Exploring policy options with a behavioral climate–economy model · 2019. 3. 1. · technology, pricing. Economy Output, capital accumulation, energy requirements, capacity utilization

Exploring policy options with a behavioralclimate–economy modelThomas S. Fiddaman*

Tom Fiddaman is asenior consultant withVentana Systems, Inc.He holds a Ph.D. inSystem Dynamicsfrom the MIT SloanSchool of Managementand a B.A. inEngineering Sciencesfrom DartmouthCollege.

Abstract

Many integrated energy–economy–climate models have been developed to address climatechange policy. While these models are quite varied in scope, most share a common core ofeconomic optimization and equilibrium assumptions. By contrast, system dynamics models ofenergy–economy interactions focus on disequilibrium dynamics, with behavioral decision rulesand explicit stocks and flows of capital, labor, resources and money. This article tests climatepolicies using a system dynamics model that includes many features missing from economicmodels. Among these are endogenous technological change and boundedly rational decisionmaking. Energy requirements are embodied in capital, and energy production capacity depends onexplicit capital stocks. The search for optimal policies is decoupled from other decisions, and usescriteria that are fair across generations. Earlier experiments with the model, briefly reported here,indicate that these features greatly alter policy outcomes. The model is used to test a family ofemissions permit and tax policies like the Kyoto Protocol under a range of assumptions. Uncertaintyis included in the analysis through Monte Carlo simulation. Results suggest that nearly all policyoptions are a net benefit, and that the landscape for policy choice is more forgiving than generallysupposed. However, implementation remains a critical issue, and the viability of tradeable permitsis questionable. Carbon tax policies are found to outperform fixed emissions permits in nearly allcircumstances. The model used in this article is available at http://www.sd3.info. Copyright 2002 John Wiley & Sons, Ltd.

Syst. Dyn. Rev. 18, 243–267, (2002)

The climate change debate has spawned many integrated climate–economymodels (Dowlatabadi 1995; Parson and Fisher-Vanden 1995; Weyant 1999).The motivation for these models is the need to identify an efficient distributionof the burdens of climate change, along with efforts to avoid it. A diverse setof models has developed around various aspects of this question. Modelers arecontinuously improving the representation of biogeophysical cycles, addingregional and sectoral detail, testing new policy instruments, and developingbetter numerical methods for model analysis.

In some ways, though, most integrated models are convergent. This isparticularly evident (and potentially troublesome) in their social and economicsystems, where there is probably more structural uncertainty than in thephysical systems of climate or greenhouse-gas cycles. Similarities amongmodels can be attributed to the roots of integrated models in the economictradition of energy modeling. Specifically, many integrated models share thefollowing assumptions, at least in their central scenarios:

Ł Dr. Thomas S. Fiddaman, Ventana Systems Inc., 8105 SE Nelson Road, Olalla, Washington 98539, U.S.A.;E-mail: [email protected]

System Dynamics Review Vol. 18, No. 2, (Summer 2002): 243–267 Received December 2001DOI: 10.1002/sdr.241 Accepted March 2002Copyright 2002 John Wiley & Sons, Ltd.

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244 System Dynamics Review Volume 18 Number 2 Summer 2002

ž discount rates on utility or cost and benefit flows that give a higher weightto the welfare of current generations and richer regions;

ž exogenous population with demographic transition to equilibrium;ž exogenous, declining rates of economic growth (in cost–benefit models) or

factor productivity (driving economic growth in general equilibrium models);ž autonomous energy efficiency improvement or carbon intensity reduction;ž exogenous energy production technology;ž consumer and producer optimization with full information and, frequently,

perfect foresight;ž instantaneous equilibration of factor inputs to optimal levels;ž no positive feedback mechanisms in the economy (other than capital

accumulation);ž no human disturbance to the environment other than climate; andž infinite, linear sinks for carbon.

Obviously, not all integrated models fit the characterization above perfectly. Ofthe well-known models, William Nordhaus’ original DICE model (Nordhaus1994) is probably the purest example of the standard paradigm. In the basecase of the DICE model, assumptions about discounting, rationality, exogenouspopulation growth and technological change, limited potential for greenhouse-gas abatement, low susceptibility of human systems to climate interference,and an optimistic model of the carbon cycle combine to suggest that littleshould be done to limit climate change (Fiddaman 1995).

Some of these assumptions are puzzling in the context of the history ofglobal modeling. Most surprising is the common assumption that technology(factor productivity) growth will slow to zero in the next century. Becausepopulation growth also stops and there are diminishing returns to capitalinvestment, the economy comes into equilibrium in about a century. The endof growth is a technical convenience for optimization models as it minimizesthe difficulty of terminal valuation of the system state, but it contradicts theassumption of inexorable technological progress that was the foundation ofmuch of the critique of World3 and World Dynamics by Nordhaus and others(Nordhaus 1973). The practical implication for climate policy is that lowgrowth minimizes pressure on the climate system, and discounting for timepreference overwhelms growth, driving the importance of future generations’welfare to zero.

The FREE model

The model used here, FREE (Feedback-Rich Energy–Economy model),incorporates several important features that are currently not addressed byother models. These include:

T. S. Fiddaman: A Behavioral Climate–Economy Model 245

ž a disequilibrium energy–economy system, with adjustment and perceptiondelays, embodiment of energy requirements in capital, and resourcedepletion;

ž inclusion of endogenous technological change and other positive feedbackeffects which may lead to lock-in of the energy–economy system to particularsupply and end-use technologies;

ž explicit behavioral rules, rather than myopic or intertemporal optimization,for decision making;

ž separation of the search for optimal social policies from savings, factorallocation, and other decisions; and

ž an equitable approach to the valuation of impacts on current vs. futuregenerations.

To facilitate exploration of these new structures, other aspects of the modelare kept simple. The model contains no regional or sectoral disaggregation,and uses simple models of the carbon cycle and climate. With appropriateparameters, the model may be reduced to a form that behaves much likesimpler neoclassical models, as in Senge (1978).

Model description

The nominal time horizon of the model is 1960–2100. However, foroptimization purposes, runs are typically extended to 2300 to reduce horizoneffects. The historical period of the model is relatively long compared to most,which typically replicate only a decade on two of history. The comparativelylong historical period proved useful for calibration and testing of energysupply–demand interactions. One of the insights from the process is that manymodels neglect structural and behavioral rigidities in energy use and as a resulthave unrealistic short-term responses that would be revealed by testing themodels in circumstances like the oil shocks of the 1970s and 1980s.

The FREE model represents the global energy–economy system and, in amore limited fashion, global biogeophysical processes (the model is availableat http://www.sd3.info). The majority of structure in the model is endogenous.Generation of economic output, investment, energy supply and demand,depletion, and energy technology development are tightly coupled to oneanother. The carbon cycle and climate are also fully endogenous, but arecoupled to the rest of the model somewhat more sparsely. Carbon and energytax policies are formulated as endogenous feedback control rules, rather thanexogenous inputs.

For simplicity, many features have been omitted from the model. There isno regional or sectoral disaggregation (except in the energy sector). Non-energynatural resources are ignored. While the energy sector includes several distinctenergy sources, energy conversion activities (such as the generation of electric


Fig. 1. Sectorboundary diagram.Shaded sectorsincorporatesubstantially newstructures; othersubsystems areconventional or verysimple

PopulationExogenous growthrates correspondingwith DICEassumptions forcomparability

Population

Intangible Damages

Labor

WelfareConventionaldiscounted utilitymodel withintergenerationally fairparameters

ImpactsMarket and non-market damages fromclimate change.

ClimateRadiative forcing,surface warming, andheat transport.

Tangible Damages

Temperature

Consumption

EnergyOrders

Emissions

Carbon CycleAtmosphericaccumulation andtransport of carbon toocean and biosphere.

CO2 EmissionsEndogenous emissionsof CO2 from energyuse: exogenousemissions from landuse and other sources.

Measured EmissionsRate

Fossil Fuelproduction

Energy DeliveryEnergy Prices

Taxes

AtmosphericCO2

Concentration

AtmosphericConcentration

EnergyPrimary production,depletion, saturation,technology, pricing.

EconomyOutput, capitalaccumulation, energyrequirements, capacityutilization.

PolicyControl heuristics fortaxes and permits oncarbon, energy, anddepletion.

power from thermal fuels) are omitted. A number of economic structures thatcontribute to disequilibrium are omitted, such as sectoral labor pools and cashreserves. Inventories and backlogs are omitted, as they equilibrate quicklyrelative to the model horizon. In a way the model can be regarded as a hybridbetween disequilibrium system dynamics energy models (Sterman 1981) andeconomic equilibrium optimization models; this difficult marriage facilitatescomparison of the two approaches through parameter changes.

The model can be divided into nine subsystems that have relatively sparseinteractions. Figure 1 illustrates the sector boundaries, internal activities, andexternal relationships.

The fundamental behavior of the model can be summarized by a few feedbackloops (Figure 2). The reinforcing process of capital accumulation driveseconomic growth (augmented by exogenous population and factor productivitygrowth). Climate change acts like a weak balancing loop that restrains growth.Economic activity requires energy input; which leads to carbon emissions.Emissions increase the concentration of CO2 in the atmosphere, causingtemperature to rise. As the global temperature rises, climate change damagesreduce economic output and diverts it from other purposes, reducing growth.The energy and economy sectors interact through the exchange of goodsfor energy. Within the energy sector, learning and depletion drive energyproduction costs. Taxes and permits raise carbon energy prices in response toincreasing CO2 emissions and atmospheric concentrations.


Fig. 2. Major feedbackprocesses

Population

Population Policy

Welfare Economy CO2 Emissions

Impacts Climate Carbon Cycle

Utility

Energyprices

EnergyOrders

EnergyProduction+

+

+

+

+

++

+

+

− ++

++

++

++

+

+

+

− −

−

+

Learning

Depletion

Capital Emissions

Carbon Taxes

Storage

Temperature

Heat Transport

Output

B

B

R

R

B

R

B

B

B

B

AtmosphericCO2Climate

Damages

−

−

The principal yardstick by which welfare implications of policies aremeasured is the concept of cumulative discounted utility (Eq. 1), in whichthe utility of an infinitely-lived representative individual is weighted by thepopulation and a discount factor for time preference:

CDU D∫

e��t�L�t�U�t�dt �1�

where CDU D cumulative discounted utility, L D population, � D rate of timepreference, and U D utility of representative individual. With the rate of timepreference � D 0, the welfare of all generations is weighted equally. Any � > 0represents a preference for current welfare—pure myopia. With � D 0.03, theweight to future welfare declines by half in only 23 years, and climate damagesin 2100 are only 5 percent as important as present costs of emissions reductions.

In the simulations presented here, intangible or non-market environmentalservices are neglected, so an individual’s utility is purely a function ofconsumption, given by Eq. 2:

U D �c/c0��1�� 11 � �

�2�


where c D consumption per capita, � D rate of inequality aversion, and c0 Dreference consumption per capita. With this formulation the marginal utilityof an additional unit of consumption declines with increasing wealth, so thatan equivalent absolute increase in consumption yields more utility for a poorindividual than for a rich one. If � D 1, utility simplifies to the logarithm ofconsumption. With higher values of �, diminishing returns set in more rapidly.

Models using this welfare framework, like DICE, often choose a positive rateof time preference of about 3 percent per year and a rate of inequality aversionof 1 (Nordhaus 1994). Because such models typically assume that growth ratesof population and economic output decline to near zero in the next century,the flow of discounted utility inevitably declines to zero as well. The primarymotivation for this parameter choice is correspondence with observed ratesof return (Manne 1994). Such a procedure is a poor basis for the choice ofparameters, as the model of behavior used to make this choice assumes perfectforesight and neglects structures (such as demographic disaggregation) thatare important in real-world savings decisions. Intergenerational allocation ofresources is not part of a consumer’s normal decision making process, somarkets do not adequately reflect intergenerational issues (Schelling 1995).Even in the absence of structural uncertainty, historical evidence does notdiscriminate sharply between fair and unfair parameter choices, as the twogenerate nearly identical historical trajectories for interest rates.

Many economists and philosophers reject pure time preference on ethicalgrounds (Ramsey 1928; Cline 1992). The author concurs, so the FREE modeluses parameters that are consistent with history but fair to future generations.The rate of time preference is set to 0, so that the welfare of all generations isweighted equally. The rate of inequality aversion is set to a higher value (2.5),so that the needs of current (poorer) generations are of greater urgency. In thiscase, the flow of discounted utility does not decline, even if population andeconomic growth cease.

Figure 3 shows the effects of discounting on welfare. The time preferencesimulation uses � D 0.03, � D 1 (as in DICE). The inequality aversion simulationuses � D 0, � D 2.5 (the base case of the FREE model). The left panel shows

Fig. 3. Effects ofdiscounting on welfare


the flow of utility of an individual as a function of the flow of consumptionper capita. The right panel shows the total flow of utility to the population,discounted for time preference, as a function of time. With positive discountingfor time preference, the flow of discounted utility tends toward zero aseconomic growth slows.

Deterministic policy analysis

The principal policy instruments in the model are permits and taxes on carbonand energy use. Figure 4 illustrates the response of the model to a carbon taxof $100 per ton. The tax is phased in smoothly (using a five-year time constant)beginning in 2002, so that it is essentially constant by 2020. In response to

Fig. 4. Behavior withand without $100/TonC carbon tax. Note thatthe flow of discountedutility shown here isconverted to its 1995consumptionequivalent by dividingthe flow of utility bythe marginal utility ofa unit of consumptionin 1995


the tax, welfare (shown here as the flow of discounted utility, lower rightpanel) rises and falls several times. Surprisingly, the first impact of the tax isa slight increase in welfare, which occurs because total energy system costsdecrease significantly. Costs fall because the carbon tax suppresses energydemand, reducing the need for new investment in coal, oil and gas production,and depressing capacity utilization, so that only the most efficient capital isused. The increase in consumption is an artifact of the implicit fungibility ofconsumption and investment goods in the model (the two are not distinguished)that would disappear with a more detailed treatment.

After about 2005, welfare falls, because productivity losses mount andthe initial savings in energy investment are replaced by higher investmentrequirements in noncarbon sources. Productivity falls because the shift inenergy prices leads to suboptimal capacity utilization in the goods producingsector until the energy intensity embodied in the capital stock can adjust.The marginal product of capital falls, diminishing investment. With reducedcapacity utilization and investment, output grows more slowly than it does withno tax. The model is actually optimistic about the potential for adjustment asthe capital lifetime is only 15 years; in reality much energy consuming capitalis very long lived (like the housing stock) and tied to settlement patterns thatchange on time scales of many decades.

After 2035, welfare rises above its baseline level, because of a combinationof factors. Most of the adjustment costs from changing energy prices are past;substitution of capital for energy offsets most of the effects of higher pricesand productivity and capacity utilization return to their normal levels. Thebenefits of reduced climate change begin to be felt. Reduced climate damagesimprove returns in the goods producing sector, leading to greater investment.Savings in the energy sector from earlier realization of learning curve benefitsfor noncarbon sources (lower left panel of Figure 4) reduce the cost of the shiftaway from fossil fuels, which is inevitable anyway because of depletion of oiland gas.

The tax stabilizes emissions above the current rate of roughly 6 billion tonscarbon per year, at 8 billion tons carbon per year in 2100 (vs 28 with no tax).Because emissions are more than double natural uptake, carbon continues toaccumulate in the atmosphere and almost doubles compared to preindustriallevels. As a result there is substantial climate change; the threefold emissionsreduction lowers warming only from 3.5 to 2.5 °C.

The cumulative effect of the carbon tax on welfare (the area under thediscounted utility curve) is still slightly negative in 2100; the breakevenpoint is reached almost exactly 100 years after the tax is initiated. By theend of the simulation in 2300, the accumulated benefit is $4.6 trillion incurrent consumption terms. While this is a huge absolute number, it is smallcompared to accumulated output over the same period. In fact, the difference intrajectories for consumption (top left panel of Figure 4) is almost imperceptible.


Optimal carbon taxes

A useful starting point for policy analysis is to identify an effective carbontax policy in deterministic runs of the model using best-estimate parameters.For simplicity, a constant tax, implemented gradually as above, is used in thetests presented this section. The criteria for policy selection is maximizationof welfare (cumulative discounted utility) over the simulation period. Theconventional wisdom from simple integrated models—which are frequentlyderived from DICE—is that abatement efforts in the near term should belimited, with modest carbon taxes on the order of 10–50 $/TonC (Nordhaus1994; 2001; Yohe and Wallace 1996; Nordhaus and Boyer 1998; Keller et al.2000).

Fiddaman (1997) explores a range of scenarios, starting with a parameteriza-tion that behaves much like the DICE model (Table 1). In this case, the optimalcarbon tax is $15/ton, a level that causes small increases in energy prices. In thebase run of FREE, the tax is $170/ton, which causes substantial shifts in energy

Table 1. Contrastingscenario assumptions.The DICE-like scenariois deliberately similarto Nordhaus’ (1994)original DICE model.The FREE base caseincorporates a morecomplex productionstructure, behavioraldynamics, depletion,endogenoustechnology, and amore realistic carboncycle

DICE-like FREE base case

Factor productivitygrowth

Asymptotically zero, sothat economic growtheventually stops

Always greater than zero;growth slows but doesnot stop

Productionstructure

Putty-putty, with low tomoderatecapital–energy andinter-energysubstitution elasticities

Putty-clay, with highlong-run elasticitiesmoderated by slowphysical and behavioraladjustments

Behavior Rapid adjustment tooptimal factor balances

Adjustment to optimalfactor balances, butsubject to delays inperception and action

Energy productioncapacity

Low share of capital inenergy production,rapid capacityadjustment and shortconstruction lead times

Capital-intensive energyproduction, with longconstruction lead times

Energy productiontechnology

Exogenous Endogenous learningcurve

Fossil fueldepletion

None Limited fossil resourcesand renewable energyproduction rates

Carbon cycle Linear, with infinitecarbon uptake capacity

Nonlinear, with limitedcarbon sinks

Welfare evaluation Time discounting ofsocial welfare

Intergenerational equity


prices and carbon emissions. FREE can also simulate plausible scenarios inwhich the optimal tax is as high as $950/ton, which has such strong effects onthe energy—economy system that it could be impossible to implement. Thedifference in conclusions is dramatic. It arises from the interactions of a num-ber of assumptions about discounting, economic growth, energy technology,the flexibility of the economy, depletion, and decision making.

Because these assumptions interact in a highly nonlinear fashion, there isno definitive way to attribute the changes between scenarios to any singleparameter. Figure 5 compares the relative impacts of the major differencesbetween the two scenarios by testing groups of assumptions individually. Eachtest applies a subset of the differences in Table 1 to the base case scenario, inwhich the optimal tax is $170/ton.

Discounting accounts for much of the difference between DICE and FREE.Adding discounting for pure time preference to FREE lowers the optimal taxby a factor of four, from $170 to $38/ton carbon. Another important differenceis the representation of the carbon cycle. The original DICE carbon cycle islinear and has no sink constraints to carbon uptake. It also introduces a discretedelay between emissions and effects, as the model is simulated with a discrete10-year time step. Because DICE discounts for time preference, the spuriousdelay diminishes the present value of emissions reductions. The FREE carboncycle, by contrast, conserves carbon and has diminishing returns to uptake bythe ocean and biosphere. Replacing the FREE carbon cycle with that of DICElowers the optimal tax by half, from $170 to $80/ton.

In the DICE model, emissions reductions can be implemented instanta-neously, without adjustment costs. FREE, by contrast, includes capital stocksin the energy system, embodied energy requirements, and delays in perception

Fig. 5. Summary ofmodel tests. Rowsindicate the optimalconstant carbon taxlevel for each test. Thesimulation identifiedas the base case isused as the startingpoint for uncertaintysimulations in thenext section

0 170 500 1000

Optimal Constant Carbon Tax ($/TonC)

Scen

ario

DICE-like

Discounting for time preference

DICE carbon cycle

Flexible short run production

Exogenous energy technology

Flexible energy system

FREE Base case

Energy price perception bias

Low growth

Myopic depletion

15

38

80

98

118

149

170

260

888

950


and action that constrain the ability of the economy to adjust to changingenergy costs in the short run. Making the energy system flexible by reducingthe role of capital stocks in energy production causes a small change in theoptimal carbon tax, from $170/TonC to $149 /TonC. Increasing the short runflexibility of the goods producing economy has a greater effect, reducing thetax from $170/ton to $98/ton. In both cases, increasing flexibility results inlower taxes because the effort required to achieve a given level of emissionsreduction falls. The true risk of assuming flexibility becomes apparent in sim-ulations including uncertainty; then the instantaneous emissions abatement inDICE creates an incentive to wait until the brink of disaster to act. In FREE,rapid abatement can be extremely expensive and disruptive.

The behavior of the energy system is strongly shaped by the evolution oftechnology. However, nearly all models treat technology in the energy systemas an exogenous factor. In FREE, learning curves are substituted for exogenoustechnological trends. Endogenous technology creates path-dependence andthe opportunity for lock-in of dominant carbon-based energy sources (Moxnes1992). Ignoring learning reduces the benefits of taxes, lowering the optimaltax from $170 to $118/ton. Consideration of other mechanisms that causepath dependency, like scale economies, network effects and complementaryinfrastructure, could change indicated tax levels significantly. Path dependencehas implications for the timing and nature of interventions. Earlier action hasa greater impact because small initial changes are amplified by the positivefeedbacks. It may be possible to discover market domains where reinforcingeffects are particularly strong, and small interventions have large impacts. Asnon-carbon or energy-efficient technologies become more prevalent, it may bepossible to relax carbon taxes and allow lock-in effects to take over.

There is a heated debate over the availability of a ‘‘free lunch’’ from costlessor negative-cost emissions reductions. Even in the absence of misperceptionsin energy decision making, subsidies on energy use and environmentalexternalities may offer a free lunch (Hall 1990; Burniaux et al. 1992). Mostmodels neglect these opportunities. The free lunch is implemented as a bias inenergy price perception. Even a modest bias (discounting energy prices by 20percent) has substantial tax implications, raising the indicated tax 50 percentto $260/ton; the higher tax compensates for the bias.

Exogenous forecasts of factor productivity or GNP growth, which drive mostintegrated models, have dramatic effects on policy conclusions. In the FREEmodel, a low-growth scenario leads to a very high optimal tax, as it is moreimportant to protect the welfare of future generations when they are not sowealthy. The importance of growth forecasts is strongly conditioned by thediscounting approach chosen, illustrating the necessity of exploring parameterand structural changes together rather than individually. The importance ofexogenous factor productivity improvements as a driver of growth suggeststhat they should be made endogenous in the same way as energy technology.Making aggregate technological progress endogenous is likely to reduce the


optimal carbon tax by increasing the importance of economic growth in thenear term (Hogan and Jorgenson 1991).

Finally, if the valuation of fossil fuel resources is myopic, i.e. resourcemanagers do not fully recover appropriate depletion rents, climate policy canhave unpleasant interactions with exhaustion of oil and gas resources. A low-to-moderate carbon tax accelerates the depletion of oil and gas by shiftingenergy consumption from coal to these lower-carbon fuels, without inducing afull transition to non-carbon sources. Rapid depletion of oil and gas makes thetransition to alternate energy sources more costly and disruptive and requiresit to occur sooner. An extraordinarily high carbon tax ($950/ton) is requiredto avoid rapid depletion, largely because it is not an ideal policy instrumentfor that purpose. This result suggests that the current enthusiasm for usinggas as a low-carbon energy source should be regarded with some caution, andthat carbon policy cannot be made without regard for other major issues in theenergy system.

Policy under uncertainty and the Kyoto Agreement

The current framework for greenhouse gas emissions reductions is the KyotoProtocol, which sets targets for emissions slightly below 1990 levels. Freezingemissions implies substantial reductions in the carbon intensity of the economyas output grows, particularly as the first commitment period begins in 2008. Toequalize the cost of meeting emissions goals globally, a permit trading systemallows regions that can cheaply reduce emissions to sell their reductions toregions where it is more costly to do so.

Analysis of the agreement can be decomposed into two questions: whetherthe scale of emissions reductions proposed is optimal, and whether the policyinstruments used to achieve it are appropriate. Many other models have alreadyaddressed valuation of the Kyoto agreement, particularly with respect to thequestion of scale. A special issue of The Energy Journal reports on the outcomeof several (Weyant 1999). Most models conclude that the agreement is toostringent and thus a net welfare loss (compared with doing nothing) or at leastvery inefficient compared to optimal policies (Nordhaus 2001). Stringencygreater than that embedded in Kyoto is usually only warranted in models withfeatures like catastrophic climate effects. (Keller et al. 2000; Roughgarden andSchneider 1999; Keller et al. 2001).

There are several attractive features of the permit structure in the agreement(Kopp 1999). If it works, it guarantees that emissions will be capped. Permittrading provides a mechanism for transferring resources from developed todeveloping nations. It fits with both market and non-market economies (bycontrast, taxes are difficult to speak of without a price system). If permitsare distributed by auction, they raise government revenue. Tradeable permitsthereafter transfer wealth among firms, rather than to governments. Permits


avoid the term ‘‘tax,’’ a seemingly trivial feature that is critical to acceptancein the U.S.A.

At the same time, there are several features that are problematic. Permittrading has high transaction costs. Permits allocated based on past emissionsinstitutionalize a distribution of emissions that is far from equitable. If permitsare given away initially, they amount to a windfall for current emitters. Mostimportantly, both future baseline emissions and the cost of a given reductionare highly uncertain, making it difficult for politicians to make commitments.

It is difficult to think about the Kyoto agreement without consideringuncertainty. A major challenge facing policymakers is the need to committo fixed emissions targets when there is great uncertainty about both the costof those reductions and the likely future trend of emissions. The presence ofdelays and rigidities in behavior and capital stocks increases the importance ofuncertainty by raising the short-run adjustment costs of policy implementationand increasing the urgency of taking near-term action to avoid later damage.

Uncontrolled emissions

Uncertainty is implemented in FREE (as in other models) by Monte Carlosimulation. Values for key parameters are drawn from subjective probabilitydistributions. For example, the sensitivity of climate to a doubling of CO2

is assumed to be normally distributed with a mean of 2.9 °C and a standarddeviation of 1 °C. Inputs subject to uncertainty include exogenous populationand technology growth rates, energy substitution elasticities, rates of carbonuptake by the ocean and biosphere, sensitivity of the climate to a doublingof CO2, and the scale of economic damages from climate change (Fiddaman1997).

In simulations without policy intervention (Figure 6), consumption percapita grows by a factor of five by 2100, with a standard deviation of about20 percent. Carbon emissions also rise—sometimes to extraordinary levels.Emissions reach between 7 and 41 billion tons carbon per year by 2100. Therange of outcomes is roughly comparable to the range of one to six times currentemissions in the IPCC IS92 and SRES emissions scenarios (IPCC 2000). As aresult, the concentration of CO2 in the atmosphere nearly always doubles (overpreindustrial levels) and sometimes triples. Global average temperature rises 1to 5 °C, with a mean of 3.2 °C and a standard deviation of 0.8 °C.

Tradeable permits

Emissions can be controlled by introducing a permit system to the model. Inmost models permit prices instantaneously equilibrate to the level needed torestrict emissions to the permitted level. Permitting is implemented throughoptimization or solution of simultaneous equations. Both approaches havebeen tested in FREE but were found to be computationally wasteful. Instead,


Fig. 6. Representativeuncontrolledtrajectories; 100random simulations ofconsumption,emissions, CO2 in theatmosphere, andtemperature

the market for permits is implemented as a proportional controller that rapidlyadjusts permit prices to whatever level is necessary to meet the target. Themodeler may trade performance (the degree to which constraints are observed)for efficiency (the time step required for stability) by choosing the gains ofthe controller. The structure shown exhibits some steady-state error that hasan insignificant effect on results; adding integral control makes only a smallnumerical difference. Additional constraints (not shown) can limit permitprices to predetermined bounds:

Pc�t� D∫

DPc�t� � Pc�t��p

dt �3�

DPc D desired permit price, �p D permit implementation time, and

DPc D P0 C P1EE0

�4�

where P0 D permit price constant, E D perceived CO2emissions rate, P1 Dpermit price emissions coefficient, and E0 D reference emissions rate.

Figure 7 shows the impact of implementing a permanent cap on emissionsat 4.75 gigatons carbon per year (92 percent of 1990 emissions in the model).


Fig. 7. Permit impactwith Kyoto targets;permit price andemissions in 100representativesimulations. Comparewith Figure 6

For purposes of the test, the cap is applied globally, though in fact targets arenonbinding in developing regions in the actual agreement. The permitted emis-sions rate is a much less aggressive change than would be needed to prevent adoubling of atmospheric CO2 and stabilize climate near its current state.

Following activation of the permit scheme, emissions constraints are met(with deviations of a few percent) through the year 2100. The side effect oftightly controlled emissions is a very wide range of permit prices in differentscenarios. Permit prices in some cases approach $1000/ton carbon—50 timesthe control effort traditional models typically identify as optimal. The highvariance in permit prices is due to the fact that permits are forcing futures withdiffering costs of emissions reduction and growth drivers to meet a commongoal. The inflexibility of permits is particularly problematic in the short run,where momentum in capital structure and behavior makes it very costly toshift the system more than a little from its baseline trajectory.

Surprisingly, even with sharp disruptions from the aggressive control, theagreement is a net benefit from a welfare perspective, with a present value ofover $5 trillion in current consumption equivalent (see Table 2). The valuationis much higher than in other models due to the fair discounting approach inFREE, which makes the model less myopic. Avoided costs of climate damagein the far future play a much larger role in the assessment of the cost–benefitbalance. It should be remembered that FREE is not a full disequilibrium model,and could understate the disruption to the economy caused by the sharprise in permit prices. More importantly, extreme permit price behavior wouldcertainly lead to political failure of the agreement.

Optimal constant permits

Still, the results of the FREE model agree with many others that the Kyotoagreement is far from ideal. The optimal constant permit level is morethan 25 percent higher (less stringent)—6.11 vs 4.75 billion tons carbon peryear. The higher permit level is justified mainly by a few bad outcomes in


Table 2. Summary of permit policies. Note that preindustrial CO2 in the atmosphere was 590 gigatons carbon, and temperatureis the change with respect to the 1960–1990 global average

Scenario Policy Mean outcomes in year 2100

Emissions Ceiling Consumption Emissions CO2 in Temperature Welfaretarget price per capita (Gigatons atmosphere change change

(Gigatons ($/ton ($/person/yr) carbon/yr) (Gigatons ( °C) (Billion $)carbon/yr) carbon) carbon)

Uncontrolled 16,111 22.86 1587 3.3 0Kyoto 4.75 16,256 4.82 985 2.2 5591Optimal �15% 5.25 16,248 5.32 1010 2.3 6119Optimal 6.11 16,233 6.18 1055 2.4 6399Optimal C15% 6.95 16,220 7.02 1099 2.5 6270$200/ton ceiling 6.11 200 16,234 6.40 1062 2.4 6381$400/ton ceiling 6.11 400 16,233 6.18 1055 2.4 6505Optimal ceiling 6.03 829 16,234 6.10 1051 2.4 6549

Fig. 8. Distribution ofwelfare outcomes

-20

-10

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60

Wel

fare

(T

rilli

on $

con

sum

ptio

n eq

uiva

lent

) Kyoto

Optimal

0.2 0.4 0.6 0.8 1.00

Cumulative Probability

which near-future abatement costs are extremely high. In these worst-casescenarios, raising the permit level drastically reduces abatement costs whileonly modestly affecting climate damages. In scenarios with better outcomes,the avoided costs of near-term abatement roughly balance the increased costsof long-term climate damage when the permitted emissions level is raised.Thus the main impact of changes to the permit level is a shift in the left tailof the outcome distribution in Figure 8, which shows cumulative distributionof welfare outcomes with constant permitted emissions at Kyoto and optimallevels. Welfare is in current consumption equivalent, with respect to a zero


baseline reflecting no abatement effort. Note that welfare here and in subsequentfigures and tables refers to cumulative discounted utility, converted to its 1995consumption equivalent by dividing the flow of utility by the marginal utilityof a unit of consumption in 1995.

The outcome is highly sensitive to the permit level. Errors in judgement onthe low side are particularly costly—setting a permit level 15 percent morestringent than optimal reduces welfare by $280 billion. Setting permit levelstoo high risks a do-nothing approach in many scenarios; under the optimalconstant permit scheme emissions are uncontrolled in 2010 in 15 percent ofthe simulations.

It is worth noting the distribution of benefits over time (Figure 9). Almostirrespective of the permit level, the breakeven point at which cumulativebenefits of avoided climate damage exceed cumulative abatement costs is morethan a century away—an extreme case of worse-before-better behavior. Thelack of short-term benefits reflects three features of the model as used here:there is no ‘‘free lunch’’ from low- or negative-cost energy conservation, thereare no other negative externalities (like pollution or warfare) associated withcarbon energy use, and there is no possibility of climate catastrophe (likedisruption of the Atlantic thermohaline circulation). Relaxing any or all ofthese assumptions could move the breakeven point much closer in time. Inany event, the long delay is likely to be problematic: it implies that there willbe an extended period of time in which the pain of permit prices subjects theagreement to intense political pressure.

Can permits be improved?

Kopp et al. (2000) propose a ‘‘safety valve’’ price for permits above agreementlevels. McKibbin (1998) proposes a similar scheme of national permits allocated

Fig. 9. Permit benefitstrajectory; cumulativeimpact of two permitlevels on welfare,relative to the baselineuncontrolled scenario


with a fixed price above a target emissions level. Both approaches modify thepermit system to behave more like a tax, where the price of emissions is fixed(or at least has an upper bound).

Simulations with the FREE model indicate that safety valves can createmodest improvements in welfare as long as they are not set too low. A ceilingprice of $200/ton carbon is near the breakeven point. A ceiling of $400/toncarbon improves welfare on the order of $100 billion. Adding the flexibilityof a ceiling allows the optimal permit level to be lowered slightly, for animprovement of $150 billion. These are very large sums but small incrementscompared with global GDP over the 300-year horizon. One problem that persistswith permit price ceilings is the lack of opportunistic control in cases whereemissions reductions turn out to be cheap or easy, a circumstance in whichcommon sense suggests doing more, while the cap prevents action.

It is easy to imagine other improvements to a constant permit. An obviousstarting point is to test schedules of permit levels rather than constant emissionsrates. Many other models, including DICE, actually operate in this fashion.However, this is computationally expensive and sensitivity tests suggestthe results are qualitatively the same. Permits must still strike a balancebetween increasing stringency—starting slow to avoid economic shocks—andthe reality of upward pressure on emissions from growth. Another possibleimprovement is to give permits a wide temporal window, recognizing thatwith delays of at least a century in the carbon cycle and climate, it makesrelatively little difference whether a unit of carbon is emitted this year or next.However, this seems likely to create more, rather than less instability, as itintroduces new possibilities for mismanagement of the stock of outstandingpermits. It would also create opportunities for cynical gaming of the permitsystem; parties could consume the bulk of available permits early in the period,then use the prospect of catastrophe to relax standards for the remainder.

It is possible that permits could be further improved by more completerevisions of their allocation mechanism. For example, the total quantity ofoutstanding permits could be regulated by an authority to maintain a set priceor price range. This would cap the upper bound to permit costs and set anopportunistic minimum so that some effort is always undertaken. However, itis hard to imagine that added complexity can contribute enough performanceto justify the practical and political difficulties of implementation.

Constant tax

Pizer (1997; 1999) concludes that taxes substantially outperform permits underuncertainty. The FREE model supports this conclusion. Figure 10 shows theresponse to the best possible constant carbon tax (phased smoothly with a five-year time constant). By contrast with permits, the price of emissions is fixed,but emissions vary over a wide range. Welfare is increased by $400 billionover any permit structure, and the mean emissions level in 2100 is actually


Fig. 10. Constantcarbon tax. Emissionstrajectory is subject toan optimal constantcarbon tax of $175/toncarbon. Compare withFigure 6 and Figure 7

Table 3. Summary of taxes. Compare with Table 2

Scenario Tax Mean outcomes in year 2100

2020 2100 Consumption Emissions CO2 in Temperature Welfare($/ton ($/ton per capita (Gigatons atmosphere change change

carbon) carbon) ($/person/yr) carbon/yr) (Gigatons ( °C) (Billion $)carbon)

Uncontrolled 16,111 22.86 1587 3.3 0Optimal �15% 146 150 16,252 4.97 1004 2.3 6767Optimal constant 171 175 16,254 4.40 983 2.2 6801Optimal C15% 195 200 16,254 3.98 967 2.2 6780Optimal adaptive 90 262 16,229 3.69 1006 2.3 7310

lower than the most stringent permit tested (see Table 3). The best constanttax is $175/ton carbon, comparable to the best-guess deterministic tax of$170/ton, and roughly 4–10 times the level in the DICE model (Nordhaus1994). Significantly, performance is insensitive to small deviations in the tax.Raising or lowering it by 15% has almost no effect on welfare.

Adaptive tax

There is no reason to suppose that a constant tax (or permit level for thatmatter) is optimal. A typical alternative is to explore taxes that change overtime, by specifying a vector of taxes at specified times or constructing a taxas a polynomial function of time. However, this is still a ballistic strategy ofselecting a tax that must fit all uncertain futures. An alternative approach isto create a feedback control rule, shown below. The tax is a linear functionof perceived emissions rates and atmospheric CO2 concentrations, with an


implementation delay (that also provides smoothing):

Tc�t� D∫

DTc�t� � Tc�t��t

dt �5�

where DTt D desired carbon tax and �t D tax implementation time;

DTc D T0 C T1EE0

C T2Ca

Ca,0�6�

where T0 D carbon tax constant, E D perceived CO2 emissions rate, T1 Dcarbon tax emissions coefficient, E0 D reference emissions rate, T2 D carbon taxconcentration coefficient, Ca D atmospheric CO2 content, and Ca,0 D referenceatmospheric CO2 content.

Figure 11 illustrates the effect of the tax, with parameters selected optimally.The adaptive tax improves welfare by an additional $500 billion (see Table 3).Exploration of other tax rules indicates that the main benefit is that theadditional degrees of freedom allow the tax to start small, minimizing short-run disruption of the economy, and to continue rising to suppress increasingemissions pressure from economic growth. However, the tax coefficients onemissions and CO2 in the atmosphere do indicate that the tax is exploiting someinformation about the state of the world. The optimal tax responds positivelyto the atmospheric concentration of CO2, so that in scenarios with slow naturaluptake of carbon, taxes will be higher, as they ought to be. Similarly, thetax responds negatively to perceived emissions, so that abatement effort isrestricted in scenarios with high abatement costs (emissions that resist policy),also as one would expect.

The adaptive tax approach could be generalized to the construction of astochastic control rule using full state information in the model. A logicalfirst step would be to include information about observed temperature andclimate damages. In this way the tax heuristic could be made to function muchlike the act-then-learn decision framework explored in some models (Valverdeet al. 1999, Nordhaus 1994). While this would be an informative pursuit, it is

Fig. 11. Adaptivecarbon tax; emissionsand tax trajectories foran optimal taxheuristic withconstant, emissions,and concentrationcomponents. Comparewith Figure 6,Figure 7, andFigure 10


Table 4. Summary of taxes with unrealistic flexibility of the energy–economy system. Note that welfare magnitudes in thistable are not directly comparable with other tables due to the different base model structure

Scenario Tax or permit price Mean outcomes in year 2100

2020 2100 Consumption Emissions CO2 in Temperature Welfare($/ton ($/ton per capita (Gigatons atmosphere change change

carbon) carbon) ($/person/yr) carbon/yr) (Gigatons ( °C) (Billion $)carbon)

Uncontrolled 16,155 19.66 1366 2.8 0Optimal constant permit 31 144 16,215 5.05 944 2.1 5199Optimal constant tax 89 89 16,257 6.56 917 1.9 4225Optimal adaptive tax 33 139 16,225 4.77 924 2.0 5615

somewhat unhelpful from a policy perspective for at least two reasons. First,it appears that the response of welfare is relatively flat around the optimal tax,so added precision may contribute little. Second, it is implausible that keyvariables (like global average temperature) can be perceived on short enoughtime scales to be usable now.

Flexibility

It is interesting to note what happens to the ranking of taxes and permitswhen the rigid short-run energy–economy in FREE is relaxed to a flexibleproduction structure as in DICE and other simple models (Table 4). Flexibility isimplemented by shortening delays in perception and energy capital acquisition,diminishing the role of capital in energy production, increasing the rate atwhich existing capital can be retrofitted to use new energy sources, andincreasing short-run elasticities of substitution among fuels and between capitaland energy.

With a flexible short-run economy, constant permits outperform constanttaxes by a substantial margin. As emissions approach the cap, the permitprice rises smoothly and gradually, so that emissions are suppressed morestrongly as the economy grows. Because the economy is flexible in the shortrun, emissions can be restricted aggressively without creating the disruptivespike in permit prices observed in Figure 7. The adaptive tax still outperformsthe constant permit, as it controls emissions even in circumstances where theywould fall below the permit threshold.

Conclusions

The FREE model identifies a number of feedback structures that have profoundeffects on climate policy recommendations. It is important that these structures


be tested by other integrated modeling efforts. In addition, this work leavesmany key features of integrated models unexplored. Making key subsystemslike population endogenous, even with the crudest and most flawed models,would yield insights not available from the exogenous forecasts currentlyin use.

Many structures from earlier system dynamics models were omitted orabstracted in FREE for simplicity. Restoring some of these would provideadditional insights. Inclusion of an explicit capital-producing sector, forexample, would impose additional constraints on the expansion of capitalstocks in energy supply. A behavioral theory of saving and investment behaviorwould be more robust and realistic than the current structure, and wouldlink naturally to a more disaggregated, endogenous treatment of population.Monetary effects may be necessary if permits induce large financial flows.

To a large extent, the journey is the destination in integrated modeling.Result-oriented optimization or sensitivity analysis ought to be preceded by athorough exploration of model dynamics, with less attention to single measuresof performance like cumulative discounted utility (Gardiner and Ford 1980).Models are not needed to justify doing little or nothing; there are many intereststhat already support this view. A more worthwhile pursuit would be to seekways of achieving radical emissions reductions if and when their necessity isrecognized. Doing so would require models that include robust representationof behavior far from current circumstances.

Taxes or permits?

The FREE model supports the conclusion that taxes outperform permits.However, the context of the conclusion is somewhat different than that ofother models. Most models heavily discount future climate damages andthus conclude that emissions reductions offer, at best, modest net benefitsthat can easily become negative through poor design and implementation.With intergenerationally fair discounting, though, the perceived benefits ofemissions reductions are much greater. Thus even policies like Kyoto that aremarginal by selfish yardsticks have a high net benefit in FREE.

The high benefits of avoided climate change provide considerably morelatitude for judgement, experimentation, and error, which suggests thatthe emphasis of discussion should shift from fine-tuning of optimal taxesor permits to other questions. One key domain is the political viabilityof agreements. Here again dynamics and uncertainty favor taxes overpermits. The risk that permits will fail because they are set too stringently(producing a backlash against soaring permit prices) or too loosely (wherethey will do nothing, as with the availability of ‘‘hot air’’ from diminishedemissions in former Soviet economies) is high. Capping permit prices helpswith the first failure mode; further refinements or the political process


could conceivably solve the second but only with an additional layer ofcomplexity.

Another key question is whether current models take the question ofclimate seriously at all. Nearly all policies proposed by modelers do no morethan stabilize emissions at historically high levels; IPCC emissions scenarioscontemplate nothing like zero emissions or stabilization of atmospheric CO2

at current levels (IPCC 2000). Nordhaus’ RICE model (a regionalized versionof DICE) suggests optimal emissions reductions of less than 10 percent, sothat emissions rise to more than 20 billion tons carbon per year (Nordhausand Boyer 1999; Nordhaus 2001). As a result, substantial climate changealways occurs. The FREE model used here is no exception—permits andtaxes fail equally to achieve a stable climate (Figure 12). Permits certainlyappear impractical for reaching ambitious targets like zero emissions; taxesmay be as well. The search for optimal policies needs to be expanded toother kinds of instruments—for example, significant technological and socialchange.

If even a few of the issues explored in the FREE model prove important, theimplications for climate policy are considerable. Together, these explorationssuggest an alternative paradigm for climate policy, in which depletion is aserious issue in the near term, policies induce technological change and otherpath-dependent effects, the economy is far from equilibrium or an optimal state,behavioral and structural factors constrain and delay action, and people areconcerned with the welfare of future generations. Even in the face of substantialadjustment costs, aggressive, immediate action is warranted to avoid climatechange.

The challenge for policymakers is to take aggressive action without causingextreme short-run economic disruption, triggering a political backlash. For thispurpose, taxes, gradually phased in, appear to be a more suitable mechanismthan emissions permits. However, since further delay is in itself expensive, it

Fig. 12. Distribution oftemperature, taxes vspermits; distributionof temperatures inyear 2100 in 100representativesimulations,comparing an optimaladaptive tax to apermit with a ceilingprice. The outcomesare essentiallyidentical (within 0.1degree)


seems sensible to make modest changes to current agreements and take firststeps as soon as possible; permits can always be scrapped for taxes later.

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