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Dynamic rational inattention: Analytical results

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  • Maćkowiak, Bartosz
  • Matějka, Filip
  • Wiederholt, Mirko

Abstract

This paper presents analytical results for dynamic rational inattention problems as in Sims (2003). The agent tracks an optimal action that follows a Gaussian process. The agent chooses the properties of the signals that he receives, so as to minimize the mean squared difference between his action and the optimal action, subject to a constraint on information flow. We prove that the optimal signal is a one-dimensional signal about the elements of the state vector, which typically has non-zero signal weights on all elements of the state vector. The intuition for these results is that an agent with memory and limited attention wants to learn about the current optimal action and the best predictors of future optimal actions. Hence, in a dynamic economy, rational inattention creates a combination of delay in actions due to noise in the optimal signal and forward-looking actions due to forward-looking information choice. We illustrate these analytical results in a macroeconomic model of price-setting and a business cycle model with news shocks.

Suggested Citation

  • Maćkowiak, Bartosz & Matějka, Filip & Wiederholt, Mirko, 2018. "Dynamic rational inattention: Analytical results," Journal of Economic Theory, Elsevier, vol. 176(C), pages 650-692.
  • Handle: RePEc:eee:jetheo:v:176:y:2018:i:c:p:650-692
    DOI: 10.1016/j.jet.2018.05.001
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    1. Hobler, Stephan, 2022. "Multi-layered rational inattention and time-varying volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 138(C).
    2. Yin, Penghui, 2021. "Optimal attention and heterogeneous precautionary saving behavior," Journal of Economic Dynamics and Control, Elsevier, vol. 131(C).
    3. Dominik Naeher, 2022. "Technology Adoption Under Costly Information Processing," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(2), pages 699-753, May.
    4. Atahan Afsar; José Elías Gallegos; Richard Jaimes; Edgar Silgado Gómez & José Elías Gallegos & Richard Jaimes & Edgar Silgado Gómez, 2020. "Reconciling Empirics and Theory: The Behavioral Hybrid New Keynesian Model," Vniversitas Económica 018560, Universidad Javeriana - Bogotá.
    5. Zhang, Yuhua & Mu, Congming, 2021. "Optimal ownership of entrepreneurial firms with rational inattention," Economics Letters, Elsevier, vol. 209(C).
    6. Alexeeva, Tatyana A. & Kuznetsov, Nikolay V. & Mokaev, Timur N., 2021. "Study of irregular dynamics in an economic model: attractor localization and Lyapunov exponents," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    7. Nimark, Kristoffer P. & Sundaresan, Savitar, 2019. "Inattention and belief polarization," Journal of Economic Theory, Elsevier, vol. 180(C), pages 203-228.
    8. Mackowiak, Bartosz Adam & Matejka, Filip & Wiederholt, Mirko, 2020. "Rational Inattention: A Review," CEPR Discussion Papers 15408, C.E.P.R. Discussion Papers.
    9. Penghui Yin, 2018. "Optimal Amount of Attention to Capital Income Risk and Heterogeneous Precautionary Saving Behavior," CESifo Working Paper Series 7413, CESifo.
    10. Chahrour, Ryan & Jurado, Kyle, 2021. "Optimal foresight," Journal of Monetary Economics, Elsevier, vol. 118(C), pages 245-259.
    11. Rupal Kamdar, 2019. "The Inattentive Consumer: Sentiment and Expectations," 2019 Meeting Papers 647, Society for Economic Dynamics.
    12. McCloud, Nadine, 2022. "Does domestic investment respond to inflation targeting? A synthetic control investigation," International Economics, Elsevier, vol. 169(C), pages 98-134.
    13. Jianjun Miao & Jieran Wu & Eric R. Young, 2022. "Multivariate Rational Inattention," Econometrica, Econometric Society, vol. 90(2), pages 907-945, March.
    14. Janssen, Aljoscha & Kasinger, Johannes, 2021. "Obfuscation and rational inattention in digitalized markets," SAFE Working Paper Series 306, Leibniz Institute for Financial Research SAFE.
    15. Alistair Macaulay, 2022. "Heterogeneous Information, Subjective Model Beliefs, and the Time-Varying Transmission of Shocks," CESifo Working Paper Series 9733, CESifo.
    16. Jérémy Boccanfuso, 2022. "Consumption Response Heterogeneity and Dynamics with an Inattention Region," Working Papers wp1172, Dipartimento Scienze Economiche, Universita' di Bologna.
    17. Bartosz Maćkowiak & Filip Matějka & Mirko Wiederholt, 2022. "Rational Inattention: A Review," Post-Print hal-03878692, HAL.
    18. Stanislav Anatolyev & Sergei Seleznev & Veronika Selezneva, 2021. "How does the financial market update beliefs about the real economy? Evidence from the oil market," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(7), pages 938-961, November.
    19. Janssen, Aljoscha & Kasinger, Johannes, 2021. "Obfuscation and Rational Inattention in Digitalized Markets," Working Paper Series 1379, Research Institute of Industrial Economics.

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    More about this item

    Keywords

    Rational inattention; Information choice; Kalman filter; Macroeconomics;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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