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Integration of choice probabilities in logit


  • Delle Site, Paolo


We find for logit with income effects a function that generates choice probabilities via Roy’s identity. We show that it possesses all the properties to qualify as an indirect utility, it has a closed-form expression for the practically interesting translog specification of the systematic utilities, it reduces in the case without income effects to the expectation of the maximum utility. We discuss the use of the findings in welfare measurement and the extension to observed heterogeneity and mixed logit.

Suggested Citation

  • Delle Site, Paolo, 2013. "Integration of choice probabilities in logit," Economics Letters, Elsevier, vol. 120(1), pages 57-60.
  • Handle: RePEc:eee:ecolet:v:120:y:2013:i:1:p:57-60 DOI: 10.1016/j.econlet.2013.03.027

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    References listed on IDEAS

    1. Constant I. Tra, 2013. "Nonlinear income effects in random utility models: revisiting the accuracy of the representative consumer approximation," Applied Economics, Taylor & Francis Journals, vol. 45(1), pages 55-63, January.
    2. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, June.
    3. Joseph A. Herriges & Catherine L. Kling, 1999. "Nonlinear Income Effects in Random Utility Models," The Review of Economics and Statistics, MIT Press, vol. 81(1), pages 62-72, February.
    4. Anderson, Simon Peter & de Palma, Andre & Thisse, Jacques-Francois, 1988. "A Representative Consumer Theory of the Logit Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(3), pages 461-466, August.
    5. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
    6. David Hensher & William Greene, 2003. "The Mixed Logit model: The state of practice," Transportation, Springer, vol. 30(2), pages 133-176, May.
    7. Hausman, Jerry A, 1981. "Exact Consumer's Surplus and Deadweight Loss," American Economic Review, American Economic Association, vol. 71(4), pages 662-676, September.
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    Cited by:

    1. 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.
    2. Paolo Delle Site, 2013. "On Duality In Random Utility Models," Working Papers 0513, CREI Università degli Studi Roma Tre, revised 2013.

    More about this item


    Logit; Income effects; Social utility; Roy’s identity;

    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory


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