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

8. Sharing the gains from marriage 383
Thus, if x1,x2....xn are iid Gumbel variables with zero mean then
E{max[v1 + x1,v2 + x2....vn + xn]} = b ln( X
e vi b ).
If we choose one alternative as a benchmark, say alternative 1, and normalize
its value to zero, the expected utility relative to this alternative is fully
determined by, and inversely related to the probability that the benchmark
alternative is selected. The marginal impact of an increase in the value of
specific alternative,j, is
∂E{max[v1 + x1,v2 + x2....vn + xn]}
=
∂vj
e vj b P
i e v , i
b
which is the probability that alternative j will be selected, pj.
8.6 References
[1] Akerlof, George A. and Rachel E. Kranton, ‘Economics and Identity’,
Quarterly Journal of Economics, 115 (2000), 715-753.
[2] Ben-Akiva, Moshe and Steven R. Lerman ,’Discrete Choice Analysis’
(MIT Press, 1985).
[3] Bately Richard ‘On Ordinal Utility Cardinal Utility and Random Utility’
Theory and Decision (2008) 64:37—63 .
[4] Botticini, Maristella and Aloysius Siow, ‘Why Dowries?’, The American
Economic Review, 93 (2003), 1385-1398.
[5] Browning, Martin and M. Gørtz, ‘Spending Time and Money Within
the Household’, unpublished manuscript, Department of Economics, University
of Oxford (2006).
[6] Choo, Eugene and Aloysius Siow, ‘Who Marries Whom and Why’,
Journal of Political Economy, 114 (2006), 175-201.
[7] Chiappori, Pierre-Andre, Bernard Fortin and Guy Lacroix, ‘Marriage
Market, Divorce Legislation, and Household Labor Supply’, Journal of
Political Economy, 110 (2002), 37-72.
[8] Chiappori, Pierre-Andre, Murat Iyigun and Yoram Weiss, ‘Investment
in Schooling and the Marriage Market’, The American Economic
Review, forthcoming (2009).
[9] Chiappori, Pierre-Andre, Bernard Salanié and Yoram Weiss ‘Assortative
Matching on the Marriage Market: A Structural Investigation’
(Columbia University, Department of Economics, in progress)
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