Pricing Carbon Under Economic and Climactic Risks: Leading-Order Results from Asymptotic Analysis

Leading-order results from asymptotic analysis for the optimal price of carbon under uncertainty are derived from a macroeconomic continuous-time DSGE model with AK growth, energy use, adjustment costs, recursive utility and costs of global warming. We consider non-climatic productivity growth uncertainty, atmospheric carbon uncertainty, climate sensitivity uncertainty and climate damage uncertainty. Explicit expressions are derived that show the leading-order dependence of the optimal carbon price on these uncertainties, the various climate betas, risk aversion, intergenerational inequality aversion and convexity of the climate damage specification. Our solution allows for skewness and mean reversion in stochastic shocks to the climate sensitivity and damage coefficients. The resulting rule for the optimal risk-adjusted carbon price incorporates precautionary, risk-insurance and risk-exposure effects to deal with future economic and climatic risks. The stochastic processes are calibrated and used to estimate and interpret the impact of each source of uncertainty on the optimal risk-adjusted carbon price.