IDEAS home Printed from https://ideas.repec.org/p/lec/leecon/13-27.html
   My bibliography  Save this paper

Foundations and Properties of Time Discount Functions

Author

Listed:
  • Ali al-Nowaihi
  • Sanjit Dhami

Abstract

A critical element in all discounted utility models is the specification of a discount function. We extend the standard model to allow for reference points for both out- comes and time. We consider the axiomatic foundations and properties of two main classes of discount functions. The first, the Loewenstein-Prelec discount function, accounts for declining impatience but cannot account for the evidence on subadditivity. A second class of discount functions, the Read-Scholten discount function accounts for declining impatience and subadditivity. We derive restrictions on an individual’s preferences to expedite or to delay an outcome that give rise to the discount functions under consideration. As an application of our framework we consider the explanation of the common difference effect.

Suggested Citation

  • Ali al-Nowaihi & Sanjit Dhami, 2013. "Foundations and Properties of Time Discount Functions," Discussion Papers in Economics 13/27, Division of Economics, School of Business, University of Leicester.
  • Handle: RePEc:lec:leecon:13/27
    as

    Download full text from publisher

    File URL: https://www.le.ac.uk/economics/research/RePEc/lec/leecon/dp13-27.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    2. Ali al-Nowaihi & Sanjit Dhami, 2008. "A general theory of time discounting: The reference-time theory of intertemporal choice," Discussion Papers in Economics 08/22, Division of Economics, School of Business, University of Leicester.
    3. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
    4. Read, Daniel, 2001. "Is Time-Discounting Hyperbolic or Subadditive?," Journal of Risk and Uncertainty, Springer, vol. 23(1), pages 5-32, July.
    5. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 185-199.
    6. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    7. al-Nowaihi, Ali & Dhami, Sanjit, 2009. "A value function that explains the magnitude and sign effects," Economics Letters, Elsevier, vol. 105(3), pages 224-229, December.
    8. al-Nowaihi, Ali & Dhami, Sanjit, 2006. "A note on the Loewenstein-Prelec theory of intertemporal choice," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 99-108, July.
    9. Wakker,Peter P., 2010. "Prospect Theory," Cambridge Books, Cambridge University Press, number 9780521765015, January.
    10. Adrian Bruhin & Helga Fehr-Duda & Thomas Epper, 2010. "Risk and Rationality: Uncovering Heterogeneity in Probability Distortion," Econometrica, Econometric Society, vol. 78(4), pages 1375-1412, July.
    11. George F. Loewenstein, 1988. "Frames of Mind in Intertemporal Choice," Management Science, INFORMS, vol. 34(2), pages 200-214, February.
    12. George Loewenstein & Drazen Prelec, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 573-597.
    13. Marc Scholten & Daniel Read, 2006. "Discounting by Intervals: A Generalized Model of Intertemporal Choice," Management Science, INFORMS, vol. 52(9), pages 1424-1436, September.
    14. 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.
    15. Paul A. Samuelson, 1937. "A Note on Measurement of Utility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 4(2), pages 155-161.
    16. Ok, Efe A. & Masatlioglu, Yusufcan, 2007. "A theory of (relative) discounting," Journal of Economic Theory, Elsevier, vol. 137(1), pages 214-245, November.
    17. al-Nowaihi, Ali & Bradley, Ian & Dhami, Sanjit, 2008. "A note on the utility function under prospect theory," Economics Letters, Elsevier, vol. 99(2), pages 337-339, May.
    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. Charemza, Wojciech & Díaz, Carlos & Makarova, Svetlana, 2019. "Quasi ex-ante inflation forecast uncertainty," International Journal of Forecasting, Elsevier, vol. 35(3), pages 994-1007.

    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. Ali al-Nowaihi & Sanjit Dhami, 2021. "Preferences over Time and under Uncertainty: Theoretical Foundations," CESifo Working Paper Series 9215, CESifo.
    2. Ali al-Nowaihi & Sanjit Dhami, 2013. "A Theory of Reference Time," Discussion Papers in Economics 13/26, Division of Economics, School of Business, University of Leicester.
    3. Ali al-Nowaihi & Sanjit Dhami, 2018. "Foundations for Intertemporal Choice," CESifo Working Paper Series 6913, CESifo.
    4. Scholten, Marc & Read, Daniel, 2006. "Beyond discounting: the tradeoff model of intertemporal choice," LSE Research Online Documents on Economics 22710, London School of Economics and Political Science, LSE Library.
    5. Mohammed Abdellaoui & Han Bleichrodt & Olivier l’Haridon, 2013. "Sign-dependence in intertemporal choice," Journal of Risk and Uncertainty, Springer, vol. 47(3), pages 225-253, December.
    6. al-Nowaihi, Ali & Dhami, Sanjit, 2009. "A value function that explains the magnitude and sign effects," Economics Letters, Elsevier, vol. 105(3), pages 224-229, December.
    7. Manzini, Paola & Mariotti, Marco, 2007. "Choice Over Time," IZA Discussion Papers 2993, Institute of Labor Economics (IZA).
    8. Faralla, Valeria & Novarese, Marco & Ardizzone, Antonella, 2017. "Framing Effects in Intertemporal Choice: A Nudge Experiment," MPRA Paper 82086, University Library of Munich, Germany.
    9. Fabrizio Adriani & Silvia Sonderegger, 2014. "Evolution of similarity judgements in intertemporal choice," Discussion Papers 2014-06, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    10. Alekseev, Aleksandr & Sokolov, Mikhail V., 2021. "How to measure the average rate of change?," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 43-59.
    11. repec:ubc:pmicro:halevy-04-10-29-10-08-43 is not listed on IDEAS
    12. Dorian Jullien, 2018. "Under Risk, Over Time, Regarding Other People: Language and Rationality within Three Dimensions," Research in the History of Economic Thought and Methodology, in: Including a Symposium on Latin American Monetary Thought: Two Centuries in Search of Originality, volume 36, pages 119-155, Emerald Group Publishing Limited.
    13. Stefan A Lipman & Arthur E Attema, 2020. "Good things come to those who wait—Decreasing impatience for health gains and losses," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-15, March.
    14. repec:cup:judgdm:v:16:y:2021:i:6:p:1324-1369 is not listed on IDEAS
    15. Hammond, Peter J & Zank, Horst, 2013. "Rationality and Dynamic Consistency under Risk and Uncertainty," The Warwick Economics Research Paper Series (TWERPS) 1033, University of Warwick, Department of Economics.
    16. Teck H. Ho & Noah Lim & Colin Camerer, 2005. "Modeling the Psychology of Consumer and Firm Behavior with Behavioral Economics," Levine's Bibliography 784828000000000476, UCLA Department of Economics.
    17. McDonald, R.L. & Chilton, S.M. & Jones-Lee, M.W. & Metcalf, H.R.T., 2017. "Evidence of variable discount rates and non-standard discounting in mortality risk valuation," Journal of Environmental Economics and Management, Elsevier, vol. 82(C), pages 152-167.
    18. Efe A Ok & Yusufcan Masatlioglu, 2003. "A General Theory of Time Preferences," Levine's Bibliography 234936000000000089, UCLA Department of Economics.
    19. Thomas Epper & Helga Fehr-Duda, 2012. "The missing link: unifying risk taking and time discounting," ECON - Working Papers 096, Department of Economics - University of Zurich, revised Oct 2018.
    20. Sudeep Bhatia & Graham Loomes & Daniel Read, 2021. "Establishing the laws of preferential choice behavior," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 16(6), pages 1324-1369, November.
    21. Adriani, Fabrizio & Sonderegger, Silvia, 2020. "Optimal similarity judgments in intertemporal choice (and beyond)," Journal of Economic Theory, Elsevier, vol. 190(C).
    22. Dorian Jullien, 2016. "Under Uncertainty, Over Time and Regarding Other People: Rationality in 3D," GREDEG Working Papers 2016-20, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.

    More about this item

    Keywords

    Hyperbolic discounting; Subadditive and superadditive discounting; Prospect theory;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

    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:lec:leecon:13/27. 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: Abbie Sleath (email available below). General contact details of provider: https://edirc.repec.org/data/deleiuk.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.