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Transition choice probabilities and welfare in ARUM's

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Author Info

  • André De Palma

    (ENS Cachan - Ecole Normale Supérieure de Cachan - École normale supérieure de Cachan - ENS Cachan, Department of Economics, Ecole Polytechnique - CNRS : UMR7176 - Polytechnique - X)

  • Karim Kilani

    (CNAM Paris - 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.

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Bibliographic Info

Paper provided by HAL in its series Working Papers with number hal-00417493.

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Date of creation: 16 Sep 2009
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Handle: RePEc:hal:wpaper:hal-00417493

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Related research

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

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  1. de Palma, Andre & Kilani, Karim, 2007. "Invariance of conditional maximum utility," Journal of Economic Theory, Elsevier, vol. 132(1), pages 137-146, January.
  2. de Palma, Andre & Kilani, Karim, 2005. "Switching in the logit," Economics Letters, Elsevier, vol. 88(2), pages 196-202, August.
  3. 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.
  4. von Haefen, Roger H., 2000. "Incorporating Observed Choice In The Construction Of Welfare Measures From Random Utility Models," 2000 Annual meeting, July 30-August 2, Tampa, FL 21836, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
  5. ANDERSON, Simon P. & de PALMA, André & THISSE, Jacques-François, . "The CES is a discrete choice model?," CORE Discussion Papers RP -764, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Daniel McFadden, 2005. "Revealed stochastic preference: a synthesis," Economic Theory, Springer, vol. 26(2), pages 245-264, 08.
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