The economic impact of climate change is often assessed using coupled climate-economy models. These models typically focus on the economic consequences of epistemic uncertainty—the uncertainty arising from our imperfect knowledge of key model parameters, such as Equilibrium Climate Sensitivity (ECS). However, a critical omission in these assessments is the failure to account for aleatory uncertainty—the inherent randomness in the climate system that persists even if all model parameters were perfectly known. This inherent variability in global mean temperature (GMT) means that even if the expected GMT is accurately predicted, the actual temperature in any given year will almost certainly deviate from this expectation. This paper addresses this gap by developing a physically grounded and tractable approach to incorporate aleatory uncertainty into the estimation of climate change damages. The study's purpose is to quantify the economic consequences of this previously neglected source of uncertainty, demonstrating its significant contribution to overall economic risks associated with climate change.

Existing economic assessments of climate change damages primarily rely on deterministic models, which generate trajectories of expected GMT based on different model parameters to account for uncertainty in the climate response to greenhouse gas concentrations. These deterministic approaches neglect the inherent variability of the climate system, which leads to deviations of actual temperatures from the expected trajectory. While some researchers recognize the stochastic nature of the climate, this understanding has not been consistently integrated into official assessments. This study builds upon existing energy balance models (EBMs) and incorporates stochasticity into the climate model to represent this variability, advancing our understanding beyond deterministic approaches.

The authors utilize a stochastic energy balance model (EBM) to represent the temporal evolution of GMT. This model incorporates a stochastic term to capture internal variability, extending the typical deterministic EBM. The model is represented by the equation: CdΔT = Fdt – λΔTdt + √2σ₀d<it>te, where C is the effective heat capacity, F is the radiative forcing, λ is the feedback parameter, σ₀ is the variance of a zero-mean Gaussian noise process, and e is the noise term. The model parameters (C, λ, σ₀) are calibrated using historical temperature data. The stochastic model generates an ensemble of temperature trajectories, each representing a possible realization of the climate system's evolution. These temperature trajectories are then fed into a damage function (e.g., Weitzman's damage function) to calculate the economic damages as a share of global output for each trajectory. The annual damages are discounted and summed over time to obtain the total economic damages. The resulting distribution of total damages quantifies the uncertainty associated with aleatory uncertainty. The risk premium, representing what a social planner would pay to avoid aleatory uncertainty, is calculated by comparing the expected utility of the deterministic and stochastic scenarios. The study also considers the interaction of aleatory and epistemic uncertainty by incorporating uncertainty in the ECS. By running the stochastic model for a range of ECS values, they assess how epistemic uncertainty influences the cost of aleatory uncertainty. The calculations are done for different Representative Concentration Pathways (RCPs), representing different greenhouse gas emission scenarios.

The study's key findings highlight the significant impact of aleatory uncertainty on climate change damage estimates. Incorporating realistic temperature variability leads to substantially higher damage estimates than those derived from deterministic models. For instance, under the RCP8.5 forcing scenario, the deterministic model predicted $486 trillion in total damages, while the stochastic model assigned a 5% chance of damages exceeding $563 trillion—a 16% increase. The 5-95% range for the stochastic model was (−13%, +16%) of the deterministic forecast. The relative dispersion was even greater for lower forcing scenarios (e.g., RCP2.6). The risk premium, representing the cost of aleatory uncertainty, was substantial. For RCP2.6, the risk premium was $3 trillion (4% of current global output), while for RCP8.5, it was $32 trillion (40% of current global output). Considering the interaction of aleatory and epistemic uncertainty further amplified these costs. With both types of uncertainty, the risk premium for RCP2.6 rose to $9 trillion (11% of current global output), and for RCP8.5, it reached $46 trillion (over half of current global output). This interaction effect stems from the fact that a higher ECS leads to both greater mean warming and greater variability, disproportionately increasing the cost of high ECS draws. Importantly, the study notes that while the risk premium is substantial, it's unlikely to significantly impact the social cost of carbon (SCC) because aleatory uncertainty affects the variability of damages but not necessarily the marginal damage of releasing one more tonne of CO2. The implications are that adaptation measures are far more crucial and economically beneficial than previously thought.

The study's findings emphasize the inadequacy of deterministic climate models in capturing the full economic consequences of climate change. The incorporation of aleatory uncertainty reveals previously hidden economic risks, highlighting the importance of explicitly accounting for this source of uncertainty in future assessments. The results strongly suggest that the benefits of adaptation strategies are much larger than previously estimated, as these strategies offer a means to mitigate the damages stemming from the unpredictable nature of the climate. The substantial increase in damage estimates emphasizes the urgency of considering and implementing adaptation measures alongside mitigation efforts. This work calls for a shift toward more comprehensive integrated assessment models that fully integrate stochasticity, thus offering a more realistic assessment of climate change risks and informing more effective policy responses.

This research demonstrates that ignoring aleatory uncertainty in climate change impact assessments leads to a significant underestimation of economic damages. The findings highlight the need for future assessments to incorporate stochasticity in climate models to provide a more accurate and complete picture of potential economic risks. The high risk premia calculated suggest the substantial economic benefits of adaptation strategies, warranting further investigation into these benefits. Future research should focus on refining damage functions and climate models to more accurately represent long-range temperature dependencies and their impact on economic losses, leading to improved policy recommendations.

The study utilizes a simplified energy balance model, which might not fully capture the complexity of the climate system. The damage function employed is also a simplification of real-world economic impacts. The study assumes a constant discount rate, which may not accurately reflect societal preferences across time. Furthermore, the model's representation of temperature autocorrelation, while accounting for persistence, does not fully capture the potential for 'long-range dependence' or 'Joseph effect' phenomena that could further increase damage variability.