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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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Article provided by Springer in its journal Economic Theory.

Volume (Year): 46 (2011)
Issue (Month): 3 (April)
Pages: 427-454

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Handle: RePEc:spr:joecth:v:46:y:2011:i:3:p:427-454
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  1. Daniel McFadden, 2005. "Revealed stochastic preference: a synthesis," Economic Theory, Springer, vol. 26(2), pages 245-264, 08.
  2. Victor Aguirregabiria & Pedro mira, 2007. "Dynamic Discrete Choice Structural Models: A Survey," Working Papers tecipa-297, University of Toronto, Department of Economics.
  3. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555.
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