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Expected net present value, expected net future value, and the Ramsey rule

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  • Gollier, Christian

Abstract

Weitzman [1] showed that when future interest rates are uncertain, using the expected net present value implies a term structure of discount rates that is decreasing to the smallest possible interest rate. On the contrary, using the expected net future value criteria implies an increasing term structure of discount rates up to the largest possible interest rate. We reconcile the two approaches by introducing risk aversion and utility maximization. We show that if the aggregate consumption path is optimized and made flexible to news about future interest rates, the two criteria are equivalent. Moreover, they are also equivalent to the Ramsey rule extended to uncertainty.

Suggested Citation

  • Gollier, Christian, 2010. "Expected net present value, expected net future value, and the Ramsey rule," Journal of Environmental Economics and Management, Elsevier, vol. 59(2), pages 142-148, March.
  • Handle: RePEc:eee:jeeman:v:59:y:2010:i:2:p:142-148
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    1. Wolfgang Buchholz & Jan Schumacher, 2008. "Discounting the Long-Distant Future: A Simple Explanation for the Weitzman-Gollier-Puzzle," CESifo Working Paper Series 2357, CESifo Group Munich.
    2. Gollier, Christian, 2009. "Should we Discount the Far-Distant Future at its Lowest Possible Rate?," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 3, pages 1-14.
    3. Elisha A. Pazner & Assaf Razin, 1976. "On Expected Present Value Vs. Expected Future Value: Further Remarks," Discussion Papers 196, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Christian Gollier & Phoebe Koundouri & Theologos Pantelidis, 2008. "Declining discount rates: Economic justifications and implications for long-run policy," Economic Policy, CEPR;CES;MSH, vol. 23, pages 757-795, October.
    5. Christian Gollier, 2008. "Discounting with fat-tailed economic growth," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 171-186, December.
    6. Hepburn, Cameron & Groom, Ben, 2007. "Gamma discounting and expected net future value," Journal of Environmental Economics and Management, Elsevier, vol. 53(1), pages 99-109, January.
    7. Gollier, Christian, 2004. "The Consumption-Based Determinants of the Term Structure of Discount Rates," IDEI Working Papers 296, Institut d'Économie Industrielle (IDEI), Toulouse.
    8. Martin L. Weitzman, 2001. "Gamma Discounting," American Economic Review, American Economic Association, vol. 91(1), pages 260-271, March.
    9. Gollier, Christian, 2002. "Discounting an uncertain future," Journal of Public Economics, Elsevier, vol. 85(2), pages 149-166, August.
    10. Martin L. Weitzman, 2007. "Subjective Expectations and Asset-Return Puzzles," American Economic Review, American Economic Association, vol. 97(4), pages 1102-1130, September.
    11. Weitzman, Martin L., 1998. "Why the Far-Distant Future Should Be Discounted at Its Lowest Possible Rate," Journal of Environmental Economics and Management, Elsevier, vol. 36(3), pages 201-208, November.
    12. Ekaterini Panopoulou & Ben Groom & Phoebe Koundouri & Theologos Pantelidis, 2004. "An Econometric Approach To Estimating Long-Run Discount Rates," Royal Economic Society Annual Conference 2004 70, Royal Economic Society.
    13. Gollier, Christian, 2004. "Maximizing the expected net future value as an alternative strategy to gamma discounting," Finance Research Letters, Elsevier, vol. 1(2), pages 85-89, June.
    14. Newell, Richard G. & Pizer, William A., 2003. "Discounting the distant future: how much do uncertain rates increase valuations?," Journal of Environmental Economics and Management, Elsevier, vol. 46(1), pages 52-71, July.
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    Cited by:

    1. Wei, Yi-Ming & Mi, Zhi-Fu & Huang, Zhimin, 2015. "Climate policy modeling: An online SCI-E and SSCI based literature review," Omega, Elsevier, vol. 57(PA), pages 70-84.
    2. Freeman, Mark C., 2009. "Yes, we should discount the far-distant future at its lowest possible rate: a resolution of the Weitzman-Gollier puzzle," Economics Discussion Papers 2009-42, Kiel Institute for the World Economy (IfW).
    3. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2014. "Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling," Papers 1404.1895, arXiv.org.
    4. Gollier, Christian & Weitzman, Martin L., 2010. "How should the distant future be discounted when discount rates are uncertain?," Economics Letters, Elsevier, vol. 107(3), pages 350-353, June.
    5. Christophe Gouel & Sébastien Jean, 2015. "Optimal Food Price Stabilization in a Small Open Developing Country," World Bank Economic Review, World Bank Group, vol. 29(1), pages 72-101.
    6. Traeger, Christian P., 2013. "Discounting under uncertainty: Disentangling the Weitzman and the Gollier effect," Journal of Environmental Economics and Management, Elsevier, vol. 66(3), pages 573-582.
    7. Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Papers 1404.1913, arXiv.org.
    8. Michael Funke & Marc Gronwald, 2009. "A Convex Hull Approach to Counterfactual Analysis of Trade Openness and Growth," Quantitative Macroeconomics Working Papers 20906, Hamburg University, Department of Economics.
    9. Wolfgang Buchholz, 2014. "Discounting in an Uncertain World - Disentangling the Debate on the Weitzman-Gollier Puzzle," CESifo Working Paper Series 4967, CESifo Group Munich.
    10. repec:eee:forpol:v:83:y:2017:i:c:p:58-69 is not listed on IDEAS
    11. Gollier, Christian, 2009. "Should we Discount the Far-Distant Future at its Lowest Possible Rate?," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 3, pages 1-14.
    12. Orlando Gomes & Alexandra Ferreira-Lopes & Tiago Sequeira, 2014. "Exponential discounting bias," Journal of Economics, Springer, vol. 113(1), pages 31-57, September.
    13. Cucchiella, Federica & D’Adamo, Idiano, 2012. "Feasibility study of developing photovoltaic power projects in Italy: An integrated approach," Renewable and Sustainable Energy Reviews, Elsevier, vol. 16(3), pages 1562-1576.
    14. Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Working Papers hal-00974831, HAL.
    15. Petković, Dalibor & Shamshirband, Shahaboddin & Kamsin, Amirrudin & Lee, Malrey & Anicic, Obrad & Nikolić, Vlastimir, 2016. "Survey of the most influential parameters on the wind farm net present value (NPV) by adaptive neuro-fuzzy approach," Renewable and Sustainable Energy Reviews, Elsevier, vol. 57(C), pages 1270-1278.
    16. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2014. "Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling," Working Papers hal-00974815, HAL.
    17. Freeman, Mark C., 2010. "Yes, we should discount the far-distant future at its lowest possible rate: A resolution of the Weitzman-Gollier puzzle," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 4, pages 1-21.
    18. Traeger, Christian P., 2012. "What's the rate? Disentangling the Weitzman and the Gollier effect," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt88x3d1vw, Department of Agricultural & Resource Economics, UC Berkeley.
    19. Szekeres, Szabolcs, 2015. "Governments Should Not Use Declining Discount Rates in Project Analysis," MPRA Paper 63438, University Library of Munich, Germany.

    More about this item

    Keywords

    Discount rate Ramsey rule Climate change Cost-benefit analysis;

    JEL classification:

    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

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