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Transition choice probabilities and welfare analysis in additive random utility models


  • André Palma


  • Karim Kilani



We study the descriptive and the normative consequences of price and/or other attributes changes in additive random utility models. We first derive expressions for the transition choice probabilities associated to these changes. A closed-form formula is obtained for the logit. We then use these expressions to compute the cumulative distribution functions of the compensating variation (CV) conditional on ex-ante and/or ex-post choices. The unconditional distribution is also provided. The conditional moments of the CV are obtained as a one-dimensional integral of the transition choice probabilities. This framework allows us to derive a stochastic version of Shephard's lemma, which relates the expected conditional CV and the transition choice probabilities. We compute the CV for a simple binary linear in income choice model and show that the information on the transitions leads to better estimates of the CV than those obtained when only ex-ante or ex-post information on individual choices is used. For the additive in income logit, we compute the conditional distribution of CV, which generalizes the logsum formula. Finally, we derive a new welfare formula for the disaggregated version of the representative consumer CES model.
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Suggested Citation

  • André Palma & Karim Kilani, 2011. "Transition choice probabilities and welfare analysis in additive random utility models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(3), pages 427-454, April.
  • Handle: RePEc:spr:joecth:v:46:y:2011:i:3:p:427-454
    DOI: 10.1007/s00199-009-0513-6

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    References listed on IDEAS

    1. Aguirregabiria, Victor & Mira, Pedro, 2010. "Dynamic discrete choice structural models: A survey," Journal of Econometrics, Elsevier, vol. 156(1), pages 38-67, May.
    2. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387, May.
    3. Daniel McFadden, 2005. "Revealed stochastic preference: a synthesis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 245-264, August.
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    Cited by:

    1. repec:kap:netspa:v:17:y:2017:i:3:d:10.1007_s11067-017-9353-2 is not listed on IDEAS
    2. Paolo Delle Site & Marco Valerio Salucci, 2012. "The Impact Of The Before-After Error Term Correlation On Welfare Measurement In Logit," Working Papers 0412, CREI Università degli Studi Roma Tre, revised 2012.
    3. Delle Site, Paolo & Salucci, Marco Valerio, 2013. "Transition choice probabilities and welfare analysis in random utility models with imperfect before–after correlation," Transportation Research Part B: Methodological, Elsevier, vol. 58(C), pages 215-242.
    4. Delle Site, Paolo & Salucci, Marco Valerio, 2015. "Transition choice probabilities in logit," Economics Letters, Elsevier, vol. 126(C), pages 135-139.
    5. Anderson, Simon P. & de Palma, André, 2012. "Oligopoly and Luce's Choice Axiom," Regional Science and Urban Economics, Elsevier, vol. 42(6), pages 1053-1060.
    6. Dekker, Thijs, 2014. "Indifference based value of time measures for Random Regret Minimisation models," Journal of choice modelling, Elsevier, vol. 12(C), pages 10-20.

    More about this item


    Random utility models; Logit; Transition choice probabilities; Compensating variation; Shephard’s lemma; Logsum; CES; D11; D60;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D60 - Microeconomics - - Welfare Economics - - - General


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