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A “quantized” approach to rational inattention

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  • Gilles Saint-Paul

    (PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, New York University [Abu Dhabi] - NYU - NYU System)

Abstract

In this paper, I propose a model of rational inattention where the choice variable is a deterministic function of the exogenous variables, and still only a finite amount of information is being used. This holds provided the choice variable is discrete rather than continuous; that is, the mapping from the realization of the exogenous variables to the endogenous ones is piece-wise constant. Thus, limited information is now a source of lumpiness in behavior, rather than a source of noise. The approach is applied to a simple static model of price-setting where individual price setters face aggregate monetary shocks and idiosyncratic productivity shocks. The effect of aggregate money shocks on output and prices is studied. It is shown that as the variance of idiosyncratic shocks become large, the aggregate log price level converges to a linear function of the aggregate money shock, with a coefficient which is strictly between 0 and 1. Consequently, unanticipated aggregate money shocks have real effects on output, in contrast to the sticky price model of Caplin and Spulber (1987). But these effects are smaller than in standard rational inattention models or in the Lucas (1972) misperception model.

Suggested Citation

  • Gilles Saint-Paul, 2017. "A “quantized” approach to rational inattention," PSE-Ecole d'économie de Paris (Postprint) halshs-01630629, HAL.
    • Handle: RePEc:hal:pseptp:halshs-01630629
    DOI: 10.1016/j.euroecorev.2017.07.004
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    Cited by:

    1. Massenot, Baptiste, 2020. "Pain of Paying in a Business Cycle Model," SAFE Working Paper Series 194, Leibniz Institute for Financial Research SAFE, revised 2020.
    2. Luo, Yulei & Young, Eric, 2013. "Rational Inattention in Macroeconomics: A Survey," MPRA Paper 54267, University Library of Munich, Germany.
    3. Li, Anqi & Yang, Ming, 2020. "Optimal incentive contract with endogenous monitoring technology," Theoretical Economics, Econometric Society, vol. 15(3), July.
    4. La Spada Gabriele & Lillo Fabrizio, 2014. "The effect of round-off error on long memory processes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(4), pages 445-482, September.
    5. Avi Goldfarb & Mo Xiao, 2024. "Transitory shocks, limited attention, and a firm’s decision to exit," Quantitative Marketing and Economics (QME), Springer, vol. 22(3), pages 223-255, September.
    6. Ellis, Andrew, 2018. "Foundations for optimal inattention," Journal of Economic Theory, Elsevier, vol. 173(C), pages 56-94.
    7. Narvin Kartik & Andreas Kleiner, 2025. "Convex Choice," CRC TR 224 Discussion Paper Series crctr224_2025_676, University of Bonn and University of Mannheim, Germany.

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    Keywords

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    JEL classification:

    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles

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