Kyoto University,
Graduate School of Economics
Research Project Center Discussion Paper Series

Directed Technical Change, Unilateral Actions, andClimate Change

Hiroaki Sakamoto

Discussion Paper No. E-11-007

Research Project Center
Graduate School of Economics
Kyoto University
Yoshida-Hommachi, Sakyo-ku
Kyoto City, 606-8501, Japan

February 2012

Directed technical change, unilateral actions,and climate change
Hiroaki Sakamoto∗February 1, 2012
Abstract
In this paper, I investigate the implications of policy-induced technological change based on a multi-region variant of the directed technical change
model developed by Acemoglu et al. (2012). On top of the pollution externality accompanied by carbon dioxide emission, different regions are connected through a global market where energy-related machine producing
firms monopolistically compete with each other. One of the main findingsof the analysis is that unilaterally introduced climate policies in developed
regions might have only a slight short-term impact at a global level, butlater will turn out to be a basis for low-carbon development in developing
regions as well as developed regions. The simulation results indicate thatan extension of the Kyoto protocol, if appropriately designed, can trigger along-term shift in energy use at a global level even without active involvement of the United States. Moreover, if the United States decides to join
the treaty and a fairly moderate abatement target is agreed upon among themember states, the similar level of long-term environmental consequence
as in the universal climate regime can be replicated without explicit participation of developing regions.

Keywords: Climate change, directed technical change, unilateral policy, innovation, Kyoto protocol
JEL codes: O31, O33, Q54, Q55, Q58∗
Graduate School of Economics, Kyoto University. Yoshida-honmachi, Sakyo-ku, Kyoto,
606- 8501, Japan. Email: hsakamoto@eco.mbox.media.kyoto-u.ac.jp

1

1 Introduction
If a transition to a low-carbon economy is seriously pursued, technological change
should play a key role. It is hard to imagine how our economy, which is heavily dependent on fossil-fuel consumption, can transform itself into a basis forsustainable development without the help of technological innovation. Technological innovation is especially needed in the field of energy production andconsumption. Although an immediate and complete shift toward non-fossil fuelenergy is theoretically possible, such a drastic option would entail unacceptably
large cost to the society. Hence, any successful strategy to build a low-carbon
economy must be based on a sensible and careful understanding of what kind oftechnological options are currently available and in which direction the technology will develop in the future.
The critical role of technology, however, does not imply that climate policies
can play only a limited part in addressing the problem. It rather implies a potentially pivotal role of climate policies. While technological change is an essential
element in designing a reasonable climate policy, a well-designed climate policy
is crucial to technological change. As Popp (2005) points out, if environmental regulations reduce uncertainty surrounding the profitability of investment inenvironmentally friendly technologies, then sufficiently stringent environmental
policies may trigger the research and development activities, which in turn leadto technological innovation. This claim is in fact supported by several empiricalstudies (Jaffe and Palmer, 1997; Berman and Bui, 2001). In addition, as empirical evidence provided by Popp (2002) suggests, energy-saving innovations
might be induced by changes in energy prices. If this is the case, the introductionof a carbon tax on fossil fuel consumption would encourage innovation towards
greater energy efficiency.
Another important aspect of technological change in the context of climate
policy is the interplay between regions. Since globalization becomes more andmore intense, economies in different regions are becoming increasingly intertwined with each other. In such a highly globalized world, an introduction ofclimate policy in one region does not only affect the decision making of domestic firms, but also influence behavior of firms operating in a global market. It
then seems not very reasonable to assume the impact of technological change isrestricted within regional boundaries. We should rather allow for the possibility
that an endogenously induced technological innovation is transmitted from one
region to another through globally operating economic agents. This aspect ofpolicy-induced technological change is of great policy relevance since it might
imply that unilateral climate policy in a group of countries can encourage clean
technological innovation in countries outside the group.
Despite the intuitive appeal and the existing empirical evidence of policy-2

induced technological innovation, most economic models used for analyzing theinteraction between climate and economy take technological development as an
exogenous variable (Nordhaus, 1994; Nordhaus and Yang, 2007; Tol, 1999)．
Among a few exceptions is Popp (2004), who considered endogenous technological innovation in the energy sector. His model is based on the DICE modelof Nordhaus (1994), which is in essence an aggregated macroeconomic modelwith a simple climate system on top of the economic module. Another notable
exception is Grimaud et al. (2011), who also allowed for policy-induced technical change based on the ENTICE-BR model of Popp (2006).
In recent years, partly due to the growing recognition of critical role thattechnological change may play, the concept of “directed technical change” hasbeen attracting much attention in the literature of economic theory (Acemoglu,
2002). Unlike the standard modeling of technological development, the directed
technical change model explicitly describes the channel through which the direction of technical change, or which type of technology is developed, is endogenously determined. By applying the concept of directed technical change
to a simple climate-economy model, Acemoglu et al. (2012) show that technicalchange can be “redirected” from dirty to clean technologies by policy intervention. Their result indicates that only a relatively short period of stringent climate
policies can facilitate the switch from dirty innovation to cleaner ones. Whilethese existing studies provide interesting insights, their analysis is based on a
globally aggregated model, and hence fails to consider the role of the interplay
between heterogeneous regions.
In this paper, I therefore investigate the implications of policy induced technological change based on a decentralized multi-region climate economy model.
Following the approach of Acemoglu et al. (2012), I distinguish fossil-fuel andnon-fossil-fuel energy production processes and allow for the possibility that innovation occurs at a particular type of energy production process. On top of thepollution externality accompanied by carbon dioxide emission, different regions
are connected through a global market where energy-related machine producing
firms monopolistically compete with each other. This way, I explicitly model achannel through which unilateral climate policies can have a dynamic influence
beyond regional boundaries. In addition to theoretical analysis, I conduct a series of numerical simulations based on a calibrated model. Based on scenario
analysis with specific climate policy, I derive concrete policy implications forthe ongoing efforts in designing an effective international framework to combat
climate change.
The remainder of this paper is structured as follows. Section 2 presents themodel in detail. Based on the model described in section 2, section 3 analyticallycharacterizes the equilibrium. By specifying functional forms and calibrating
the entire model, section 4 examines more concrete policy implications based3

on numerical simulations. Section 5 concludes the paper.

2 The Model
I consider a stylized world consisting of J > 1 regions. Each region has its own
economy within which households and firms interact with each other througha competitive domestic market. Interaction among different regions exists in
two respects: climate damage and technological innovation. In line with theliterature on climate-economy modeling, I assume that each region locally emit
carbon dioxide as a byproduct of economic activities and thus contribute to theglobal atmospheric carbon concentration. The increased carbon concentration
then changes the dynamics of global mean temperature, which in turn causes
adverse climatic impacts across different regions. As another channel of interaction, I introduce an energy-related machine production sector where individual firms supply their machines in a global market. Following the literature on
endogenous technical change, I assume these firms are monopolistically competitive and their profits are the driving force behind technological innovations.
Since profits of these globally-operating firms naturally depend on energy demand of each region, policy interventions on regional energy sector affects thescale and the direction of technological development. In the following, I describe the model in detail.
Production
Each economy contains three production sectors: final output, final energy production, and primary energy production. Final output Yjt of region j at period t
is produced using capital Kjt , final energy input Xjt , and labor Ljt through theaggregate production function
α β 1−α−βYjt = ψjt Kjt
Xjt Ljt.

(2.1)

So the profit Πjt of the representative firm in the final output sector is given byΠjt = Yjt − (rjt + δ k )Kjt − pjt Xjt − wjt Ljt ,(2.2)

where rjt is the interest rate, δ k is the capital depreciation rate, pjt is the priceof energy input, and wjt is the wage of labor input. The price of final output isnormalized to unity.
The final energy input is supplied by the representative firm in the final
energy-producing sector according to the production functionϵ{ ϵ−1ϵ−1 } ϵ−1
ϵ
ϵ
,
(2.3)
Xjt = Xjct + Xjdt

4

where Xjct and Xjdt denote the primary energy input based on non-fossil fuel(or ‘clean’) and fossil fuel (or ‘dirty’) resource, respectively. The parameter ϵrepresents the elasticity of substitution between the two primary energy inputs.
The two inputs are substitutes when ϵ > 1 and complements when ϵ < 1. Since
non-fossil fuel inputs can usually substitute for fossil ones, I assume hereafter
ϵ > 1.
The main difference between the two primary energy inputs is that the ‘clean’energy can be produced without emitting carbon dioxide whereas the ‘dirty’ onenecessarily pollutes the climate. This fact is captured by assuming the level ofcarbon emission Ejt is determined by
Ejt = σjt Xjdt ,(2.4)

meaning that carbon emission only depends on the fossil-fuel-based energy input. If the level of carbon emission is to be controlled, governments can introduce a carbon tax τjt on the final energy producing firm. So the profit πjt of thefirm in energy-producing sector is given by
πjt = pjt Xjt − pjct Xjct − pjdt (1 + τjt )Xjdt ,(2.5)

where pjct and pjdt denote the price of non-fossil fuel and fossil fuel primaryenergy input, respectively.
The primary energy production sector consists of two representative firms:
one for ‘clean’ energy and the other for ‘dirty’ energy. For k ∈ {c, d}, thecorresponding primary energy input Xjkt is produced by using labor Ljkt and avariety of machines xjkt(i) supplied by a continuum of energy-related machine
production firms in a global market. Following Acemoglu et al. (2012), I specify
the production function by
∫ 1
γ
1−γ
A1−γ
(2.6)
Xjkt = Ljkt
jkt(i) xjkt(i) di,0

where Ajkt(i) represents the productivity of machine of type i ∈ [0, 1] used byfirm k in region j at time t. The profit of the firms in energy-technology sector
is thus given by∫ 1
πjkt = pjkt Xjkt − wjt Ljkt −pkt(i) xjkt(i) di,(2.7)
0

where pkt(i) is the price of machine of type i used by firm k at time t.
In addition to these domestic sectors, I assume there exists a global market
where a continuum of machine producing firms operates. As in Acemoglu et al.
(2012), I assume that, regardless of the quality of machines and of the sector for5which they are employed, producing one unit of any machine costs χ unit of a
final good. This means that the profit of firms in the machine-producing sector
is given by∑
πkt(i) = (pkt(i) − χ)xjkt(i) ,j

for k ∈ {c, d} and i ∈ [0, 1]. Notice here that pkt(i) is independent of j. This isbecause the machine producing firms operate in the global market, and thus theprice is equalized across regions.
Directed technical change
The innovation dynamics in productivity of the energy-related machine is governed by∫ 1
Ajkt+1 = [1 + gjkt (st )] Ajkt , where Ajkt =Ajkt(i) di(2.8)
0

for k ∈ {c, d}. Here, gjkt denotes the growth rate of Ajkt , which represents
the average productivity of machines used for producing energy input of typek. The growth rate depends on st , the fraction of ‘scientists’ or ‘entrepreneurs’
who engage in the clean-energy related sector. We assume ∂gjkt (st )/∂st > 0
for k = c and ∂gjkt (st )/∂st < 0 for k = d so that the more scientists engage ina sector, the more likely innovations are induced in the sector.
A key assumption here is that these scientists work in the global job market
or the global financial market if interpreted as entrepreneurs. In other words, st isintended to capture the global trend of energy-related research and development
activities. It thus seems natural to assume that this trend is influenced by the
relative profitability υt of clean energy industry,/∫ 1∫ 1
st = F (υt ), where υt =πct(i) diπdt(i) di,
(2.9)
0

0

for some distribution function F with support R+ . I assume F (1) = 0.5 so thatwhen υt = 1, or the two different energy industries are equally profitable, thesame number of scientists are allocated to each industry.
Households
I assume the utility of households depend on per capita consumption Cjt /Njt
and they behave so as to maximize the discounted sum of aggregate utilities
over time
)t−1
T (
∑
1
Njt log(Cjt /Njt )(2.10)
Wj =
1
+
ρ
t=1

6

subject to the budget constraints
θ
rjt Kjt + wjt Njt + πjt= Cjt + Kjt+1 − Kjt + Tjt ,(2.11)

andNjt = Ljt + Ljct + Ljdt ,where Tjt is the lump sum tax imposed by regional governments. The profitθgained by scientists is denoted as πjt, which is defined by
]
[∫ 1
∫ 1
∑
θ
θjt = 1,
(2.12)
πjt = θjt
πct(i) di +πdt(i) di , with00jwhere θjt is the share of the global stock of scientists living in region j at time
t. For simplicity, I assume θjt = 1/J, which means scientists are uniformly
distributed across regions and this does not change over time.
Climate, damage, and government
Climate system of this model is a simplified version of the DICE model of Nordhaus (1994). As in the standard climate-economy model, the global carbon concentration Mt evolves over time according to the dynamic function
Mt+1 = (1 − δ )Mt +
c

J
∑

Ejt ,

(2.13)

j=1

where δ c is the depreciation rate of carbon stock in the air. Global mean temperature Zt is then determined by
(
)
F×2
a
c log(Mt /M1750 )Zt+1 = Zt + ι Ft + F×2−
Zt ,(2.14)
log(2)
Z×2
where Fta is the (exogenous) radiative forcing from other greenhouse gasses.
Although this is much simpler than the original DICE model, I believe thisspecification can capture the essence of the climate-economy interaction withoutcausing unnecessary complexities in the analysis.
As in the DICE model, the monetary valuation Djt of climatic damage isdetermined by
Djt =

djt
Yjt
1 + djt

where djt = ξ1,j Zt + ξ2,j Zt2 .

(2.15)

I assume any damage caused by climate change is covered by governmental
spending, which can be financed by the lump sum taxation on households or7   % &    
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Figure 1: Model at a glance
the carbon tax on energy producing firms. Hence, the budget constraint of thegovernment is given by
Tjt + pjdt τjt Xjdt = Djt .

(2.16)

Notice that in the laissez-faire or business as usual scenario, where τjt = 0 for
all j and t, the adverse impacts of climate change are, in essence, directly borneby households.
Some aspects of our model is depicted in Figure 1. I define the equilibrium of
this economy by a set of variables which simultaneously solves a) firms’ profit
maximization problems in each sector, and b) households’ utility maximization
problems, given the behaviors of the other regions and a fixed policy variableτjt .

3 Theoretical predictions
In this section, I briefly characterize the equilibrium with an emphasis on some
important variables, although I do not go through technical details of each expression. Derivation of the equilibrium is relegated to Appendix A.1. The primary purpose of this section is to show that the model can provide a reasonable
description of the reality, and thus can be readily applied to the numerical analysis in the next section to derive more concrete implications.

83.1 Laissez-faire economy
The laissez-faire economy, which is defined as the equilibrium with τjt = 0,
is a useful baseline scenario since it describes how the economy evolves overtime without policy interventions. In particular, two aspects of the economy arehighlighted: energy structure and technological innovation. First, energy structure, by which I mean how non-fossil fuel and fossil fuel primary energies are
mixed to produce final energy, is important both in terms of environmental andeconomic variables. From an environmental point of view, it affects carbon intensiveness of the economy. As is clear from the production function (2.3) forfinal energy, various combinations of non-fossil fuel and fossil fuel primary energies are possible to produce a fixed level of final energy. Since carbon dioxide
is emitted from using fossil fuel primary energy, more use of non-fossil fuel primary energy should be encouraged if low-carbon development is to be achieved.
From an economic point of view, on the other hand, switching to ‘clean’ energy from ‘dirty’ one is not always desirable. This is primarily due to technological constraints. When the non-fossil fuel based energy production technology
is immature relative to the fossil fuel counterpart and it is thus relatively difficult to produce ‘clean’ energy, switching the primary energy sources in favor ofcleaner alternatives would be costly to the economy. In fact, at the laissez-faireequilibrium of this economy, the relative price of non-fossil fuel primary energy
is determined by
(
)1−γ
pjct
Ajdt
=
.
(3.1)
pjdt
Ajct
This means that non-fossil fuel energy is more expensive when fossil fuel based
technology is relatively more advanced (i.e., when Ajdt > Ajct ).
At the laissez-faire equilibrium, where the hidden price of carbon emission is
not internalized in individuals’ decision making, the choice of energy structureis almost entirely driven by the relative cost of each energy source. Hence, amore technologically advanced and thus less expensive primary energy source
is preferred. This point can be well illustrated by noting at the equilibrium, theenergy structure, which is essentially captured by the ratio Xjct /Xjdt , is given
by
(
)−ϵ (
)ϵ(1−γ)
Ajct
Xjct
pjct
=
.
(3.2)
=
Xjdt
pjdt
Ajdt
As a result, the fossil fuel energy input will continue to be used unless production
process of non-fossil fuel energy is technologically advanced and becomes lessexpensive in the future.
This brings us to the second important question: how is the direction of technological development determined? As explained in the preceding section, it is9

assumed to depend on the global trend of energy-related research and development, and such a trend is affected by the relative profitability of each primaryenergy industry. Where a relatively large profit is expected, intellectual and financial resources flow into and, as a consequence, technological innovations are
more likely to occur. This assumption is captured by (2.8) and (2.9) above.
A question of particular interest then is what the determinants of the relative
profitability are. This question can be readily investigated by looking at therelative profitability of non-fossil fuel energy industry at the equilibrium, whichis computed as∑
υt = ∑

11−γ
j Ljct pjct Ajct
11−γ

j Ljdt pjdt Ajdt

]
∑ [ φ
φ
φ
A
/(A
+
A
)
Yjt
jct
jct
jdt
j
] ,
=∑ [ φφφ
j Ajdt /(Ajct + Ajdt ) Yjt(3.3)

where φ := −(1 − γ)(1 − ϵ) > 0. Let us first examine the right-hand side of
the first equality. This expression tells us the relative profitability depends on
Ljkt , pjkt , and Ajkt . As Acemoglu et al. (2012) points out, each of the three determinants encourages (i) innovation in the sector with greater employment, andthus with the larger market for machines, (ii) innovation towards the sector withhigher prices, and (iii) innovation in the sector with higher productivity, which
results from what they call the ‘building-on-the-shoulders-of-giants’ effect.
Taking a look at the very right-hand side of the equation reveals another insight. This expression clearly shows that the relative profitability is in large part
determined by the relative productivity of each primary energy source. Hence,
this result also indicates that a positive feedback effect or ‘inertia’ in technological innovations exists. When energy-related technology of a particular type ismore advanced than the other, the corresponding energy industry would become
relatively more profitable, attracting more intellectual and financial resources
for research and development, and as a result, would enjoy further technologicaladvancement in the future. Put differently, a currently advanced energy-related
technology will be even more advanced in the future for the very reason that it iscurrently advanced. This is an alarming result in the context of climate change.
It basically implies that if the fossil-fuel-based technology is relatively more advanced than the cleaner alternatives, we are and will continue to be locked in thecurrent energy structure which produces a large amount of carbon dioxide.
Also worth noting here is that the direction of technological development
can be reversed by changing the relative productivity of non-fossil fuel energy
against fossil fuel energy, especially in regions with a large economy. As is clear
from (3.3), not only the relative productivity among different energy sources,
but also the relative size of economy across different regions (captured by theterm Yjt ) play a part. If, for instance, the relative productivity of non-fossil
fuel technology is significantly improved in large economies, then the global

10

trend of energy-related research and development could be redirected towardcleaner technologies even if the fossil-fuel-based technology is currently moreadvanced in smaller economies. Consequently, the productivity of ‘clean’ technology could outweigh that of ‘dirty’ technology in smaller economies as wellin the long run.

3.2 Temporary and dynamic impacts of policy interventions
Let us now turn to the case when governments introduce a carbon tax scheduleτjt > 0 in some regions. This policy intervention increases the effective priceof fossil fuel primary energy from pjdt to pjdt (1 + τjt ). So the energy structure,
determined by (3.2) in the laissez-faire equilibrium, is now rewritten as)−ϵ(()ϵ(1−γ)
Xjct
pjct
Ajct
ϵ
= (1 + τjt )
=
,
(3.4)
Xjdt
pjdt (1 + τjt )Ajdt
which is increasing in τjt . This means that a carbon tax can facilitate a shift
from fossil fuel to non-fossil fuel energy input for a given level of technologies.
Hence, introducing a carbon tax in a region is actually effective in changing
energy structure of the region in favor of climate. Yet, of course, this does notcome without cost. A bit tedious algebra shows that a marginal increase of τjt
from the laissez-fair equilibrium decreases the output Yjt of final good wheneverϵ > 2 − γ. As we will see in the numerical analysis below, ϵ is likely to be larger
than 2 in the case of energy production. Therefore, in the short run, switchingfrom fossil fuel to non-fossil fuel energy can be realized only at the expense of
economic benefit.
What is of greater interest, however, is the dynamic consequence of a carbon
tax. Once a carbon tax is imposed on firms in the final energy sector, they replace a part of their demand for fossil fuel primary energy input with a non-fossil
fuel alternative, which in turn affects the profit of globally-operating machineproducing firms in each energy industry. Such a change in the relative profitability of different energy industries then redirects intellectual and financial
resources from one industry to the other, resulting in a dynamic shift of growth
paths of energy-related technologies.
This can be formally shown by observing that the relative profitability ofclean energy industry is now given by
]
∑ [ φ
φ
φ
1−ϵ
) Yjt
j Ajct /(Ajct + Ajdt (1 + τjt )] .
υt = ∑ [ φ(3.5)−ϵ /(Aφ + Aφ (1 + τ )1−ϵ ) Y
A
(1
+
τ
)
jt
jt
jt
jct
jdt
jdt
j
Again, this is increasing in τjt , meaning that the introduction of a carbon tax
changes the relative profitability in favor of non-fossil fuel energy. Hence, climate policy of this kind could help non-fossil fuel energy industry attract more11

resources for research and development. An immediate consequence of this isthat technologies relating to cleaner energy production will be more advanced in
the subsequent periods than they would be in the absence of a carbon tax. The
improved productivity of non-fossil-fuel-based technologies then pushes down
the cost of producing cleaner energy, making it more competitive in the market.
A less obvious, but perhaps more important role of the carbon tax is that it
could even reverse the inertia in technological innovation mentioned above. We
have already seen that innovation is more likely to occur in the relatively advanced type of energy. This finding is, on one hand, worrying. If the technology
of fossil fuel energy production is already more advanced, the non-fossil fuel energy industry will have no chance of catching up with the fossil fuel counterpart.
On the other hand, this same fact could be rather encouraging. If the carbon tax
is imposed at a sufficiently high rate and for a sufficiently long period, up to thepoint where the growth paths of technologies are entirely redirected, switchingfrom fossil fuel to non-fossil fuel energy will be autonomous thereafter. Taking into account this dynamic effect of the carbon tax, it might be stated that a
temporal climate policy, if appropriately designed and implemented, would be
sufficient to address climate change.
The significance of this observation can be highlighted if we notice that the
introduction of a carbon tax only in a limited number of regions can trigger theredirection of technological development at a global level. In particular, the expression (3.5) tells us that the dynamic effect of the carbon tax on the directionof technological development is larger in regions with larger output. This implies that developed regions, which usually have larger output, play a relatively
larger role in determining which type of energy-related technology is advanced
at a global level. In other words, unilateral climate policies in developed regions could trigger a shift in energy use in developing regions and thus facilitate
their low-carbon development in the future. This theoretical prediction will be
examined in the following section by using a numerically calibrated model.

4 Numerical simulations
In order to derive more concrete policy implications, this section provides theresults of numerical simulations based on the model described above.

4.1 Calibration and policy scenarios
The model is calibrated in such a way that the equilibrium path of the laissezfaire economy matches a version of the IPCC A2 scenario provided by Riahi
et al. (2007). Following their regional specification, I divide the world into12

eleven different regions: Western Europe (WEU), Pacific OECD (PAO), Former Soviet Union (FSU), Eastern Europe (EEU), North America (NAM), China
and centrally planned Asia (CPA), South Asia (SOA), Other Pacific and Asia
(OPA), Latin America and the Caribbean (LAM), Middle East and North Africa(MEA), and Sub-Saharan Africa (AFR). The precise definition of these regions
is presented in Table 2 of Appendix A.2. While each is treated as a separate
economic unit throughout the simulations, we sometimes aggregate the last five
regions into one region as the “rest of the world” or ROW, just for an illustrative
purpose.
To calibrate the dynamics of technological development, I specify the functional forms of F , gjct , and gjdt as
F (υt ) = 1 −1,
1 + υt−η

(4.1)

and
gjct (st ) = ḡjct + δca st ,gjdt (st ) = ḡjdt + δda (1 − st ),(4.2)

respectively. In (4.1), the parameter η can be interpreted as an index of adjustment cost for scientists to switch from fossil fuel to non-fossil fuel energy
industry. A smaller value of η, for example, means that scientists can easily
switch industries depending on the relative profitability. The benchmark valueof this parameter is η = 0.5. Given the current level of fossil fuel and non-fossil
fuel primary energy consumption, this assumption implies that about 10% of
scientists are currently engaging in cleaner energy industry while the rest are
all in fossil-fuel-based energy industry. Following Acemoglu et al. (2012), we
assume δca = δda = 0.02 (annual value). The exogenous trend of energy-related
technological innovation which cannot be explained by changes in st is capturedby the parameters ḡjkt ’s.
Every other parameter value is pinned down from estimations and projections provided by Riahi et al. (2007) and Nordhaus and Boyer (2000). Amongthe most important parameters is ϵ, the elasticity of substitution between fossil
fuel and non-fossil fuel primary energies. I choose the value of this parametersuch that the difference between simulated and projected values of final energy is
minimized. The calibrated value is ϵ = 8.81. This means that, just as expected,
fossil fuel and non-fossil fuel primary energy sources are highly substitutable.
As shown in Figure 2, carbon dioxide emission under the laissez-faire scenario grows very rapidly. This is a consequence of our calibration. The emission
level is the same as in the IPCC A2 scenario, which assumes relatively large carbon emissions. In 2010, the largest contributor to the global carbon emission
is NAM, which includes the United States and Canada. The WEU and PAO
regions, which contain the rest of the developed countries, also account for a13  !!""#$! %"&    

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Figure 2: CO2 emission and concentration in the baseline scenario (laissez-faire)
relatively large share of the total emission. Over time, however, the share of
the developed regions declines and a larger part of the global carbon dioxide
emission comes from developing regions. This predicted trend emphasizes thenecessity of building a low-carbon economy, especially in developing countries.
The level of carbon concentration rises from 810 GtC (or 380 ppm) in 2010 to2888 GtC (or 1356 ppm) in 2150. This results in an increase of global mean
temperature by 5.5o C relative to the level of 2010.
Taking the laissez-faire equilibrium as a baseline scenario, I consider six
other scenarios with different assumptions on policy interventions. These scenarios are listed in Table 1. The first scenario is the Kyoto-low scenario. Under
this scenario, a group of developed regions (WEU and PAO) introduces a common carbon tax scheme for a predetermined period of time (from 2015 to 2025).
The common tax scheme in these like-minded regions is designed in such a waythat the price of fossil-fuel based energy increases by 4%. This tax rate is moreor less comparable to 35 US$ per tonne of carbon dioxide in these regions. In
the light of the ongoing negotiation process of international climate treaties, it
can be said that the assumption of this scenario corresponds to a weak extensionof the Kyoto protocol. Neither the largest polluter among developed regions(namely, USA) or the rapidly growing developing regions (China in particular)
joins the framework of international coordination. WEU and PAO take unilateral
actions against climate change.
The second scenario, named Kyoto-high, assumes the same type of policy
intervention within the same group of regions, but to a stronger extent. A higher

14scenarios

policy intervention assumed in the scenario

Laissez-faire
Kyoto-low

No policy intervention assumed in any region
A low rate of carbon tax (4% increase in the price of fossilfuel primary energy) is introduced in the WEU and PAO regions from 2015 to 2025
Kyoto-high
A high rate of carbon tax (6% increase in the price of fossilfuel primary energy) is introduced in the WEU and PAO regions from 2015 to 2025
KyotoUS-low A low rate of carbon tax is introduced in the WEU, PAO, andNAM regions from 2015 to 2025
KyotoUS-high A high rate of carbon tax is introduced in the WEU, PAO, andNAM regions from 2015 to 2025
Global-low
A low rate of carbon tax is introduced in every region from2015 to 2025
Global-high A high rate of carbon tax is introduced in every region from2015 to 2025

Table 1: Specification of policy scenarios
rate of carbon tax is introduced in WEU and PAO, which increases the priceof fossil-fuel primary energy by 6%. This corresponds to around 50 US$ per
tonne of carbon dioxide emission from fossil-fuel consumption. This scenario
is intended to describe the situation in which the Kyoto protocol is extended by
the like-minded countries with more ambitious abatement targets.
The third and fourth scenarios are labeled as KyotoUS-low and KyotoUShigh, respectively. These scenarios assumes an extension of the Kyoto protocol
with the United States joining back to the treaty. To be more precise, in bothscenarios, the NAM region as well as WEU and PAO introduce a carbon tax
scheme. As in the Kyoto scenarios, 10 years of policy intervention is assumed
from 2015. The two KyotoUS scenarios are only different in terms of the carbon
tax rate. The former assumes a lower rate which causes 4% rise in the fossil-fuelenergy price while the latter assumes a higher rate with 6% price hike in thefossil-fuel energy. These scenarios are relatively more optimistic than the first
two. Yet participation of developing countries is still missing.
The last two scenarios, Global-low and Global-high, assume effective involvement of developing regions. In these scenarios, the carbon-tax regime isexpanded to cover all the regions, including China and other developing countries. The tax scheme is designed in exactly the same way as in the first four scenarios; Global-low and Global-high assumes 4% and 6% increase in the fossilfuel energy price, respectively. Notice that since the primary energy price ischeaper in developing regions, 4% price increase in the fossil-fuel energy leads

15

to around 10 to 15 US$ per tonne of carbon dioxide in developing regions. For
the same reason, 6% price increase in the fossil-fuel energy in developing regions leads to 15 to 24 US$ per tonne of carbon dioxide. Obviously, a universal
participation of this kind is not likely to materialize in the near future. But thesescenarios provide a useful benchmark against which other policy scenarios canbe evaluated.

4.2 Results
I have discussed in the preceding section that the most direct impact of policy
interventions can be found in the relative size of non-fossil fuel energy consumption, Xjct /Xjdt . This index plays a key role in addressing climate change since
it controls how much carbon dioxide Ejt is emitted from final energy consumption. Table 3 and 4 summarize the results of these variables in seven different
scenarios for selected regions. Table 3 shows that under the laissez-faire scenario, non-fossil-fuel based primary energy is not utilized much in all regions.
The share of non-fossil fuel energy gradually increases over time, especially in
WEU. Even in the WEU region, however, non-fossil fuel energy consumption
does not catch up with fossil fuel energy until 2060. In NAM and CPA, fossil
fuel will continue to be a dominant source of primary energy even in 2060. Consequently, a sharp increase of carbon dioxide emission can be seen over the next
fifty years, especially in NAM and CPA. This is depicted in Table 4.
## Tables 3 and 4 are around here ##Once a carbon tax scheme is introduced in a region, primary energy use in theregion experiences a temporary shift in favor of non-fossil fuel energy sources.
In WEU, for instance, introduction of a low rate of carbon tax increases the ratio
Xjct /Xjdt from 0.36 to 0.53 in 2020 under the Kyoto-low scenario. A higher tax
rate introduced under the Kyoto-high scenario pushes the same index further up
to 0.64. As a result, carbon dioxide emission in WEU declines by 14% relative
to the laissez-faire scenario in the case of the low tax rate. The reduction rate is
21% if the higher rate of carbon tax is imposed. The carbon tax scheme works
in the same way in other regions as well. In the KyotoUS-low and KyotoUShigh scenarios, both of which assume a successful return of the United States tothe Kyoto protocol, immediate shifts toward more use of cleaner primary energy
are seen in NAM in 2020, resulting in 11% and 17% reduction in the regional
carbon dioxide emission, respectively. If developing regions join the carbon
tax regime, as assumed under the Global-low and Global-high scenarios, carbon
dioxide emission in CPA, which primarily consists of China, is reduced by 15%
in the case of the low tax rate and by 22% in the case of the high tax rate right16

after the introduction of the carbon tax. These results are just as expected fromthe theoretical analysis above.
It should be noticed here that as far as the short-term impact is concerned,
a carbon tax has almost no influence on the carbon emission from the regions
outside the regime. In 2020, under the Kyoto scenarios, energy structure andcarbon emission of NAM and CPA remain almost the same as in the laissez-faire
scenario Hence, a unilateral carbon tax is not effective outside the tax regime,
at least in the short run. Also worth noting is that the impacts generated by
the introduction of the carbon tax significantly weaken after the tax is lifted in
2025. This is particularly the case in the Kyoto-low scenario. Table 4 showsthat in 2030, right after policy intervention ceases, carbon dioxide emission in
the WEU region regains the momentum and the emission level bounces backtoward the level of the laissez-faire scenario. This ‘rebound effect’ is more orless true for the other scenarios as well. Therefore, at first glance, a temporary
carbon tax seems to just make a short-lived push toward a low-carbon economy
only in the regions within the cooperative regime.
In the long run, however, a carbon tax makes a striking difference eventhough the policy intervention itself is only temporary. Under the Kyoto scenarios, for example, the energy structure of WEU continuously shifts toward
more use of clean energy even after the carbon tax is lifted, and the difference
from the laissez-faire scenario becomes wider and wider as time goes by. This
long-term consequence of a temporary carbon tax is more clearly highlighted
if a higher tax rate is chosen and when a larger number of regions join the tax
regime during the period of policy intervention. In the KyotoUS-high scenario,
the share of non-fossil fuel in the total primary energy consumption reaches 94%(since Xjct /Xjdt = 15.64) in WEU in 2060 compared with 53% in the laissezfaire equilibrium. This remarkable shift in energy use is accompanied by an 85%
reduction of regional carbon dioxide emission relative to the laissez-faire. The
Global-low scenario has a slightly weaker, yet reasonably comparable long-term
consequence.
The results indicate that seemingly small impacts of a carbon tax turn out tobe very huge in the long run. This is primarily due to the dynamic impact ofcarbon tax discussed in the previous section. When a carbon tax is introduced ina region, the final energy sector of the region shifts the demand for primary energy from fossil fuel to non-fossil fuel sources. This means that regional demand
for those machines required to produce fossil-fuel primary energy is temporarily suppressed, which in turn decreases the profit of machine-producing firms
in the fossil-fuel industry at a global level. On the flip side, relative profitability of machine-producing firms in non-fossil fuel industry temporarily surges,
encouraging scientists or entrepreneurs to redirect their intellectual and financial resource from fossil fuel to non-fossil fuel industry. In this model, this

17

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Figure 3: Fraction of scientists engaging in clean industry
phenomenon is nicely captured by the expression (3.5) and is numerically wellconfirmed in the simulations.
Figure 3 illustrates the dynamic impact of carbon tax on the direction oftechnological development. According to the calibration results, the fraction ofscientists engaging in clean energy industry only gradually changes over timein the laissez-faire scenario, rising from 10% in 2010 to 44% in 2100. Put differently, scientists in the energy industry hesitantly migrate from fossil fuel tonon-fossil fuel sector. This is reasonable since without policy intervention, profit
of machine-producing firms in clean energy industry is and will continue to besmaller than the firms in the fossil-fuel industry. When a carbon tax is introduced
in some regions, the global market for fossil-fuel energy production shrinks, tilting up the relative profitability of the clean energy industry, and thus prompting
an earlier migration of scientists to the non-fossil energy sector. As a result,innovation in clean-energy related technologies becomes more likely to occur
than in the laissez-fare scenario. In other words, direction of technological development in energy industry is changed in favor of clean energy. As is clear
from the figure, how much the technological development is redirected depends
on the magnitude of the carbon tax imposed and on how many regions join the
tax regime.
Also clear from the figure is that the ‘gold-rush effect’ in the clean energy
sector during the period of policy intervention fades away after the carbon tax
is lifted. Yet those scientists who migrate to the clean energy industry do notcompletely go back to the fossil fuel energy industry. Moreover, unlike thelaissez-faire scenario, scientists switch from the fossil fuel to the non-fossil fuelenergy sector at an accelerating pace after 2025. This is due to the positive feedback nature of technological innovation. The gold rush brings about significant

18changes in the determinants of relative profitability mentioned above. The market for clean energy expands during the period of intervention, and the shoulderof the giants becomes higher thanks to the temporary surge of innovation inclean energy sector. Since those changes do not disappear even after the endof the policy intervention, relative profitability of clean energy industry remains
relatively higher than the laissez-faire scenario even after 2025. Although small
in the beginning, this change provides a basis for the positive feedback effect ofclean innovation in the subsequent periods.
Another important point to note is that the dynamic impact of a carbon tax
stretches beyond the boundary of the tax regime. In fact, it can be seen from
Table 3 and 4 that the regions outside the regime are, in the long run, affectedby a unilateral policy intervention. In the Kyoto scenarios, where a carbon tax is
introduced only in WEU and PAO, the policy intervention at first does not affectenergy structure nor carbon emission in NAM and CPA. But the dynamic impact
gradually kicks in, not only to WEU, but also to NAM and CPA, changing theenergy structure and reducing carbon emission in those regions. This result indicates that unilateral actions, if appropriately designed, do play a positive role in
reducing global carbon emission in the long run although they seem to make little difference at first. If, for example, the United States come back to the Kyoto
protocol and all the members to the treaty agree on a stricter abatement target
as assumed in the KyotoUS-high scenario, that kind of agreement can significantly reduce carbon dioxide emission at a global level even without effective
participation of developing countries.
Having said that, burden sharing among regions is a matter of great concern
both form normative and practical point of views. Although detailed discussion
about the burden sharing is beyond the scope of this paper, we can still ask
ourselves how different the distributional consequence would be under different
scenarios. To investigate this point, I take the Global-low and KyotoUS-highscenarios, and compare them in terms of final output in each region. These two
scenarios assume different policy intervention and different members of the tax
regime, but result in a similar long-term consequence. Global mean temperature
under these scenarios gradually rises over time up until the year 2100, then bends
downward as carbon concentration is reduced, peaking at around 2.1o C relative
to the level of 2010. Then the question of interest is, if this environmental benefit
is to be achieved, how the burden is shared across regions in each scenario.
Figure 4 summarizes the result. Each panel of the figure shows the percentage change in final output in five aggregated regions under the Global-low andKyotoUS-low scenarios, respectively, relative to the level of the laissez-faire scenario. The first point to observe is that the cost of policy intervention continues
to be felt until around 2060, followed by a sequence of growing benefits thereafter. This is another consequence of the dynamic impact of the carbon tax. As

19

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Figure 4: Final good output in Global-low (left panel) and KyotoUS-high (rightpanel) scenarios relative to the laissez-fare (percentage)
discussed above, the introduction of a carbon tax redirects the resource flow fromfossil to non-fossil fuel energy production. This means that the fossil fuel primary energy sector, which at least in the short run can produce final energy in amore efficient way, enjoys a smaller amount of intellectual and financial resource
than it would in the case of laissez-fare. As a result, economies suffer from a
relatively less efficient energy production process until the clean energy sector
becomes sufficiently productive and, more importantly, until the corresponding
climate benefits materialize to make up for the loss. This phenomenon takes
place at a global level. This is why the long-term burden of policy intervention
is felt by the regions outside the regime as well. Thus, in the long run, impactsof policy intervention on the final output growth are almost the same under thetwo scenarios. What is noticeably different is its short-term impact, especiallyduring the period of policy intervention. In the Global-low scenario, the shortterm cost of policy intervention is evenly shared by all regions while the burden
is relatively more concentrated on WEU, PAO, and NAM in the KyotoUS-highscenario.
From the perspective of policy design, it will be also of interest to policy
makers if we could evaluate the impact of longer commitment periods. The
benchmark simulations assume for all policy scenarios the same commitment
period of 10 years, which might seem a bit short. Henc, I have also conductedsimulations with a longer period (20 years, from 2015 to 2035) of policy intervention as a variant for each scenario. Another question of practical importance concerns the timing of policy intervention. Considering the fact that political feasibility of any effective multilateral agreement is questionable under thecurrent circumstance, we could not deny the possibility that the ongoing international negotiation might end up with delayed policy intervention. With this

20

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Figure 5: Temperature changes for different duration and timings of policy intervention
political conundrum of climate negotiation in mind, two extra simulations havebeen conducted with different timings of policy intervention; one starting from2025, and the other initiated at 2035.
The results of these extra simulations are well summarized in Figure 5. The
top left panel of the figure shows the benchmark result, which assumes 10 yearsof policy intervention starting from 2015. The top right panel presents the consequence of longer period of policy intervention. As shown in the figure, thetemperature increase would be better controlled if carbon tax can be introduced
for a longer period of time. For each scenario, the peak of the temperature curveis pushed down by about 0.4o C on average. Delays of policy intervention, on
the other hand, naturally push up the peak of the temperature curves. The bottom panels of the figure show that the temperature reaches its peak at 0.2o C
higher level than in the benchmark result if the effective intervention is delayedby 10 years. The difference from the benchmark will be 0.6o C if the effective
intervention is delayed by 20 years. Although these results are in line with theconventional wisdom about climate policy, this extra experiment provides anadditional insight with respect to its concrete consequence.

21

5 Conclusions
The relationship between policy intervention and technological innovation has
long been discussed in the context of climate change. In particular, it is often argued that such a policy intervention as carbon tax promotes research anddevelopment activities in non-fossil fuel energy sectors, and thus encourages
innovation in cleaner energy production technologies. While this line of argument captures some important aspects of reality, policy-induced technologicalinnovations have not been treated in a satisfactory way, especially in the literature of climate-economy modeling. In most of the existing studies, both extent and direction of technological development are exogenously given or are
endogenously determined only at a highly aggregated level. A more satisfactory approach requires a decentralized model which explicitly describes decision
making process of individual agents as a driving force behind the endogenous
innovation.
Another missing piece in the literature lies in the interaction among different
regions. Despite the widely recognized nature of climate change as a global public good, research on the endogenous technological development has often been
conducted based on a globally aggregated model, and hence fails to consider therole of interplay between heterogeneous regions. Moreover, as globalization intensifies, economies in different regions are becoming increasingly intertwinedwith each other. Given such a globalized world, introduction of climate policyin one region does not only affect the decision making of domestic firms, butalso influences behavior of firms operating in a global market or entrepreneurs
working all around the world. It then seems reasonable to ask ourselves how an
endogenously induced technological innovation is transmitted from one region
to another via globally operating economic agents.
In this paper, I therefore have investigated the implications of policy-induced
technological innovation based on a decentralized multi-region climate-economy
model. I distinguished fossil-fuel and non-fossil-fuel energy production and described the process in which innovation occurs at a particular type of energy
production process. Hence, unlike the conventional treatment of technologicaldevelopment, direction of innovation was endogenously determined. In addition
to the standard pollution externality accompanied by carbon dioxide emission,different regions are connected through a global market where energy-related
machine producing firms monopolistically compete with each other. This way, I
explicitly modeled a channel through which unilateral climate policies can havea dynamic influence beyond regional boundaries. Taking into account these newfeatures in a full-blown climate-economy model, the theoretical and numericalanalysis together provide some novel insights.
One of the main findings of the analysis is that unilateral climate policies can22

have a significantly large impact at a global level. As far as the short-term consequence is concerned, the introduction of a carbon tax in a region does not affectcarbon dioxide emission in other regions. It only encourages a temporary change
in local energy use and reduces the corresponding amount of carbon emission
in the region. In the long run, however, the locally implemented carbon tax cancause a dynamic shift in favor of non-fossil fuel energy at a global scale. It isshown by theoretical analysis that this dynamic and global impact of carbon tax
can be particularly large when such a climate policy is implemented in a region
with large output. This indicates that unilaterally introduced climate policies indeveloped regions might have only a slight short-term impact at a global level,
but later will turn out to be a basis for low-carbon development in developing
regions as well as developed regions.
This theoretical prediction is well confirmed by numerical simulations. The
simulation results essentially indicate that an extension of the Kyoto protocol,
if appropriately designed, can trigger a long-term shift in energy use at a global
level even without active involvement of the United States. Moreover, if theUnited States decides to join the treaty and a fairly moderate abatement target isagreed upon among the member states, the similar level of long-term environmental consequence as in the universal climate regime can be replicated without
explicit participation of developing regions. Although disputes surrounding theburden sharing among regions remain unsolved, the controversy might be lessintense than commonly expected. What is implied by the simulation analysis isthat the abatement cost is only differentiated during the period of policy intervention and the policy intervention is necessary only for a decade or so. Nevertheless, this result is conditional on the feasibility of a sufficiently stringent
carbon tax scheme or some other comparable climate policies implemented at
the right timing.

References
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Acemoglu, D., P. Aghion, L. Bursztyn, and D. Hemous (2012), “The environment and directed technical change,” American Economic Review, forthcoming.
Berman, E. and L. T. M. Bui (2001), “Environmental regulation and productivity: evidence from oil refineries,” Review of Economics and Statistics, 83(3),pp. 498―–510.

23

Grimaud, A., G. Lafforgue, and B. Magné (2011), “Climate change mitigation
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24

A AppendicesA.1 Solving for the equilibrium
The first-order conditions of the profit maximization in the final output sector
imply
αYjt /Kjt = (rjt + δ),(A.1)
βYjt /Xjt = pjt ,(A.2)(1 − α − β)Yjt /Ljt = wjt .

(A.3)

The first-order conditions of the profit maximization in the final energy sector
are given by]{[(ϵ−1)/ϵ
Xjkt
pjct
k=c
1
pjt Xjt=(A.4)(ϵ−1)/ϵ(ϵ−1)/ϵ X
pjdt (1 + τjt ) k = djkt
Xjkt+ Xjdtwhich imply
1−ϵ
1−ϵ
p1−ϵ
.
jt = pjct + [pjdt (1 + τjt )](A.5)

The first-order conditions of the profit maximization in the primary energy sector
imply(1 − γ)pjkt Xjkt /Ljkt = wjt ,
(A.6)
1−γ
γ
γpjkt L1−γ
jkt Ajkt(i) xjkt(i) /xjkt(i) = pkt(i) ,(A.7)

for k ∈ {c, d}. The first-order conditions of the profit maximization in themachine-producing sector imply)∑(∑ ∂xjkt(i) pkt(i)∂xjkt(i) pkt(i)pkt(i)
1+xjkt(i) = χxjkt(i) , (A.8)
∂p
x
∂p
x
kt(i)
jkt(i)kt(i)jkt(i)jj
where xjkt(i) is the inverse demand function defined by (A.7).
Note that (A.1), (A.2), and (A.3) imply
1 − α − β pjt Xjt= wjt ,
βLjt
Also, (A.4) imply
Xjct
=
Xjdt

(

α pjt Xjt
= rjt + δ.
β Kjt

pjct
pjdt (1 + τjt )

(A.9)

)−ϵ
,

(A.10)and thus (A.6) implies
Ljct
pjct Xjct==
Ljdt
pjdt Xjdt

(

25

pjct
pjdt

)1−ϵ
(1 + τjt )ϵ .

(A.11)

Note (A.7) and (A.8) imply pkt(i) = χ/γ. Hence,[]1/(1−γ)xjkt(i) = Ljkt Ajkt(i) (γ 2 /χ)pjkt,(A.12)

which, together with (A.6), implies[∫ 1]1/γ []1/γ(1 − γ)pjkt
1−γγ
Ljkt =
Ajkt(i) xjkt(i) di
wjt
0
1/γ

1/γ(1−γ)= Ljkt Ajkt (γ 2 /χ)1/(1−γ) (1 − γ)1/γ pjkt
or
pjkt =

pjct
=
pjdt

(

which in turn implies()ϵ(1−γ)Xjct
Ajct=(1 + τjt )ϵ ,
Xjdt
Ajdt
Xjkt
=
Xjt

{

−1/γ

wjt

,

(χ/γ 2 )γ−(1−γ) 1−γ
Awjt ,(1 − γ)(1−γ) jkt

for k ∈ {c, d}. This means

Therefore,(A.13)Ajdt
Ajct(A.14)(A.15)

)1−γ

Ljct
=
Ljdt

,
(

(A.16)Ajct
Ajdt(Ajct /Ajt )ϵ(1−γ)(Ajdt /Ajt )ϵ(1−γ) (1 + τjt )−ϵ)φ(1 + τjt )ϵ .

(A.17)

k=c
k=d(A.18)

where Ajt := [Aφjct + Aφjdt (1 + τjt )1−ϵ ]1/φ and
Aφjct
Ljct
= φ
.
Ljct + Ljdt
Ajct + Aφjdt (1 + τjt )−ϵAlso observe that (A.5) and (A.16) imply
(
)γ−1
pjkt
Ajkt
=
,
pjt
Ajt

(A.19)(A.20)and hence, noting that (Ljt + Ljct )/Njt = 1 − Ljdt /Njt , (A.2), (A.3) and (A.6)
then imply)(
pjct Xjct + pjdt Xjdt
1 − α − β 1 − Ljt /Njt=β(1 − γ)
Ljt /Njt
pjt XjtφAjct + Aφjdt (1 + τjt )−ϵ= φ.
(A.21)
Ajct + Aφjdt (1 + τjt )1−ϵ
|
{z
}
=:Ωjt

26

meaning that1Njt ,1 + ζΩjt

Ljt =Ljct + Ljdt =

ζΩjt
Njt ,
1 + ζΩjt(A.22)

where ζ := β(1 − γ)/(1 − α − β). On the other hand, (A.12) implies
γ

γ

1−γ
Xjkt = (γ 2 /χ) 1−γ Ljkt Ajkt pjktγ

= (γ 2 /χ) 1−γ

Ajkt
Ljkt
Ljct + Ljdt Ajt

(

pjkt
pjt

(A.23)γ) 1−γ

γ(Ljct + Ljdt )Ajt pjt1−γ . (A.24)

Hence,(
Xjt = Xjct

Ajct
Ajt

ϵφ
) 1−ϵ

γ
( 2 ) 1−γγζγ=
Njt Ajt pjt1−γ .
χ
1 + ζΩjt

Then (A.9) and (A.1) implies−γ (( 2 ) 1−γ
)−1
1
γ
Yjt
ζ
1−γ
pjt = β,χ
1 + ζΩjt
Njt Ajt
and thus( 2 )γ (
)1−γ
γ β
ζ
γ
Xjt =
Njt1−γ A1−γ
jt Yjt .
χ
1 + ζΩjt(A.25)(A.26)(A.27)

Thereforeα1−α−βγβ∗
Yjt = ψjt
Kjt1−βγ Njt 1−βγ [Aφjct + Aφjdt (1 + τjt )1−ϵ ] (1−βγ)(ϵ−1) ,

where

1

βγ

β−βγ

1−α−βγ∗ψjt:= ψjt1−βγ (βγ 2 /χ) 1−βγ ζ 1−βγ (1 + ζΩjt )− 1−βγ .

Finally, observe∫ 11() 1 1−γxjkt(i) di = γ 2 /χ 1−γ pjkt
Ljkt Ajkt
0{(βγ 2 /χ) Yjt (Ajct /Ajt )φ=(βγ 2 /χ) Yjt (Ajdt /Ajt )φ (1 + τjt )−ϵand hence
υt =

∫ 1∑
0

(χ/γ − χ)xjct(i) di

/∫ 1∑
0

j

=∑ [
j

k=c
k=d

(A.29)(A.30)(χ/γ − χ)xjdt(i) di

j

]
∑ [ φ
φ
φ
1−ϵ
) Yjt
j Ajct /(Ajct + Ajdt (1 + τjt )] .
Aφjdt (1 + τjt )−ϵ /(Aφjct + Aφjdt (1 + τjt )1−ϵ ) Yjt

27(A.28)(A.31)

A.2 Regional specification
Abbr.

Regional specification

NAM North America: Canada, Guam, Puerto Rico, United States of America, Virgin
Islands
WEU Western Europe: Andorra, Austria, Azores, Belgium, Canary Islands, Channel
Islands, Cyprus, Denmark, Faroe Islands, Finland, France, Germany, Gibraltar,
Greece, Greenland, Iceland, Ireland, Isle of Man, Italy, Liechtenstein, Luxembourg, Madeira, Malta, Monaco, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, Turkey, United Kingdom
PAO Pacific OECD: Australia, Japan, New Zealand
FSU Former Soviet Union: Armenia, Azerbaijan, Belarus, Estonia, Georgia, Kazakhstan, Kyrgyzstan, Latvia, Lithuania, Republic of Moldova, Russian Federation, Tajikistan, Turkmenistan, Ukraine, Uzbekistan
EEU Eastern Europe: Albania, Bosnia and Herzegovina, Bulgaria, Croatia, Czech
Republic, The former Yugoslav Rep. of Macedonia, Hungary, Poland, Romania,
Slovak Republic, Slovenia, Yugoslavia
LAM Latin America and the Caribbean: Antigua and Barbuda, Argentina, Bahamas, Barbados, Belize, Bermuda, Bolivia, Brazil, Chile, Colombia, Costa
Rica, Cuba, Dominica, Dominican Republic, Ecuador, El Salvador, French
Guyana, Grenada, Guadeloupe, Guatemala, Guyana, Haiti, Honduras, Jamaica,
Martinique, Mexico, Netherlands Antilles, Nicaragua, Panama, Paraguay, Peru,
Saint Kitts and Nevis, Santa Lucia, Saint Vincent and the Grenadines, Suriname,
Trinidad and Tobago, Uruguay, Venezuela
MEA Middle East and North Africa: Algeria, Bahrain, Egypt, Iraq, Iran, Israel,
Jordan, Kuwait, Lebanon, Libya/SPLAJ, Morocco, Oman, Qatar, Saudi Arabia,
Sudan, Syria, Tunisia, United Arab Emirates, Yemen
AFR Sub-Saharan Africa: Angola, Benin, Botswana, British Indian Ocean Territory, Burkina Faso, Burundi, Cameroon, Cape Verde, Central African Republic, Chad, Comoros, Cote d’Ivoire, Congo, Djibouti, Equatorial Guinea,
Eritrea, Ethiopia, Gabon, Gambia, Ghana, Guinea, Guinea-Bissau, Kenya,
Lesotho, Liberia, Madagascar, Malawi, Mali, Mauritania, Mauritius, Mozambique, Namibia, Niger, Nigeria, Reunion, Rwanda, Sao Tome and Principe,
Senegal, Seychelles, Sierra Leone, Somalia, South Africa, Saint Helena, Swaziland, Tanzania, Togo, Uganda, Zaire, Zambia, Zimbabwe
CPA China and centrally planned Asia: Cambodia, China, North Korea, Laos,
Mongolia, Viet Nam
SAS South Asia: Afghanistan, Bangladesh, Bhutan, India, Maldives, Nepal, Pakistan, Sri Lanka
PAS Other Pacific and Asia: American Samoa, Brunei Darussalam, Fiji, French
Polynesia, Gilbert-Kiribati, Indonesia, Malaysia, Myanmar, New Caledonia,
Papua, New Guinea, Philippines, Republic of Korea, Singapore, Solomon Islands, Taiwan, Thailand, Tonga, Vanuatu, Western Samoa

Table 2: Definition of the regions

28

29

0.36
0.53
0.64
0.54
0.67
0.56
0.70

0.19
0.20
0.20
0.29
0.35
0.29
0.37

0.30
0.31
0.32
0.32
0.33
0.46
0.58

0.49
0.55
0.59
0.60
0.69
0.65
0.81

0.22 0.29
0.25 0.33
0.27 0.35
0.27 0.35
0.31 0.40
0.30 0.38
0.37 0.46

2030
WEU NAM CPA
0.70
0.86
0.99
1.01
1.33
1.20
1.87

0.26 0.30
0.32 0.36
0.36 0.40
0.37 0.41
0.48 0.53
0.44 0.48
0.67 0.72

2040
WEU NAM CPA
0.92
1.35
1.77
1.85
3.38
2.68
7.08

0.31 0.31
0.45 0.44
0.58 0.57
0.61 0.59
1.08 1.03
0.87 0.84
2.20 2.05

2050
WEU NAM CPA
1.12 0.36 0.33
2.46 0.78 0.70
4.47 1.39 1.23
4.95 1.54 1.36
15.64 4.70 4.03
10.42 3.17 2.75
44.73 13.00 10.76

2060
WEU NAM CPA

1.25
1.07
0.99
1.06
0.97
1.05
0.95

2.73
2.71
2.69
2.42
2.26
2.40
2.22

2.48
2.45
2.44
2.44
2.41
2.12
1.94

1.22
1.17
1.13
1.13
1.06
1.09
0.99

3.24 3.35
3.15 3.25
3.09 3.18
3.08 3.17
2.96 3.05
3.01 3.09
2.82 2.90

2030
WEU NAM CPA
1.15
1.05
0.98
0.97
0.84
0.89
0.69

3.64 4.08
3.45 3.86
3.32 3.72
3.29 3.69
3.01 3.38
3.12 3.50
2.65 2.98

2040
WEU NAM CPA

1.12
0.92
0.78
0.76
0.51
0.60
0.29

3.84 4.65
3.41 4.15
3.10 3.79
3.04 3.72
2.33 2.90
2.60 3.21
1.54 1.96

2050
WEU NAM CPA

1.13
0.70
0.46
0.42
0.16
0.23
0.06

4.47 5.78
3.33 4.40
2.48 3.34
2.34 3.17
1.09 1.55
1.46 2.04
0.48 0.71

2060
WEU NAM CPA

Table 4: CO2 emission from fossil-fuel consumption under different scenarios (GtC). Shaded cells indicate that values in thecells are under direct influence of policy intervention.

Laissez-faire
Kyoto-low
Kyoto-high
KyotoUS-low
KyotoUS-high
Global-low
Global-high

2020
WEU NAM CPA

Table 3: Relative size of non-fossil-fuel primary energy consumption, Xjct /Xjdt , under different scenarios. Shaded cells
indicate that values in the cells are under direct influence of policy intervention.

Laissez-faire
Kyoto-low
Kyoto-high
KyotoUS-low
KyotoUS-high
Global-low
Global-high

2020
WEU NAM CPA