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

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(i, j) such that i ∈ I and j ∈ J , where 8. Sharing the gains from marriage 379 ui = UIJ + αiJ vj = VIJ + β Ij (8.57) UIJ + VIJ = zIJ In words: the differences ui−αiJ and vj −β jI only depend on the spouses’ classes, not on who they are. Note, incidentally, that (8.56) is also valid for singles if we set UI0 = ζ I0 and U0J = ζ 0J. The economic interpretation of this result is as follows. The contribution of women j and j0 whoareinthesameclassJ to a marriage with all men in class I differ by β Ij 0 −β Ij. Ifvj 0 −vj >β Ij 0 −β Ij no men in I will marry woman j0 because she is ‘too expensive’ relative to woman j. Conversely, if vj 0 − vj
380 8. Sharing the gains from marriage In principle, it is possible to calculate these coefficients directly by solving the market equilibrium (that is the linear programming problem) associated with a stable assignment. More interestingly, one can use data on actual marriage patterns and the observed attributes of participants in a "marriage market" to estimate the gains from marriage of these individuals (relative to remaining single). 14 Basically, the preferences for different types of spouses are "revealed" from the choice probabilities of individuals. Taking the simplest case without covariates, we see Pr (i ∈ I is matched with j ∈ J) ln Pr (i ∈ I is single) Pr (j ∈ J is matched with i ∈ I) ln Pr (j ∈ J is single) = UIJ − UI0 = UIJ − UJ0. (8.59) Estimating separate multinomial logit for men and women, one can estimate the utilities for each gender in a marriage of each type. Summing the estimated utilities one can recover, for each matching of types (I,J), the systematic output of the marriage ξ IJ (which, under the normalization that being single yields zero utility, equals the total surplus ZIJ). The estimated matrix ZIJ can then be analyzed in terms of the assortative matching that it implies. Of particular interest is whether or not this matrix is supermodular (implying positive assortative mating) or not. As noted by Choo and Siow (2006) and Siow (2009), in the absence of covariates the super modularity of ZIJ is equivalent to the supermodularity of ln (μ(I,J))2 σ(I)σ(J) where μ(I,J) is the total number of type (I,J) marriages and σ(I) and σ(J) are the number of single men and single women, respectively. Such supermodularity requires that for all I 0 >I and J 0 >J ln μ(I0 ,J0 )μ(I,J) μ(I,J0 )μ(I0 > 0. ,J) Siow (2009) uses census data on married couples in the US, where the husband and wife are 32-36 and 31-35 respectively. In each couple, the wife and the husband can belong to one of five possible schooling classes (less than high school, high school, some college, college and college plus). He compares the marriage patterns in the years 1970 and 2000 and finds that in each of the two years strict supermodularity fails to hold as in some of the off diagonal cells, the log odds ratio is negative. Looking at the 14 Because the probabilities in (8.58) are unaffected by a common proportionality factor, some normalization is required. A common practice is to set the utility from being single to zero for all individuals.
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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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430 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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