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A note on uncertainty and discounting in models of economic growth

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  • Kenneth Arrow

Abstract

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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  • 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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    1. Jerusalem D. Levhari & T. N. Srinivasan, 1969. "Optimal Savings under Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(2), pages 153-163.
    2. Gollier, Christian, 2002. "Discounting an uncertain future," Journal of Public Economics, Elsevier, vol. 85(2), pages 149-166, August.
    3. Christian Gollier, 2008. "Discounting with fat-tailed economic growth," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 171-186, December.
    4. Partha Dasgupta, 2008. "Discounting climate change," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 141-169, December.
    5. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
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    Cited by:

    1. Richard S.J. Tol, 2018. "The impact of climate change and the social cost of carbon," Working Paper Series 1318, Department of Economics, University of Sussex Business School.
    2. 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.
    3. 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.
    4. Andrea Rampa, 2020. "Climate change, catastrophes and Dismal Theorem: a critical review [Klimawandel, Katastrophen und das „Dismal Theorem“: eine kritische Überprüfung]," Review of Regional Research: Jahrbuch für Regionalwissenschaft, Springer;Gesellschaft für Regionalforschung (GfR), vol. 40(2), pages 113-136, October.
    5. BRECHET, Thierry & THENIE, Julien & ZEIMES, Thibaut & ZUBER, Stéphane, 2010. "The benefits of cooperation under uncertainty: the case of climate change," LIDAM Discussion Papers CORE 2010062, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Paul A. David & Adriaan van Zon, 2012. "Optimal Multi-Phase Transition Paths toward A Stabilized Global Climate: Integrated Dynamic Requirements Analysis for the 'Tech Fix'," Discussion Papers 12-006, Stanford Institute for Economic Policy Research.
    7. Richard S J Tol, 2018. "The Economic Impacts of Climate Change," Review of Environmental Economics and Policy, Association of Environmental and Resource Economists, vol. 12(1), pages 4-25.
    8. 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.
    9. Millner, Antony, 2013. "On welfare frameworks and catastrophic climate risks," Journal of Environmental Economics and Management, Elsevier, vol. 65(2), pages 310-325.
    10. Antony Millner, 2013. "On Welfare Frameworks and Catastrophic Climate Risks," CESifo Working Paper Series 4442, CESifo.
    11. 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.
    12. 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.
    13. 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.
    14. Partha Dasgupta, 2014. "Pricing climate change," Politics, Philosophy & Economics, , vol. 13(4), pages 394-416, November.
    15. Masako Ikefuji & Roger Laeven & Jan Magnus & Chris Muris, 2014. "Expected Utility and Catastrophic Risk," Tinbergen Institute Discussion Papers 14-133/III, Tinbergen Institute.
    16. 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 Business School.
    17. Barrett, Scott, 2013. "Climate treaties and approaching catastrophes," Journal of Environmental Economics and Management, Elsevier, vol. 66(2), pages 235-250.
    18. Andreozzi, Luciano, 2021. "Ergodicity in Economics: a Decision theoretic evaluation," SocArXiv axkfg, Center for Open Science.

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    More about this item

    Keywords

    Uncertainty; Discount rate; Intertemporal optimization; Relative risk aversion; C61; D9; H43; O41;
    All these keywords.

    JEL classification:

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

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