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

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10. An equilibrium model of marriage, fertility and divorce 445 probability 0.5, sothat W1 = EW1,0(θ) = 7 2 Y + 1 4 1 5 Y + a = 2 6 (10.22) If p =0, W1,1(θ) is the highest for all θ, implying that all couples marry, have children and do not divorce, so that W1 = EW1,1(θ) =4Y +(q ∗ − c) = 3 6 (10.23) The calculation of welfare is a bit more complex if p =0.25. Inthiscase, the maximum is given by W0(θ) if θ ≤ 0 and by W1(θ) if θ ≥ 0. Thus, W1 = 7 2 Y + 1 4 Y + 1 2 3 a + 2E(θ/θ ≤ 0) + 2 4Y +(q∗ − c)+2E(θ/θ ≥ 0) 2 = 4 6 (10.24) These calculations illustrate that ex-antewelfarerisesaswemovetoequilibrium points with higher p, reflecting the positive externality associated with an increase in the aggregate number of singles. 10.3 Income uncertainty and ex-post heterogeneity The simple model assumed perfect symmetry among spouses and that all individuals have the same incomes which remain fixed over time. We now allow income to change over time, which creates income heterogeneity expost. As before, all men and women have the same income, Y ,inthefirst period of their life. However, with probability λ income in the second period rises to Y h and with probability 1−λ it declines to Y l . To maintain ex-ante symmetry, we assume that the incomes of men and women follow this same process. To simplify, we shall assume now that the quality of the match, θ, is revealed only at the end of each period. The realized value of θ at the end of the first period can trigger divorce, while the realized value of θ at the end of the second period has no behavioral consequences in our two period model. Since there are gains from marriage, and the commitment is only for one period, everyone marries in the first period. However, in this case, changes in incomes as well as changes in the quality of match can trigger divorce. We continue to assume risk neutrality and joint consumption. The main difference from the previous model is that at the beginning of the second period there will be two types of potential mates, rich and poor. Let α be the expected remarriage rate and π the proportion of high income individuals among the divorcees, and let y = πY h +(1− π)Y l be the average income of the divorcees. Then the expected values of being unattached in the beginning of the second period for each type are V j (α, π) =Y j + αy, j = l, h. (10.25)
446 10. An equilibrium model of marriage, fertility and divorce This expression is obtained because type j consumes Y j alone and expects to consume Y j + y when married and the expected value of the quality of a new match θ in the second (and last) period is zero. Clearly, a richer person has a higher expected value from being unattached. At the end of the first period, the quality of the current match and the new income values (Y h or Y l ) for each spouse are revealed, and each partner can choose whether to stay in the current match or divorce and seek an alternative mate. An hh couple divorces if: An ll couple divorces if: 2Y h + 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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244 6. Uncertainty and Dynamics in
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294 7. Matching on the Marriage Mar
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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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496 11. Marriage, Divorce, Children
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Pierre André Chiappori (Columbia) "Family Economics" - Cemmap

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