IDEAS home Printed from https://ideas.repec.org/p/cpr/ceprdp/7739.html
   My bibliography  Save this paper

A "quantum" approach to rational inattention

Author

Listed:
  • Saint-Paul, Gilles

Abstract

In this paper, I propose a model of rational inattention where the choice variable is a deterministic function of the exogenous variables, and still only a finite amount of information is being used. This holds provided the choice variable is discrete rather than continuous; that is, the mapping from the realization of the exogenous variables to the endogenous ones is piece-wise constant. Thus, limited information is now a source of lumpiness in behavior, rather than a source of noise. A central result is that the mutual information between the exogenous variable and the endogenous one is simply equal to the entropy, in the usual discrete sense, of the endogenous variable. The approach is illustrated with two applications: a general linear-quadratic problem with a uniform distribution, and a simple static model of price-setting where individual price setters face aggregate monetary shocks and idiosyncratic productivity shocks.

Suggested Citation

  • Saint-Paul, Gilles, 2010. "A "quantum" approach to rational inattention," CEPR Discussion Papers 7739, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:7739
    as

    Download full text from publisher

    File URL: https://cepr.org/publications/DP7739
    Download Restriction: CEPR Discussion Papers are free to download for our researchers, subscribers and members. If you fall into one of these categories but have trouble downloading our papers, please contact us at subscribers@cepr.org
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Peter J. Klenow & Oleksiy Kryvtsov, 2008. "State-Dependent or Time-Dependent Pricing: Does it Matter for Recent U.S. Inflation?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(3), pages 863-904.
    2. Christian Hellwig & Ariel Burstein, 2007. "Prices and Market Shares in a Menu Cost Model," 2007 Meeting Papers 327, Society for Economic Dynamics.
    3. Moscarini, Giuseppe, 2004. "Limited information capacity as a source of inertia," Journal of Economic Dynamics and Control, Elsevier, vol. 28(10), pages 2003-2035, September.
    4. 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.
    5. N. Gregory Mankiw & Ricardo Reis, 2002. "Sticky Information versus Sticky Prices: A Proposal to Replace the New Keynesian Phillips Curve," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(4), pages 1295-1328.
    6. Bartosz Mackowiak & Mirko Wiederholt, 2009. "Optimal Sticky Prices under Rational Inattention," American Economic Review, American Economic Association, vol. 99(3), pages 769-803, June.
    7. 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.
    8. Gilles Saint-Paul, 2005. "Some Evolutionary Foundations for Price Level Rigidity," American Economic Review, American Economic Association, vol. 95(3), pages 765-779, June.
    9. Martin Eichenbaum & Nir Jaimovich & Sergio Rebelo, 2008. "Reference Prices and Nominal Rigidities," NBER Working Papers 13829, National Bureau of Economic Research, Inc.
    10. Paciello, Luigi, 2007. "The Response of Prices to Technology and Monetary Policy Shocks under Rational Inattention," MPRA Paper 5763, University Library of Munich, Germany.
    11. Filip Matejka & Christopher A. Sims, 2011. "Discrete Actions in Information-Constrained Tracking Problems," CERGE-EI Working Papers wp441, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    12. Emmanuel Dhyne & Luis J. Alvarez & Herve Le Bihan & Giovanni Veronese & Daniel Dias & Johannes Hoffmann & Nicole Jonker & Patrick Lunnemann & Fabio Rumler & Jouko Vilmunen, 2006. "Price Changes in the Euro Area and the United States: Some Facts from Individual Consumer Price Data," Journal of Economic Perspectives, American Economic Association, vol. 20(2), pages 171-192, Spring.
    13. Andrew S. Caplin & Daniel F. Spulber, 1987. "Menu Costs and the Neutrality of Money," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(4), pages 703-725.
    14. Lucas, Robert Jr., 1972. "Expectations and the neutrality of money," Journal of Economic Theory, Elsevier, vol. 4(2), pages 103-124, April.
    15. Weitzman, Martin L, 1985. "The Simple Macroeconomics of Profit Sharing," American Economic Review, American Economic Association, vol. 75(5), pages 937-953, December.
    16. Ricardo J. Caballero & Eduardo M. R. A. Engel, 1993. "Heterogeneity and Output Fluctuations in a Dynamic Menu-Cost Economy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(1), pages 95-119.
    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. Matějka, Filip, 2015. "Rigid pricing and rationally inattentive consumer," Journal of Economic Theory, Elsevier, vol. 158(PB), pages 656-678.
    19. Caballero, Ricardo J & Engel, Eduardo M R A & Haltiwanger, John, 1997. "Aggregate Employment Dynamics: Building from Microeconomic Evidence," American Economic Review, American Economic Association, vol. 87(1), pages 115-137, March.
    Full references (including those not matched with items on IDEAS)

    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. Saint-Paul, Gilles, 2017. "A “quantized” approach to rational inattention," European Economic Review, Elsevier, vol. 100(C), pages 50-71.
    2. Etienne Gagnon & David López-Salido & Nicolas Vincent, 2013. "Individual Price Adjustment along the Extensive Margin," NBER Macroeconomics Annual, University of Chicago Press, vol. 27(1), pages 235-281.
    3. 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.
    4. Antonella Tutino, 2013. "Rationally inattentive consumption choices," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 16(3), pages 421-439, July.
    5. 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.
    6. Hellwig, Christian & Venkateswaran, Venky, 2009. "Setting the right prices for the wrong reasons," Journal of Monetary Economics, Elsevier, vol. 56(S), pages 57-77.
    7. Stéphane Dupraz, 2024. "A Kinked‐Demand Theory of Price Rigidity," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 56(2-3), pages 325-363, March.
    8. Bartosz Mackowiak & Frank Smets, 2008. "On implications of micro price data for macro models," Conference Series ; [Proceedings], Federal Reserve Bank of Boston.
    9. Leonardo Melosi, 2009. "A Likelihood Analysis of Models with Information Frictions," PIER Working Paper Archive 09-009, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    10. George-Marios Angeletos & Jennifer La'O, 2010. "Noisy Business Cycles," NBER Chapters, in: NBER Macroeconomics Annual 2009, Volume 24, pages 319-378, National Bureau of Economic Research, Inc.
    11. 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.
    12. 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.
    13. Klenow, Peter J. & Malin, Benjamin A., 2010. "Microeconomic Evidence on Price-Setting," Handbook of Monetary Economics, in: Benjamin M. Friedman & Michael Woodford (ed.), Handbook of Monetary Economics, edition 1, volume 3, chapter 6, pages 231-284, Elsevier.
    14. Schenkelberg, Heike, 2011. "Why are Prices Sticky? Evidence from Business Survey Data," Discussion Papers in Economics 12158, University of Munich, Department of Economics.
    15. George-Marios Angeletos, 2018. "Frictional Coordination," Journal of the European Economic Association, European Economic Association, vol. 16(3), pages 563-603.
    16. Hahn, Volker & Marenčák, Michal, 2020. "Price points and price dynamics," Journal of Monetary Economics, Elsevier, vol. 115(C), pages 127-144.
    17. Christian Hellwig & Venky Venkateswaran, 2024. "Dispersed Information, Nominal Rigidities and Monetary Business Cycles: A Hayekian Perspective," NBER Working Papers 33215, National Bureau of Economic Research, Inc.
    18. Fernando E. Alvarez & Francesco Lippi & Luigi Paciello, 2011. "Optimal Price Setting With Observation and Menu Costs," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(4), pages 1909-1960.
    19. Bartosz Mackowiak & Mirko Wiederholt, 2009. "Optimal Sticky Prices under Rational Inattention," American Economic Review, American Economic Association, vol. 99(3), pages 769-803, June.
    20. Mikael Carlsson & Oskar Nordstrom Skans, 2012. "Evaluating Microfoundations for Aggregate Price Rigidities: Evidence from Matched Firm-Level Data on Product Prices and Unit Labor Cost," American Economic Review, American Economic Association, vol. 102(4), pages 1571-1595, June.

    More about this item

    Keywords

    Mutual information; Price-setting; Rational inattention; Monetary policy; Entropy; Lumpy adjustment;
    All these keywords.

    JEL classification:

    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles

    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:cpr:ceprdp:7739. 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: the person in charge (email available below). General contact details of provider: https://www.cepr.org .

    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.