Time horizon and the discount rate

We discuss the selection of the socially efficient discount rate for public investment projects that entail costs and benefits in the far distant future. We show that the discount rate should be a decreasing function of time horizon under some specific restrictions on the distribution of uncertain growth and on preferences. We consider a logarithmic random walk for consumption. The benchmark result is that, in the absence of any risk of recession, the yield curve is decreasing if relative risk aversion is decreasing. Relaxing the assumption on the absence of recession requires more restrictions on preferences, as increasing relative prudence.