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Hybrid Exponential†Hyperbolic Discounting and Growth Without Commitment


  • Christopher Tsoukis
  • Frédéric Tournemaine
  • Max Gillman


We analyse the time†consistent intertemporal behaviour of an individual who discounts the future hyperbolically (HD) in the absence of commitment. In continuous†time, we extend Barro's (Quarterly Journal of Economics, Vol. 114 (1999), pp. 1125–1152) analysis of a ‘sophisticated’ present†bias in a deterministic setup and characterize consumption in an analytically tractable way. Furthermore, we embed this analysis into a ‘flexible AK’ model. Greater present bias increases the consumption†capital ratio, decreases the steady†state growth rate, while it increases the interest rate†growth rate wedge. Dynamically, as the interest rate fluctuates over the business cycle, a greater present bias causes the consumption†output ratio to be more procyclical and volatile, thus helping to resolve the ‘consumption†output puzzle’. In the transitional dynamics, greater present bias causes a lower steady state capital stock. All of these effects are only present or at least more pronounced under HD than present value†equivalent exponential discounting.

Suggested Citation

  • Christopher Tsoukis & Frédéric Tournemaine & Max Gillman, 2017. "Hybrid Exponential†Hyperbolic Discounting and Growth Without Commitment," Manchester School, University of Manchester, vol. 85(S2), pages 45-74, December.
  • Handle: RePEc:bla:manchs:v:85:y:2017:i:s2:p:e45-e74
    DOI: 10.1111/manc.12197

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    Cited by:

    1. Cabo, Francisco & Martín-Herrán, Guiomar & Martínez-García, María Pilar, 2020. "Present bias and the inefficiency of the centralized economy: The role of the elasticity of intertemporal substitution," Economic Modelling, Elsevier, vol. 93(C), pages 702-716.
    2. Francisco Cabo & Guiomar Martín-Herrán & María Pilar Martínez-García, 2020. "Non-constant Discounting, Social Welfare and Endogenous Growth with Pollution Externalities," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 76(2), pages 369-403, July.
    3. Choi, Yoonseok & Kim, Sunghyun Henry, 2021. "Understanding the effects of government spending in a time-inconsistent model," Economic Modelling, Elsevier, vol. 98(C), pages 266-279.

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