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A note on uncertainty and discounting in models of economic growth


  • Kenneth Arrow



The implications of uncertainty for appropriate discounting in models of economic growth have been studied at some length, notably, Levhari and Srinivasan (1969), Gollier (2002). A detailed account has now appeared in Dasgupta (2008), sections 4 and 5 (pp. 160-166). One interesting, if perhaps minor, aspect is that under certain circumstances, there appeared to be no solution or at least no satisfactory one. More importantly, the formulas are usually given for the log normal case and are somewhat complicated and hard to interpret intuitively. I show here that assuming a general distribution for returns to capital gives simpler and more understandable results.
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Suggested Citation

  • Kenneth Arrow, 2009. "A note on uncertainty and discounting in models of economic growth," Journal of Risk and Uncertainty, Springer, vol. 38(2), pages 87-94, April.
  • Handle: RePEc:kap:jrisku:v:38:y:2009:i:2:p:87-94
    DOI: 10.1007/s11166-009-9065-1

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    References listed on IDEAS

    1. Gollier, Christian, 2002. "Discounting an uncertain future," Journal of Public Economics, Elsevier, vol. 85(2), pages 149-166, August.
    2. Christian Gollier, 2008. "Discounting with fat-tailed economic growth," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 171-186, December.
    3. Partha Dasgupta, 2008. "Discounting climate change," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 141-169, December.
    4. Jerusalem D. Levhari & T. N. Srinivasan, 1969. "Optimal Savings under Uncertainty," Review of Economic Studies, Oxford University Press, vol. 36(2), pages 153-163.
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    Cited by:

    1. W. Henry Chiu, 2014. "A Note on Discounting an Increasingly Uncertain Future," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 16(6), pages 981-993, December.
    2. David McInerney & Robert Lempert & Klaus Keller, 2012. "What are robust strategies in the face of uncertain climate threshold responses?," Climatic Change, Springer, vol. 112(3), pages 547-568, June.
    3. Nævdal, Erik & Vislie, Jon, 2012. "Resource Depletion and Capital Accumulation under Catastrophic Risk: The Role of Stochastic Thresholds and Stock Pollution," Memorandum 24/2012, Oslo University, Department of Economics.
    4. Millner, Antony, 2013. "On welfare frameworks and catastrophic climate risks," Journal of Environmental Economics and Management, Elsevier, vol. 65(2), pages 310-325.
    5. Antony Millner, 2013. "On Welfare Frameworks and Catastrophic Climate Risks," CESifo Working Paper Series 4442, CESifo Group Munich.
    6. Ikefuji, Masako & Laeven, Roger J.A. & Magnus, Jan R. & Muris, Chris, 2015. "Expected utility and catastrophic consumption risk," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 306-312.
    7. Nævdal, Eric & Vislie, Jon, 2013. "Resource Depletion and Capital Accumulation under Catastrophic Risk: Policy Actions against Stochastic Thresholds and Stock Pollution," Memorandum 24/2013, Oslo University, Department of Economics.
    8. Masako Ikefuji & Roger Laeven & Jan Magnus & Chris Muris, 2014. "Expected Utility and Catastrophic Risk," Tinbergen Institute Discussion Papers 14-133/III, Tinbergen Institute.
    9. In Chang Hwang & Richard S.J. Tol & Marjan W. Hofkes, 2013. "Tail-effect and the Role of Greenhouse Gas Emissions Control," Working Paper Series 6613, Department of Economics, University of Sussex.
    10. Partha Dasgupta, 2011. "The Ethics of Intergenerational Distribution: Reply and Response to John E. Roemer," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 50(4), pages 475-493, December.
    11. Barrett, Scott, 2013. "Climate treaties and approaching catastrophes," Journal of Environmental Economics and Management, Elsevier, vol. 66(2), pages 235-250.

    More about this item


    Uncertainty; Discount rate; Intertemporal optimization; Relative risk aversion; C61; D9; H43; O41;

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions


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