The choice of discount rate has a significant impact on net benefit estimates when costs today have benefits over long time horizons. Standard U.S. government practice for cost–benefit analysis is to bound such analysis using two alternative rates. These rates are meant to represent the rate of return paid by capital investment and the rate received by consumers. Previous work has shown this approach legitimately bounds the analysis—but only when future benefits accrue directly to consumers either in a two-period model or as a perpetuity. We generalize to consider arbitrary patterns of future benefits, accruing either directly to consumers or indirectly through future investment. We derive an expression for the appropriate discount rate and show that it converges to the consumption rate for benefits increasingly far into the future. More generally, the bounding rates depend on the temporal pattern of the undiscounted dollars. As an application, we estimate the appropriate discount rate for climate change damages from carbon dioxide, finding it lies in a narrow range ( ±0.5 percent) around the consumer rate of interest.

当今天的成本在很长一段时间内都有收益时，折现率的选择会对净收益估计产生重大影响。美国政府成本效益分析的标准做法是使用两种替代率来限制这种分析。这些利率旨在表示资本投资所支付的回报率和消费者所获得的回报率。先前的工作表明，这种方法合理地限制了分析的范围，但是只有当未来的利益以两个周期的模型或永久地直接累积给消费者时，这种分析方法才是合理的。我们一般性地考虑任意形式的未来收益，这些收益可以直接产生给消费者，也可以通过未来投资间接产生。我们得出了适当折现率的表达式，并表明它已收敛到消费率，从而使收益越来越远。更普遍，边界率取决于未贴现美元的时间模式。作为一种应用，我们估计了二氧化碳对气候变化造成损害的适当折现率，发现它在消费者的消费率附近处于窄范围内（±0.5％）。