# Gamma discounting and expected net future value

with Groom, *Journal of Environmental Economics and Management*,**53**:1, 99-109, 2007.

Recent research suggests that the long term future should be discounted with a declining discount rate. One such line of research, exemplified by Weitzman [Gamma discounting, Amer. Econ. Rev. 91 (2001) 261–271], shows that the certainty equivalent discount rate is declining when future capital productivity is uncertain. However, in a recent paper Gollier [Maximising the expected net future value as an alternative strategy to gamma discounting, Finan. Res. Lett. 1 (2004) 85–89] puts forward a puzzle that casts doubt on the validity of this conclusion. He asserts that using expected net future value, rather than conventional expected net present value, implies that the certainty equivalent discount rate *increases* over time. This paper resolves the apparent puzzle by encompassing the models of Gollier [Maximising the expected net future value as an alternative strategy to gamma discounting, Finan. Res. Lett. 1 (2004) 85–89] and Weitzman [Gamma discounting, Amer. Econ. Rev. 91 (2001) 261–271]. In fact, Gollier proves that as the *evaluation date* moves further into the future, the discount rate at a given point in time will increase. However, given a particular evaluation date, the schedule of discount rates is declining.