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Transition choice probabilities and welfare analysis in additive random utility models

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  • André Palma

  • Karim Kilani

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 (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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  • André Palma & Karim Kilani, 2011. "Transition choice probabilities and welfare analysis in additive random utility models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(3), pages 427-454, April.
    • Handle: RePEc:spr:joecth:v:46:y:2011:i:3:p:427-454
    DOI: 10.1007/s00199-009-0513-6
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    Cited by:

    1. Richard Batley & Thijs Dekker, 2019. "The Intuition Behind Income Effects of Price Changes in Discrete Choice Models, and a Simple Method for Measuring the Compensating Variation," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 74(1), pages 337-366, September.
    2. Charles Gauthier & Sebastiaan Maes & Raghav Malhotra, 2023. "Consumer Welfare Under Individual Heterogeneity," Papers 2303.01231, arXiv.org, revised Sep 2025.
    3. Delle Site, Paolo & Salucci, Marco Valerio, 2015. "Transition choice probabilities in logit," Economics Letters, Elsevier, vol. 126(C), pages 135-139.
    4. Naqavi, Fatemeh & Sundberg, Marcus & Västberg, Oskar Blom & Karlström, Anders & Hugosson, Muriel Beser, 2023. "Mobility constraints and accessibility to work: Application to Stockholm," Transportation Research Part A: Policy and Practice, Elsevier, vol. 175(C).
    5. Anders Karlström, 2014. "Appraisal," Chapters, in: Stephane Hess & Andrew Daly (ed.), Handbook of Choice Modelling, chapter 24, pages 601-626, Edward Elgar Publishing.
    6. Paolo Delle Site, 2017. "On the Equivalence Between SUE and Fixed-Point States of Day-to-Day Assignment Processes with Serially-Correlated Route Choice," Networks and Spatial Economics, Springer, vol. 17(3), pages 935-962, September.
    7. Anderson, Simon P. & de Palma, André, 2012. "Oligopoly and Luce's Choice Axiom," Regional Science and Urban Economics, Elsevier, vol. 42(6), pages 1053-1060.
    8. Min Qiang Zhao & Ju-Chin Huang, 2018. "The Representative Consumer Approximation Bias in Discrete Choice Welfare Analysis," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 71(4), pages 969-984, December.
    9. Paolo Delle Site & Marco Valerio Salucci, 2012. "The Impact Of The Before-After Error Term Correlation On Welfare Measurement In Logit," Working Papers 0412, CREI Università degli Studi Roma Tre, revised 2012.
    10. Delle Site, Paolo & Parmar, Janak, 2024. "On the Linear Probability Model as binary choice random utility model," Journal of choice modelling, Elsevier, vol. 52(C).
    11. André de Palma & Karim Kilani & Gilbert Laffond, 2013. "Best and worst choices," Working Papers halshs-00825656, HAL.
    12. Delle Site, Paolo & Salucci, Marco Valerio, 2013. "Transition choice probabilities and welfare analysis in random utility models with imperfect before–after correlation," Transportation Research Part B: Methodological, Elsevier, vol. 58(C), pages 215-242.
    13. Dekker, Thijs, 2014. "Indifference based value of time measures for Random Regret Minimisation models," Journal of choice modelling, Elsevier, vol. 12(C), pages 10-20.
    14. Paolo Delle Site & André de Palma & Karim Kilani, 2021. "Consumers’ welfare and compensating variation: survey and mode choice application," Thema Working Papers 2021-11, THEMA (Théorie Economique, Modélisation et Applications), CY Cergy-Paris University, ESSEC and CNRS.
    15. Bart Capéau & Liebrecht De Sadeleer & Sebastiaan Maes & André Decoster, 2020. "Nonparametric welfare analysis for discrete choice: levels and differences of individual and social welfare," Working Papers of Department of Economics, Leuven 674666, KU Leuven, Faculty of Economics and Business (FEB), Department of Economics, Leuven.
    16. Maes, Sebastiaan & Malhotra, Raghav, 2024. "Robust Hicksian Welfare Analysis under Individual Heterogeneity," CRETA Online Discussion Paper Series 84, Centre for Research in Economic Theory and its Applications CRETA.
    17. Delle Site, P. & Kilani, K., 2024. "Welfare measurement with income-dependent discrete choice," Economics Letters, Elsevier, vol. 245(C).

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    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D60 - Microeconomics - - Welfare Economics - - - General

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