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Uncertain growth and the value of the future


  • Jaume Masoliver
  • Miquel Montero
  • Josep Perell'o
  • John Geanakoplos
  • J. Doyne Farmer


For environmental problems such as global warming future costs must be balanced against present costs. This is traditionally done using an exponential function with a constant discount rate, which reduces the present value of future costs. The result is highly sensitive to the choice of discount rate and has generated a major controversy as to the urgency for immediate action. We study analytically several standard interest rate models from finance and compare their properties to empirical data. From historical time series for nominal interest rates and inflation covering 14 countries over hundreds of years, we find that extended periods of negative real interest rates are common, occurring in many epochs in all countries. This leads us to choose the Ornstein-Uhlenbeck model, in which real short run interest rates fluctuate stochastically and can become negative, even if they revert to a positive mean value. We solve the model in closed form and prove that the long-run discount rate is always less than the mean; indeed it can be zero or even negative, despite the fact that the mean short term interest rate is positive. We fit the parameters of the model to the data, and find that nine of the countries have positive long run discount rates while five have negative long-run discount rates. Even if one rejects the countries where hyperinflation has occurred, our results support the low discounting rate used in the Stern report over higher rates advocated by others.

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  • Jaume Masoliver & Miquel Montero & Josep Perell'o & John Geanakoplos & J. Doyne Farmer, 2013. "Uncertain growth and the value of the future," Papers 1311.4068,
  • Handle: RePEc:arx:papers:1311.4068

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    References listed on IDEAS

    1. Roncalli, Thierry, 2013. "Introduction to Risk Parity and Budgeting," MPRA Paper 47679, University Library of Munich, Germany.
    2. repec:dau:papers:123456789/4688 is not listed on IDEAS
    3. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    4. T. Heller & R. Huet & Bénédicte Vidaillet, 2013. "Introduction," Post-Print hal-00848256, HAL.
    5. Cazalet, Zelia & Grison, Pierre & Roncalli, Thierry, 2013. "The Smart Beta Indexing Puzzle," MPRA Paper 48823, University Library of Munich, Germany.
    6. Bruder, Benjamin & Roncalli, Thierry, 2012. "Managing risk exposures using the risk budgeting approach," MPRA Paper 37246, University Library of Munich, Germany.
    7. Roncalli, Thierry, 2013. "Introducing Expected Returns into Risk Parity Portfolios: A New Framework for Tactical and Strategic Asset Allocation," MPRA Paper 49821, University Library of Munich, Germany.
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    Cited by:

    1. Rob Aalbers & Marjon Ruijter & Kees Oosterlee (CWI), 2014. "The social discount rate under a stochastic A2 scenario," CPB Discussion Paper 296, CPB Netherlands Bureau for Economic Policy Analysis.

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