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

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9. Investment in Schooling and the Marriage Market 395 the externality argument. But the logic of competitive matching requires the three aspects to be considered - and the unambiguous conclusion is that efficiency is restored. Finally, what about the opposite line of argument, according to which agents actually invest too much? The story goes as follows: since agents compete for the best spouse, a ‘rat race’ situation follows, whereby all males overinvest in human capital. Well, again, the argument is incorrect in a matching setting in which transfers are feasible between spouses. Indeed, one should take into account not only the ‘quality’ (here the wealth) of the spouse who will be attracted by a higher second period wealth, but also the ‘price’ that will have to be paid (in terms of surplus sharing). In a matching game, wealthier spouses come with a higher reservation utility, thus require giving up a larger fraction of the surplus; as illustrated by the previous example, this is exactly sufficient to induce the right investment level. An important remark, however, is that this conclusion would not hold in a Gale-Shapley framework, in which transfers are not possible and the spouses’ respective gains are exogenously determined (and do not respond to competitive pressures on the marriage market). In such a setting, the ‘rat race’ effect is much more likely to occur! The model developed in this chapter assumes a large competitive marriage market without frictions and we shall demonstrate that premarital investments in schooling are efficient. 9.2 The Basic Model We begin with a benchmark model in which men and women are completely symmetric in their preferences and opportunities. However, by investing in schooling, agents can influence their marriage prospects and labor market opportunities. Competition over mates determines the assignment (that is, who marries whom) and the shares in the marital surplus of men and womenwithdifferent levels of schooling, depending on the aggregate number of women and men that acquire schooling. In turn, these shares together with the known market wages guide the individual decisions to invest in schooling and to marry. We investigate the rational-expectations equilibrium that arises under such circumstances. 9.2.1 Definitions When man i and woman j form a union, they generate some aggregate material output ζ ij that they can divide between them and the utility of each partner is linear in the share he\she receives (transferable utility). Man i alone can produce ζ i0 and woman j alone can produce ζ 0j. The
396 9. Investment in Schooling and the Marriage Market material surplus of the marriage is defined as zij = ζ ij − ζ i0 − ζ 0j. (9.2) In addition, there are emotional gains from marriage and the total marital surplus generated by a marriage of man i and woman j is sij = zij + θi + θj, (9.3) where θi and θj represent the non-economic gains of man i and woman j from their marriage. 9.2.2 Assumptions There are two equally large populations of men and women to be matched. 4 Individuals live for two periods. Each person can choose whether to acquire schooling or not and whether and whom to marry. Investment takes place in the first period of life and marriage in the second period. Investment in schooling is lumpy and takes one period so that a person who invests in schooling works only in the second period, while a person who does not invest works in both periods. To simplify, we assume no credit markets. 5 All individuals with the same schooling and of the same gender earn the same wage rate, but wages may differ by gender. We denote the wage of educated men by w m 2 and the wage of uneducated men by wm 1 , where wm 2 >wm 1 .The wage of educated women is denoted by w w 2 and that of uneducated women by w w 1 , where w w 2 >w w 1 . Market wages are taken as exogenous and we do not attempt to analyze here the feedbacks from the marriage market and investments in schooling to the labor market. We shall discuss, however, different wage structures. We denote a particular man by i and a particular woman by j. We represent the schooling level (class) of man i by I(i) where I(i) =1if i is uneducated and I(i) =2if he is educated. Similarly, we denote the class of woman j by J(j) where J(j) =1if j is uneducated and J(j) =2if she is educated. An important simplifying assumption is that the material surplus generated by a marriage of man i and woman j depends only on the class to which they belong. That is, sij = z I(i)J(j) + θi + θj. (9.4) We assume that the schooling levels of married partners complement each other so that z11 + z22 >z12 + z21. (9.5) 4 We address the impact of the sex ratio in a separate section below. 5 Allowing borrowing and lending raises issues such as whether or not one can borrow based on the income of the future spouse and enter marriage in debt.
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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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460 11. Marriage, Divorce, Children
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Pierre André Chiappori (Columbia) "Family Economics" - Cemmap

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