IDEAS home Printed from https://ideas.repec.org/p/lsg/lsgwps/wp112.html
   My bibliography  Save this paper

Discounting under disagreement

Author

Listed:
  • Geoffrey Heal
  • Antony Millner

Abstract

A group of time consistent agents has access to a common productive resource stock whose output provides their consumption needs. The agents disagree about the appropriate pure rate of time preference to use when choosing a consumption policy, and thus delegate the management of the resource to a social planner who allocates consumption efficiently across individuals and over time. We show that the planner's optimal policy is equivalent to that of a representative agent with a time varying rate of impatience. The representative agent's time preferences depend on the distribution of time preferences in the group, on the agents' tolerance for consumption uctuations, and on the productivity of the resource. The representative agent's rate of impatience coincides with that of the individual with the lowest rate of impatience in the long run, and under plausible conditions, is monotonically declining. In the work-horse case of iso-elastic felicity functions, and Gamma distributed rates of impatience, analytic solutions are possible, and the representative agent has hyperbolic time preferences. We thus provide a normative justification for the use of declining rates of time preference in dynamic welfare analysis.

Suggested Citation

  • Geoffrey Heal & Antony Millner, 2013. "Discounting under disagreement," GRI Working Papers 112, Grantham Research Institute on Climate Change and the Environment.
  • Handle: RePEc:lsg:lsgwps:wp112
    as

    Download full text from publisher

    File URL: http://www.lse.ac.uk/GranthamInstitute/wp-content/uploads/2013/04/w18999.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Diego Nocetti & Elyès Jouini & Clotilde Napp, 2008. "Properties of the Social Discount Rate in a Benthamite Framework with Heterogeneous Degrees of Impatience," Management Science, INFORMS, vol. 54(10), pages 1822-1826, October.
    2. Martin L. Weitzman, 2001. "Gamma Discounting," American Economic Review, American Economic Association, vol. 91(1), pages 260-271, March.
    3. Weitzman, Martin L., 2010. "Risk-adjusted gamma discounting," Journal of Environmental Economics and Management, Elsevier, vol. 60(1), pages 1-13, July.
    4. Farrell, Joseph & Maskin, Eric, 1989. "Renegotiation in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 327-360, December.
    5. repec:dau:papers:123456789/2326 is not listed on IDEAS
    6. Yvan Lengwiler, 2005. "Heterogeneous Patience and the Term Structure of Real Interest Rates," American Economic Review, American Economic Association, vol. 95(3), pages 890-896, June.
    7. Li, Chuan-Zhong & Lofgren, Karl-Gustaf, 2000. "Renewable Resources and Economic Sustainability: A Dynamic Analysis with Heterogeneous Time Preferences," Journal of Environmental Economics and Management, Elsevier, vol. 40(3), pages 236-250, November.
    8. Ben Groom & Cameron Hepburn & Phoebe Koundouri & David Pearce, 2005. "Declining Discount Rates: The Long and the Short of it," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 32(4), pages 445-493, December.
    9. Heal, Geoffrey, 2005. "Intertemporal Welfare Economics and the Environment," Handbook of Environmental Economics,in: K. G. Mäler & J. R. Vincent (ed.), Handbook of Environmental Economics, edition 1, volume 3, chapter 21, pages 1105-1145 Elsevier.
    10. Partha Dasgupta, 2008. "Discounting climate change," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 141-169, December.
    11. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," Review of Economic Studies, Oxford University Press, vol. 35(2), pages 185-199.
    12. Hara, Chiaki, 2008. "Heterogeneous Impatience in a Continuous-Time Model," PIE/CIS Discussion Paper 396, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
    13. Kocherlakota, Narayana R., 1996. "Reconsideration-Proofness: A Refinement for Infinite Horizon Time Inconsistency," Games and Economic Behavior, Elsevier, vol. 15(1), pages 33-54, July.
    14. Karp, Larry, 2005. "Global warming and hyperbolic discounting," Journal of Public Economics, Elsevier, vol. 89(2-3), pages 261-282, February.
    15. Evans, Robert & Maskin, Eric, 1989. "Efficient renegotiation--proof equilibria in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 361-369, December.
    16. Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
    17. 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.
    18. George Loewenstein & Drazen Prelec, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 573-597.
    19. 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.
    20. repec:hrv:faseco:33373344 is not listed on IDEAS
    21. William D. Nordhaus, 2007. "A Review of the Stern Review on the Economics of Climate Change," Journal of Economic Literature, American Economic Association, vol. 45(3), pages 686-702, September.
    22. Robert J. Barro, 1999. "Ramsey Meets Laibson in the Neoclassical Growth Model," The Quarterly Journal of Economics, Oxford University Press, vol. 114(4), pages 1125-1152.
    23. Dumas, Bernard, 1989. "Two-Person Dynamic Equilibrium in the Capital Market," Review of Financial Studies, Society for Financial Studies, vol. 2(2), pages 157-188.
    24. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, Oxford University Press, vol. 112(2), pages 443-478.
    25. Martin L. Weitzman, 2007. "A Review of the Stern Review on the Economics of Climate Change," Journal of Economic Literature, American Economic Association, vol. 45(3), pages 703-724, September.
    26. Christian Gollier & Richard Zeckhauser, 2005. "Aggregation of Heterogeneous Time Preferences," Journal of Political Economy, University of Chicago Press, vol. 113(4), pages 878-896, August.
    27. Robert A. Becker, 1980. "On the Long-Run Steady State in a Simple Dynamic Model of Equilibrium with Heterogeneous Households," The Quarterly Journal of Economics, Oxford University Press, vol. 95(2), pages 375-382.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. repec:eee:jeeman:v:84:y:2017:i:c:p:1-17 is not listed on IDEAS
    2. Maureen L. Cropper & Mark C. Freeman & Ben Groom & William A. Pizer, 2014. "Declining Discount Rates," American Economic Review, American Economic Association, vol. 104(5), pages 538-543, May.
    3. Eveson, Simon P. & Thijssen, Jacco J.J., 2016. "Pareto optimality and existence of quasi-equilibrium in exchange economies with an indefinite future," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 138-152.

    More about this item

    JEL classification:

    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D99 - Microeconomics - - Micro-Based Behavioral Economics - - - Other

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:lsg:lsgwps:wp112. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (The GRI Administration). General contact details of provider: http://edirc.repec.org/data/grlseuk.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.