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A comparison between Tsallis’s statistics-based and generalized quasi-hyperbolic discount models in humans

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  • Takahashi, Taiki

Abstract

Intertemporal choice has drawn attention in econophysics and neuroeconomics. Both impulsivity and inconsistency in intertemporal choice can be parametrized with a Tsallis’s statistics-based q-exponential discount model. Although a recent neuroeconomic study has proposed a dual-self discounting model (a generalized quasi-hyperbolic discounting), no study to date has examined the relationship between the q-exponential and quasi-hyperbolic models. We empirically estimated the inconsistency parameter 1−q in the q-exponential discount function and the parameter of an internal conflict between dual selves in intertemporal choice by humans. We observed that (i) the inconsistency parameter in the q-exponential model is positively related to a conflict between selves within a subject and (ii) q-exponential discounting better fits group data, while quasi-hyperbolic discounting better fits individual data. Our results indicate that (i) inconsistent intertemporal decision-makers may experience strong internal conflict during intertemporal choice behavior, and (ii) the q-exponential and the quasi-hyperbolic discount models should respectively be utilized for group and individual data. The usefulness of the q-exponential and the quasi-hyperbolic in studies of addiction and economic behavior is discussed.

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  • 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.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:2:p:551-556
    DOI: 10.1016/j.physa.2007.09.007
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    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.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. dos Santos, Lindomar Soares & Destefano, Natália & Martinez, Alexandre Souto, 2018. "Decision making generalized by a cumulative probability weighting function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 250-259.
    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. 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.
    7. 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.
    8. 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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