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Dynamic Rational Inattention: Analytical Results

Author

Listed:
  • Bartosz Maćkowiak

    (ECB - European Central Bank, CEPR - Center for Economic Policy Research)

  • Filip Matějka

    (CERGE-EI - Center for Economic Research and Graduate Education - Economics Institute, CEPR - Center for Economic Policy Research)

  • Mirko Wiederholt

    (Goethe University Frankfurt = Goethe-Universität Frankfurt am Main, CEPR - Center for Economic Policy Research, ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

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

  • Bartosz Maćkowiak & Filip Matějka & Mirko Wiederholt, 2018. "Dynamic Rational Inattention: Analytical Results," Post-Print hal-03943597, HAL.
    • Handle: RePEc:hal:journl:hal-03943597
    DOI: 10.1016/j.jet.2018.05.001
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    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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