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

Is climate change concerning because of its expected damages, or because of the risk that damages could be very high? Climate damages are uncertain, in particular they depend on whether the accumulation of greenhouse gas emissions will trigger a tipping point. In this article, we investigate how much risk contributes to the Social Cost of Carbon in the presence of a tipping point inducing a higher-damage regime. To do so, we decompose the effect of a tipping point as an increase in expected damages plus a zero-mean risk on damages. First, using a simple analytical model, we show that the social cost of carbon (SCC) is primarily driven by expected damages, while the effect of pure risk is only of second order. Second, in a numerical experiment using a stochastic Integrated Assessment Model, we show that expected damages account for most of the SCC when the tipping point induces a productivity shock lower than 10%, the high end of the range commonly used in the literature. It takes both a large productivity shock and high risk aversion for pure risk to significantly contribute to the SCC. Our analysis suggests that the risk aversion puzzle, which is the usual finding that risk aversion has a surprisingly little effect on the SCC, occurs since the SCC is well estimated using expected damages only. However, we show that the risk aversion puzzle does not hold for large productivity shocks, as pure risk greatly contributes to the SCC in these cases.