Introduction and motivation
The vast evidence that the climate of the Earth is changing due to the
anthropogenic increase in greenhouse gases (GHGs) is compiled in the
successive reports of the Intergovernmental Panel on Climate Change
(IPCC, 1996a, 2001, 2007, 2013), carbon dioxide (CO2) being
the largest contributor (Stott et al., 2000; Stern, 2008; Mokhov
et al., 2012; Farmer and Cook, 2013, p. 4). Typically, the effect of
global warming on the economic system is modeled using integrated
assessment models (IAMs); see also Meyers (2012, 5399–5428) and
Rasch (2012, Ch. 8) for a further discussion. IAMs are motivated by
the need to balance the dynamics of carbon accumulation in the
atmosphere and the dynamics of de-carbonization of the economy
(Nordhaus, 1994a). A specific goal of these studies is to evaluate
different abatement scenarios as to economic welfare and their effects
on GHG emissions.
In this paper, we study the interaction between global warming and
economic growth, along the lines of the Dynamic Integrated model of
Climate and the Economy (DICE) of Nordhaus (1994a), with subsequent
updates in Nordhaus and Boyer (2000) and Nordhaus (2007, 2008, 2010,
2013). Greiner (2004) (see also, Greiner and Semmler, 2008) extended
the DICE framework by including endogenous growth, to account for the
fact that environmental policy affects not only the level of economic
variables but also the long-run growth rate. Using the extended DICE
model, Greiner argues that higher abatement activities reduce GHG
emissions and may lead to a rise or decline in growth. The net effect
on growth depends on the specification of the function between the
economic damage and climate change.
Since anthropogenic GHGs are the result of economic activities, the
main shortcoming in Greiner's (2004) approach is that of treating
industrial CO2 emissions as constant over time. Another
problematic aspect of Greiner's emissions formulation is its inability
to allow for zero abatement activities. In fact, his formulation only
holds for a minimum level of abatement.
We address these issues in the present Part 1 of a two-part paper by
using a novel approach to formulating emissions that depend on
economic growth and vary over time; in this approach, abatement equal
to zero corresponds to Business As Usual (BAU).
We further use the extended DICE modeling framework by considering
both human and physical capital accumulation, in addition to the GHG
emissions, as well as a ratio of abatement spending to the tax revenue
or abatement share (see also, Greiner, 2004; Greiner and Semmler,
2008). Our methodology can analytically clarify the mutual causality
between economic growth and the climate change-related damages and
show how to alter this relationship by the use of various mitigation
measures geared toward reduction of CO2 emissions (Metz
et al., 2007; Hannart et al., 2013). We will use the abatement share
to invest in the increase of overall energy efficiency of the economy
(Diesendorf, 2014, p. 143) and decrease of overall carbon intensity of
the energy system. It will be shown below that over the next few
decades, up to the mid-21st century, mitigation costs do hinder
economic growth, but that this growth reduction is compensated later
on by the having avoided negative impacts of climate change on the
economy; see also Kovalevsky and Hasselmann (2014, Fig. 2).
The companion paper, Part 2, complements the model by introducing
carbon capturing and storing (CCS) technologies and control of
deforestation, as well as increasing photosynthetic biomass sinks as
a method of controlling atmospheric CO2 and consequently the
intensity and frequency of climate change related damages.
Our Coupled Climate–Economy–Biosphere (CoCEB) model is not intended
to give a detailed quantitative description of all the processes
involved, nor to make specific predictions for the latter part of this
century. It is a reduced-complexity model that tries to incorporate
the climate–economy–biosphere interactions and feedbacks with the
minimum amount of variables and equations needed. We merely wish to
trade realism for greater flexibility and transparency of the
dynamical interactions between the different variables. The need for
a hierarchy of models of increasing complexity is an idea that dates
back – in the climate sciences – to the beginnings of numerical
modeling (e.g. Schneider and Dickinson, 1974), and has been broadly
developed and applied since (Ghil, 2001, and references
therein). There is an equivalent need for such model hierarchy to deal
with the higher-complexity problems at the interface of the
biogeophysical-biogeochemical climate sciences and of socio-economic
policy.
The CoCEB model lies toward the highly idealized end of such
a hierarchy: it takes an integrated assessment approach to simulating
global change. By using an endogenous economic growth module with
physical and human capital accumulation, this paper considers the
sustainability of economic growth, as economic activity intensifies
greenhouse gas emissions that in turn cause economic damage due to
climate change (Stern, 2007; Nordhaus, 2008; Dell et al., 2014 and the
references therein).
As different types of fossil fuels produce different volumes of
CO2 in combustion, the dynamics of fossil fuel consumption –
that is, the relative shares of coal, oil, and natural gas – has to
be taken into account when calculating the future dynamics of
CO2 emission (see also, Akaev, 2012). These shares are not
known at this time (Akaev, 2012), nor is it easy to predict their
evolution. In order to describe the dynamics of hydrocarbon-based
energy share into the global energy balance of the 21st century and
their replacement with renewable energy sources we use, following
Sahal (1981), logistic functions (see also, Probert et al.,
2004, p. 108, and references therein). This is a novel approach with
respect to most other integrated assessment modeling studies in the
climate change mitigation literature, which often assume an
unrealistic approach of fixed, predictable technological change,
independent of public policy, as well as the treatment of investment
in abatement as a pure loss (Stanton et al., 2009). Technology change
in these IAMs is modeled in a simple way by using an autonomous energy
efficiency improvement (AEEI) parameter that improves the energy
efficiency of the economy by some exogenous amount overtime: see, for
instance, Bosetti et al.'s (2006, 2009) World Induced Technical Change
Hybrid (WITCH) model and van Vuuren et al.'s (2006) Integrated Model
for the Assessment of the Global Environment (IMAGE) model. However,
the use of AEEI ignores the causes that influence the evolution of
technologies (Lucas, 1976; Popp et al., 2010 and references
therein). Even though this shortcoming can be remedied by including
endogenous technological change in IAMs either through direct
price-induced, research and development-induced, or learning-induced
approaches (see Popp et al., 2010 for details), there is no accord in
the climate change mitigation literature regarding a single best
approach (Grubb et al., 2002; Popp et al., 2010).
Various climate change mitigation policy measures are
considered. While many integrated assessment models treat abatement
costs merely as an unproductive loss of income (e.g. Nordhaus and
Boyer, 2000; Nordhaus, 2007, 2008, 2010, 2013), we consider abatement
activities also as an investment in overall energy efficiency of the
economy and decrease of overall carbon intensity of the energy
system. The paper shows that these efforts help to reduce the volume
of industrial carbon dioxide emissions, lower temperature deviations,
and lead to positive effects in economic growth.
The model is, of course sensitive, to the choice of key parameters. We
do carry out a sensitivity study, but do not intend to make precise
calibrations; rather, we want to provide a tool for studying
qualitatively how various climate policies affect the economy.
The next section describes the theoretical model,
detailing the additions with respect to Nordhaus (2013),
Greiner (2004) and Greiner and Semmler (2008). Section 3
discusses the numerical simulations and results, while
Sect. 4 tests the sensitivity of the results to key
parameters. Section 5 concludes with caveats and avenues
for future research.
Model description
Climate module
The time evolution of the average surface temperature T (SAT) on
Earth is given by
dTdt=(1-αT)Q4ch-εσTτachT4+6.3β1(1-ξ)chlnCC^,
see, for instance, Ghil and Childress (1987, Ch. 10), McGuffie and
Henderson-Sellers (2005, p. 81–85; 2014) or Hans and Hans (2013,
Ch. 2). Here the first and second terms on the right-hand side are
incoming and outgoing radiative fluxes respectively, while the third
term is radiative forcing due to increase in GHGs (Kemfert, 2002;
Greiner and Semmler, 2008); σT is the
Stefan–Boltzmann constant, τa the infrared (long-wave)
transmissivity of the atmosphere, ε the emissivity that
gives the ratio of actual emission to blackbody emission,
αT the mean planetary albedo, Q is the average
solar constant. The specific heat capacity ch of Earth is
largely determined by the oceans (Levitus et al., 2005) and it is
taken equal to 16.7 Wm-2K-1 (Schwartz, 2007, 2008),
which corresponds to an ocean fractional area of 0.71 and a depth of
150 m of the ocean mixed layer. The current CO2
concentration C is given in gigatons of carbon (Gt C,
1 Gt =1015 g) and C^ is the pre-industrial
CO2 concentration. All the feedbacks, are represented in this
highly idealized model by the factor β1, which is assumed to
take values between 1.1 and 3.4 (Greiner and Semmler, 2008, p. 62); in
this study, it was assumed that β1=3.3. The parameter ξ=0.23 captures the fact that part of the warmth generated by the
greenhouse effect is absorbed by the oceans and transported from their
upper layers to the deep sea (Greiner and Semmler, 2008). The other
parameters have standard values that are listed in Table 1.
At equilibrium, that is for dT/dt=0, Eq. (1)
gives an average SAT of 14 ∘C for the pre-industrial GHG
concentration, i.e. for C=C^. Doubling the CO2
concentration in Eq. (1) yields an increase of about 3.3 ∘C
in equilibrium temperature, to 17 ∘C. This increase lies
within the range of IPCC estimates, between 1.5 and 4.5 ∘C
(Charney et al., 1979; IPCC, 2001, p. 67, 2013) with a best
estimate of about 3.0 ∘C (IPCC, 2007, p. 12).
We represent the evolution C of the concentration of CO2 in
the atmosphere, following Uzawa (2003) and Greiner and Semmler (2008),
as
dCdt=β2EY-μo(C-C^),
where EY is industrial CO2 emissions. The excess
C above pre-industrial level is reduced by the combined effect of
land and ocean sinks. The inverse μo of the atmospheric
lifetime of CO2 is estimated in the literature to lie within
an uncertainty range that spans 0.005–0.2 (IPCC, 2001, p. 38); we
take it here to equal μo=1/120=0.0083, i.e. closer to
the lower end of the range (Nordhaus, 1994a, p. 21; IPCC, 2001,
p. 38). The fact that a certain part of GHG emissions is taken up by
the oceans and does not remain in the atmosphere is reflected in Eq. (2) by the parameter β2.
Economy module
In Greiner (2004) and Greiner and Semmler (2008) the per capita gross domestic product (GDP),
Y, is given by a modified version of a constant-return-to scale
Cobb–Douglas production function (Cobb and Douglas, 1928),
Y=AKαH1-αD(T-T^).
Here K is the per capita physical capital, H is the per capita
human capital, A>0 the total factor of productivity, 0<α<1
is the capital share, D(T-T^) is the damage, expressed as
a function of the temperature difference due to climate change. The
damage function is described in Section “Damage function” below.
The economy income identity in per capita variables is given by
Y-X=I+ME+GE,
with X=τY the (per capita) tax revenue, 0<τ<1 the per
annum tax rate, I investment, ME consumption, and
GE abatement activities. This means that national income
after tax is used for investment, consumption, and abatement. We
assume that GE is expressed as a fraction of X,
GE=τbX=τbτY,
with 0≤τb<1 the ratio of per annum abatement share,
used as a policy tool. Consumption is also expressed as a fraction of
Y after tax, that is,
ME=c(1-τ)Y,
with 0<c<1 the global annual consumption share.
The accumulation of per capita physical capital K is assumed to obey
dKdt=Y-X-ME-GE-(δK+n)K,
the logistic-type human population growth rate 0<n<1 is given, in
turn, by
dndt=11-δn-1n,
with δn being the per year decline rate of n, and
δK the per year depreciation rate of physical
capital. Substituting the definitions of Y, X, ME,
and GE into Eq. (7) we get
dKdt=AKαH1-αD(T-T^)[1-τ(1+τb)-c(1-τ)]-(δK+n)K.
For physical capital to increase, dK/dt>0, the
parameters must satisfy the inequality 0<[τ(1+τb)+c(1-τ)]<1. Now, proceeding as above for K, we assume
that the per capita human capital H evolves over time as
dHdt=φAKαH1-αD(T-T^)[1-τ(1+τb)-c(1-τ)]-(δH+n)H,
here φ>0 is a coefficient that determines how much any unit
of investment contributes to the formation of the stock of knowledge
and δH gives the depreciation of knowledge.
Note that we take, as a starting point, the Solow–Swan approach
(Solow, 1956; Swan, 1956; Greiner and Semmler, 2008), in which the
share of consumption and saving are given. We do this because we want
to focus on effects resulting from climate change, which affect
production as modeled in Eqs. (3)–(10) and, therefore, neglect
effects resulting from different preferences.
Our formulation assumes, furthermore, that government spending, except
for abatement, does not affect production possibilities. Emissions of
CO2 are a byproduct of production and hence are a function of
per capita output relative to per capita abatement activities. This
implies that a higher production goes along with higher emissions for
a given level of abatement spending. This assumption is frequently
encountered in environmental economics (e.g. Smulders, 1995). It
should also be mentioned that the emission of CO2 affect
production indirectly by affecting the climate of the Earth, which
leads to a higher SAT and to an increase in the number and intensity
of climate-related disasters (see, e.g. Emanuel, 2005; Min et al.,
2011).
Industrial CO2 emissions
In Greiner (2004) and Greiner and Semmler (2008), emissions
EY are formally described, as a function of the production
Y, by
aYGEγ=aYτbτYγ=aτbτγ,
here γ>0 is a constant and a>0 a technology index that
describes how polluting a given technology is. Note that Eq. (11) is
defined only for τb different from zero; hence, it does
not consider a no-abatement or BAU scenario. Moreover, Eq. (11) also
gives constant emissions over time even when the economic activity is
changing, which is unrealistic. Here, we use instead a formulation of
emissions EY that vary over time and in which we can let
abatement be zero.
Specifically, we use the Kaya–Bauer identity (Kaya, 1990; Bauer,
2005) that breaks down CO2 emissions EY (in GtCyr-1) into a product of five components: emissions per
unit of energy consumed (carbon intensity of energy), energy use per
unit of aggregate GDP (energy intensity), per capita GDP, human
population, and carbon emission intensity, as shown below:
EY=EtotenergyenergyY‾Y‾LLEYEtot=ccecYLκccs=σYLκccs.
Here Y‾ is aggregate GDP,
Y=(Y‾/L) is per capita GDP, L is the human
population, cc=Etot/energy is the carbon
intensity of energy, ec=energy/Y‾ is
the energy intensity, ccec=Etot/Y‾=σ is the ratio of industrial
carbon emissions to aggregate GDP or the economy carbon intensity,
EY/Etot=κccs is the fraction
of emissions that is vented to the atmosphere and involves CCS.
The EY level also depends on abatement activities, as
invested in the increase of overall energy efficiency in the economy
and decrease of overall carbon intensity of the energy system. The
case of τb=0 in Eq. (5) corresponds to unabated
emissions, i.e. BAU. Emissions are reduced as the abatement share
increases. Taking the natural logarithms and differentiating both
sides of the Kaya–Bauer identity yields
dEYdt=[gσ+gY+n+gccs]EY,
where gσ is the growth rate of σ, gY is the
growth rate of Y, n is the population growth rate and
gccs is the CCS growth rate. If CCS is applied, then
EY<Etot. There are many concerns and
uncertainties about the CCS approach and it is usually not taken as
a real sustainable and environmental friendly mitigation option to
reduce emissions over a longer period (Tol, 2010). We will not
consider it in this part of the paper, that is, we take EY=Etot or κccs=1.
We now formulate the technology-dependent carbon intensity
σ. We follow the approach of Sahal (1981), who models the
replacement of one technology by another using a logistic law. The
energy intensity ec, in tons of reference fuel
(TRF)/USD 1000 of Y‾, is the share
of hydrocarbon-based energy (coal, oil, and natural gas) in the global
energy balance (GEB) of the twenty-first century. Its dynamics are
described by a descending logistic function (Akaev, 2012),
ec=fc1-rexp(ψt)1+r(exp(ψt)-1),
here we take 1990 as the time when the use of renewable energy sources
(biomass and wastes, hydropower, geothermal energy, wind energy, and
solar energy) and biofuels became significant in the GEB. The
multiplier fc=0.881 corresponds to 1.0107×1010 TRF as the share of fossil fuels in the GEB (1.1472×1010 TRF) in 1990 (Akaev, 2012, Table 2). The parameters r and ψ are
derived by assuming a level of 95 % fossil fuels used for year
2020 and of 5 % for year 2160. They are r=0.05 and ψ=ψ0[1/(1-αττb)], with
ψ0=0.042; ατ>0 here is an abatement efficiency
parameter, chosen such that for the path corresponding to
τb=0.075, carbon emissions reduction from baseline is
about 50 % by year 2050; see Sect. 2.5 for details. Calculations
based on Eq. (13) using these values indicate that the share of fossil
fuels will be significant throughout the whole twenty-first century
and, when τb=0, this share decreases to 35 % only
by its end (Akaev, 2012).
As different types of fossil fuels produce different volumes of
CO2 in combustion, the dynamics of fossil fuel consumption –
i.e. the relative shares of coal, oil, and natural gas – should be
taken into account when calculating the future dynamics of CO2
emission. Since these shares are not known at this time, we assume
a logistic function for describing a reduction of the carbon intensity
of energy cc, in tons of carbon/tons of reference fuel
(tCTRF-1), throughout the 21st century (Akaev, 2012),
cc=c-∞+ac1+rexp(-ψt),
with ac>0 a constant.
Thus the carbon intensity σ, which is technology-dependent and
represents the trend in the CO2-output ratio, can now be given
by the product of the energy intensity ec in Eq. (13) and
the carbon intensity of energy cc in Eq. (14), thus:
σ=fc1-rexp(ψt)1+r(exp(ψt)-1)c-∞+ac1+rexp(-ψt).
We can now calculate the de-carbonization of the economy, i.e. the
declining growth rate of σ, by taking the natural logarithms of
Eq. (15) and getting the derivative with respect to time:
gσ=fcec[ψrexp(ψt)][1+r(exp(ψt)-1)]-[ψr2exp(ψt)][1+r(exp(ψt)-1)]2+1ccacψrexp(-ψt)[1+rexp(-ψt)]2.
In a similar way as Eq. (16) was derived from Eq. (15), the growth
rate gY of per capita output is obtained from Eq. (3) as
1YdYdt=αKdKdt+(1-α)HdHdt+1DdDdTdTdt,
or,
gY=αgK+(1-α)gH+1DdDdTdTdt,
with gK the per capita physical capital growth and gH the
per capita human capital growth.
Human population evolves; cf. Golosovsky (2010), as
dLdt=nL{1-exp[-(L/L(1990))]},
where n is the population growth rate as given in Eq. (8). Equation (18)
yields L=9×109 people in the year t=2100. This value
is consistent with the 2100 population projections of scenarios in the
literature (e.g. van Vuuren et al., 2012, Table 3).
Damage function
The damage function D gives the decline in Y, the global GDP,
which results from an increase of the temperature T above the
pre-industrial temperature T^. Nordhaus (1994a) formulates it
as
D(T-T^)=1+m1(T-T^)χ-1,
with m1>0 and χ>0, and the damage is defined as
Y-DY=(1-D)Y. The greater T-T^, the smaller the value of
D(T-T^), and accordingly the smaller the value DY of the
remaining GDP, after the damage.
The representation of climate change damages is both a key part and
one of the weakest points of IAMs (Tol and Fankhauser,
1998). Temperature was used originally by Nordhaus (1994a) as a proxy
for overall climate change. This may have taken the research
community's focus off from potentially dangerous changes in
climate apart from temperature (Toth, 1995). However, without using
a detailed climate model, temperature remains the best option
available. We assume, in choosing this option, that physical and human
capitals are distributed across infinitely many areas in the economy,
and that the damages by natural disasters are uncorrelated across
areas. With such an assumption, some version of the law of large
numbers can justify a result like Eq. (19) above; see Dell
et al. (2014) for an insightful discussion about the damage function.
Nordhaus (1994a) first estimated the damage from CO2 doubling
– which, in his calculations was equivalent to a 3 ∘C
warming – to be 1.33 % of global GDP (Nordhaus, 1992).
Additionally, he argued that damage would increase sharply as
temperature increases; hence he used a quadratic function, in which
χ=2, and m1 is chosen to have 1.33 % loss of GDP for
a 3 ∘C warming.
Roughgarden and Schneider (1999), using the same functional form
(Eq. 19), derived damage functions for each of the disciplines
represented in an expert opinion solicited by a climate change survey
(Nordhaus, 1994b). Taking an average of their values, we get m1=0.0067; see, for instance, Table 1 in Labriet and Loulou (2003). On
the other hand, we calibrated the nonlinearity parameter χ=2.43
so that our model's BAU emissions of CO2yr-1 and
concentrations by 2100 mimic the Representative Concentration Pathway
(RCP) 8.5 (Riahi et al., 2007; IPCC, 2013). In fact, our projected
climate change damages before and after abatement, as given by the
damage function D in Eq. (19), are consistent with the damages
projected in Stern (2007); see also Creedy and Guest (2008) as well as
Chen et al. (2012, p. 5).
Climate change abatement measures
A key part of the mitigation literature concentrates on the
feasibility of different climate targets, often defined by GHG
concentrations or by radiative forcing levels, and the associated
costs; see van Vuuren et al. (2012) and the citations therein. The
broad range of options available for mitigating climate change
includes the reduction of CO2 emissions (increasing energy
efficiency, increasing non-fossil fuel-based energy production, and
the use of CCS), and CO2 removal (Edenhofer et al., 2012;
Steckel et al., 2013).
Abatement policies
For reasons of political feasibility as well as of efficiency, the
focus of climate policy has been on energy intensity and carbon
intensity of energy, and not on population and wealth (Tol, 2010). All
the popular policies point to increased de-carbonization efforts,
i.e. to an increase in gσ. The historical record, however,
shows quite clearly that global and regional rate of de-carbonization
have seen no acceleration during the recent decade and in some cases
even show evidence of re-carbonization (Canadell et al., 2007; Prins
et al., 2009).
Among the various market-based (or economic) instruments adopted to
reduce CO2 emissions, carbon taxes and
tradable permits are the most widely discussed
cost-efficient policies, both at a national and international
level (Weitzman, 1974; Fiddaman, 1997; Pizer, 1999, 2002, 2006;
Fischer et al., 2003; Uzawa, 2003; IPCC, 2007; Mankiw, 2007; Nordhaus,
2008). Forestry policies, particularly deforestation control,
also emerge as additional low cost measures for the reduction of
CO2 emissions. Deforestation control would cut CO2
emissions and increased afforestation would sequester CO2 from
the atmosphere (see, e.g. Tavoni et al., 2007; Bosetti et al., 2011).
Abatement share
The abatement costs of several IAMs tend to cluster in the range of
about 1–2 % of GDP as the cost of cutting carbon emissions from
baseline by 50 % in the period 2025–2050, and about
2.5–3.5 % of GDP as the cost of reducing emissions from baseline
by about 70 % by 2075–2100 (Boero et al., 1991; Cline, 1992, p.
184; Boero, 1995; Clarke et al., 1996; Tol, 2010, p. 87, Fig. 2.2)
with an increasing dispersion of results as higher emission reduction
targets are set (Boero et al., 1991).
Using the definition of abatement in Eq. (5) and the GDP evolution in
Eq. (3), we obtain an abatement share that gives an abatement cost
equivalent to 1 % of GDP by 2050 to be
GEY=τbτ=0.01⇒τb=0.05.
Similarly, the abatement share giving an abatement cost equivalent to
2 % of GDP by 2050 is τb=0.1. We take, as our
lower abatement share, the average τb=0.075 of the two
abatement shares that give an abatement cost equivalent to 1.5 %
of GDP by 2050.
Next, we choose the abatement efficiency parameter ατ=1.8 such that, for the path corresponding to τb=0.075, carbon emissions reduction from baseline is about 50 % by
2050. Our scenario corresponding to τb=0.075 also
happens to mimic the RCP6.0 by 2100 (Fujino et al., 2006; Hijioka
et al., 2008; IPCC, 2013). For the other non-BAU scenarios, we choose
abatement shares of τb=0.11 and 0.145, such that an
emissions reduction of 50 % or more from baseline by 2050 and
beyond gives a reduction in GDP of 2.2 and 2.9 %, respectively;
the scenario given by τb=0.11 also mimics RCP4.5
(Clerke et al., 2007; Wise et al., 2009; IPCC, 2013). Note that the
abatement shares in Greiner (2004) and Greiner and Semmler (2008),
which use Eq. (11), are about 10 times lower than the ones chosen
here.
Summary formulation of CoCEB
Our coupled CoCEB model is described by Eqs. (1), (2), (9), (10) and
(12). The model describes the temporal dynamics of five variables: per
capita physical capital K, per capita human capital H, the average
global surface air temperature T, the CO2 concentration in
the atmosphere C, and industrial CO2 emissions
EY. The other variables are connected to these five
independent variables by algebraic equations. In Part 2,
a supplementary equation will be added for the biomass. The equations
are grouped for the reader's convenience below:
dKdt=A1-τ(1+τb)-c(1-τ)KαH1-αD(T-T^)-(λK+n)K,dHdt=φA[1-τ(1+τb)-c(1-τ)]KαH1-αD(T-T^)-(λH+n)H,dTdt=(1-αT)Q4ch-εσTτachT4+β1(1-ξ)ch6.3lnCC^,dCdt=β2EY-μo(C-C^),dEYdt=gσ+gY+nEY.
The parameter values used in the model are as described in the text
above and in Table 1 below. They have been chosen according to
standard tables and previous papers.
Numerical simulations and abatement results
In the following, we confine our investigations to the transition path
for the 110 years from the baseline year 1990 to the end of
this century. We consider four scenarios with an aggregate CO2
concentration larger than or equal to the pre-industrial level:
(i) a baseline or BAU scenario, with no abatement activities, i.e. τb=0;
and (ii)–(iv) three scenarios with abatement
measures, corresponding to τb=0.075, 0.11 and 0.145,
as chosen in Sect. 2.6.
The CoCEB model is integrated in time starting from the initial values
at year 1990, as listed in Table 1. The damage function exponent
χ in Eq. (19) is taken to be super-quadratic, χ=2.43; all
other parameter values are as in Table 1. The time step is
1 year and the integration is stopped at year 2100. The values
of CO2 emissions and concentration, temperature, damage and
GDP growth at the end of the integrations are shown in Table 2 for the
four scenarios.
From the table, it is clear that, if no action is taken to reduce
baseline CO2 emissions, these will attain 29.3 GtCyr-1 by 2100, leading to an atmospheric CO2
concentration of 1842 Gt C, i.e. about 3.1 times the pre-industrial
level at that time. As a consequence, global average SAT will rise by
5.2 ∘C from the pre-industrial level with a corresponding
damage to the per capita GDP of 26.9 %. This compares well with
the IPCC results for their RCP8.5 scenario, cf. Table 4 below.
The year-2100 changes in our three non-BAU scenarios' global mean SAT
from the pre-industrial level are 3.4, 2.6, and 2 ∘C. The
RCP6.0, RCP4.5, and RCP2.6 give a similar range of change in global
SAT of 1.4–3.1 ∘C with a mean of 2.2 ∘C,
1.1–2.6 ∘C with a mean of 1.8 ∘C, and
0.3–1.7 ∘C with a mean of 1 ∘C, respectively (IPCC,
2013). We note that our scenarios' change in temperature compare well
with the IPCC ones.
The cumulative CO2 emissions for the 1990–2100 period in this
study's non-BAU scenarios are 1231, 1037, and 904 Gt C. On the other
hand, for the 2012–2100 period, RCP6.0 gives cumulative CO2
emissions in the range of 840–1250 Gt C with a mean of 1060 Gt C;
RCP4.5 gives a range of 595–1005 Gt C with a mean of 780 Gt C,
while RCP2.6 gives a range of 140–410 Gt C with a mean of 270 Gt C. The two former RCPs agree rather well with our results, while
RCP2.6 is less pessimistic.
In Fig. 1, the time-dependent evolution of the CoCEB output is shown,
from 1990 to 2100. The figure shows that an increase in the abatement
share τb from 0 to 0.145 leads to lower CO2
emissions per year (Fig. 1a) as well as to lower atmospheric
CO2 concentrations (Fig. 1b) and, as a consequence, to a lower
average global SAT (Fig. 1c), compared to the baseline value. This
physical result reduces the economic damages (Fig. 1d) and hence the
GDP growth decrease is strongly modified (Fig. 1e).
Figure 1e is the key result of our study: it shows that abatement
policies do pay off in the long run. From the figure, we see that –
because of mitigation costs – per capita GDP growth on the paths with
nonzero abatement share, τb≠0, lies below growth on
the BAU path for the earlier time period, approximately between 1990
and 2060. Later though, as the damages from climate change accumulate
on the BAU path (Fig. 1d), GDP growth on the BAU slows and falls below
the level on the other paths (Fig. 1e), i.e. the paths cross.
This crossing of the paths means that mitigation allows GDP growth to
continue on its upward path in the long run, while carrying on BAU
leads to great long-term losses. As will be shown in Table 3 below,
the losses from mitigation in the near future are outweighed by the
later gains in averted damage. The cross-over time after which
abatement activities pay off occurs around year 2060; its exact timing
depends on the definition of damage and on the efficiency of the
modeled abatement measures in reducing emissions.
The average annual growth rates (AAGRs) of per capita GDP between 1990
and 2100, are given in our model by (1/110)∑t=1990t=2100gY(t) and their values, starting from the BAU scenario, are
2.6, 2.4, 2.1 %yr-1, and 1.8 %yr-1,
respectively. Relative to 1990, these correspond to approximate per
capita GDP increase of 5.5–14.5 times, that is
USD1990 34×103–90×103 in year 2100, up from
an approximate of USD 6×103 in 1990. Our scenarios' AAGRs
and the 2100-to-1990 per capita GDP ratio agree well with scenarios
from other studies, which give AAGRs of 0.4–2.7 %yr-1
and a per capita GDP increase of 3–21 fold, corresponding to
USD1990 15×103–106×103 (Leggett et al.,
1992; Holtz-Eakin and Selden, 1995; Rabl, 1996; Chakravorty et al.,
1997; Grübler et al., 1999; Nakićenović and Swart, 2000;
Schrattenholzer et al., 2005, p. 59; Nordhaus, 2007; Stern, 2007; van
Vuuren et al., 2012; Krakauer, 2014).
Now, according to the United Nations Framework Convention on Climate
Change (UNFCCC, 1992), the average global SAT should not exceed its
pre-industrial level by more than 2 ∘C. This SAT target means
that global efforts to restrict or reduce CO2 emissions must
aim at an atmospheric CO2 concentration of no more than
1171.5 Gt C. This CO2 target can be achieved if carbon
emissions are reduced to no more than 3.3 GtCyr-1, or
nearly half relative to the 1990 level of 6 GtCyr-1
(Akaev, 2012). This goal is met, in our highly simplified model, by
the path with the highest abatement share of the four,
τb=0.145. From Table 2 and Fig. 1, we notice that this
level of investment in the increase of overall energy efficiency of
the economy and decrease of overall carbon intensity of the energy
system enable emissions to decrease to 2.5 GtCyr-1 by
year 2100 (Fig. 1a), about a 58 % drop below the 1990 emissions
level. This emissions drop enables the deviation from pre-industrial
SAT to reach no higher than 2 ∘C by year 2100 (Fig. 1c).
The per capita abatement costs GE=τbX=τbτY from Eq. (5) and the damage costs (1-D)Y
from Eq. (19) for the various emission reduction paths are given in
Table 3 for the year 2100. From the table we notice that, generally,
the more one invests in abatement, the more emissions are reduced
relative to baseline and the less the cost of damages from climate
change. From Tables 2 and 3, we notice that limiting global average
SAT to about 2 ∘C over pre-industrial levels would require an
emissions reduction of 92 % from baseline by 2100, at a per capita
cost of USD1990 990, which translates to 2.9 % of per capita
GDP. Although attaining the 2 ∘C goal comes at a price, the
damages will be lower all along and the GDP growth better than for BAU
starting from the cross-over year 2058.
Recall, moreover, that the benefits of GHG abatement are not limited
to the reduction of climate change costs alone. A reduction in
CO2 emissions will often also reduce other environmental
problems related to the combustion of fossil fuels. The size of these
so-called secondary benefits is site-dependent (IPCC, 1996b, p. 183),
and it is not taken into consideration as yet in the CoCEB model.
Table 4 gives a comparative summary of our CoCEB model's results and
those from other studies that used more detailed IAM models and
specific IPCC (2013) RCPs. We notice that the CO2 emissions
per year and the concentrations in the transition path up to year 2100
agree fairly well with those of RCP8.5, RCP6.0 and RCP4.5.
Sensitivity analysis
We conducted an analysis to ascertain the robustness of the CoCEB
model's results and to clarify the degree to which they depend on
three key parameters: the damage function parameters m1 and
χ and the abatement efficiency parameter ατ. The
values of these parameters are varied below in order to gain insight
into the extent to which particular model assumptions affect our
results in Sect. 3 above.
Damage function parameters m1 and χ
We modify the values of the parameters m1 and χ by +50 and
–50 % from their respective values m1=0.0067 and χ=2.43 in Tables 1–4 above, and examine how that affects model
results for year 2100. In Table 5 are listed the per annum CO2
emissions, CO2 concentrations, SAT, damages, and growth rate
of per capita GDP. All parameter values are as in Table 1, including
ατ=1.8.
From the table we notice that reducing m1 by 50 % lowers the
damages to per capita GDP from 26.9 to 20.3 %, i.e. a 24.5 %
decrease on the BAU (τb=0) path. This depresses the
economy less and contributes to higher CO2 emissions of
50.8 GtCyr-1. On the other hand, increasing m1 by
50 % increases the damages from 26.9 to 30.3 %, i.e. a 12.6 %
increase on the BAU path. This depresses the economy
more and lowers CO2 emissions in 2100 to 20.4 GtCyr-1.
The sensitivity to the nonlinearity parameter χ is considerably
higher. Decreasing it by 50 % reduces the damages to per capita
GDP from 26.9 to about 6.3 %, i.e. a 76.6 % reduction on the
BAU path. This contributes to higher economic growth and higher
emissions of 99.6 GtCyr-1. Conversely, increasing χ
by 50 % increases the damages to per capita GDP from 26.9 to about
41.6 %, i.e. a 54.6 % increase on the BAU path. This
contributes to a decrease in economic growth and to lower emissions of
6 GtCyr-1 in the year 2100.
In Fig. 2 are plotted the GDP growth curves with time for the
experiments summarized in Table 5. It is clear from the figure that
the growth rate of per capita GDP is more sensitive to the
nonlinearity parameter χ than to m1. A decrease of m1
by 50 % pushes the crossover point further into the future, from
year 2058 to 2070 (Fig. 2a), while an increase by 50 % pulls the
crossover point closer to the present, to about 2053
(Fig. 2b). Decreasing χ by 50 %, on the other hand, pushes
the crossover point even further away, past the end of the century
(Fig. 2c), while an increase of χ by 50 % pulls it from year
2058 to about 2037 (Fig. 2d).
Abatement efficiency parameter ατ
Next, we modify the value of the parameter ατ by +50
and -50 % from the standard value of ατ=1.8 used
in Tables 1–5 above, and examine in Table 6 how that affects the
model emissions reduction from baseline by the year 2100, as well as
the per capita abatement costs and the per capita damage costs.
A 50 % decrease of the abatement efficiency gives ατ=0.9 in the upper half of the table. There is a substantial decrease
in emissions reduction for all three scenarios with τb>0, compared to Table 3, and hence more damages for the same
abatement costs. Furthermore, the increased damages increase the
depression of the economy and contribute to low economic growth.
On the other hand, a 50 % increase in the abatement efficiency, to
ατ=2.7, leads to an increase in the emissions reduction
from baseline by 2100. This reduces the damages and hence lessens the
depression to the economy, enabling economic growth to increase.
Conclusions and way forward
Summary
In this paper, we introduced a simple coupled climate–economy (CoCEB)
model with the goal of understanding the various feedbacks involved in
the system and also for use by policy makers in addressing the climate
change challenge. In this Part 1 of our study, economic activities are
represented through a Cobb–Douglas output function with constant
returns to scale of the two factors of production: per capita physical
capital and per capita human capital. The income after tax is used for
investment, consumption, and abatement. Climate change enters the
model through the emission of GHGs arising in proportion to economic
activity. These emissions accumulate in the atmosphere and lead to
a higher global mean surface air temperature (SAT). This higher
temperature then causes damages by reducing output according to
a damage function. The CoCEB model, as formulated here, was summarized
as Eqs. (21a)–(21e) in Sect. 2.7.
Using this model, we investigated in Sect. 3 the relationship between
investing in the increase of overall energy efficiency of the economy
and decrease of overall carbon intensity of the energy system through
abatement activities, as well as the time evolution, from 1990 to
2100, of the growth rate of the economy under threat from climate
change–related damages. The CoCEB model shows that taking no
abatement measures to reduce GHGs leads eventually to a slowdown in
economic growth; see also Kovalevsky and Hasselmann (2014, Fig. 2).
This slowdown implies that future generations will be less able to
invest in emissions control or adapt to the detrimental impacts of
climate change (Krakauer, 2014). Therefore, the possibility of
a long-term economic slowdown due to lack of abating climate change
(Kovalevsky and Hasselmann, 2014) heightens the urgency of reducing
GHGs by investing in low-carbon technologies, such as electric cars,
biofuels, CO2 capturing and storing (CCS), renewable energy
sources (Rozenberg et al., 2014), and technology for growing crops
(Wise et al., 2009). Even if this incurs short-term economic costs,
the transformation to a de-carbonized economy is both feasible and
affordable according to Azur and Schneider (2002), Weber et al. (2005),
Stern (2007), Schneider (2008), and would, in the long term,
enhance the quality of life for all (Hasselmann, 2010). The great
flexibility and transparency of the CoCEB model has helped us
demonstrate that an increase in the abatement share of investments
yields a win-win situation: higher annual economic growth rates, on
average, of per capita GDP can go hand-in-hand with a decrease in GHG
emissions and, as a consequence, to a decrease in average global SATs
and the ensuing damages. These results hold when considering the
entire transition path from 1990 to 2100, as a whole.
Discussion
The CoCEB model builds upon previous work on coupled models of global
climate–economy interactions, starting from the pioneering work of
Nordhaus (1994a), as extended in Greiner (2004) by the inclusion of
endogenous growth. Greiner (2004) treated industrial CO2
emissions as constant over time, while excluding the particular case
of zero abatement activities (BAU); in fact, his model only applied
for a minimum level of abatement. The present paper takes into
account, more generally, emissions that depend on economic growth and
vary over time, while including the case of abatement equal to zero,
i.e. BAU. This was done by using logistic functions (Sahal, 1981;
Akaev, 2012) in formulating equations for the evolution of energy
intensity and carbon intensity of energy throughout the whole 21st
century (Akaev, 2012).
The CoCEB model, as developed in this paper, analyzes the carbon
policy problem in a single-region global model with the aim to
understand theoretically the dynamic effects of using the abatement
share as a climate change mitigation strategy. To be able to draw more
concrete, quantitative policy recommendations is it important to
account for regional disparities, an essential development left to
future research.
A finite-horizon optimal climate change control solution can be gotten
by assuming that the government takes per capita consumption and the
annual tax rate as given and sets abatement such that welfare is
maximized. As to welfare, one can assume that it is given by the
discounted stream of per capita utility times the number of
individuals over a finite time horizon. The Pontryagin Maximum
Principle (Pontryagin et al., 1964; Hestenes, 1966; Sethi and
Thompson, 2000) is used to find the necessary optimality conditions
for the finite-horizon control problem. The Maximum Principle
for infinite-horizon control problems is presented in Michel
(1982), Seierstadt and Sydsaeter (1987), Aseev and Kryazhimskiy (2004,
2007), and Maurer et al. (2013). For a modern theory of
infinite–horizon control problems the reader is referred to Lykina
et al. (2008). The determination of an optimal abatement path along
the lines above will be the object of future work.
Concerning the damage function, Stern (2007) states that “Most
existing IAMs also omit other potentially important factors – such as
social and political instability and cross-sector impacts. And they
have not yet incorporated the newest evidence on damaging warming
effects,” and he continues “A new generation of models is needed in
climate science, impact studies and economics with a stronger focus on
lives and livelihoods, including the risks of large-scale migration
and conflicts” (Stern, 2013). Nordhaus (2013) suggests, more
specifically, that the damage function needs to be reexamined
carefully and possibly reformulated in cases of higher warming or
catastrophic damages. In our CoCEB model, an increase in
climate-related damages has the effect of anticipating the crossover
time, starting from which the abatement-related costs start paying off
in terms of increased per capita GDP growth.
A major drawback of current IAMs is that they mainly focus on
mitigation in the energy sector. For example, the RICE (Regional
Dynamic Integrated model of Climate and the Economy) and DICE
(Nordhaus and Boyer, 2000) models consider emissions from
deforestation as exogenous. Nevertheless, GHG emissions from
deforestation and current terrestrial uptake are significant, so
including GHG mitigation in the biota sinks has to be considered
within IAMs. Several studies provide evidence that forest carbon
sequestration can help reduce atmospheric CO2 concentration
significantly and could be a cost-efficient way for curbing climate
change (e.g. Tavoni et al., 2007; Bosetti et al., 2011).
In Part 2 of this paper, we report on work along these lines, by
studying relevant economic aspects of deforestation control and carbon
sequestration in forests, as well as the widespread application of CCS
technologies as alternative policy measures for climate change
mitigation.
Finally, even though there are several truly coupled IAMs (e.g. Nordhaus
and Boyer, 1998; Ambrosi et al., 2003; Stern, 2007), these
IAMs disregard variability and represent both climate and the economy
as a succession of equilibrium states without endogenous
dynamics. This can be overcome by introducing business cycles into the
economic module (e.g. Akaev, 2007; Hallegatte et al., 2008) and by
taking them into account in considering the impact of both natural,
climate-related and purely economic shocks (Hallegatte and Ghil, 2008;
Groth et al., 2014).