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

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 with risk aversion, 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 t 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. This lends support for substantial immediate spending to combat climate change.