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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. In this paper, we take this critique seriously by assuming that the random walk of economic growth is affected by some parametric uncertainty. We show that the same arguments proposed in the literature to justify a decreasing term structure for the safe discount rate also apply to justify an increasing term structure for the risk premium. It also implies that, under the assumption that the cumulants of the distribution of growth are statistically independent, the discount rate is increasing with maturity if and only 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. We apply these general results to the case of an uncertain probability of macroeconomic catastrophes à la Barro (2006), and to the case of an uncertain trend or volatility of growth à la Weitzman (2007). 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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Paper provided by LERNA, University of Toulouse in its series LERNA Working Papers with number 12.28.385.

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Date of creation: Nov 2012
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Handle: RePEc:ler:wpaper:26571

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  1. Martin L. Weitzman, 2007. "Subjective Expectations and Asset-Return Puzzles," American Economic Review, American Economic Association, vol. 97(4), pages 1102-1130, September.
  2. 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.
  3. Robert J. Barro, 2007. "Rare Disasters, Asset Prices, and Welfare Costs," NBER Working Papers 13690, National Bureau of Economic Research, Inc.
  4. David Backus & Mikhail Chernov & Ian Martin, 2011. "Disasters Implied by Equity Index Options," Journal of Finance, American Finance Association, vol. 66(6), pages 1969-2012, December.
  5. Martin L. Weitzman, 2009. "Risk-Adjusted Gamma Discounting," NBER Working Papers 15588, National Bureau of Economic Research, Inc.
  6. Barro, Robert, 2006. "Rare Disasters and Asset Markets in the Twentieth Century," Scholarly Articles 3208215, Harvard University Department of Economics.
  7. Philippe Weil, 1989. "The Equity Premium Puzzle and the Riskfree Rate Puzzle," NBER Working Papers 2829, National Bureau of Economic Research, Inc.
  8. Martin L. Weitzman, 2009. "On Modeling and Interpreting the Economics of Catastrophic Climate Change," The Review of Economics and Statistics, MIT Press, vol. 91(1), pages 1-19, February.
  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. Miles S. Kimball, 1989. "Precautionary Saving in the Small and in the Large," NBER Working Papers 2848, National Bureau of Economic Research, Inc.
  11. Christian Gollier, 2008. "Discounting with fat-tailed economic growth," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 171-186, December.
  12. Dreze, Jacques H. & Modigliani, Franco, 1972. "Consumption decisions under uncertainty," Journal of Economic Theory, Elsevier, vol. 5(3), pages 308-335, December.
  13. 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.
  14. Ian Martin, 2010. "Consumption-Based Asset Pricing with Higher Cumulants," NBER Working Papers 16153, National Bureau of Economic Research, Inc.
  15. Laibson, David I., 1997. "Golden Eggs and Hyperbolic Discounting," Scholarly Articles 4481499, Harvard University Department of Economics.
  16. 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.
  17. Martin L. Weitzman, 2012. "Rare Disasters, Tail-Hedged Investments, and Risk-Adjusted Discount Rates," NBER Working Papers 18496, National Bureau of Economic Research, Inc.
  18. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
  19. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  20. Gollier, Christian, 2002. "Time Horizon and the Discount Rate," Journal of Economic Theory, Elsevier, vol. 107(2), pages 463-473, December.
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Cited by:
  1. Christian Gollier, 2013. "Asset Pricing with Uncertain Betas: A Long-Term Perspective," CESifo Working Paper Series 4072, CESifo Group Munich.

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