IDEAS home Printed from https://ideas.repec.org/p/ces/ceswps/_168.html
   My bibliography  Save this paper

Discounting an Uncertain Future

Author

Listed:
  • Christian Gollier
  • Jean-Charles Rochet

Abstract

We discuss the selection of the socially optimal discount rate for public investment projects that entail costs and benefits in the very long run. More specifically, we examine in an expected utility framework how the uncertainty on the growth rate of the GNP per head affects this rate. Under various conditions on preferences, as positive prudence, decreasing relative risk aversion or decreasing absolute risk aversion, we prove that (1) the fact that growth is uncertain reduces the optimal discount rate, and that (2) this discount rate should be smaller the longer the time horizon is. We characterize the asymptotic value of the discount rate. We also examine the case of Kreps-Porteus social welfare functions.

Suggested Citation

  • Christian Gollier & Jean-Charles Rochet, 1998. "Discounting an Uncertain Future," CESifo Working Paper Series 168, CESifo.
    • Handle: RePEc:ces:ceswps:_168
    as

    Download full text from publisher

    File URL: https://www.cesifo.org/DocDL/ces_wp168.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Guiso, Luigi & Jappelli, Tullio & Terlizzese, Daniele, 1996. "Income Risk, Borrowing Constraints, and Portfolio Choice," American Economic Review, American Economic Association, vol. 86(1), pages 158-172, March.
    2. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    3. George Loewenstein & Richard H Thaler, 2003. "Anomalies: Intertemporal Choice," Levine's Working Paper Archive 618897000000000784, David K. Levine.
    4. Miles Kimball & Philippe Weil, 2009. "Precautionary Saving and Consumption Smoothing across Time and Possibilities," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(2-3), pages 245-284, March.
    5. repec:bla:revinw:v:37:y:1991:i:3:p:249-66 is not listed on IDEAS
    6. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    7. David E. Bell, 1988. "One-Switch Utility Functions and a Measure of Risk," Management Science, INFORMS, vol. 34(12), pages 1416-1424, December.
    8. repec:hal:wpspec:info:hdl:2441/8703 is not listed on IDEAS
    9. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-286, April.
    10. repec:hal:spmain:info:hdl:2441/8703 is not listed on IDEAS
    11. Denis Kessler & Edward N. Wolff, 1991. "A Comparative Analysis Of Household Wealth Patterns In France And The United States," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 37(3), pages 249-266, September.
    12. Harvey, Charles M., 1994. "The reasonableness of non-constant discounting," Journal of Public Economics, Elsevier, vol. 53(1), pages 31-51, January.
    13. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 443-478.
    14. Hansen, Lars Peter & Singleton, Kenneth J, 1983. "Stochastic Consumption, Risk Aversion, and the Temporal Behavior of Asset Returns," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 249-265, April.
    15. Loewenstein, George & Thaler, Richard H, 1989. "Intertemporal Choice," Journal of Economic Perspectives, American Economic Association, vol. 3(4), pages 181-193, Fall.
    16. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
    17. Hayne E. Leland, 1968. "Saving and Uncertainty: The Precautionary Demand for Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 82(3), pages 465-473.
    18. Dreze, Jacques H. & Modigliani, Franco, 1972. "Consumption decisions under uncertainty," Journal of Economic Theory, Elsevier, vol. 5(3), pages 308-335, December.
    19. Robert B. Barsky & F. Thomas Juster & Miles S. Kimball & Matthew D. Shapiro, 1997. "Preference Parameters and Behavioral Heterogeneity: An Experimental Approach in the Health and Retirement Study," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 537-579.
    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.
    21. Larry Selden, 1979. "An OCE Analysis of the Effect of Uncertainty on Saving under Risk Preference Independence," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(1), pages 73-82.
    22. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-1123, September.
    23. Dybvig, Philip H & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1996. "Long Forward and Zero-Coupon Rates Can Never Fall," The Journal of Business, University of Chicago Press, vol. 69(1), pages 1-25, January.
    24. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gollier, Christian, 2002. "Time Horizon and the Discount Rate," Journal of Economic Theory, Elsevier, vol. 107(2), pages 463-473, December.
    2. Nocetti, Diego & Smith, William T., 2011. "Price uncertainty, saving, and welfare," Journal of Economic Dynamics and Control, Elsevier, vol. 35(7), pages 1139-1149, July.
    3. Diego Nocetti & William T. Smith, 2011. "Precautionary Saving and Endogenous Labor Supply with and without Intertemporal Expected Utility," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43(7), pages 1475-1504, October.
    4. AJ A. Bostian & Christoph Heinzel, 2016. "Consumption Smoothing and Precautionary Saving under Recursive Preferences," FOODSECURE Working papers 44, LEI Wageningen UR.
    5. Aj A Bostian & Christoph Heinzel, 2020. "Robustness of Inferences in Risk and Time Experiments to Lifecycle Asset Integration," Post-Print hal-03358620, HAL.
    6. Donatella Baiardi & Marco Magnani & Mario Menegatti, 2020. "The theory of precautionary saving: an overview of recent developments," Review of Economics of the Household, Springer, vol. 18(2), pages 513-542, June.
    7. Echazu Luciana & Nocetti Diego & Smith William T., 2012. "A New Look into the Determinants of the Ecological Discount Rate: Disentangling Social Preferences," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 12(1), pages 1-44, April.
    8. Christian Gollier, 2010. "Debating about the Discount Rate:The Basic Economic Ingredients," Perspektiven der Wirtschaftspolitik, Verein für Socialpolitik, vol. 11(s1), pages 38-55, May.
    9. Miles Kimball & Philippe Weil, 2009. "Precautionary Saving and Consumption Smoothing across Time and Possibilities," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(2-3), pages 245-284, March.
    10. White, Lucy, 2008. "Prudence in bargaining: The effect of uncertainty on bargaining outcomes," Games and Economic Behavior, Elsevier, vol. 62(1), pages 211-231, January.
    11. Jouini, Elyès & Napp, Clotilde & Nocetti, Diego, 2013. "On multivariate prudence," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1255-1267.
    12. Gollier, Christian, 2004. "The Consumption-Based Determinants of the Term Structure of Discount Rates," IDEI Working Papers 296, Institut d'Économie Industrielle (IDEI), Toulouse.
    13. Chaigneau, Pierre, 2013. "Explaining the structure of CEO incentive pay with decreasing relative risk aversion," Journal of Economics and Business, Elsevier, vol. 67(C), pages 4-23.
    14. Heinzel Christoph & Richard Peter, 2021. "Precautionary motives with multiple instruments," Working Papers SMART 21-09, INRAE UMR SMART.
    15. Christoph Basten & Andreas Fagereng & Kjetil Telle, 2016. "Saving and Portfolio Allocation Before and After Job Loss," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 48(2-3), pages 293-324, March.
    16. AJ A. Bostian & Christoph Heinzel, 2018. "Comparative precautionary saving under higher-order risk and recursive utility," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(1), pages 95-114, May.
    17. He, Rong & Li, Heqing & Lian, Zeng & Zheng, Jie, 2020. "The effect of culture on consumption: A behavioral approach," Journal of Asian Economics, Elsevier, vol. 67(C).
    18. repec:cup:judgdm:v:8:y:2013:i:3:p:268-277 is not listed on IDEAS
    19. Carroll, Christopher D. & Kimball, Miles S., 2006. "Precautionary Saving and Precautionary Wealth," CFS Working Paper Series 2006/02, Center for Financial Studies (CFS).
    20. Jouini, Elyès & Marin, Jean-Michel & Napp, Clotilde, 2010. "Discounting and divergence of opinion," Journal of Economic Theory, Elsevier, vol. 145(2), pages 830-859, March.
    21. Adam Eric Greenberg, 2013. "When imagining future wealth influences risky decision making," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 8(3), pages 268-277, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ces:ceswps:_168. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Klaus Wohlrabe (email available below). General contact details of provider: https://edirc.repec.org/data/cesifde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.