Fiddaman, Thomas, "Formulation Experiments with a Simple Climate/ Economy Model", 1995

Plenary Program

Formulation Experiments
with a Simple Climate/Economy Model

Thomas Fiddaman

System Dynamics Group
MIT Sloan School of Management
Room E60-365, 30 Memorial Drive
Cambridge, MA 02142, U.S.A.
(617) 253-3958 —
tomfid@mit.edu

Abstract

Much of the science and policy debate around global climate change has focused on models.
Most models focus on a single aspect of climate change - atmospheric physics and chemistry,
macroeconomic effects of abatement policies, or impacts on land cover from changing temperature
and rainfall for example. Only a few models attempt to make climate change fully endogenous by
including both the influence of human activities on climate and the impact of climate change on
human activity.

The best-known climate-economy model is William Nordhaus' DICE model. The model is a
conventional macroeconomic Ramsey growth model with simple carbon and temperature
subsystems added. These create a negative feedback loop which tends to reduce economic output
due to climate impacts on economic activity. Experiments with the model suggest that only limited
effort should be addressed to CO2 emissions abatement. While the DICE model meets some of the
expectations of a system dynamics model, in other ways it falls short. Key variables are
exogenous, such as the growth of population and emissions reduction technology. Output is
generated by optimization, rather than by simulation with explicit decision rules.

This paper explores the impact of structural changes to the model specification that attempt to
bring it closer to the system dynamics paradigm. The impact of exogenous population and
technology drivers is explored. Carbon flows are made more explicit, to demonstrate the
importance of sink constraints and temperature feedbacks to the carbon cycle. A path dependent
energy sector with endogenous technology is tested. Boundedly rational decision rules are
substituted for optimization. These tests generally yield results suggesting substantially higher
abatement levels than Nordhaus concludes are necessary.

Copies of the DICE model and the revisions described in this paper are available in Vensim format
from the author at the address above.

40

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System Dynamics '95 — Volume I

Many energy and economic models have been used to evaluate the cost of reducing greenhouse
gas emissions (Beaver 1993; OECD 1993; Wilson and Swisher 1993). Some models also
incorporate damage functions for evaluating the costs of climate change (Rotmans 1990; Hope
1993). Few make climate change fully endogenous, closing a feedback loop between the global
economy and climate (Hatlebakk and Moxnes 1992; Nordhaus 1992; Nordhaus 1992; Peck and
Teisberg 1993; Nordhaus 1994).

The DICE model shares much with a typical system dynamics model. It incorporates stocks
and flows, nonlinearities, and disequilibrium, and is problem-oriented. However, it differs from a
typical system dynamics model in several important ways. The time paths of decision variables in
the model are determined by optimization, rather than explicit behavioral rules. Exogenous
variables play a large role in the model behavior. Sources and sinks are treated less thoroughly.
While the model is expressed in continuous equations, the simulation interval is long enough that it
effectively runs in discrete time, and integration error is significant. The level of aggregation is
higher than the level at which recognizable policy levers operate, so some supplementary analysis
is necessary when experimenting with the model.

Table 1. Features of the DICE model

Endogenous Exogenous Excluded

Capital Population CO, in ocean, biota, soils
Output Factor productivity Temperature feedback to
Investment (technology) carbon cycle
Consumption Emissions reduction Spatial and regional dynamics
CO emissions technology Energy sector

Emissions abatement costs Other greenhouse gas Pollutant interactions
Atmospheric CO emissions Trade

Temperature Agriculture

Climate change damage

The DICE model is probably the simplest of the integrated climate-economy models. The
causal structure of the model is shown in figure 1. There are 2 positive and 5 negative feedback
loops. Three other sets of feedback loops - population growth, factor productivity increase, and the
decline of CO) intensity of economic output - may be considered exogenous inputs to the model,
as their rates of change are specified by fixed parameters. It has a one-sector economy with a single
stock of capital. Economic output is generated by inputs of labor, capital, and technology.
Economic activity drives the emission of CO2, which contributes to an increase in the atmospheric
stock. The CO) intensity of economic activity decreases autonomously and may be further reduced
by costly policies. Over time, CO2 is removed from the atmosphere by storage and transport
processes. Elevated concentrations of CO. and other greenhouse gases (GHGs) in the atmosphere
increase radiative forcing, which warms the atmosphere and upper layers of the ocean. Positive
feedback strengthens the warming, but much of the excess heat absorbed by the atmosphere and

Al
Plenary Program

upper ocean is transferred to the deep ocean. Temperature changes in the atmosphere and upper
ocean cause climate damage costs which reduce economic output.

Figure 1. Causal Structure of the DICE Model

Preindustrial CO2 Level

_— Atmospheric Retention :

Utility C02 Storage
* +
+ %s)
Net C02 Emissions
; coz in Other GHas
Consumption 4 Population Binion a ~~ }

eee

+
aw ot Wo 02 Reduction Cost “4.
Atmosphere & Upper
‘Climate Impact ee -_ CcseniTemnnerstixe

XY?) Factor NN ‘Atmosphere & Upper
oa ‘ Pie @ Ocean Heat Capacity
Depreciation * Heat Transfer
Deep Oce:
a

Capital Lite Deep Ocean

Positive feedback or Reinforcing loops are labeled R#, while negative feedback or Balancing loops are labeled B#.
The structure of the utility discounting process is omitted. The decision variables in the optimization are shown in
boldface.

The gross behavior of the model arises from the positive feedback in population growth and
factor productivity (exogenous) and capital accumulation (loop R1), which leads to exponential
growth of output. This growth can be attenuated as increasing economic activity leads to
accumulation of greenhouse gases in the atmosphere, which reduces output through climate change
damage after a long delay (loop B1). The action of this balancing loop is weak and delayed,
because there are large accumulations and negative feedback loops that intervene between GHG
emissions and their consequences.

Policies that reduce greenhouse gas emissions reduce the gain around both the strong positive
loop of capital growth and the weak, delayed loop of climate change. The costs of weakening the
economic growth loop generally outweigh the benefits of avoided climate change. Because of this
fact, and time discounting, emissions reductions indicated by the model are very modest - on the
order of 10%. It is preferable to grow the economy to pay for the cost of future climate damages
than to reduce emissions to avoid them.

This paper explores assumptions and formulations of the model and proposes some structural
revisions, which alter the preferred balance between growth and emissions reductions. These

42
System Dynamics '95 — Volume I

issues can be grouped into three areas: discounting and utility in the objective function, the capital
growth loop, and the climate change loop. Each will be considered in turn.

2e+014 Figure 2. Standard Run
2et0ld of the DICE Model
Output, the stock of carbon in the
atmosphere, and the temperature
1e+014 of the atmosphere and upper
tele ocean all grow substantially over

the next century. Time paths for
the savings rate and greenhouse
gas abatement fractions are from

: Nordhaus (Nordhaus 1992).
0
1965 1985 2005 2025 2045 2065 2085 2105
Time
Output $year
CO2in Atmosphere = were n enn nee nnn-=--- TonC
Absolute Temperature Change —— — — DegreesC

Objective Function

The objective of the optimization performed in the DICE model is to maximize cumulative
discounted utility over the simulation period. Cumulative discounted utility is given by:

cpu = fe" P{[ce/Pal”* -1}/a-ayat,
where P is population, C is consumption, p is the pure rate of time preference (or discount rate on
utility), and © is the rate of inequality aversion (or marginal utility of consumption). The reference
value of the rate of inequality aversion is 1, in which case the objective function reduces to
CDU = fer P(t)In(C(t)/P(t))dt. This implies that the fractional increase in utility for a given.

fractional increase in consumption is constant, so that an American would benefit proportionally as
much from a doubling of income as a Somalian would.

The choice of rate of time preference is motivated by the desire for correspondence between the
model and observed behavior. In particular, Nordhaus seeks to reconcile the discount rate and
marginal product of capital (net of depreciation) in the model with observed interest rates. In steady
state in the Ramsey model, the real interest rate (r) is equal to the sum of the discount rate and the
growth rate (g) multiplied by the rate of inequality aversion, r= ag + p. Thus observed rates of
return and growth in the vicinity of 6% and 3% respectively are consistent with a 3% rate of time
preference and a rate of inequality aversion of 1.

With these values, the present value of utility decreases by half every 23 years. The choice of
rate of time preference thus weights current outlays for abatement more heavily than future avoided
damage. It effectively sets a time horizon for concern some time in the late 21st century. Since the
discount rate is greater than the rate of growth of per capita consumption, after that time further
changes are unimportant. By the end of the 21st century, a year of consumption contributes less
than 25% as much to cumulative discounted utility as consumption in 1990, and the discounted

43
Plenary Program

value of consumption of an individual in 2100 is 10% of that of an individual in 1990, in spite of
growing wealth.

6B Figure 3. Discounted
Utility
Discounted utility measures the
linia annual contribution of the world
population's utility to the
3B objective function (cumulative
discounted utility). Dimensions
: of the vertical axis are
15B . unimportant; only the relative
N values matter. As can be seen
NAY from the graph, by 2100, further
0 tT contributions to cumulative
legs" 999" (NSH! "2067" (2101) 218s, “216s 2203) 2257, ZayK| 2308 discounted utility are negligible.
‘ime
Discounted Utility utiles/year

Assuming for the moment that observed investment behavior is even relevant to the essentially
ethical choice of a utility function, rates of time preference and inequality aversion of 0% and 2,
respectively, would be equally consistent with the observed rates of interest and growth. Then the
welfare of individuals in all generations is weighted equally, but there is a bias towards current
consumption when the economy is growing, as the marginal utility of a unit of consumption is
lower to wealthier future generations. Given the ethical absurdity of discounting away the welfare
of future generations when making social decisions about an intergenerational problem, these
values seem much more appropriate, and will be tested below. An alternative approach would be to
select a rate of time preference that diminishes over time, as suggested by Rothenburg (1993).
Cline (1992) provides a thorough discussion of discounting and climate change policy.

Table 2. Impact_of Discounting _

Simulation Optimal Carbon Tax CO, Emissions
$/Ton C 109 Ton C/year
Year 2005 2105 2005 2105
DICE, p=.03,a=1 8 22 9.8 20
DICE, p=0,a=2 44 202 8.6 14

Eliminating pure time preference dramatically increases the optimal abatement level. The carbon tax reported here and
elsewhere is the implicit marginal productivity of carbon in the production function. Note that the optimal carbon
tax and emissions levels vary slightly in the standard runs of the DICE model reported in this paper, as some
changes required simulating the model with a shorter time step than Nordhaus uses. In all cases results reported in a
single table are comparable, however. .
Nearly as important as the issue of discount rate selection is the fact that utility is purely a
function of consumption. This means that health and environmental services are excluded from
consideration insofar as they are not reflected in the value of goods and services in the economy.
Though Nordhaus points out that the model is intended only to address economic considerations,

and that policy decisions must take ethical, aesthetic, or other concerns about the environment into

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System Dynamics '95 — Volume I

account by other means, the issue is more subtle than this. The environment provides free services
which are arguably not represented in current prices or national accounts. Tol (1994) addresses
these issues by transferring a portion of climate damages into the utility function. This reduces the
ability of changes in investment to allow substitution of goods for intangible or non-market
services of the environment, and raises the indicated emissions abatement levels.

Capital Growth Loop

The core of the DICE model is a Ramsey growth model. Capital is aggregated to a single capital
sector. Capital and labor are combined using a Cobb-Douglas production function to generate
output. A fraction of output each year is saved and reinvested in capital, and the remainder is
consumed. The savings rate varies over time according to the optimization. Capital depreciates with
a fixed lifetime, stated to be 10 years. However, because the model is simulated with a time step of
1 decade, Nordhaus corrects the capital life to account for compounding, using a fractional
depreciation rate of .65 per decade. This is simply incorrect; the stock of capital has an inflow as
well as an outflow, and the two may not be compounded in isolation from one another. The
appropriate way to correct for integration error in this case would be to use a smaller time step.
Nordhaus’ correction yields an effective capital life of 15.38 years, which is not implausible and is
retained for comparability.

Population

Population increase is driven by an exogenous growth rate. The rate of population growth is
assumed to decline, so that population stabilizes at a level near 10.5 billion in the second half of the
21st century, 3.15 times its initial value. This equilibrium population estimate is consistent with the
lower bound of projections of population increase. This is an optimistic assumption; it requires that
the rate of population growth decline faster in the coming decades than has been observed in the
last three decades (Population Reference Bureau 1991).

There is no feedback from the economic or environmental sectors of the model to the
population growth rate; birth and death rates are decoupled from economic conditions (income,
health services) and environmental conditions (pollution, disease). If increasing wealth is an
important factor determining the declining rate of population growth, Nordhaus’ formulation may
understate the importance of avoiding costs of greenhouse gas abatement now. Expenditures which
reduce consumption or growth in the short term lead to a larger population, greater emissions, and
lower per capita consumption in the long term. At the same time, policies that reduce population
growth may offer high economic leverage (though they may be politically difficult to implement).

As a test, population can be made endogenous by linking it to wealth, as in World3, for
example (Meadows 1972). This highlights the fact that the objective function is only appropriate
when population is an exogenous input to the model. Otherwise, it behaves perversely (figure 4),
as it rewards policies that favor population growth at the expense of per capita consumption. The
objective function implies that having a population of 10 billion with a per capita income of
$5000/year is better than having a population of 5 billion with a per capita income of $10000/year.

45
Plenary Program

6 CTT lotto) Figure 4. Endogenous

Population
45 \ Endogenous population growth
leads to unrealistic investment
behavior with the standard
3 objective function. A high rate of

investment early in the
A--L simulation reduces consumption,
45 VA “CTW SS aaeaeee so that population grows larger
before stabilizing. While per
capita incomes are then lower, the
0 larger population outweighs its
1965 1979 1993 2007 2021 a 2049 2063 2077 2091 2105 | effects.
ime

Investment_Fraction - Endogenous Population ———_—__—_—_—_—_——_ dmn]
Investment_Fraction - Standard Run

Factor Productivity

The output for a fixed level of capital and labor inputs increases over time due to an exogenous
increase in factor productivity (technology). The rate of technological improvement declines from
1.5% per year in the late 20th century to 0.5% per year in the late 21st century, and saturates at a
level 3.91 times greater than its initial value. As a result, consumption per capita roughly triples
over the next century, and levels off at about six times the initial (1965) value. It's unclear what
real-world feedback loops are responsible for the decline, but it would be preferable if they were
explicit in the model.

100B Figure 5. COp Emissions
When the rates of growth of
5B factor productivity and emissions
yy technology do not decline, CO?
Va emissions rise far higher than in
50B the standard run.
25B =
Lt
0
1965 2016 2067 2118 2169 2220 2271
Time
CO2 Emissions - Infinite Technology —————_--_—_—_ TonC//year

CO2 Emissions - Standard Run TonC/year

The assumptions of declining technology and population growth reduce economic output and
emissions, so that there is less pressure on the climate system. This is dramatically evident when
one removes the assumption of declining factor productivity growth (see figure 5 and table 3). In
spite of continually improving emissions technology, emissions rise to more than 10 times current
levels in two centuries.

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System Dynamics '95 — Volume I

Table 3. Impact of Continuos Technological Progress

Simulation Optimal Carbon Tax CO. Emissions
$/Ton C 10° Ton C/year
Year 2005 2105 2005 2105
DICE, declining technology 6 20 9.5 19
growth rate
DICE, constant technology 7 59 9.6 25
growth rate

Eliminating the assumption of a declining rate of technological progress in factor productivity and emissions
intensity leads to much higher emissions, necessitating stronger controls.

Investment

The choices in the utility function described above are especially crucial in the DICE model because
the investment and greenhouse gas abatement decisions explicitly maximize utility. This is an
extremely strong assumption, requiring that economic agents make investment decisions that
maximize cumulative discounted utility over an infinite horizon for the global population, acting
with perfect foresight in a system with fully internalized costs and benefits. It means that
investment behavior in 1965 is already changing to compensate for the consequences of climate
change occurring late in the 21st century (in Nordhaus severe climate damage run this adjustment
to investment is about $3 billion per year).

While optimization is useful for finding effective policies, it is preferable to have decisions in
the model use reasonable cognitive resources and rely on information which is actually available to
individuals. To allow for the possibility of imperfectly functioning markets and institutions and
imperfect individual action in pursuit of long-term goals, the social objective function should be
decoupled from the decision making process. While many investment formulations exist in the
system dynamics literature, it would be useful here to choose one which maintains close
correspondence with the optimal investment path of the Ramsey model.

Table 4. Impact of Behavioral Investment Rule

Simulation Optimal Carbon Tax Savings Rate
$/Ton C fraction of output
Year 2005 2105 2005 2105
DICE: p=.03,a=1 9 25 .20 18
Objective: p= .03,a=1 9 22 19 18
Behavior: p= .03,a=1
Objective: p=0,a=2 58 106 19 -18
Behavior: p = .03,a=1

p and o are the rate of time preference and rate of inequality aversion, respectively, for the objective function and
investment rule. The behavioral investment rule prevents changes in the objective function from affecting savings
behavior.

47
Plenary Program

This can be accomplished by using the optimal growth path, r = ag + p, to produce a simple
heuristic in which investors form a desired rate of return on capital based on the perceived growth
rate of wealth, compare it to the prevailing rate of return, and adjust their investment behavior
accordingly. If the parameters p and o describing observed behavior are identical to the parameters
of the utility function, this rule produces decisions identical to the optimization in steady state.
When population and factor productivity are growing, the decision heuristic underinvests slightly,
but the path is hard to distinguish from the optimal path. This rule uses no information about the
future, and allows the possibility of investment behavior different from what is socially optimal. It
prevents intertemporal reallocation of investment without explicit signals from policy levers like a
carbon tax.

CO2 Emissions Reduction

Greenhouse gas emissions in the DICE model are separated into two components, CO2, and other
greenhouse gases (such as methane or NOx). CO} is assumed to be controllable; the latter group is
assumed to be difficult to assess and control, and is therefore taken as an exogenous impact on
total radiative forcing. To the extent that these emissions are controllable, this is a restrictive
assumption. Much of the methane emitted by gas production, municipal landfills, and ruminant
animals may in fact be controllable, for example. The atmospheric chemistry of these pollutants is
very complex, so that linkages among them may be important as well (White 1989). The focus on
CO means that the model is concerned almost entirely with the energy system and forestry.

CO} emissions are driven by increasing economic output and the intensity of CO2 emissions
per unit of output. The COz intensity declines over time at an exogenous, diminishing rate. This
decrease corresponds with observed decreases, principally in the developed world, and is
attributed to autonomous technological change and sectoral shifts. Since technological change is
not autonomous in reality, there is a significant possibility that the trend will not continue in the
future. This will be especially true if the depletion of low-carbon gas and oil resources leads to a
shift toward use of carbon-intensive coal, and if economic growth accelerates in the developing
world. The estimated rate of change relies mainly on data from the developed countries, and may
be biased by the shift of energy intensive industries to locations in the developing world (Rosa and
Tolmasquim 1993).

The cost of reducing emissions is embedded in a single curve in the DICE model. The cost
curve is derived from estimates by Nordhaus and other top-down model-based analyses. It is
assumed that the first half of emissions reductions can be obtained at minimal cost - roughly 1% of
output. Eliminating all emissions, which requires halting deforestation and converting the energy
system to higher efficiency and non-carbon technology, requires roughly 7% of output. This
implies that non-carbon emitting energy technologies can replace fossil fuels at three to four times
the current cost of the energy system.

Nordhaus' estimates of the cost curve are comparable to the estimates produced by a variety of
energy/economy models (Nordhaus 1991). It assumes that the present level of CO} intensity in the
economy is optimal - that is, there are no free or negative-cost emissions to be had. Other studies

48
System Dynamics '95 — Volume I

indicate substantial opportunities for negative-cost emissions reductions (Lovins 1977; Lovins and
Lovins 1991; Wilson and Swisher 1993). In considering this possibility, Nordhaus justifies the
omission of such reductions by assuming that they will happen anyway, without intervention.
However, he neglects to make corresponding reductions in absolute emissions levels (Wilson and
Swisher 1993).

The cost of reducing emissions is based on the absolute level of emissions reductions, rather
than on the rate of change of emissions reductions. This means that rapid changes in carbon
intensity may be achieved at the same cost as gradual changes. In reality, long delays in technology
development, exploration, and capital lifetimes impose substantial constraints on the energy
system. In this respect, the DICE model is optimistic about the potential for abatement. However,
the abatement cost curve is fixed over time, and thus insensitive to future technological
developments.

England (1994) cites three reasons for promoting fossil fuel alternatives which are relevant to
the estimation of emissions abatement costs: negative social externalities, institutional factors, and
technology lock-in. Negative social externalities from fossil fuel use include the cost of acid rain
and other pollutants as well as the cost of maintaining stability in the Middle East. Hohmeyer
(1990) identifies externalities of -.0284 to -.0769 DM/kWh for fossil fuel electricity generation in
Germany, and +.051 to +.168 DM/kWh for solar and photovoltaic electricity. Hall (1990)
identifies zero external costs for conservation, wind, and solar energy, and significant external
costs of coal, gas, oil, and nuclear energy . The presence of externalities to fossil fuel use could be
represented in the DICE model by shifting the CO2 emissions reduction cost curve downward,
creating some additional negative-cost emissions reductions.

Technological lock-in in the energy system is dynamically more interesting than externalities.
Lock-in arises from positive-feedback processes that reinforce the position of dominant energy
supply and use technologies. Principal among these are learning-by-doing, revenue-driven
research and development, economies of scale, and network or bandwagon effects. If one assumes
that actors or markets behave with sufficient foresight and understanding, the energy system will
follow the socially optimal path, and lock-in is not an issue. However, Arthur (1989) shows that
under some conditions, actors' anticipation of lock-in enhances lock-in. If current decisions result
in development along differing energy technology paths, there is no reason to believe that the
underlying parameters of the DICE cost curve will remain stable.

To the author's knowledge, no detailed energy sector models with empirically parameterized
endogenous energy technology exist, though some are under development (DOE 1995). A variety
of technology models have been explored in the optimal depletion literature, but they tend to be
highly abstract (Davison 1977; Kamien and Schwartz 1977; Hung and Quyen 1993). This paper
draws on a simple model of a path-dependent energy system by Moxnes (1992) and a model of
nonconventional gas exploitation by Rowse (1994) to create a simple example of the consequences
of path dependence for GHG policy. It focuses on energy supply because that portion of the
system is easier to aggregate and parameterize, though the opportunities for emissions reductions

49
Plenary Program

from energy conservation are generally more extensive and attractive. In this respect the model
underestimates the importance of path dependence.

To implement path dependence, it is necessary to replace the cost curve for CO emissions
reductions in the DICE model with an explicit energy sector. The structure of the added energy
system is shown in figure 6. The capital term in the economic production function is replaced with
a composite capital-energy good described by a CES production function in capital and energy.
The energy intensity of capital is a stock that adjusts to the optimal intensity with a delay; there is
implicitly some costless retrofit potential. Similarly, the effective energy delivered to the capital-
energy aggregate is a composite of carbon and non carbon energy inputs, so that the optimal share
of each energy source is given by the relative prices and an interfuel substitution elasticity. The
actual share adjusts to the optimal share with a delay. Since fossil fuels represent only about two
thirds of recent CO2 emissions, the remaining nonenergy emissions are treated with the abatement
cost curve from the DICE model. Autonomous technological progress reduces the energy and CO2
intensity of output, as in the DICE model.

Figure 6. Energy System Added to the DICE Model

La Depletion: / Tax
oul Production.

” aC Learning
Capital os
te eroniia YZ. £
+ LD)
+ Eneryy Price
Energy Demand UD) © Share | _—_ optimal shar e
+
SENG Production 2h NG Erice
Cumulative NC Production —PNc ccmege
RS) . Efficiency Technology
Energy Intensity of Capital + + Optimal Energy Intensity
ey 5

Cand NC refer to carbon and noncarbon energy sources, respectively. The key loops added to the model are R1 and
R2, which represent the learning curve effect. Associated with these are R3 and R4, which represent increasing
energy demand with falling prices, but they are dominated by the impact of efficiency technology. Loops B1 and B2
represent the effects of rising prices from depletion of fossil fuels on the market share of carbon energy sources and
overall energy demand. Two energy sources are shown here for simplicity, though the model includes a third,
nonconventional carbon resource.

Energy is supplied by three sources: conventional carbon, nonconventional carbon
(representing shale oil or coal liquefaction, for example), and noncarbon (renewable or nuclear).
The cost of each source is determined by technology, depletion, and the carbon tax rate. Initially,
nonconventional and noncarbon energy are four and six times more expensive than conventional
carbon energy, respectively. Technology for each source is endogenous and implemented by a
standard learning curve (Towill 1990). The learning rate selected, 10% per doubling of experience,
is identical for fossil and non-fossil energy. The rate is lower than those reported for the thermal

50
System Dynamics '95 — Volume I

efficiency of coal electricity generation (Sharp and Price 1990) and nuclear electricity construction
costs (Cantor and Hewlett 1988). Depletion affects only the conventional carbon source.

The alternative energy costs and substitution elasticities are chosen so that the model roughly
reproduces the cost curve in the DICE model, leading to results similar to its standard run when the
effects of learning and depletion are switched off. When learning and depletion are active, the
conventional carbon source is dominant initially. As it is depleted, its cost rises, and the
nonconventional carbon resource begins to gain market share. The cost of nonconventional carbon
energy then falls rapidly with accumulating experience, until it becomes the dominant source.
Noncarbon energy never becomes important, as it does not move down the learning curve quickly
enough.

1 | a ll a tas Figure 7. Energy
- Transition
75 ‘i é ith a strong carbon tax, tl
IN With ‘bi the
' energy system shifts from carbon

to noncarbon energy sources,

5 which achieve a dominant cost
Fy position as they accumulate
i experience. Were it not for the
25 7] need to control nonenergy
a emissions, the carbon tax could
0 44 LN be reduced substantially toward

tine haar memarsandnd Saas F . Es
1965. 1999 2033 2067 2101 2135 2169 2203 2237 2271 2305 | the end of the simulation.
Time

Share[carbon]
Share[non carbon]
Share[nonconventional carbon]

Table 4. Impact of Path-Dependent Energy Sector

Simulation Carbon Tax Energy COz Emissions
$/Ton C 10° Ton C/year
Year 2005 2105 2005 2105
Static, no tax 0 0 8.5 16
Static, optimal tax 20 30 8.3 13
Path dependent, no tax 0 0 8.8 10
Path dependent, optimal tax 45 43 8.1 8.1
Path dependent, optimal tax, 176 228 7.6 0.4

no discounting

A path-dependent energy sector increases the optimal abatement effort and the sensitivity of the emissions response.
Carbon taxes in this version of the model are only roughly comparable to those in other runs presented in this paper,
as the carbon tax is an explicit policy affecting energy prices rather than estimated from the implicit marginal
productivity of carbon in the economy.

Introducing the energy sector replaces the CO» emissions reduction fraction decision in the
DICE model with two decisions: the energy intensity capital and the share of carbon vs. non-
carbon energy. While it is possible to use optimization to find the paths for these decisions, this
model assumes instead that agents respond only to price, so that abatement efforts must be driven

51
Plenary Program

by an explicit carbon tax. A sufficiently large carbon tax causes the energy system to adopt the
noncarbon energy source rather than the nonconventional carbon source. Because it accumulates
more learning, the noncarbon energy source then establishes permanent dominance (see figure 7).

Climate Change Loop

Emissions from the human/economic system drive the behavior of the carbon cycle and climate in
the DICE model. The key state variables in this part of the model represent the stock of greenhouse
gases in the atmosphere, the heat stored in the atmosphere and upper ocean, and the heat stored in
the deep ocean. The major feedback loop between the economic and climate systems (B1 in figure
1) is relatively weak and delayed. The large stock of atmospheric CO. and negative-feedback CO2
storage processes buffer changes in emissions. Radiative forcing of the climate system from CO,
is proportional to the logarithm of its concentration, so the loop gain decreases as the CO? stock
rises. While feedback warming boosts the response of the climate to radiative forcing, the large
thermal mass of the earth introduces long delays.

Carbon Cycle

The carbon cycle model in the DICE model is extremely simple (see figure 8), with a single stock
of atmospheric carbon, an inflow of emissions (net of short-term storage), and an outflow of long-
term storage. It is assumed that the atmosphere and the surface layer of the ocean are well mixed,
so that only a fraction of emissions, given by an Atmospheric Retention parameter, remain in the
atmosphere. This is somewhat misleading, as very little carbon actually remains in the mixed layer
of the ocean; it instead is transported deeper. The Atmospheric Retention parameter is misleadingly
named; it does not describe the actual fractional retention of emissions in the atmosphere, as the
storage of carbon must be accounted for as well. To avoid confusion, the proportion of emissions
remaining in the atmosphere, net of short- and long-term storage processes, will be referred to as
the airbome fraction.

Figure 8. Carbon Cycle of the DICE model

CO2 in

Atmosphere
Emissions Long Term Storage

Storage Rate

Short Term Transport <———— Atmospheric Retention

The flow of short-term transport is not included in the model, but it is implicit in the assumption that only a
fraction of emissions remain in the atmosphere. The remainder must be removed by a short term transport flow
proportional to emissions.

A more detailed carbon sector model is desirable, as the variation of atmospheric retention may
have policy implications. As Firor (1988) notes, the effect of reductions in emissions may be
amplified by transient effects of carbon transport in the ocean. This means that stabilization of the

52
System Dynamics '95 — Volume I

atmospheric concentration of CO2 may be easier than anticipated. Adding a more detailed carbon
cycle to the DICE model, based on classic models by Oeschger (1975) and Goudriaan (1984), with
temperature feedback from Fung (1991), demonstrates this fact. In a partial model test against a
scenario in which emissions are reduced substantially, the airborne fraction of emissions falls more

quickly in the more detailed model, leading to a slightly lower steady-state CO2 concentration

(figure 9).
6 dmnl Figure 9. Airborne
8B TonC/Year Fraction
When subjected to a hypothetical
declining emissions path, the
airborne fraction drops more
im Sint oar quickly in the modified model,
which has more sensitive
transient behavior..
-1 dmnl
0 TonC/Year | =
1970 1980 1990 2000 2010 2020 2030
Time
Airbome Fraction - DICE dmnl
Airborne Fraction - Modified ----~++---+----=------------- dmnl
Emissions — TonC/Year

The transient differences between the models affect the results only slightly. There are two
reasons for this. First, the climate system has long delays in temperature adjustment, so that
transient effects in the carbon cycle tend to be filtered out. Second, the response of radiative
forcing and hence temperature to the concentration of CO, unlike minor trace gases, is roughly
logarithmic (Rotmans 1990; Nordhaus 1994). Thus large changes to the stock of carbon are
necessary before changes in radiative forcing are significant.

6e+012

1

4,5e+012

3e+012

1,5e+012

)

b=
| ep

1965 2005 2045

2085 «2125 «2165 2205 2245 2285

Time
TonC

-- TonC

Figure 10. Nordhaus and
Modified Carbon Cycles

When subjected to the emissions
of Nordhaus’ standard run, the
stock of atmospheric carbon in
the modified model is nearly
identical to that of the DICE
model over the historical period.
However, the stock grows much
larger in the future, due mainly to
saturation of the oceanic sink for
carbon.

Comparison with the modified model highlights a more important problem with the DICE

model carbon cycle, though: the sources and sinks of carbon are assumed to be infinite. At first
this would seem to be a reasonable assumption, given that the initial stock of carbon in the deep

53
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ocean is roughly 60 times as large as that in the atmosphere. The chemistry of carbon in the oceans
renders the effective size of the sink only 6 times as large as the atmosphere, though. Cumulative
emissions of carbon through the year 2305 are nearly as large as total estimated resources of fossil
fuels and larger than the combined total current stock of carbon in the atmosphere, surface ocean,
biomass, and soils (Bolin 1986). The revised model incorporates explicit sinks for carbon in the
ocean and biosphere; saturation of these sinks reduces the rate of storage and transport, so that the
atmospheric concentration rises much higher.

Table 5. Impact of Realistic Carbon Cycle

Simulation Optimal Carbon Tax CO, in Atmosphere
$/TonC 109 Ton C

Year 2005 2105 2005 2105 2305

DICE 8 24 820 1430 2280

Modified carbon cycle il 36 840 1740 4870

Modified carbon cycle, 14 121 840 2060 14920

constant tech. growth rate

Incorporation of a realistic carbon cycle suggests modest increases in the optimal tax policy. If one assumes
continuing economic growth, (see table 3), the impact is much more dramatic.

Climate System

The final element of the climate change loop is the climate system itself. The atmosphere and
oceans are divided into two cells: the atmosphere and surface layers of the ocean, and the deep
ocean. Radiative forcing from increasing GHG concentrations initiates warming, which is
augmented by positive feedback processes. The central issue here is the estimation of the
temperature feedback parameter, which determines the amount of additional warming from a given
increase in atmospheric temperature (loop R2 in figure 1), and the heat capacity of the atmosphere
and upper ocean, which determines the delay in the warming effect.

In the DICE model, these two parameters are estimated by regression. As Nordhaus notes,
because the observed temperature change in recent decades, when most of the cumulative
emissions have occurred, has been relatively small, either the estimated temperature feedback of the
system will be small or the estimated time delay will be large (Nordhaus 1992). Some physical
models suggest that some other factor, such as sulfate aerosol emissions, may be masking the
actual temperature trend, leading estimates based on historical data to underestimate the actual
temperature sensitivity of the system. Like the carbon sector model, this illustrates the danger of
estimating parameters from time series data when the model structure is substantially incomplete.

Climate Change Damages

The impact of climate change on the economic system is represented by a climate damage cost
curve similar to the emissions reduction cost curve. The impact of climate change is a quadratic
function of temperature. It is parameterized so that a 3° change would impose 1.3% decrease in
output, while a 6° change would cost four times as much.

54
System Dynamics '95 — Volume I

This formulation of the impact of climate change suffers from some of the same difficulties as
the abatement cost curve. The economic impact of climate change depends on the absolute change
rather than the rate of change of temperature. If temperature change is slow and human and natural
systems can adapt at low cost over long time frames, the actual cost may be less than the estimates.
But if temperature change is rapid and adaptation involves protecting or abandoning long-lived
infrastructure capital, the rate of change may be very important. The instantaneous rate of change is
not the issue (indeed, it is not even observable); rather it is the gap between the current temperature
and the temperature to which the economy or biosphere are adapted (Hatlebakk and Moxnes 1992).
The rate of temperature change and the temperature gap are more responsive to policy changes than
the absolute temperature; Nordhaus demonstrates that the optimal abatement effort is much higher
when damages are rate-dependent (Nordhaus 1994).

206 DegreesCiyeat Figure 11. Possible
6 Degre Drivers of Climate
6 DegreesC = Impacts
“1 oe ena - The temperature trend reflects the
03 DegreesC/year c eT instantaneous rate of change in
‘3 DegreesC pss the model, which oddly declines
3 DegreesC / L ms throughout the simulation. The
4 os . temperature gap is the difference
tT tween th it temperature
b Deep <u be hee
0 DegreesC a human or biological systems are
1975 2015 2055 2095 2135 2175 2215 2255 adapted (a 20-year adaptation delay
Time is assumed here). The absolute
temperature change is the
ican = difference between the current -
Absolute Temperature Change temperature and the preindustrial
temperature.

The damage cost function is estimated on the basis of current conditions. Climate change
impacts, changes in consumer preferences, or other factors may produce structural changes in the
economy, such as an increasing share of agriculture in economic activity, which would alter the
estimates. This is particularly important in developing countries, where population pressure forces
the use of increasingly marginal land. Since agriculture comprises a larger share of national income
in the developing nations, it can be expected that they will bear proportionately larger costs. At the
same time they have fewer resources. This raises important equity issues which must be
considered outside the framework of the model. The transfer of large sums of capital to the
developing countries to ensure equity can be expected to be problematic.

Conclusions

The general conclusion of the DICE model is that only modest emissions abatement efforts are
necessary. This is so because abatement efforts are costly in the short term, restricting economic
growth, and have only marginal effects on the costs of climate change in the long term. This
conclusion rests on three features of the model: emissions which are limited by declining growth

55
_ Plenary Program

and autonomous technology but are resistant to policy, insensitivity of the climate system to
marginal changes in emissions, and time discounting.

The objective function in the DICE model effectively discounts the consumption of future
generations twice; once because they are richer than us (inequality aversion) and once out of pure
impatience (time preference). Eliminating time preference to yield an objective function which is
fair to future generations dramatically increases the indicated abatement effort. While this produces
unrealistic historical investment behavior in the DICE model, decoupling investment from the
objective function by creating a behavioral investment rule solves this problem. This amounts to
recognition of the fact that cognitive limitations, market failures, and imperfect knowledge of the
future may cause observed behavior to deviate from the path which would actually maximize social
welfare.

The impact of the human and economic system on the carbon cycle and climate is limited by the
assumption of declining population growth and factor productivity, which causes emissions to
eventually stabilize with no intervention. While it is clear that population will stabilize, it is not so
clear that this is true of factor productivity. The assumption of limited factor productivity seems to
internalize the argument of the Limits to Growth study without acknowledging what feedback
loops might be responsible for the achievement of steady state (Meadows 1972). The consequence
of limited growth is that the load on natural systems remains tractable, reducing the need for costly
interventions.

The potential cost of policy measures to influence CO? emissions is overstated. There may be
significant negative-cost emissions reductions available from internalizing negative social
externalities to energy use and removing institutional barriers to energy efficiency. More
importantly, the evolution of energy efficiency and supply technologies is implicitly fixed in the
DICE model. The impact of a carbon tax is only to induce substitution of other inputs for CO. If,
instead, the energy system is path dependent, a carbon tax will change the technological frontier
along which substitution decisions are made. This means that abatement efforts may eventually be
relaxed, and that there may be policy levers which yield large results for small initial efforts,
magnified by positive feedback.

The effect of abatement efforts on climate change is limited by several factors in the DICE
model. The large stock of CO buffers the impact of changes in emissions. Because the
contribution of CO? to radiative forcing is logarithmic, the marginal effect of an increasing CO
concentration in the atmosphere decreases. The large thermal mass of the oceans and upper
atmosphere delays the impact of increased radiative forcing several decades. While sluggish stocks
and long delays are realistic characteristics of the climate system, the DICE model understates the
strength of the climate feedback to the economy in several ways. The carbon cycle model assumes
infinite carbon sinks and no nonlinear or feedback effects of rising temperature and CO
concentrations. Treating the carbon cycle in a more realistic manner demonstrates that carbon
concentrations in the atmosphere could rise to much higher levels than predicted by the DICE
model. In this case, abatement efforts should be stronger, and we can have less confidence that the
global system will remain in an operating regime which we understand.

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System Dynamics '95 — Volume I

While the impact of the modified carbon cycle is limited by the logarithmic relation of radiative
forcing to the atmospheric CO> concentration, this may not be true of the climate system or the
complex interactions among other atmospheric trace gases. There is a possibility of relatively rapid
events, such as cessation of the Atlantic thermohaline circulation, large-scale release of high-
latitude methane hydrates, or breakup of the Antarctic ice sheet, that have extreme consequences
(Cline 1992; Kutzbach 1992; Townsend, Frolking et al. 1992). While there may be mitigating
feedbacks as well (Lindzen 1990), it would be preferable to represent them explicitly and explore
them in more detail than parameter sensitivity analysis in the DICE model permits.

The economic and biogeophysical systems in the DICE model are necessarily highly
aggregated. Many speculative feedback loops are omitted. This allows thorough analysis of the
model and makes it practical to conduct the hundreds of simulations necessary for optimization.
However, it reduces the ability of the model to represent real-world policy levers explicitly. More
importantly, it increases the range of uncertainty of the model. Nordhaus conducts a thorough
Monte Carlo analysis of the model by assigning subjective probability distributions to a variety of
variables to get a sense of the uncertainties, but because important feedback loops are missing (as
in the carbon cycle), this analysis is likely to understate the true level of uncertainty. It is important
to test the structural uncertainties as well. While the structural revisions here are tested in isolation,
it appears possible to construct a model with parameter values and historical behavior very similar
to the DICE model that generates very different conclusions about the effort which should be
allocated to greenhouse gas emissions abatement.

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