### Coase Theorem and Divorce

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Negative Externalities
Consider the polluting factory:
the cost of the smoke and
pollution to residents nearby is
external to the factory.
Total Marginal Costs
P
Private Marginal Cost
D
Pm
Q
Q*
QToo Much
• Pigouvian analysis:
(inefficiency)
• Solution: tax factory so
private costs=total costs
• Internalize the externality
In 1960 Coase showed that the Pigouvian analysis was wrong.
External costs do not necessarily create inefficiencies.
Consider our polluting factory again. If firm cuts output from QToo
Much to Q* it loses C in producer surplus.
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Total Marginal Costs
P
Private Marginal
Cost
D
A
C
B
Q
Q
QToo Much
• Nearby homeowners benefit by D+C,
more than the loses by the factory.
• If transaction costs are low the two
parties should be able to find an
exchange to make both better off.
• e.g. homeowners pay factory D/2+C to
reduce output to Q*
• Both parties gain!
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Market will internalize some externalities automatically
Opportunity cost
• If homeowners are willing to pay to have externality reduced
then the external cost is a cost to the firm.
• A profit maximizing firm will take into account the costs it
imposes on others as long as it is efficient to do so
P
Private marginal costs when
transaction costs are low and
damages tax is imposed
Private marginal costs when
transaction costs are low
Private Marginal Cost,
• Now look at effect of damages
tax
• An efficient outcome becomes
an inefficient one!
D
A
C
B
Q
QToo Little
Q*
QToo Much
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The divorce rate in the United States has increased
significantly over last 30 years.
One way to classify divorce: unilateral vs. mutual.
Under a mutual divorce rule both parties must agree to
divorce.
Under a unilateral divorce rule only one party needs to
desire divorce for the divorce to be granted.
In the 1970s there was a movement towards unilateral
divorce.
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Using the assumptions and predictions of the
Coase theorem what should be effect of either law
on divorces?
Consider John and Mary and Tom and Gerri, who
place different values on being married:
John
\$7
Tom
Mary
-\$5 Gerri
\$10
Total
\$2
-\$2
Total
-\$12
• Coase theorem says that John and Mary should stay together, and
Tom and Gerri should split up.
• Unilateral divorce: John pays Mary to stay together; Tom and Gerri
divorce with no payment.
• Mutual divorce: Tom pays Gerri to divorce; John and Mary stay
together with no payment.
Image from Divorce-Education.com
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Law should not change the number of divorces, divorce
still takes place when joint benefit of marriage < joint
cost of marriage
It should, however, effect how partners are
compensated
• Mutual divorce gives “property rights” to the spouse
that wants to stay married, they must be
compensated in order for a divorce to ocurr.
• Unilateral divorce gives “property rights” to the
spouse who wants to leave, they must be
compensated if the marriage is to stay intact.
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The actual effect of the change in trend from mutual to
unilateral divorce on divorces in the United States has
been debated in the literature.
Elizabeth Peters (1986) finds that this change had no
effect on the number of divorces, but did effect
compensation in the form of spousal support at divorce.
Leora Friedberg (1998) finds the shift to unilateral
divorce had a positive and permanent effect on the
divorce rate (but explains only 17 percent of the
change in divorce rates between 1968 and 1988.)
Justin Wolfers (2006) argues that this positive effect was
that in the end it had no discernable effect.
Stevenson/Wolfers (2003) show the effect of divorce
law change on well-being and spousal relations.
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Peters suggests two possible models for the marriage
contract
• Symmetric Information
 Both spouses have the same information about the value of
their alternatives to marriage (value of divorce)
 Bargaining is costless
 Similar to Coase theorem assumptions
• Asymmetric Information
 Neither spouse knows the value of the other’s alternatives
 Incentives to lie about opportunities to gain larger share of
marital wealth
 Bargaining is successfully prevented
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X=Initial marriage
wage for wife
Aw/h=Value of
opportunities outside
of marriage for wife or
husband
Wife wants divorce
when Aw>X (A,C,D)
M is the joint product
in marriage.
Husband when Ah>MX or M-Ah<X (A,E,F)
They agree in A, but
disagree elsewhere.
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Result:
With symmetric
information a
compensation scheme
exists so that divorce will
only occur when JOINT
benefit < JOINT cost (Areas
A, C, E)
However, if bargaining is
prevented by asymmetric
information:
Under mutual rule then
divorce will only occur in
A, where both parties
agree (lower than optimal)
Under unilateral rule
divorce will occur in all
highlighted areas (A + C +
E + F + D) when either
spouse desires divorce
(higher than optimal)
Under symmetric information law should not change number of divorces
Under asymmetric information we get more divorces under unilateral rule
than mutual rule
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Data on individuals from the March/April 1979 Current
Population Survey
• Demographic Variables (age, children, income, education, etc..)
• For those ever divorced: marital history, spousal support, value
of property settlements
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Categorized state divorce laws three ways
• Pure unilateral
• Mutual divorce (with binding arbitration if no agreement)
• Unilateral divorce possible, but large cost involved (i.e.
separation periods). Due to burden of high cost these states
are included under mutual divorce
• Note from Table 3 the sample sizes!
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Logit regression
Dependent variable: Probability of becoming a
divorcee during 1975-1978 given no previous divorces
Controls:
• Demographic variables
• Region of the US the woman lives
• State Divorce Rate in 1970
 Used to control for any unobserved propensity for divorce in the
given state
• Percent of Catholics in the state of residence
• Unilateral: a dummy variable, =1 if state of residence has pure
unilateral laws, =0 otherwise.
• The probability of divorce
decreases with age, education,
kids under 18 and varies
somewhat by region.
• Most importantly the
coefficient on unilateral is not
statistically significant and
negative (!) in one regression.
• Remarriage is less likely in a
state with unilateral divorce.
Why?
• But remember the sample
size!
• If such an effect exists is
it consistent with Coase?
Peters, H. Elizabeth. Marriage and Divorce: Informational Constraints and Private Contracting
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Under unilateral divorce there is compensation to keep the
marriage together – compensation goes to the party that wants out
of the marriage.
Under mutual divorce there is compensation to get the divorce –
compensation goes to the party that wants to stay in.
Therefore at divorce we should expect to see more compensation
under mutual divorce then under unilateral.
Divorce settlements consist of:
• Alimony
• Child Support
• Property Settlement
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We should also see a higher variance of settlement payments
under mutual divorce since you have to compensate the worse off
spouse which could be the husband or wife, while compensation
payments are not required under unilateral divorce.
Peters, H. Elizabeth. Marriage and Divorce: Informational Constraints and Private Contracting
• Variance of settlements
are larger in mutual
states.
• Mean is also lower in
unilateral states,
however, so we may want
to look at variance
relative to the mean.
• Thus Peters look also at
the “coefficient of
variation.” What is this?
• In both cases the
compensation is more
variable in mutual states
although less so for the
coefficient of variation
than the pure variance.
Peters, H. Elizabeth. Marriage and Divorce: Informational Constraints and Private Contracting
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Empirical results point to symmetric information model
(Coase theorem model)
• Bargaining occurs such that divorce only takes place
when joint benefit < joint cost, law has no effect on
number of divorces
• Law does have effect on compensation schemes
 Alimony/Child Support are lower in unilateral states
• Variance of payments is higher in mutual divorce
states
 Assumes
same model as used in Peters
(1986)
 Attempts to reconcile Peters (1986) and
Allen (1992)
• Allen(1992) argued that region dummies and
state divorce rate in 1970 just absorb the
variation in divorce laws and should not be
included. He found a significant, positive effect
of unilateral divorce laws on divorce rates.
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Claims there are two major difficulties in literature
• Controlling for differences in state/regional divorce
propensities
• Defining and categorizing state divorce laws
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Uses state level divorce rates as dependent variable
rather than individual propensities to divorce.
Uses state fixed effects: serve same purpose as Peters
inclusion of 1970 divorce rate but is more general.
• allows unobserved state divorce propensities to
trend linearly or quadratically and vary across states
Model:
• Divratest = c0 + c1*unilateralst + c2s*states + c3s*yeari +
c4s*states*timet + c5s*state*timet2 + ust
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Data on state divorce rates from Vital Statistics of the
United States.
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Regression 3.3 is similar to Peters’ with state fixed effects (Peters included state’s 1970 divorce
rate). Note that without fixed effects the result is positive and with fixed effects the affect
disappears. What does this mean? What does it imply about the unobserved variable?
3.4 and 3.5 then introduce linear and quadratic state trends. Note that there are still year
effects in the regression so what do these mean?
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Unilateral raised the divorce rate.
Thus only impefect Coasian bargaining takes place
among spouses.
State-specific trends matter.
Note, however, that her estimate is that unilateral raised
the divorce rate by about 10% or .4/4.6 per thousand.
The divorce rate doubled between about 1960 and
1980 from around 2.2 to 5 so unilateral explains
perhaps 14-15% of the increase. Much less than one
might imagine. A picture tells the real story.
 Besides
the endogeneity issue, another issue
plaguing research on divorce laws is
classification of states as unilateral or mutual
• Some unilateral states impose a mandatory
separation period which may impose a high cost on
unilateral divorce
• Other no-fault unilateral states still have fault
grounds for property settlement, which could distort
property rights from the spouse wishing to leave to
the one wishing to stay
 Friedberg
classifies “very strict” unilateral
divorce as divorce with no separation
requirement and no fault grounds for property
settlement.
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Type of unilateral divorce matters
Versions of unilateral divorce that impose more
requirements have smaller effects, i.e. strictest form of
unilateral divorce raises divorce rates the most.
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Did rising divorce rates cause a state to change its law from mutual
to unilateral? If so, the effect of unilateral on divorce rates will be
confounded by reverse causality.
Best solution is instrumental variables. Find a variable correlated
with the change in the law but not with divorce rates.
 E.g. # of women in the state legislature?
 # of state legislators who have been divorced?
 Whether a state has a referendum possibility?
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Friedberg doesn’t use IV but she does make an interesting
observation:
 She finds that the divorce rate does predict if a state adopts a unilateral law
but not when it adopts such a law. Since she has fixed effects in her
regression the estimated effect is identified by what happens within a state
when the law changes and not by differences across the states – hence she
suggests she is ok on this issue.
 But there is something peculiar going on. (Recall our discussion of fixed
effects and omitted variables.) Without state trends the effect of unilateral is
zero and with trends it is positive so the omitted variable which is correlated
with unilateral must be negatively correlated with trends in divorce rates, ie.
Driving divorce rates down. But the most plausible argument is that states
that passed unilateral laws did so because of omitted variables that would
have driven the divorce rate up!
The
method of controlling for
geographical heterogeneity in
divorce propensities is important
More flexible controls of unobserved
characteristics is crucial
Significant, positive, permanent
impact of the switch to unilateral
divorce law on divorce rates
 Are
state fixed effects/trends always a
good idea?
 The problem of efficiency
 The problem of dynamic effects
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Again assumes similar model as in Peters (1986)
Concerns about sensitivity to state-specific trends in
Friedberg’s model
Besides endogeneity issue, a major problem is
separating pre-existing trends from dynamic effects of
a policy shock
Thus, Wolfers considers that divorce can have a
dynamic response to changes in the law (policy shock)
Believes that immediately following reform there could
be a large rise in the divorce rate due to pent-up
demand for unilateral divorce
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Vertical line at 1969
represents change from
mutual to unilateral divorce
The bold line represents
Wolfers hypothetical model,
where divorce spikes right
after law change, then
eventually levels off to new
Notice Friedberg’s trend is
derived mostly from postchange data.
Lines marked “Before” and
“After” represent the
average difference between
the divorce rate and trend
before and after legal
change
• This difference is what is picked up in the “unilateral” dummy
variable in Friedberg’s regression
• Compare before and after after subtracting post-law trend with true
difference.
• Thus Friedberg’s model may overstate effect of law change in the
long run
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Adds dummy variables that model the dynamic
response:
• For first two years of new legal regime
• Then years three, four, five, etc..
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Dependent variable is divorce rate
Includes state fixed effects, time fixed effects, and
state-time effects
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All three regressions suggest that divorces spiked immediately
after legal change, and then the effect declines over subsequent
years
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Also does analysis on the stock of divorces.
Finds, following Gruber, that the stock of divorces
increases (contrary to the earlier results).
But currently divorced population from census data
does not include those that have remarried
• Data show that only 49% of those ever-divorced are currently
divorced
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So Wolfers creates a measure of the ever-divorced
population: which includes those currently divorced
and those currently married, separated, or widowed
but are on their second marriage
Then analyzes effect of divorce law on ever-divorced
population
•No effect of divorce laws on ever-divorced population by 1980
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Though there is an immediate spike in divorce rate
following the switch to unilateral divorce, this effect
falls over time
In the long run the switch to unilateral divorce appears
to have no discernible effect on the amount of divorces
or the size of the ever divorce population
Both regressions seem to indicate that unilateral
divorce laws explain only a small fraction of large rises
in divorce rates
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Coasian prediction is much closer to reality than the
opposite.
Let p=prob. that divorce will be desired.
Then p^2 is prob. both partners will desire divorce.
Assume a mutual consent state and no bargaining then
p^2 is the divorce probability.
Divorce in states with unilateral divorce should then be
2p-p^2
In mutual consent state in 1960 about .2 are divorced
thus .2=p^2 and p=.45 so increase in divorce should be
on the order of
2p-p^2-p^2=.9-.2-.2=.5=50%!
Actual increase is 0.5%
Thus Coasian bargaining very much supported.
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Coase Theorem says no impact of divorce law on
number of divorces. Coase Theorem holds up well
empirically.
But Coase Theorem also says that changing from
mutual to unilateral divorce changes the bargaining
power of spouses.
This effects spousal relations and well-being even if it
has no effect on the divorce rate.
Recall:
• Mutual divorce gives “property rights” to the spouse that wants
to stay married, they must be compensated in order for a
divorce to occur.
• Unilateral divorce gives “property rights” to the spouse who
wants to leave, they must be compensated if the marriage is to
stay intact.
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Women file for divorce more often than men so there is
a suggestion that unilateral divorce benefits women.
 There
is no necessary benefit to women,
however.
 Three measures of well-being and spousal
relations: suicide, domestic violence and
spousal murder.
 Expected sign is difficult to hypothesize:
• Suicide and Divorce may be substitutes, so easier
divorce could mean a lower suicide rate.
• Easier divorce may leave more upset and
abandoned spouses, increasing suicide rate.
• Unilateral divorce offers a credible threat of exit
which may reduce domestic violence.
• However, domestic violence could be used to
enforce the marriage contract which the law no
longer offers.
 Common
preferences – Rotten Kid
Theorem.
 Threat Points – internal and exit.
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Use state-based panel data
A dummy variable indicates whether the state had
unilateral divorce at that time
State and time fixed effects are included in all
regressions
Dependent variables: suicide rate, domestic violence
(a dummy variable indicating whether a specified type
of violence occurred in the household), intimate
murder rate.
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Dependent variable: suicide of all persons
Controls:
• unilateralk, a series of dummies that equal one if a state
changed to unilateral divorce k years ago (thus shows dynamic
response of the suicide rate
• State fixed effects
• Year fixed effects
• Male/Female employment rates, state income per capita,
unemployment, share of state population on welfare, availabilty
of abortion, racial/age composition of state
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Also disaggregated data on women by age
• Would expect smaller or no effect in very young and very old
women
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Statistically significant
reduction in female suicides
after change to unilateral
regime
No effect on male suicide
changes effect of unilateral
divorce
Note, however, that with state
specific time trends less can
be concluded.
• Note that there is
little or no evidence
change in divorce law.
•Little or no effect of switch to unilateral divorce on teens and the elderly
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Data comes from Family Violence Surveys in 1976 and
1985
Compares treatment states (those who changed to
unilateral divorce) to control states (those yet to adopt
unilateral or those with pre-existing regimes involving
unilateral divorce)
Expect changing violence propensities in treatment
group relative to controls
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Treatment led to a decrease in husband to wife domestic violence
rates.
Note that a large fraction of the change comes from the control
states.
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Dependent variable: domestic violence dummy, =1 if certain type of
violence occurred in household
DV rates declined with treatment (adoption of unilateral divorce)
Data on homicides come
from FBI Uniform Crime
Reports (UCR).
Includes relationship
of the victim to
murderer
• Significant decline in
rate of women
murdered after
divorce
• Robust to a set of
controls including
demographic/economic
variables and criminal
justice variables
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Uses time to/since adoption of unilateral
Again, a decrease in women murdered after switch to unilateral.
Endogeneity issues? What else is going on?
However, seems decline started before passage of law
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