Discounting an uncertain future

The objective of this paper is to determine the socially optimal discount rate for public investment projects that entail costs and benefits in the very long run. We suppose that there is an exogenous process for the growth of consumption per capita, which is stochastic. We first evaluate the determinants of the discount rate for a specific horizon when the representative agent has a recursive utility. We then explore the influence of the time horizon in the expected utility model. Under various conditions on preferences, as positive prudence, decreasing relative risk aversion or decreasing absolute risk aversion, we prove that (1) the fact that growth is uncertain reduces the efficient discount rate at any horizon, and that (2) this discount rate should be smaller for more distant futures. We characterize the asymptotic value of the discount rate. (C) 2002 Elsevier Science B.V. All rights reserved.