IDEAS home Printed from https://ideas.repec.org/a/wly/emetrp/v90y2022i2p907-945.html
   My bibliography  Save this article

Multivariate Rational Inattention

Author

Listed:
  • Jianjun Miao
  • Jieran Wu
  • Eric R. Young

Abstract

We study optimal control problems in the multivariate linear‐quadratic‐Gaussian framework under rational inattention. We propose a three‐step procedure to solve this problem using semidefinite programming and derive the optimal signal structure without strong prior restrictions. We analyze both the transition dynamics of the optimal posterior covariance matrix and its steady state. We characterize the optimal information structure for some special cases and develop numerical algorithms for general cases. Applying our methods to solve three multivariate economic models, we obtain some results qualitatively different from the literature.

Suggested Citation

  • Jianjun Miao & Jieran Wu & Eric R. Young, 2022. "Multivariate Rational Inattention," Econometrica, Econometric Society, vol. 90(2), pages 907-945, March.
    • Handle: RePEc:wly:emetrp:v:90:y:2022:i:2:p:907-945
    DOI: 10.3982/ECTA18086
    as

    Download full text from publisher

    File URL: https://doi.org/10.3982/ECTA18086
    Download Restriction: no
    File URL: https://libkey.io/10.3982/ECTA18086?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jakub Steiner & Colin Stewart & Filip Matějka, 2017. "Rational Inattention Dynamics: Inertia and Delay in Decision‐Making," Econometrica, Econometric Society, vol. 85, pages 521-553, March.
    2. Bartosz Maćkowiak & Mirko Wiederholt, 2015. "Business Cycle Dynamics under Rational Inattention," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(4), pages 1502-1532.
    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.
    6. Woodford, Michael, 2009. "Information-constrained state-dependent pricing," Journal of Monetary Economics, Elsevier, vol. 56(S), pages 100-124.
    7. 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.
    8. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, December.
    9. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    10. Peng, Lin, 2005. "Learning with Information Capacity Constraints," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 40(2), pages 307-329, June.
    11. Mondria, Jordi, 2010. "Portfolio choice, attention allocation, and price comovement," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1837-1864, September.
    12. Jianjun Miao & Jieran Wu & Eric R. Young, 2022. "Multivariate Rational Inattention," Econometrica, Econometric Society, vol. 90(2), pages 907-945, March.
    13. 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.
    14. Hebert, Benjamin & Woodford, Michael, 2017. "Rational Inattention with Sequential Information Sampling," Research Papers repec:ecl:stabus:3457, Stanford University, Graduate School of Business.
    15. Peng, Lin & Xiong, Wei, 2006. "Investor attention, overconfidence and category learning," Journal of Financial Economics, Elsevier, vol. 80(3), pages 563-602, June.
    16. Ellen R. McGrattan & Edward C. Prescott, 2010. "Unmeasured Investment and the Puzzling US Boom in the 1990s," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(4), pages 88-123, October.
    17. 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.
    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. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
    22. Christopher A. Sims, 2006. "Rational Inattention: Beyond the Linear-Quadratic Case," American Economic Review, American Economic Association, vol. 96(2), pages 158-163, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. 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.
    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. 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. Roc Armenter & Michèle Müller-Itten & Zachary Stangebye, 2020. "Rational Inattention via Ignorance Equivalence," Working Papers 20-24, Federal Reserve Bank of Philadelphia.
    7. J r my Boccanfuso, 2022. "Consumption Response Heterogeneity and Dynamics with an Inattention Region," Working Papers wp1172, Dipartimento Scienze Economiche, Universita' di Bologna.
    8. Jaehyuk Choi & Lan Ju & Jian Li & Zhiyong Tu, 2023. "Information extraction and artwork pricing," Papers 2302.08167, arXiv.org.
    9. Roc Armenter & Michèle Müller-Itten & Zachary Strangebye, 2021. "Geometric Methods for Finite Rational Inattention," Working Papers 21-30, Federal Reserve Bank of Philadelphia.
    10. Davide Carpentiere & Angelo Petralia, 2023. "Identification of consideration sets from choice data," Papers 2302.00978, arXiv.org, revised Mar 2024.
    11. Jianjun Miao & Jieran Wu & Eric R. Young, 2022. "Multivariate Rational Inattention," Econometrica, Econometric Society, vol. 90(2), pages 907-945, March.
    12. Jurado, Kyle, 2023. "Rational inattention in the frequency domain," Journal of Economic Theory, Elsevier, vol. 208(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bartosz Maćkowiak & Filip Matějka & Mirko Wiederholt, 2023. "Rational Inattention: A Review," Journal of Economic Literature, American Economic Association, vol. 61(1), pages 226-273, March.
    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. Penghui Yin, 2018. "Optimal Amount of Attention to Capital Income Risk and Heterogeneous Precautionary Saving Behavior," CESifo Working Paper Series 7413, CESifo.
    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 18560, Universidad Javeriana - Bogotá.
    5. Pasten, Ernesto & Schoenle, Raphael, 2016. "Rational inattention, multi-product firms and the neutrality of money," Journal of Monetary Economics, Elsevier, vol. 80(C), pages 1-16.
    6. Angeletos, G.-M. & Lian, C., 2016. "Incomplete Information in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 1065-1240, Elsevier.
    7. Bartosz Maćkowiak & Mirko Wiederholt, 2015. "Business Cycle Dynamics under Rational Inattention," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(4), pages 1502-1532.
    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. Dasgupta, Kunal & Mondria, Jordi, 2018. "Inattentive importers," Journal of International Economics, Elsevier, vol. 112(C), pages 150-165.
    10. Luo, Yulei & Young, Eric, 2013. "Rational Inattention in Macroeconomics: A Survey," MPRA Paper 54267, University Library of Munich, Germany.
    11. Luo, Yulei & Nie, Jun & Wang, Gaowang & Young, Eric R., 2017. "Rational inattention and the dynamics of consumption and wealth in general equilibrium," Journal of Economic Theory, Elsevier, vol. 172(C), pages 55-87.
    12. Bartosz Maćkowiak & Mirko Wiederholt, 2021. "Rational Inattention and the Business Cycle Effects of Productivity and News Shocks," SciencePo Working papers Main hal-03878704, HAL.
    13. 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.
    14. Matějka, Filip & Mackowiak, Bartosz & Wiederholt, Mirko, 2018. "Survey: Rational Inattention, a Disciplined Behavioral Model," CEPR Discussion Papers 13243, C.E.P.R. Discussion Papers.
    15. Zhang, Yuhua & Mu, Congming, 2021. "Optimal ownership of entrepreneurial firms with rational inattention," Economics Letters, Elsevier, vol. 209(C).
    16. George Loewenstein & Zachary Wojtowicz, 2023. "The Economics of Attention," CESifo Working Paper Series 10712, CESifo.
    17. Luigi Paciello & Mirko Wiederholt, 2014. "Exogenous Information, Endogenous Information, and Optimal Monetary Policy," Review of Economic Studies, Oxford University Press, vol. 81(1), pages 356-388.
    18. Ellison, Martin & Macaulay, Alistair, 2021. "A rational inattention unemployment trap," Journal of Economic Dynamics and Control, Elsevier, vol. 131(C).
    19. Roc Armenter & Michèle Müller-Itten & Zachary Stangebye, 2020. "Rational Inattention via Ignorance Equivalence," Working Papers 20-24, Federal Reserve Bank of Philadelphia.
    20. Maćkowiak, Bartosz & Matějka, Filip & Wiederholt, Mirko, 2018. "Dynamic rational inattention: Analytical results," Journal of Economic Theory, Elsevier, vol. 176(C), pages 650-692.

    More about this item

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:emetrp:v:90:y:2022:i:2:p:907-945. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.