Marriage Contracts and Divorce an Equilibrium Analysis

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Marriage Contracts and Divorce an Equilibrium Analysis Powered By Docstoc
					Birth control and women's
       empowerment

      Pierre Andre Chiappori
          Sonia Oreffice

  Conference: The economics of the family
         London, September 2006
          Introduction: Abortion and
            ‘Female Empowerment’
                   General view:
         abortion as ‘empowering’ women

•       Common claim in feminist and sociological literatures
•       However, not obvious: clearly some women are made
        better off, but should we expect all women to benefit
        from the reform?
•       In particular:
    –      What about women who want children / exclude abortion?
    –      What impact on the ‘market for marriage’?
    –      What consequences on intrahousehold allocations?
          Introduction: Abortion and
            ‘Female Empowerment’
                   General view:
         abortion as ‘empowering’ women

•       Common claim in feminist and sociological literatures
•       However, not obvious: clearly some women are made
        better off, but should we expect all women to benefit
        from the reform?
•       In particular:
    –      What about women who want children?
    –      What impact on the ‘market for marriage’?
    –      What consequences on intrahousehold allocations?
                    This paper
•   Marriage as matching (as opposed to bargaining)
•   Identical men; women differ in their preferences for
    children
•   Abortion as exogenous change in birth control
    technology
                         This paper
    •    Marriage as matching (as opposed to bargaining)
    •    Identical men; women differ in their preferences for
         children
    •    Abortion as exogenous change in birth control
         technology


                        Conclusions
•       Two cases (which side in excess supply?), various regimes
•       Women in excess supply: all women benefit in general
•       Crucial conditions: technology available to single as well
•       Plus: comparative statics
•       Difference with bargaining: the commitment issue
                      Related work
•   Akerlof, Yellen and Katz (1996) on out-of-wedlock
    child bearing in the United States (‘shotgun
    marriages’)
    –   Related issues, different approach
    –   Major differences:
        •   ‘Change in social norms’
        •   Intrahousehold allocation as exogenous in AYK, whereas
            endogeneity crucial here
                      Related work
•   Akerlof, Yellen and Katz (1996) on out-of-wedlock
    child bearing in the United States (‘shotgun
    marriages’)
    –   Related issues, different approach
    –   Major differences:
        •   ‘Change in social norms’
        •   Intrahousehold allocation as exogenous in AYK, whereas
            endogeneity crucial here
•   Neal (2004): matching model
    –   Similar approach; different emphasis
•   ‘Collective’ models of household behavior
    –   Same family
    –   Idea: endogeneize the sharing rule
    –   Examples: Chiappori-Iyigun-Weiss
                        The model
•   Continuum of men and women; one private commodity →
    intrahousehold allocation of consumption an issue; children
•   Men all identical; quasi linear utility U H H , ka H  H . k
                                                  a          u
    if married; zero utility of children if single.
•   Women: quasi linear utility U ka  where u
                                      a,            uk
    distributed of [0,U], density f; note that utility is transferable.
•   Unwanted pregnancies, probability p
•   Income: men Y, women y without children, z < y with children
                        The model
•   Continuum of men and women; one private commodity →
    intrahousehold allocation of consumption an issue; children
•   Men all identical; quasi linear utility U H H , ka H  H . k
                                                  a          u
    if married; zero utility of children if single.
•   Women: quasi linear utility U ka  where u
                                      a,            uk
    distributed of [0,U], density f; note that utility is transferable.
•   Unwanted pregnancies, probability p
•   Income: men Y, women y without children, z < y with children

•   Frictionless marriage market (matching model); surplus
    generated by children
      → equilibria as stable matches
•   Mass 1 of women, M of men
     → excess supply of women if M < 1
                Fertility decisions
•     Single women
    –    If u < y – z = ū : no children
    –   Otherwise: children
                  Fertility decisions
•     Single women
    –    If u < y – z = ū : no children
    –     Otherwise: children

•       Couples
    –     Efficiency: children if maximizes total surplus
    –     Hence: children if u >   y z u H  u;
                  Fertility decisions
•     Single women
    –    If u < y – z = ū : no children
    –     Otherwise: children

•       Couples
    –     Efficiency: children if maximizes total surplus
    –     Hence: children if u >   y z u H  u;
•     Hence three types of women (depending on preferences):
    –   ‘low’:              u<u
    –   ‘intermediate’: u<u<ū
    –   ‘high’:             u>ū
                  Fertility decisions
•     Single women
    –    If u < y – z = ū : no children
    –     Otherwise: children

•       Couples
    –     Efficiency: children if maximizes total surplus
    –     Hence: children if u >   y z u H  u;
•     Hence three types of women (depending on preferences):
    –   ‘low’:              u < u never want a child
    –   ‘intermediate’: u < u < ū want a child only when married
    –   ‘high’:             u > ū always want a child
                Stable match:
           excess supply of women
Basic graph: husband’s maximal utility (as a function of u)




 Y + uH




                                           H
Y + p.uH
                             I
             L
                     u              u                    u
                Stable match:
           excess supply of women
Basic graph: husband’s maximal utility (as a function of u)



              Singles              Married


 Y + uH




Y + p.uH




                        u   u(M)       u                     u


                                           Number of males
                Stable match:
           excess supply of women
Basic graph: husband’s maximal utility (as a function of u)



              Singles              Married


 Y + uH




Y + p.uH




                        u   u(M)       u                     u


                                           Number of males
              Hence: three cases


 Y + uH




Y + p.uH




                    u                    u
                                   u


   Small excess supply of women (SESW)
              Hence: three cases


 Y + uH




Y + p.uH




                     u                          u
                                    u


   Intermediate excess supply of women (IESW)
             Hence: three cases


 Y + uH




Y + p.uH




                    u                            u
                                  u


           Large excess supply of women (LESW)
               Hence three regimes
1.       ‘Large’ ESW → marginal woman high type.
     –     Some H women not matched → out-of-wedlock births
     –     No surplus
                Hence three regimes
1.       ‘Large’ ESW → marginal woman high type.
     –     Some H women not matched → out-of-wedlock births
     –     No surplus

2.       ‘Intermediate’ ESW → marginal woman intermediate type
                                             U
     –     Marginal woman: u(M) with         f M
                                             uM
                                                  t dt
     –     No out-of-wedlock birth unless unwanted; all married couples have
           children
     –     Surplus for all married women, increases with M, max for high type
 Y + uH




Y + p.uH




                       u                                u
                                      u
                            u(M)

           Intermediate excess supply of women (IESW)
                Hence three regimes
1.       ‘Large’ ESW → marginal woman high type.
     –     Some H women not matched → out-of-wedlock births
     –     No surplus

2.       ‘Intermediate’ ESW → marginal woman intermediate type
                                             U
     –     Marginal woman: u(M) with         f M
                                             uM
                                                  t dt
     –     No out-of-wedlock birth unless unwanted; all married couples have
           children
     –     Surplus for all married women, increases with M, max for high type

3.       ‘Small’ ESW → marginal woman low type
     –     No out-of-wedlock birth unless unwanted; some married couples
           don’t have children
     –     Surplus for all married women, independent of M, max for high.
 Y + uH




Y + p.uH




                       u                         u
                                  u
                u(M)

           Small excess supply of women (IESW)
   Excess Supply of Men

At any stable equilibrium:
• All women married, receive all the
    surplus
• ‘High’ and ‘intermediate’ types have
    children
• ‘Low’ type don’t.
     Comparative statics: income
•    Women’s welfare non decreasing in y and z.
•    Assume, for instance, a proportional increase
     in y and z. Then:
    – Less H, more L → fertility decreases
    – The equilibrium may switch (from LESW to IESW
      to SESW) → larger rents for women, smaller for
      men


    → In a sense, income growth alleviates ESW
u              u
           u
    u(M)
u              u
           u
    u(M)
           Comparative statics:
           cutting male supply
•   Within each regime:
    – No impact if LESW or SESW
    – IESW: higher u(M) reduces female surplus
           Singles          Married


 Y + uH




Y + p.uH




                     u(M)
           Singles          Married


 Y + uH




Y + p.uH




                     u(M)
           Comparative statics:
           cutting male supply
•   Within each regime:
    – No impact if LESW or SESW
    – IESW: higher u(M) reduces female surplus


•   Change of regime:
    – All women lose
    – From IESW to LESW: reduces total fertility,
      increases out-of-wedlock fertility.
 Y + uH




Y + p.uH




           u                   u
                        u


           From IESW to LESW
          Single parent benefits
•   More high type women → fertility increases
•   May change regime to LESW → out-of-
    wedlock fertility increases
•   Welfare: within a constant regime
    – All women gain
    – Married women (who do not receive the benefit)
      may gain more (per capita) than most singles.
    – Men lose the same amount.
•   If regime changes: more complex
Application: the US over three
           decades
Major trends:
Application: the US over three
           decades
Major trends:
   1. Per capita benefits increase
   then decrease
                   Benefits




Source: Moffit JEL 1992
Application: the US over three
           decades
Major trends:
   1. Per capita benefits increase
   then decrease
   2. Drop in the ‘supply’ of black,
   HS drop-out males
Source: U.S. Department of Justice
Source: U.S. Department of Justice
Source: Western-Pettit, ILRR 2000
Source: Neal JHR 2004
Source: Neal JHR 2004
Source: Neal JHR 2004
                       Hence:
•   Benefits:
    – Inverted U-shape
    – Note that the impact is not differentiated by race


•   Supply of male:
    – Strong reduction of male supply…
    – … concentrated on young, black, HS dropouts
                        Hence:
•    Benefits:
     – Inverted U-shape
     – Note that the impact is not differentiated by race


•    Supply of male:
     – Strong reduction of male supply…
     – … concentrated on young, black, HS dropouts


    Impact on marriage and fertility?
Source: Neal JHR 2004
Source: Neal JHR 2004
Source: Neal JHR 2004
Source: Neal JHR 2004
          Legalizing abortion
•   ESM: straightforward
•   ESW: more interesting
               Legalizing abortion
•        ESM: straightforward
•        ESW: more interesting



Y + uH




Y + p.uH

    Y


                    u   u(M)         u
                                 u
           Legalizing abortion
•   ESM: straightforward
•   ESW: more interesting
    – Women not wanting kids gain
            Legalizing abortion
•   ESM: straightforward
•   ESW: more interesting
    – Women not wanting kids gain
    – If LESW: no impact on married women



•   Men’s welfare: cannot increase
    – If LESW: no difference
u       u
    u
            Legalizing abortion
•   ESM: straightforward
•   ESW: more interesting
    – Women not wanting kids gain
    – If LESW: no impact on married women
    – If S- or I-ESW: all married women gain, including
      those who want children
      Intuition: single are better off, and indifference
•   Men’s welfare: cannot increase
    – If LESW: no difference
    – If IESW: total surplus unchanged, wife’s share
      increased
u       u
    u
            Legalizing abortion
•   ESM: straightforward
•   ESW: more interesting
    – Women not wanting kids gain
    – If LESW: no impact on married women
    – If S- or I-ESW: all married women gain, including
      those who want children
      Intuition: single are better off, and indifference
•   Men’s welfare: cannot increase
    – If LESW: no difference
    – If IESW: total surplus unchanged, wife’s share
      increased
    – If SESW: LT lose unwanted births; for all others,
      wife’s share increased
u       u
    u
            Legalizing abortion
•   ESM: straightforward
•   ESW: more interesting
    – Women not wanting kids gain
    – If LESW: no impact on married women
    – If S- or I-ESW: all married women gain, including
      those who want children
      Intuition: single are better off, and indifference
•   Men’s welfare: cannot increase
    – If LESW: no difference
    – If SESW or IESW:
                 net transfer to the wife!
                 ‘The Pill’
What if technology reserved to married women?
                    ‘The Pill’
What if technology reserved to married women?




    Y + uH




   Y + p.uH




               u1       u   u2
                             ‘The Pill’
What if technology reserved to married women?


              Married          Singles        Married

    Y + uH




   Y + p.uH




                        u1         u     u2
                      Hence:
•   Women with u ≥ u2(M): married, children, lose
•   Women with u (M) ≤ u < u2(M): single (instead of
    married), lose
•   Women with u 1(M) ≤ u < u(M): single anyway, no
    change
•   Women with u < u1(M): married (instead of single),
    gain

      Conclusion: most married women lose
                      Hence:
•   Women with u ≥ u2(M): married, children, lose
•   Women with u (M) ≤ u < u2(M): single (instead of
    married), lose
•   Women with u 1(M) ≤ u < u(M): single anyway, no
    change
•   Women with u < u1(M): married (instead of single),
    gain

    Conclusion: most married women lose
The new technology helps married women (who
      do not use it), but only insofar as it is
               available to singles
     Extension 1: costly access
Idea: fixed cost c for all




   Y + uH


Y-(1-p)c+uH


  Y + p.uH


   Y+pc

        Y


                             u-c   u
     Extension 1: costly access

•   New technology favors all women in general,
    including those who do not want to use it
    (idea: one marginal woman at least uses it)
•   However, restrictions to access harm all
    women in general, including those who do
    not want to use it and those who can afford it.
•   Example: Hyde Amendment (1976)!
•   Problem: definition of a ‘market’!
             Extension 2:
         heterogeneous costs
•   Idea; ‘psychological’ costs differ
•   Extreme case: zero for some, large for others
                  Extension 2:
              heterogeneous costs


   Y + uH


Y-(1-p)c+uH


  Y + p.uH


   Y+pc

        Y
        Extension 2: shotgun
             marriages
Claim (AYK 96): abortion lead to disappearance
   of shotgun marriages, which harmed women.
        Extension 3: shotgun
             marriages
Claim (AYK 96): abortion lead to disappearance
   of shotgun marriages, which harmed women.
Empirical problems (Neal 2004):
• Why only for poor and minorities?
• Adoptions did not increase.
        Extension 3: shotgun
             marriages
Claim (AYK 96): abortion lead to disappearance
   of shotgun marriages, which harmed women.
Empirical problems (Neal 2004):
• Why only for poor and minorities?
• Adoptions did not increase.
Theoretical problem:
 Intrahousehold allocation is not exogenous!
→ ‘female pauperization’ a complex issue…
       Extension 3: shotgun
         marriages (cont.)
In our model:
• Suppressing shotgun marriage does not
    harm women…
• … unless it cuts the supply of men.


Empirically: unclear
           Fraction of single men among all employed men (PSID)

0.12

 0.1

0.08

0.06

0.04

0.02

  0
  1968   1969   1970   1971   1972   1973   1974   1975   1976   1977   1978   1979   1980
                                            Year
           Fraction of single men among all employed men (PSID)

0.12

 0.1

0.08

0.06

0.04

0.02

  0
  1968   1969   1970   1971   1972   1973   1974   1975   1976   1977   1978   1979   1980
                                            Year
         Deviation from the average annual change in the fraction of single
                                   men (PSID)

0.008
0.006
0.004
0.002
    0
-0.002   1968   1969   1970   1971   1972   1973   1974   1975   1976   1977   1978   1979   1980

-0.004
-0.006
-0.008
 -0.01
   ‘Female empowerment’:
 empirical test 1 (Oreffice 2004)

Basic idea: labor supply (CFL 1998)
  – ‘empowerment’: she receives a larger share
    of household resources
  – If leisure normal:
    •   she should work less
    •   he should work more
  – Need to control for wages, education,…
  – Findings: Prediction confirmed!
Source: Oreffice 2004
Source: Oreffice 2004
    ‘Female empowerment’: empirical
    test 2 (Mazzocco, Chiappori 2004)
                    Divorce in Ireland
Stylized facts:
•    legalization of divorce, but actual number very small
•    Strong labor demand, increase in participation
Theory:
•    Labor demand → potential empowerment of women
•    Divorce law as triggering renegotiations
•    Working women: same effect as before
•    Non working women: need to ‘build up a threat point’
     → increased participation
Tests: confirm the predictions
                           Discussion
Heterogeneous males
•       by income: same
•       by preferences: supermodular; more complex, similar
        predictions

Commitment versus bargaining
•       Basic insight: ‘market’ conditions matter
•       One interpretation: commitment (‘prenuptial agreement’)
•       Alternative polar case: ‘pure’ bargaining.
•       Differences:
    –     the existence of an ‘abortion threat’ matters only if credible
    –     therefore: no impact on women unwilling to use abortion.
    –     exclusive availability to married women does not matter
                  Conclusions
Very simple model …
•   Multiple dimensions (income,…)
•   Frictions
•   Dynamics (age of marriage; divorce;…)

… but some robust conclusions:
•   Intrahousehold allocation crucial; equilibrium
•   Various ‘submarkets’ (empirical translation?)
•   General insight: an innovation (technology, but also
    policy,…) can have a major impact on people not directly
    affected
                → Cost-benefit analysis!

				
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