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

TL;DR

This study empirically estimates long-term discount rates using century-long bond data, revealing negative real interest rates and yield curve inversions, and employs an Ornstein-Uhlenbeck model to fit the data, supporting substantial climate spending.

Contribution

It introduces a comprehensive empirical approach incorporating risk aversion and negative rates, using the Ornstein-Uhlenbeck model to estimate long-term discount rates from historical bond data.

Findings

Estimated long-term discount rate: 1.7% (UK), 2.2% (US)

Real interest rates are negative about a third of the time

Yield curves are inverted more than a third of the time

Abstract

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.