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Discrete Choice and Rational Inattention: a General Equivalence Result�

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  • Fosgerau, Mogens
  • Melo, Emerson
  • Shum, Matt

Abstract

This paper establishes a general equivalence between discrete choice and rational inattention models. We show that the choice probabilities emerging from any random utility discrete choice model can be obtained from a class of suitably generalized rational inattention models, and vice versa. Thus any discrete choice model can be given an interpretation in terms of boundedly rational behavior. The underlying idea is that the surplus function of a discrete choice model has a convex conjugate that is a generalized entropy (which is a suitable generalization of the Shannon entropy function). These generalized entropies are used to construct an information cost function for a generalized rational inattention model. We denote this class of rational inattention problems as Generalized Entropic Rational Inattention (GERI) models.

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  • Fosgerau, Mogens & Melo, Emerson & Shum, Matt, 2017. "Discrete Choice and Rational Inattention: a General Equivalence Result�," MPRA Paper 76605, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:76605
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    References listed on IDEAS

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    1. Mogens Fosgerau & André de Palma, 2016. "Generalized entropy models," Working Papers hal-01291347, HAL.
    2. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    3. de Oliveira, Henrique & Denti, Tommaso & Mihm, Maximilian & Ozbek, Kemal, 2017. "Rationally inattentive preferences and hidden information costs," Theoretical Economics, Econometric Society, vol. 12(2), May.
    4. Filip Matêjka & Alisdair McKay, 2015. "Rational Inattention to Discrete Choices: A New Foundation for the Multinomial Logit Model," American Economic Review, American Economic Association, vol. 105(1), pages 272-298, January.
    5. Hebert, Benjamin & Woodford, Michael, 2017. "Rational Inattention with Sequential Information Sampling," Research Papers repec:ecl:stabus:3457, Stanford University, Graduate School of Business.
    6. Khai Xiang Chiong & Alfred Galichon & Matt Shum, 2016. "Duality in dynamic discrete‐choice models," Quantitative Economics, Econometric Society, vol. 7(1), pages 83-115, March.
    7. Sims, Christopher A., 2010. "Rational Inattention and Monetary Economics," Handbook of Monetary Economics, in: Benjamin M. Friedman & Michael Woodford (ed.), Handbook of Monetary Economics, edition 1, volume 3, chapter 4, pages 155-181, Elsevier.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Matveenko, Andrei & Mikhalishchev, Sergei, 2021. "Attentional role of quota implementation," Journal of Economic Theory, Elsevier, vol. 198(C).
    2. Mogens Fosgerau & Julien Monardo & André de Palma, 2024. "The Inverse Product Differentiation Logit Model," American Economic Journal: Microeconomics, American Economic Association, vol. 16(4), pages 329-370, November.
    3. Botond Kőszegi & Filip Matějka, 2020. "Choice Simplification: A Theory of Mental Budgeting and Naive Diversification [“Fungibility, Labels, and Consumption,”]," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 135(2), pages 1153-1207.
    4. Arindrajit Dube & Jeff Jacobs & Suresh Naidu & Siddharth Suri, 2020. "Monopsony in Online Labor Markets," American Economic Review: Insights, American Economic Association, vol. 2(1), pages 33-46, March.
    5. Doron Ravid, 2020. "Ultimatum Bargaining with Rational Inattention," American Economic Review, American Economic Association, vol. 110(9), pages 2948-2963, September.
    6. Mogens Fosgerau & Dennis Kristensen, 2021. "Identification of a class of index models: A topological approach," The Econometrics Journal, Royal Economic Society, vol. 24(1), pages 121-133.
    7. Lindbeck, Assar & Weibull, Jörgen, 2020. "Delegation of investment decisions, and optimal remuneration of agents," European Economic Review, Elsevier, vol. 129(C).
    8. Victor H. Aguiar & Maria Jose Boccardi & Nail Kashaev & Jeongbin Kim, 2023. "Random utility and limited consideration," Quantitative Economics, Econometric Society, vol. 14(1), pages 71-116, January.
    9. S. Cerreia-Vioglio & F. Maccheroni & M. Marinacci & A. Rustichini, 2017. "Multinomial logit processes and preference discovery: inside and outside the black box," Working Papers 615, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    10. Fosgerau, Mogens & Jiang, Gege, 2019. "Travel time variability and rational inattention," Transportation Research Part B: Methodological, Elsevier, vol. 120(C), pages 1-14.
    11. Kashaev, Nail & Aguiar, Victor H., 2022. "A random attention and utility model," Journal of Economic Theory, Elsevier, vol. 204(C).
    12. T. Tony Ke & Song Lin, 2020. "Informational Complementarity," Management Science, INFORMS, vol. 66(8), pages 3699-3716, August.
    13. David Muller & Yurii Nesterov & Vladimir Shikhman, 2021. "Dynamic pricing under nested logit demand," Papers 2101.04486, arXiv.org.
    14. Quaglione, Davide & Cassetta, Ernesto & Crociata, Alessandro & Marra, Alessandro & Sarra, Alessandro, 2019. "An assessment of the role of cultural capital on sustainable mobility behaviours: Conceptual framework and empirical evidence," Socio-Economic Planning Sciences, Elsevier, vol. 66(C), pages 24-34.
    15. Cristina Gualdani & Shruti Sinha, 2019. "Identification in discrete choice models with imperfect information," Papers 1911.04529, arXiv.org, revised Dec 2023.
    16. André de Palma & Julien Monardo, 2017. "The General Nesting Logit (GNL) Model using Aggregate Data," Working Papers hal-01552455, HAL.
    17. David Muller & Yurii Nesterov & Vladimir Shikhman, 2019. "Discrete choice prox-functions on the simplex," Papers 1909.05591, arXiv.org.
    18. Benjamin Hébert & Michael Woodford, 2017. "Rational Inattention and Sequential Information Sampling," NBER Working Papers 23787, National Bureau of Economic Research, Inc.
    19. Jiang, Gege & Fosgerau, Mogens & Lo, Hong K., 2020. "Route choice, travel time variability, and rational inattention," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 188-207.
    20. Jorge Lorca & Emerson Melo, 2020. "Choice Aversion in Directed Networks," Working Papers Central Bank of Chile 879, Central Bank of Chile.
    21. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2020. "Multinomial logit processes and preference discovery: outside and inside the black box," Working Papers 663, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.

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    More about this item

    Keywords

    Rational Inattention; discrete choices; general entropy; con- vex analysis;
    All these keywords.

    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • E03 - Macroeconomics and Monetary Economics - - General - - - Behavioral Macroeconomics

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