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Intertemporal choice as a tradeoff between cumulative payoff and average delay

Abstract

Intertemporal choice involves outcomes that are received in different moments of time. This paper presents a new framework for analyzing intertemporal choice as a tradeoff between the cumulative payoff of a stream of intertemporal outcomes and its average delay (similar to the mean–variance approach in modelling risk preferences). Ceteris paribus, a decision maker prefers a stream of intertemporal payoffs with a higher cumulative payoff and a lower average delay. A decision maker with such time preferences always dislikes a partial delay in consumption (splitting one payoff into two, one of which is slightly delayed in time). In contrast, many existing models (e.g. discounted utility, quasi-hyperbolic discounting, generalized hyperbolic discounting or liminal discounting) imply a preference for partial delay. Our proposed model is compatible with the common difference effect (corresponding to a horizontal fanning-out of indifference curves) and the absolute magnitude effect (corresponding to a vertical fanning-in of indifference curves). The proposed model is applied to the standard consumption-savings problem with a constant interest rate. A simple experimental test of the proposed model vs. discounted utility and quasi-hyperbolic discounting is presented.

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Notes

  1. Similarly, Blavatskyy (2018) shows that when one payoff is split into two payoffs, one of which is payed slightly sooner, a decision maker with an additively-separable utility (e.g. discounted utility, quasihyperbolic discounting, generalized hyperbolic discounting or liminal discounting) and a convex utility function prefers the delayed unsplit payment.

  2. Baucells and Sarin (2007a) consider a similar example with streams A and B.

  3. For example, Read et al. (1999) find that many subjects prefer to rent a “highbrow” movie rather than a “lowbrow” movie in the long term but switch their preference in the short term. Read and van Leeuwen (1998) report a similar reversal for healthy and unhealthy snacks.

  4. If N subjects choose 50%-50% between the first and the second streams, then an experimenter observes N/4 subjects consistently choosing the first stream; N/4 subjects consistently choosing the second stream; and N/2 subjects switching between the first and the second stream. The highest number N that is consistent with choice frequencies observed in the experiment is thus the highest N such that N/4 ≤ 28, N/4 ≤ 23 and N/2 ≤ 49; or N = 92.

  5. Gigliotti and Sopher (1997) also find that many subjects reveal a preference for a constant stream over increasing and decreasing streams.

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Acknowledgements

I am grateful to the editor Kip Viscusi and the referee Daniel Read for very helpful comments. Pavlo Blavatskyy is a member of the Entrepreneurship and Innovation Chair, which is partof LabEx Entrepreneurship (University of Montpellier, France) and is funded by the French government (Labex Entreprendre, ANR-10-Labex-11-01).

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Correspondence to Pavlo R. Blavatskyy.

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Appendix

Appendix

Experimental Instructions

Welcome to our experiment! This is an experiment in choice over time. It is financed from research funds. We would like to ask you to take six decisions in this experiment.

At the end of the experiment you will receive one or two discount coupons for a supermarket chain valid only on a specific day. Your payoff depends only on your decisions and the realization of random events. Your payoff does not depend on the decisions of other participants. Your anonymity will be preserved during and after the experiment.

During the experiment you need to answer six questions printed in your booklet. Please note that that there are no right or wrong answers in this experiment. Here is an example of a typical question that you may face during the experiment:

Question 1

Please choose your preferred alternative:

figure a

Please raise your hand when you answered all six questions. We will ask you to come forward with your booklet to our table. We then ask you to toss a die to randomly select one question number. This question will be used to determine your payoff.

For instance, suppose that the die comes up one. Then question 1 is selected. Suppose that question 1 in your booklet is the question shown above. If you have ticked the right alternative in this question, you receive one discount coupon worth €20 valid only on May 8th.

Please note that any question can be randomly selected at the end to determine your payoff. So it is in your best interest to answer all six questions carefully. Good luck!

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Blavatskyy, P.R. Intertemporal choice as a tradeoff between cumulative payoff and average delay. J Risk Uncertain 64, 89–107 (2022). https://doi.org/10.1007/s11166-022-09370-3

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  • DOI: https://doi.org/10.1007/s11166-022-09370-3

Keywords

  • Intertemporal choice
  • Time preference
  • Cumulative payoff
  • Average delay
  • Temporal tradeoff

JEL Classification

  • D15