Nordhaus DICE model

Nordhaus DICE model
Name	DICE model
Developer	William D. Nordhaus
First release	1990
Latest release	ongoing
Programming languages	Fortran, MATLAB, Python
Discipline	Integrated assessment

Nordhaus DICE model The Nordhaus DICE model is an integrated assessment framework combining climate science, economic growth, and policy analysis developed by William Nordhaus to evaluate interactions among climate change drivers, carbon dioxide emissions, and welfare. The model links simplified representations of atmospheric physics, carbon cycle processes, and a neoclassical growth formulation to generate projections used by policymakers, researchers, and institutions for estimating metrics such as the social cost of carbon. It has informed debates in climate economics, environmental policy, and intergenerational equity across venues including Nobel Prize attention, academic journals, and governmental assessments.

Overview

DICE (Dynamic Integrated model of Climate and the Economy) integrates representations of global economy production, greenhouse gas concentrations, radiative forcing, temperature response, and damage functions in a single cost–benefit optimization. The model was introduced by William Nordhaus and evolved through iterations engaging commentators from Intergovernmental Panel on Climate Change participants, IPCC authors, and scholars at Yale University and Cowles Foundation–affiliated networks. DICE has been used alongside other integrated assessment models like PAGE model, FUND model, and platform comparisons in Model Intercomparison Projects to inform policy analysis at bodies including United States Environmental Protection Agency, UK Committee on Climate Change, and European Commission panels.

Model Structure and Components

DICE couples a stochastic or deterministic climate module to a Ramsey-type optimal growth model with capital accumulation, labor, and productivity parameters linked to exogenous demographic projections from United Nations scenarios. The climate component uses a simplified two- or three-box energy balance representation inspired by formulations in Hansen studies and Arrhenius forcings, mapping CO2 concentrations to radiative forcing and surface temperature change. The carbon cycle is represented by impulse response functions drawn from Bern model studies and calibrated against observations from Mauna Loa Observatory and paleoclimate data discussed in Paleoclimatology reports. Economic output is produced via a Cobb–Douglas production function analogous to frameworks used by Solow, Ramsey, and Swan, with damage functions derived from empirical studies published in journals like The American Economic Review and Nature Climate Change. Mitigation is represented by abatement cost functions with parameters reflecting energy technology pathways seen in reports by International Energy Agency and Intergovernmental Panel on Climate Change chapters on mitigation.

Calibration and Parameters

Calibration in DICE relies on historical datasets from agencies such as World Bank, OECD, BP Statistical Review, and paleoclimate proxies discussed in IPCC AR5 and IPCC AR6 reports. Key parameters include climate sensitivity informed by Charney report and later assessments by IPCC, carbon cycle lifetimes informed by studies at NOAA and research groups like Law Dome ice core analyses, and productivity trends tied to Penn World Table and Bureau of Economic Analysis data. Discount rates in DICE reflect debates traced to works by Frank Ramsey, Martin Weitzman, and Nicholas Stern; the social time preference parameter and pure rate of time preference choices align with discussions in Stern Review and responses by Nordhaus critics. Damage function shapes borrow from empirical cross-sectional studies of extreme weather impacts published in Proceedings of the National Academy of Sciences and sectoral assessments by IPCC Working Groups.

Policy Applications and Social Cost of Carbon

DICE has been applied to compute the optimal carbon price path, policy scenarios for emissions trajectories compatible with targets discussed at United Nations Framework Convention on Climate Change negotiations, and estimates of the social cost of carbon used by regulatory agencies including US EPA and Office of Management and Budget. Outputs inform carbon tax proposals debated in parliaments such as US Congress, European Parliament, and policy institutes like Brookings Institution and Resources for the Future. Scenario analyses using DICE have been compared with mitigation pathways in Paris Agreement-aligned studies and national commitments submitted under Nationally Determined Contributions to evaluate cost–benefit tradeoffs.

Criticisms and Limitations

Critiques of DICE target its aggregated single-region representation, limited treatment of uncertainty, and reliance on functional forms for damages and abatement costs debated in literature by Martin Weitzman, Richard Tol, Nicholas Stern, and Robert Pindyck. Scholars from climate science and development economics emphasize regional heterogeneity flagged in reports by World Bank and IPCC as important for evaluating distributional impacts. Economists from Harvard University, Massachusetts Institute of Technology, and London School of Economics have contested discounting choices and the representation of catastrophic risks discussed in economic theory critiques and legal-economic analyses in venues like Journal of Political Economy and Journal of Environmental Economics and Management.

Variants and Extensions

Several extensions adapt DICE to multi-region frameworks, stochastic damage processes, endogenous technological change, and integration with energy system models developed at institutions like MIT, IIASA, Potsdam Institute for Climate Impact Research, and Princeton University. Examples include regionalized IAMs used by National Academies panels, stochastic formulations engaged by Weitzman-inspired analyses, and hybridizations coupling DICE-style macroeconomics with detailed energy system models such as those in MESSAGE, GCAM, and REMIND. Empirical researchers implement DICE variants in programming environments maintained by Yale researchers and open-source communities on GitHub to explore sensitivity to parameters highlighted by IPCC and academic debates.

Category:Integrated assessment models