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On the functional form of temporal discounting: An optimized adaptive test

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Abstract

The tendency to discount the value of future rewards has become one of the best-studied constructs in the behavioral sciences. Although hyperbolic discounting remains the dominant quantitative characterization of this phenomenon, a variety of models have been proposed and consensus around the one that most accurately describes behavior has been elusive. To help bring some clarity to this issue, we propose an Adaptive Design Optimization (ADO) method for fitting and comparing models of temporal discounting. We then conduct an ADO experiment aimed at discriminating among six popular models of temporal discounting. Rather than supporting a single underlying model, our results show that each model is inadequate in some way to describe the full range of behavior exhibited across subjects. The precision of results provided by ADO further identify specific properties of models, such as accommodating both increasing and decreasing impatience, that are mandatory to describe temporal discounting broadly.

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Notes

  1. In addition, adaptive titration procedures have been developed, which adjust the amount or delay in response to the subject’s choices on a trial-by-trial basis, thereby reducing the risk of floor and ceiling effects (Mazur 1987; Johnson and Bickel 2002). Several studies have also employed adaptive heuristics in which stimuli depend on subjects’ responses. For instance, Abdellaoui et al. (2010) employed a two-stage design in which the first stage measured utilities, separately for each subject, which were then used in the second stage to construct stimuli for measuring time weights.

  2. Each mini-experiment could be a single trial or a block of several trials of trials.

  3. A geometric spacing of the independent variable (time) has been shown to be beneficial for discriminating between power and exponential decay curves in the study of memory retention (Cavagnaro et al. 2011). These sets of reward values were constructed to maximize the number of distinct ratios between the smaller and larger amounts.

  4. The following studies were consulted to develop reasonable expectations about the parameter ranges: Ebert and Prelec (2007); Frederick et al. (2002); Green and Myerson (2004); Killeen (2009); Laibson (1997); Loewenstein and Prelec (1992); McClure et al. (2004, 2007); McKerchar et al. (2009); Simpson and Vuchinich (2000).

  5. The raw AIC is an unbiased estimator of minus twice the expected log-likelihood of the model.

  6. Stephan et al. (2009) formulate this method in a Bayesian framework, using the posterior model probability in place of the Akaike weight.

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Authors and Affiliations

  1. Mihaylo College of Business and Economics, California State University Fullerton, Fullerton, CA, USA

    Daniel R. Cavagnaro

  2. Department of Neurology, University of California, San Francisco, San Francisco, CA, USA

    Gabriel J. Aranovich

  3. Department of Psychology, Arizona State University, Tempe, AZ, USA

    Samuel M. McClure

  4. Department of Psychology, The Ohio State University, Columbus, OH, USA

    Mark A. Pitt & Jay I. Myung

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  1. Daniel R. Cavagnaro
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  2. Gabriel J. Aranovich
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  3. Samuel M. McClure
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  4. Mark A. Pitt
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  5. Jay I. Myung
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Correspondence to Daniel R. Cavagnaro.

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Cavagnaro, D.R., Aranovich, G.J., McClure, S.M. et al. On the functional form of temporal discounting: An optimized adaptive test. J Risk Uncertain 52, 233–254 (2016). https://doi.org/10.1007/s11166-016-9242-y

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