Time and risk perceptions mediate the causal impact of objective delay on delay discounting: An experimental examination of the implicit-risk hypothesis

Abstract

Delay discounting refers to the decline in the value of a payoff as the objective delay to its fulfillment increases. Recent research on delay discounting has examined its relationship with time and risk perceptions through correlational studies. Manipulated experiments were conducted in the current research to further investigate the causal links among the relevant variables. Experiment 1 revealed causal influences of objective delay on both risk perception and delay discounting as well as a positive correlation between risk perception and delay discounting. By manipulating risk perception, Experiment 2 demonstrated further a causal impact of risk perception on delay discounting. Experiment 3 manipulated time perception and provided further evidence for causal pathways from time perception to risk perception and delay discounting. Overall, the results verified a causal chain from objective delay to delay discounting through time and risk perceptions in support of the implicit-risk hypothesis regarding delay discounting.

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Notes

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    The datasets generated and/or analyzed during this and the following studies are available at https://osf.io/q96en/.

References

  1. Benzion, U., Rapoport, A., & Yagil, J. (1989). Discount rates inferred from decisions: an experimental study. Management Science, 35(3), 270–284.

  2. Bixter, M. T., & Luhmann, C. C. (2015). Evidence for implicit risk: delay facilitates the processing of uncertainty. Journal of Behavioral Decision Making, 28(4), 347–359.

  3. Blackburn, M., & El-Deredy, W. (2013). The future is risky: discounting of delayed and uncertain outcomes. Behavioural Processes, 94, 9–18.

  4. Dai, J., & Busemeyer, J. R. (2014). A probabilistic, dynamic, and attribute-wise model of intertemporal choice. Journal of Experimental Psychology: General. 143, 1489–1514.

    Article  Google Scholar 

  5. Dai, J., Pachur, T., Pleskac, T., & Hertwig, R. (2019). Tomorrow never knows: Why and how uncertainty matters in intertemporal choice. In R. Hertwig, T. J. Pleskac, T. Pachur & the Center for Adaptive Rationality, Taming Uncertainty. Cambridge: MIT.

    Google Scholar 

  6. DeHart, W. B., & Odum, A. L. (2015). The effects of the framing of time on delay discounting. Journal of the Experimental Analysis of Behavior, 103, 10–21.

  7. Du, W., Green, L., & Myerson, J. (2002). Cross-cultural comparisons of discounting delayed and probabilistic rewards. The Psychological Record, 52(4), 479–492.

    Article  Google Scholar 

  8. Epper, T., Fehr-Duda, H., & Bruhin, A. (2011). Viewing the future through a warped lens: why uncertainty generates hyperbolic discounting. Journal of Risk & Uncertainty, 43(3), 169–203.

  9. Frederick, S., Loewenstein, G., & O'Donoghue, T. (2002). Time discounting and time preference: a critical review. Journal of Economic Literature, 40(2), 351–401.

  10. JASP Team. (2019). JASP (Version 0.10.2)[Computer software].

  11. Jeffery, H. (1961). Theory of probability. Oxford, UK: Oxford University Press.

    Google Scholar 

  12. Johnson, K. L., Bixter, M. T., & Luhmann, C. C. (2020). Delay discounting and risky choice: Meta-analytic evidence regarding single-process theories. Judgment and Decision Making, 15(3), 381—400.

    Google Scholar 

  13. Kagel, J. H., Green, L., & Caraco, T. (1986). When foragers discount the future: constraint or adaptation?. Animal Behaviour, 34, 271–283.

  14. Keren, G., & Roelofsma, P. (1995). Immediacy and certainty in intertemporal choice. Organizational Behavior and Human Decision Processes, 63(3), 287–297.

  15. Kruschke, J. K., & Liddell, T. M. (2018). Bayesian data analysis for newcomers. Psychonomic Bulletin & Review, 25(1), 155-177.

    Article  Google Scholar 

  16. LeBoeuf, R. A. (2006). Discount rates for time versus dates: the sensitivity of discounting to time-interval description. Journal of Marketing Research, 43(1), 59-72.

    Article  Google Scholar 

  17. Lindley, D. V. (1965). Introduction to probability and statistics from a Bayesian point of view, part 2: inference. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  18. Mischel, W., & Grusec, J. (1967). Waiting for rewards and punishments: Effects of time and probability on choice. Journal of Personality and Social Psychology, 5, 24–31.

    Article  Google Scholar 

  19. Muthén, L. K., & Muthén, B. O. (1998-2017). Mplus User’s Guide: Eighth Edition. Los Angeles, CA: Muthén & Muthén.

  20. Myerson, J., Green, L., & Warusawitharana, M. (2001). Area under the curve as a measure of discounting. Journal of the Experimental Analysis of Behavior, 76(2), 235–243.

  21. Ostaszewski, P., Green, L., & Myerson, J. (1998). Effects of inflation on the subjective value of delayed and probabilistic rewards. Psychonomic Bulletin & Review, 5(2), 324–333.

  22. Patak, M., & Reynolds, B. (2007). Question-based assessments of delay discounting: do respondents spontaneously incorporate uncertainty into their valuations for delayed rewards? Addictive Behaviors, 32(2), 0–357.

  23. Prelec, D., & Loewenstein, G. (1991). Decision making over time and under uncertainty: A common approach. Management science, 37(7), 770-786.

    Article  Google Scholar 

  24. Rachlin, H., Logue, A. W., Gibbon, J., & Frankel, M. (1986). Cognition and behavior in studies of choice. Psychological Review, 93(1), 33–45.

  25. Rachlin, H. C., Raineri, A., & Cross, D. V. (1991). Perceived probability and delay. Journal of the Experimental Analysis of Behavior, 55(2), 233–244.

  26. Rae, J. (1834). The Sociological Theory of Capital (reprint 1834 ed.). London: Macmillan.

  27. Read, D. (2004). Intertemporal choice. In D. J. Koehler & N. Harvey (Eds.), Blackwell Handbook of Judgment and Decision Making (pp. 3–19). Oxford: Blackwell Publishing.

  28. Read, D., Frederick, S., Orsel, B., & Rahman, J. (2005). Four score and seven years from now: the date/delay effect in temporal discounting. Management Science, 51(9), 1326–1335.

  29. Reynolds, B., Patak, M., & Shroff, P. (2007). Adolescent smokers rate delayed rewards as less certain than adolescent nonsmokers. Drug and Alcohol Dependence, 90, 301–303.

    Article  Google Scholar 

  30. Rouder, J. N., Speckman, P. L., Sun, D., & Morey, R. D. (2009). Bayesian t tests for accepting and rejecting the null hypothesis. Psychonomic Bulletin & Review, 16, 225–237.

    Article  Google Scholar 

  31. Rung, J. M., Argyle, T. M., Siri, J. L., & Madden, G. J. (2018). Choosing the right delay-discounting task: Completion times and rates of nonsystematic data. Behavioural Processes, 151, 119–125.

  32. Saito, K. (2009). A relationship between risk and time preferences (No. 1477). Discussion Paper, Center for Mathematical Studies in Economics and Management Science.

  33. Sozou, P. D. (1998). On hyperbolic discounting and uncertain hazard rates. Proceedings of the Royal Society of London. Series B: Biological Sciences, 265(1409), 2015-2020.

    Article  Google Scholar 

  34. Stephens, D. W. (2002). Discrimination, discounting and impulsivity: a role for an informational constraint. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences, 357, 1527–1537.

  35. Stevenson, M. K. (1986). A discounting model for decisions with delayed positive or negative outcomes. Journal of Experimental Psychology: General, 115, 131–154.

    Article  Google Scholar 

  36. Takahashi, T., Ikeda, K., & Hasegawa, T. (2007). A hyperbolic decay of subjective probability of obtaining delayed rewards. Behavioral and Brain Functions, 3(1), 52.

  37. Weber, B. J., & Chapman, G. B. (2005). The combined effects of risk and time on choice: does uncertainty eliminate the immediacy effect? Does delay eliminate the certainty effect? Organizational Behavior and Human Decision Processes, 96(2), 104–118.

  38. Weber, B. J., & Huettel, S. A. (2008). The neural substrates of probabilistic and intertemporal decision making. Brain Research, 1234, 104–115.

    Article  Google Scholar 

  39. Wendt, S., & Czaczkes, T. J. (2017). Individual ant workers show self-control. Biology Letters, 13(10), 20170450.

  40. Yi, R., de la Piedad, X., & Bickel, W. K. (2006). The combined effects of delay and probability in discounting. Behavioural Processes, 73(2), 149–155.

    Article  Google Scholar 

  41. Zauberman, G., Kim, B. K., Malkoc, S. A., & Bettman, J. R. (2009). Discounting time and time discounting: subjective time perception and intertemporal preferences. Journal of Marketing Research, 46(4), 543–556.

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Acknowledgements

This research was supported by National Nature Science Foundation of China to Junyi Dai (Grant No. 31872780) and the Fundamental Research Funds for the Central Universities of China to Junyi Dai (Grant No. 2018QNA3014).

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Correspondence to Junyi Dai.

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The data and materials for all experiments are available from https://osf.io/q96en/. None of the experiments was preregistered.

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Appendix

Appendix

The titration procedure for adjusting the amount of the immediate reward in the delay-discounting task

For each delay, the amount of the delayed reward was fixed at 40 CNY (Chinese Yuan) and two adjustment bounds were set for the immediate amount, with the initial upper bound (UB) equal to the delayed amount (i.e., 40 CNY) and the initial lower bound (LB) fixed at 0 CNY. The immediate amount was always equal to the average of the two adjustment bounds, leading to an initial immediate reward of 20 CNY. After each choice, the UB would be updated to the average of the UB after the previous trial and the immediate amount for the current trial if the immediate reward was chosen, or the LB would be updated to the average of the LB after the previous trial and the immediate amount of the current trial if the delayed reward was chosen. In either case, the immediate amount would be updated to the average of the two adjustment bounds as in the first trial. For each delay, the titration procedure would stop, and the updated immediate amount would be treated as the indifference point if the two bounds were sufficiently close to each other (i.e., the distance between the bounds was no more than 2 CNY). Unlike the common adjustment method in which the LB or UB was updated to the current immediate amount after the respective choice response, the titration procedure used in the current studies was more lenient and thus allowed for probabilistic choice responses which had enjoyed substantial support from empirical studies (e.g., Dai & Busemeyer, 2014). Consequently, the indifference points revealed by this titration procedure were more likely to approach the “true” indifference points whose choice probabilities against the delayed reward were 50%.

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Jiang, J., Dai, J. Time and risk perceptions mediate the causal impact of objective delay on delay discounting: An experimental examination of the implicit-risk hypothesis. Psychon Bull Rev (2021). https://doi.org/10.3758/s13423-021-01890-4

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Keywords

  • Delay discounting
  • Risk perception
  • Time perception
  • Causality
  • Implicit risk hypothesis