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

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10. An equilibrium model of marriage, fertility and divorce 451 There are two cases to consider. Case 1, W1,0(θm) =V1 >W1,1(θm), which implies θc >θm. Inthiscase or 2Y +θm + Y + θm + Z∞ h0−θm Z∞ h0−θm (2Y +θm +ε)f(ε)dε+F (h0 −θm)V2,0 = Y +V2,0, (10.44) (2Y + θm + ε)f(ε)dε =(1− F (h0 − θm))(h0 +2Y ). (10.45) Differentiating totally both sides of (10.45) yields [1 + (1 − F (h0 − θm)+f(h0 − θm)(2Y + h0)]dθm −f(h0 − θm)(h0 +2Y )(Y + β)dp = f(h0 − θm)((h0 +2Y )dθm +[(1 − F (h0 − θm)) − (h0 +2Y )f(h0 − θm)](Y + β)dp.(10.46) Cancelling equal terms and rearranging, we obtain ∂θm ∂p =(Y + β)1 − F (h0 − θ) 2 − F (h0 − θ) > 0 if θc >θm. (10.47) Case 2, W1,1(θm) =V1 >W1,0(θm), which implies θc 0 if θc . (10.51) ∂p
452 10. An equilibrium model of marriage, fertility and divorce 10.5.4 Calculations for the example Properties of θc in the example We first prove that if the costs of having children are relatively high, that is if q∗ >c> q∗ +q 0 2 , then an intersection of W1,0(θ) with W1,1(θ) cannot occur in the region [h1 − a, h0 − a]. The proof is by contradiction. Assume for some θ ∈ [h1 − a, h0 − a], W1,0(θ) =W1,1(θ). Then this θ must satisfy 7 3 1 Y + θ + p(Y + β)+1 a +(1 2 2 2 2 2 q0 + 1 2 q∗ − c) (10.52) = 3Y + θ + p(Y + β). Solving for θ and denoting the solution by θc ,wehave θc = p(Y + β) − Y − a +2c − (q ∗ + q 0 ). (10.53) Recalling equation (10.6) forn =0: we obtain, using c> q∗ +q 0 2 , h0 = −Y + p(Y + β), θc = h0 − a +2c − (q ∗ + q 0 ) >h0 − a. (10.54) Properties of θm in the example Proof of (10.20). Consulting Figure 10.2 and allowing V1 to move up or down, we see that we have to consider three cases for equation 10.42 First, low values of V1 give an intersection with W1,0 (θ) below θ = h0−a. Equating V1 with W1,0 (θ) this gives: This requires that: θm = −Y (10.55) −Y = θm ≤ h0 − a = −Y + p(Y + β) − a (10.56) ⇒ p(Y + β) ≥ a For intermediate values of θ ∈ [h0 − a, θc] we equate V1 with W1,0 (θ) evaluated in the intermediate region of equation (10.17). This gives: θm = 1 (p(Y + β) − a) − Y. (10.57) 3 Sincewehaveθm≤θc this value and (10.19) requires that: p(Y + β) ≥ 3(q ∗ − c) − 2a (10.58)
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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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502 11. Marriage, Divorce, Children
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Pierre André Chiappori (Columbia) "Family Economics" - Cemmap

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