Risk-adjusted gamma discounting

Abstract

It is widely recognized that the economics of distant-future events, like climate change, is critically dependent upon the choice of a discount rate. Unfortunately, it is unclear how to discount distant-future events when the future discount rate itself is unknown. In previous work, an analytically-tractable approach called ‘‘gamma discounting’’ was proposed, which gave a declining discount rate schedule as a simple closed-form function of time. This paper extends the previous gamma approach by using a Ramsey optimal growth model, combined with uncertainty about future productivity, in order to ‘‘risk adjust’’ all probabilities by marginal utility weights. Some basic numerical examples are given, which suggest that the overall effect of risk-adjusted gamma discounting on lowering distant-future discount rates may be significant. The driving force is a ‘‘fear factor’’ from risk aversion to permanent productivity shocks representing catastrophic future states of the world.