Pierre André Chiappori (Columbia) "Family Economics" - Cemmap

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6. Uncertainty and Dynamics in the Collective model 283 where q1 denotes the joint consumption in the first period, while q2 is the joint consumption if the partners remain married or the sum of their private consumptions if they separate. Thus, the allocation of time in the first period determines the consumption available to the parents each period as well as the quality of the child that they enjoy in the second period. The only issue then is how is this allocation determined. A necessary condition for an efficient allocation of time is that the cost of producing child quality, in terms of the foregone earnings of the couple during the two periods of life, should be minimized. In the this example, these costs are C(Q) =(1+γ)(w a t a + w b t b ) (6.50) and cost minimization takes a simple form. In particular if there is an interior solution and both partners contribute time to the child20 then we must have w b (1 + t b )=1+t a (6.51) Whether or not an interior solution arrises, efficiency requires that the low wage person, b, should contribute more time to the child and the question is if and how such unequal contribution can be implemented. The answer depends on the contracting options that the couple have. We shall assume here that the partners can always commit, at the time of marriage, on some post divorce allocation of resources, provided that it falls within some legal bounds. The justification for this assumption is that the event of separation and the resources available upon separation can be verified so that contracts contingent on these variables can be enforced by law. Denoting by β the share received by the low wage person, b, the post divorce consumption levels are q a d = (1−β)[γwa (1 − t a )+γw b (1 − t b )] (6.52) q b d = β[γw a (1 − t a )+γw b (1 − t b )]. It is more difficult, however, to verify the time allocation and in particular time spent on children, and we shall allow for the possibility that partners cannot commit at the time of marriage on how much time they will spend with the child. Following the realization of θ at the beginning of the second period, and given the predetermined quality of children and divorce contract, marriage will continue if α ln Q +lnq2 + θ ≥ (1 − δ)α ln Q +max{(αln q a d,αln q b d) (6.53) 20 The efficiency requirements include regions in which only one person contributes. These regions depend on the desire for children relative the wages of the two spouse. If αα>1. Then for αw b > 1, both partners work part time at home and part time in the market.
284 6. Uncertainty and Dynamics in the Collective model and dissolve otherwise. This rule holds because, by assumption, utility is not transferable within marriage and each partner is free to walk away from the marriage. Clearly, the person who can attain higher consumption outside marriage will trigger the divorce. Examining equation (6.52), we see that if b receives a higher share of family resources upon divorce, β> 1 2 , he will trigger the divorce and divorce occurs if θ
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Family Economics Martin Browning Pi
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iv 3.2 Householdproduction ........
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vi 6.4 IntertemporalBehavior ......
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viii 11 Marriage, Divorce, Children
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List of Figures 1.1 Marriage Rates
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xiii 4.2 Apotentiallycompensatingva
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Introduction The existence of a nuc
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two distinct solution concepts; one
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were affectedbytherisinginvestments
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Murat Iyigun, Guy Lacroix, Valérie
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Part I Models of Household Behavior
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14 1. Facts there appear to be age,
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16 1. Facts 1.1.4 Transitions The m
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18 1. Facts sumption goods within h
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20 1. Facts may not capture the ful
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22 1. Facts This process is driven
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24 1. Facts 1.4 Children Children a
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26 1. Facts a major policy concern
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28 1. Facts have means for, say, hi
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30 1. Facts [21] Michael, Robert,
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32 1. Facts Age group USA Denmark 1
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34 1. Facts Birth cohort 1931-36 19
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36 1. Facts USA Canada UK Norway Ye
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38 1. Facts Country Male Participat
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40 1. Facts Mother’s Age 20-30 31
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42 1. Facts rate per 1000, 20+ 18 1
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44 1. Facts Marriage rate per 1000
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46 1. Facts percent entering first
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48 1. Facts percent entering divorc
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50 1. Facts 100% 90% 80% 70% 60% 50
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52 1. Facts 1 0.8 0.6 0.4 0.2 0 23
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54 1. Facts 0.8 0.6 0.4 0.2 0 23 25
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56 1. Facts 0.8 0.6 0.4 0.2 0 1968
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58 1. Facts 6.8 6.6 6.4 6.2 6 5.8 2
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60 1. Facts 0.4 0.2 0 -0.2 -0.4 196
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62 1. Facts 0.6 0.4 0.2 0 1968 1970
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64 1. Facts FIGURE 1.23. Age Pyrami
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66 1. Facts 0.6 0.4 0.2 0 1930 1933
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68 1. Facts 100% 80% 60% 40% 20% 0%
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70 1. Facts 0.35 0.3 0.25 0.2 0.15
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72 1. Facts 100% 80% 60% 40% 20% 0%
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74 1. Facts Average number of child
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76 1. Facts Age 28 27 26 25 24 23 1
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78 1. Facts FIGURE 1.37. Consumptio
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80 1. Facts
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82 2. The gains from marriage for o
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84 2. The gains from marriage Q 2 y
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86 2. The gains from marriage this
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88 2. The gains from marriage as wh
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90 2. The gains from marriage ing a
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92 2. The gains from marriage absen
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94 2. The gains from marriage 2.5 C
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96 2. The gains from marriage 2.5.3
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98 2. The gains from marriage This
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100 2. The gains from marriage [14]
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102 2. The gains from marriage
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104 3. Preferences and decision mak
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158 4. The collective model: a form
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200 5. Empirical issues for the col
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334 8. Sharing the gains from marri
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392 9. Investment in Schooling and
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436 10. An equilibrium model of mar
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460 11. Marriage, Divorce, Children
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Pierre André Chiappori (Columbia) "Family Economics" - Cemmap

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