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

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6. Uncertainty and Dynamics in the Collective model 287 We can, therefore, rewrite condition (6.60) in the form 2 √ wb 1+wb − √ wb α =[1−δF(−δα ln Q − ln 2] . (6.65) Q Q Condition (6.65) then determines the desired child quality and we can then use the efficiency conditions to trace back the implied allocation of time. The left hand side of (6.65) represents the marginal disutility (associated with lost consumption) and unambiguously rises with Q.However,theright hand side of (6.65), which represents the expected marginal utility from having children in the second period, involves two conflicting effects: A higher level of child quality reduces the marginal utility from children and also reduces the probability of divorce. Therefore, the marginal expected utility can either rise or fall and the outcome depends on the shape of the hazard associated with the distribution of quality match F (θ) .Specifically, d − δF(−δ ln Q − ln 2) α[1 ] dQ Q = α[ (δ2f(−δ ln Q − ln 2) − (1 − δF(−δ ln Q − ln 2)) Q2 ] which is negative if. δ 2 f(−δ ln Q − ln 2) < 1. 1 − F (−δ ln Q − ln 2) This condition is satisfied, for instance, for the normal distribution if σ ≥ 1, because q then the hazard is an increasing function and its value at zero is 2 1 π σ . Assuming that the expected marginal utility from children declines with Q, it is easy to see that the investment in children is reduced in response to increasing risk, represented here by a mean preserving increase in the spread of the shocks to match quality. However, that the expected marginal utility from children declines with Q, the investment in children may rise in order to stabilize the marriage. In either case, the "efficient" family responds to such change in circumstances in a way which is optimal for both spouses, without having equality in action. What is required, of course, is for both partners to have equal interest in the outcome and, given that all goods in marriage are public, such harmony can be achieved by a binding commitments of an equal division of resources upon divorce. This considerations can go part of the way in explaining the prevalence of equal divisions following divorce. A binding commitment is required, because, ex post, after divorce has occurred and the investments have been made, there is no incentive for further transfers. However at the time of marriage, a spouse with a higher income may be willing to commit on a post divorce transfer in order to induce the seemingly less powerful spouse to invest in children.
288 6. Uncertainty and Dynamics in the Collective model 6.6 References [1] Altonji, Joseph G., Hayashi, Fumio and Laurence J. Kotlikoff, ‘Isthe Extended Family Altruistically Linked? Direct Tests Using Micro Data’, American Economic Review, 82 (1992), 1177-1198. [2] Basu, Kaushik, ‘Gender and Say: A Model of Household Behaviour With Endogenously Determined Balance of Power’, Economic Journal, 116 (2006), 558-580. [3] Becker, Gary, Treatise on the family, (Cambridge Mass: Harvard University Press, 1991). [4] Brossolet, C., ‘Fondement de la division du travail dans les modéles économiques du ménage’, Paris, Editions Arguments, (1992). [5] Bourguignon, Francois, Browning, Martin, Chiappori, Pierre-André and Valérie Lechene, ‘Intra Household Allocation of Consumption: A Model and Some Evidence from French Data’, Annales d’Economie et de Statistique, 29 (1993), 137-156. [6] Browning, Martin, ‘Love Betrayal and Commitment’, University of Oxford, (2009). [7] Browning, Martin and Annamaria Lusardi, ‘Household Saving: Micro Theories and Micro Facts’, Journal of Economic Literature, 34 (1996), 1797-1855. [8] Bergstrom, Theodore C., ‘A Fresh Look at the Rotten Kid Theorem— and Other Household Mysteries’, Journal of Political Economy, 97 (1989), 1138-1159. [9] Borch, Karl, ‘The Safety Loading of Reinsurance Premiums’, Skandinavisk Aktuarietidskrift, 43 (1960), 163—184. [10] Chiappori, Pierre-André, ‘Characterizing the Properties of the Generalized Quasi-linear Utilities’, Columbia University, (2007). [11] Chiappori, Pierre-André and Philip J. Reny, ‘Matching to Share risk’, Columbia University, (2005). [12] Chiappori, Pierre-André, Krislert Samphantharak, Sam Schulhofer- Wohl and Robert M. Townsend, ‘Heterogeneity and Risk Sharing in Thai Villages’, Working paper, Columbia University (2010). [13] Chiappori, Pierre-André, Robert M. Townsend and Hiro Yamada, ‘Sharing wage risk’, Columbia University (2008). [14] Chiappori, Pierre-André and Yoram Weiss, ‘Marriage Contracts and Divorce: an Equilibrium Analysis’, Tel Aviv University, (2009).
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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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392 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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