Aggregate social discount rate derived from individual discount rates

In the economic evaluation of large public-sector projects, an aggregate social discount rate may be used in present worth comparison of alternatives. This paper uses the assumptions that individual discount rates are constant over time and approximately Normally distributed across the affected population, with mean μ and variance σ², to derive an aggregate discount function that is exponential in form but with time-dependent aggregate discount rate ρ(t) = μ − σ²t/2, where t is the time of occurrence of the cost or benefit. This equation agrees with numerical simulations. If σ² > 0, then the aggregate discount rate is less than the mean individual discount rate, and use of the time-dependent aggregate discount rate ρ(t) = μ − σ²t/2 instead of the constant discount factor ρ(t) = μ would result in larger discounted present values for public-sector projects for which the benefits lie far in the future. This could mean that public-sector investments that would be rejected under the assumption ρ(t) = μ might be justified using the time-dependent aggregate discount rate ρ(t) = μ − σ²t/2.