Discounting the Distant Future: How Much Do Uncertain Rates Increase Valuations?
Costs and benefits in the distant future—such as those associated with global warming, long-lived infrastructure, hazardous and radioactive waste, and biodiversity—often have little value today when measured with conventional discount rates. We demonstrate that when the future path of this conventional rate is uncertain and persistent (i.e., highly correlated over time), the distant future should be discounted at lower rates than suggested by the current rate. We then use two centuries of data on U.S. interest rates to quantify this effect. Using both random walk and mean-reverting models (which are indistinguishable based on historical data), we compute the certainty-equivalent rate—that is, the single discount rate that summarizes the effect of uncertainty and measures the appropriate forward rate of discount in the future. Using the random walk model, which we consider more compelling, we find that the certainty-equivalent rate falls from 3% now to 2% after 100 years, to 1% after 200 years, and down to 0.5% after 300 years. The mean-reverting model leads to a certainty-equivalent rate that remains above 3% for the next 200 years, then falls to 2% after 300 years and to 1% after 400 years. If we use these rates to value consequences at horizons of 400 years, the discounted value increases by a factor of 7,000 based on the random walk model and by a factor of 30 based on the mean-reverting model — both relative to conventional discounting. These results are relevant for a wide range of policy questions involving the distant future. Applying the random walk model to the consequences of climate change, for example, we find that inclusion of discount rate uncertainty doubles the expected present value of mitigation benefits. Other applications and alternative beliefs about the random walk–mean-reverting distinction are easily explored with our table of discount factors over time.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Cropper, Maureen L & Aydede, Sema K & Portney, Paul R, 1994. "Preferences for Life Saving Programs: How the Public Discounts Time and Age," Journal of Risk and Uncertainty, Springer, vol. 8(3), pages 243-65, May.
- Brown, Stephen J & Dybvig, Philip H, 1986. " The Empirical Implications of the Cox, Ingersoll, Ross Theory of the Term Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 41(3), pages 617-30, July.
- Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
- Sims, Christopher A., 1988.
"Bayesian skepticism on unit root econometrics,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 12(2-3), pages 463-474.
- Christopher A. Sims, 1988. "Bayesian skepticism on unit root econometrics," Discussion Paper / Institute for Empirical Macroeconomics 3, Federal Reserve Bank of Minneapolis.
- Ainslie, George, 1991. "Derivation of "Rational" Economic Behavior from Hyperbolic Discount Curves," American Economic Review, American Economic Association, vol. 81(2), pages 334-40, May.
- Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
- Charles L. Ballard & Don Fullerton, 1992.
"Distortionary Taxes and the Provision of Public Goods,"
Journal of Economic Perspectives,
American Economic Association, vol. 6(3), pages 117-131, Summer.
- Charles L. Ballard & Don Fullerton, 1990. "Distortionary Taxes and the Provision of Public Goods," NBER Working Papers 3506, National Bureau of Economic Research, Inc.
- William R. Cline, 1992. "Economics of Global Warming, The," Peterson Institute Press: All Books, Peterson Institute for International Economics, number 39.
- John Y. Campbell, 1995.
"Some Lessons from the Yield Curve,"
Harvard Institute of Economic Research Working Papers
1713, Harvard - Institute of Economic Research.
- Mandler, Michael, 1999.
"Dilemmas in Economic Theory: Persisting Foundational Problems in Microeconomics,"
Oxford University Press, number 9780195100877.
- Mandler, Michael, 2001. "Dilemmas in Economic Theory: Persisting Foundational Problems of Microeconomics," OUP Catalogue, Oxford University Press, number 9780195145755.
- Pizer, William A., 1999. "The optimal choice of climate change policy in the presence of uncertainty," Resource and Energy Economics, Elsevier, vol. 21(3-4), pages 255-287, August.
- Brown, Roger H. & Schaefer, Stephen M., 1994. "The term structure of real interest rates and the Cox, Ingersoll, and Ross model," Journal of Financial Economics, Elsevier, vol. 35(1), pages 3-42, February.
- Martin L. Weitzman, 1998.
Harvard Institute of Economic Research Working Papers
1843, Harvard - Institute of Economic Research.
- Heal, G., 1998. "Valuing the Future: Economic Theory and Sustainability," Papers 98-10, Columbia - Graduate School of Business.
- Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990.
"Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?,"
8905, Michigan State - Econometrics and Economic Theory.
- Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
- Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale University.
- Ball, Clifford A. & Torous, Walter N., 1996. "Unit roots and the estimation of interest rate dynamics," Journal of Empirical Finance, Elsevier, vol. 3(2), pages 215-238, June.
- Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
- Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-44, January.
- Lloyd B. Thomas, 1999. "Survey Measures of Expected U.S. Inflation," Journal of Economic Perspectives, American Economic Association, vol. 13(4), pages 125-144, Fall.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Weitzman, Martin L., 1998. "Why the Far-Distant Future Should Be Discounted at Its Lowest Possible Rate," Journal of Environmental Economics and Management, Elsevier, vol. 36(3), pages 201-208, November.
- Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1992. "Waiting to Invest: Investment and Uncertainty," The Journal of Business, University of Chicago Press, vol. 65(1), pages 1-29, January.
- Peter C.B. Phillips, 1985.
"Time Series Regression with a Unit Root,"
Cowles Foundation Discussion Papers
740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-84, March.
- Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, volume 1, number 5474.
- Cropper, Maureen & Laibson, David, 1998. "The implications of hyperbolic discounting for project evaluation," Policy Research Working Paper Series 1943, The World Bank.
- Chan, K C, et al, 1992.
" An Empirical Comparison of Alternative Models of the Short-Term Interest Rate,"
Journal of Finance,
American Finance Association, vol. 47(3), pages 1209-27, July.
- Tom Doan, . "RATS programs to replicate CKLS(1992) estimation of interest rate models," Statistical Software Components RTZ00035, Boston College Department of Economics.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
- Coleman Bazelon & Kent Smetters, 1999. "Discounting Inside the Washington D.C. Beltway," Journal of Economic Perspectives, American Economic Association, vol. 13(4), pages 213-228, Fall.
When requesting a correction, please mention this item's handle: RePEc:rff:dpaper:dp-00-45. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Webmaster)
If references are entirely missing, you can add them using this form.