The Ghosts of Climates Past and the Specters of Climates Future
7. Empirical Modeling of Optimal Policies
Sketching the optimal policy in Figure 8 demands little more than pencil, paper, and a rudimentary understanding of intermediate economics. To move from theory t o useful empirical models requires developing a wide variety of empirical economic and geophysical models. Work has progressed t o the point where the economics and natural science can be integrated t o estimate optimal control strategies. In one study, I developed a simple cost- benefit analysis for determining the optimal steady-state control of C 0 2 and other greenhouse gases based on the comparative statics framework shown in Figure 8 (Nordhaus, 1991). This earlier study came t o a middle-of-the-road conclusion that the threat of greenhouse warming was sufficient t o justify low-cost steps t o slow the pace of climate change.
A more complete elaboration has been made using an approach I call the
"DICE model," shorthand for a Dynamic Integrated model of Climate and the
cono om^.^
The DICE model is a global dynamic optimization model for estimating the optimal path of reductions of GHGs. The basic approach is7The basic model and results are resented in Nordhaus (1992a, 1992b), while complete documentation and analysis are forthcoming in Nordhaus (1994).
t o calculate the optimal path for both capital accumulation and reductions of GHG emissions in the framework of the Ramsey model of intertemporal choice (Ramsey, 1928). The resulting trajectory can be interpreted as the most efficient path for slowing climate change given inputs and technologies;
a n alternative interpretation is as a competitive market equilibrium in which externalities or spillover effects are corrected using the appropriate social prices for GHGs.
T h e question addressed in the DICE model is whether t o consume goods and services, invest in productive capital, or slow climate change via reducing GHG emissions. The optimal path chosen is one that maximizes an objective function that is the discounted sum of the utilities of per capita consump- tion. Consumption and investment are constrained by a conventional set of economic relationships (Cobb-Douglas production function, capital-balance equation, and so forth) and by a novel set of aggregate geophysical con- straints (interrelating economic activity, GHG emissions and concentrations, climate change, costs of abatement, and impacts from climate change). T h e impact function is based on the discussion in the last section, while other relationships are drawn from sources in economics and the natural sciences.
To give the flavor of the results from the DICE model, we will con- sider the economic optimum and compare it t o two alternative policies that have been proposed by governments or by the environmental community. 1.5OC (compare this with the projections in Figure 7).
Solving the DICE model for the three policies just described produces a time sequence of consumption, investment, GHG emissions limitations, and carbon taxes. T h e carbon taxes can be interpreted as the taxes on GHGs (or the regulatory equivalent, say in auctionable emissions rights) that would lead t o the emissions that would attain the policy objectives described in the last paragraph.
Figure 9 shows the resulting carbon taxes. For calibration purposes, in the United States, a carbon tax of $100 per ton would raise coal prices by about $70 per ton, or 300%, would increase oil prices by about $8 per barrel, and would raise around $200 billion of revenues (before taking account of emissions reductions). The economic optimum produces relatively modest carbon taxes, rising from around $5 per ton carbon t o around $20 per ton by the end of the next century. The stabilization scenarios require much more
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Economic optimum 4 Stabilize climate 4 Stabilize emissions [ Figure 9. Carbon tax rate (tax in $ per ton C equivalent).stringent restraints. For emissions stabilization, the carbon t a x would rise from around $40 per ton currently t o around $500 per ton carbon late in the next century; climate stabilization involves current carbon taxes over $100 per ton today rising t o nearly $1000 per ton by the end of the next century.
We can also inquire into the estimated net economic impact of alterna- tive approaches in the DICE model. For the global economy, the economic optimum has a value over no controls (in terms of the discounted present value measured in 1990 consumption) of $270 billion. On the other hand, sta- bilizing emissions a t 1990 levels leads t o a net present-value loss of around
$11 trillion relative t o the optimum while attempting t o stabilize climate would have a net present-value cost of around $30 trillion. If we annualize these a t a discount rate of 6%, these represent, respectively, a gain of 0.8%
and losses of 3 and 9% of today's annual gross world output.
At present, there are several other economic studies of efficient ap- proaches t o slowing global warming. The studies of Manne and Richels (1990,1992), Peck and Teisberg (1992), and Kolstad (1993) find conclusions that are roughly similar to those reported here. The studies by Jorgenson and Wilcoxen (see especially (1991)) show a lower set of carbon taxes needed
t o stabilize GHG emissions that those shown here, in part because of the induced innovation in the Jorgenson-Wilcoxen model.
Three studies - those of Cline (1992), Peck and Teisberg (1992), Kolstad (1993) as well as earlier studies by the present author (1979, 1991) - also determine the optimal emissions control rates and carbon taxes. With the exception of Cline (1992), all the earlier studies show optimal policies in the general range of those determined here. A study by Hammitt, Lempert, and Schlesinger (1992) traces out alternative control strategies t o attain certain temperature constraints; while not determining an optimal path, this study concludes that a "moderate reduction strategy" is less costly than an "aggressive" approach if either the temperature response t o GHG concentrations is low or if the allowable temperature change is above 3OC.
The study by Cline (1992), by contrast, proposes much higher control rates.
The more stringent controls in the Cline study are due t o a number of features - primarily, however, because the Cline result is not grounded in explicit intertemporal optimization and assumes a rate of time preference that is lower than would be consistent with observed real interest rates.