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Lower-order logsums


  • André De Palma

    () (ENS Cachan - École normale supérieure - Cachan)

  • Karim Kilani

    () (LIRSA - Laboratoire Interdisciplinaire de Recherche en Sciences de l'Action - CNAM - Conservatoire National des Arts et Métiers [CNAM])


The logsum formula, which provides the expected maximum utility for the multinomial logit model, is often used as a measure of welfare. We provide here a closed form formula of the welfare measure of an individual who has not access to his first-best choice, but has access to his rth-best choice, r = 2, ...n, where n is the number of alternatives. The derivation is based on a standard identity in order statistics.

Suggested Citation

  • André De Palma & Karim Kilani, 2012. "Lower-order logsums," Working Papers hal-00690299, HAL.
  • Handle: RePEc:hal:wpaper:hal-00690299
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    References listed on IDEAS

    1. de Palma, Andre & Picard, Nathalie & Waddell, Paul, 2007. "Discrete choice models with capacity constraints: An empirical analysis of the housing market of the greater Paris region," Journal of Urban Economics, Elsevier, vol. 62(2), pages 204-230, September.
    2. de Jong, Gerard & Daly, Andrew & Pieters, Marits & van der Hoorn, Toon, 2007. "The logsum as an evaluation measure: Review of the literature and new results," Transportation Research Part A: Policy and Practice, Elsevier, vol. 41(9), pages 874-889, November.
    3. de Palma, Andre & Kilani, Karim, 2007. "Invariance of conditional maximum utility," Journal of Economic Theory, Elsevier, vol. 132(1), pages 137-146, January.
    4. N. Salakbishnan, 1988. "Recurrence relations for order statistics from n independent and non-identically distributed random variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(2), pages 273-277, June.
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    Discrete choice models; Gumbel distribution; Logit; Logsum; Order statistics;

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