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Multivariate Rational Inattention

Author

Listed:
  • Jianjun Miao

    (Boston University)

  • Jieran Wu

    (Zhejiang University)

  • Eric Young

    (University of Virginia)

Abstract

We study optimal control problems in the multivariate linear-quadratic-Gaussian framework under rational inattention and show that the multivariate attention allocation problem can be reduced to a dynamic tracking problem in information theory. We propose a general solution method to solve this problem by using rate distortion functions and semidefinite programming and derive the optimal form and dimension of signals without strong prior restrictions. We provide generalized reverse water-filling solutions for some special cases. Applying our method to solve three multivariate economic models, we obtain some results qualitatively different from the literature.

Suggested Citation

  • Jianjun Miao & Jieran Wu & Eric Young, 2018. "Multivariate Rational Inattention," Boston University - Department of Economics - Working Papers Series WP2019-07, Boston University - Department of Economics, revised Jan 2019.
    • Handle: RePEc:bos:wpaper:wp2019-007
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    References listed on IDEAS

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    3. Zorn, Peter, 2016. "Investment under Rational Inattention: Evidence from US Sectoral Data," VfS Annual Conference 2016 (Augsburg): Demographic Change 145572, Verein für Socialpolitik / German Economic Association.
    4. Jianjun Miao, 2019. "Multivariate LQG Control under Rational Inattention in Continuous Time," Boston University - Department of Economics - Working Papers Series WP2019-06, Boston University - Department of Economics.
    5. 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.
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    18. Andrew Caplin & Mark Dean & John Leahy, 2019. "Rational Inattention, Optimal Consideration Sets, and Stochastic Choice," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(3), pages 1061-1094.
    19. Maćkowiak, Bartosz & Matějka, Filip & Wiederholt, Mirko, 2018. "Dynamic rational inattention: Analytical results," Journal of Economic Theory, Elsevier, vol. 176(C), pages 650-692.
    20. Yulei Luo & Eric R. Young, 2010. "Risk-Sensitive Consumption and Savings under Rational Inattention," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(4), pages 281-325, October.
    21. Yulei Luo, 2008. "Consumption Dynamics under Information Processing Constraints," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 11(2), pages 366-385, April.
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    Citations

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    Cited by:

    1. Roc Armenter & Michèle Müller-Itten & Zachary Strangebye, 2021. "Geometric Methods for Finite Rational Inattention," Working Papers 21-30, Federal Reserve Bank of Philadelphia.
    2. Jianjun Miao & Dongling Su, 2023. "Asset market equilibrium under rational inattention," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(1), pages 1-30, January.
    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. Kamdar, Rupal & Ray, Walker, 2024. "Attention-Driven Sentiment and the Business Cycle," CEPR Discussion Papers 18984, C.E.P.R. Discussion Papers.
    5. Bartosz Maćkowiak & Mirko Wiederholt, 2021. "Rational Inattention and the Business Cycle Effects of Productivity and News Shocks," SciencePo Working papers Main hal-03878704, HAL.
    6. Joshua Bernstein & Rupal Kamdar, 2023. "Rationally Inattentive Monetary Policy," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 48, pages 265-296, April.
    7. Davide Carpentiere & Angelo Petralia, 2023. "Identification of consideration sets from choice data," Papers 2302.00978, arXiv.org, revised Mar 2024.
    8. Jianjun Miao, 2019. "Multivariate LQG Control under Rational Inattention in Continuous Time," Boston University - Department of Economics - Working Papers Series WP2019-06, Boston University - Department of Economics.
    9. Roc Armenter & Michèle Müller-Itten & Zachary Stangebye, 2020. "Rational Inattention via Ignorance Equivalence," Working Papers 20-24, Federal Reserve Bank of Philadelphia.
    10. Jianjun Miao & Jieran Wu & Eric R. Young, 2022. "Multivariate Rational Inattention," Econometrica, Econometric Society, vol. 90(2), pages 907-945, March.
    11. Jurado, Kyle, 2023. "Rational inattention in the frequency domain," Journal of Economic Theory, Elsevier, vol. 208(C).
    12. J r my Boccanfuso, 2022. "Consumption Response Heterogeneity and Dynamics with an Inattention Region," Working Papers wp1172, Dipartimento Scienze Economiche, Universita' di Bologna.
    13. Jaehyuk Choi & Lan Ju & Jian Li & Zhiyong Tu, 2023. "Information extraction and artwork pricing," Papers 2302.08167, arXiv.org.

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    More about this item

    Keywords

    Rational Rational Inattention; Endogenous Information Choice; Rate Distortion Function; Dynamic Tracking Problem; Optimal Control;
    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
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation

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