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A "quantum" approach to rational inattention


  • Saint-Paul, Gilles


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

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    References listed on IDEAS

    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, Oxford University Press, vol. 123(3), pages 863-904.
    2. Gilles Saint-Paul, 2005. "Some Evolutionary Foundations for Price Level Rigidity," American Economic Review, American Economic Association, vol. 95(3), pages 765-779, June.
    3. Christian Hellwig & Ariel Burstein, 2007. "Prices and Market Shares in a Menu Cost Model," 2007 Meeting Papers 327, Society for Economic Dynamics.
    4. Bartosz Maćkowiak & Mirko Wiederholt, 2015. "Business Cycle Dynamics under Rational Inattention," Review of Economic Studies, Oxford University Press, vol. 82(4), pages 1502-1532.
    5. 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.
    6. 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.
    7. 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, Oxford University Press, vol. 117(4), pages 1295-1328.
    8. Andrew S. Caplin & Daniel F. Spulber, 1987. "Menu Costs and the Neutrality of Money," The Quarterly Journal of Economics, Oxford University Press, vol. 102(4), pages 703-725.
    9. Lucas, Robert Jr., 1972. "Expectations and the neutrality of money," Journal of Economic Theory, Elsevier, vol. 4(2), pages 103-124, April.
    10. Bartosz Mackowiak & Mirko Wiederholt, 2009. "Optimal Sticky Prices under Rational Inattention," American Economic Review, American Economic Association, vol. 99(3), pages 769-803, June.
    11. Weitzman, Martin L, 1985. "The Simple Macroeconomics of Profit Sharing," American Economic Review, American Economic Association, vol. 75(5), pages 937-953, December.
    12. Eichenbaum, Martin & Jaimovich, Nir & Rebelo, Sérgio, 2008. "Reference Prices and Nominal Rigidities," CEPR Discussion Papers 6709, C.E.P.R. Discussion Papers.
    13. Ricardo J. Caballero & Eduardo M. R. A. Engel, 1993. "Heterogeneity and Output Fluctuations in a Dynamic Menu-Cost Economy," Review of Economic Studies, Oxford University Press, vol. 60(1), pages 95-119.
    14. Paciello, Luigi, 2007. "The Response of Prices to Technology and Monetary Policy Shocks under Rational Inattention," MPRA Paper 5763, University Library of Munich, Germany.
    15. 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.
    16. Matějka, Filip, 2015. "Rigid pricing and rationally inattentive consumer," Journal of Economic Theory, Elsevier, vol. 158(PB), pages 656-678.
    17. 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.
    18. 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.
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    More about this item


    entropy; lumpy adjustment; monetary policy; mutual information; price-setting; rational inattention;

    JEL classification:

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


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