Paper: arXiv 2312.17157

Authors: J. Doyne Farmer, John Geanakoplos, Matteo G. Richiardi, Miquel Montero, Josep Perelló, Jaume Masoliver

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.

Complexity vs Empirical Score

  • Math Complexity: 6.0/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong empirical analysis using century-long dataset histories for the US and UK to address long-term real discount rates. It rigorously applies the Ornstein-Uhlenbeck process using Fourier transforms to handle negative real rates and yield curve inversions, linking quantitative finance directly to environmental economics.

Research Flowchart

  flowchart TD
    A[Research Goal: Estimate long-term discount rates for climate policy] --> B[Data Inputs: Century-long UK & US 3m bonds, 10y bonds, inflation]
    B --> C[Empirical Analysis: Observe real rates negative ~33% & yield curves inverted >33%]
    C --> D[Model Selection: Adopt Ornstein-Uhlenbeck Model to allow negative real rates]
    D --> E[Computation: Derive discount function via Fourier transforms & fit to data]
    E --> F[Findings: Estimated long-term rate is 1.7% UK and 2.2% US]
    F --> G[Policy Outcome: Supports Stern 1.4% rate, reinforcing immediate climate spending]