IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i3p367-d329593.html
   My bibliography  Save this article

Delay Effect and Subadditivity. Proposal of a New Discount Function: The Asymmetric Exponential Discounting

Author

Listed:
  • Salvador Cruz Rambaud

    (Departamento de Economía y Empresa, Universidad de Almería, La Cañada de San Urbano, s/n, 04120 Almería, Spain)

  • Piedad Ortiz Fernández

    (Departamento de Economía y Empresa, Universidad de Almería, La Cañada de San Urbano, s/n, 04120 Almería, Spain)

Abstract

The framework of this paper is intertemporal choice and, more specifically, the so-called delay effect. Traditionally, this anomaly, also known as decreasing impatience, has been revealed when individuals reverse their preferences over monetary or non-monetary rewards. In this manuscript, we will analyze the delay effect by using preference relations and discount functions. The treatment of the delay effect with discount functions exhibits several scenarios for this paradox. Thus, the objective of this paper is to deduce the different expressions of the delay effect and their mathematical characterizations by using discount functions in stationary and dynamic settings. In this context, subadditivity will be derived as a particular case of decreasing impatience. Finally, we will introduce a new discount function, the so-called asymmetric exponential discount function, able to describe decreasing impatience.

Suggested Citation

  • Salvador Cruz Rambaud & Piedad Ortiz Fernández, 2020. "Delay Effect and Subadditivity. Proposal of a New Discount Function: The Asymmetric Exponential Discounting," Mathematics, MDPI, vol. 8(3), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:367-:d:329593
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/3/367/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/3/367/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kirby, Kris N. & Marakovic, Nino N., 1995. "Modeling Myopic Decisions: Evidence for Hyperbolic Delay-Discounting within Subjects and Amounts," Organizational Behavior and Human Decision Processes, Elsevier, vol. 64(1), pages 22-30, October.
    2. Drazen Prelec & George Loewenstein, 1991. "Decision Making Over Time and Under Uncertainty: A Common Approach," Management Science, INFORMS, vol. 37(7), pages 770-786, July.
    3. Pender, John L., 1996. "Discount rates and credit markets: Theory and evidence from rural india," Journal of Development Economics, Elsevier, vol. 50(2), pages 257-296, August.
    4. Uri Benzion & Amnon Rapoport & Joseph Yagil, 1989. "Discount Rates Inferred from Decisions: An Experimental Study," Management Science, INFORMS, vol. 35(3), pages 270-284, March.
    5. Salvador Cruz Rambaud & María José Muñoz Torrecillas, 2016. "Measuring Impatience in Intertemporal Choice," PLOS ONE, Public Library of Science, vol. 11(2), pages 1-17, February.
    6. Jonathan Baron, 2000. "Can We Use Human Judgments to Determine the Discount Rate?," Risk Analysis, John Wiley & Sons, vol. 20(6), pages 861-868, December.
    7. 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.
    8. Ikeda, Shinsuke & Kang, Myong-Il & Ohtake, Fumio, 2010. "Hyperbolic discounting, the sign effect, and the body mass index," Journal of Health Economics, Elsevier, vol. 29(2), pages 268-284, March.
    9. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
    10. Harrison, Glenn W. & Lau, Morten I. & Rutström, E. Elisabet, 2010. "Individual discount rates and smoking: Evidence from a field experiment in Denmark," Journal of Health Economics, Elsevier, vol. 29(5), pages 708-717, September.
    11. Drazen Prelec, 2004. "Decreasing Impatience: A Criterion for Non‐stationary Time Preference and “Hyperbolic” Discounting," Scandinavian Journal of Economics, Wiley Blackwell, vol. 106(3), pages 511-532, October.
    12. Takahashi, Taiki & Oono, Hidemi & Radford, Mark H.B., 2007. "Empirical estimation of consistency parameter in intertemporal choice based on Tsallis’ statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 338-342.
    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. Angelina Lazaro & Ramon Barberan & Encarnacion Rubio, 2001. "Private and social time preferences for health and money: an empirical estimation," Health Economics, John Wiley & Sons, Ltd., vol. 10(4), pages 351-356, June.
    15. Cairns, John & van der Pol, Marjon, 2000. "Valuing future private and social benefits: The discounted utility model versus hyperbolic discounting models," Journal of Economic Psychology, Elsevier, vol. 21(2), pages 191-205, April.
    16. Read, Daniel & Roelofsma, Peter H. M. P., 2003. "Subadditive versus hyperbolic discounting: A comparison of choice and matching," Organizational Behavior and Human Decision Processes, Elsevier, vol. 91(2), pages 140-153, July.
    17. Robert Scharff, 2009. "Obesity and Hyperbolic Discounting: Evidence and Implications," Journal of Consumer Policy, Springer, vol. 32(1), pages 3-21, March.
    18. Salvador Cruz Rambaud, 2014. "A New Argument In Favor Of Hyperbolic Discounting In Very Long Term Project Appraisal," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(08), pages 1-17.
    19. Read, Daniel, 2001. "Is Time-Discounting Hyperbolic or Subadditive?," Journal of Risk and Uncertainty, Springer, vol. 23(1), pages 5-32, July.
    20. 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.
    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. Cruz Rambaud, Salvador & Ortiz Fernández, Piedad & Parra Oller, Isabel María, 2023. "A systematic review of the main anomalies in intertemporal choice," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 104(C).

    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. 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.
    2. Manzini, Paola & Mariotti, Marco, 2007. "Choice Over Time," IZA Discussion Papers 2993, Institute of Labor Economics (IZA).
    3. Anke Gerbe & Kirsten I.M. Rohde, 2010. "Risk and Preference Reversals in Intertemporal Choice," Post-Print hal-00911832, HAL.
    4. Yusuke Kinari & Fumio Ohtake & Yoshiro Tsutsui, 2009. "Time discounting: Declining impatience and interval effect," Journal of Risk and Uncertainty, Springer, vol. 39(1), pages 87-112, August.
    5. Kumar, Pradeep & Kant, Shashi, 2019. "Endogenous time preferences of forest goods and community-based forest management," Ecological Economics, Elsevier, vol. 163(C), pages 205-214.
    6. Gerber, Anke & Rohde, Kirsten I.M., 2010. "Risk and preference reversals in intertemporal choice," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 654-668, December.
    7. Serdar Sayman & Ayse Öncüler, 2009. "An Investigation of Time Inconsistency," Management Science, INFORMS, vol. 55(3), pages 470-482, March.
    8. Cruz Rambaud, Salvador & Parra Oller, Isabel María & Valls Martínez, María del Carmen, 2018. "The amount-based deformation of the q-exponential discount function: A joint analysis of delay and magnitude effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 788-796.
    9. 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.
    10. László Á. Kóczy, 2010. "Strategic Aspects of the 1995 and 2004 EU Enlargements," Group Decision and Negotiation, Springer, vol. 19(3), pages 267-277, May.
    11. Takeuchi, Kan, 2011. "Non-parametric test of time consistency: Present bias and future bias," Games and Economic Behavior, Elsevier, vol. 71(2), pages 456-478, March.
    12. Jos'e Cl'audio do Nascimento, 2019. "Decision-making and Fuzzy Temporal Logic," Papers 1901.01970, arXiv.org, revised Feb 2019.
    13. McAlvanah, Patrick, 2010. "Subadditivity, patience, and utility: The effects of dividing time intervals," Journal of Economic Behavior & Organization, Elsevier, vol. 76(2), pages 325-337, November.
    14. W. David Bradford & Paul Dolan & Matteo M. Galizzi, 2019. "Looking ahead: Subjective time perception and individual discounting," Journal of Risk and Uncertainty, Springer, vol. 58(1), pages 43-69, February.
    15. Faralla, Valeria & Novarese, Marco & Ardizzone, Antonella, 2017. "Framing Effects in Intertemporal Choice: A Nudge Experiment," MPRA Paper 82086, University Library of Munich, Germany.
    16. Andrew Meyer, 2013. "Estimating discount factors for public and private goods and testing competing discounting hypotheses," Journal of Risk and Uncertainty, Springer, vol. 46(2), pages 133-173, April.
    17. Wang, Mei & Rieger, Marc Oliver & Hens, Thorsten, 2016. "How time preferences differ: Evidence from 53 countries," Journal of Economic Psychology, Elsevier, vol. 52(C), pages 115-135.
    18. Read, Daniel & Roelofsma, Peter H. M. P., 2003. "Subadditive versus hyperbolic discounting: A comparison of choice and matching," Organizational Behavior and Human Decision Processes, Elsevier, vol. 91(2), pages 140-153, July.
    19. Destefano, Natália & Martinez, Alexandre Souto, 2011. "The additive property of the inconsistency degree in intertemporal decision making through the generalization of psychophysical laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(10), pages 1763-1772.
    20. Lazaro, Angelina & Barberan, Ramon & Rubio, Encarnacion, 2002. "The discounted utility model and social preferences:: Some alternative formulations to conventional discounting," Journal of Economic Psychology, Elsevier, vol. 23(3), pages 317-337, June.

    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:gam:jmathe:v:8:y:2020:i:3:p:367-:d:329593. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.