anyway)

 Since polygyny increases competition among men, women get larger share of overall gain

 Flip-side: this will make many (most) men worse off relative to monogamy

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Some political economy

 If…  …steep MP works against polygyny  …polygyny implies potentially large

redistributive consequences within marriage in favor of women

 …polygyny reduces many men’s utility by either leaving them wifeless or with lower share

… then why would any male-dominated society ever allow this?

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Will men vote for monogamy?

Abby 5

Barbara 4

Carrie 3

Dana 2

Jake 7 34, 31, 26, 19

27, 24, 19, 12

20, 17, 12, 5 13, 10, 5, -2

Kyle 5 24, 21, 16, 9 19, 16, 11, 4 14, 11, 6, -1 9, 6, 1, -6

Len 3 14, 11, 6, -1 11, 8, 3, -4 8, 5, 0, -7 5, 2, -3, -10

Martin 2

9, 6, 1, -6 7, 4, -1, -8 5, 2, -3, -10 3, 0, -5, -12

3:0

Following Shapley-Shubik, stable matches max Σu.

6:2

14:5

24:10 13:18 11:13

8:6

2:3

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Nature of marriage law in polygynous societies

 Bride-price (bride-service) instead of dowry  Women do not choose their husbands, their

fathers do  Fathers also collect bride price

 All wives are not equal by law (concubines have lower standing, weaker claim on resources etc.)

 Some societies have a cap on number of wives  Women are not in a position to divorce (either

legally or factually):  Outside options reduced  Competition inside marriage is intensified

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Bait & switch marriage  Bargaining strength may change

significantly right after wedding  We will see some evidence of it next time  With polygyny, men compete before the

wedding but then women compete afterwards

 We have seen that competition reduces the net gains claimed by competitors

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Who’s in favor of polygyny?

 Fathers of daughters (if they can sell them)

 High-θ men if law supports them inside marriage

 Societies where high-θ men hold power  Societies with badly skewed sex ratios

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Empirical predictions about polygamy

 It is a form of inequality  It is likely to arise where

 Sex ratio is out of whack  Militarized/fighting societies with high male casualty

 There is high inequality among men’s resources  Most productive men may take on a second wife

 Steep decline in MP of wife works agst poly  Relatively small proportion of men go poly  For most men and women it is not a winning

proposition

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Empirics of polygamy  How is it measured?

 Law vs practice  Unit of observation: Individual vs society  Household formation vs parenthood issues

 Result: many gray areas  Concubinage  Extra-marital relationships  Open marriages  Man-sharing

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Are Westerners different?  Debate on western monogamy

 Alexander (1987), Betzig (1986), MacDonald (1990) – male compromise theory

 Compromise: “Loyalty to king in return for a wife in every bed”

 Kanazawa & Still (1999) – falling inequality theory

 High inequality among men breeds polygyny  Declining inequality will produce monogamy  The switch is made by women (or whoever

decides for them)

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But then again: are westerners different?

 Powerful men have things going on the side in all societies

 “Dagobert I repudiated one wife and married three others simultaneously, while maintaining so many concubines that the chronicler Fredegar declared that he could not spare space to name them all.” (MacDonald, 1990: 230)

 Chinese law: 1 wife + any # concubines  European law: 1 wife + any # mistresses

 Nobles and even high churchmen had “harems”  Difference is mostly legal

 For women: who has the stronger bargaining position  For children: who is the legitimate heir

 Remember: this is before the rise of “love” in marriage  Marriage serves primarily as a property-rights institution

Polygamy around the world

26Source: Stolen from Wikipedia

Fenske’s (2012) data on polygamy in Africa

 DHS survey data  From 34 countries  Spans 1986 – 2009

 Some 300K women:  Red are polygamous  Blue are monogamous

 Distribution:  72% are sole wives  19% have 1 co-wife  7% have 2 co-wives  2% have 3 or more co-wives

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What explains polygamy?  Fenske tests numerous hypotheses out there:

 Agricultural productivity of women (rejects)  Inequality (rejects for current, but not for past)  Slavery (sort of not rejects)  Women’s education (rejects for modern, not for

historical)  Economic growth correlates with reduction of poly  Legislation = bans (rejects)

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Fenske (2012) – Inequality

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Gould, Moav and Simhon (2008)

 The mystery of monogamy:  Why are developed societies monogamous

and poor ones polygynous?  If polygyny is a result of inequality among

men, economic growth may (should?) encourage it

 There are potentially bigger inequalities among Americans than among the !Kung

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Gould, Moav and Simhon (2008)

 Quality-quantity trade-off:  In poor societies:

 Inequality stems from non-labor income (inherited wealth)  Demand for quality in children is relatively low  Quality of children is secondary, quantity matters  Women are close substitutes as child-bearers  Men care about quantity of women (and children)

 In rich societies  Inequality arises from human capital inequality  If men care about their children, they put greater stress on child

quality  Quality of children matters, quantity declines (low TFR)  Women are not easily substitutable: high-quality women are preferred  Price of quality in women increases, making polygyny less affordable  Lower demand for child quantity also reduces men’s willingness to pay

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Gould, Moav and Simhon (2008)

 Issues:  What is polygyny in this paper?  How do we know it has declined?  How does the definition rule out serial

polygyny (i.e. divorce and remarriage)?

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Tertilt (2006)  How is polygyny related to poverty?

 Polygyny is usually associated with bride-price, bride-wealth or bride-service

 Daughters are therefore a valuable asset  Sons are a wash

 Macro impact:  Children (especially daughters) are a good

investment  Men will demand high fertility from many wives  Age gap between men and women is higher than

under monogamy and population growth is also high  Investment is siphoned-off into “wife-trade”  Lower investment in physical capital (less growth)

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How to break the vicious cycle

 Tertilt (2008) argues that banning polygyny has not worked much

 It is hard to enforce it  All you need, in fact, is personal autonomy for

women and monogamy will (likely) follow  Women will now collect bride price  This means fathers’ returns to children decline  This will reduce demand for children and by extension for

multiple wives  Macro impact of monogamy:

 Less investment in obtaining wives and breeding children  More investment in physical capital  More economic growth

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Tertilt (2006)  Issues:

 If ban on polygyny is hard to enforce, why should women’s property rights be any easier?

 This is a redistributive policy – how does that affect, however, the overall gains from marriage?

 Still, the paper highlights the fact that polygyny is unpopular among women because it is associated with HUGE disparity in bargaining power between men and women

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Conclusions  Polygyny is not just a question of law  Generally, it is affected by the technology of producing gains

from relationship  The size and shape of MP curve for extra spouses

 Given current technology (of child production), 2 people per marriage is likely the optimum

 There may be a few high-quality men who can pull off multiple partners but they are a tiny minority

 On the face of it, polygyny leads to more competition for women which should benefit them

 Bride-price: result of high demand  However, women never benefit in traditional societies because

they do not “own themselves” = make their own decisions  Widespread polygyny can potentially be a cause of poverty