Discounting the Future: on Climate Change, Ambiguity Aversion and Epstein-Zin Preferences

Abstract

We focus on the effect of preference specifications on the current day valuation of future outcomes. Specifically, we analyze the effect of risk aversion, ambiguity aversion and the elasticity of intertemporal substitution on the willingness to pay to avoid climate change risk. The first part of the paper analyzes a general disaster (jump) risk model with a constant arrival rate of disasters. This provides useful intuition in how preferences influence valuation of long-term risk. The second part of the paper extends this model with a climate model and a temperature dependent arrival rate. Since the model yields closed form solutions up to solving an integral, our model does not suffer from the curse of dimensionality of numerical IAMs with several state variables. Introducing Epstein-Zin preferences with an elasticity of substitution higher than one and ambiguity aversion leads to much larger estimates of the social cost of carbon than obtained under power utility. The dominant parameters are the risk aversion coefficient and the elasticity of intertemporal substitution. Ambiguity aversion is of second order importance. JEL codes: Q51, Q54, G12, G13 1 For a very different (and strongly worded) view focusing on the social welfare aspects of the rate of time preference rather than on individual preferences, see Chichilnisky, Hammond, and Stern (2018);Stern (2015) who look at a positive rate of time preference as discrimination between generations that happen to have been born at different moments in time.2 This list is not exhaustive, but is used to give an idea of the nature of an IAM. 3 The references do not contain the most recent versions of the IAMs.1. Power utility, no ambiguity aversion r 1 = r P ow − γλm − λ(e −γ(µ J − 1 2 γσ 2 J ) − 1) 2. SDU utility, no ambiguity aversion3. Power utility, ambiguity aversion r 3 = r SDU − γλ * m * − λ * (e −γ(µ J +b * σ 2 J − 1 2 γσ 2 J ) − 1) 4. SDU utility, ambiguity aversion r 4 = r

Commit to a Credible Path of Rising CO2 Prices

“…If integrated assessment models are extended to allow for long-run risk in economic growth with temperatureinduced tail risks, the temperature risk premium increases with temperature (25,26) and it is even more difficult to get a declining carbon price. Although ambiguity aversion has surprisingly little impact on the optimal carbon price (27,28), other than one might have been expected given the worst-case assumption that optimal requires one to taken when faced with the multiple priors framework (29), the optimal carbon price under ambiguity aversion still rises. Finally, if one allows for learning after a tipping point when it becomes known that the climate sensitivity has increased or carbon sinks have been weakened, the optimal response is to have a rising path of CO2 prices before and a rising but higher path after the tipping point (30, Figure 4, Panel D).…”

On current and future carbon prices in a risky world

“…If integrated assessment models are extended to allow for long-run risk in economic growth with temperature-induced tail risks, the temperature risk premium increases with temperature (Bansal and Yaron, 2004;Bansal et al, 2016) and it is even more difficult to get a declining carbon price. Adding to all this, Olijslagers and van Wijnbergen (2019) show that ambiguity aversion (i.e. the aversion of unmeasurable or Knightian uncertainty) has a major impact on the optimal carbon price: the direct effect on the aversion-adjusted valuation of future income flows substantially exceeds the effect ambiguity aversion also has in the opposite direction because it also increases the appropriate discount rate.…”

Investment, insurance and weather shocks: Evidence from Cambodia

“…Climate-related disasters, in fact, often have large impacts on the economy. However, they occur rarely and take place abruptly (Olijslagers and van Wijnbergen, 2019). Moreover, despite the remarkable accomplishments achieved by climate scientists and experts, the currently available information about future climate risks is still not perfectly specified by stochastic setups (Etner et al, 2020).…”