The United Nations Framework Convention on Climate Change (UNFCCC) and the Paris Agreement aim to prevent dangerous anthropogenic climate change, specifically keeping global mean temperature increase well below 2°C and pursuing efforts to limit it to 1.5°C. This goal's determination is complex, involving socio-economic, geophysical, and ethical aspects. Integrated Assessment Models (IAMs) are used to explore this complexity by describing the interplay of relevant factors. Existing IAMs fall into two categories: cost-minimizing models focusing on pathways to achieve specific climate targets, and cost-benefit models determining optimal pathways balancing costs and benefits of climate policy. These model types have developed relatively independently. While both use a (shadow) carbon price as a key indicator, a comprehensive analysis comparing cost-benefit and cost-minimizing pathways, including uncertainty analysis, is lacking. This paper addresses this gap by developing a flexible and transparent model to calculate optimal carbon price paths under various assumptions regarding damage functions, temperature goals, mitigation costs, climate sensitivities, discount rates, and socio-economic developments. The model directly compares insights from cost-minimizing and cost-benefit modeling communities. The research first analyzes each parameter's effect on the timing of mitigation in cost-minimizing paths. Then, it quantifies how these paths are impacted when including the economic impact of climate damages, not just mitigation costs. Further, it analyzes the relative importance of each parameter's uncertainty over time. Beyond cost-minimizing paths, the study analyzes optimal cost-benefit paths without a preset carbon budget, providing a comprehensive analysis of how the optimal end-of-century temperature depends on literature ranges of relevant parameters and investigating under which assumptions the 2°C target is optimal. The model moves beyond sensitivity analysis by conducting a systematic uncertainty analysis using literature-based ranges and analyzing parameter interactions and their effect on the optimal carbon price and end-of-century temperature. The model is based on a simple economic growth model, similar to DICE and FAIR, combining a production function with estimates on mitigation costs and climate damages from recent literature. A global carbon price is applied to maximize discounted utility, and the model is calibrated using literature ranges on key parameters, including socio-economic variables from Shared Socioeconomic Pathways (SSPs), damage functions, Transient Climate Response to Emissions (TCRE), mitigation costs, and discount rates.

The paper references a plethora of existing IAMs, noting the varying degrees of complexity and differing focuses within the cost-minimizing and cost-benefit modeling approaches. It highlights that several studies have analyzed the effects of various assumptions and uncertainties (discount rate, climate sensitivity, climate change damages) on optimal pathways. However, it points out limitations in existing research, including limited scope, sensitivity analysis instead of full uncertainty analysis, outdated insights, and simulations instead of optimizations. The key gap identified is the lack of studies comparing cost-minimizing and cost-benefit pathways using the same model framework, except for limited comparisons by Nordhaus. The authors emphasize the need for a model simple enough to use optimal control theory but complex enough to capture relevant dynamics and easily calibrated to literature ranges. They cite several key studies that informed their model development and parameter choices, such as IPCC AR5 data for TCRE and mitigation costs, and meta-analyses of damage functions by Howard et al. and empirical damage functions by Burke et al.

The authors developed a flexible and transparent model to calculate optimal carbon price paths. The model is based on a simple economic growth model incorporating a Cobb-Douglas production function, mitigation costs, and climate damages. The model's economic module calculates GDP using exogenous population and total factor productivity, dividing it between investments and consumption. Investments are added to the global capital stock, which, along with labor, determines the next time step's GDP. Labor development is linked to population developments. The model aims to maximize discounted utility, with utility being an increasing function of consumption. The emissions module calculates CO2 emissions based on GDP and an emission factor. The interaction between the economic and emission modules happens through climate change damages and mitigation costs. Unlike the DICE model's two-box climate module, the model uses a linear and instantaneous TCRE relation to translate cumulative CO2 emissions into global mean temperature (GMT). The increase in GMT causes GDP loss, quantified by damage functions. A global carbon price is used to reduce emissions, defined by a quadratic Marginal Abatement Cost (MAC) curve with technological learning. A minimum emission level is imposed to represent limitations on carbon dioxide removal technologies. Inertia is modeled by constraining the difference in CO2 emissions between consecutive years. The optimization runs throughout the 22nd century to avoid end-of-horizon problems. The optimal carbon price is calculated using the Bellman equation, with cumulative emissions and capital stock as state variables, the carbon price as a control variable, and discounted utility as the objective function. The model allows the use of literature ranges for key parameters. Socio-economic variables are from SSPs. Damage functions cover a low (DICE 2016R2), medium (Howard Total), and high (Burke LR) range. TCRE spans the 5–95th percentile range from IPCC AR5 data. Mitigation costs are calibrated to IPCC AR5 data, spanning the 5–95th percentile range. Three pure rates of time preference (0.1%, 1.5%, 3%) are used. Sobol indices, calculated with a Monte Carlo simulation, quantify each parameter's contribution to the variance. The model distinguishes between scenarios with a fixed carbon budget (cost-minimizing) and those without (cost-benefit). The authors note some modeling differences between their model and DICE, primarily in parameter calibration. Sensitivity analyses were conducted to assess the impact of changes in marginal abatement costs and discount rates. The model code is available online.

The study's key findings can be categorized into cost-minimizing and cost-benefit analyses: **Cost-Minimizing Setting (Fixed Carbon Budget):** * Including medium damages in cost-minimizing pathways reaching the Paris Agreement's temperature target can double the initial carbon price compared to considering only mitigation costs. Decreasing the pure rate of time preference also significantly increases the initial carbon price. * Higher marginal abatement costs lead to higher carbon prices. The level of mitigation costs dominates the variance of the carbon price. The discount rate, damage function, and socio-economic scenario contribute almost equally to the remaining variance. Uncertainty in the TCRE is negligible. * Socioeconomic scenarios (SSPs) substantially impact the optimal carbon price. Higher baseline emissions lead to earlier and more rapid carbon price growth. Population growth and GDP affect the linearity of the mitigation effort. * The TCRE directly impacts the carbon price and emission pathway, with higher TCREs leading to earlier mitigation. * Higher discount rates delay mitigation efforts, with a lower discount rate almost doubling the initial carbon price. * Analysis of variance using Sobol indices shows that mitigation cost levels dominate variance, especially in the longer term. The damage function, SSP, and discount rate contribute almost equally to the variance for medium mitigation cost levels. For low mitigation costs, the damage function is more important, while for high mitigation costs, the SSP dominates. * For all 2°C pathways, the majority show avoided damages exceeding mitigation costs, with the magnitude of damages, more than mitigation costs or discount rates, determining this outcome. **Cost-Benefit Setting (No Carbon Budget):** * Even with high mitigation costs, the optimal end-of-century temperature with medium damages and a low discount rate does not exceed 2.5°C. With low mitigation costs or high damage functions, the optimal temperature is 1.5°C or less. * The TCRE has negligible impact on scenarios with optimal temperatures between 1.5 and 2°C. * Uncertainty analysis shows damages account for over 50% of the total variance in optimal temperature, while TCRE accounts for only 2%. * The optimal temperature is highly sensitive to the damage function, discount rate, and mitigation costs. Lower discount rates lead to lower optimal temperatures. Higher damages lead to lower optimal temperatures. Socioeconomic scenarios significantly influence optimal temperatures, with SSP5 consistently yielding higher temperatures than others. The choice of damage function is the most important factor in determining the optimal temperature, followed by the discount rate and the mitigation cost level. * Optimal carbon price paths in a cost-benefit setting increase almost linearly, mostly influenced by the initial carbon price except for the SSP (which affects the steepness). Uncertainty in mitigation costs has a smaller impact than the damage function and discount rate in the cost-benefit setting. The study also provides comprehensive figures visualizing the results of these analyses.

The paper's findings provide insight into critical factors influencing climate mitigation pathways. It extends existing literature on cost-benefit analysis by offering a comprehensive overview of the relative importance of different parameters. The results nuance claims in recent literature suggesting that the Paris Agreement's 2°C target is always optimal. The authors demonstrate that the optimal temperature is sensitive to variations in mitigation costs and discount rates. This highlights the importance of considering the full literature range for these parameters. The study's comparison with other studies reveals differences likely attributable to different modeling choices, such as the climate module and damage function calibrations. The study highlights the large uncertainty range in optimal temperatures, underscoring the role of normative choices and acceptable risk levels in climate policy decision-making. The research suggests that the risk of high damages is higher than the risk of high mitigation costs. This, combined with a preference for low discount rates for long-term climate policy, suggests that cost-optimal temperatures for low discount rates and medium to high damages align with the Paris Agreement's long-term objectives. The analysis potentially reduces uncertainties over time.

This study presents a comprehensive analysis of the factors influencing optimal climate targets, using a novel meta-model that incorporates full literature ranges for key parameters. The research demonstrates the significant impact of damage functions, discount rates, and mitigation costs on both cost-minimizing and cost-benefit pathways. The findings highlight the sensitivity of optimal temperature targets and carbon pricing to these parameters, challenging simplistic conclusions about the optimality of 2°C targets. The study emphasizes the crucial role of considering full parameter uncertainty and making informed normative choices (such as the discount rate) in climate policy decision-making. Future research could focus on disentangling the uncertainties within damage functions (e.g., incorporating natural capital and bottom-up sectoral damages) and incorporating stochasticity and tipping points into the model to provide even more robust analyses.

The model simplifies several aspects of climate change and the economy. Key factors not included are heterogeneous impacts across societal groups, environmental feedbacks, tipping points, and stochastic behavior. The model uses a global perspective, limiting insights into regional heterogeneity. Although the Howard Total damage function accounts for catastrophic damages through a proxy, more detailed modeling of tipping points and stochasticity would enhance the analysis. The use of a simple linear TCRE relation also represents a simplification of the climate system's complex dynamics. The calibration of some parameters, such as the Burke damage function, involves approximations that may affect the results. Incorporating more detailed sectoral models and a broader array of damage scenarios would further refine the analysis. Finally, the study's reliance on literature ranges for parameter values represents uncertainty in a deterministic manner and lacks a thorough exploration of stochastic uncertainty.