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

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8. Sharing the gains from marriage 353 of this reversal is due to the narrowing wage gap between men and women and part of it is due to the reduction in the female-male sex ratio over the period. 8.2.4 Taxation Changes in the income distribution can also arise from a government intervention in the form of taxes and subsidies. For instance, we may consider a linear transfer scheme, such that the after tax (subsidy) income of a person with income s is κ +(1−τ) s, withκ>0 and 0
354 8. Sharing the gains from marriage ˜h (x + y) ≡ ˜ H(2κ +(1−τ)(x + y)). Assume, in addition, that male and female income distributions satisfy condition (8.21) so that ψ (x) =αx − β and φ (y) = y+β α . Then, for a larger female population (r >1), utilities become: ˜v (y) = H (κ +(1−τ) y0)+ Z y+φ(y) (1 − τ) H 0 0 (κ +(1−τ) s) αds α +1 Z ψ(x)+x ũ (x) = θ +(1−τ) H 0 0 (κ +(1−τ) s) ds (8.34) α +1 with k = τ ¯x+r¯y 1+r . The impact of a change in the marginal income tax, t, on the utilities of women and men, respectively, is µ ∂˜v (y) x + ry = − y0 H ∂t 1+r 0 (α + βy0) − αD (x + y) ∂ũ (x) = −D (x + y) , (8.35) ∂t where Y denotes total family income and Z Y D (Y ) = H 0 0 (κ +(1−τ) s) ds α +1 Z Y µ x + ry +(1− τ) s − H 0 1+r 00 (κ +(1−τ) s) ds α +1 . (8.36) The term D (Y ) is typically positive for richer households (who therefore lose from the introduction of the tax/benefit system) and negative for poorer ones. In this simple context, the corresponding gain or loss is allocated between husband and wife in respective proportions 1 and α. In addition, since single women are at the bottom of the female income distribution, their utility is typically increased by the tax/benefit scheme (this is the case whenever their income is below the mean). Equilibrium then requires the gain of the marginal woman (that is, of the wealthiest single or poorest married woman) ³ to be´ forwarded to all womeninthe x+ry distribution; hence the term 1+r − y0 H0 (α + βy0) in equation (8.35) representing the gain of the marginal woman. Note that this boost in income does not go to the poorer spouse, but to the spouse whose population is in excess supply. Should males outnumber females (r
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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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404 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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