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

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G F 8. Sharing the gains from marriage 347 FIGURE 8.3. A linear upward shift The case r
348 8. Sharing the gains from marriage The linear shift property implies that, under assortative matching and with populations of equal size, a man with income x is paired with a woman with income y = αx − β. With the previous notations, therefore, φ (y) = (y + β) /α and ψ (x) =αx − β. Equations(8.15) and(8.16) thenbecome du(x) dx dv(y) dy yielding upon integration : and where = H 0 ((α +1)x− β) , and (8.22) = H 0 (((α +1)y + β) /α) , (8.23) v (y) =K + α H (φ (y)+y) (8.24) 1+α u (x) =K 0 + 1 H (x + ψ (x)) (8.25) 1+α K + K 0 = θ. In words, the marriage between Mr. x and Mrs. y = ψ (x) generates a marital output θ + H (x + ψ (x)), which is divided linearly between the spouses. The non monetary part, θ, is distributed between them (he receives K, shereceivesK 0 ) in a way that is not determined by the equilibrium conditions (this is the standard indeterminacy when r =1)butmustbe the same for all couples (note that K or K 0 may be negative). Regarding the economic output, however, the allocation rule is particularly simple; he receives some constant share α/ (1 + α) of it, and she gets the remaining 1/ (1 + α). 8.2.3 Comparative Statics We now turn to examine the impact of changes in the sex ratio and income distribution. Increasing the proportion of women We begin by noting an important feature of the model, namely that if all marriages yield a strictly positive surplus then the allocation rule has a discontinuity at r =1. Indeed, examining the expressions in (8.17) and (8.18) we see that if r approaches 1 from above we get in the limit u (x) = H (a + b) − H (b)+θ + v (y) = H (b)+ Z y b Z x a H 0 (s + ψ (s)) ds (8.26) H 0 (φ (t)+t) dt (8.27)
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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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244 6. Uncertainty and Dynamics in
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294 7. Matching on the Marriage Mar
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398 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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