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Empirical estimation of consistency parameter in intertemporal choice based on Tsallis’ statistics

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  • Takahashi, Taiki
  • Oono, Hidemi
  • Radford, Mark H.B.

Abstract

Impulsivity and inconsistency in intertemporal choice have been attracting attention in econophysics and neuroeconomics. Although loss of self-control by substance abusers is strongly related to their inconsistency in intertemporal choice, researchers in neuroeconomics and psychopharmacology have usually studied impulsivity in intertemporal choice using a discount rate (e.g. hyperbolic k), with little effort being expended on parameterizing subject's inconsistency in intertemporal choice. Recent studies using Tsallis’ statistics-based econophysics have found a discount function (i.e. q-exponential discount function), which may continuously parameterize a subject's consistency in intertemporal choice. In order to examine the usefulness of the consistency parameter (0⩽q⩽1) in the q-exponential discounting function in behavioral studies, we experimentally estimated the consistency parameter q in Tsallis’ statistics-based discounting function by assessing the points of subjective equality (indifference points) at seven delays (1 week–25 years) in humans (N=24). We observed that most (N=19) subjects’ intertemporal choice was completely inconsistent (q=0, i.e. hyperbolic discounting), the mean consistency (0⩽q⩽1) was smaller than 0.5, and only one subject had a completely consistent intertemporal choice (q=1, i.e. exponential discounting). There was no significant correlation between impulsivity and inconsistency parameters. Our results indicate that individual differences in consistency in intertemporal choice can be parameterized by introducing a q-exponential discount function and most people discount delayed rewards hyperbolically, rather than exponentially (i.e. mean q is smaller than 0.5). Further, impulsivity and inconsistency in intertemporal choice can be considered as separate behavioral tendencies. The usefulness of the consistency parameter q in psychopharmacological studies of addictive behavior was demonstrated in the present study.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:381:y:2007:i:c:p:338-342
    DOI: 10.1016/j.physa.2007.03.038
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    References listed on IDEAS

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    1. Yamano, Takuya, 2002. "Some properties of q-logarithm and q-exponential functions in Tsallis statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(3), pages 486-496.
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    Cited by:

    1. Takahashi, Taiki, 2011. "Psychophysics of the probability weighting function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(5), pages 902-905.
    2. Takahashi, Taiki & Oono, Hidemi & Radford, Mark H.B., 2008. "Psychophysics of time perception and intertemporal choice models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2066-2074.
    3. Rambaud, Salvador Cruz & Pascual, Joaquín López & de los Ángeles del Pino Álvarez, María, 2019. "Preferences over sequences of payments: A new validation of the q-exponential discounting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 332-345.
    4. Takahashi, Taiki, 2007. "A probabilistic choice model based on Tsallis’ statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 335-338.
    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. do Nascimento, José Cláudio, 2021. "The personal wealth importance to the intertemporal choice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    7. Takahashi, Taiki, 2008. "A comparison between Tsallis’s statistics-based and generalized quasi-hyperbolic discount models in humans," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 551-556.
    8. Jos'e Cl'audio do Nascimento, 2019. "Rational hyperbolic discounting," Papers 1910.05209, arXiv.org, revised Feb 2020.
    9. Natalia Destefano & Alexandre Souto Martinez, 2010. "The additive property of the inconsistency degree in intertemporal decision making through the generalization of psychophysical laws," Papers 1010.5648, arXiv.org, revised May 2011.
    10. Takahashi, Taiki & Hadzibeganovic, Tarik & Cannas, Sergio & Makino, Takaki & Fukui, Hiroki & Kitayama, Shinobu, 2009. "Cultural neuroeconomics of intertemporal choice," MPRA Paper 16814, University Library of Munich, Germany.
    11. 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.
    12. Martinez, Alexandre Souto & González, Rodrigo Silva & Terçariol, César Augusto Sangaletti, 2008. "Continuous growth models in terms of generalized logarithm and exponential functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5679-5687.
    13. Han, Ruokang & Takahashi, Taiki, 2012. "Psychophysics of time perception and valuation in temporal discounting of gain and loss," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6568-6576.
    14. 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.
    15. 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.
    16. Alexandre Souto Martinez & Rodrigo Silva Gonzalez & Cesar Augusto Sangaletti Tercariol, 2008. "Continuous growth models in terms of generalized logarithm and exponential functions," Papers 0803.2635, arXiv.org, revised May 2008.
    17. Rivera-Castro, Miguel A. & Miranda, José G.V. & Borges, Ernesto P. & Cajueiro, Daniel O. & Andrade, Roberto F.S., 2012. "A top–bottom price approach to understanding financial fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1489-1496.
    18. Takahashi, Taiki, 2010. "A social discounting model based on Tsallis’ statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3600-3603.

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