Marriage and Divorce

Economic DemographyDemog/Econ C175Prof. Ryan Edwards

April 2, 2020

4/2/20 12:17 PM demog/econ c175 1

Betsey Stevenson and Justin Wolfers

4/2/20 12:17 PM demog/econ c175 2

Betsey Stevenson and Justin Wolfers

4/2/20 12:17 PM demog/econ c175 3

Serious, useful stuff from IHME

• https://covid19.healthdata.org/

• Epidemiology models show possible timing of COVID-19 impacts

• “Flatten the curve” = postpone the peak• Interesting to compare CA, OR, WA and

others

4/2/20 12:19 PM demog/econ c175 4

Agenda

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

• Divorce• Hopefully some modernity

4/2/20 12:17 PM demog/econ c175 5

A note on “Why” vs. “why not”

• Becker tries to explain “why marry”

• Contrast this with the Malthusian approach, which views marriage as a “normal good”

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

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Some discussion

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

forming a "firm"?

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What are we trying to explain?(USA example)

Becker tries to explain “why marry”

4/2/20 12:17 PM demog/econ c175 8

But is marriage really declining?

1970 1990 2010

020

4060

80100

survey year

Per

cent

eve

r-m

arrie

d By age 25

4/2/20 12:17 PM demog/econ c175 9

But is marriage really declining?

1970 1990 2010

020

4060

80100

survey year

Per

cent

eve

r-m

arrie

d By age 25

By age 50

4/2/20 12:17 PM demog/econ c175 10

But is 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

4/2/20 12:17 PM demog/econ c175 11

12

Stevenson and Wolfers (2007)

13

Stevenson and Wolfers (2007)

14

• The outcome of a coupling correlates with perspectives reported by the couple

• The majority group is those who think they’re in a precursor to marriage, and a majority of those couples were later married

• But there is much heterogeneity too!

Bianchi and Casper (2000)

17

marriage, a substitute for marriage, orsimply a serious boyfriend-girlfriendrelationship.34 In a 1987-1988 survey,46 percent of cohabitors character-ized their living arrangement as a pre-cursor to marriage (see Table 1).Another 15 percent of these relation-ships were classified as a trial mar-riage and 10 percent as a substitutefor marriage. Nearly 30 percent of therelationships were characterized ascoresidential dating.

Some researchers believe thatcohabitation closely resembles mar-riage. If so, family life as we know it isnot likely to be altered much as aconsequence of cohabitation becausethese cohabitors will either eventuallymarry (precursor) or are already in arelationship which functions like amarriage (substitute).

Other researchers maintain thatcohabitation is more like being single.Cohabitation is seen as an enjoyablerelationship of convenience that provides intimacy without the long-term commitment of marriage. Thisinterpretation worries many peoplebecause it suggests that the increasein cohabitation signals a retreat frommarriage. It allows for an intimate,but temporary, relationship without commitment or responsibility.

Still others argue that livingtogether before marriage is some-where between marriage and single-hood and that cohabitation provides acouple the opportunity to assess theircompatibility before getting married.In this trial period, incompatiblemates can easily end their relationshipand presumably escape an unsuitablemarriage. Thus, cohabitation mightstrengthen marriage and family lifebecause some unsuited couples areweeded out before they marry.

About 40 percent of all unmarriedcouples surveyed in 1987-1988 weremarried within five to seven years.Their reasons for forming the rela-tionship were strongly related to itseventual outcome.35 Those with thestrongest commitment to one anotherand to marriage were most likely toget married. More than one-half ofcouples who characterized their living

together as a precursor to marriagedid marry within five to seven years,compared with 33 percent of “dating”couples with no long-term expecta-tions about their partner, their relationship, or marriage. About one-quarter of unmarried couples in “trialmarriage” or “substitute marriage”married within the seven years.

How do unmarried couples com-pare with married couples? Althoughmany cohabiting couples eventuallymarry, men and women who choose tolive together outside marriage differfrom married couples in some veryinteresting ways. In general, cohabitingcouples tend to be more egalitarianand less traditional than married cou-ples. Compared with a woman who ispart of a married couple, for example,a woman in a cohabiting relationshipis more likely to be older than theman, to be of a different race or eth-nic group than the man, to contributea greater percentage to the couple’sincome, and to have more educationthan the man.

American women tend to marrymen a few years older than themselvesand relatively few marry a muchyounger man. Yet nearly one-fourth ofwomen in cohabiting couples were twoor more years older than their malepartner, compared with one-eighth of

Table 1Unmarried Couples by Relationship Type in1987–1988, and After Five to Seven Years

Outcome of relationshipafter 5 to 7 years

Type of relationship All couples Still live in 1987-1988 Percent together1 Married 2 Separated3

All unmarried couples 100 21 40 39

Substitute for marriage 10 39 25 35Precursor to marriage 46 17 52 31Trial marriage 15 21 28 51Coresidential dating 29 21 33 46

Note: Couples were interviewed between 1987 and 1988 and again from 1992 to 1994.

1 Couple was still cohabiting at the time of the second survey. 2 Got married some time between the two surveys (may or may not be currently married).3 No longer cohabiting.

Source: L.M. Casper and L.C. Sayer, “Cohabitation Transitions: Different Attitudes andPurposes, Different Paths.” (Paper presented at the annual meeting of the PopulationAssociation of America, Los Angeles, March 2000.)

15

Stevenson and Wolfers (2007)

In the U.S., more “churn” just like in the labor market!

The economics of marriage, partnering, and divorce

• Economists tend to believe that people tend to do things that are in their own best interest

• Thus marrying or not, partnering or not, getting divorced or not, all rational decisions about maximizing the gains to marriage relative to not marrying or divorcing

• Aren’t we silly?

• But in traditional societies, marriages were and are a more obviously rational choice, typically made by extended families

• Still, during the 20th century, the nature of the gains marriage has probably changed a lot

16

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

4/2/20 12:17 PM demog/econ c175 17

Economies of scale

• Easier and cheaper for one adult to: – Vacuum 2 rooms rather than both vacuum 1

room– Cook a meal for 2 rather than for 1– Rent space for 2 rather than 1 (think: do you

have a roommate?)– Buy a single refrigerator that holds food for 2

rather than two fridges each holding food for 1

4/2/20 12:17 PM demog/econ c175 18

Public Goods• These are goods that 1 person consuming

doesn't leave less for the other • (The downside is a reduced incentive to

purchase if the benefits aren’t excludable)• Examples

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

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Children

• Biological children are product of male and female contributions

• Also possible to obtain outside of a partnership

• Investments in children provide utility to both parents(?)

• Few perfect substitutes (adoption? pets?)

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“Own Children” and other somewhat outdated perspectives

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)4/2/20 12:17 PM demog/econ c175 21

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.

4/2/20 12:17 PM demog/econ c175 22

So why not just live with roommates?

• Can benefit from economies of scale and public goods

• Can benefit from trade (comparative advantage), if roommates split up chores

• So what's the difference?– Becker points to "own children"– Marriage contract (vs. roommate contract)

encourages investments in relationship-specific capital4/2/20 12:17 PM demog/econ c175 23

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 spouse specializes in its comparative advantage then combined production will be higher — even if one spouse is better at both

• Same as comparative advantage and international trade4/2/20 12:17 PM demog/econ c175 24

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• (It doesn’t have to be this way but often is.

There are many kinds of partnerships)

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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?4/2/20 12:17 PM demog/econ c175 26

Production possibility frontiers

X = marketpurchasedgoods

H = home produced goods

women men

a married man or woman(with “trade”)

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"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.

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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

4/2/20 12:17 PM demog/econ c175 29

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"4/2/20 12:17 PM demog/econ c175 30

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?

4/2/20 12:17 PM demog/econ c175 31

Our Lab 10

• Compare straight and gay couples in the ACS

• We won't ask who is more likely to marry (interesting, but we don't have good data)

• Instead, we’ll look at whether partners in gay marriages differ from each other more than partners in straight marriages

• We’ll talk more next time about “assortative mating”

4/2/20 12:17 PM demog/econ c175 32

A more modern 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)4/2/20 12:17 PM demog/econ c175 33

A more modern 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?

• But we see big differences in marital trends across socioeconomic and educational classes

4/2/20 12:17 PM demog/econ c175 34

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?

4/2/20 12:17 PM demog/econ c175 35

Divorce by duration of marriage

4/2/20 12:17 PM demog/econ c175 36

Divorce trends

4/2/20 12:17 PM demog/econ c175 37

A feedback model of divorce:Causes, consequences = causes

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

=

4/2/20 12:17 PM demog/econ c175 38

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

4/2/20 12:17 PM demog/econ c175 39

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.

4/2/20 12:17 PM demog/econ c175 40

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?

4/2/20 12:17 PM demog/econ c175 41

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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4/2/20 12:17 PM demog/econ c175 42