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

  • Christian Gollier

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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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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  1. Martin L. Weitzman, 2001. "Gamma Discounting," American Economic Review, American Economic Association, vol. 91(1), pages 260-271, March.
  2. 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.
  3. 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.
  4. 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.
  5. Martin L. Weitzman, 2007. "Subjective Expectations and Asset-Return Puzzles," American Economic Review, American Economic Association, vol. 97(4), pages 1102-1130, September.
  6. 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.
  7. 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.
  8. Christian Gollier, 2008. "Discounting with fat-tailed economic growth," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 171-186, December.
  9. 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.
  10. 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.
  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. Gollier, Christian, 2002. "Discounting an uncertain future," Journal of Public Economics, Elsevier, vol. 85(2), pages 149-166, August.
  13. Christian Gollier, 2005. "The Consumption-Based Determinants of the Term Structure of Discount Rates," CESifo Working Paper Series 1375, CESifo Group Munich.
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