Transition choice probabilities and welfare in ARUM's
AbstractWe 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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Date of creation: 16 Sep 2009
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Additive random utility models (ARUM); Logit; Transition choice probabilities; Compensating variation; Shephard's Lemma; Logsum; CES;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-09-26 (All new papers)
- NEP-DCM-2009-09-26 (Discrete Choice Models)
- NEP-UPT-2009-09-26 (Utility Models & Prospect Theory)
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