Reliability of a Measure of Temporal Discounting (original) (raw)
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Within-Subject Comparison of Real and Hypothetical Money Rewards in Delay Discounting
Journal of the Experimental Analysis of Behavior, 2002
A within-subject design, using human participants, compared delay discounting functions for real and hypothetical money rewards. Both real and hypothetical rewards were studied across a range that included 10to10 to 10to250. For 5 of the 6 participants, no systematic difference in discount rate was observed in response to real and hypothetical choices, suggesting that hypothetical rewards may often serve as a valid proxy for real rewards in delay discounting research. By measuring discounting at an unprecedented range of real rewards, this study has also systematically replicated the robust finding in human delay discounting research that discount rates decrease with increasing magnitude of reward. A hyperbolic decay model described the data better than an exponential model.
Temporal discounting of gains and losses of time: An experimental investigation
Journal of Risk and Uncertainty, 2018
This paper investigates "asymmetries" between non-monetary gains and losses in intertemporal choice. We considered gains and losses of spare/working time with respect to a reference duration defined in a working contract. Specifically, we elicited a behavioral model of intertemporal choice that accounts for a gain/lossdependent discounting function and a reference-dependent utility. Additionally, we did not impose preference for the present (positive discounting) and allowed for both decreasing and increasing impatience. While our results are standard regarding the discount of money (our baseline treatment), our subjects heavily discounted gains of time. More patience was observed for losses of time and a sizable portion of subjects even exhibited negative discounting, i.e. they preferred to expedite losses of time. Our econometric estimations also reveal a much larger heterogeneity of behavior in terms of both utility and discounting for gains and losses of spare time as compared to money.
Delay discounting: concepts and measures
Delay discounting, one element which underlies decision-making, can be defined as the depreciation of the value of a reward related to the time that it takes to be released. High rates of delay discounting are found in subjects who are willing to forgo greater rewards available only after some length of time and who show a preference for smaller rewards that are available immediately. Widely used as a measure of impulsiveness, delay discounting can be evaluated using experimental tasks. The present review evaluated tasks of delay discounting, their features, measures of evaluation and anomalies, and some variables that can affect delay discounting results and applications in the study of individual and intra-individual differences.
Temporal Discounting When the Choice Is Between Two Delayed Rewards
Journal of Experimental Psychology: Learning, Memory, and Cognition, 2005
The present experiments extend the temporal discounting paradigm from choice between an immediate and a delayed reward to choice between 2 delayed rewards: a smaller amount of money available sooner and a larger amount available later. Across different amounts and delays, the data were consistently well described by a hyperbola-like discounting function, and the degree of discounting decreased systematically as the delay to the sooner reward increased. Three theoretical models (the elimination-by-aspects, present-value comparison, and common-aspect attenuation hypotheses) were evaluated. The best account of the data was provided by the common-aspect attenuation hypothesis, according to which the common aspect of the choice alternatives (i.e., the time until the sooner reward is available) receives less weight in the decision-making process.
Journal of Behavioral Decision Making
Research on delay discounting and inter-temporal choice has yielded significant insights into decision making. Although research has focused on delayed gains, the discounting of losses is potentially important in precisely those areas where the discounting of gains has proved informative (e.g., substance use and abuse). Participants in the current study completed both a questionnaire consisting of choices between immediate and delayed gains and an analogous questionnaire consisting of choices between immediate and delayed losses. For almost all participants, the likelihood of choosing the delayed gain decreased with increases in the wait until it would be received. In contrast, when losses (i.e., payments) were involved, different participants showed quite different patterns of choices. More specifically, although the majority of the participants became increasingly likely to choose to pay later as the delay was increased, some participants appeared to be debt averse, in that they were more likely to choose the immediate payment option when the delay was long than when it was brief. These debt-averse participants also were more likely to choose to wait for a larger delayed gain than other participants and scored lower on Impulsiveness than those who showed the typical pattern of discounting delayed losses. Taken together, these results suggest that in the case of delayed gains, people differ only quantitatively (i.e., in how steeply they discount), whereas in the case of delayed losses, people differ qualitatively as well as quantitatively, contrary to the common assumption that a single impulsivity trait underlies choices between immediate and delayed outcomes.
The combined effects of delay and probability in discounting
Behavioural processes, 2006
Human discounting studies have frequently observed hyperbolic discounting of rewards that are delayed or probabilistic. However, no studies have systematically combined delay and probability in a single discounting procedure. Indifference points of hypothetical money rewards that are both delayed and probabilistic were determined. Probabilities were converted into comparable delays according to the h/k constant of proportionality determined by Rachlin et al. (1991), and discounting rates were calculated. These data provided a very good fit to the hyperbolic model of discounting, suggesting that delay and probability can be combined into a single metric in studies of discounting. The inclusion of a magnitude condition found the Magnitude Effect commonly found in studies of temporal discounting. A temporal resolution of uncertainty condition found no effect. The present paper offers a novel statistical method, within an established framework, for the analysis of data from studies of discounting that combine delay and probability.
A comparison of four models of delay discounting in humans
The present study compared four prominent models of delay discounting: a one-parameter exponential decay, a one-parameter hyperbola . An adjusting procedure for studying delayed reinforcement. In: Commons, M.L., Mazur, J.E., Nevin, J.A., Rachlin, H. (Eds.), Quantitative Analyses of Behavior: The Effect of Delay and of Intervening Events on Reinforcement Value, vol. 5. Erlbaum, Hillsdale, NJ, pp. 55-73], a two-parameter hyperboloid in which the denominator is raised to a power [Green, L., Myerson, J., 2004. A discounting framework for choice with delayed and probabilistic rewards. Psychol. Bull. 130, 769-792], and a two-parameter hyperbola in which delay is raised to a power [Rachlin, H., 2006. Notes on discounting. J. Exp. Anal. Behav. 85, 425-435].
TOWARDS A GENERAL MODEL OF TEMPORAL DISCOUNTING
Psychological models of temporal discounting have now successfully displaced classical economic theory due to the simple fact that many common behavior patterns, such as impulsivity, were unexplainable with classic models. However, the now dominant hyperbolic model of discounting is itself becoming increasingly strained. Numerous factors have arisen that alter discount rates with no means to incorporate the different influences into standard hyperbolic models. Furthermore, disparate literatures are emerging that propose theoretical constructs that are seemingly independent of hyperbolic discounting. We argue that, although hyperbolic discounting provides an eminently useful quantitative measure of discounting, it fails as a descriptive psychological model of the cognitive processes that produce intertemporal preferences. Instead, we propose that recent contributions from cognitive neuroscience indicate a path for developing a general model of time discounting. New data suggest a means by which neuroscience-based theory may both integrate the diverse empirical data on time preferences and merge seemingly disparate theoretical models that impinge on time preferences. A tremendous variety of decisions faced by humans and animals require selecting between actions whose outcomes are realized at different times in the future. Moreover, it is quite commonly the case that more desirable outcomes can only be had at the expense of greater time or effort. As such, doing well in many behavioral contexts requires the ability to forego immediate temptations and to delay gratification. Given the ubiquity and importance of delaying gratification, there has been a longstanding interest in understanding and describing how humans and other animals respond to such decisions. The standard approach to investigating these phenomena is to present intertempo-ral choices-decisions, for example, between an immediate and a delayed reward-and to describe mathematically how choices are made. Both humans and other animals often prefer the immediate reward even when the delayed reward is larger. Mathematically, this can be summarized by asserting that the subjective value of a reward is discounted by an amount that depends on the delay until receipt (Ainslie, 1975; Rubinstein, 2003; Samuelson, 1937). From a research standpoint, the critical question is the nature of this delay discounting function. Fundamentally, this question can be satisfied by establishing a mathematical formulation of discounting that accounts for the diversity of behaviors involving choices over delays. Identifying such an equation seems likely to benefit from a close coupling between the mathematical function and the psychological and cognitive processes that underlie decision-making. Advances in understanding the delay discounting equation have been tremendous. In the next section we review these efforts that ultimately culminate in quasi-hyperbolic discounting models that capture behavior with impressive precision (published r 2 values commonly greater than 0.9). However, hyperbolic models are clearly limited in the range of discounting phenomena that they account for. In particular, the models capture behavior well in isolated contexts but are unequipped to account for how discounting varies across situations. These contextual effects can be profound. We believe this limitation arises from the fact that hyperbolic discounting models are distant from the basic cognitive processes that underlie decision-making. We review some highly cited models of discounting. However, our primary focus is on neuroscience, with the goal of proposing a brain-inspired model of discounting that (a) preserves the overall structure of hyperbolic discounting, but (b) is This work was supported by NIDA grant R03 032580 (SMM) and a Netherlands Organization for Scientific Research (NWO) Rubicon postdoctoral fellowship (WVDB).
Behavioural Processes, 2013
Delay discounting (DD) and probability discounting (PD) refer to the reduction in the subjective value of outcomes as a function of delay and uncertainty, respectively. Elevated measures of discounting are associated with a variety of maladaptive behaviors, and confidence in the validity of these measures is imperative. The present research examined (1) the statistical equivalence of discounting measures when rewards were hypothetical or real, and (2) their 1-week reliability. While previous research has partially explored these issues using the low threshold of nonsignificant difference, the present study fully addressed this issue using the more-compelling threshold of statistical equivalence. DD and PD measures were collected from 28 healthy adults using real and hypothetical $50 rewards during each of two experimental sessions, one week apart. Analyses using area-under-the-curve measures revealed a general pattern of statistical equivalence, indicating equivalence of real/hypothetical conditions as well as 1-week reliability. Exceptions are identified and discussed.