Discounting the Distant Future: How Much Do Uncertain Rates Increase Valuations?

Abstract

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.