On the social cost of carbon and discounting in the DICE model

The social cost of carbon (SCC) has emerged as one of the relevant measures in integrated assessment models in climate economics, to quantify costs related to global warming and climate change. While the SCC is used in different models, including DICE (Dynamic Integrated model of Climate and Economy), PAGE (Policy Analysis of the Greenhouse Effect), and FUND (Climate Framework for Uncertainty, Negotiation, and Distribution), its exact definition and computation depend on the reference and, frequently lacking consistency within research streams whether focusing on a single model or on different models. In this study, we investigated three different methods for the computation of the SCC using the integrated assessment model DICE. While the first two methods are commonly known and used, the novel formula derived for the third method allows a direct analysis of the impact of the discount factor in the calculation of the SCC. We provide a detailed proof for the correctness of the third method and validate the consistency of all three methods by numerical experiments.