Optimal climate policy when warming rate matters

Studies of the Social Cost of Carbon assume climate change is a stock externality for which damages stem from warming level. However, economic and natural systems are also sensitive to the rate at which warming occurs. In this paper, I study the optimal carbon tax when such a feature is accounted for. Damages caused by warming rates do not aect optimal long-term warming, but they delay the use of the same carbon budget. They also make carbon price less sensitive to discounting assumptions. Numerically, when controlling for the welfare loss from climate change, the more damages stem from warming rates rather than warming levels, the higher the initial carbon price. This suggests that mitigation strategies that overlook this issue might lead to too rapidly increasing temperature pathways.