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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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    1. Peng, Lin & Xiong, Wei, 2006. "Investor attention, overconfidence and category learning," Journal of Financial Economics, Elsevier, vol. 80(3), pages 563-602, June.
    2. Bartosz Maćkowiak & Mirko Wiederholt, 2015. "Business Cycle Dynamics under Rational Inattention," Review of Economic Studies, Oxford University Press, vol. 82(4), pages 1502-1532.
    3. 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.
    4. 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.
    5. Woodford, Michael, 2009. "Information-constrained state-dependent pricing," Journal of Monetary Economics, Elsevier, vol. 56(S), pages 100-124.
    6. Zorn, Peter, 2016. "Investment under Rational Inattention: Evidence from US Sectoral Data," Annual Conference 2016 (Augsburg): Demographic Change 145572, Verein für Socialpolitik / German Economic Association.
    7. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
    8. Maćkowiak, Bartosz & Matějka, Filip & Wiederholt, Mirko, 2018. "Dynamic rational inattention: Analytical results," Journal of Economic Theory, Elsevier, vol. 176(C), pages 650-692.
    9. Lawrence J. Christiano & Martin Eichenbaum & Charles L. Evans, 2005. "Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy," Journal of Political Economy, University of Chicago Press, vol. 113(1), pages 1-45, February.
    10. Thomas M. Loughin, 2006. "SAS-super-® for Mixed Models, 2nd edition Edited by Littell, R. C., Milliken, G. A., Stroup, W. W., Wolfinger, R. D., and Schabenberger, O," Biometrics, The International Biometric Society, vol. 62(4), pages 1273-1274, December.
    11. Yulei Luo & Jun Nie & Eric R. Young, 2015. "Slow Information Diffusion And The Inertial Behavior Of Durable Consumption," Journal of the European Economic Association, European Economic Association, vol. 13(5), pages 805-840, October.
    12. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, December.
    13. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    14. Peng, Lin, 2005. "Learning with Information Capacity Constraints," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 40(2), pages 307-329, June.
    15. 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.
    16. Christopher A. Sims, 2006. "Rational Inattention: Beyond the Linear-Quadratic Case," American Economic Review, American Economic Association, vol. 96(2), pages 158-163, May.
    17. Mondria, Jordi, 2010. "Portfolio choice, attention allocation, and price comovement," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1837-1864, September.
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    More about this item

    Keywords

    Rational Rational Inattention; Endogenous Information Choice; Rate Distortion Function; Dynamic Tracking Problem; Optimal Control;

    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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