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
We use a series of different approaches to extract information about crash risk from option prices for the Euro-Dollar exchange rate, with each step sharpening the focus on extracting more specific measures of crash risk around dates of ECB measures of Unconventional Monetary Policy. Several messages emerge from the analysis. Announcing policies in general terms without precisely describing what exactly they entail does not move asset markets or actually increases crash risk. Also, policies directly focused on changing relative asset supplies do seem to have an impact, while measures aiming at easing financing costs of commercial banks do not.
CO2 pricing is essential for an efficient transition to the green economy. Despite Daniel, Litterman and Wagner (2019)' claim that CO2 prices should decline, CO2 prices should rise over time. First, damages from global warming are proportional to economic activity and this makes CO2 prices grow at the same rate as the economy. Second, even if uncertainty about the damage ratio is gradually resolved over time, this only slows down the price rise. Third, if CCS is allowed for, the optimal CO2 price will rise before it declines but this decline does not occur until more than two centuries ahead. Fourth, damages are likely to be a very convex function of temperature which with rising temperature implies that CO2 prices must grow faster than the economy. Fifth, internalizing the social benefits of learning by doing or a shift towards technical progress in renewable energy production requires a subsidy for renewable energy, not a temporary spike in CO2 prices. Having high CO2 prices upfront is an artefact of failing to separate out renewable energy subsidies from the carbon price. Finally, efficient intertemporal allocation of policy efforts implies that a temperature cap or cap on cumulative emissions requires that CO2 prices must rise at a rate equal to the risk-adjusted interest rate, typically higher than the economic growth rate. Summing up, CO2 prices must rise at a rate at least equal to the economic growth rate and at most to the risk-adjusted interest rate. They should not decline.
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