Evaluation of long-dated investments under uncertain growth trend, volatility and catastrophes

Abstract

Because of the uncertainty about how to model the growth process of our economy, there is still much confusion about which discount rates should be used to evaluate actions having long-lasting impacts, as in the contexts of climate change, social security reforms or large public infrastructures for example. We characterize efficient discount rates when the growth of log consumption follows a random walk with uncertain parameters. We examine different models in which the parametric uncertainty affects the trend and the volatility of growth, or the frequency of catastrophes. This uncertainty implies that the term structures of the risk free discount rate and of the aggregate risk premium are respectively decreasing and increasing. It also implies that the discount rate is increasing with maturity if the beta of the investment is larger than half of relative risk aversion. Another important consequence of parametric uncertainty is that the risk premium is not proportional to the beta of the investment. Finally, we apply our findings to the evaluation of climate change policy. We argue in particular that the beta of actions to mitigate climate change is relatively large, so that the term structure of the associated discount rates should be increasing.

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Reference

Christian Gollier, “Evaluation of long-dated investments under uncertain growth trend, volatility and catastrophes”, IDEI Working Paper, n. 754, November 2012, revised September 2015.