On the optimality of 2°C targets and a decomposition of uncertainty

Countries under the UNFCCC have agreed to prevent dangerous anthropogenic climate change, with the Paris Agreement specifying a goal to keep warming well below 2°C and pursue 1.5°C. Determining such targets is complex, involving socio-economic, geophysical, and ethical aspects. Integrated Assessment Models (IAMs) help explore this complexity. Two IAM strands have evolved: (1) cost-minimising models that derive least-cost pathways to meet exogenously set climate targets, and (2) cost-benefit models that endogenously balance mitigation costs against climate damages to determine optimal pathways and temperatures. While both use carbon price trajectories as key indicators, they have largely developed independently. Prior analyses of uncertainties (e.g., discount rates, climate sensitivity, damages) are often limited in scope, rely on older damage functions, or conduct simulations instead of optimization, and very few compare cost-minimising and cost-benefit outcomes within a unified framework. This study develops a transparent meta-model calibrated to literature ranges that can directly compare cost-minimising and cost-benefit perspectives, quantify parameter impacts on mitigation timing and carbon prices, and assess conditions under which including climate damages alters least-cost pathways and whether the 2°C target is optimal.

The paper situates itself among a broad literature of IAMs. Cost-minimising IAMs compute least-cost emission or carbon price pathways to meet climate targets, while cost-benefit IAMs optimize welfare by weighing damages and abatement costs, yielding endogenous temperature targets. Previous work has examined sensitivities to discounting, climate response, and damages, but often with limited ranges, sensitivity (not uncertainty) analyses, outdated damage functions, or simulation rather than optimization. Nordhaus provided a limited comparison of cost-minimising versus cost-benefit settings for selected assumptions. More recent studies argue 2°C may be optimal, but often use narrower ranges for damages and mitigation costs or different climate modules. This paper fills gaps by employing full literature ranges for key parameters, systematically decomposing uncertainty, and comparing cost-minimising and cost-benefit outcomes within one model.

The authors develop a simple yet transparent global meta-model with two coupled modules: (1) an economic growth module with a Cobb–Douglas production function, exogenous population and total factor productivity (from SSPs), fixed savings rate for investment, and utility as an increasing function of consumption; (2) an emissions module where CO2 emissions derive from GDP and an emissions intensity, reduced via a global carbon price acting on a quadratic marginal abatement cost (MAC) curve with learning-by-doing. Cumulative CO2 emissions are mapped to global mean temperature (GMT) via an instantaneous linear TCRE relation calibrated to IPCC AR5 (5–95th percentile 0.42–0.82°C per 1000 GtCO2; median 0.62), implicitly capturing correlated non-CO2 forcing. Climate damages reduce GDP via damage functions selected to span literature ranges: low (DICE 2016R2), medium (Howard et al. “Howard Total” including catastrophic components), and high (Burke, Hsiang & Miguel long-run empirical damages). The MAC is calibrated to low/medium/high mitigation cost levels using IPCC AR5 WGIII consumption loss ranges (quantile regression to 5th/50th/95th percentiles). Policy and feasibility constraints include a minimum emissions floor of −20 GtCO2/yr to reflect limited negative emissions and an inertia constraint limiting annual emissions change to 2.2 GtCO2/yr. The optimization horizon extends to 2100 with continuation into the 22nd century to mitigate end-of-horizon effects. The control variable is the global carbon price path; state variables are cumulative emissions and capital stock. Optimal policies are computed using dynamic programming via the Bellman equation to maximize discounted utility. Two problem classes are solved: (i) cost-minimising pathways under a fixed carbon budget (e.g., 1344 GtCO2 to achieve 2°C with 67% likelihood given TCRE uncertainty) without or with damage internalization; and (ii) cost-benefit pathways with no preset temperature/budget, fully internalizing damages. Uncertainty analysis uses Sobol variance decomposition computed from Monte Carlo sampling over discrete distributions approximating literature ranges for each parameter: SSP (socio-economics), damage function, TCRE (5th/50th/95th with weighted discrete distribution), mitigation cost level (5th/50th/95th weighted), and pure rate of time preference (PRTP; 0.1%, 1.5%, 3% with uniform discrete). Variance contributions and interactions are reported over time for carbon prices (cost-minimising case) and for end-of-century temperature (cost-benefit case). Sensitivity tests examine alternative MAC curvature (cubic), alternative welfare parameters from expert elicitation (joint PRTP/elasmu), and removal of overshoot by setting minimum emissions to 0.

- Cost-minimising with fixed 2°C-consistent carbon budget (1344 GtCO2): - Carbon prices generally rise over time and may fall once the emissions floor binds. Including damages shifts mitigation earlier, linearizing price paths; effect strongest under high damages (Burke) and weakest under low damages (DICE). In some high-damage cases, optimization yields smaller-than-target carbon budgets. - Mitigation cost level strongly affects price levels: with medium damages, the initial carbon price is 32% higher than no-damages for high mitigation costs and 282% higher for low mitigation costs; similar but larger/smaller effects under high/low damage functions. - Discounting materially affects initial prices: lowering PRTP from 3% to 1.5% almost doubles the initial price; from 1.5% to 0.1% nearly doubles it again. - Socio-economics (SSP) shape timing and steepness: high baseline emissions (SSP5) lead to earlier, faster price growth and reaching emissions floor before 2100; high population/low GDP (SSP3) yields more linear effort with higher initial prices and lower end-century prices. - TCRE affects preference for early mitigation; initial price increases almost linearly with TCRE. - Variance decomposition (Sobol) of optimal carbon price over time: mitigation cost level dominates variance, especially long-term; SSP, PRTP, and damages contribute roughly equally to the remainder for medium cost levels. There is a notable dip in variance around 2070 due to compensating shifts in effort timing. TCRE contributes <0.5% of price variance. - Cost–benefit comparison for 2°C pathways: For medium or high damages, 95% of parameter combinations yield avoided damages (NPV as % of GDP) exceeding abatement costs; for low damages (DICE), only 40% do. Thus, damages magnitude largely determines whether 2°C yields net benefits. - Cost-benefit (no preset target): - With medium damages and low discount rate, optimal 2100 temperature does not exceed 2.5°C even with high mitigation costs; with low mitigation costs, the optimal temperature falls to 1.5°C or less. - Optimal temperatures are higher under SSP5 (about 3–4.5°C) and lower under SSP1/SSP4 (about 1–3°C), reflecting baseline emissions. With high discounting or low damages, SSP differences become more influential. - TCRE shifts optimal temperature approximately linearly: lower TCRE reduces, higher TCRE increases the optimum; impact is minimal for scenarios with ~2°C optimal temperatures due to compensating abatement responses. - Variance decomposition of optimal 2100 temperature: damages account for the largest share (about 58% overall), discount rate ~15%, mitigation cost level ~14%, with notable interaction terms (especially damage×SSP and damage×TCRE). Conditional analyses show that under medium/high damages, discount rate and cost level dominate residual variance; under low damages with high discounting, SSP and TCRE become relatively more important. - Optimal carbon price paths in cost-benefit settings increase approximately linearly; damage functions steepen slope modestly, while SSPs mainly affect the slope. In this setting, mitigation cost uncertainty explains only ~10% of carbon price variance; damage function explains ~45–60%, and the discount rate is pivotal under low damages. - Sensitivities: - Using a cubic MAC slightly narrows optimal temperature spread; increases cost-benefit carbon prices by ~20% in low-cost scenarios; and raises cost-minimising prices notably only under high mitigation costs. - Disallowing net-negative emissions (minimum emissions 0) shifts cost-minimising effort earlier and raises prices (e.g., +18% under medium assumptions without damages); in cost-benefit runs above 2°C the impact is negligible, while for lower temperatures end-of-century temperature can rise by up to 0.2°C (SSP2) to 0.3°C (SSP5).

The results provide a unified comparison of cost-minimising and cost-benefit approaches using full literature ranges. They nuance claims that 2°C is universally optimal: while low discount rates and medium-to-high damages often imply optimal temperatures at or below ~2–2.5°C (and 1.5°C with low costs), different assumptions on mitigation costs and discounting can raise the optimum to 3°C or higher, particularly under SSP5. The model explains differences with earlier studies by employing updated damage functions and a TCRE-based climate module rather than multi-box modules with longer lags. Variance decompositions highlight that damages dominate uncertainty in optimal temperatures and in social cost-like carbon prices, while mitigation cost uncertainty dominates variance in cost-minimising price paths. Socio-economic pathways significantly shape timing and slope of carbon pricing and can dominate variance under high mitigation costs. Policy-relevant insights include: valuing damages and selecting discount rates substantially affect near-term carbon prices even in cost-minimising settings; risks from high damages appear greater than from high mitigation costs; choosing low social discount rates for long-term policy aligns optimal temperatures with Paris goals. The comprehensive uncertainty decomposition underscores where narrowing uncertainty (particularly in damage estimates) or making normative choices (discounting) will most reduce policy ambiguity.

The study develops and applies a transparent meta-model that bridges cost-minimising and cost-benefit IAM perspectives, calibrated to full literature ranges for socio-economics (SSPs), climate response (TCRE), damages (DICE/Howard/Burke), mitigation costs, and discounting. Including damages and low discount rates substantially increase near-term optimal carbon prices in cost-minimising 2°C pathways, while mitigation cost levels dominate price variance. In cost-benefit analysis, optimal end-of-century temperatures are generally ≤2.5°C under medium damages with low discount rates and can fall to ≤1.5°C with low mitigation costs; damage functions are the primary driver of uncertainty in optimal temperatures. These findings indicate that, under plausible normative choices and updated damage estimates, optimal climate outcomes are consistent with or stricter than the Paris targets. Future research should incorporate stochasticity and tipping points, regional heterogeneity and inequality, decompose damage uncertainty further (including biodiversity, ecosystem services, and natural capital in production), and continue updating damage and cost estimates to refine uncertainty bounds.

The model is global and stylized, omitting regional heterogeneity, distributional and inequality effects, and heterogeneous impacts across sectors and groups. It does not explicitly represent environmental feedbacks or stochastic tipping points (addressed only indirectly via the choice of a damage function that includes catastrophic components). The climate response is simplified via an instantaneous TCRE relation. Negative emissions and transition inertia are represented via simple constraints. Uncertainty analysis uses discrete approximations to literature ranges and assumes uniform discrete distributions for parameters without well-defined distributions (SSP, damages, PRTP). Absolute numerical results should be interpreted cautiously; the primary value lies in comparative insights and uncertainty decomposition.