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13.02.2018 | Research Article

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

verfasst von: Salvador Cruz Rambaud, Isabel González Fernández, Viviana Ventre

Erschienen in: Annals of Finance | Ausgabe 3/2018

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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 \(\theta \) of these new discount functions is extended from (0, 1] to the union of the intervals \((-\,\infty ,0) \cup (0,+\,\infty )\).

Vorheriger Artikel What determines the share of non-resident public debt ownership? Evidence from Euro Area countries

Nächster Artikel Correction to: Modeling the inconsistency in intertemporal choice: the generalized Weibull discount function and its extension

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Here, the discount fraction is denoted by \(F_{t_1 \rightarrow t_2}\).

It is possible to find a discount function in which \(\displaystyle \lim _{t \rightarrow t_0} F(t) >0\) but, taking into account that F(t) is continuous, there will exist a \(t_1 > t_0\) (possibly \(t_1 = +\,\infty \)) such that \(\displaystyle \lim _{t \rightarrow t_1} F(t) \ge 0\), which describes the three considered cases.

There is another noteworthy deformation of time given by \(D(t) = \alpha \ln (1+\beta t)\), where \(\alpha > 0\) and \(\beta > 0\) (Takahashi 2005). Nevertheless, this deformation will not be considered in this paper.

The original name of this function is q-exponential, where \(q = 1 - \theta \). However, in order to avoid some confusion, we will adapt the notation to the parameter \(\theta \) introduced by Takeuchi (2011) and hereinafter it will be named the \(\theta \)-exponential discount function.

In Cruz Rambaud and Ventre (2015), this condition is equivalent to satisfy the so-defined Q-property.

Cajueiro, D.O.: A note on the relevance of the \(q\)-exponential function in the context of intertemporal choices. Phys A 364, 385–388 (2006)CrossRef

Cruz Rambaud, S., Muñoz Torrecillas, M.J.: Some considerations on the social discount rate. Environ Sci Policy 8, 343–355 (2005)CrossRef

Cruz Rambaud, S., Muñoz Torrecillas, M.J.: A generalization of the \(q\)-exponential discounting function. Phys A 392(14), 3045–3050 (2013)CrossRef

Cruz Rambaud, S., Muñoz Torrecillas, M.J.: Some characterizations of (strongly) subadditive discounting functions. Appl Math Comput 243, 368–378 (2014)

Cruz Rambaud, S., Muñoz Torrecillas, M.J.: Measuring impatience in intertemporal choice. PLoS ONE 11(2), e0149256 (2016)CrossRef

Cruz Rambaud, S., Muñoz Torrecillas, M.J., Takahashi, T.: Observed and normative discount functions in addiction and other diseases. Front Pharmacol 8, article 416 (2017)

Cruz Rambaud, S., Ventre, A.G.S.: Subadditive discount functions with a transition period. Int J Intell Syst 30(7), 837–849 (2015)CrossRef

Cruz Rambaud, S., Ventre, V.: Deforming time in a non-additive discount function. Int J Intell Syst 32(5), 467–480 (2017)CrossRef

Frederick, S., Loewenstein, G., O’Donoghue, T.: Time discounting and time preference: a critical review. J Econ Lit 40(2), 351–401 (2002)CrossRef

Lidl, R., Pilz, G.: Applied Abstract Algebra, 2nd edn. Springer, New York (1998)CrossRef

Mazur, J.E.: An adjusting procedure for studying delayed reinforcement. In: Commons, M.L., Mazur, J.E., Nevins, J.A., Rachlin, H. (eds.) The Effect of Delay and of Intervening Events on Reinforcement Value, Quantitative Analyses of Behavior, vol. 5, pp. 55–73. Erlbaum, Hillsdale (1987)

Samuelson, P.: A note on the measurement of utility. Rev Econ Stud 4, 155–161 (1937)CrossRef

Scholten, M., Read, D.: Beyond discounting: the tradeoff model of intertemporal choice. In: Working paper of the London School of Economics and Political Science (2006)

Scholten, M., Read, D.: Discounting by intervals: a generalized model of intertemporal choice. Manage Sci 52(9), 1424–1436 (2006)CrossRef

Soman, D., Ainslie, G., Frederick, S., Li, X., Lynch, J., Moreau, P., Mitchell, A., Read, D., Sawyer, A., Trope, Y., Wertenbroch, K., Zauberman, G.: The psychology of intertemporal discounting: Why are distant events valued differently from proximal ones? Market Lett 16(3/4), 347–360 (2005)CrossRef

Sozou, P.D.: On hyperbolic discounting and uncertain hazard rates. Proc R Soc B Biol Sci 265(1409), 2015–2020 (1998)CrossRef

Stevens, S.S.: On the psychophysical law. Psychophys Rev 64(3), 153–181 (1957)CrossRef

Takahashi, T.: Loss of self-control in intertemporal choice may be attributable to logarithmic time-perception. Med Hypotheses 65(4), 691–693 (2005)CrossRef

Takahashi, T.: A comparison of intertemporal choices for oneself versus someone else based on Tsallis’ statistics. Phys A 385, 637–644 (2007)CrossRef

Takahashi, T., Han, R., Nakamura, F.: Time discounting: psychophysics of intertemporal and probabilistic choices. J Behav Econ Finance 5, 10–14 (2012)

Takeuchi, K.: Non-parametric test of time consistency: present bias and future bias. Game Econ Behav 71, 456–478 (2011)CrossRef

Tsallis, C.: What are the numbers that experiments provide? Quim Nova 17(6), 468–471 (1994)

Titel: Modeling the inconsistency in intertemporal choice: the generalized Weibull discount function and its extension
verfasst von: Salvador Cruz Rambaud
Isabel González Fernández
Viviana Ventre
Publikationsdatum: 13.02.2018
Verlag: Springer Berlin Heidelberg
Erschienen in: Annals of Finance / Ausgabe 3/2018
Print ISSN: 1614-2446
Elektronische ISSN: 1614-2454
DOI: https://doi.org/10.1007/s10436-018-0318-3

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