Journal of Risk and Uncertainty

, Volume 46, Issue 2, pp 133–173 | Cite as

Estimating discount factors for public and private goods and testing competing discounting hypotheses

  • Andrew Meyer


The observation of declining discount rates in experimental settings has led many to promote hyperbolic discounting over standard exponential discounting as the preferred descriptive model of intertemporal choice. I develop a new framework, consistent with the random utility model, which directly models the intertemporal utility function and produces explicit maximum likelihood estimates of discounting parameters. I apply this estimation method to a stated-preference survey of river basin cleanup options and revealed-preference lottery payment choices. Formal statistical tests fail to find evidence in support of hyperbolic or quasi-hyperbolic discounting. Annual discount rates range from ten to fourteen percent across the data sets and empirical specifications.


Discounting Hyperbolic Random utility Intertemporal choice 

JEL Classifications

D90 Q25 Q53 H43 



I thank Nicholas Flores for helpful comments concerning the survey design and data collection, for allowing me to borrow liberally from his MRB description, and for guidance throughout my dissertation process. I thank Randy Walsh for helpful comments at the inception of this research. I thank two anonymous reviewers for multiple insightful comments that greatly enhanced the quality of this paper. Finally, I thank participants at the 2008 AERE Sessions at the Summer Meeting of the AAEA and at the 10th Occasional Workshop on Environmental and Resource Economics at UC Santa Barbara.


  1. Alberini, A., & Chiabai, A. (2007). Discount rates in risk versus money and money versus money tradeoffs. Risk Analysis, 27(2), 483–498. M3: doi: 10.1111/j.1539-6924.2007.00899.x.CrossRefGoogle Scholar
  2. Andersen, S., Harrison, G.W., Lau, M.I., Rutstrom, E.E. (2008). Eliciting risk and time preferences. Econometrica, 76(3), 583–618.CrossRefGoogle Scholar
  3. Andreoni, J., & Sprenger, C. (2010a). Estimating time preferences from convex budgets. Working Paper.Google Scholar
  4. Andreoni, J., & Sprenger, C. (2010b). Risk preferences are not time preferences: discounted expected utility with a disproportionate preference for certainty. Working Paper.Google Scholar
  5. Bosworth, R., Cameron, T.A., DeShazo, J.R. (2006). Preferences for preventative public health policies with jointly estimated rates of time preference. Working paper.Google Scholar
  6. Cairns, J., & van der Pol, M. (1997). Saving future lives. A comparison of three discounting models. Health Economics, 6(4), 341–350.CrossRefGoogle Scholar
  7. Cairns, J., & van der Pol, M. (2000). Valuing future private and social benefits: the discounted utility model versus hyperbolic discounting models. Journal of Economic Psychology, 21(2), 191–205.CrossRefGoogle Scholar
  8. Cameron, T.A., & Gerdes, G.R. (2003). Eliciting individual-specific discount rates. Working Paper.Google Scholar
  9. Clotfelter, C.T., Cook, P.J., Edell, J.A., Moore, M. (1999). State lotteries at the turn of the century: report to the national gambling impact study commission. Available online:
  10. Coller, M., & Williams, M.B. (1999). Eliciting individual discount rates. Experimental Economics, 2(2), 107–127.Google Scholar
  11. DeShazo, J.R., & Fermo, G. (2002). Designing choice sets for stated preference methods: the effects of complexity on choice consistency. Journal of Environmental Economics and Management, 44(1), 123–143.CrossRefGoogle Scholar
  12. Frederick, S., Loewenstein, G., O’Donoghue, T. (2002). Time discounting and time preference: a critical review. Journal of Economic Literature, 40(2), 351–401.CrossRefGoogle Scholar
  13. Harrison, G.W., Lau, M.I., Williams, M.B. (2002). Estimating individual discount rates in Denmark: a field experiment. American Economic Review, 92(5), 1606–1617.CrossRefGoogle Scholar
  14. Harvey, C.M. (1986). Value functions for infinite-period planning. Management Science, 32(9), 1123–1139.CrossRefGoogle Scholar
  15. Herrnstein, R. (1981). Self-control as response strength. In C. M. Bradshaw, E. Szabadi, C. F. Lowe (Eds.), Quantification of steady-state operant behavior (pp. 3–20). New York: Elsevier/North-Holland.Google Scholar
  16. Horowitz, J.K., & Carson, R.T. (1990). Discounting statistical lives. Journal of Risk and Uncertainty, 3(4), 403–413.CrossRefGoogle Scholar
  17. Huber, J., & Zwerina, K. (1996). The importance of utility balance in efficient choice designs. Journal of Marketing Research, 33(3), 307–317.CrossRefGoogle Scholar
  18. Johannesson, M., & Johansson, P.-O. (1997a). Quality of life and the WTP for an increased life expectancy at an advanced age. Journal of Public Economics, 65(2), 219–228.CrossRefGoogle Scholar
  19. Johannesson, M., & Johansson, P.-O. (1997b). The value of life extension and the marginal rate of time preference: a pilot study. Applied Economics Letters, 4, 53.CrossRefGoogle Scholar
  20. Keller, L.R., & Strazzera, E. (2002). Examining predictive accuracy among discounting models. Journal of Risk and Uncertainty, 24(2), 143–160.CrossRefGoogle Scholar
  21. Kirby, K.N., & Marakovic, N.N. (1995). Modeling myopic decisions: evidence for hyperbolic delay-discounting within subjects and amounts. Organizational Behavior and Human Decision Processes, 64(1), 22–30.CrossRefGoogle Scholar
  22. Laibson, D. (1997). Golden eggs and hyperbolic discounting. Quarterly Journal of Economics, 112(2), 443–477.CrossRefGoogle Scholar
  23. Lee, L.-F. (1999). Statistical inference with simulated likelihood functions. Econometric Theory, 15(3), 337–360.CrossRefGoogle Scholar
  24. Loewenstein, G., & Prelec, D. (1992). Anomalies in intertemporal choice: evidence and an interpretation. Quarterly Journal of Economics, 107(2), 573–597.CrossRefGoogle Scholar
  25. Mathworks, T. (2006). Matlab.Google Scholar
  26. Mazur, J.E. (1987). An adjustment procedure for studying delayed reinforcement. In M. L. Commons, J. E. Mazur, J. A. Nevin, H. Rachlin (Eds.), Quantitative analysis of behaviour: the effect of delay and intervening events on reinforcement value. Hillsdale: Erlbaum.Google Scholar
  27. Minnesota River Basin Data Center (2007). Minnesota river basin data center. Available at Accessed 15 Nov 2007.
  28. Phelps, E.S., & Pollak, R.A. (1968). On second-best national saving and game-equilibrium growth. The Review of Economic Studies, 35(2), 185–199.CrossRefGoogle Scholar
  29. Read, D. (2001). Is time-discounting hyperbolic or subadditive? Journal of Risk and Uncertainty, 23(1), 5–32.CrossRefGoogle Scholar
  30. Samuelson, P.A. (1937). A note on measurement of utility. The Review of Economic Studies, 4(2), 155–161.CrossRefGoogle Scholar
  31. Slonim, R., Carlson, J., Bettinger, E. (2007). Possession and discounting behavior. Economics Letters, 97(3), 215–221.CrossRefGoogle Scholar
  32. Thaler, R. (1981). Some empirical evidence on dynamic inconsistency. Economics Letters, 8(3), 201–207.CrossRefGoogle Scholar
  33. Train, K.E. (2003). Discrete choice methods with simulation. New York: Cambridge University Press.CrossRefGoogle Scholar
  34. United States Census Bureau (2007). American factfinder: 2007 American community survey 3-year estimates.Google Scholar
  35. University of Houston Center for Public Policy (2007). Demographic survey of Texas lottery players 2007. Available at Accessed 1 Oct 2010.
  36. University of Houston Center for Public Policy (2008). Demographic survey of Texas lottery players 2008. Available at Accessed 1 Oct 2010.
  37. van der Pol, M., & Cairns, J. (2001). Estimating time preferences for health using discrete choice experiments. Social Science and Medicine, 52(9), 1459–1470.CrossRefGoogle Scholar
  38. Viscusi, W.K., Huber, J., Bell, J. (2008). Estimating discount rates for environmental quality from utility-based choice experiments. Journal of Risk and Uncertainty, 37(2–3), 199–220.CrossRefGoogle Scholar
  39. Warner, J.T., & Pleeter, S. (2001). The personal discount rate: evidence from military downsizing programs. American Economic Review, 91(1), 33–53.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of EconomicsOhio Wesleyan UniversityDelawareUSA

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