标题： 忽略遥远的未来：历史债券价格对长期贴现率意味着什么？ 显示英文标题

标题： Discounting the distant future: What do historical bond prices imply about the long term discount rate?

摘要： 我们通过引入风险价格来包括风险厌恶因素，对实际利率进行了详尽的实证研究。 从复杂系统科学及其跨学科方法的角度出发，我们使用债券定价理论来研究长期贴现率。 长达一个世纪的3个月债券、10年期债券和通货膨胀的历史记录使我们能够估算英国和美国的实际利率。 实际利率大约有三分之一的时间为负，实际收益率曲线超过三分之一的时间呈倒挂状态，有时倒挂幅度相当大。 这排除了大多数标准债券定价模型，这些模型是为假设为正的名义利率设计的。 因此，我们使用了Ornstein-Uhlenbeck模型，该模型允许负利率，并且与收益率曲线的倒挂情况有很好的匹配。 我们使用傅里叶变换的方法推导出贴现函数，并将其拟合到历史数据上。 估计的长期贴现率为英国的$1.7$% 和美国的$2.2$%。 Stern使用的$1.4$% 值比我们对英国长期回报率的估计值低不到一个标准差，比美国估计值低不到两个标准差。 所有这一切再次加强了对立即和大量支出以应对气候变化的支持。 显示英文摘要

摘要： We present a thorough empirical study on real interest rates by also including risk aversion through the introduction of the market price of risk. With the view of complex systems science and its multidisciplinary approach, we use the theory of bond pricing to study the long term discount rate. Century-long historical records of 3 month bonds, 10 year bonds, and inflation allow us to estimate real interest rates for the UK and the US. Real interest rates are negative about a third of the time and the real yield curves are inverted more than a third of the time, sometimes by substantial amounts. This rules out most of the standard bond pricing models, which are designed for nominal rates that are assumed to be positive. We therefore use the Ornstein-Uhlenbeck model which allows negative rates and gives a good match to inversions of the yield curve. We derive the discount function using the method of Fourier transforms and fit it to the historical data. The estimated long term discount rate is $1.7$ \% for the UK and $2.2$ \% for the US. The value of $1.4$ \% used by Stern is less than a standard deviation from our estimated long run return rate for the UK, and less than two standard deviations of the estimated value for the US. All of this once more reinforces the support for immediate and substantial spending to combat climate change.