Carbon pricing under climate uncertainty: A dynamic climate-economy approach

The social cost of carbon is a key metric for evaluating the external impacts of carbon emissions and for informing carbon pricing policies. As anthropogenic emissions continue to drive global warming, the economic and societal impacts associated with climate change have become increasingly severe. Moreover, temperature dynamics exhibit substantial stochasticity, which adds complexity to the assessment of climate impacts and optimal policy design. To address this issue, this paper develops a dynamic stochastic general equilibrium framework that explicitly incorporates stochastic temperature dynamics. The model captures the evolution of temperature under the joint influence of anthropogenic carbon accumulation, mitigation efforts, and exogenous uncertainty. The model is used to examine the effects of global warming on economic welfare, total factor productivity, and climate-related damages. The resulting Hamilton–Jacobi-Bellman (HJB) equations are solved numerically using the Deep Galerkin Method (DGM). The results indicate that optimal energy use and mitigation decisions respond nonlinearly to economic productivity, climate sensitivity, and damage severity, even when welfare evolves smoothly across states. Stronger and earlier mitigation involves short-run economic costs but yields long-run benefits through lower climate risks, more stable carbon prices, and faster energy system adjustment. Higher productivity increases carbon exposure while improving the capacity to absorb climate damages, though this buffering effect weakens sharply under severe climate risks. • Evaluates the social cost of carbon to inform optimal carbon tax policies. • Introduces stochastic temperature dynamics driven by emissions, mitigation, and uncertainty. • Solves the HJB equations numerically using the deep Galerkin method. • Mitigation lowers fossil fuel use but reduces the need for damage compensation and pricing. • Net output declines as productivity gains fail to offset rising abatement costs.