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Transition choice probabilities and welfare in ARUM's

Author

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  • André De Palma

    (ENS Cachan - École normale supérieure - Cachan, Department of Economics, Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

  • Karim Kilani

    (CNAM Paris - Conservatoire National des Arts et Métiers - Paris - CNAM - Conservatoire National des Arts et Métiers [CNAM])

Abstract

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 conditional on ex-ante and/or ex-post choices. The unconditional distribution is also provided. The conditional moments of the compensating variation 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 compensating variation and the transition choice probabilities. We compute the compensating variation for a simple binary linear in income choice model and show that the information on the transitions leads to better estimates of the compensating variation than those obtained when only ex-ante or ex-post information on individual choices is observed. For the additive in income logit, we compute the conditional distribution of compensating variation, which generalizes the logsum formula. Finally, we derive a new welfare formula for the disaggregated version of the represen- tative consumer CES model.

Suggested Citation

  • André De Palma & Karim Kilani, 2009. "Transition choice probabilities and welfare in ARUM's," Working Papers hal-00417493, HAL.
    • Handle: RePEc:hal:wpaper:hal-00417493
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00417493
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    File URL: https://hal.archives-ouvertes.fr/hal-00417493/document
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    References listed on IDEAS

    as
    1. de Palma, Andre & Kilani, Karim, 2005. "Switching in the logit," Economics Letters, Elsevier, vol. 88(2), pages 196-202, August.
    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. von Haefen, Roger H., 2003. "Incorporating observed choice into the construction of welfare measures from random utility models," Journal of Environmental Economics and Management, Elsevier, vol. 45(2), pages 145-165, March.
    5. John K. Dagsvik & Anders Karlström, 2005. "Compensating Variation and Hicksian Choice Probabilities in Random Utility Models that are Nonlinear in Income," Review of Economic Studies, Oxford University Press, vol. 72(1), pages 57-76.
    6. Anderson, Simon P. & De Palma, Andre & Thisse, Jacques-Francois, 1987. "The CES is a discrete choice model?," Economics Letters, Elsevier, vol. 24(2), pages 139-140.
    7. 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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    More about this item

    Keywords

    Additive random utility models (ARUM); Logit; Transition choice probabilities; Compensating variation; Shephard's Lemma; Logsum; CES;

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