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Expected Net Present Value, Expected Net Future Value, and the Ramsey Rule

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  • Christian Gollier

Abstract

Weitzman (1998) 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 criterion 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 risk-neutral probabilities. We show that if the aggregate consumption path is optimized, the two criteria are equivalent. Moreover, they are also equivalent to the Ramsey rule extended to uncertainty.

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File URL: http://www.cesifo-group.de/portal/page/portal/DocBase_Content/WP/WP-CESifo_Working_Papers/wp-cesifo-2009/wp-cesifo-2009-05/cesifo1_wp2643.pdf
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Bibliographic Info

Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 2643.

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Date of creation: 2009
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Handle: RePEc:ces:ceswps:_2643

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Keywords: discount rate; asset price; Ramsey rule; cost-benefit analysis;

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References

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  1. GOLLIER Christian, 2008. "Should we discount the far-distant future at its lowest possible rate?," LERNA Working Papers 08.30.274, LERNA, University of Toulouse.
  2. Christian Gollier, 2008. "Discounting with fat-tailed economic growth," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 171-186, December.
  3. Pizer, William & Newell, Richard, 2000. "Discounting the Distant Future: How Much Do Uncertain Rates Increase Valuations?," Discussion Papers dp-00-45, Resources For the Future.
  4. GOLLIER Christian & KOUNDOURI Phoebe & PANTELIDIS Theologos, 2008. "Declining Discount Rates : Economic Justifications and Implications for Long-Run Policy," LERNA Working Papers 08.17.261, LERNA, University of Toulouse.
  5. Martin L. Weitzman, 2001. "Gamma Discounting," American Economic Review, American Economic Association, vol. 91(1), pages 260-271, March.
  6. Martin L. Weitzman, 2007. "Subjective Expectations and Asset-Return Puzzles," American Economic Review, American Economic Association, vol. 97(4), pages 1102-1130, September.
  7. 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.
  8. Christian Gollier, 2005. "The Consumption-Based Determinants of the Term Structure of Discount Rates," CESifo Working Paper Series 1375, CESifo Group Munich.
  9. 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.
  10. 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.
  11. Gollier, Christian, 2002. "Discounting an uncertain future," Journal of Public Economics, Elsevier, vol. 85(2), pages 149-166, August.
  12. Gollier, Christian, 2003. "Maximizing the Expected Net Future Value as an Alternative Strategy to Gamma Discounting," IDEI Working Papers 213, Institut d'Économie Industrielle (IDEI), Toulouse.
  13. 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.
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Citations

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Cited by:
  1. 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.
  2. 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.
  3. 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.
  4. 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, vol. 4(13), pages 1-21.
  5. Gollier, Christian & Weitzman, Martin, 2009. "How Should the Distant Future be Discounted When Discount Rates are Uncertain?," IDEI Working Papers 588, Institut d'Économie Industrielle (IDEI), Toulouse.
  6. Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Working Papers hal-00974831, HAL.
  7. Michael Funke & Marc Gronwald, 2009. "A Convex Hull Approach to Counterfactual Analysis of Trade Openness and Growth," CESifo Working Paper Series 2692, CESifo Group Munich.
  8. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2014. "Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling," Papers 1404.1895, arXiv.org.
  9. Christophe Gouel & Sébastien Jean, 2012. "Optimal Food Price Stabilization in a Small Open Developing Country," Working Papers 2012-01, CEPII research center.
  10. 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, vol. 3(25), pages 1-14.
  11. Traeger, Christian P., 2012. "What’s the Rate? Disentangling the Weitzman and the Gollier Effect," CUDARE Working Paper Series 1121, University of California at Berkeley, Department of Agricultural and Resource Economics and Policy.
  12. Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Papers 1404.1913, arXiv.org.
  13. Orlando Gomes & Alexandra Ferreira-Lopes & Tiago Neves Sequeira, 2012. "Exponential Discounting Bias," Working Papers Series 2 12-05, ISCTE-IUL, Business Research Unit (BRU-IUL).
  14. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2014. "Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling," Working Papers hal-00974815, HAL.

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