Linking Decision and Time Utilities

Kontek, Krzysztof (2010): Linking Decision and Time Utilities.

Abstract

This paper presents the functional relationship between two areas of interest in contemporary behavioral economics: one concerning choices under conditions of risk, the other concerning choices in time. The paper first presents the general formula of the relationship between decision utility, the survival function, and the discounting function, where decision utility is an alternative to Cumulative Prospect Theory in describing choices under risk (Kontek, 2010). The stretched exponential function appears to be a simple functional form of the resulting discounting function. Solutions obtained using more complex forms of decision utility and survival functions are also considered. These likewise lead to the stretched exponential discounting function. The paper shows that the relationship may also have other forms, including the hyperbolic functions typically used to describe the intertemporal experimental results. This solution has however several descriptive disadvantages, which restricts its common use in the description of lottery and intertemporal choices, and in financial asset valuations.

• Item Type: MPRA Paper
• Language: English
• Keywords: Discounted Utility, Hyperbolic Discounting, Decision Utility, Prospect Theory, Asset Valuation
• Subjects: D - Microeconomics > D0 - General > D03 - Behavioral Microeconomics: Underlying Principles; E - Macroeconomics and Monetary Economics > E4 - Money and Interest Rates > E43 - Interest Rates: Determination, Term Structure, and Effects; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty; D - Microeconomics > D9 - Intertemporal Choice > D90 - General; C - Mathematical and Quantitative Methods > C9 - Design of Experiments > C91 - Laboratory, Individual Behavior

References

Andersen, S., Harrison, G. W., Lau, M., Rutström, E. (2010). Discounting Behavior: A Reconsideration.

Doyle, J. R. (2010). Survey of time preference, delay discounting models. Working Paper, Cardiff Business School, Cardiff University. Available at: http://ssrn.com/abstract=1685861.

Ebert.J., Prelec, D. (2007). The fragility of time: Time insensitivity and valuation of the near and far future. Management Science, 53, pp. 1423-1438.

Epper, T., Fehr-Duda, H., Bruhin, A. (2009). Uncertainty Breeds Decreasing Impatience: The Role of Risk Preferences in Time Discounting. Working Paper No. 412. Institute for Empirical Research in Economics, University of Zuerich. http://ssrn.com/abstract=1416007.

Frederick, S., Loewenstein, G., O’Donoghue, T. (2002). Time Discounting and Time Preference: A critical Review. Journal of Economic Literature, vol. 40, No.2 pp. 351-401.

Halevy, Y. (2008). Strotz Meets Allais: Diminishing Impatience and the Certainty Effect. American Economic Review, 98(3), pp. 1145-1162.

Kahneman, D., Tversky, A., (1979). Prospect theory: An analysis of decisions under risk. Econometrica, 47, pp 313-327.

Killeen, P. R. (2009). An additive-utility model of delay discounting. Psychological review, 116, pp. 602-619.

Kim, B. K., Zauberman, G., (2009). Perception of Anticipatory Time in Temporal Discounting. Journal of Neuroscience, Psychology, and Economics. Vol. 2, pp. 91-101.

Kontek, K. (2010). Decision Utility Theory: Back to von Neumann, Morgenstern, and Markowitz. Working Paper available at: http://ssrn.com/abstract=1718424.

Loewenstein, G., Prelec, D. (1992). Anomalies in intertemporal choice: Evidence and interpretation. Quarterly Journal of Economics, 107(2), pp. 573-597.

Mazur, J. E. (1987). An adjusting procedure for studying delayed reinforcement. In M. L. Commons, J.E. Mazur, J.A. Nevin, and H. Rachlin (Eds), Quantitative analysis of behavior, Vol. 5. Mahwah NJ: Erlbaum

Myerson, J., Green, L. (1995). Discounting of delayed rewards: Models of individual choice. Journal of Experimental Analysis of Behavior, 64, pp. 263-276.

Prelec, D. (1990). On the Shape of the Decision Weight Function. Harvard Business School Working Paper, 1990.

Prelec, D. (1998). The probability weighting function. Econometrica 60, pp. 497-528.

Prelec, D. (2000). Compound Invariant Weighting Functions in Prospect Theory. In D. Kahneman, A. Tversky (Eds). Choices, Values, and Frames. Russell Sage Foundation, Cambridge University Press.

Prelec, D., Loewenstein, G. (1991). Decision Making Over Time and Under Uncertainty: A Common Approach. Management Science, 37(7), pp. 770-786.

Rachlin, H. (2006). Notes on discounting. Journal of the Experimental Analysis of Behavior, 85, pp. 425-435.

Read, D. (2001). Is time discounting hyperbolic or subadditive? Journal of Risk and Uncertainty, 23(1), pp. 5-32.

Saito, K. (2008). Hyperbolic Discounting: It’s Just Allais Paradox. University of Tokyo, COE Discussion Papers, No. F-218.

Saito, K. (2009). A Relationship Between Risk and Time Preferences. Discussion Paper 1477, Northwestern University.

Samuelson, P. (1937). A note on Measurement of Utility. Review of Economic Studies, 4 pp. 155-161.

Sozou, P. D. (1998). On hyperbolic discounting and uncertain hazard rates. Proc. Royal Society London B 265, pp. 2015-2020.

Tversky A., Kahneman D., (1992). Advances in Prospect Theory: Cumulative Representation of Uncertainty. Journal of Risk and Uncertainty, vol. 5(4), October, pp 297-323.

Walther, H. (2008). S-shaped probability weighting and hyperbolic discounting – an intimate relationship. Working Paper, Vienna University of Economics and Business Administration.

Zauberman, G., Kyu Kim, B, Malkoc, S., Bettman, J. R. (2009). Discounting Time and Time Discounting: Subjective Time Perception and Intertemporal Preferences. Journal of Marketing Research, Vol. XLVI, pp. 543-556.