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, 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 4%, to 2% after 100 years, 1% after 200 years, and 0.5% after 300 years. If we use these rates to value consequences at horizons of 400 years, the discounted value increases by a factor of over 40,000 relative to conventional discounting. Applying the random walk model to the consequences of climate change, we find that inclusion of discount rate uncertainty almost doubles the expected present value of mitigation benefits.