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

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

“…x are also consistent across these models (see [36]). Despite similar parameter estimates, the mean-reverting and random walk models paint starkly different pictures of the future.…”

“…1. We also note that our basic results are robust to the market interest rate used, the approach selected for inflation adjustment, and whether the data are smoothed before estimation; see [36] for further detail.…”

“…Based on these nominal rates, we create a series of real interest rates by subtracting, after 1950, a measure of expected inflation using the Livingston Survey of professional economists [45], also described in [36]. We then convert these rates to their continuously compounded equivalents.…”

Éléments sur l'actualisation et l'environnement

“…L'intuition de ce résultat tient dans le fait que la bonne façon de faire est de prendre l'espérance sur tous les états du monde non pas des taux d'escompte mais des facteurs d'escompte, et qu'à la limite l'équivalent-certain des facteurs d'escompte correspond au taux d'escompte minimum, parce que le passage du temps a rendu tous les autres taux d'escompte insigni…ants par rapport au taux minimum. Newell et Pizer (2003) soulignent que le résultat de Weitzman est fondé sur le fait que le taux d'escompte est non seulement incertain mais aussi persistant, extrêmement corrélé au cours du temps (chez Weitzman, le vrai taux d'escompte, une fois l'incertitude levée, sera le même à toutes les périodes, forme extrême de persistance). Intuitivement on sent bien qu'une incertitude sans persistance aura peu d'e¤et : tout taux élevé à une période pourra être compensé par un taux faible à une autre.…”

Delay Discounting and Social Policy Issues

“…But discounting can be applied to other outcomes and, in fact, a large literature continues to emerge in the field of economics on the discounting of environmental policies (e.g., li & lofgren, 2000;Newell & Pizer, 2003). Psychologists have also started to measure discounting of a wide range of outcomes as well as to try to understand how the discounting of these outcomes relates to the discounting of money.…”