A simple formula for the social cost of carbon

The social cost of carbon (SCC) is the monetized damage from emitting one unit of CO₂ to the atmosphere, often obtained from computational Integrated Assessment Models (IAMs). We develop a closed-form formula that approximates the SCC for a general economy, and then explore the capacity of the analytical approach to capture the key SCC drivers and thus to replicate the results of the deterministic IAMs. The formula explains the parameter-driven SCC variation of a mainstream IAM without a systematic bias. The sensitivity analysis identifies and measures the performance limits of the closed-form formulas. We then use the analytic formula to structurally interpret a distribution of SCCs from deterministic IAMs, and develop an analytical breakdown and quantification of how different sets of parameters contribute to the SCC distribution. This allows the user of the formula to evaluate where particular parameter choices tend to place the resulting SCC outcome in the distribution of outcomes for the universe of deterministic IAMs.