An analysis of intertemporal inconsistency through the hyperbolic factor

Abstract

Intertemporal choices play a fundamental role in the lives of individuals, and the Discounted Utility model is the essential framework for describing decision makers’ attitudes in front of alternatives structured over multiple periods. The classical formulation of the model assumes constant preferences over time, i.e., it assumes that individuals’ choices are consistent. Empirical evidence, however, shows that individuals’ preferences do not respond to this assumption, generating temporally inconsistent decisions. This paper addresses the problem of temporal inconsistency in order to interpret and describe anomalous choices, i.e., not rationalizable from a theoretical point of view, through the cognitive distortions of the decision-maker. Indeed, even if we assume that the investor is a rational subject, behavioral finance suggests that an anomaly is part of the human being and must be recognized as a systematic condition of the decision-making process. Exploiting the relationship between the rate of impatience and temporal preference, this work aims to demonstrate that the degree of decrease in impatience quantifies the weight of emotional drives in the anomalies of intertemporal choices. An experimental approach based on constructing the hyperbolic factor for each individual in different contexts is presented to test our results. The variability in the collected data highlights that individuals’ behavior is very different, suggesting the need to project strategies in personalized finance.

Subjective perception of time and decision inconsistency in interval effect

“…The interval effect is an anomaly of the Discounted Utility Model, i.e., an attitude that is difficult to rationalise by the classical model (Thaler 1993;Kahneman and Riepe 1998;Shefrin 1999;Shiller 2000;Waeneryd 2001;Loewenstein and Prelec 1992). Anomalies are due to a distortion of the decisionmaking process Tversky 1979, 2000) and refer to the phenomenon of decision inconsistency, that is, when preferences vary over time (Ventre et al 2022). The description we offer makes it possible to quantify the extent to which the stages of evaluation and selection of alternatives are distorted by a subjective perception of time (Blavatskyy 2017).…”

“…In the exponential case, both impatience and discount rate are constant over time. However, empirical evidence (Green and Myerson 1996;Dasgupta and Maskin 2005;Lu and Yang 2015) of temporally inconsistent preferences, that is, inconsistency over time (Ventre et al 2022), has urged the formalisation of alternative discount function. Prelec (2004) was the first to prove that the irrationality underlying temporally inconsistent preferences is reflected in a degree of impatience that decreases over time.…”

“…In particular, the assumption t 0 = 0 refers to the fact that the behavioral anomalies that generate the financial anomaly affects periods closer to the present. In fact, because in Ventre et al (2022) it has been proven that the interval effect is determined by a decrease in impatience, as time increases the behavior of the anomaly stabilises and the study becomes meaningless. Therefore,…”

“…Hyperbolic discounting is characterised by a variable discount rate and a degree of impatience that decreases over time (Prelec 2004). These elements are strongly associated with the influence of emotional drives in decision-making (Ventre et al 2022;Andrade and Ariely 2009). Recent research has considered time perception as the third key element in understanding the psychological mechanisms underlying hyperbolic discounting (Van Boven et al 2010;Zauberman et al 2009;Kim and Zauberman 2019;Agostino et al 2021).…”

“…In addition to contributing new properties of the hyperbolic discount function to the present literature, this paper offers a new measure that could be used to quantify decision inconsistency from the normative model in the intertemporal choice. In fact, other financial anomalies can also be described by starting with a degree of impatience that decreases over time and a decreasing discount rate (Ventre et al 2022).…”