Li and Pizer in the short-run: A comment on discounting

Li and Pizer derived upper and lower bounds on the time-dependent social discount rate that both converge in the long run to the consumption rate of interest. They went on to recommend using the consumption rate of interest as the social discount rate for investments relating to climate change for which the bulk of the benefits accrue in the far future. However, the bounds can be quite wide in the short-run, providing little guidance for shorter term discounting. Here, we show that if uncertainty in the social discount rate is encoded in a uniform distribution, then its expected value converges much more rapidly to the consumption rate of interest. The implications of this for project evaluation are more complicated than in the deterministic case considered by Li and Pizer.