The DICE ModelThe DICE model, developed by William Nordhaus, is a dynamic integrated model of climate change in which a single world producer-consumer makes choices between current consumption, investing in productive capital, and reducing emissions to slow climate change. Population growth and technological change yielding productivity growth are both externally assumed to decline asymptotically to zero, eventually yielding stabilized population and productivity.
The single consumer maximizes discounted present value of utility of consumption, subject to a Cobb-Douglas production function that includes damages from climate change. Emissions per unit output are assumed to decline exogenously at a fixed rate, and can be further reduced by costly emission-control measures. An increasing, convex emission-control cost function is estimated from prior studies, in which reducing emissions 50 percent from the prevailing level at any time costs about 1 percent of the world economy. Current carbon emissions add to atmospheric concentrations via a fixed retention ratio, and realized temperature change is modeled by a three-box model representing the atmosphere, mixed-layer upper ocean, and deep ocean. Damage from climate change is a quadratic function of realized temperature change with a 3-degree change calibrated to cause a 1.3 percent world GNP loss. A detailed description of the DICE model, including derivations of model equations, results, and sensitivity analysis can be found in Nordhaus (1994).
In an earlier analysis, Nordhaus developed an estimate of the sensitivity to climate change of the U.S. economy by looking separately at each major sector. His best estimate for the impact of an equilibrium 3-degree global temperature change was a loss of 0.25 percent of GNP. Judgmentally incorporating cross-sectoral linkages or other overlooked damages, he estimated that 1 to 2 percent of GNP was a plausible upper-bound for the cost of climate change of this magnitude. Several researchers developing other integrated-assessment models use points from Nordhaus' estimated damage range to calibrate their damage functions (Nordhaus 1991a, 1991b, and 1992).
Two extensions of the DICE model have recently been developed. RICE, developed by Nordhaus and Yang, includes multiple regions and decision makers, to permit analysis of more strategies and protocols. RICE exists in six-region and 10-region versions. The six regions are the United States, Japan, China, the European Union, the former Soviet Union, and the rest of the world; the 10-region version separates the rest of the world into five groups clustered by size. RICE has been used to analyze the implications of three broad international policy approaches: "do nothing" (the market solution); an efficient solution ignoring distributional effects (the cooperative solution); and a solution in which each nation chooses the best policy for itself (the nationalistic solution) (Nordhaus and Yang 1995). PRICE, under development, will include uncertainty in some key parameters.
These models are nonproprietary and are easiest to use with GAMS. Six short pages of GAMS code for DICE are published in the appendix of Nordhaus 1994. The equations used for RICE are published in the appendix of Nordhaus and Yang 1995. For more information contact the following:
Department of Economics
ATTN: William Nordhaus
New Haven, CT 06520
The next section is The PAGE Model.