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Discounting the Distant Future with Uncertain Rates

Costs and benefits in the distant future have little consequence today when valued with conventional discount rates. This is particularly relevant for assessing policies with effects hundreds of years in the future, such as mitigating the damages from global warming. Many authors and analysts have responded by arguing for the use of lower discount rates over longer horizons, based primarily on normative and stated preference arguments. We explore an alternative rationale for declining future discount rates based on uncertainty about future market interest rates. In particular, we show that when discount rates are uncertain and persistent (i.e., highly correlated over time), the distant future should be discounted at much lower rates than suggested by the average historical rate. The crucial question that we will explore is whether there is sufficient uncertainty and persistence in the historical data to suggest a significant effect in the future. To address this issue, we examine two centuries of historical data on U.S. interest rates by modeling their stochastic behavior over time, including their variance and autocorrelation. We specify the log of the interest rate as either a random walk or a meanreverting series. Although these models are not statistically distinguishable in the historical data, they have important consequences for the appropriate discount rate in the future. Based on the random walk model, the certainty-equivalent rate—that is, the single discount rate which summarizes the effect of uncertainty—falls from 3% now, to 2% after 100 years, down to 1% after 200 years, and to 0.5% after 300 years. Based on the mean-reverting model, however, the rate remains above 3% for the next 200 years, falling to 2% after 300 years, and 1% after 400 years. We then apply these rates to the valuation of future consequences from climate change. Based on a time profile of marginal benefits from carbon mitigation, we estimate a present value of about $7 per ton of carbon using a constant discount rate of 3.6%. While the mean-reverting model yields a modest 7% increase in this estimate, the random walk model indicates benefits of over $13 per ton of carbon—nearly double the estimates that ignore uncertainty. We conclude that uncertainty about future discount rates has the potential to dramatically alter valuations in the distant future and, when interest rates are viewed as a random walk, this uncertainty has important implications for the current debate on climate change mitigation. Although the historical data over the last 200 years does not statistically distinguish between the random walk and mean-reverting models, we find the random walk model more appealing based primarily on our view that mean rates in the distant past are less informative about the future than current rates.