Transition choice probabilities and welfare in ARUM's
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.
|Date of creation:||16 Sep 2009|
|Note:||View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00417493|
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- de Palma, Andre & Kilani, Karim, 2007. "Invariance of conditional maximum utility," Journal of Economic Theory, Elsevier, vol. 132(1), pages 137-146, January.
- A.de Palma & K. Kilani, 2003. "Invariance of Conditional Maximum Utility," THEMA Working Papers 2003-04, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
- 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.
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- 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.
- 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, 08. Full references (including those not matched with items on IDEAS)
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