ROLLING DICE FOR THE FUTURE OF THE PLANET

ROLLING DICE FOR THE FUTURE OF THE PLANET DUANE CHAPMAN. VIVEK SURI, and STEVEN G. HALL*

In an iqfluential paper published in Science, Nordhaus employs an integrated climate-economy model to study climate change. He finds that optimizing climate change policy requires low levels $ controls on emissions @greenhouse gases. This paper follows his pioneering methodology but challenges his conclusions. Nordhaus’s results depend crucially on certain parameters such as the discount rate and the autonomous decline in energy intensity of production. However, choosing a set $ different though equally plausible values for these parameters causes the control rate to rise substantially. This translates into a greater level $action for slowing climate change.

I. INTRODUCTION

In November 1992, Science published William Nordhaus’s ”An Optimal Transi- tion Path for Controlling Greenhouse Gases.” Now accompanying that work is Managing the Global Commons: the Econom- ics @Climate Change (19941, as well as an earlier monograph version (1993a) and related articles in The Economic Journal (1991a) and The American Economic Review (1991b, 199313). This work follows by a decade Nordhaus’s original contributions to the National Academy of Sciences (1983) report Changing Climate. Nordhaus exem- plifies an important part of the scientific tradition: his methodology and assumptions are clearly specified in published form.

‘The authors are respectively, Professor, Depart- ment of Agricultural, Resource and Managerial Eco- nomics; Ph.D. student in Resource and Environmental Economics; and Ph.D. student in Agricultural and Bio- logical Engineering, Cornell University, Ithaca. This paper is based upon a presentation by Chapman and Hall at the Western Economic Association Interna- tional 69th Annual Conference, Vancouver, British Co- lumbia, June 3, 1994. The authors are grateful to the Cornell National Supercomputer Facility, a resource of the Come11 Theory Center, for computer support. They also thank Phillip Bishop for computational advice and an anonymous reviewer for helpful suggestions. In particular, they acknowledge William Nordhaus’s af- finity for openness in his work, which makes this paper possible.

Contemporary Economic Policy (ISSN 1074-3529)

1

In Science, Nordhaus finds that optimizing climate change policy improves the utility value of consumption by an insignificant three-hundredths of one percent. The optimal control level of CO, release is itself insignificant, peaking at a mere 15 percent. In his 1994 book, Nordhaus intro- duces some changes in the model, but the conclusions for his base case remain virtu- ally unaltered.

This paper challenges Nordhaus’s conclusions. In particular the analysis here involves changing some key parameter values. Choosing a set of different though equally plausible parameter values substantially alters Nordhaus’s conclusions about the optimal control rate.

II. SUMMARIZING THE DICE MODEL

The dynamic integrated climate-economy model (DICE) as developed by Nord- haus and his colleagues has two interact- ing components, the global economy and

ABBREVIATIONS DICE: Dynamic Integrated Climate Economy

GHG: Greenhouse Gas IPCC: Intergovernmental Panel on Climate

Change SDICE: Simplified Dynamic Integrated Climate

Model

Economy Model

Vol. XIII, July 1995 OWestem Economic Association International

2 CONTEMPORARY ECONOMIC POLICY

a climate model. In the global macroeconomy, aggregate gross world output is a Cobb-Douglas production function with Hicks-neutral technical change and con- stant returns to scale for capital and population. Capital stock reflects current investment and the depreciated remainder from the prior period. Gross world product is allocated between consumption and investment in each period. The objective of the model is to optimize the discounted present value of world utility:

T

h7 represents total world population, c is per capita consumption, Y is the rate of social time preference, and T is the length of the time horizon. V, discounted world utility, is optimized for trajectories of investment I t and the control rate of carbon dioxide emissions, CRt.

Three parts of this objective function represent philosophical assumptions. First, note that population N appears in the argument of the objective function. Apparently, more people translate into more world utility. (In a separate calcula- tion with the model, Jean Agras shows that higher population projections increase world utility and consumption as well a average global temperature.) The problem here is two-fold. Evidently, world utility is insatiable as world population and consumption increase. Also, population growth has no negative externality interaction with utility.

Second, the time horizon seriously may affect the optimal policy solution. Con- sider another model specification of geological assumptions. Here, over time, ocean absorption of CO, saturates, atmospheric decay declines, and damage is sharply convex with respect to greenhouse gas concentration and temperature change. In this hypothetical model, different values of T imply different impacts of the geological variables. A low value for T

would mean that the adverse conse- quences of these variables that occur at a later date will not be part of the policy calculus. Thus, T can become an index of the modeler's farsightedness.

The last philosophical assumption im- plicit in the objective function is the discount rate. The existence of r, the pure rate of time preference, is important as it re- duces the significance of future climate damage, or utility of future generations. Nordhaus uses Y = 3 percent.

Equations (2) through (4) represent the global macroeconomy:

This conventional formulation uses K (capital stock), 6 (annual depreciation), C (aggregate consumption), Q (output, or gross world economic product), 0 (a climate change impact variable described below), and y (which defines the elasticities of output with respect to capital and labor). In Equation (4), the term N1-r is equivalent to an assumption that the pro- portion of world population participating in the labor force as well as labor produc- tivity can be jointly represented by the world population variable with the (1-y) exponent.

The A term represents technological progress over time, or total factor produc- tivity growth. In Science, Nordhaus esti- mated this to have increased at 1.3 percent per annum between 1960 and 1989. He as- sumed that growth in A would decline slowly over the coming decades. To illus- trate, if growth in A declines at 1 percent per annum, then today's capital and labor transported 100 years into the future would produce 227 percent more gross world product.

CHAPMAN et al.: ROLLING DICE FOR THE FUTURE OF THE PLANET 3

Equations (5) through (7) represent the emissions-climate interaction:

(6)

(7)

Mt+l= .64*€, + [l - 0.9917IMt-1,

M , DT, = P*ln(-), P = 4.328. 749

Here, for equation (5), E is greenhouse gas emissions in C02 equivalent units, CR is the control rate for reducing C02 emissions, and s is the ratio of uncontrolled C02 emissions to Q. The C02/Q ratio declines independently at 1.25 percent. In other words, in 100 years, a dollar of gross world product will have only 28 percent of today’s C02 emissions.

Consider the interaction over time of technological change (A) and emission intensity (s). A given amount of capital and labor will have 35 percent less emissions in 100 years, although output will be 2.27 times higher. These autonomous trends in the model are quite favorable to a low controls policy.

Equation (6) shows the Nordhaus assumption for the atmospheric interaction of emissions and CO, concentrations. Equation (7) is not the actual Nordhaus relationship. In his work, the basic relationship between ocean, atmosphere, ra- diative forcing, greenhouse gas concentrations, and average temperature change are summarized in a more complex equation (1994, pp. 1718). However, equation (7) does reflect the Nordhaus representation of a greenhouse gas doubling causing a 3°C increase (1992, p. 1,316). The value reflects this assumption.

Climate change economics is in two parts, a damage function equation (8) and a cost of control function equation (9). They are combined in equation (lo), which feeds into equation (4).

(8) DT, 2 darn, = 0.0133*(-) , 3

(9) TC, = 0.068&CR:.887,

(10) l-TC,

CD- ,- 1 +darn,’

Here, darn is the fractional loss in gross world production Q from climate change damage. TC is the fractional reduction in available Q that is diverted to controlling C02 emissions. The ratio @ feeds into equation (4). Full discussion of the logical basis for all parameter and initial variable values can be found in the Nordhaus references.

111. EQUALLY PLAUSIBLE PLANETARY FUTURES

The full Nordhaus model optimizes V in equation (1). Finding the maximum sum of present value ”utils” (or ”discounted utility dollars”) involves determining the optimal time trajectories for I (aggregate investment) and CR (control rate fraction for CO, emissions). The Nordhaus work uses versions of this optimizing model to examine the economic implications of several global policies. These policies include a carbon emission tax and agreements to stabilize emissions or to stabilize greenhouse gas concentrations.

Figure 1 includes a reproduction of base case optimized greenhouse gas (GHG) concentrations from Nordhaus’s model. Figure 1 also shows the simplified replication results from the analysis here. Imply- ing originality for the analysis here would be inappropriate. Thus, ”DICE” represents Nordhaus’s results from the use of his model, and ”SDICE” represents the results from the simplified replication of DICE. Both Nordhaus and the analysis here use the same GAMS optimization programs.

Note that in figure 1, SDICE concentrations lie below DICE concentrations. Fig- ures 2 and 3 show a similar pattern for temperature change and optimal control rate. Consequently, any error in our SDICE relative to DICE understates climate change response to economic activity. The


FIGURE 1 Base GHG Projections: DICE and SDICE

T

+DICE -X-SDIC

Source for DICE: Nodhaus (1992. p. 1318)

dramatically different conclusions arise from parameter values rather than from a bias introduced by the adaptation.

Using a discount rate for making intertemporal comparisons has generated much controversy among economists. Consider a 5 percent rate: it would discount $100 million in economic loss occur- ring 100 years from today to only three- quarters of 1 percent of that amount now. This obviously raises questions of inter- generational equity. It is important here to distinguish between three concepts; time discounting, growth discounting, and goods discounting. As Nordhaus and others point out, in the context of optimal growth, these are related as follows:

d = r + a * g

Here I is the pure rate of social time preference. It is the rate at which utility is discounted in equation (1) above. This rate reflects an impatience to consume now rather than later. This phenomenon is called time discounting. In the second term, a is the elasticity of marginal utility of consumption, and g is the growth of consumption per capita. If consumption per person is growing, the marginal utility of an additional unit will be lower for the future (and richer) generations. The second term reflects discounting on this account and is referred to as growth discounting. The sum of the two, d, is the goods discount rate (or the real rate of interest).

Economists often argue that a value of r greater than zero cannot be justified on ethical grounds. According to Pigou (19521, people discount the future only because their "telescopic faculty is defec-


a" E .- M

5 v +a

FIGURE 2 Base Temperature Change: DICE and SDICE

[ 4 D I C E -X-SDICE I Source for DICE: Nordhaup (1992. p. 1318) converted lo 1995 b e .

FIGURE 3 Optimal CO, Control: DICE and SDICE

14 ..

.- ti +a y 12-

2 I 19% 2005 2015 2025 xus 2045 2055 2075 23% zos 2105 2115

[+DICE -x-SMCE]

Source for DICE: Optimal Base Case, Nodhaus (1992. p. 1317) and (1994. p. 94)

6 CONTEMPOR4RY ECONOMIC POLICY

tive." People display this myopia even if they can predict future events with cer- tainty. Thus, in most cases it could be at- tributed to the finiteness of the lifetimes of the individuals concerned. Ramsey (1928) also endorsed Pigou's point of view. For Ramsey, discounting later enjoyments in comparison with earlier ones was an "ethi- cally indefensible" practice and arose "merely from the weakness of the imagi- nation. "

Nordhaus finds that a zero or low rate is inconsistent with observed real rates of interest and contends that the choice of a discount rate is fundamentally an empirical matter and not an ethical one. He uses Y = 3 percent, which in combination with his assumptions for a = 1 and g = 3 percent implies an initial goods discount rate of 6 percent. Others (e.g., Cline, 1992) advocate a zero value for r, a = 1.5, and 8 = 1 percent, implying, according to Nordhaus, an em- pirically unsupported goods discount rate of 1.5 percent. In an early Intergovernmen- tal Panel on Climate Change (IPCC) version, Arrow et al. (1994) suggest r = 1/10 of 1 percent as a central value.

One thus can view the debate as follows: given that people ordinarily behave in a myopic manner, should policy plan- ners account for this fact in long-term policy decisions? Clearly, this issue combines complex questions of philosophy, moral- ity, and economics and will not be settled soon, if ever. Thus, while Nordhaus makes a strong case for one side of the debate, it is equally important to consider the other-i.e., the impact of r = 0 percent on h s results.

Fjgure 4 shows the impact of a zero percent rate of time preference on the optimal control path. The apparently optimal path is noticeably higher, reaching 35 percent in 2110. Whether the question of an appropri- ate value of r is an ethical or an empirical one, the above result proves that it is cru- cial for policy. Not only does it translate into a greater level of action, but also a greater urgency.

Next consider the impact of reducing the autonomous C02 decarbonization rate. In Science, the decarbonization of economic activity proceeded at a -1.25 percent rate (1992, p. 1,316). In later work, Nordhaus assumes a reduction in the decline (1994, pp. 16, 67). The empirical data provide evidence for the DICE -1.25 percent rate as well as for a much lower value. Nordhaus shows that from 1929 to 1989, the emissions intensity rate declined from 0.409 to a value of 0.232 metric tons per thousand dollars of GNP. (This latter figure is equivalent to 8 ounces of C02 per dollar.) In the United States, Japan, and other OECD countries, the decline ex- ceeded -1.4 percent annually (1994, p. 67). This is the basis for a projected -1.25 percent value.

However, including the rest of the world actually makes the global value somewhat higher (not lower) in 1989 than in 1960 (table 1). The global values reflect the growth in manufacturing and trade outside the OECD countries since 1960. Hence, s = 0 percent is somewhat more plausible than s = -1.25 percent. Figure 5 illustrates the increase in the control rate associated with s = 0 percent.

In figure 5, optimized CR: (s = 0) is similar to the path for optimal control with the discount rate at zero. With respect to temperature change, however, setting decarbonization at zero leads to much higher increases, reaching 4.8"C (8.7"F) in 2110. The surprise is that the result of both assumptions ( r = 0 and s = 0) is multiplica- tive. Optimal control now reaches 76 percent at the end of the time period.

Also consider cases where the response to a doubling of greenhouse gasses is stronger, at 4.5"C rather than 3°C. In this instance (not shown), optimal control reaches 50 percent at the end of the time period for r = 0 and s = 0 separately, and rises to 100 percent in 2090 when both r = 0, and s = 0.

What is the explanation for these dramatic results? Recall that Nordhaus found


FIGURE 4 SDICE Optimal Control and Discount Rates

i lW5 2005 2015 2021, 2035 2M5 2056 ZC85 1175 2oss 2095 2105 2116

FIGURE 5 SDICE Decarbonization and Optimal Control

T

.- Y

Y 8 a

W bn Y

ti d E

42 sZO%,r=O%


TABLE 1 Carbon Intensity, Global

Tons of Carbon Emissions per 1,000 GEE 1989$

Year World

1929 0.409

1960 0.219

1989 0.232

Motes: The highest value is 0.409 in 1929, declining to 0.219 in both 1960 and 1970, reaching 0.241 in 1980 and 0.232 in 1989. GEP is real gross economic product. From Nordhaus (1994, p. 67).

a peak optimal control rate of about 15 percent, yet the discussion here implies much higher optimal control rates reaching 76 percent. Simply put, two factors ex- plain the dramatic difference. First, the DICE base case values for the social rate of time preference r and carbon-output ratio s are believable, but there are other different values that also are justifiable. Sec- ond, there is a separability issue, in that variation in the carbon-output ratio s has more impact on the optimal control rate when r is very low, and this variation in s and r is more important when climate re- sponsiveness is greater.

As a mental experiment, assume that the central value for r is 1.5 percent and for s is -0.625 percent per year. Then, if all other parameters in the model take on their base values, one can argue that the true optimal control rate has a 4 percent probability of lying at or below the Nord- haus Science optimal C R (see the appendix).

IV. CONCLUSION

The analysis here uses the Science version of the dynamic integrated climate- economy model (slightly simplified). Equally plausible parameter values lead to dramatically higher optimal control rates. Consequently, the result that the true

optimal control rate curve probably is a very low one is unacceptable. In fact, a low control rate has a low probability of being correct.

APPENDIX

These results differ from Nordhaus’ sensitivity analysis (1994, especially p. 159) because the basic DICE parameters for r, s, and the p factor seem to interact to define very low optimal control rate paths. As a result of his for- mal sensitivity analysis, Nordhaus finds that “the probability that the optimal control rate is greater than 20 percent is around 5 percent for 1995,12 percent for 2045, and about 20 percent for 2095.” The low probabilities associated with higher control rates likely result from a prior choice of favorable ranges for parameters such as r and s. For his uncertainty runs, Nord- haus chooses a discrete distribution for the eight variables that he considers. Each variable can take five values, each with 20 percent probability. For Y , these values range from 1 percent to 5 percent per year, while for s, these go from -1.1 percent to -23 percent per decade (or about -0.1 percent to -2.5 percent per year). The third quintile values are the ones that are used in the base run. These correspond to 3 percent for T and -1.25 percent per year for s.

Suppose as an illustration that all other variables take on the base values that Nordhaus employs. Then one can choose a total of 25 combinations of Y and s. Given the above ranges, at least nine combinations of Y and s


will produce a control rate at or lower than Nordhaus’. These nine combinations are those in which r is greater than or equal to 3 percent and s is less than or equal to -1.25 percent. However, suppose one modifies the above ranges for r and s such that they begin at zero percent and end at the third quintile value that Nordhaus chooses. These other endpoints thus would be 3 percent for r and -1.25 percent for s. Then the probability of getting a control rate at or lower than his falls to only 1/25. The point of this illustration is that the range cho- sen for the parameters can strongly influence the probabilities of the outcomes.

REFERENCES

Arrow, K. J., W. R. Cline, K. Goran-Maler, M. Munas- inghe, and J. E. Stiglitz, “Intertemporal Equity and Discounting,” chapter 4 in IPCC, 1995, Second Assessment Report, Working Group 111 on Economic Implications, drafts, October 1994 and January 1995.

Cline, William R., The Economics of Global Warming, Institute for International Economics, Washing- ton, D.C., June 1992.

National Academy of Sciences, Changing Climate: Re- port o f the Carbon Dioxide Assessment Comyittee, National Academy Press, Washington, D.C., 1983.

Nordhaus, William D., Managing the Global Commons: The Economics $Climate Change, MIT Press, Cam- bridge, Mass., 1994.

, Managing the Global Commons: The Econom- ics $Climate Change, Yale University, monograph, January 1993a.

, “Optimal Greenhouse-Gas Reductions and Tax Policy in the ’DICE Model,” The American Economic Review (Papers and Proceedings), May 1993b, 313-317.

, “An C)ptimal Transition Path for Control- ling Greenhouse Gases,” Science, November 1992.

, ”To Slow or Not to Slow: The Economics of the Greenhouse Effect,” The Economic lournul, July 1991a, 920-937.

, “A Sketch of the Economics of the Green- house Effect,” The American Economic Review (Pu- pets and Proceedings), May 1991b, 146-150.

Pigou, A. C., The Economics $ We@re, 4th ed., Macmil- Ian, London, 1952.

Ramsey, F. P., “A Mathematical Theory of Saving,” The Economic lournal, Vol. 38, 1928, 543-559.

ROLLING DICE FOR THE FUTURE OF THE PLANET

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