Yes, We Should Discount the Far-Distant Future at Its Lowest Possible Rate: A Resolution of the Weitzman–Gollier Puzzle

Abstract

In this paper the author proves that the Expected Net Future Value (ENFV) criterion can lead a risk neutral social planner to reject projects that increase expected utility. By contrast, the Expected Net Present Value (ENPV) rule correctly identifies the economic value of the project. While the ENFV increases with uncertainty over future interest rates, the expected utility decreases because of the planner's desire to smooth consumption across time. This paper therefore shows that Weitzman (1998) is "right" and that, within his economy, the far-distant future should be discounted at its lowest possible rate.JEL D61, E43, G12, G31, Q51

Positively Gamma Discounting: Combining the Opinions of Experts on the Social Discount Rate

“…The theoretical case for using ENPVs within environmental economics was presented by Weitzman () and subsequently discussed in detail by Gollier (), Freeman (), Gollier and Weitzman () and Traeger (), amongst others. In our online Appendix B we note that also has a long tradition in financial economics.…”

Harnessing the uncertainty monster: Putting quantitative constraints on the intergenerational social discount rate

“…In a final step, those candidates were integrated into a single certainty-equivalent declining discount rate (CE-DDR) using a process known as "Gamma Uncertainty and Social Discount Rates 14 discounting" (K. Arrow et al, 2013;Pearce et al, 2003;Weitzman, 2001), which is sometimes known instead as "Expected Net Present Value". Freeman, 2010;Gollier, 2002;Weitzman, 1998Weitzman, , 2001. One outcome of this research has been that it is not the discount rates that are to be averaged (e.g., by computing the mean of 1% and 7%, viz.…”

“…A common theme of this work is the convergence to a low value over time (e.g., K. Arrow et al, 2013; K. J. Arrow et al, 2014;Freeman, 2010;Freeman & Groom, 2015;Gollier, 2002;Gollier & Hammitt, 2014;Groom et al, 2007;Newell & Pizer, 2003;Pearce et al, 2003;Weitzman, 2001). Our results confirm this convergence under a new set of circumstances, when various different sources of uncertainty and ambiguity are considered and when future growth rates are modeled based on a robust historical relationship between temperatures and economic production.…”

Gamma discounters are short-termist

“…If the compounded interest rate for this maturity is r, the future benefit of the project can be transferred to the present by a loan of exp( ) F rt  today to be reimbursed at the termination date t. The portfolio containing the project and the loan has a single payoff which occurs today and is equal to the project's tends asymptotically to the smallest plausible interest rate. This argument for a decreasing term structure of the discount rate was first presented by Weitzman (1998Weitzman ( , 2001, followed by Newell and Pizer (2003), Hepburn and Groom (2007), Groom, Koundouri, Panopoulou and Pantelidis (2007), Gollier, Koundouri and Pantelidis (2008), Freeman (2010), Freeman and Groom (2010), Traeger (2013), Arrow et alii (2013Arrow et alii ( , 2014, and Farmer, Geanakoplos, Masoliver, Montero and Perello (2014) for example. Because Weitzman (2001) used a gamma distribution for r, this approach based on the expected NPV is often referred to as "gamma discounting".…”