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Multivariate LQG Control under Rational Inattention in Continuous Time

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  • Jianjun Miao

    (Boston University)

Abstract

I propose a multivariate linear-quadratic-Gaussian control framework with rational inattention in continuous time. I propose a three-step solution procedure and numerical methods. The critical step is to transform the problem into a rate distortion problem and derive a semidefinite programming representation. I provide generalized reverse water-filling solutions for some special cases and characterize the optimal signal dimension. I apply my approach to study a consumption/saving problem and illustrate two pitfalls in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:bos:wpaper:wp2019-006
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    File URL: http://people.bu.edu/miaoj/RIcont03.pdf
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    References listed on IDEAS

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    1. Wang, Neng, 2004. "Precautionary saving and partially observed income," Journal of Monetary Economics, Elsevier, vol. 51(8), pages 1645-1681, November.
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    5. Peng, Lin, 2005. "Learning with Information Capacity Constraints," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 40(2), pages 307-329, June.
    6. Jianjun Miao & Jieran Wu & Eric R. Young, 2022. "Multivariate Rational Inattention," Econometrica, Econometric Society, vol. 90(2), pages 907-945, March.
    7. Hebert, Benjamin & Woodford, Michael, 2017. "Rational Inattention with Sequential Information Sampling," Research Papers repec:ecl:stabus:3457, Stanford University, Graduate School of Business.
    8. Matějka, Filip & Mackowiak, Bartosz & Wiederholt, Mirko, 2018. "Survey: Rational Inattention, a Disciplined Behavioral Model," CEPR Discussion Papers 13243, C.E.P.R. Discussion Papers.
    9. Peng, Lin & Xiong, Wei, 2006. "Investor attention, overconfidence and category learning," Journal of Financial Economics, Elsevier, vol. 80(3), pages 563-602, June.
    10. 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.
    11. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
    12. Kenneth Kasa, 2006. "Robustness and Information Processing," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(1), pages 1-33, January.
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    Cited by:

    1. 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.
    2. 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.
    3. Jianjun Miao & Jieran Wu & Eric R. Young, 2022. "Multivariate Rational Inattention," Econometrica, Econometric Society, vol. 90(2), pages 907-945, March.

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    More about this item

    Keywords

    Rational Inattention; Optimal Control; Semidefinite Programming; Consumption; Information Theory;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • E2 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment

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