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Estimating representations of time preferences and models of probabilistic intertemporal choice on experimental data

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Abstract

We here estimate a number of alternatives to discounted-utility theory, such as quasi-hyperbolic discounting, generalized hyperbolic discounting, and rank-dependent discounted utility with three different models of probabilistic choice. The data come from a controlled laboratory experiment designed to reveal individual time preferences in two rounds of 100 binary-choice problems. Rank-dependent discounted utility and its special case—the maximization of present discounted value—turn out to be the best-fitting theory (for about two-thirds of all subjects). For a great majority of subjects (72%), the representation of time preferences in Luce’s choice model provides the best fit.

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Notes

  1. One option temporally dominates another if, at any moment of time, the cumulative payoff of the first option up to that moment is at least as high as that of the other option. See Section 2.1 for more details.

  2. In other words, one alternative first-order temporally dominates another if it can be obtained from the other via a sequence of increased and/or bought-forward payments.

  3. The large majority of subjects preferred cash.

  4. The Fechner model of homoscedastic errors does not require F0,s(.) to be the cumulative distribution function of the normal distribution. It could be any monotonically increasing function, e.g., the cumulative distribution function of the logistic distribution, which is known as a softmax choice rule.

  5. Using multiple starting values produced the same results as using the best-fitting parameter for the nested model.

  6. We use the critical value of the chi-squared distribution with two degrees of freedom in the test against the maximization of cumulative payoff, and with one degree of freedom in that against the maximization of present discounted value.

  7. We use the critical value of the chi-squared distribution with three degrees of freedom in the test against the maximization of cumulative payoff, with two degrees of freedom in that against the maximization of present discounted value, and with one degree of freedom in that against discounted-utility theory.

  8. We use the critical value of the chi-squared distribution with six degrees of freedom in the test against maximization of cumulative payoff, and with five degrees of freedom in that against the maximization of present discounted value.

  9. The AIC ranks the different models by penalizing the extra parameters of the less-restrictive models. Formally, the AIC is \( 2k-2\mathit{\ln}\widehat{L} \), with \( \widehat{L} \) being the maximized log-likelihood for a particular model and k the number of model parameters. The lower the value of AIC, the better the model explains the observed behavior.

  10. When we focus the analysis on the subjects whose preferences are best-fitted by RDDU, this convexity is less pronounced.

  11. We use a sign-rank test to test, for each specification of time preferences, the null hypothesis that the subjective discount factor d (b) is the same under the Luce and Fechner models. The sign-rank test rejects the null hypothesis at the 1% level for four comparisons, and at the 5 and 10% levels for one comparison.

  12. By convention, the present is not discounted (the discount factor is one). The delay of one month is discounted with a factor d and that of two months with a factor bd.

  13. I.e., the one with the minimum value of the Akaike information criterion.

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Authors and Affiliations

  1. Montpellier Business School, Montpellier Research in Management, 2300, Avenue des Moulins, 34185, Montpellier Cedex 4, France

    Pavlo R. Blavatskyy

  2. Université Paris 8, 2 Rue de la Liberté, 93200, Saint-Denis, France

    Hela Maafi

Authors
  1. Pavlo R. Blavatskyy
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  2. Hela Maafi
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Correspondence to Pavlo R. Blavatskyy.

Additional information

We are grateful to the editor Kip Viscusi and one anonymous referee, as well as the participants of D-TEA 2017 (Paris) and BRIC 2017 (London) for helpful comments.

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Table 3 Questions used in the experiment
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Blavatskyy, P.R., Maafi, H. Estimating representations of time preferences and models of probabilistic intertemporal choice on experimental data. J Risk Uncertain 56, 259–287 (2018). https://doi.org/10.1007/s11166-018-9281-7

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  • DOI: https://doi.org/10.1007/s11166-018-9281-7

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