# Viewing the future through a warped lens: Why uncertainty generates hyperbolic discounting

- 1.4k Downloads
- 55 Citations

## Abstract

A large body of experimental research has demonstrated that, on average, people violate the axioms of expected utility theory as well as of discounted utility theory. In particular, aggregate behavior is best characterized by probability distortions and hyperbolic discounting. But is it the same people who are prone to these behaviors? Based on an experiment with salient monetary incentives we demonstrate that there is a strong and significant relationship between greater departures from linear probability weighting and the degree of decreasing discount rates at the level of individual behavior. We argue that this relationship can be rationalized by the uncertainty inherent in any future event, linking discounting behavior directly to risk preferences. Consequently, decreasing discount rates may be generated by people’s proneness to probability distortions.

## Keywords

Time preferences Risk preferences Hyperbolic discounting Probability weighting Institutionally generated uncertainty## JEL Classification

D01 D81 D91## Notes

### Acknowledgements

We thank Ernst Fehr, Drew Fudenberg, David Laibson, David Levine, Drazen Prelec, Peter Wakker and Herbert Walther for helpful comments. The usual disclaimer applies. This research is supported by the Swiss National Science Foundation (Grants 100012-109907 and 100014-120705). An earlier version of this paper, “Uncertainty Breeds Decreasing Impatience: The Role of Risk Preferences in Time Discounting”, is available at http://www.iew.uzh.ch/wp/iewwp412.pdf.

## References

- Abdellaoui, M. (2000). Parameter-free elicitation of utility and probability weighting functions.
*Management Science, 46*(11), 1497–1512.CrossRefGoogle Scholar - Abdellaoui, M., Attema, A., & Bleichrodt, H. (2010). Intertemporal tradeoffs for gains and losses: An experimental measurement of discounted utility.
*Economic Journal, 120*, 845–866.CrossRefGoogle Scholar - Abdellaoui, M., Diecidue, E., & Öncüler, A. (2011). Risk preferences at different time periods: An experimental investigation.
*Management Science, 57*(5), 975–987.CrossRefGoogle Scholar - Ahlbrecht, M., & Weber, M. (1997). An empirical study on intertemporal decision making under risk.
*Management Science, 43*, 813–826.CrossRefGoogle Scholar - Ainslie, G. (1991). Derivation of ‘rational’ economic behavior from hyperbolic discount curves.
*American Economic Review Papers and Proceedings, 81*(2), 334–340.Google Scholar - Allais, M. (1953). L’Extension des Theories de l’Equilibre Economique General et du Rendement Social au Cas du Risque.
*Econometrica, 21*(2), 269–290.CrossRefGoogle Scholar - Anderhub, V., Güth, W., Gneezy, U., & Sonsino, D. (2001). On the interaction of risk and time preferences: An experimental study.
*German Economic Review, 2*(3), 239–253.CrossRefGoogle Scholar - Andersen, S., Harrison, G., Lau, M., & Rutström, E. (2008). Eliciting risk and time preferences.
*Econometrica, 76*(3), 583–618.CrossRefGoogle Scholar - Anderson, L., & Stafford, S. (2009). Individual decision-making experiments with risk and intertemporal choice.
*Journal of Risk and Uncertainty, 38*, 51–72.CrossRefGoogle Scholar - Baucells, M., & Heukamp, F. (2010). Common ratio using delay.
*Theory and Decision, 68*, 149–158.CrossRefGoogle Scholar - Benjamin, D., Sebastian, A., & Shapiro, J. (2006). Who is ‘behavioral’? Cognitive ability and anomalous preferences. Harvard University mimeo.Google Scholar
- Benzion, U., Rapoport, A., & Yagil, J. (1989). Discount rates inferred from deciions: An experimental study.
*Management Science, 35*(3), 270–284.CrossRefGoogle Scholar - Bruhin, A., Fehr-Duda, H., & Epper, T. (2010). Risk and rationality: Uncovering heterogeneity in probability distortion.
*Econometrica, 78*(4), 1375–1412.CrossRefGoogle Scholar - Caplin, A., & Leahy, J. (2001). Psychological expected utility theory and anticipatory feelings.
*Quarterly Journal of Economics, 116*(1), 55–79.CrossRefGoogle Scholar - Chesson, H., & Viscusi, W. (2000). The heterogeneity of time-risk tradeoffs.
*Journal of Behavioral Decision Making, 13*, 251–258.CrossRefGoogle Scholar - Chesson, H., & Viscusi, W. (2003). Commonalities in time and ambiguity aversion for long-term risks.
*Theory and Decision, 54*, 57–71.CrossRefGoogle Scholar - Coble, K., & Lusk, J. (2010). At the nexus of risk and time preferences: An experimental investigation.
*Journal of Risk and Uncertainty, 41*, 67–79.CrossRefGoogle Scholar - Coller, M., & Williams, M. (1999). Eliciting individual discount rates.
*Experimental Economics, 2*, 107–127.Google Scholar - Dohmen, T., Falk, A., Huffman, D., & Sunde, U. (2007). Are risk aversion and impatience related to cognitive ability?
*American Economic Review, 100*(3), 1238–1260.CrossRefGoogle Scholar - Eckel, C., Johnson, C., & Montmarquette, C. (2004). Saving decisions of the working poor: Short- and long-term horizons. In
*Research in experimental economics*(Vol. 10, pp. 219–260). Emerald Group Publishing Limited.Google Scholar - Fehr-Duda, H., Bruhin, A., Epper, T., & Schubert, R. (2010). Rationality on the rise: Why relative risk aversion increases with stake size.
*Journal of Risk and Uncertainty, 40*(2), 147–180.CrossRefGoogle Scholar - Fehr-Duda, H., de Gennaro, M., & Schubert, R. (2006). Gender, financial risk, and probability weights.
*Theory and Decision, 60*, 283–313.CrossRefGoogle Scholar - Fischbacher, U. (2007). z-Tree: Zurich toolbox for ready-made economic experiments.
*Experimental Economics, 10*, 171–178.CrossRefGoogle Scholar - Fisher, I. (1930).
*The theory of interest as determined by impatience to spend income and opportunity to invest it*. New York: Macmillan.Google Scholar - Frederick, S. (2005). Cognitive reflection and decision making.
*Journal of Economic Perspectives, 19*(4), 25–42.CrossRefGoogle Scholar - Frederick, S., Loewenstein, G., & O’Donoghue, T. (2002). Time discounting and time preference: A critical review.
*Journal of Economic Literature, 40*, 351–401.CrossRefGoogle Scholar - Gonzalez, R., & Wu, G. (1999). On the shape of the probability weighting function.
*Cognitive Psychology, 38*, 129–166.CrossRefGoogle Scholar - Hagen, O. (1972). Towards a positive theory of preference under risk. In M. Allais & O. Hagen (Eds.),
*Expected utility and the Allais paradox*(pp. 271–302). Dordrecht, Boston.Google Scholar - Halevy, Y. (2008). Strotz meets Allais: Diminishing impatience and the certainty effect.
*American Economic Review, 98*(3), 1145–1162.CrossRefGoogle Scholar - Harless, D., & Camerer, C. (1994). The predictive utility of generalized expected utility theories.
*Econometrica, 62*(6), 1251–1289.Google Scholar - Hey, J. D., & Orme, C. (1994). Investigating generalizations of expected utility theory using experimental data.
*Econometrica, 62*(6), 1291–1326.CrossRefGoogle Scholar - Holt, C., & Laury, S. (2002). Risk aversion and incentive effects.
*American Economic Review, 92*(5), 1644–1655.Google Scholar - Kachelmeier, S., & Shehata, M. (1992). Examining risk preferences under high monetary incentives: Experimental evidence from the People’s Republic of China.
*American Economic Review, 82*(5), 1120–1141.Google Scholar - Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk.
*Econometrica, 47*(2), 263–291.CrossRefGoogle Scholar - Karmarkar, U. S. (1979). Subjectively weighted utility and the Allais paradox.
*Organizational Behavior and Human Performance, 24*, 67–72.CrossRefGoogle Scholar - Keren, G., & Roelofsma, P. (1995). Immediacy and certainty in intertemporal choice.
*Organizational Behavior and Human Decision Processes, 63*(3), 287–297.CrossRefGoogle Scholar - Kirby, K. (1997). Bidding on the future: Evidence against normative discounting of delayed rewards.
*Journal of Experimental Psychology, 126*(1), 54–70.Google Scholar - Laibson, D. (1997). Golden eggs and hyperbolic discounting.
*Quarterly Journal of Economics, 112*(2), 443–477.CrossRefGoogle Scholar - Lattimore, P., Baker, J., & Witte, A. D. (1992). The influence of probability on risky choice: A parametric examination.
*Journal of Economic Behavior and Organization, 17*, 377–400.CrossRefGoogle Scholar - Leigh, J. (1986). Accounting for tastes: Correlates of risk and time preferences.
*Journal of Post Keynesian Economics, 9*(1), 17–31.Google Scholar - Myerson, J., & Green, L. (1995). Discounting of delayed rewards: Models of individual choice.
*Journal of the Experimental Analysis of Behavior, 64*, 263–276.CrossRefGoogle Scholar - Myerson, J., Green, L., Hanson, J., Holt, D., & Estle, S. (2003). Discounting delayed and probabilistic rewards: Processes and traits.
*Journal of Economic Psychology, 24*, 619–635.CrossRefGoogle Scholar - Noussair, C., & Wu, P. (2006). Risk tolerance in the present and the future: An experimental study.
*Managerial and Decision Economics, 27*, 401–412.CrossRefGoogle Scholar - Onay, S., & Öncüler, A. (2007). Intertemporal choice under timing risk: An experimental approach.
*Journal of Risk and Uncertainty, 34*, 99–121.CrossRefGoogle Scholar - Patak, M., & Reynolds, B. (2007). Question-based assessment of delay discounting: Do respondents spontaneously incorporate uncertainty into their valuations for delayed rewards?
*Addictive Behaviors, 32*, 351–357.CrossRefGoogle Scholar - Prelec, D. (1998). The probability weighting function.
*Econometrica, 66*(3), 497–527.CrossRefGoogle Scholar - Prelec, D. (2000). Compound invariant weighting functions in prospect theory. In D. Kahneman & A. Tversky (Eds.),
*Choices, values, and frames*(pp. 67–92). Cambridge, U.K.: Cambridge University Press.Google Scholar - Prelec, D. (2004). Decreasing impatience: A criterion for non-stationary time preference and ‘Hyperbolic’ Discounting.
*Scandinavian Journal of Economics, 106*(3), 511–532.CrossRefGoogle Scholar - Prelec, D., & Loewenstein, G. (1991). Decision making over time and under uncertainty: A common approach.
*Management Science, 37*(7), 770–786.CrossRefGoogle Scholar - Quiggin, J. (1982). A theory of anticipated utility.
*Journal of Economic Behavior and Organization, 3*, 323–343.CrossRefGoogle Scholar - Rachlin, H., Raineri, A., & Cross, D. (1991). Subjective probability and delay.
*Journal of the Experimental Analysis of Behavior, 55*(2), 233–244.CrossRefGoogle Scholar - Rottenstreich, Y., & Hsee, C. K. (2001). Money, kisses, and electric shocks: On the affective psychology of risk.
*Psychological Sciences, 12*(3), 185–190.CrossRefGoogle Scholar - Saito, K. (2011). A relationship between risk and time preferences.
*American Economic Review, 101*(5), 2271–2275.Google Scholar - Segal, U. (1987). Some remarks on Quiggin’s anticipated utility.
*Journal of Economic Behavior and Organization, 8*, 145–154.CrossRefGoogle Scholar - Starmer, C., & Sugden, R. (1989). Violations of the independence axiom in common ratio problems: An experimental test of some competing hypotheses.
*Annals of Operations Research, 19*, 79–102.CrossRefGoogle Scholar - Takahashi, T., Ikeda, K., Hasegawa, T., & Greene, A. (2007). A hyperbolic decay of subjective probability of obtaining delayed rewards.
*Behavioral and Brain Functions, 3*(52).Google Scholar - Thaler, R. (1981). Some empirical evidence on dynamic inconsistency.
*Economics Letters, 8*, 201–207.CrossRefGoogle Scholar - Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty.
*Journal of Risk and Uncertainty, 5*, 297–323.CrossRefGoogle Scholar - Wakker, P. (1994). Separating marginal utility and probabilistic risk aversion.
*Theory and Decision, 36*, 1–44.CrossRefGoogle Scholar - Wakker, P. (2008). Explaining the characteristics of the power (CRRA) utility family.
*Health Economics, 17*, 1329–1344.CrossRefGoogle Scholar - Walther, H. (2003). Normal-randomness expected utility, time preference and emotional distortions.
*Journal of Economic Behavior and Organization, 52*, 253–266.CrossRefGoogle Scholar - Walther, H. (2010). Anomalies in intertemporal choice, time-dependent uncertainty and expected utility—A common approach.
*Journal of Economic Psychology, 31*, 114–130.CrossRefGoogle Scholar - Weber, B., & Chapman, G. (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*, 104–118.CrossRefGoogle Scholar - Wu, G. (1999). Anxiety and decision making with delayed resolution of uncertainty.
*Theory and Decision, 46*, 159–198.CrossRefGoogle Scholar