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Discounting the Distant Future: An Experimental Investigation

Abstract

We use a laboratory experiment to elicit discount rates over a 20-year time horizon using government savings bonds as a payment vehicle. When using a constant (exponential) discount rate function, we find an implied average discount rate of 4.9 %, which is much lower than has been found in previous experimental studies that used time horizons of days or months. However, we also find strong support for non-constant, declining discount rates for longer time horizons, with an extrapolated implied annual discount rate approaching 0.5 % in 100 years. There is heterogeneity in discount rates and risk preferences in that people with more optimistic beliefs about technological progress have higher discount rates. These findings contribute to the debate over the appropriate discount rate to use in comparing the long-term benefits of climate change mitigation to the more immediate costs.

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Fig. 1
Fig. 2

Notes

  1. See Dasgupta (2008) or Weitzman (2007) for some discussion on the interpretation of \(\eta \) and normative arguments for its magnitude; or Stern (2006), Becker et al. (2010), or Nordhaus (2007) for similar discussions on \(\delta \).

  2. The issue of hyperbolic discounting has been considered in the climate change debate by authors such as Hepburn et al. (2010), Groom et al. (2005), Karp (2005), Weitzman (1998).

  3. A copy of the full set of experimental instructions is available at http://faculty.weber.edu/tgrijalva/Experiment%20V1.pdf.

  4. The payouts for the randomly selected subjects included: a $25 payment tomorrow, a $95 payment tomorrow, two $100 payments in 1 year, and 3 savings bonds, two $1,000 bonds and one $500 bond. Further, a $1,000 bond was purchased for one subject who participated in the pretests.

  5. The Series EE paper bonds are stated as 30 years bonds, but are guaranteed to be worth the face value at 20 years. It should be noted that we explored a number of security and savings instruments with varying maturity dates. Advantages of Series EE bonds include the fact that this is among the longest-term securities in the market and is relatively risk-free, the ability to name a beneficiary different than the purchaser (i.e. gift), and the fact that the paper bonds have a stated face value, where they are purchased at a discount (half face value). Not all of these features are true of other treasury securities or electronic Series EE bonds. Similarly, we did not use certificates of deposit due to the fact that they have shorter maturity dates (typically ranging from 3 to 5 years) with future values being a function of the fixed interest rate offered by banks and early withdrawal penalties. For information on treasury securities and programs go to http://treasurydirect.gov/indiv/products/products.htm.

  6. Andreoni and Sprenger (2012) stress the importance ensuring that all aspects of the choices must be equivalent except for the timing of the payment. Researchers should equalize payment transaction costs across all time periods and take steps to ensure confidence or trust in receipt of payment.

  7. Andersen et al. 2006 randomize the sequence of time horizon MPL tables to test for order and learning effects. They find that the second task is associated with slightly higher, and statistically significant, discount rates, which can be attributed to pure order effects (although, they note that these order effects are not very large). Further, they are unable to reject they hypothesis that the average rates for task 2 and 3 are the same. This suggests that there is some learning, but only after the initial task.

  8. A note in regards to the longer-term intertemporal choice exercises of 1 or 20 years: while this might imply more noise surrounding our estimates of the 1-year discount rates than that surrounding the 20-year discount rate, both discount rates are estimated without bias. For future research, one might design the variation in monetary outcomes across time horizons in any number of different ways, testing for the robustness of the results we obtain.

  9. Our experimental tasks did not actually involve any choices over risky outcomes; however, such choices are not required to estimate the parameter \(r\), which simply provides an estimate of the extent of diminishing marginal utility. The use of multiple payout amounts ranging from $5 to $1,000 provides ample variation in payouts to detect curvature in the utility function.

  10. Interestingly, a much smaller percentage of those who did not know about the early redemption option said it would have influenced their decision (19 of 50, or about 38 %).

  11. Income across the subject pool does not vary enough to allow the use of this variable in estimation of the model, and many students provide misleading answers to income questions, as they do not consider all sources if income in their responses.

  12. An anonymous reviewer raised an interesting question in regards to the bond, “Is there a difference between possessing the good and not possessing the good?” While we do not have an a priori expectation, the reviewer did note that from a pure rate of time preference standpoint, it should not matter because the bond removes some of the uncertainty or transaction costs associated with a cash payment in 20 years. It is worth considering this question as laboratory experiments are refined to handle long-term horizons and possible confounds.

References

  • Alberini A, Chiabai A (2007) Discount rates in risk versus money and money versus money tradeoffs. Risk Anal 27(2):483–491

    Article  Google Scholar 

  • Alberini A, Cropper M, Krupnick A, Simon NB (2006) Willingness to pay for mortality risk reductions: does latency matter? J Risk Uncertain 32(3):231–245

    Article  Google Scholar 

  • Alberini A, Ščasný M (2011) Context and the VSL: evidence from a stated preference study in Italy and the Czech Republic. Environ Res Econ 49(4):511–538

    Article  Google Scholar 

  • Andersen S, Harrison GW, Lau MI, Rutsröm EE (2008) Eliciting risk and time preferences. Econometrica 76(3/May):583–618

    Article  Google Scholar 

  • Andersen S, Harrison GW, Lau MI, Rutsröm EE (2006) Elicitation using multiple price list formats. Exp Econ 9:383–405

    Article  Google Scholar 

  • Andreoni J, Sprenger C (2012) Estimating time preferences from convex budgets. Am Econ Rev 102(7):3333–3356

    Google Scholar 

  • Anthoff D, Tol RS, Yohe GW (2009) Risk aversion, time preference and the social cost of carbon. Environ Res Lett 4 doi:10.1085/1748-9326/4/2/024002

  • Atkinson G, Dietz S, Helfgeson J, Hepburn CJ, Saelen H (2009) Siblings, not triplets: social preferences for risk, inequality and time in discounting climate change. Economics: The Open-Access, Open-Assessment E-Journal 3

  • Becker GS, Murphy KM, Topel RH (2010) On the economics of climate change. B.E. J Econ Anal Policy 10(2). doi:10.2202/1935-1682.2854

  • Bond CA, Larson DM (2009) Joint estimation of discount rates and willingness to pay for public goods. Ecol Econ 68:2751–2759

    Article  Google Scholar 

  • Booij AS, van Praag BMS (2009) A simultaneous approach to the estimation of risk aversion and the subjective time discount rate. J Econ Behav Org 70:374–388

    Article  Google Scholar 

  • Coller M, Williams MB (1999) Eliciting individual discount rates. Exp Econ 2:107–127

    Google Scholar 

  • Cropper ML, Aydede SK, Portney P (1994) Preferences for life saving programs: how the public discounts time and age. J Risk Uncertain 8:243–265

    Article  Google Scholar 

  • Dasgupta P (2008) Discounting climate change. J Risk Uncertain 37:141–169

    Article  Google Scholar 

  • Dasgupta P (2011) Reply and Response to John E. Roemer. Environ Res Econ Ethics Int Distrib. doi:10.1007/s10640-011-9496-4

  • Fechner G (1966) Elements of psychophysics, Vol. 1. Holt, Rinehart and Winston, New York (originally published, 1860)

  • Frederick S, Loewenstein G, O’Donoghue T (2002) Time discounting and time preference: a critical review. J Econ Lit XL:351–401

    Article  Google Scholar 

  • Gerber A, Rohde KIM (2010) Risk and preference reversals in intertemporal choice. J Econ Behav Org 76:654–668

    Article  Google Scholar 

  • Goulder L, Williams RC (2012) The choice of discount rate for climate change policy evaluation. NBER Working paper 18301

  • Grijalva TC, Berrens RP, Shaw WD (2011) Species preservation versus development: an experimental investigation under uncertainty. Ecol Econ 70:995–1005. doi:10.1016/j.ecolecon.2011.01.002

    Article  Google Scholar 

  • Groom B, Hepburn C, Koundouri P, Pearce D (2005) Declining discount rates: the long and the short of it. Environ Res Econ 32:445–493. doi:10.1007/s10640-005-4681-y

    Article  Google Scholar 

  • Gruber J, Kőszegi B (2001) Is addiction “Rational”? theory and evidence. Q J Econ 116(4):1261–1303

    Article  Google Scholar 

  • Hardisty DJ, Thompson KJ, Krantz DH, Weber EU (2012) How to measure discount rates? An experimental comparison of three methods. Discussion paper, Columbia University

  • Harrison GW, Lau MI, Rutsröm EE (2010) Individual discount rates and smoking: evidence from a field experiment in Denmark. J Health Econ 29:708–717. doi:10.1016/j.jhealeco.2010.06.006

    Article  Google Scholar 

  • Harrison GW, Lau MI, Rutsröm EE (2009) Risk attitudes, randomization to treatment, and self-selection into experiments. J Econ Behav Org 70:498–507

    Article  Google Scholar 

  • Harrison GW, Lau MI, Williams MB (2002) Estimating individual discount rates in Denmark: a field experiment. Am Econ Rev 92(5):1606–1617

    Article  Google Scholar 

  • Harrison GW, List JA (2004) Field experiments. J Econ Lit 42(4):1009–1055

    Article  Google Scholar 

  • Heal G (2009) Climate economics: a meta-review and some suggestions for future research. Rev Environ Econ Policy 3:4–21. doi:10.1093/reep/ren014

    Article  Google Scholar 

  • Herrnstein RJ (1981) Self-control as response strength. In: Bradshaw CM, Szabadi E, Lowe CF (eds) Quantification of steady-state operant behavior. North-Holland, Amsterdam

    Google Scholar 

  • Hepburn C, Duncan S, Papachristodoulou A (2010) Behavioural economics, hyperbolic discounting and environmental policy. Environ Res Econ 46:189–206. doi:10.1007/s10640-010-9354-9

    Article  Google Scholar 

  • Holt CA, Laury SK (2002) Risk aversion and incentive effects. Am Econ Rev 92(5):1644–1655

    Article  Google Scholar 

  • Horowitz JK, Carson RT (1990) Discounting statistical lives. J Risk Uncertain 3(4):403–413

    Article  Google Scholar 

  • Ida T, Goto R (2009) Simultaneous measurement of time and risk preferences: stated preference discrete choice modeling analysis depending on smoking behavior. Int Econ Rev 50:1169–1182

    Article  Google Scholar 

  • Kan K (2007) Cigarette smoking and self-control. J Health Econ 26:61–81

    Article  Google Scholar 

  • Karp L (2005) Global warming and hyperbolic discounting. J Public Econ 89:261–282

    Article  Google Scholar 

  • Koopmans TC (1960) Stationary ordinal utility and impatience. Econometrica 28(2):287–309

    Article  Google Scholar 

  • Kovacs KF, Larson DM (2008) Identifying Individual Discount Rates and Valuing Open Space with Stated-Preference Models. Land Economics 84:209–24

    Google Scholar 

  • Laibson D (1994) Essays in hyperbolic discounting. Ph.D. dissertation, MIT

  • Laibson D (1997) Golden eggs and hyperbolic discounting. Q J Econ 112:443–477

    Article  Google Scholar 

  • Laux FL (2000) Addiction as a market failure: using rational addiction results to justify Tobacco regulation. J Health Econ 19:421–437

    Article  Google Scholar 

  • Loewenstein G, Prelec D (1992) Anomalies in intertemporal choice: evidence and an interpretation. Q J Econ 107(2):573–597

    Article  Google Scholar 

  • Luce RD (1959) Individual choice behavior. Wiley Press, New York

    Google Scholar 

  • Lusk JL, Schroeder TC (2004) Are choice experiments incentive compatible? A test with quality differentiated beef steaks. Am J Agri Econ 86(2):467–482

    Article  Google Scholar 

  • Mazur JE (1987) An adjustment procedure for studying delayed reinforcement. In: Commons ML, Mazur JE, Nevin JA, Rachlin H (eds) The effect of delay and intervening events on reinforcement value. Erlbaum, Hillsdale

    Google Scholar 

  • McFadden D (1974) Conditional logit analysis of qualitative choice behavior. In: Zarembka P (ed) Frontiers in econometrics. Academic Press, New York, pp 105–142

    Google Scholar 

  • Meyer A (2013) Intertemporal valuation of river restoration. Environ Res Econ 54:41–61

    Article  Google Scholar 

  • Moore MA, Boardman AE, Vining AR, Weimer D, Greenberg DH (2004) Just give me a number! Practical values for the social discount rate. J Policy Anal Manag 23(4):789–812

    Google Scholar 

  • Moore MA, Boardman AE, Vining AR (2013) More appropriate discounting: the rate of social time preference and the value of the social discount rate. J Benefit-Cost Anal 4(1):1–16

    Article  Google Scholar 

  • Nordhaus WD (2007) A review of the Stern review on the economics of climate change. J Econ Lit XLV(3):686–702

    Article  Google Scholar 

  • Nordhaus WD (1994) Managing the global commons: the economics of climate change. MIT Press, Cambridge

    Google Scholar 

  • Plott C (1996) Rational individual behavior in markets and social choice processes: the discovered preference hypothesis. In: Arrow K, Colombatto K, Perlemann M, Schmidt C (eds) The rational foundations of economic behavior. Macmillan and St Martin Press, London, pp 225–50

    Google Scholar 

  • Prince JT, Shawhan DL (2011) Is time inconsistency primarily a male problem? Appl Econ Lett 18(6):501–504

    Article  Google Scholar 

  • Ramsey F (1928) A mathematical theory of saving. Econ J 38:543–559

    Article  Google Scholar 

  • Richards TJ, Hamilton SF (2012) Obesity and hyperbolic discounting: an experimental analysis. J Agri Res Econ 37(2):181–198

    Google Scholar 

  • Schilizzi S (2006) Discounting the distant future: why so many voices and so little consensus? In: Pannell DJ, Schilizzi S (eds) Economics and the future: time and discounting in private and public decision making, chapter 11. Edward Elgar Press

  • Schunk D, Winter J (2009) The relationship between risk attitudes and heuristics in search tasks: a laboratory experiment. J Econ Behav Org 71:347–360

    Article  Google Scholar 

  • Stern N (2008) The economics of climate change. Am Econ Rev Papers Proc 98:1–37. doi:10.157/aer.98.2.1

    Article  Google Scholar 

  • Stern NH (2006) The stern review of the economics of climate change. Cambridge University Press, Cambridge

    Google Scholar 

  • Viscusi VK, Huber J, Bell J (2008) Estimating discount rates for environmental quality from utility-based choice experiments. J Risk Uncertain 37:199–220

    Article  Google Scholar 

  • Vossler C, Doyon M, Rondeau D (2012) Truth in consequentiality: theory and field evidence on discrete choice experiments. Am Econ J 4(4):145–171

    Google Scholar 

  • Warner JT, Pleeter S (2001) The personal discount rate: evidence from military downsizing programs. Am Econ Rev 91(1):33–53

    Article  Google Scholar 

  • Weitzman ML (2007) A review of the stern review on the economics of climate change. J Econ Lit XLV(3):703–724

    Article  Google Scholar 

  • Weitzman ML (1998) Why the far-distant future should be discounted at its lowest possible rate. J Environ Econ Manag 36:201–208

    Google Scholar 

  • Winkler R (2009) Now or never: environmental protection under hyperbolic discounting. Economics: The Open Access Journal, 3

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Acknowledgments

The authors thank Glenn Harrison and Greg Parkhurst for their careful and constructive comments on an initial design of the experiment instrument, participants at seminars at the University of Denver and Texas A&M University (Department of Psychology) for feedback, Partha Dasgupta for his comments and sending a forthcoming paper of his, and Andrea Galeotti, David Hardisty, Anthony Kwasnica, and Edward Morey for their comments on an earlier draft of the manuscript. Two anonymous reviewers for this journal made very helpful comments which have led to improvements in this paper. Grijalva acknowledges funding from the Hemingway family. Shaw and Lusk acknowledge funding from USDA NIFA Hatch grants.

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Correspondence to Jayson L. Lusk.

Appendix A

Appendix A

Table 5 presents models using stated bond cash-in dates and amounts (to be contrasted with Table 3 which uses terminal, “objective” cash in dates and amounts for bond). Figures 3 and 4 present the discount factors and rates when using the stated bond cash-in dates and amounts (to be contrasted with Figs. 1 and 2 which are based on the terminal cash in dates).

Table 5 Model results using stated bond cash-in dates and amounts
Fig. 3
figure 3

Discount factor using stated bond cash-in dates and amounts

Fig. 4
figure 4

Discount rates using stated bond cash-in dates and amounts

In Table 6, we present the results for the constant discounting model, where we interact the key shape coefficients or parameters of interest (discount factor and coefficient of relative risk aversion) with climate questions, experimental treatments and demographic variables. This is presented as a comparison to Table 4.

Table 6 Constant discounting model with climate questions, experimental treatments and demographic variables

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Grijalva, T.C., Lusk, J.L. & Shaw, W.D. Discounting the Distant Future: An Experimental Investigation. Environ Resource Econ 59, 39–63 (2014). https://doi.org/10.1007/s10640-013-9717-0

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Keywords

  • Discount rate
  • Hyperbolic discount rates
  • Time inconsistent preference
  • Climate change
  • Experiment