Integrated Assessment Models (IAM)

• Integrated Assessment Models are formal frameworks that couple economic, technological, and Earth system models to evaluate the consequences and trade-offs of climate policies.
• They employ coupled differential and algebraic equations, such as Cobb-Douglas production functions and multi-box climate models, to simulate emissions, temperature changes, and mitigation costs.
• Recent advances include Monte Carlo sampling, Bayesian learning, and robust control methods integrated with high-resolution sectoral coupling to better capture uncertainties and inform policy design.

An Integrated Assessment Model (IAM) is a formal modeling framework that couples core elements of human society (notably the economic system), technological and energy systems, and the Earth system (climate, carbon cycle, biosphere) within a unified computational platform to explore the consequences and trade-offs of alternative climate policies. IAMs play a central role in producing quantitative scenarios for emissions, temperature change, mitigation costs, and climate damages, underpinning policy design and international negotiations. At their core, IAMs encode dynamical, economic, and physical processes in sets of coupled differential and algebraic equations, governed by uncertain parameters and subjected to exogenous and endogenous shocks.

1. Mathematical Foundations and Model Structure

IAMs typically comprise several coupled sub-systems, each specified via explicit mathematical relationships:

• Economic module: Commonly based on a Cobb-Douglas or Constant Elasticity of Substitution (CES) production function, for example,

$Y_t = A_t\,K_t^\alpha\,L_t^{1-\alpha}$

with $Y_t$ output, $K_t$ capital, $L_t$ labor, and $A_t$ total factor productivity.

• Energy and emissions modules: Map economic output or sectoral activity into energy demand, fossil and renewable supply, and subsequent greenhouse gas emissions, often linked through carbon intensity parameters.
• Climate and carbon cycle sub-models: Represented by multi-box (e.g., three-reservoir) models for carbon transfer and energy-balance equations for global mean temperature,

$$F_t = \eta\, \ln(M_t^{\mathrm{AT}}/M_0^{\mathrm{AT}})$$

$T_{t+1} = \phi_T\,T_t + \xi\,F_t$

where $M^{\mathrm{AT}}_t$ is atmospheric carbon and $F_t$ is radiative forcing.

• Damage and adaptation module: Damages reduce usable output by a function $D(T)$ of temperature, specified as quadratic or higher-order:

$D(T) = a_1 T + a_2 T^2$

• Decision and welfare module: Policy optimization is formulated as a dynamic program, maximizing a discounted utility functional, commonly under constant relative risk aversion (CRRA) or with Epstein-Zin recursive utility:

$$\max \mathbb{E} \sum_{t=0}^T \beta^t \frac{C_t^{1-\eta}}{1-\eta}$$

Models such as DICE, RICE, FUND, REMIND, and E3ME-FTT-GENIE vary in structural detail, regional disaggregation, treatment of uncertainty, and equilibrium concepts (Mercure et al., 2017, Renting et al., 2023).

2. Technology Representation and Transition Dynamics

IAMs deploy diverse strategies for representing technological change and substitution:

• CES-based substitution: Most process- and optimization-based IAMs use a two-factor CES function to model energy substitution:

$$Y = [\alpha F^{-\rho} + (1-\alpha) E^{-\rho}]^{-1/\rho}$$

Constant or time-varying elasticity $\sigma=1/(1+\rho)$ sets substitutability. However, fixed CES forms generate unphysical carbon price inflation and fail to capture S-curve (sigmoidal) diffusion observed in historical transitions (Sgouridis et al., 2016).

• Replicator dynamics and discrete choice: Simulation-based and agent-based IAMs such as E3ME-FTT-GENIE and FTT:Transport use evolutionary equations for market shares,

$$\frac{dS_i}{dt} = \sum_j S_i S_j (F_{ij} - F_{ji})/\tau$$

with binary logit preferences $F_{ij}$ parameterized by detailed, empirically observed cost distributions and learning-by-doing (Mercure et al., 2017, Mercure et al., 2017).

• Physical-energy system approaches: Alternative frameworks emphasize resource-constrained logistic or Bass diffusion processes, learning-curve cost reductions, and explicit power-system operation (Sgouridis et al., 2016).

The endogenous representation of learning, adoption inertia, and resource constraints is critical in capturing technological path-dependence and realistic mitigation cost curves.

3. Uncertainty Quantification and Robust Policy Design

IAMs are inherently uncertain due to parameter, scenario, model-structural, risk, and deep uncertainties (Cai, 1 Nov 2025). Contemporary approaches include:

• Monte Carlo sampling: Runs ensemble simulations under sampled parameter sets to capture output distributions.
• Bayesian learning: Sequential updating of parameter posteriors in response to new data; can be embedded within value-function iteration.
• Stochastic dynamic programming: Embedding risk aversion and recursive preferences (Epstein–Zin utility) in value iteration, enabling analysis of risk-adjusted social cost and adaptive policy.
• Robust control and min–max regret: Optimizing over worst-case realizations, reflecting ambiguity aversion and policy robustness to model misspecification.
• Machine-learning-assisted surrogates: Neural networks and Chebyshev polynomials for high-dimensional value-function approximation and tractable solution of stochastic dynamic programs.

Concrete illustrations include the DSICE platform for stochastic DICE extensions (persistent TFP risk, tipping hazards, multimodal SCC distributions), global cap-and-trade equilibria (showing aggregate welfare gains from trading compared to Nash), and robust dynamic R&D investments (Cai, 2020, Cai, 1 Nov 2025).

4. Model Coupling, Sectoral Disaggregation, and High-Resolution Emulation

IAMs increasingly combine macro-integrated frameworks with sector-specific, high-resolution submodels:

• Bidirectional coupling: Soft-coupling strategies integrate IAMs (e.g., REMIND) with sub-annual, detailed sector models (e.g., DIETER) via iterative harmonization of price signals, capacity, and dispatch, imposing convergence in both decision variables and shadow prices (Gong et al., 2022).
• Marginal abatement cost (MAC) curve emulation: Reduced-form emulators (emIAM) extract region/gas-specific MAC curves from full-scale IAM runs, enabling rapid, transparent scenario generation in simple climate models (Xiong et al., 2022).
• Agent-based and heterogeneity-rich modules: Agent-based IAMs (ABIAMs) incorporate micro-level heterogeneity, explicit financial systems, and policy mix simulation to capture distributional impacts, systemic risk, and political-economic dynamics not accessible to equilibrium IAMs (Naumann-Woleske, 2023).

These advances allow for sector-, agent-, and region-specific policy design, improved representation of power system flexibility, and alignment with observed S-curve technological transitions.

5. Policy-Relevant Insights, Critiques, and Practical Limitations

IAMs deliver quantitative assessments of mitigation costs, social cost of carbon, optimal carbon pricing/taxation, technological trajectories, and distributional impacts. Noted findings and challenges include:

• Quantification of social cost of non-CO₂ gases: Incorporation of climate–methane feedbacks increases the estimated social cost of methane by ~44% ($1,163/t-CH₄ at 3% discount) (Colbert et al., 2020).
• Pathologies and structural critiques: Canonical RICE/DICE-type IAMs can exhibit action masking and zones of irrelevance in control space, problematic for both optimization and RL-based policy analysis (Renting et al., 2023). Damage and abatement cost function forms (e.g., overly optimistic quadratic damage, shallow convex MAC) can severely bias policy recommendations.
• Opportunity for reinforcement learning (RL): RL has been shown to probe even simplified IAMs effectively, identifying intervention timing and portfolios that outperform fixed policies under multiple reward structures. In such settings, agents rapidly exploit the dynamics to reach desirable “green” attractors, though real-world application requires higher-dimensional, heterogeneous, and uncertain environments (Wolf et al., 2023).
• Limitations in aggregation, resolution, and realism: Many IAMs operate at high levels of aggregation, masking regional heterogeneity and potential critical transitions. Process-based or agent-based models offer richer dynamics but are computationally intensive and less standardized for large-scale scenario generation.

IAM-based projections, while foundational for international climate assessments, require ongoing scrutiny and methodological development to address these structural and epistemic challenges.

6. Future Directions and Methodological Innovations

Active research avenues focus on:

• Multi-region, multi-agent, and coupled-economy extensions: To capture geopolitical, spatial, and political-economy feedbacks and distributional impacts.
• Dynamic, endogenous technology substitution and learning: Utilizing physical-diffusion models, logistic adoption, and endogenized learning rather than static CES forms, to recapture observed S-curve transitions and inform realistic cost trajectories (Sgouridis et al., 2016).
• Meta-modeling and explainability: Application of explainable RL, counterfactual analysis, and neural approximation to enable transparent, interpretable policy recommendations in high-dimensional, uncertain settings (Wolf et al., 2023).
• Integrated uncertainty modeling: Seamless fusion of risk, ambiguity, and scenario uncertainty, backed by high-performance computation and recent advances in neural dynamic programming (Cai, 1 Nov 2025).

These directions will yield IAMs with increased policy salience, improved robustness, and greater alignment with empirical technological, behavioral, and Earth system dynamics.