Abstract
High future discounting rates favor inaction on present expending 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 countries 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 priority 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.
Highlights
The presence of fluctuations can dramatically alter the functional form of the discounting function
Statistical analysis and stochastic interest rate modeling for valuing the future with implications in climate change mitigation nates 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
Our empirical analysis proves that real interest rates are often negative—roughly a quarter of the time—which implies that one must use a discount model that is compatible with this property
Summary
Real interest rates are nominal rates corrected by inflation so we need first of all to study nominal rates and inflation separately. The details of each sample are reported in table 1. Nominal rates can be obtained through the 10 years Government Bond Yield (see table 1 for further details). Following the standard procedure provided by the literature (see, for instance, [41]), we transform the annual rate β(t|T), where T = 10 years, into logarithmic rates, and denote the resulting nominal rates time series by n(t) = ln[1 + β(t|T )]. The inflation rate i(t) is estimated through the consumer price index (CPI) C(t) by. We have smoothed inflation rates with a 10 years forward moving average as this is again the standard procedure in these cases
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