Statistical analysis and stochastic interest rate modeling for valuing the future with implications in climate change mitigation

Abstract

High future discounting rates favor inaction on present expend- ing while lower rates advise for a more immediate political action. A possible approach to this key issue in global economy is to take historical time series for nominal interest rates and inflation, and to construct then real interest rates and finally obtaining the resulting discount rate according to a specific stochastic model. Extended periods of negative real interest rates, in which inflation dominates over nominal rates, are commonly observed, occurring in many epochs and in all countries. This feature leads us to choose a well-known model in statistical physics, the Ornstein-Uhlenbeck model, as a basic dynamical tool in which real interest rates randomly fluctuate and can become negative, even if they tend to revert to a positive mean value. By covering 14 countries over hundreds of years we suggest different scenarios and include an error analysis in order to consider the impact of statistical uncertainty in our results. We find that only 4 of the countries have positive long-run discount rates while the other ten coun- tries have negative rates. Even if one rejects the countries where hyperinflation has occurred, our results support the need to consider low discounting rates. The results provided by these fourteen countries significantly increase the prior- ity of confronting global actions such as climate change mitigation. We finally extend the analysis by first allowing for fluctuations of the mean level in the Ornstein-Uhlenbeck model and secondly by considering modified versions of the Feller and lognormal models. In both cases, results remain basically unchanged thus demonstrating the robustness of the results presented.