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| DICE model | |
|---|---|
| Name | DICE model |
| Inventor | William Nordhaus |
| First publication | 1992 (earlier versions 1991) |
| Field | Integrated assessment modeling, climate economics |
| Institutions | Yale University, Cowles Foundation |
| Notable awards | Nobel Prize in Economic Sciences (2018) awarded to William Nordhaus |
DICE model
The DICE model is a widely cited integrated assessment model that links greenhouse gas emissions, climate change dynamics, and macroeconomic outcomes to evaluate optimal mitigation pathways and welfare-maximizing carbon prices. Developed as a compact, dynamic-recursive framework, it combines modules for emissions, the carbon cycle, radiative forcing, temperature change, and economic growth to produce policy-relevant metrics such as social cost of carbon and optimal abatement trajectories. The model underpins debates in climate policy and environmental economics, influencing academic research and governmental assessments.
DICE couples a simple representation of the atmosphere-ocean carbon exchange with a Ramsey-style optimal growth model originally inspired by the work of Frank Ramsey and subsequent formalizations by the Solow growth model lineage. The model’s economic core treats a representative-agent social planner balancing consumption, capital accumulation, and emissions-intensive production, drawing on methods from John Hicks and Paul Samuelson-inspired welfare economics. Radiative forcing and temperature responses borrow from climate science traditions established by researchers associated with institutions such as NASA, NOAA, and the IPCC assessment reports. Outputs include projections comparable with scenarios from Representative Concentration Pathways and assessments used by bodies like the U.S. Environmental Protection Agency.
DICE was introduced by William Nordhaus in the early 1990s while he was affiliated with Yale University and the Cowles Foundation. Its evolution reflects cross-disciplinary dialogue among economists and climate scientists, paralleling work at centers such as the Tyndall Centre, Hadley Centre, and the Potsdam Institute for Climate Impact Research. Subsequent updates incorporated empirical findings from studies by James Hansen, Syukuro Manabe, and Gavin Schmidt on climate sensitivity and by macroeconomists such as Robert Solow and Thomas Sargent on growth dynamics. The model’s prominence grew with debates preceding international negotiations such as the Kyoto Protocol and the Paris Agreement, and with attention following Nordhaus’s receipt of the Nobel Prize in Economic Sciences.
DICE integrates modules: an economic production function typically using a Cobb–Douglas specification inspired by Paul Romer and Robert Lucas Jr., a carbon emissions module driven by sectoral output and emissions intensity, and a climate module representing the carbon cycle and thermal response calibrated against estimates from studies by James Hansen and groups like IPCC Working Group I. The optimization problem is formulated as an intertemporal welfare maximization with discounting mechanisms influenced by debates between proponents from schools associated with Kenneth Arrow and Amartya Sen on social welfare aggregation. Damage functions relate temperature change to GDP loss, drawing on empirical estimations similar to research by Solomon Hsiang and Michael Deschenes. Numerical solution techniques employ dynamic programming and calibration routines in the tradition of computational approaches used by researchers at RAND Corporation and NBER.
Key parameters include climate sensitivity, carbon cycle transfer coefficients, damage function curvature, and the pure rate of time preference. Calibration sources span paleoclimate reconstructions championed by Claude Lorius and Philippe Ciais, instrumental records curated by James Hansen and NOAA datasets, and macroeconomic series compiled by institutions such as the World Bank and the OECD. Estimation strategies use econometric approaches akin to those of Angus Deaton and James Heckman for income dynamics, while uncertainty analysis borrows Monte Carlo and scenario techniques popularized in studies at Lawrence Berkeley National Laboratory and the Intergovernmental Panel on Climate Change.
DICE has been used to compute social cost of carbon estimates for policy guidance adopted or evaluated by agencies such as the U.S. Environmental Protection Agency, central banks engaging with climate stress tests like the Bank of England, and advisory panels in countries represented within the European Commission. It informs cost–benefit comparisons relevant to instruments discussed at forums such as the United Nations Framework Convention on Climate Change negotiations and national carbon pricing debates involving jurisdictions like Sweden, Canada, and New Zealand. Academics employ DICE to explore sensitivity to discount rates, technology assumptions influenced by research at MIT and Stanford University, and adaptation-versus-mitigation tradeoffs considered in policy reviews by the World Resources Institute.
Critiques originate from scholars associated with diverse traditions including climate science, ethics, and heterodox economics. Concerns highlight oversimplified damage functions relative to empirical work by Hsiang and Marshall Burke, limited representation of tipping points emphasized by researchers like Tim Lenton and Hugo T.-affiliated studies, and normative sensitivity to discounting discussed in literature by Nicholas Stern and Martin Weitzman. Critics from institutions such as Climate Action Network and some contributors to IPCC assessments argue that aggregated, representative-agent assumptions obscure distributional and regional risks documented in studies by Ishita Haldar and Robert Kopp. Methodological limits also include coarse temporal resolution compared with integrated assessment models developed at IIASA and the Potsdam Institute.
Successor models and forks adapt DICE’s core into alternative frameworks including the RICE model variants tailored for regionally disaggregated analysis by Jagdish Bhagwati-adjacent scholarship, and stochastic extensions incorporating fat-tailed risks explored by researchers influenced by Martin Weitzman and Leonard Mlodinow-style probability analysis. Hybridizations couple DICE-like economics with detailed energy-system modules found in models from Lawrence Berkeley National Laboratory, Energy Information Administration, and projects at Imperial College London and MIT Energy Initiative to assess technology pathways, carbon capture options, and sectoral decarbonization consistent with scenarios from IRENA and IRENA-linked studies.