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Evaluation of long-dated investments under uncertain growth trend, volatility and catastrophes

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  • Gollier, Christian

Abstract

Because of the uncertainty about how to model the growth process of our economy, there is still much confusion about which discount rates should be used to evaluate actions having long-lasting impacts, as in the contexts of climate change, social security reforms or large public infrastructures for example. We characterize efficient discount rates when the growth of log consumption follows a random walk with uncertain parameters. We examine different models in which the parametric uncertainty affects the trend and the volatility of growth, or the frequency of catastrophes. This uncertainty implies that the term structures of the risk free discount rate and of the aggregate risk premium are respectively decreasing and increasing. It also implies that the discount rate is increasing with maturity if the beta of the investment is larger than half of relative risk aversion. Another important consequence of parametric uncertainty is that the risk premium is not proportional to the beta of the investment. Finally, we apply our findings to the evaluation of climate change policy. We argue in particular that the beta of actions to mitigate climate change is relatively large, so that the term structure of the associated discount rates should be increasing.

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Bibliographic Info

Paper provided by Toulouse School of Economics (TSE) in its series TSE Working Papers with number 12-361.

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Date of creation: Nov 2012
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Handle: RePEc:tse:wpaper:26574

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Keywords: asset prices; term structure; risk premium; decreasing discount rates; parametric uncertainty; CO2 beta; rare events; macroeconomic catastrophes.;

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References

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  1. Christian Gollier, 2012. "Pricing the Planet's Future: The Economics of Discounting in an Uncertain World," Economics Books, Princeton University Press, edition 1, volume 1, number 9894.
  2. Weitzman, Martin L., 2009. "On Modeling and Interpreting the Economics of Catastrophic Climate Change," Scholarly Articles 3693423, Harvard University Department of Economics.
  3. Martin L. Weitzman, 2012. "Rare Disasters, Tail-Hedged Investments, and Risk-Adjusted Discount Rates," NBER Working Papers 18496, National Bureau of Economic Research, Inc.
  4. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
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  7. Martin L. Weitzman, 2009. "Risk-Adjusted Gamma Discounting," NBER Working Papers 15588, National Bureau of Economic Research, Inc.
  8. David Backus & Mikhail Chernov & Ian Martin, 2009. "Disasters implied by equity index options," NBER Working Papers 15240, National Bureau of Economic Research, Inc.
  9. Philippe Weil, 1989. "The Equity Premium Puzzle and the Riskfree Rate Puzzle," NBER Working Papers 2829, National Bureau of Economic Research, Inc.
  10. Dreze, Jacques H. & Modigliani, Franco, 1972. "Consumption decisions under uncertainty," Journal of Economic Theory, Elsevier, vol. 5(3), pages 308-335, December.
  11. GOLLIER Christian, 2008. "Discounting with fat-tailed economic growth," LERNA Working Papers 08.19.263, LERNA, University of Toulouse.
  12. Martin L. Weitzman, 2007. "Subjective Expectations and Asset-Return Puzzles," American Economic Review, American Economic Association, vol. 97(4), pages 1102-1130, September.
  13. Robert J. Barro, 2009. "Rare Disasters, Asset Prices, and Welfare Costs," American Economic Review, American Economic Association, vol. 99(1), pages 243-64, March.
  14. Laibson, David, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, MIT Press, vol. 112(2), pages 443-77, May.
  15. Ravi Bansal & Amir Yaron, 2000. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," NBER Working Papers 8059, National Bureau of Economic Research, Inc.
  16. Barro, Robert, 2006. "Rare Disasters and Asset Markets in the Twentieth Century," Scholarly Articles 3208215, Harvard University Department of Economics.
  17. Gollier, Christian, 2002. "Time Horizon and the Discount Rate," Journal of Economic Theory, Elsevier, vol. 107(2), pages 463-473, December.
  18. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  19. Arrow, Kenneth J & Lind, Robert C, 1970. "Uncertainty and the Evaluation of Public Investment Decisions," American Economic Review, American Economic Association, vol. 60(3), pages 364-78, June.
  20. 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.
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Cited by:
  1. Gollier, Christian, 2012. "Asset pricing with uncertain betas: A long-term perspective," IDEI Working Papers 752, Institut d'Économie Industrielle (IDEI), Toulouse.

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