Discounting the distant future: how much do uncertain rates increase valuations?

Abstract

We demonstrate that when the future path of the discount rate is uncertain and highly correlated, the distant future should be discounted at significantly lower rates than suggested by the current rate. We then use two centuries of US interest rate data to quantify this effect. Using both random walk and meanreverting models, we compute the ''certainty-equivalent rate'' that summarizes the effect of uncertainty and measures the appropriate forward rate of discount in the future. Under the random walk model we find that the certainty-equivalent rate falls continuously from 4% to 2% after 100 years, 1% after 200 years, and 0.5% after 300 years. At horizons of 400 years, the discounted value increases by a factor of over 40,000 relative to conventional discounting. Applied to climate change mitigation, we find that incorporating discount rate uncertainty almost doubles the expected present value of mitigation benefits. r

“Just give me a number!” Practical values for the social discount rate

“…More formally, the confidence interval surrounding any forecast widens with the length of the forecast. Furthermore, allowing for this uncertainty means that lower and lower discount rates should be used to discount consumption flows that occur farther and farther in the future (Newell and Pizer, 2003;Weitzman, 2001).…”

“…In the distant future, only the very lowest possible rate matters; all the higher rates result in discount factors that approach zero. Note that this motivation for time-declining rates is due solely to uncertainty and so does not imply time inconsistency in social choices (Azfar, 1999;Newell and Pizer, 2003).…”

“…After a given period of time, all future generations are essentially treated alike. As only the lowest possible rates apply to the far distant future, the choice of the specific rate for discounting intragenerational projects turns out not to matter very much for the evaluation of very long-term, intergenerational projects (Newell and Pizer, 2003).…”

Drovers’ Roads as Environmental Assets: Use Value for Recreational Purposes of the <i>Cañada Real del Reino de Valencia</i>

“…These two variables are not free from controversy in the aggregation process, as the estimated social benefit depends specifically on the values used. Newel and William (2003) [41] propose, for environmental valuations, that the rate should be reduced from 4% al 2% after 100 years and they advise using 1% if the time period considered exceeds 200 years. For our case, rates of between 1% and 6% were used, in order to be able to include the rate of 6%, which is the one which Spain's Ministry of Public Works (Ministerio de Fomento) uses as shown in Table 6.…”

The Impact of Climate Change on the Balanced Growth Equivalent: An Application of FUND

“…At the same time, our results mimic some key features of the Stern Review results: higher time preference rates and higher risk aversion always lead to lower impacts estimates. For time discounting, this is rather well established in the literature (e.g., Guo et al 2006;Newell and Pizer 2003). That higher η values lead to lower damages is less straight forward, as it controls two effects at the same time.…”