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Discounting the Distant Future: An Experimental Investigation

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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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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.

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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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Authors and Affiliations

  1. Weber State University, 3807 University Circle, Ogden, UT, 84408-3807 , USA

    Therese C. Grijalva

  2. Department of Agricultural Economics, Oklahoma State University, 411 Agricultural Hall, Stillwater, OK, 74078 , USA

    Jayson L. Lusk

  3. Texas A&M University, College Station, TX, 77843-2124 , USA

    W. Douglass Shaw

Authors
  1. Therese C. Grijalva
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  2. Jayson L. Lusk
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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
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Fig. 3
figure 3

Discount factor using stated bond cash-in dates and amounts

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Fig. 4
figure 4

Discount rates using stated bond cash-in dates and amounts

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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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