
The Ramsey discounting formula for a hidden-state stochastic growth process
The paper highlights how the choice of an appropriate discount rate is a critical issue in economics, and arguably more so for projects involving long time horizons. In particular, environmental projects and activities whose effects will be felt in the future pose significant challenges. The paper models such challenges as an evolving hidden-state stochastic process.
Please login or join for free to read more.

OVERVIEW
Report’s relevance and ESG
This proposal is relevant to investors who seek to incorporate ESG factors into decision-making processes. ESG issues related to environmental risks, such as climate change, present unique challenges due to their long-time horizons. As a result, this paper provides a methodology for addressing uncertainty regarding discount rates for such investments. By creating a model that captures this uncertainty, investors can estimate discount rates for such investments and incorporate them into financial decision-making processes.
The Ramsey discounting formula
The paper derives a simple expression for the time-declining Ramsey discount rate. The underlying trend growth rate is an unobservable random walk hidden by noisy transitory shocks and recoverable only as a probability distribution through Bayesian updating. It analysed the components of this hidden-state Ramsey discounting formula then discusses the possible implications and applications.
Background and motivation
As technological progress and long-term prospects for growth are difficult to predict, Weitzman emphasises that there is no deep reason of principle that allows us to extrapolate past growth rates into the distant future. As a result, it is essential to recognise that we need to deal with fuzzy distant uncertainty to infer long-term future discount rates.
Growth rates as random walks
The paper breaks time into discrete periods represented by the integer-valued variable t, where present corresponds to time zero, future times correspond to integer values t > 0, and past times correspond to integer values t < 0. Consumption in period t is Ct. The growth rate of consumption in period t is ln Ct/ln Ct-1 = Yt. In this section, it provides background material for the evolution of the underlying growth rate distribution for future consumption.
The hidden-state stochastic growth process
The paper addresses the issue of fuzzy distant uncertainty by introducing an evolving hidden-state stochastic process. Bayesian techniques typically applied to econometric problems with time-sequential dependence enable him to estimate probability distributions.
Results and numerical examples
The paper demonstrates that even a small amount of random walking in the underlying trend growth rate can lead to non-negligible long-term impacts on lowering the discount rate. It highlights that there is no simple solution to calculating a discount rate that produces reliable and sustainable outcomes. The models we use in approximations are all oversimplified approximations, which are increasingly breaking down as the time horizon lengthens.
Conclusion
Overall, the paper provides a methodology for addressing uncertainty regarding discount rates for investments with long-time horizons. It emphasises the importance of recognising the challenges inherent in estimating growth rates and projecting future changes in global affairs. However, while Weitzman’s model allows investors to estimate discount rates for a climate change investment, the results remain uncertain as the numbers are highly sensitive materials that can showcase a wide range of fluctuations. Nonetheless, the model presents an important step in accounting for ESG considerations in investment decisions.