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Resource and Energy Economics I5 (1993) 27-50. North-Holland

William D. NordhausYale University, New Hauen, CT 06520, USA

Final version received November 1992

Economic analyses of eflkient policies to slow climate change require combining economic andscientific approaches. The present study presents a dynamic integrated climate-economy (DICE)model. This model can be used to investigate alternative approaches to slowing climate change.Evaluation of five policies suggest that a modest carbon tax would be an efficient approach toslow globzl warming, while rigid emissions-stabilization approaches would impose significant neteconomic costs.

1. IntroductionThe threat of climate change has become a major economic and politicalissue, symbolic of growing concerns that humans are making irreversible andpotentially calamitous interventions in life-support systems. Climatologistsand other scientists have warned that the accumulation of carbon dioxide(CO,) and other greenhouse gases (GHGs) is likely to lead to globalwarming and other significant climatic changes over the next century. Many

scientific bndies. along with a growing chorus of environmentalists andgovernments, are calling for severe curbs on the emissions of greenhousegases, as for example the reports of the Intergovernmental Panel on ClimateChange [IPPC (1990)] and the Second World Climate Conference (October1990). Governments have recently approved a framework treaty on climatechange to monitor trends and national efforts, and this treaty formed thecenterpiece of the Earth Summit held in Rio in June 1992.To date, the calls to arms and treaty negotiations have progressed more orCorrespondence to: Professor William D. Nordhaus, Cowles Foundation, Yale University, Box1972, Yale Station, New Haven, CT 06520, USA.*Thi- research was supported by the National Science Foundation. The author is grateful forhelpful suggestions from Jesse Ausubel, Richard Cooper, William Hogan, Allan Manne, ThomasSchelling, Stephen Schneider, Paul Waggoner, and John Weyant, and for patient researchassistance from Zili Yang.

092%7655/93/$06.00 M:, 1993-Elsevier Science Publishers 5-V. All rights reserved


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28 W.D. Nordhaus, Controll ing greenhouse .gases

less independently of economic studies of the costs and benefits of measuresto s low greenhouse warming. Over the last few years, however, a growing(but not unanimous) body of evidence has pointed to the likelihood thatgxenhouse warming will have only modest economic impacts in industrialcountries, while programs to cut GHG emissions will impose substantialcosts. Like two ships passing in the night, the economic studies and thetreaty negotiations seems te be proceeding independently under their ownsteam.Notwithstanding the difficulties of marrying the economic analysis with thepolicy process, the need to address the potentia issues raised by futureclimate change is daunting for those who take policy analysis seriously. Itraises fomridable issues of data, modeling, uncerta ty, international coordi-nation, and institutional design. In addition, economic stakes areenormous, involving investments on the order of hundreds of billions ofdo!lars a year to slow or prevent climate change.In earlier studies, I developed a simple cost-benefit framework fordetermining the optimal steady-state control of CO, and other greenhousegases. This earlier study came to a middle-of-the-road conclusion that thethreat of greenhouse warming was sufficient to justify modest steps to slowthe pace of climate change, but I found that the calls for draconian cuts inGHG emissions by 50% or more were not warranted by the current scientificand economic evidence on costs and impacts.The earlier studies had a number of shortcomings, but one of the mostsignificant from an analytical point of view was the inadequate treatment ofthe dynamics of the economy and the climate. The steady-state approach isunsatisfactory primarily because of the extraordinarily long time lagsinvolved in the reaction of the climate and ecolromy to greenhouse gasemissions. Current scientific estimates indicate that the major GHGs have anatmospheric residence time over 100 years; moreover, because of the greatthermal inertia of the oceans, the climate appears to have a lag of severaldecades behind the changes in GHG concentrations; and there are long lagsin introduction of new technologies in human economies to changingeconomic conditions. It would appear, therefore, that the dynamics are of theessence and that an examination of the steady state may provide misleadingconclusions for the steps that we should take at the dawn of the age ofgreenhouse warming.

The plan of the present study is to develop a dynamic, global model ofboth the impacts of and policies to slow global warming. it is an integratedmodel that incorporates both the dynamics of emissions and impacts and theeconomic costs of policies to curb emissions. We call it the DlCE model as

*The latest version appears in abbreviated form in Nordhaus (199la) and in greaiyr detail inNordhaus ( I99 1b).


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W .D. Nordhaus, Controlling greenhouse gases 29

an acronym for a Dynamic Integrated Climate-Economy model. This newmodel is an advance over earlier studies in that it allows for different policiesin the transition path from those in the ultimate steady state. It does thisthrough the extension of the standard tools of modern optimal economicgrowth theory and adding to this analysis both a climate sector and aclosed-loop interaction between the climate and the economy. The model issufftciently small as to be transparent (or at least translucent), to allow arange of sensitivity analyses, and to be available for a number of furtherextensions.The purpose of this paper is to lay out in details the structure of the modeland the nature of the assumptions. The first section lays out the algebra ofthe model in simplified form. The following sections derive the parameters ofthe model in detail. The final sections then show some empirical runs of themodel and provide estimates of the optimal policy along with somealternative approaches.

2. MethodologyExisting empirical studies of the interaction between climate char.ge andeconomic growth have generally been of a partial-equilibrium or static

nature. Much economic work has to date analyzed the costs of differentGHG restrictions. Estimating the economic and other impacts of greenhousewarming has proved extremely difficult. I have attempted to summarize theresults of studies for the United States [see Nordhaus (19914, bit theseremain incomplete in a number of respects.The present study constructs a dynamic optimization model for estimatingthe optimal path of reductions of GHG gases. The basic approach is to use aRamsey model of optimal economic growth with certain adjustments and toestimate the optimal path for both capital accumulation and GHG-emissionreductions. The resulting trajectory can be interpreted as either (i) the mostefficient path for slowing climate change given initial endowments or (ii) asthe competitive equilibrium among market economies where the externalitiesare internalized using the appropriate sncial shadow prices for GHGs. Wefirst describe the approach verbally and then present the model in equationform.In intuitive language, the approach is the following. Begin with the marketsector of the economy. The global economy is assumed :o produce acomposiic cllllh&itj;. This nxxm 111a.i cax~tries cart differ in their quan.lita-

The complete mode! is presented in a forthcoming book [Nordhaus (1993a)]. In addition, ;hetheoretical underpinnings of the model pre developed in a companion paper, Nordhaus (1993bLwhich developed an optimal growth mcdel in which to analyze the issue of the optimal responseto the threat of climate change under conditions of certainty.


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xi W.D. Nordhaus, Controlling gwrnhouse gasestive attributes, but there cannot be large differences in the composition orrelative proportions of different commodities. While this is a restrictiveassumption, preliminary work with a more complete multi-country modelsuggests that aggregation does not affect the ma_jo:- onclusions.Our composite economy is endowed with an initial stock of capital, labor,and technology, and all industries behave competitively. Each countrymaximizes an intertemporal objective function, identical in each region,which is the sum of discounted utilities of per capita consumption timespopulation. Output is produced by a Cobb-Douglas production function incapital, labor, and technology. Population growth and technological changeare exogenous, while capital accumulation is determined by optimizing theflow of consumption over time.

The next part of the model introduces a number of relationships thatattempt to capture the major forces affecting climate change. This partincludes an emissions equation, a concentrations equation, a climate equa-tion: a damage relationship, and a cost function for reducing emissions.Emissions represent all GHG emissions, although they are most easilyinterpreted as CO,. Uncontrolled emissions are a slowly declining fraction ofgross output; this assumption is consistent with a complex set of assumptionsabout the underlying production functions. GHG emissions can becontrolled by increasing the prices of factors or outputs that areGHG-intensive.3Atmospheric concentrations are increased with emissions, with concen-trations reduced with an atmospheric residence time of 120 years. Climatechange is represented by realized global mean surface temperature, whichuses an equilibrium relationship drawn from the consensus of climatemodelers and a lag given by a recent coupled ocean-atmospheric models. Theeconomic impacts of climate change are assumed to be increasing in therealized temperature increase.We note that this model has one major shortcoming as a representation ofeconomic and political reality. It assumes that the public goods nature ofclimate change 5 somehow overcome. That is, it assumes that, through somemechanism, countries internalize in their national decision making the globalcosts of their emissions decisions. This seems unlikely, but the currentsolution has the virtue of calculating the equilibrium that would emerge wereeach country to behave in such a farsighted and altruistic fashion.One c onc ern that has arisen a bout this set of assump tions is whether it is c onsistent with

Funda me ntal laws of physics. Is it possible, in other words, to have an indefinite dec line inemissions-output ratros? In princip le, the answer is c learly y es be cause output is me asured inutiis (or, more prec isely, in ratios of ma rginal utilities), not in physica i terms. Reductions arise ifthe composition of output moves towa rd go ods and service s that have lower intensities ofco nstrained physica l units (away from c opp er wire a nd toward moving a few electrons in fibers).Morcswr, the waste of energy in c urrent ec onom ic ac tivity is prod igious.


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W.D. Nordhaus. Corar~oilinggreenhouse gases 31

3.3.1. Basic outline,

In estimating the eflicient path of capital accumulation and emissionsreduction, we use the following model and assumptions. The different regionsof the world are aggregated together and we analyze the optimal policy for

dividual Clearly, this assumption misses much of the currentdilemma and debate between developed and poor countries, and it alsoaverages out the losers and the winners from climate change, The defense ofthis assumption is that this s:udy is concerned with the efficient intertemporalpolicies, not with the issues concerning the distribution of income acrosscountries or people.

The model operates in steps of 10 years centered on 1965, 1975, 1985, . . .,2095, . . . . The model is calibrated by fitting the solution for the first threedecades to the actual data for 1965, 1975 and 1985 and is then optimizing forcapital accumulation and GHG emissions in the future. This approachassumes that it is desirable to maximize a social welfare function that is thediscounted sum of the utilities of per capita consumption. The major decisionis about the level of consumption today, where abstaining from consumptiontoday increases consumption for future generations. In technical language, wedesire to maximize the objective function:

maxC Wdt), W)]( 1+ p) -I,W)l g (1)

which is the discounted sum of the utilitie, of consumption, U[c(t), P(t)],summed over the relevant time horizon. Here U is the flow of utility orsocial well-being, c(t) is the flow of consumption per capita at time t, P!t) isthe level of population at time t, and p is the pure rate of sock1 timepreference. 5

The maximization is subject to a number of constraints. The first set

4This section presents the bare bones of a longer study which documents the data,assumptions, and literature more fully. Tht ionger study is currently available in Nordhaus(1992) and will be forthcoming as a monograph from MIT Press in Nordhaus (1993a).5No issue is more controversial than the role of discounting in long-term environmentalproblems. Much confusion arises because of the failure to distinguish between time discountingand goods discounting, a distinctian that is well handled in the Ramsey model. Timediscounting refers to the trade-off between the utility or well-being of different generations and isrepresented by the pure rate of time preference, p. in the objective function. However, mostsocial decisions involve goods and services rather than well-being. Society must decide whetherto make an rnvestment aimed at reducing todays consumption in order to increase consumptionin the future: this app roac h is one of good s discounting, and the intertemfwa ! prier is reflectedm the real interest rate, r. In the framuwork used hcrr with no population growth, with agrowt!, rate of real income at rate R. and in steady state. goods discounting is :c!a!ed to timediscounting by the equilibrium formula r = 1)+ 2~.


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represents economic constraints, while the second is the nove! set ofclimate-emissions constraints.

3.2. Econontic constraints6The first set of constraints is those relating to the growth of output.

Economists will recognize these as a standard model of optimal economicgrowth know- ,. as the Ramsey model [Ramsey ( 1928); Solow 11988)]. Thefirst equation is the definition of utility, which is equal to the size ofpopulation [P(t)] times the utility of per capita consumption u e(t)]. We takea power function to represent the form of the utility function.

U[c(t), P(t)] = P(t){[c(t)] -*- 11;( -r). (2)In this equation, the parameter x is a measure of the social valuation ofdifferent levels of consumption. which we call the rate of inequality aversion.When x=0. the utility function is linear and there IS no social aversion toinequality; as r gets large, the social attitude becomes increasingly egalitar-ian. In the experiments reported here. we take r= 1, which is the logarithmicor Bernoullian utility function.

Output [Q(t)] is given by a standard Cobb--Douglas production functionin capital in technology [,4(t)], capital [K(t)], and labor, which is pro-portional to population. The term Q(t) relates to climatic impacts and will bedescribed in eq. (12):

(3)where ; is the elasticity of output with respect to capital. We assumeconstant returns to scale in capital snd labor.

The next equation shows the disposition of output between consumption[C(t)] and gross investment [Z(t)]:

W--Q(t)--Z(t). (4)This simply notes that output can be devoted either to investment or toconsumption.

The next equation is the definition of per capita consumption:c(t) = C(t)/P(t).

Finally, we have the capital balance equation for the capital stock:(5)

hThis section presents a summary of a more exrensive analysis of the DICE model. The fulldocumentakm is given in Nordhaus (1993a).


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W.D. Nordhaus, Conrrollittg greenhouse gabe~

K(t)=(l -b,)K(t- l)+Z(t),33

(6)where 6, is the rate of depreciation of the capital stoc

3.3. Climate-emissions-damage equationsThe next set of constraints will be unfamiliar to most economists andconsists of a simple representation of the relationship between economicactivity, emissions, concentrations, and climate change. As with the economicrelationships, these equations are highly aggregated.

3.3. I. EmissionsThe first equation links greenhouse-gas emissions to economic activity. Enthe analysis that follows, we translate each of the GHGs into its CO,equivalent. To aggregate the different GHGs, we use a measure of the totalwarming potential, which is the contribution of a GHG to global warmingsummed over the indefinite future. Approximately 80% of the totai warmingpotential is due to COZ, and we therefore put most of our effort intoanalyzing that gas.In modeling GHG ernissions, I assume that the ratio of uncontrolledGHG emissions to gross output is a slowly moving parameter represented byo(t). In what follows, we assume that the exogenous decline in cr is 1.25% perannum. GHG emissions can be reduced through a wide range of policies. Werepresent the rate of emissions reduction by an emissions control factor,p(t). This is the fractional reduction of emissions relative to the uncontrolledlevel. One of the key questions investigated here is the optimal trajectory ofemissions control. The emissions equation is given as:

(7)In this equation, E(t) is GHG emissions, a(t) is determined from historicaldata, and it is assumed that GHG emissions were uncontrolled through 1990.The variable p(t) is determined by the optimization.

3.3.2. ConcentrationsThe next relationship in the economy-climate nexus represents theaccumulation of GHGs in the atmosphere. For the non-CO, Gissues are relatively straightforwardlifetimes or chemical transformations.that is likely to be the most important gas for greethat C z accumulation and trans


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34 W.D. Nordhaus, Controlling greenhouse gases

boxes in which each of the boxes is well mixed. The background study[Nordhaus (1992a, 1993)] shows that this can be represented by thefollowing equation:M(t)=PE(t)+(l --&)IL/l(r- l), (3)

where M(t) is the change in concentrations from pre-industrial times, /I is themarginal atmospheric retention ratio, and S, is the rate of transfer from thequickly mixing reservoirs to the deep ocean. This equation is the GHGanalog of the capital accumulation equation. Atmospheric concentrations ina period are determined by last periods concentrations [M(t- l)] times(l-d,), where &, is the rate of removal of GHGs. We have estimated thisrelationship on historical data (186(,!-1985) and derived the followingequation:M(t) -0.9917M(t - 1) =0.64E(t) R* =0.803, SEE=0.519(0.015) (3)

This is the equation we use in the modeP.

3.3.3. Climate changeThe next step concerns the relationship between the accumulation ofgreenhouse gases and climate change. Climate modelers have developed awide variety of approaches for estimating the impact of rising GHGs onchmatlc variables. an the whole, existing models are, unfortunately, muchtoo complex to be included in economic models. Another difficulty withcurrent general circulation models (GCMs) is that they have generally beenused to estimate the equilibrium impact of a change in CO, cencentrationsupon the level of temperature and other variables. For economic analyses, itis essential to understand the dynamics or transient properties of theresponse of climate to GHG concentrations.The basic approach is to develop a small model that captures thesummary relationship between GHG concentrations and the dynamics ofclimate change. In what follows, we represent the climate system by a multi-layer* system; more precisely, there are three layers - the atmosphere, themixed layer of the oceans, and the deep oceans - each of which is assumedto be well mixed. The accumulation of GHGs warms the atmospheric layer,which then warms the mixed ocean, which in turn diffuses into the deepoceans. The s in the system are primarily ue to the thermal inertia of thetbrec laye:rs. can write the model as follows:


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W.D. Nordhaus, Controlling greenhouse gases 35

T,(t)=T,(t-l)+(l/R,)(F(t)-ilT,(t-l)-(&lQCT,(t- l)- Vf- l)]L

(9)G(t)= T2(t- l)+(lIR,)((R,Ir,)CT,(t- l)- T2(f- I)]),

where T(t)=temperature of layer i in period t (relative to the pre-industrialperiod); i= 1 for the atmosphere and upper oceans (rapidly mixed layer) andi = 2 for the deep oceans; F(t) = radiative forcing in the atmosphere (relativeto the pre-industrial period); Ri = the thermal capacity of the different layers;r2 = the transfer rate from the upper layer to the lower layer; and A=feedback parameter.

The next step is to find the appropriate numerical representation of thesimplified climate model in (9). We estimate the parameters in (9) bycalibrating the smaller model to transient runs from larger GCMs and bycomparing the predictions with historical data. Unfortunately, the modelsdisagee by a wide margin, and the historical data are even further at variancefrom the climate models. In the study here, we use the results from a studyby Schlesinger and Jiang (1990) for calibration purposes. This study has atemperature-CO, sensitivity of 3C for CO, doubling, which is close to thatof thz scientific consensus [see National Academy of Sciences (1992)].

3.3.4. ImpactsThe next link in the chain is the impact of climate change on human and

natural systems. Estimating the damages from greenhouse warming hasproven extremely difficclc. An early discussion is contained in Schelling(1983), EPA summarized a number of studies (1989), and I put those studiesinto the context of the national-income accounts in Nordhaus (1991 b). Theoverall assessment of the cost of greenhouse warming in the U.S. was thatthe net economic damage from a 3C warming is likely to be around 0.25%of national income for the United States in terms of those variables could bequantified. This figure ic c!early incomplete. for it neg!ects a number of areasthat are either inadequately studied or inherently unquantifiable. As a roughadjustment, I increased this number to around 1% of total U.S. output toallow for these unmeasured and unquantifiable factors. Making adjustmentsfor output composition in different countries, I further raised the estimatedimpact to 1.33% of global output for all countries. In addition, there isevidence that the impact increases nonlinearly as the temperature increases,and we assume that the relationship is quadratic. Therefore, the finalrelationship between global temperature increase and income loss is:

d(t)=O.O133[T(t)/3]2Q(t), (10)where d(t) is the loss of global out greenhouse war


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36 W.D. ordltaus, Controlling greenhouse gases

there is much controversy about the parameters of (lo), using alternativeestimates of impacts does not change the basic results markedly.

3.3.5. Cost of emissions reductionThe last major link in the chain is the costs of reduction of greenhousegases. This is the one area that has been extensively studied and, while notwithout controversy, the general shape of the cost function has been sketchedon a number of occasions. There are numerous estimates, particularly forCO,, of the cost of reducing GHGs; see the extensive surveys in EPA (1990),Nordhaus ( 1991c), Dean and Hoeller (1992), Amano (1992), EC (1992a, b)and the results of EMF-12. Using current annual emissions of 8 billion tonsof CO2 equivalent, my survey suggested that a modest reduction of GHGemissions can be obtained at low cost. After 10% reduction, however, thecurve rises as more costly measures are required. A 50% reduction in GHGemissions is estimated to cost almost $200 billion per year in todays globaleconomy, or around 1% of world output. This estimate is understated to theextent that policies are inefficient or are implemented in a crash program.The final form of the equation used in the model is:

(11)where p is the fractional reduction in GHG emissions and TC/GNP is thetotal cost of the reduction as a fraction of world output.Combining the cost and damage relationships, we have the Q relationshipin the production function as follows:

A thorough review of impacts by Cline (1992) finds an estimated impacts of I.176 of GNP fora 2SC warming as opposed to the estimate of 1% for 3C warming by the present author. Amore recent unpublished study by Fankhauser (1992) estimates total impacts of a doubling ofCO1 would !ead to a 1.3% cost to the US, a 1.4% cost to the OECD, and a 1.57: cost to theworld. Because estimating the impacts of climate change has proven extremely dimcult, thepresent author is in the process of undertaking a survey of experts on the economic impacts ofclimate change on human and non-human systems. At the mid-point of the survey, the trimmedmean of the experts estimate of the impact of a 3C warming is approximately 20% higher thanthe estimate used in the DICE model while the experts estimate of the impact of a 6C warmingis about 30% lower than that in the DICE model. One major concern of most respondents isthat the impact is thought to be considerably higher for low-income countries than in high-income countries.The -nest systematic study is the model comparison study of the Stanford Energy ModellingForum 12 under the general direction of John Weyant. The results of this study have beenpresented informally and conform for the most part to the survey in Nordhaus (1991~).Alternative views of the costs of mitigation are contained in National Academy of Sciences(1992) and Cline (1992). The major difference among studies concerns the possibility of zero-costor low-cost mitigation in areas where informational deliciencies or market failures hinderrtiaping all cost-benelicial investments in energy conservation. National Academy of Sciences(1992) estimates these to range between 10 and 40:;; of U.S. GHG emissions, whereas this studyis at the lower end of that range.


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W.D. Nordhaus, Controlling greenhouse gases

= [l -O.o686~(t)2~**]/[1 +o.o0144T(t)q.37

(12)

ata, calibration, and sensitivity analysis4.1. Fitting the model

This section describes briefly the sources of the data used for the modeland the cahbration of the model to the data. Data on the major variableswere collected for three years, 1965, 1975 and 1985, while future periods areestimated by the calculations described above. Data on population, GNP,consumption, and investment are obtained from existing data sources of theWorld Rank, UNESCO, the OECD and the U.S. and other nationalgovernments.

The parameters of the Cobb-Douglas production function are obtained byassuming that the output-elasticity of capital is 0.25 and then by estimatingthe level and rate of Hicks-neutral technological change directly as aresidual. The utility L&on is assumed to be logarithmic, and the rate ofsocial time preference is taken to be three percent per year. This preferencefunction leads to predictions of the rate of return on capital and the grosssavings rate that are close to observed levels.

Assumptions about future greT.vth trends are as follows: the rate of growthof population is assumed to decrease slowly, stabilizing at 10.5 billion peoplein the 22nd century. The rate of growth of total factor productivity iscalculated to be 1.3/, per annum in the 1960-1989 period. This rate isassumed to decline slowly over the coming decades.

The model has been run using the 486 version of the GAMS algorithm onvarious 386 compatible machines. The canonical runs presented below use a40-period calculation with terminal valuations (or transversality conditions)on carbon, capital, and atmospheric temperature; these terminal valuationswere obtained from a 60-period run and are sufficient to stabilize thesolution for the first 20 periods. The canonical 40-period run can be solvedin about two minutes on an Intel 486/33 processor.

Optimization models of the kind analyzed here have proven extremelyresistant to conventional econometric estimation. In the place of a formalstatistical procedure, we have simply chosen parameters so that the valuestaken by the model in the first three periods are tolerably close to actualdata. The current solution matches global GNP, emissions, GHG concen-trations, and even estimates of global temperature change reasonably well forthe historical periods.

The details of the data are described in Nordhaus (1993a).


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4.2. Sensitivity analysesThe DICE model contains many parameters and assumptions that will

affect the projections and policy conclusions. The present study presents thecentral or best-guess case and does not at this stage include sensitivityanalyses. In work underway, however, an extensive and systematic attempt toevaluate the major uncertainties has been undertaken, and that analysis willbe presented in Nordhaus (1993a). A brief description of the approach andtentative results of the sensitivity analysis will be provided here.

The sensitivity analysis first screens each of the parameters and majormodel components in the DICE model to determine which are important foreconomic, environmental, and policy variables, Among the two dozenparameters, nine which have the most impact upon key outcomes are thenselected for detailed analysis - these nine including parameters such aspopulation and productivity growth, the parameters of the climate, emissions,and concentrations modules, and the rate of time preference. A Monte Carlorun then provides estimates of the uncertainty due to each parameter as wel!as the underlying uncertainty about the major variables (such as tempera-ture, GHG concentrations, and GHG control rates). The major results of thisstage to data are that the results are modestly sensitive to alternative valuesof major variables. Among the important variables that produ,-e largeuncertainties are population and productivity growth, the trend in the GHGemissions-output ratio, and the pure rate of time preference.

The final stage of the analysis is to determine the impact upon the optimalpolicy of uncertainty. Should we pay an insurance premium to reflect theimpact of uncertainty, non-linearity, and risk aversion upon our optimalpolicy? While the research on the issue is still underway, it appears that theuncertainty about the size and impacts of future climate change would add asignificant risk premium to, perhaps even doubling, the best guess policiesanalyzed here.

We now describe the different scenarios or policy experiments to which themodel is applied.

Many readers of this and associated studies have expressed concern that the results areinherent in assuming too high a discount rate. While there is some merit !n this point, thewhole story is more complicated. In the first point, the distinction between !ime discounting andgoods discounting is often obscured. While people may raise ethical objections to timepreference in the form of a high pure rate of time preference, there is no analogous objection toa high rate of goods discounting in the form of a high real interest rate where that reflects rapidgrowth of living standards. Second, when the pure rate of time preference is lowered to 0.1% peryear while adjusting the rate of inequality aversion to maintain the same real rate of interest,there is only a modest change in the optimal policy (either the carbon tax or the GHG controlrate). The change in the optimal policy occurs because an increase in the net savings rate drivesdown the real interest rate.


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W .D. Nordhaus, Cent roIling greenhouse gases 39

5.1. No cont rols (baseline)The first run is one in which there are no policies taken to slow or reversegreenhouse warming. Individuals would adapt to the changing climate, but

governments would take no steps to curb greenhouse-gas emissions or tointernalize the greenhouse externality. This policy is one which has beenfollowed for the most part by nations through 1989.

5.2. Optimal policyThe second case undertakes to construct economically efficient or optimal

policies to slow c!imstc change. This run -WVAmizcr the present value ofeconomic welfare; more precisely, this case maximizes the discounted value ofutility in (1) subject to the constraints and relationships in (2) to (12). Thispolicy can be thought of as one in which the nations of the wor!d gather toset the efficient policy for internalizing the greenhouse externality. It isassumed that the policy is efficiently implemented, say through uniformcarbon taxation, in the decade beginning 1990.

5.3. Ten-year delay of optimal policyThis policy is one which delays implementing the optimal policy for tenyears. This policy examines the issue of the costs and benefits of delayingimplementing policies until our knowledge about the greenhouse effect, alongwith its costs and benefits, is more secure. This approach has been advocatedby the US. government during the Bush administration. In this scenario, weassume that sufficient information is in hand so that the optimal policy is

implemented beginning in the decade starting in 2000.

5.4. Tw enty percent emiss ions reductiorz from 1990 levelsMany environmentalists and some governments are proposing a substan-tial cut in CO2 or GHG emissions. One target that has been prominentlymentioned is a 20% cut in emissions. This is interpreted here as a 20% cut ofthe combination of CFC and CO2 emissions from 1990 levels, where these

are converted to a CO,-equivalent basis. In quantitative terms, this repre-sents an emissions limitation of 6.8 billion tons per year of CO2 equivalent.This policy has no particular analytical, scientific, or economic merit, but ithas the virtue of simplicity; it implies a growing percentage reduction in thefuture given a growing uncontrolled emissions path.


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40 W.D. ordkaus, Controlling greenhouse gasesTable 1

Impact of alternative policies on discounted consumption.~~ ____ .~~__ _ - __~~._ _..... _ ~__._.._ ~__.Discounted valueof consumption, 1990 Difference[trillions from no controls PercentDescription of 1989 us $1 [billions of $1 difference__ -No controls 731.694 0. 0.000Optimal policy 731.965 271 0.037Ten-year delay 731.937 243 0.033Stabilize emission 720.786 ( 10,908) - 1.491Geoengineering 737.296 5,602 0.766

Runno.-~12345

5.5. GeoengineeringA final policy would be to determine the benefit of a technology whichwould provide costless mitigation of climate change. This could occur, forexample, if some of the geoengineering options proved technically feasibleand environmentally benign. Two interesting proposals include shootingsmart mirrors into space with 16inch naval rifles or seeding the oceans withiron to accelerate carbon sequestration. An alternative interpretationwould be that the greenhouse effect has no harmful economic effects. Thisscenario is useful as a baseline to determine the overall economic impact ofgreenhouse warmins and of policies to combat warming.

esults and conclusionsWe riow summarize the overall results for the five scenarios described

above. A longer description of the model and a presentation of the numericalresults is contained in Nordhaus (1993a).

6. I. Overall resultsTable ! shows the overall evaluation of the different policies. The first

column shows the discounted value of consumption for the five paths. This iscalculated as the present value of consumption after 1990 discounted at themarket rate of return on capital (discounted back to 1990 in 1989 prices).

The optimal policy in row 2 has greater value than the three other policiesin rows 1, 3 and 4.13 The optimal policy has a net benefit of $271 billionrelative to a policy in which no controls are undertaken. This number is

The issues of geoengineering are discussed in National Academy of Sciences (1992).13The values in wtwnn 3 for run i are equal to the pres(:ntplus the algbr2ic differeme in tll- :talue of consumption for run I. ._.~!!~-IP(! vz!v.e of the objc:,ive function from run i to run 1.


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W.D. Nordhaus, Conrrolling gree nhouse ga ses 41

absolutely large, although it is only 0.037% of the discounted value of theconsumption. The cost of delaying the optimal policy by ten years isestimated to be $28 billion.The environmentali~?s policy of reducing emissions 20% below 1990 levelsis extremely costly. We estimate that this policy will cost $10.9 trillion inpresent value terms. This constitutes 1.5% of the total discounted value ofconsumption.The last row shows the overall economic impact of climate change. Thenet damage from global warming is estimated to be $5.9 trillion relative tothe optimal policy and Fj.6 trillion relative to a policy of no controls. Theserepresent 0.81 and 0.77% of the discounted value of consumption.In general, these numbers are mind-numbing in absolute size - largelybecause we are considering global output over the indefinite future. On theother hand, with the exception of the policy of stabilizing emissions, thenumbers are modest relative to the total size of the global economy.6.2 Emissions and concentrations

We next show some of the details of the model runs. Figs. 1 and 2 showthe emissions control rates in different scenarios. These show the extent towhich GHG emissions are reduced below their uncontrolled levels. In theoptimal path, the rate of emissions reduction is approximately 10% of GHGemissions in the near future, rising to 15% late in the next century. (Recallthat this is primarily CO1 emissions.) The environmental path of a 20% cutin emissions from the 1990 level shows steeply rising control rates, with therate of control reaching 70% by the end of the next century.Fig. 3 shows projected CO,-equivalent atmospheric concentrations inbillions of tons COZ equivalent (again, this includes both CO2 and CFCs).The impact of the optimal control strategy is noticeable, reducing concen-trations by a little more than 100 billion tons at the end of the next century.Note that even with emissions stabilized at 80% of 1990 levels, theatmospheric concentrations of CO,-equivalent concentrations continue torise. The ten-year delay in implementing greenhouse gas restraints showvirtually no difference from the optimai path and is not included in thegraph.

6.3. Global temperatureFig. 4 shows the resulting projected increase in realized mean globalsurface temperatures (relative to temperatures in the 19th century). The

uncontrolled path shows an initial increase of around 0.6C today, rising to3.1C by 2100.

he optimal shows a I rowth rate of


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42 W.D. Nordhaus, Controll ing greenhouse gases

0.8

8=e= 0.6S!aB.g 0.4eb225 0.2ES

0

0.20

0.00

____._____ _---_-----.--- ---- ------._-_I1965 1985 2005 2025 2045 2065 2085 2105Time

++ Optimal - 20% cut -+ Uncont - IO-yr delayFig. 1. Greenhouse-gas control rate (reduction in GHG emissions).

Time

-8- Optimal * Uncont - 1 O-yr delayFig. 2. Greenhouse-gas control rate (reduction in GHG emissions).


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W.D. Nordhaus, Controll ing greenhouse gases 43

_---_--

--.--~----------- -------------_

------.----_--------___

1965 1965 20% 2025 2ti5T i me 2065 2085

* Optimal - 20% cut -a-- UncontFig. 3. Atmospheric greenhouse gas concentrations (billion tons CO, equiv., C weight).

3.5

0.0

.C:.

---------_-----------------

.--_ ---___----.-___--_-- ..A _ ._ . . - - .~.

--.------------ _ .~ ____ ._. ..__~

_--.----.. - _-.-------.

---_-------- ________. .-~__--._-.-

1965 19bS 20b5 2025 2045 2065 2085 2105Time

- 20% cut .o-. Uncont ----_ lo-yr delayFig. 4. Global mean temperature (C, difference from 1860).


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44 W.D. Nordhaus, Conlrollirlg grcenhortw gases

--_--- __------- __----- --____.

___.-----------.--- ----___---

___------ ------.-_ _--__._-__-

------- _ _ -- _- - - - _. -. - _ _ _.- -_ - - __ --

1965 1985 2005 2025 2045 2085 2085 2105Time1 0- Optimal + Uncont + lo-yr delay 1

Fig. 5. Carbon tax, different scenarios (tax in $ ton C equiv.).

4965 1985 2005 2025 2045 2065 2085 2105Timeptimal - 20% cut * Uncont - l O- y r delay

Fig. 6. Carbon tax, different scenarios (tax in $ ton C equiv.)


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W.D. Nordhaus, Controllivv~ greenhouse gasses 4s

2 1gE=5 00.5O -1.r$s -2$E -3

1965 1985 2005 2025 2045 2065 2085 2105Time- 20% cut - Uncont -+ lo-yr delay -8- Geoeng 1

Fig. 7. Differences in global output (from baseline, trillions 1989 US $).

0.2

-0.6

-_

I I I 11965 1975 1985 1995 2005 2015Time

Fig. 8. Differences in global output (from baseline, trillions 1989 US $).


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temperatures, with a rise of about 0.2C less than the uncontrolled path bythe end of the nexk century. The policy that cuts emissions to 80% of the1990 level shows continued growth in temperatures, rising to 2.25C by theend of the next century. This surprising result shows that even draconianpolicies will slow clim.ate change only modestly. The reason is primarilybecause of the momentum in the system kom existing concentrations ofGHGs.

6.4. Carboat taxesFigs. 5 and 6 show the carbon tax that would be necessary to implement

each of the policies. The carbon tax should be thought of as the tax (or itsregulatory equivalent) that would be necessary to raise fossil fuel and otherprices sufficiently to induce economic agents to substitute other goods andservices for carbon-intensive ones;The optimal path shows a carbon tax of around $5 per ton carbon (or theequivalent in other GWGs) for the first control period, 1990-1999. Forreference, a $10 per ton carbon tax will raise coal prices by $7 per ton, about25% at current U.S. coal prices. The carbon tax increases gradually over timeto around $20 per ton carbon by the end of the next century. The rising taxprimarily reflects the rising level of global output rather than increasinglystringent control efforts.The ten-year delay has a zero tax in the fourth period, but then is virtuallyindistinguishable from the optimal policy. The policy of no mitigationobviously has ,Lzero carbon tax. Fig. 6 shows the trajectory of the policythat cut emissio.As 20:; from 1990 levels. This tax reaches about $100 per tonearly in the 21st century and climbs to almost $500 per ton by the end of thenext century. Clearly, very substantial fiscal or regulatory steps are necessaryto bring about a traj:=tory with constant CQZ emissions.

6.5. 01rtputFigs. 7 and 8 show the impact of different policies on output. The firstshows the estimates for the entire period while the second zooms in on thefirst few periods. For these calculations, the value of output is green grossworld output (GGWP). Conceptually, GGWP equals output less the flow of

damages from climate change less the costs of mitigation. The surprisingresult of these figures is that the difference between a policy of no controlsand the optimal policy is relatively small through the next century. The flowimpact, relative to the optimum, is so hat less than one percent of realage (equal to the


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0 I I 8 I I 11965 1985 2005 2025 2045 2065 2085 2105The-+ Optimal - - 20% cut -. .. Uncont - Geoeng

Fig. 9. Per capita consumption (1989 US $).

difference between the no controls and the geoengineering) is much largerthan the cost of no controls relative to the optimum. But the latter appearssmall because a fair amount of economic cost would occur even in theoptimal trajectory.

While the difference between the no-controls and the aptimaf policies issmall, there are big stakes in both the geoengineering option and in theenvironmental option. The impact of a geoengineering solution would bequite substantial - because it would cut the costs of both climate damageand of mitigation.

There is also potential for a major waste of resources if the greenhousepolicies go too far. Fig. 7 shows the impact on green world output of goingtoo far in the control of greenhouse gases - leading to net losses in output ofover $3 trillion annually by the end of the next century.

Finally, fig. 9 shows the trajectory of real consumption per capita in thefour cases. The striking feature of this figure is that, even though there aredifferences among the cases studied here, the overall economic growthprojected over the coming years swamps the p.rojected impacts of climatechange or of the policies to offset climate ch;rlge. In these scenarios, futuregenerations may be worse off as a result of climate change, but ;h:y 3re sti!llikely to be much better off than current generations. In looking at thisgraph, I was reminded of Tom Schellings remark a few years ago tdiffer-c;nce between a climate-change an a no-climate-change scenario WQbe thinner than the line drawn by a number 2


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48 W.D. ordhaus, Controlling greenhouse gases

curves. Thanks to the improved resolution of computerized graphics, we cannow barely spot the difference!

The present study has investigated the implications of economic growth onthe environment as well as the economic impact of different environmentalcontrol strategies upon the global economy. This study takes the approachthat an efficient strategy for coping with greenhouse warming must weigh thecosts and benefits of different policies in an intertemporal framework. Usingthis approach, the major results and reservations are the following,

This study has examined five different approaches to GHG control: nocontrol, an economic optimization, geoengincering, stabilization of emissions,and a ten-year delay in undertaking climate-change policies. Among thesefive, the rank order from a pure economic point of view at the present timeis geoengineering, economic optimum, ten-year delay, no controls, andstabilizing emissions. The advantage of geoenginzering over other policies isenormous, although this result assumes the existence of an environmentallybenign geoengineering option. The policies of no controls, the economicoptimum, ten-year delay, and emissions stabilization have differential impactsthat are less than one percent of discounted consumption.

It is instructive to compare these results with those from other economicstudies. The studies of Manne and Richels (1990, 1992), Peck and Teisberg(1991), and Kolstad (1992) find conclusions that are roughly similar to thosereported here. All these studies contain explicit or implicit relationshipsbetween emissions control rates and carbon taxes; the relationships arebroadly similar to those found in figs. 1, 2 and 5 of this paper, althoughpapers with more detailed energy sectors have more complex dynamics thanthose seen here. The studies by Jorgenson and Wilcoxen ( 199 1 expecially)show a lower set of carbon taxes needed to reduce GHG emissions thanthose shown here in part because of the icduced innovation in theJorgenson-Wilcoxen model.

Three other studies - those of Cline (1992), Peck and Teisberg (!%I),Kolstad (1992) as well as earlier studies by the present author (1979, 19914 L)- also determine the optimal emissions control rates and carbon taxes. Withthe exception of Cline (1992), all the earlier studies show optimal policies irrthe general range of those determined here. A study by Hammitt et al. (1992)traces out alternative control strategies to attain certain temperature con-straints; while not determining an optimal path, this study concludes that a

reduction strategy is less costly t an an aggressive aerature-conco,nr.rations sc~sitiv~ty (1/i) is low or if the

ange is above 3C. The study of Cilr,e (1992), by


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W.D. Nordhaus, Controlling greenhouse gases 49

contrast, has much higher control rates. The more stringent controls in theCline study are due to a number of features - primarily, however, becausethe Cline result is not grounded in explici-t intertemporal optimization andassumes a rate of time preference that is lower than would be consistent withobserved real interest rates.r4It must be emphasized that the present analysis has a number ofimportant qualifications. The most important shortcoming is that thedamage function, particularly the response of developing countries andnatural ecosystems to climate change, is poorly understood at present;moreover, the potential for catastrophic climatic change, for which precisemechanisms and probabilities have not been determined, cannot currently beruled out. Furthermore, the calculations omit other potential market failures,such as ozone depletion, air pollution, and R&D, which might reinforce thelogic behind greenhouse gas reduction or carbon taxes. Issues of sensitivityanalysis with respect to either parameters or components of the model havenot been addressed in this study, although an examination of these issues isunderway, as discussed above. And finally, this study abstracts from issues ofuncertainty, in which risk aversion and the possibility of learning maymodify the stringency and timing of control strategies. Notwithstanding thesequalifications, the optimal-growth approach may he!p clarify the questionsand help identify the scientific, economic and policy issues that rnslstunderpin any rational decision.

14See the discussion in footnote 5 above.

ReferencesAmano, A., 1992, Economic costs of reducing CO2 emissions: A study of modeling experience in

Japan, Paper presented to the International Workshop on Costs, Impacts, and PossibleBenefits of CO, Mitigation, IIASA, Laxenburg, Austria, September.

Cline, W., 1992, The economics of global warming (Institute of International Economics,Washington, DC).

Dean, A. and P. Hoeller, 1992, Costs of reducing CO* emissions: Evidence from six globalmodels, OECD/GD (92) 140 (Organisation for Economic Co-operation and Development,Paris) processed.

EPA, 1989, U.S. Environmental Protection Agency, The potential effects of global climatechange on the United States Report to Congress, EPA-230-0589-050, Crc.

EPA, 1990, D.A. Lashof and D.A. Tirpak, eds., Policy options for stabilizing glcbal climate(Hemisphere, hew York).EC, 1992a, The ec.Jnomics of limiting COz emissions, Commission of the European Communi-ties, Special Edi:;on no. I (ECSC-EEC-EAEC. Brussels).

EC, 19CZb, The &r.late challenge: Economic aspects of the communitys strategy for limitingCOz emissions, Commission of the European Communities, n3. 51 (ECSC-EEC-EAFC,Brussels) May.

Fankhauser, S., 1992, The economic costs of global warming: Some monetary estimates, Paperpresented to the International Workshop on Costs Jmpacts, and Possible Benefits of CMitigation. IIASA, Laxenburg, Austria, Sept.

ammitt, J.K., R.J. Lemperl and M.F. Schlesinger, !992. A seq~~~~~~-.;~*t-~&r.icion strategy fo rabating climate cllange, Nature 357. 28 May, 315--31X.


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50 W .D. Nordhaus, Controlling greenhouse gases

IPCC, 1990. Intergovernmental panel on climate change, climate change: The IPCC scientificassessment, J.T. Houghton, G.J. Jenkins and J.J. Ephraums, eds. (Cambridge UniversityPress, New York).Jorgenson, D.W. and P.J. Wilcoxen, 1991. Reducing U.S. carbon dioxide emissions: The cost ofdifferent goals, in: J.R. Moroney, ed., Energy, growth and the environment (JAI Press,Greenwich, CT) 125128.Rolstad, C.D., 1992, Looking vs. leaping: The timing of CO, control in the face of uncertaintyand learning, Paper presented to the International Workshop on Costs, Impacts, andPossible Benefits of CO, Mitigation, IIASA, Laxenburg, Austria, Sept.Manne, A.S. and R.G. Richels, 1990, CO, emission limits: An economic cost analysis for theU.S.A., The Energy Journal I I, no. 2, 51-74.Manne, A.S. and R.G. Richels. 1992, Buying greenhouse insurance: The economic costs of CO,emission limits (MIT Press, Cambridge, MA).National Academy of Sciences, 1992, Committee on Science, Engineering and Public Policy,policy implications of greenhouse warming: Mititagion, adaptation, and the science base(National Academy Press, Washington, DC).

National Research Council, 1983, Changing climate (National Academy Press, Washington,DC).Nordhaus, W.D.. 1979, The efficient use of energy resources (Yale University Press, New Haven,CT).Nordhaus, W.D., 1991a. A sketch of the economics of the greenhouse elfect, The AmericanEconomic Review 81, no. 2, 146-150.Nordhaus, W.D.. 1991b, To slow or not to slow: The economics of the greenhouse effect, TheEconomic Journal 101, July, 920-937.Nordhaus. W.D.. 1991c, A survey of the costs of reduction of greenhouse gases, The EnergyJournal 12, no. 1. 37-65.Nordhaus, W.D., 1992. Explaining the DICE: Background paper on dynamic integrated modelof clim, ;e change and the economy, Mimeo. (Yale University, New Haven, CT).Nordhaus. vV.D.. 1993a, Managing the global commons: The economics of g!oba! warmingtM IT Press, Cambridge, MA) forthcoming.Nordhaus, W.D., 1993b, How much should we invest to slow climate change?, in: H. Giersch,ed., Policies on economic growth (Springer-Verlag, Berlin) forthcoming.Ramsey, F.P., 1928, A mathematical theory of saving, The Economic Journal, Dec., 543-559.Peck, SC. and T.J. Teisberg, 1991. CETA: A model for carbon emissions trajectory assessment,The Energy Journal 13. no. I. 55577.Schelling, T.C., 1983, Climatic change: Implications for welfare and policy, in: National ResearchCouncil, 1983. 449-48:.Schlesinger, M.E. and X. Jiang, 1990, Simple model representation of atmosphere-ocean GCMsand estimation of the time scale of CO,-induced climate change, Journal of Climate 3, Dec.,

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