Why Marry?One economist's answer

Prof. GoldsteinEconomic Demography

Econ/Demog C175Week 10, Lecture A

UC BerkeleySpring 2019

Agenda

• Becker’s theory of “gains to marriage”– Many advantages– Specialization

• Divorce

A note on “Why” vs. “why not”

• Becker tries to explain “why marry”

• Contrast with Malthus approach, which views marriage as a “normal good”

• Malthus: “why not?” Answer: "can't afford it"

Some discussion

• Why live together?• Why marry?• What's the difference?• How is this similar or different from

forming a "firm"?

What are we trying to explain?(USA example)

Becker tries to explain “why marry”

Are marriage really declining?

1970 1990 2010

020

4060

80100

survey year

Per

cent

eve

r-m

arrie

d By age 25

Are marriage really declining?

1970 1990 2010

020

4060

80100

survey year

Per

cent

eve

r-m

arrie

d By age 25

By age 50

Are marriage really declining?

1970 1990 2010

020

4060

80100

survey year

Per

cent

eve

r-m

arrie

d By age 25

By age 50

1940 1960 1980

020

4060

80100

birth cohort

Per

cent

eve

r-m

arrie

d By age 25

By age 50

Becker’s theory of gains to marriage

• An extension of international trade theory • Many of gains to marriage come from

comparative advantage• Ideology sounds like 1950s (we should ask if it

applies today)• But first: other advantages:

– economies of scale– household public goods – own-children– can build marriage-specific capital

Economies of scale

• Easier and cheaper to vacuum 2 rooms (than each to vacuum 1 room)

• Making noodles?• What else?

Public Goods

• These are goods that 1 person consuming doesn't leave less for the other (Challenge is lack of investment incentive)

• Examples– A clean house – A view of the Golden Gate– Subscription to internet, cable, magazine, …– Others?

"Own Children"

• Biological children are product of both mother and father

• Investments in children provide utility to both parents

• Few perfect substitutes (adoption? pets? ...?)

"Own Children"

8I8 JOURNAL OF POLITICAL ECONOMY

wl" > wf and if.MPtf 2 MP, when tf = tm. Indeed, F would specialize in the nonmarket sector (If 0) if either Wm/w or AlIP tfMPt, were sufficiently large.

A singles household is taken to be exactly the same as a married one

except that T1 = 0 when Al is single and Tm = 0 when F is single. A

singles household allocates only its own time between the market and

nonmarket sectors to satisfy equation (7). Single persons generally allocate

their time differently than married persons because the former do not

have time and goods supplied by a mate. These differences depend partly

on the elasticities of substitution among the xi, tf and ti) and partly on the differences between the market wage rates wm and Wf. For example, single F are more likely to "work" more than married F and single M

less than married Al, the greater the percentage excess of wm over Wf.

Empirically, single women clearly "work" more than married women and

single men less than married men.7

If ZnO and Zof represent the maximum outputs of single M and F, and rnmf andfInf their incomes when married, a necessary condition for M and F to marry is that

MMf > ZM 0

fmf > ZOf (8)

If ?fn1nf + fmf5 the total income produced by the marriage, is identified witlh the output of the marriage,8 a necessary condition for marriage is then that

mmf + fnf Znf > ZmO + ZOf (9) Since most men and women over age 20 are married in all societies,

equation (9) must generally hold because of fundamental reasons that

are not unique to time or place. We have a useful framework for discover-

ing these reasons.

The obvious explanation for marriages between men and women lies

in the desire to raise own children and the physical and emotional

attraction between sexes. Nothing distinguishes married households

more from singles households or from those with several members of the

same sex than the presence, even indirectly, of children. Sexual gratifica- tion, cleaning, feeding, and other services can be purchased, but not own

children:9 both the man and woman are required to produce their own

children and perhaps to raise them. The physical and emotional involve- ment called "love" is also primarily between persons of the opposite sex.

7 See, e.g., Eniployment Status and Work Experience (U.S., Bureau of the Census 1963), tables 4 and 12.

8 Income and output can differ, however, because some output may be jointly con- sumed. See the discussion in section 3 and Part II.

9 The market in adoptions is used primarily by couples experiencing difficulties in having their own children and by couples paid to raise other persons' children.

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Becker (1973: 818)

Marriage-specific capital• Analogy to firms• Capital that is worth something only with specific

firm (marriage). If we change partners, lose it all.• In marriage

– Learning partner's preferences and how to get along– Specialization (giving up work to stay at home and take

care of kids)– Getting to know in-laws– What else?

• Important point: a contract (to stay together) provides incentive to invest in marriage-specific capital. Risky without contract.

So why not just live with roommates?

• Can benefit from economies of scale and public goods

• Can benefit from trade (comp. adv.)• So what's the difference?

– Becker points to "own children"– Marriage contract (vs. roommate contract)

encourages investments in relationship-specific capital

Comparative Advantage in Marriage

• One spouse specializes in market work• One specializes in home production• Why?

– endowments? (biology)– human capital investments? (culture)– feedback: small initial differences get

reinforced• If each sex specializes in its comparative

advantage then combined production will be higher

In Becker's world

• Two kinds of activities (home and market)• Men have comparative advantage in market• Women have comparative adv. in home• This logic à specialization

An simple example

If each person spends alltheir energy doing home or market production

Home MarketWoman 20 | 10Man 10 | 20

If each splits own time 50-50

Home MarketWoman 10 + 5Man 5 + 10

Total prod 15 15

Can they do better?

Production possibility frontiers

X = marketpurchasedgoods

H = home produced goods

women men

a married man or woman(with “trade”)

"terms of trade"

• One person can compensate other: they agree on amount of market goods for home goods.

• Subject to negotiation. • Doesn't have to be 1:1• Just as long as both parties benefit.

Notes on Comparative Advantage

• Surprising result: Could have one person be a more efficient producer of both goods. As long as relative efficiency is different, trade benefits both people.

• One way to understand comparative advantage is that each person has a different opportunity cost

Opportunity Cost

• OC(A) = Units of B that could be produced in time it takes to produce 1 unit of A (slopes of PPF)

• If both parties have same OC, then no benefits to specialization and trade

• If OC differs, then there are "gains to trade" – even if one party better at both!

• Becker calls these "gains to marriage"

Implications of comparative advantage theory ...?

What will be the impact of: • Male and female convergence?• Lower fertility?• Improved home technology?• For straight vs. gay marriage?

Our Lab

• Compare straight and gay couples• We won't ask who is more likely to marry

(interesting, but don't have data)• Instead, we'll look at whether partners in

gay marriages differ from each other more than partners in straight marriages

• Will talk about more on Thursday "Assortative mating"

A dissenting voice

28 Journal of Economic Perspectives

ity of birth control and abortion has affected the potential consequences of sex both in and out of marriage, while changes in divorce laws have altered the terms of the marital bargain. These forces also have important feedback effects, changing the pool of marriageable singles across the age distribution, thereby affecting search, marriage, remarriage, and the extent of "churning" in the marriage market.

To remain relevant to the twenty-first century, the economics of the family will

need to push beyond the production of own children and traditional notions of specialization, and seek to uncover the forces that yield the modern family form. This may mean reconceiving the notion of household production or, as we argue, extending models of the family beyond the notion of a household-based firm and toward emphasizing motivations such as consumption complementarities and in- surance as central to marriage. Furthermore, the economic theory of the family as originally developed was a theory of household formation, rather than a theory of legal marriage. Couples have become increasingly likely to form households with- out entering into a marriage, adding a new dimension for considering decisions surrounding family formation. This article lays the groundwork for a reconsidera- tion of the theory of the family by describing the tremendous changes in family forms related to marriage and divorce, pointing to some of their driving forces, and

suggesting ways of expanding our thinking about the family to understand its future better.

Trends in Marriage and Divorce

Figure 1 lays out some facts about marriage and divorce in the United States over the last 150 years: the divorce rate-measured as the number of new divorces each year on a per capita basis-has risen, while the marriage rate has fluctuated around a relatively stable mean. The timing of these changes suggests that social and economic factors strongly influence the marriage market. Marriage rates rose during, and in the wake of, the two world wars and fell during the Great Depres- sion. The divorce rate fell during the Depression and spiked following World War II.

Developments since the 1960s appear to reflect more subtle influences, and have been the focus of heated political debate. Divorce rates rose sharply, doubling between the mid-1960s and the mid-1970s. During this period, family life was potentially altered by many factors: the rise of the women's liberation movement; the sexual revolution; the Supreme Court's granting of marriage as a "fundamen- tal" right under the U.S. Constitution and thus the abolition of laws restricting marriage between races; the elimination in many states of fault-based divorce; and a sharp rise in women's labor force participation. Yet when viewed over a longer time period, we see that while the 1970s had exceptionally high divorce rates, the low divorce rates in previous decades were also somewhat exceptional. Fitting a simple trend line to the divorce rate between 1860 and 1945 (thereby excluding the post-World War II surge in divorce) as shown in Figure 1, suggests that some of the

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Any guesses? (Hint: this weeks reading)

A dissenting voice, cont.

• In consumption, being alike makes marriage more fun (movies, books, politics, identity, children …)

• So men and women becoming more alike should make marriage more common?

Divorce

• Why do people divorce?– Gains to marriage less than to divorce– Poor information leads to mismatch

• Declining gains to marriage– less sex-specialization– fewer marriage-specific investments (e.g., kids,

building own house, kin ties)– a vicious circle?

Divorce by duration of marriage

Divorce trends

Divorce feedback model

higher divorce

declines in gains to marriage• less marriage-specific investment• dangers for women of specialization• increased market training for women• increased home technology for men

declining costs to divorce• less stigma• better remarriage market• fewer kids

+

The future

• Big changes were in 60s and 70s• Since 1980

– divorce rate flat– marriage still getting later, but not much less common– fertility is flat

• Divorce inequality: decrease for more educated, increase for less educated

Recent trends: A puzzle

0

10

20

30

40

1960-64 1965-69 1970-74 1975-79 1980-84 1985-89 1990-94

Year of Marriage

Perc

ent

No 4-Year College Degree 4-Year College Degree

Source: SIPP (2001)

Percent of U.S. Women with a Marital Dissolution within 10 Years of a First Marriage, by Year of Marriage and Educational Attainment.

Broader puzzles in marriage inequality

• Why marriage inequality? Wouldn't poor and those with fewer resources have the most to gain?

• Black vs. White differences?• Education differences?• Cross-country differences?

Next time

• Who marries whom, why do "likes like likes"?

A THEORY OF MARRIAGE 823

3. The Marriage Market and Sorting of Mates

a) Optimal Sorting

We now consider not one M and F who must decide whether to marry

or remain single, but many M's and F's who must decide whom to

marry among numerous potential candidates, as well as whether to marry.

If there are n M's and n F's (unequal numbers of M and F are discussed in section 4), each is assumed to know all the relevant22 entries in an

n + 1 x n + 1 payoff matrix showing the maximum household com-

modity output that can be produced by any combination of M and F:

F1 ... F

M Z ~~... M11 l 1 I ff ln 10 M~ z~ ...zn,,zj (12) Mn Zn *-.. Znn ZnO .12 Z01 ... ZOn

The last row and column give the output of single M and F. Each person

has n + 1 possibilities and the 2n persons together have n2 + 2n pos- sibilities. We assume that each person gains from marriage, so that the

singles row and column of the payoff matrix can be ignored.

There are n! different combinations that permit each M to marry one

F and vice versa; that is, there are n! ways to select one entry in each

married row and column. The total output over all marriages produced by any one sorting can be written as

Zk = E Z~jj k = 1,.. ., n!. (13) ieM, jeF

Number one of the sortings that maximizes total output so that its entries lie along the diagonal and write

n

= ZZ = maxkZ > Zk all k. (14) i j= 1

If the total output of any marriage is divided between the mates,

mij + fij = Zip (15)

where mij is the income of the ith M from marriage to the jth F, and similarly for fij. If each chooses the mate who maximizes his or her "income," the optimal sorting must have the property that persons not

married to each other could not marry and make one better off with-

out making the other worse off. In game theoretic languiaome the ontimal

22 That is, all the entries relevant to their decisions. This strong assumption of sufficient information is relaxed in Part II, where "search" for a mate is analyzed.

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