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Hyperbolic discounting may be time consistent


  • Nicolas Drouhin

    () (Ecole normale supérieure de Cachan- Centre d''Economie de la Sorbonne - Paris School of Economics)


Using dynamic programming methodology, the paper analyzes the most general conditions for an additive utility functional to represent time consistent preferences. It challenges the conventional wisdom of the domain, which, following Strotz(1956), assume that only exponential discounting is compatible with time consistent behavior. The paper gives some examples of special time consistent hyperbolic discount functions and also discuss the relation between time consistency and stationarity.

Suggested Citation

  • Nicolas Drouhin, 2009. "Hyperbolic discounting may be time consistent," Economics Bulletin, AccessEcon, vol. 29(4), pages 2549-2555.
  • Handle: RePEc:ebl:ecbull:eb-09-00453

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    References listed on IDEAS

    1. Harris, Christopher & Laibson, David, 2001. "Dynamic Choices of Hyperbolic Consumers," Econometrica, Econometric Society, vol. 69(4), pages 935-957, July.
    2. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
    3. Salanie, Francois & Treich, Nicolas, 2006. "Over-savings and hyperbolic discounting," European Economic Review, Elsevier, vol. 50(6), pages 1557-1570, August.
    4. H. Stuart Burness, 1976. "A Note on Consistent Naive Intertemporal Decision Making and an Application to the Case of Uncertain Lifetime," Review of Economic Studies, Oxford University Press, vol. 43(3), pages 547-549.
    5. Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
    6. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, Oxford University Press, vol. 112(2), pages 443-478.
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    Cited by:

    1. André Lapied & Olivier Renault, 2012. "An Investigation of Time Consistency for Subjective Discontinued Utility," AMSE Working Papers 1210, Aix-Marseille School of Economics, Marseille, France.
    2. Nicolas Drouhin, 2017. "Non stationary additive utility and time consistency," Working Papers halshs-01238584, HAL.
    3. Strulik, Holger & Trimborn, Timo, 2016. "Hyperbolic discounting can be good for your health," ECON WPS - Vienna University of Technology Working Papers in Economic Theory and Policy 11/2016, Vienna University of Technology, Institute for Mathematical Methods in Economics, Research Group Economics (ECON).
    4. André Lapied & Olivier Renault, 2012. "A subjective discounted utility model," Economics Bulletin, AccessEcon, vol. 32(2), pages 1171-1179.
    5. Drouhin, Nicolas, 2015. "A rank-dependent utility model of uncertain lifetime," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 208-224.
    6. Cabo, Francisco & Martín-Herrán, Guiomar & Martínez-García, María Pilar, 2016. "Unbounded growth in the Neoclassical growth model with non-constant discounting," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 93-104.
    7. Nicolas Drouhin, 2012. "A rank-dependent utility model of uncertain lifetime, time consistency and life insurance," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00748662, HAL.
    8. Orlando Gomes & Alexandra Ferreira-Lopes & Tiago Sequeira, 2014. "Exponential discounting bias," Journal of Economics, Springer, vol. 113(1), pages 31-57, September.
    9. Strulik, Holger, 2017. "Hyperbolic discounting and the time-consistent solution of three canonical environmental problems," Center for European, Governance and Economic Development Research Discussion Papers 319, University of Goettingen, Department of Economics.
    10. Nicolas Drouhin, 2016. "Non stationary additive utility and time consistency," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01238584, HAL.

    More about this item


    intertemporal choice; consumption and saving; time consistency; time discounting; exponential discounting; hyperbolic discounting;

    JEL classification:

    • D9 - Microeconomics - - Micro-Based Behavioral Economics
    • E2 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment


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