Social Cost of Carbon under stochastic tipping points: when does risk play a role?

Carbon dioxide emissions impose a social cost on economies, owing to the damages they will cause in the future. In particular, emissions increase global temperature that may reach tipping points in the climate or economic system, triggering large economic shocks. Tipping points are uncertain by nature, they induce higher expected damages but also dispersion of possible damages, that is risk. Both dimensions increase the Social Cost of Carbon (SCC). However, the respective contributions of higher expected damages and risk have not been disentangled. We develop a simple method to compare how much expected damages explain the SCC, compared to the risk induced by a stochastic tipping point. We find that expected damages account for more than 90% of the SCC with productivity shocks lower than 10%, the high end of the range of damages commonly assumed in Integrated Assessment Models. It takes both high productivity shock and high risk aversion for risk to have a significant effect. Our results also shed light on the observation that risk aversion plays a modest role in determining the SCC (the ''risk aversion puzzle''): they suggest that too low levels of damages considered in previous studies could be responsible for the low influence of risk aversion.