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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.
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Suggested Citation

  • GOLLIER Christian, 2008. "Expected net present value, expected net future value, and the Ramsey rule," LERNA Working Papers 08.29.273, LERNA, University of Toulouse.
    • Handle: RePEc:ler:wpaper:08.29.273
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    1. Christian Gollier & Phoebe Koundouri & Theologos Pantelidis, 2008. "Declining discount rates: Economic justifications and implications for long-run policy [‘Regime switches in interest rates’]," Economic Policy, CEPR, CESifo, Sciences Po;CES;MSH, vol. 23(56), pages 758-795.
    2. 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.
    3. Martin L. Weitzman, 2001. "Gamma Discounting," American Economic Review, American Economic Association, vol. 91(1), pages 260-271, March.
    4. Gollier, Christian, 2002. "Discounting an uncertain future," Journal of Public Economics, Elsevier, vol. 85(2), pages 149-166, August.
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    6. Gollier, Christian, 2004. "The Consumption-Based Determinants of the Term Structure of Discount Rates," IDEI Working Papers 296, Institut d'Économie Industrielle (IDEI), Toulouse.
    7. 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.
    8. 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.
    9. Pazner, Elisha A & Razin, Assaf, 1975. "On Expected Value vs. Expected Future Value," Journal of Finance, American Finance Association, vol. 30(3), pages 875-877, June.
    10. Gollier, Christian, 2009. "Should we Discount the Far-Distant Future at its Lowest Possible Rate?," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 3, pages 1-14.
    11. Wolfgang Buchholz & Jan Schumacher, 2008. "Discounting the Long-Distant Future: A Simple Explanation for the Weitzman-Gollier-Puzzle," CESifo Working Paper Series 2357, CESifo.
    12. 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.
    13. Martin L. Weitzman, 2007. "Subjective Expectations and Asset-Return Puzzles," American Economic Review, American Economic Association, vol. 97(4), pages 1102-1130, September.
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    JEL classification:

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

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