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Modeling the inconsistency in intertemporal choice: the generalized Weibull discount function and its extension

Author

Listed:
  • Salvador Cruz Rambaud

    (Universidad de Almería)

  • Isabel González Fernández

    (Universidad de Almería)

  • Viviana Ventre

    (Università della Campania “Luigi Vanvitelli”)

Abstract

The aim of this paper is to obtain the family of the so-called generalized Weibull discount functions, introduced by Takeuchi (Game Econ Behav 71:456–478, 2011), by deforming the q-exponential discount function by means of the Stevens’ “power” law. The obtained discount functions exhibit different degrees of inconsistency and so they can be classified according to the value of their characteristic deforming parameters. Moreover, we extend the construction of the generalized Weibull discount function starting from any discount function instead of the q-exponential discounting. In any case, the value of the parameter $$\theta $$ θ of these new discount functions is extended from (0, 1] to the union of the intervals $$(-\,\infty ,0) \cup (0,+\,\infty )$$ ( - ∞ , 0 ) ∪ ( 0 , + ∞ ) .

Suggested Citation

  • Salvador Cruz Rambaud & Isabel González Fernández & Viviana Ventre, 2018. "Modeling the inconsistency in intertemporal choice: the generalized Weibull discount function and its extension," Annals of Finance, Springer, vol. 14(3), pages 415-426, August.
    • Handle: RePEc:kap:annfin:v:14:y:2018:i:3:d:10.1007_s10436-018-0318-3
    DOI: 10.1007/s10436-018-0318-3
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    References listed on IDEAS

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    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. Takahashi, Taiki, 2007. "A comparison of intertemporal choices for oneself versus someone else based on Tsallis’ statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 637-644.
    3. Dilip Soman & George Ainslie & Shane Frederick & Xiuping Li & John Lynch & Page Moreau & Andrew Mitchell & Daniel Read & Alan Sawyer & Yaacov Trope & Klaus Wertenbroch & Gal Zauberman, 2005. "The Psychology of Intertemporal Discounting: Why are Distant Events Valued Differently from Proximal Ones?," Marketing Letters, Springer, vol. 16(3), pages 347-360, December.
    4. Cajueiro, Daniel O., 2006. "A note on the relevance of the q-exponential function in the context of intertemporal choices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 385-388.
    5. 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.
    6. 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.
    7. Cruz Rambaud, Salvador & Muñoz Torrecillas, María José, 2013. "A generalization of the q-exponential discounting function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(14), pages 3045-3050.
    8. 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.
    9. Marc Scholten & Daniel Read, 2006. "Discounting by Intervals: A Generalized Model of Intertemporal Choice," Management Science, INFORMS, vol. 52(9), pages 1424-1436, September.
    10. 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.
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    Cited by:

    1. Viviana Ventre & Cruz Rambaud Salvador & Roberta Martino & Fabrizio Maturo, 2023. "A behavioral approach to inconsistencies in intertemporal choices with the Analytic Hierarchy Process methodology," Annals of Finance, Springer, vol. 19(2), pages 233-264, June.
    2. Viviana Ventre & Salvador Cruz Rambaud & Roberta Martino & Fabrizio Maturo, 2023. "An analysis of intertemporal inconsistency through the hyperbolic factor," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(1), pages 819-846, February.
    3. 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).
    4. Salvador Cruz Rambaud & Isabel González Fernández, 2019. "A measure of inconsistencies in intertemporal choice," PLOS ONE, Public Library of Science, vol. 14(10), pages 1-24, October.

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    More about this item

    Keywords

    Dynamic inconsistency; Exponential; Hyperbolic; q-exponential; Generalized Weibull discount function;
    All these keywords.

    JEL classification:

    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D99 - Microeconomics - - Micro-Based Behavioral Economics - - - Other

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