Structural change and climate policy
in developing countries
Aaron Gertz∗†
June 14, 2013
(Preliminary and incomplete)
Abstract
Some argue that developing countries cannot reduce carbon emission as aggressively as developed countries without serious harm to their economic development.
However, most analyses of the cost of carbon policy omit the potential impact of
structural change; that is, the transition from industry to services as an economy develops. This may be important because services are much less carbon intensive than
industry. I use a 2-sector nonbalanced growth model to study the impact of structural
change on carbon intensity. I calibrate the model to China and find that structural
change can play an important role in reducing carbon intensity and lowers the impact
of a carbon tax on GDP. In the absence of a carbon tax, I find that structural change
is responsible for 3/4 of a 38% reduction in emissions intensity over the next 30 years.
When a carbon tax is introduced, structural change remains important. I also find
that a carbon tax ramped up over time generates similar intensity reductions at a
lower cost compared to a constant tax set at an initially higher level.
∗
The author would like to thank Jim MacGee and John Whalley for guidance and suggestions as well
as seminar participants at UWO and the 47th Annual Conference of the CEA.
†
The University of Western Ontario, email: agertz2@uwo.ca
1
1
Introduction
International negotiations to secure a climate treaty to avoid potentially disastrous climate
change have been ongoing since the 1997 Kyoto Protocol. One shortcoming of the Kyoto
Protocol was that it did not include developing countries. As a result, some developed
countries were hesitant to make emissions cuts while countries like China and India grew
their emissions rapidly. In fact, China is now the world leader in carbon emissions and it is
widely agreed that rapidly-growing developing countries will be the major source of future
emissions (see table 1). To keep greenhouse gas (GHG) concentrations within safe levels,
developing countries must significantly reduce emissions compared to a business-as-usual
scenario (Stern, 2007).
While limiting emissions by developing countries is recognized as essential, some argue developing countries cannot make significant GHG reductions without doing serious
harm to their economic development. The basis for this argument is that the economies
of developing countries are much more carbon intensive than developed nations. That is,
developing countries emit more carbon (burn more fossil fuels) to produce a unit of GDP,
making it more costly to cut back emissions. Thus it is important to understand the potential economic costs and benefits of enacting emission-reducing policies such as a carbon
tax in developing countries.
One important aspect that this argument neglects is the role of structural change.
Broadly, the literature documents a shift from agriculture to industry to services as an
economy develops (see Kuznets (1957), Duarte & Restuccia (2010)). Structural change
could be very important for climate change because services are less carbon-intensive than
industry. The Euro Area went from about 50% services in 1970 to nearly 70% services in
2000 (World Bank, n.d.). If, for example, industry is twice as carbon intensive as services,
then structural change alone would account for a 15% reduction in emissions intensity over
the 30-year period.
In this paper I study how carbon emissions intensity is impacted over time by the dynamic process of structural change. Structural change can lower carbon intensity, however
efficiency gains may dominate depending on the stage of development and energy/carbon
prices. I assess the relative importance of each mechanism in decreasing emissions intensity.
This will include examining whether the introduction of a carbon tax has an impact on
the role for structural change and if the economic cost of implementing a carbon tax is
significantly lowered by structural change. This paper will also examine the effect of the
time path of a carbon tax; specifically, whether it is better to initially set a carbon tax at a
high level and hold it constant or whether it is better to start low and increase over time.
2
To tackle these questions I develop a 2-sector non-balanced growth model that builds
on Acemoglu & Guerrieri (2008). The two sectors are industry and services. Each sector
uses capital, labour and fossil fuels as inputs to production. Fossil fuels generate carbon
emissions with industry being more emissions-intensive. Each sector’s growth rate is determined by the growth rates of the inputs, the share parameters of the inputs and the
exogenous total factor productivity (TFP) growth rate. Depending on parameter values,
one sector can grow more rapidly than the other and dominate asymptotically, even if
both sectors have the same TFP growth rate. To match the observed historical trend of
a growing service sector, I consider parameter values where the service sector grows more
rapidly than industry. The two goods are combined into a final good that the representative
household can choose to consume or invest.
The model features three mechanisms that can drive down carbon intensity: 1) Substitution of services (low carbon) for industry (high carbon); 2) Substitution of value added
for fossil fuels at the sectoral level; 3) Total factor productivity growth at the sectoral level.
The first mechanism is the key focus of the paper. As the less emissions-intensive service
sector’s share of output grows, the overall carbon intensity of the economy decreases (e.g.
more restaurants and fewer steel mills). I compare the first mechanism with the other two
more common mechanisms. They can be interpreted as efficiency gains via new machines
or processes (e.g. more green energy or more energy efficient machines). A carbon tax can
be introduced, which increases the price fossil fuels. Since fossil fuels are endogenously
determined in the model, this drives substitution away from fossil fuels in both sectors and
drives up the price of the more carbon-intensive industrial goods relative to services. This
can lead to additional substitution toward services. 1
In order to determine if structural change is quantitatively important to lowering carbon
intensity in developing countries, I calibrate the model to the Chinese economy. I choose
China for the numerical exercise because it is a developing country with a relatively small
service sector and it the largest emitter of GHGs in the world. I find that with no carbon tax
or other climate policy, aggregate emissions intensity in China is decreased by 38% after 30
years, with structural change accounting for roughly 3/4 of that reduction (the remaining
1/4 reduction is due to TFP growth). In this simulation the price of fossil fuels is constant
in time while wages are increasing. As a result the relative price of fossil fuels decreases
driving substitution toward carbon. Yet, the carbon intensity still decreases mostly due to
the relative growth in the size of the service sector. Thus if we ignore the effect of TFP
1
There is no climate feedback on the economy in this model, thus only the cost side of a carbon tax
is captured. This is a reasonable abstraction since emissions accrue to the entire world and the model
considers a closed economy. It is also consistent with the literature for studying climate policy impacts on
a single country.
3
growth, emissions intensity would actually increase if not for structural change.
Structural change remains important in the presence of a carbon tax, however the higher
price of carbon primarily drives substitution of value added for fossil fuels in each sector.
This is seen when carbon taxes are introduced to the simulations. Structural change lowers
the carbon intensity by 28.5% over 30 years in the absence of a carbon tax, while efficiency
gains contribute a 9.5% reduction. With a 5$/ton carbon tax, structural change lowers
carbon intensity by 29.4% while efficiency gains contribute a 22.6% reduction.
The exercises above show that structural change is quantitatively important to lowering
carbon intensity in a world with structural change. However, counterfactual simulations of
the model that do not allow for structural change show the full impact of structural change;
it lowers the carbon intensity and reduces the cost of a carbon tax. With no carbon tax, a
1-sector model reduces the carbon intensity by 15% over 30 years, whereas the model with
structural change lowers the carbon intensity by 38%. Furthermore the cost of a $5/ton
carbon tax is 1.7% of GDP after 30 years in a 1-sector model compared to 1.2% of GDP
for the model with structural change. This difference is because in the 1-sector model, the
more carbon-intensive industrial sector does not shrink relative the the aggregate economy.
Finally, I consider different time paths for the carbon tax to test if it is better to implement
a high carbon tax quickly or ramp up the tax more slowly. A slowly ramped-up carbon tax
proves to deliver similar carbon intensity reductions at a lower cost compared to a tax set
at an initially high level. This is because with a ramped up tax, the economy has time to
build up the capital stock (and population) as a response to deal with the eventual higher
taxes.
Although the impact of structural change on climate policy has not been studied in
detail, modelling structural change itself goes as far back as Baumol (1967). He assumed
that labour productivity is fixed in some professions but not others, although I will not have
to assume productivity differences between industry and services in this study. Kongsamut
et al. (2001) used non-homothetic preferences to achieve structural change from the demand
side. However, this approach leads to parameter restrictions I prefer to avoid. Furthermore,
service shares in consumption and production are similar so there is no clear advantage of a
demand-driven approach over a supply-driven approach. More recently, Ngai & Pissarides
(2007) generalized structural change to n sectors driven by supply side TFP growth rate
differences. However, I follow (Acemoglu & Guerrieri, 2008) because TFP growth rate
differences are not needed. Furthermore their model accurately replicated the evolution of
capital-intensive and non-capital intensive sectors of the U.S. economy and China’s service
sector is much more capital-intensive than industry.
Numerous studies of climate change policy have been carried out at the global and
4
national levels. Global models do not account for structural change as regional interactions
are the focus of those studies (e.g. Whalley & Wigle (1991)). At the national level, the
literature offers more detailed sectoral modelling using CGE models. Many studies of
climate policy in developing countries have focused on China. Zhang (1998) and Dai et al.
(2011) quantified the cost of reducing emissions in China. Garbaccio et al. (1999) and
Fisher-Vanden & Ho (2007) studied how non-market aspects of China’s economy affect
climate policy. Fisher-Vanden & Ho (2007) and Vennemo et al. (2009) incorporated health
and agricultural impacts, while Wang et al. (2009) allowed for endogenous technical change
and Hübler (2011) considered technology spillovers. While these studies all have significant
sectoral detail, the focus is not on structural change across sectors of the economy but the
composition of the energy sector and energy usage. This paper is the first to isolate the
role of structural change in reducing carbon intensity.
CGE models typically use Leontief or Cobb-Douglas functional forms to aggregate intermediate goods, which inhibits structural change in quantities and values, respectively.
Some of the studies above use differing sectoral growth rates to achieve structural change,
however that assumption is not needed here. Others exogenously vary share parameters
over time to achieve some structural change, that also is not needed in this model, which
allows the structural change to respond endogenously to the carbon tax. In addition, this
model employs endogenous investment which is typically not done with CGE models. This
may be important because as the price of fossil fuels increases firms may demand more
capital (for example more energy efficient buildings).
The rest of the paper is organized as follows. Section 2 discusses data on carbon
emissions and the service sector, section 3 presents the model and section 4 describes the
characterization of the solution to the model. Section 5 details the numerical experiments
and section 6 offers a discussion of the results.
2
Emissions and the service sector
Most carbon emissions in the atmosphere result from the burning of fossil fuels. This
activity is associated largely with industrial processes including power generation. Since
CO2 emissions remain in the atmosphere for roughly 100 years, countries that developed
earlier are responsible for a majority of the emissions currently in the atmosphere. However,
lowering or stabilizing atmospheric concentrations depends on slowing current and future
emissions.2 Table 1 shows that some developing countries are already among the world
2
There has been discussion of technologies to remove carbon from the atmosphere, however those
technologies are far from the stage of implementation.
5
leaders in emissions, and since they are growing at a faster rate their share of emissions is
likely to increase over time.
Table 1 also shows the carbon intensity and service sector share of GDP for these
countries. Developing countries are much more carbon intensive and their service sectors
are smaller. The fact that the service sectors are smaller is one reason for the higher
intensities, although those countries also generally have dirtier fuel mixes (i.e. more coal)
and are less energy efficient than developed countries when performing the same tasks. If
the sectoral mix of developing countries did not change, it might be very difficult to lower
the carbon intensity resulting in unprecedented levels of emissions.
CO2 Emissions 2011 GDP CO2 Intensity
(kt)
growth (kg per USD)
China
7,687,114
9.3%
0.93
India
1,979,425
6.3%
0.58
Russian Federation
1,574,386
4.3%
0.81
South Africa
499,016
3.1%
1.08
United States
European Union
Japan
Australia
5,299,563
3,617,580
1,101,134
400,194
1.7%
1.5%
-0.7%
1.9%
0.42
0.27
0.29
0.54
Service
share
43%
55%
62%
66%
79%
74%
73%
76%
Table 1: 2009 emissions, intensity and service share. Source: World Bank (n.d.).
Figure 1 shows the CO2 intensity and service sector share of the United States since
1970. Although the intensity is decreasing while the service share is increasing, the sharpest
decline in intensity occurs in the 1970s and early 1980s when the service sector is growing
modestly. In fact, empirical studies by Schipper et al. (1990) and Rose & Chen (1991) found
that sectoral efficiency gains, or technological progress, was the dominant mechanism for
reducing energy intensity during that period. It is important to recognize that energy
prices were particularly high during the 1970s and early 1980s; Popp (2002) found that the
high energy prices were important in inducing technical change. However, Wing (2008)
found that for the period from 1958-2000, structural change is responsible for 2/3 of the
reduction in energy intensity in the U.S., with the caveat that efficiency gains are most
important after 1973. Thus the experience of the United States shows that the importance
of structural change in lowering energy intensity (and correspondingly carbon intensity)
potentially depends on the stage of development and energy prices. If energy prices do not
spike in the coming decades, it is reasonable to assume that structural change will play a
6
more important role in reducing carbon intensity for currently developing countries than
it did for the United States.
4.5
80
4
78
76
3.5
74
Intensity
72
2.5
70
2
68
Service share
3
1.5
66
1
64
0.5
0
1970
62
1975
1980
1985
1990
Intensity
1995
2000
2005
60
2010
Service share
Figure 1: U.S. CO2 intensity declines over time, service sector share of GDP increases.
There have also been studies on the impact of structural change on energy intensity
for other countries. Gardner (1993) examined Ontario industry between 1962 and 1984
and found structural change to be equally as important as efficiency gains. Diakoulaki &
Mandaraka (2007) examined the impact of structural change on total carbon emissions for
countries in Europe between 1990 and 2003 and found an important role for structural
change. There have been a few studies about energy intensity and structural change in
China, although typically for small time windows. Fisher-Vanden et al. (2004) found that
sectoral shifts accounted for 17.6% of the decrease in energy intensity from 1997-1999. Liao
et al. (2007) found that the energy intensity increase from 2003-2005 was driven by the
expansion of high-energy sub-sectors of the economy. In summary, structural change has
been observed to lower energy (and carbon) intensity across countries over different periods
of time. This paper examines the potential role for structural change in lowering carbon
intensity over the coming decades in developing countries.
7
3
The Model
The economy is a 2-sector non-balanced growth model where one sector represents industry
and the other represents services. Goods produced by each sector are aggregated into a
final good. The two sectors use labour, capital and fossil fuels as inputs to production.
The fossil fuels emit carbon (that can be taxed). The production function for each sector
has the same functional form but the parameters may differ which allows for differences in
the growth rates and emissions intensities. I will impose parameter restrictions which force
the service sector to grow faster than industry. Consumers maximize utility by choosing
consumption and investment.
3.1
Production
The intermediate goods are combined using a CES function to produce a final good:
Y (t) = [γYI (t)
−1
+ (1 − γ)YS (t)
−1
] −1
(1)
Here, Y (t) is the final good output at time t, YI (t) is the industrial intermediate, YS (t)
is the services intermediate, γ is a share parameter and is the elasticity of substitution
between industrial goods and services. The resource constraint is given by:
K̇(t) + δK(t) + C(t) = Y (t)
(2)
Here, K(t) is the capital stock, C(t) is consumption and δ is depreciation.
3.1.1
Intermediate goods
Intermediates are also produced using a CES function:
Yi (t) = Ai (t)[γi Fi (t)
i −1
i
+ (1 − γi )VAi (t)
i −1
i
i
] i −1 , i ∈ (I, S)
VAi (t) = Ki (t)αi Li (t)1−αi
(3)
(4)
Fi (t) is fossil fuels demanded and VAi (t) is value added demanded at time t in sector i,
where Li (t) is labour. Ai (t) is the total factor productivity, αi and γi are share parameters
and i is the elasticity of substitution between fossil fuels and value added.
The profit function for the intermediates is:
πi (t) = pi (t)Yi (t) − pFi (t)Fi (t) − R(t)Ki (t) − w(t)Li (t) − τ (t)Zi (t)
8
(5)
Here, pi (t) is the price of good i, pFi (t) is the price of fossil fuels for sector i, R(t) is the rental
rate of capital, w(t) is the wage, τ (t) is the carbon tax and Zi (t) are emissions generated
in production.3 Emissions are generated by the use of fossil fuels, so Zi (t) = φ1i Fi (t). As a
result, we can simplify the production and profit functions:
Yi (t) = Bi (t)[γi0 Zi (t)
i −1
i
+ (1 − γi0 )VAi (t)
i −1
i
i
] i −1
πi (t) = pi (t)Yi (t) − (pFi (t)φi + τ (t))Zi (t) − R(t)Ki (t) − w(t)Li (t)
(6)
(7)
Fossil fuels could be omitted altogether in the formulation of the model, skipping directly
to carbon emissions as an input. This would be consistent with environmental studies such
as Copeland & Taylor (2005), however the specification above makes the calibration exercise
in section 5.1 more intuitive. It may seem that because the relationship between emissions
and fossil fuels is constant in time there is no scope for substitution between different
fossil fuels. However, this can be interpreted in the model as a substitution of value added
for emissions since new capital would be needed to use a different fuel in the production
process. In fact, any substitution within a sector is possible by substituting toward value
added. This would include oil and gas power plants, green energy, more energy efficient
machines and buildings, and inter-sectoral shifts such as light manufacturing for heavy
industry. Note that efficiency gains also occur via growth in the total factor productivity
term, Bi (t).
3.2
Household
Household preferences are represented by
Z
∞
exp(−(ρ − n)t)
0
c(t)1−θ − 1
dt,
1−θ
(8)
where ρ is the discount rate, n is population growth, c(t) is per capita consumption and
1/θ is the intertemporal elasticity of substitution. Households have an initial endowment of
capital, K0 > 0, and an endowment of labour L(t) which grows exogenously and is supplied
inelastically.
The law of motion of capital is given by:
K̇(t) = r(t)K(t) + w(t)L(t) + pZ (t)Z(t) − c(t)L(t)
3
(9)
Each sector can have a different price of fossil fuels due to differing mixes of coal, oil and gas. The
price of capital and wages are the same across sectors, as is the carbon tax.
9
Here, r(t) = R(t) − δ is the interest rate, w(t) is the wage, and pZ (t) is the average price
of emissions. Note that the household receives a lump-sum payment for the right to emit
carbon. The household problem gives the following standard Euler equation:
ċ(t)
1
= (r(t) − ρ)
c(t)
θ
(10)
The transversality condition ensures that investment does not dominate consumption asymptotically:
Z
t
lim K(t) exp −
t→∞
3.3
r(τ )dτ
=0
(11)
0
Equilibrium
The competitive equilibrium is given as the path of factor and intermediate good prices
VA
[R(t), w(t), pZI (t), pZS (t), pVA
I (t), pS (t), pI (t), pS (t)]t≥0 ; emissions, value added, capital and
employment allocations [ZI (t), ZS (t), VAI (t), VAS (t), KI (t), KS (t), LI (t), LS (t)]t≥0 such that
given prices firms maximize profits and markets clear; and consumption and investment
[c(t), K̇(t)]t≥0 that maximize representative household utility given prices and initial capital
stock K0 . Solving the competitive equilibrium yields the following price equations:
pVA
i (t)VAi (t)
Ki (t)
pVA (t)VAi (t)
(1 − αi ) i
Li (t)
1/i
i −1
Yi (t)
0
i
γi B(t)
pi (t)
Zi (t)
1/i
i −1
Y
(t)
i
0
(1 − γi )B(t) i pi (t)
VAi (t)
1/
Y (t)
ωi
Yi (t)
R(t) = αi
w(t) =
pZi (t) =
pVA
i (t) =
pi (t) =
(12)
Here, ωI = γ, ωS = 1 − γ and the final good is the numeraire. Market clearing is given by:
K(t) = KI (t) + KS (t)
L(t) = LI (t) + LS (t)
Z(t) = ZI (t) + ZS (t)
10
(13)
4
Characterizing the solution
As in Acemoglu & Guerrieri (2008), a constant growth path (CGP) is defined such that
the growth rate of consumption is asymptotically constant.4
ċ(t)
= gc∗ = gC∗ − n
t→∞ c(t)
lim
(14)
By equation (10), this means that the interest rate is also asymptotically constant. Furthermore, the final good must grow at the rate of consumption, g ∗ = gC∗ , otherwise the
transversality condition is violated. By differentiating (1), we can obtain the growth rate
of the final good:
−1
−1
γYI (t) gI (t) + (1 − γ)YS (t) gS (t)
Ẏ (t)
=
g(t) =
−1
−1
Y (t)
γYI (t) + (1 − γ)YS (t) (15)
Thus, the final good asymptotic growth rate, g ∗ , is equal to the the minimum ( < 1) or
maximum ( > 1) of the sectoral growth rates (gI∗ , gS∗ ). In order to be consistent with the
stylized fact that the service sector increases its share of output with time, I impose gS∗ > gI∗
and > 1.
Since the sectoral production functions are also CES form, the sectoral growth rates
are derived similarly to the final good above (except there is also TFP growth to include).
As a result, there are four cases to consider when solving for the remaining growth rates;
two for each sector5 :

VAi
a + g
i
VAi if Zi → 0 and i < 1
gi∗ =
(16)
a + g if VAi → ∞ and < 1
i
Zi
i
Zi
All of the sectoral asymptotic growth rates can be solved for using the fact that gS∗ = g ∗
plus equations (4), (12), (13) and (16). The asymptotic growth of the rate of return on
capital is 0 (in both sectors) and the growth rate of the wage is the same in both sectors.
The market clearing conditions imply that the growth rate of an aggregate input grows at
the rate of that input in the sector which is using that input at a faster-growing rate. For
example, if n∗S > n∗I then n∗S = n. Otherwise n∗I = n.
i
Below I give the resulting asymptotic growth rates for the case in which VA
→ 0 in
Zi
4
Acemoglu & Guerrieri (2008) show the saddle-path stability of their model which implies the equilibrium solution converges to the unique CGP.
5
I consider only when i < 1 because that is the case in the numerical exercise. However, for i > 1 the
two cases are simply reversed.
11
both industries. This solution is the case of the numerical work shown later in the paper.
gS∗ = g ∗ = gC∗
n∗S = n
∗
∗
gK
= gK
= g∗
S
gZ∗ S = (S − 1)aS + g ∗ − S gpZS
[(1 − αS )aI − (1 − αI )aS ]
gI∗ = gS +
1 − αS
−1 ∗
n∗I = n∗S +
(gI − gS∗ )
∗
∗
∗
∗
gK
=
g
+
(n
KS
I − nS )
I
1
{( − 1)(1 − αS )aI + [(1 − S )(1 − αS )
gZ∗ I = gZ∗ S +
1 − αS
+(I − )(1 − αI )]aS } − I gpZI + S gpZS
Notice that for > 0, αS > αI and aS = aI (as in numerical exercise), we get that
∗
∗
. If we further assume that
> gK
> gI∗ as required. Furthermore, n∗S > n∗I and gK
I
S
S = I and gpZS = gpZI (also in accordance with the numerical exercise), we get that
gZ∗ S > gZ∗ I . In order for this solution to hold we also require that emissions grow faster
than value added. This is true in both sectors if aS = aI > gpZ . Thus, asymptotically,
the service sector converges to the aggregate economy and emissions grow faster than value
added if the price of carbon grows more slowly than TFP. For total emissions to be constant
in the long-run, that is gZ∗ S = 0, the price of emissions must grow at the rate of TFP. For
emissions to decrease the price must grow faster than TFP.6
For the numerical exercise, we can solve for the TFP growth rate in terms of the long-run
growth rate of the aggregate economy and the population growth rate:
gS∗
aS = (1 − αS )(g ∗ − n)
5
(17)
Experiments
To quantify the impact of structural change on carbon intensity in a developing economy,
numerical simulations of the model are carried out. Specifically, the experiments compare
the relative importance of structural change and efficiency gains in lowering carbon intensity. Output losses from a carbon tax are also calculated to determine the savings to GDP
due to structural change.
6
Under those scenarios the growth rates above do not hold as we enter into cases where
12
VAi
Zi
→ ∞.
The model is calibrated to the Chinese economy. As mentioned previously, China is
chosen because it is the world’s leading emitter of GHGs and has a relatively small service
sector. A baseline scenario is simulated with no carbon tax. Four carbon tax scenarios are
also simulated:
1. Low level, constant in time.
2. Low level, ramp-up over time.
3. High level, constant in time.
4. High level, ramp-up over time.
Two different tax levels are considered in order to quantify the impact of structural change
as the price on emissions increases. There is a debate in the literature over whether a
carbon tax should be phased in slowly or rapidly. Thus two different time paths for the
carbon tax (constant and increasing) are simulated. More details on why structural change
may be relevant to this debate are given in section 5.2.4.
Across these scenarios I use Laspeyres additive index to quantify the contribution of
structural change to lowering carbon intensity. I examine emissions intensity reductions
and output losses compared to baseline across the different tax schemes.
The index method quantifies the contribution of structural change in a model with multiple mechanisms to reduce carbon intensity. However, a counterfactual simulation without
structural change allows for isolating the overall impact. Thus I consider a calibration of
the model that does not allow for structural change (i.e. a 1-sector model). I then compare
the emissions intensity reduction and loss of output from a carbon tax in the 1-sector and
2-sector models.
5.1
Data and calibration
I calibrate the model to the Chinese economy using economic and energy data from the
Chinese Statistical Yearbook (CSY, National Bureau of Statistics of China (2007)), emissions data from the World Development Indicators (World Bank, n.d.) and emission factors
from the Energy Information Administration (EIA). Sectoral-level data is from the most
recent (2007) input-output table in the CSY (135 industries).
The industry sector includes manufacturing, chemical processing, construction, agriculture and mining (sectors 1-95, with an exception explained below). The service sector
includes transportation, retail, financial intermediation, entertainment, healthcare and education (96-135). Power and heat generation and fuel processing are treated uniquely
13
because they are both responsible for significant carbon emissions and both serve the industrial and service sectors. 70% of power generation is used by industry, thus 70% of that
sector is included with industry and the rest with services. 45% of processed fuels spending
is done by industry, thus that sector is divided 45-55. With this division of activities, the
emissions from each sector should be accurately modelled as both sectors grow.
The initial shares in output of industry and services are calculated by summing the
value added of the respective sub-sectors. The share parameters for labour are calculated
by summing “employee compensation” across appropriate sub-sectors and dividing by the
corresponding value added. The capital share is 1 minus the labour share. Since I assume
that emissions are linear in fossil fuels, Zi = φ1i Fi , the share of emissions is the same as
that of fossil fuels. This is shown below:
∂Yi
∂Yi ∂Fi
pF F i
pZ Z i
=
⇒ pZi = φi pFi ⇒ i
= i
∂Zi
∂Fi ∂Zi
pi Yi
pi Yi
Thus the share parameter for emissions in each sector, γi0 , is simply the spending on coal,
oil and gas relative to value added. To calculate the ratio of emissions in each sector
which is used to get the initial price of emissions, the emission factor φi is needed. This
is calculated by taking the energy consumption by fuel type by industry from the CSY
and multiplying it by the emission factor for each fuel type from the EIA. The elasticity
of substitution between industry and services is chosen such that in the baseline scenario
structural change matches the historical pace of the United States and Europe; that is, a
20% increase in the service sector share over 30 years.
The elasticity of substitution between emissions and value added is set to the elasticity
of substitution between energy and value added from Su et al. (2012). This parameter has
been estimated for the aggregate economy, and I use the same value for both industry and
services. A population growth rate of 0.3% is taken from Vennemo et al. (2009), and the
initial capital output ratio of 1.72 is taken from Bai et al. (2006).
A long-run growth rate of 6% is chosen. China’s growth has been above 10% for much of
the past decade, falling below 8% more recently. Since no fast-developing country has been
able to maintain growth near 10%, I argue that 6% is a reasonable compromise between
a growth rate faster than developed countries but slower than recent growth in China.
Standard values are chosen for the discount rate, intertemporal elasticity of substitution
and depreciation: ρ = 2%, δ = 5%, θ = 4. The initial aggregate output and emissions are
taken from the World Bank (n.d.).
For the calibration of the one sector model, I re-calculate aggregate labour, capital and
emission shares. This is done in the same fashion as described above except there is no
14
Output share (γ)
Capital share (αi )
Labour share (βi )
Emissions share (γi0 )
Emission factor (φi )
Elasticity, Z and VA (i )
Elasticity, YI and YS ()
Population growth (n)
Capital output ratio ( K
)
Y
Industry Services
Match
0.52
0.48
Data
0.53
0.64
Data
0.47
0.36
Data
0.10
0.08
Data, calculation
3.86
2.14
Data, calculation
0.76
0.76
Su et al. (2012)
6.5
Service share transition
0.003
Vennemo et al. (2009)
1.72
Bai et al. (2006)
Table 2: Key parameter values.
division of industries. The values are: α = 0.59, β = 0.41, γ 0 = 0.094. I then run the
two-sector model with those parameter values in each sector and the initial output, labour
and emissions divided evenly between the two sectors.
5.2
Numerical simulations
The calibrated model described above is simulated over a 500-year period, although I focus
on the behaviour of the first 30 years. The differential equations are discretized using the
Euler method and a shooting algorithm is used to solve for the time path of the model.
I examine the role of structural change in lowering emissions intensity for the baseline
scenario and the four carbon tax scenarios. Furthermore I compare intensity reductions
and output losses from a carbon tax in the model of structural change to a 1-sector model.
Finally, I compare intensity reductions and output losses for carbon taxes that are set
initially high to those that ramp up over time.
5.2.1
Baseline scenario
The baseline scenario generates significant structural change from industry to services. This
occurs because services are more capital intensive than industry and the capital-labour ratio
increases with time. Figure 2 shows the service sector share of output increasing from less
than 45% to roughly 65% after 30 years, the rate of change experienced by the U.S. and
Europe as their economies developed.
Figure 3 shows the carbon intensity of the entire economy decreasing; after 30 years,
it has decreased by 38%. In year 0 the carbon intensity is nearer to the intensity of the
industrial sector but converges to the intensity of the service sector over time. After 100
years, the total intensity is almost equal to that of the service sector. Using the Laspeyres
15
1
Labour
Capital
Emissions
Output (value)
0.9
0.8
Service sector share
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
20
40
60
80
100
Years
Figure 2: Structural change: The service sector shares of output, capital, labour and
emissions increase over time (baseline scenario).
additive index7 , structural change is responsible for 3/4 of that drop. Thus, the economy
is moving toward the less carbon-intensive service sector and this is significantly lowering
the carbon intensity.
The remaining 1/4 of the decrease in carbon intensity is due to sectoral intensity gains.
Sectoral carbon intensities are given by Ii = pZi Yi i . Figure 4 shows the different growth rates
in the service sector (the story is the same in the industrial sector). It is clear that there
is very little movement in the price of services, thus the decreasing intensity is a result of
output (quantity) growing faster than emissions at the sectoral level. Recall the production
function for services:8
YS (t) = BS (t)[γS0 Z(t)ρS + (1 − γS0 )VAρS ]1/ρS
Figure 4 shows that emissions are growing faster than value added, meaning firms are
substituting toward emissions (fossil fuels). This occurs because the price of emissions
7
8
See Ang & Zhang (2000) for details of different index methods.
Here, ρS = S−1
.
S
16
remains constant while wages are increasing, driving substitution away from value added.
However, the sectoral emissions intensity decreases nonetheless because TFP growth makes
up for the growth in emissions. That is, firms become more efficient in the use of all inputs
and their ability to produce more with fewer inputs compensates for the relative increase
in the use of emissions compared to value added.
3.5
Total
Industry
Service
3
Emissions / Output
2.5
2
1.5
1
0.5
0
20
40
60
80
100
Years
Figure 3: Carbon intensity by sector (baseline scenario).
It is also worth noting that under the baseline scenario China does not meet its Copenhagen target of reducing carbon intensity by 40-45% over 2005 levels by 2020. Taking year
0 to be 2007 in the simulation, the carbon intensity is only reduced by 26% over 2005 levels
by 2020.
5.2.2
Carbon taxes
Having established the behaviour of the baseline scenario, I now consider four carbon tax
price paths:
1. Constant tax, $1.39 per ton.
2. Tax increasing at 2% per year, average price over 30 years: $1.39/t.
17
0.1
Output
Emissions
Value added
Price of good
0.09
0.08
0.07
Growth rate
0.06
0.05
0.04
0.03
0.02
0.01
0
-0.01
0
20
40
60
80
100
Years
Figure 4: Carbon intensity by sector (baseline scenario).
3. Constant tax, $5/t.
4. Tax increasing at 2% per year, average price over 30 years: $5/t.
Carbon taxes that have been implemented in developed countries are typically in the range
of $20-$25 per ton. Since China’s GDP per capita is only about 1/5 developed country
standards, I chose lower carbon tax levels accordingly. I chose to match the discount rate
for the 2% rate of increase in the non-constant tax scenarios.
The time paths of the carbon taxes are shown in figure 5. The model is simulated with
all parameters the same as in the baseline scenario except for the carbon tax. Note that
China meets the Copenhagen target under the $5/t tax level but not the $1.39/t tax level.
The carbon intensity by scenario is shown in figure 6. As expected, higher taxes lead
to greater reductions in emissions intensity; emissions intensity is roughly 8% lower than
the baseline scenario under the low carbon taxes after 30 years and roughly 23% lower
under the high taxes. As would be expected, the intensity is initially lowered more under
the constant tax schemes since the tax is set higher in year 0. However, after 30 years
the situation is reversed and the “ramped-up” carbon taxes result in lower intensities. As
18
7
6
USD per ton
5
4
3
2
1
0
0
5
10
15
Years
20
25
30
Figure 5: Carbon tax scenarios.
a result, total emissions (not intensity) over the period are lower under the “ramped up”
schemes. This occurs because under the ramped up scheme, the intensity is lower during
the later years when output is higher. It makes up for the intensity being higher in the
early years when output is lower.
There is still a question of whether structural change is more or less important in the
presence of a carbon tax. That is, does a tax drive more substitution toward value added
in each sector, or more substitution of services for industrial goods. In table 3, we see
that structural change reduces carbon intensity by almost 30% in all scenarios. We can
see that the tax generates very little additional structural change compared to the baseline
scenario. Therefore, the tax plays a greater role in reducing sectoral carbon intensities via
the substitution of value added for emissions.
5.2.3
Comparison with 1-sector model
In order to illustrate how incorporating structural change into a model impacts the economic assessment of climate policy, I compare the 2-sector model to a 1-sector model.9 The
9
A multi-sector model without structural change can be aggregated to a 1-sector model.
19
2.2
Baseline
Low - flat
Low - increasing
High - flat
High - increasing
2
Emissions / Output
1.8
1.6
1.4
1.2
1
0.8
0
5
10
15
Years
20
25
30
Figure 6: Carbon intensity by scenario.
1-sector model is calibrated using the same data and techniques as described at the end
of section 5.1. In figure 7, we see that in the no-tax scenario, carbon intensity only drops
by 20% after 30 years in the 1-sector model compared to nearly 40% in the model with
structural change. When a tax is added, the result is similar. This shows how the changing sectoral composition toward less carbon-intensive services in the model with structural
change results in fewer emissions, this is not captured in the 1-sector model. Figure 8
shows the output loss in the two models from the ‘high’ carbon tax (at increasing rate).
The output loss is greater every year in the model without structural change, and after 30
years the loss is 1.7% of GDP compared to 1.2% in the model with structural change. Furthermore, the gap continues to grow with time. The higher price of emissions has a smaller
impact on the service sector compared to industry because it is less emissions-intensive. As
a result, the higher price of emissions is less costly in the model with structural change due
to the increasing importance of the service sector. Thus, the model with structural change
generates considerably more emissions savings at a much lower cost for the same carbon
tax.
20
Scenario
No tax, t=0
No tax, t=30
Low tax, constant
Low tax, ramp-up
High tax, constant
High tax, ramp-up
Service
share
0.432
0.686
0.688
0.689
0.692
0.695
Intensity Structural
change component
N/A
N/A
-38%
-28.5%
-42%
-28.7%
-43%
-28.8%
-48%
-29.1%
-52%
-29.4%
Table 3: Contribution of structural change to reducing carbon intensity after 30 years
5.2.4
Carbon tax timing
There is no consensus in the literature regarding the correct marginal cost of carbon (for
a review see Tol (2009)). This is primarily due to the high degree of uncertainty regarding
climate change, although there is also some debate about the appropriate discount rate
which plays a central role in quantifying the cost of carbon. If the marginal cost of carbon
is low (or the discount rate is high) then with economic growth and technological improvements, it will be relatively cheaper to avoid emissions in the future. This implies that
a carbon tax should start low and ramp up over time. However, if the marginal cost of
carbon is high (or the discount rate is low) then more urgent policy intervention may be
needed, especially since carbon emissions remain in the atmosphere for roughly 100 years.
With structural change, there is another perspective to consider in terms the timing of
a carbon tax for developing countries. We have seen that developing countries can lower
emissions at low cost via structural change. However, as the service sector grows the rate
of change must slow since the share is bounded at 100%. This means that it may be less
costly for developing countries to immediately tax emissions heavily while the service sector
is small to force a faster transition to services.
I have considered different carbon tax time paths for the two tax levels to test this
idea. We see in figure 6 that while the initially high tax results in a lower carbon intensity
at year 0, the “ramp up” tax results in a lower intensity by year 30. Over the 30 year
window, the “ramp up” scenarios result in slightly fewer total emissions. This is a result
of the intensity being lower during the later years when output is higher in the increasing
tax scenarios. It makes up for the intensity being higher in the early years when output
is lower. Figure 9 compares the output loss under the different tax schemes. We see that
output losses are roughly the same after 30 years, but over most of the period the losses
are smaller for the “ramp up” taxes. Thus the “ramp up” schemes deliver slightly greater
emissions reductions at lower cost.
21
2.2
With structural change - baseline
With structural change - tax
One sector - baseline
One sector - tax
2
Emissions / Output
1.8
1.6
1.4
1.2
1
0.8
0
5
10
15
Years
20
25
30
Figure 7: Carbon intensity - 1-sector model vs 2-sector model.
It should not be too surprising that structural change did not make the initially higher
tax more appealing. If we look back to table 3, we see that the carbon tax schemes have
little impact on the pace of structural change in this model. If it were harder to substitute
value added for emissions, it may be that the carbon taxes would drive a faster transition
to services.10 This might make the initially higher taxes perform better.
Note the model considered here does not consider a variety of factors, most notably
damage to output from climate change. Therefore, this paper only argues that the structural change mechanism does not help the case of the “initially high” carbon tax. It remains
possible that this tax is optimal for reasons described above and detailed in the literature.
6
Discussion
With the growing global focus on mitigating climate change and the important role for
developing countries, more studies of the economic impact of climate change and associated
10
In the next version of this paper I will add robustness checks on the elasticity of substitution between
emissions and value added to test this idea.
22
2
With structural change
One-sector
Output - pct loss
1.5
1
0.5
0
0
5
10
15
Years
20
25
30
Figure 8: Output loss from carbon tax - 1-sector model vs 2-sector model
policies are being conducted. However, most studies do not account for structural change;
in this case, the growing share of the service sector as an economy develops. This can be
an important consideration because services are typically much less carbon intensive than
industry. This paper has focused on how structural change affects carbon intensity. I use
a non-balanced growth model with carbon emissions as an input. The service sector grows
more rapidly than industry which reduces the aggregate carbon intensity. Intensity is also
reduced by efficiency gains via substitution of value added for emissions (fossil fuels) and
TFP growth.
The model is calibrated to the Chinese economy. Numerical simulations show that
structural change plays an important role in reducing carbon intensity (3/4 of the intensity
reduction in the baseline scenario). Structural change remains important in the presence
of carbon taxes, although the relative impact decreases. Structural change also reduces
the loss in output from a carbon tax. Thus it is clear that structural change can create
significant savings for a country like China when lowering carbon emissions. I also find
that even with structural change, a “ramped up” carbon tax is better than an initially
high carbon tax in terms of emissions reductions and output losses.
23
Low - flat
Low - increasing
High - flat
High - increasing
1.4
1.2
Output - pct loss
1
0.8
0.6
0.4
0.2
0
0
5
10
15
Years
20
25
30
Figure 9: Output loss from carbon tax across tax schemes.
The implication of these results is significant. From the Chinese perspective, they show
that for a given carbon price, the economic loss is much lower (and emissions reductions
higher) than what would be expected based on an analysis that does not account for
structural change. This opens the door for China to set more ambitious climate policy.
Furthermore, the optimal time path of the carbon tax should be the same as for developed
countries. This is important as it will allow for easier coordination on a carbon pricing
scheme. Finally, the model determines that China cannot meet its Copenhagen commitments based solely on structural change; a price on carbon will be needed.11
The results also matter from an international perspective. Since it will be more costly
for developing countries to reduce emissions (see Stern (2007)), it is likely that developed
countries will have to make transfers to developing countries to offset economic losses.
However, transfers may not have to be as large when structural change is taken into account.
It is important to note that structural change will not have the same significant impact
on all economies. For developed economies which are already 70%-80% services, there is
much less scope for a transition to services lowering emissions. Among developing countries,
11
A carbon price is part of China’s current 5-year plan.
24
examining the service sector share of the economy may be an important consideration
when determining where to apply resources to lowering emissions. For example, India is a
significant emitter and source of future emissions, but its service sector is already 56% of
GDP. Thus countries like India may require more focus and resources to lower emissions
than countries with relatively smaller service sectors like China.
25
References
Acemoglu, D., & Guerrieri, V. (2008). Capital deepening and nonbalanced economic
growth. Journal of Political Economy, 116 (3), 467–498.
Ang, B. W., & Zhang, F. Q. (2000). A survey of index decomposition analysis in energy
and environmental studies. Energy, 25 , 1149–1176.
Bai, C.-E., Hsieh, C.-T., & Qian, Y. (2006). The return to capital in China. Brookings
Papers on Economic Activity, 37 (2), 61–102.
Baumol, W. J. (1967). Macroeconomics of unbalanced growth: The anatomy of urban
crisis. American Economic Review , 57 , 415–426.
Copeland, B. R., & Taylor, M. S. (2005). Free trade and global warming: a trade theory
view of the kyoto protocol. Journal of Environmental Economics and Management,
49 , 205–234.
Dai, H., Masui, T., Matsuoka, Y., & Fujimori, S. (2011). Assessment of China’s climate
commitment and non-fossil energy plan towards 2020 using hybrid AIM/CGE model.
Energy Policy, 39 (5), 2875–2887.
Diakoulaki, D., & Mandaraka, M. (2007). Decomposition analysis for assessing the
progress in decoupling industrial growth from CO2 emissions in the EU manufacturing sector. Energy Economics, 29 , 636–664.
Duarte, M., & Restuccia, D. (2010). The role of the structural transformation in aggregate productivity. The Quarterly Journal of Economics, 125 (1), 129–173.
Fisher-Vanden, K., & Ho, M. S. (2007). How do market reforms affect China’s responsiveness to environmental policy? Journal of Development Economics, 82 (1), 200–233.
Fisher-Vanden, K., Jefferson, G. H., Liu, H., & Tao, Q. (2004). What is driving China’s
decline in energy intensity? Resource and Energy Economics, 26 , 77–97.
Garbaccio, R. F., Ho, M. S., & Jorgenson, D. W. (1999). Controlling carbon emissions in
China. Environment and Development Economics, 4 (4), 493–518.
Gardner, D. (1993). Industrial energy use in Ontario from 1962 to 1984. Energy Economics, 15 (1), 25–32.
26
Hübler, M. (2011). Technology diffusion under contraction and convergence: A CGE
analysis of China. Energy Economics, 33 (1), 131–142.
Kongsamut, P., Rebelo, S., & Xie, D. (2001). Beyond balanced growth. Review of Economic Studies, 68 (4), 869–882.
Kuznets, S. (1957). Quantitative aspects of the economic growth of nations: Ii. industrial
distribution of national product and labour force. Economic Development and Cultural
Change, 5 (4 (suppl.)), 1–112.
Liao, H., Fan, Y., & Wei, Y.-M. (2007). What induced China’s energy intensity to fluctuate: 1997-2006? Energy Policy, 35 , 4640–4649.
National Bureau of Statistics of China (2007). China Statistical Yearbook.
Ngai, L. R., & Pissarides, C. A. (2007). Structural change in a multisector model of
growth. American Economic Review , 97 (1), 429–443.
Popp, D. (2002). Induced innovation and energy prices. The American Economic Review ,
92 (1), 160–180.
Rose, A., & Chen, C. Y. (1991). Sources of change in energy use in the U.S. economy,
1972-1982: A structural decomposition analysis. Resources and Energy, 13 (1), 1–21.
Schipper, L., Howarth, R. B., & Geller, H. (1990). United States energy use from 1973 to
1987: the impacts of improved efficiency. Annual Review of Energy, 15 , 455–504.
Stern, N. (2007). The economics of climate change: the Stern review . Cambridge, U.K.:
Cambridge University Press.
Su, X., Zhou, W., Nakagami, K., Ren, H., & Mu, H. (2012). Capital stock-labor-energy
substitution and production efficiency study for china. Energy Economics, 34 (4),
1208–1213.
Tol, R. S. J. (2009). The economic effects of climate change. The Journal of Economic
Perspectives, 23 (2), 29–52.
Vennemo, H., Aunan, K., Jianwu, H., Tao, H., & Shantong, L. (2009). Benefits and costs
to China of three different climate treaties. Resource and Energy Economics, 31 (3),
139–160.
27
Wang, K., Wang, C., & Chen, J. (2009). Analysis of the economic impact of different
Chinese climate policy options based on a CGE model incorporating endogenous technological change. Energy Policy, 37 (8), 2930–2940.
Whalley, J., & Wigle, R. (1991). The international incidence of carbon taxes. In
R. Dornbusch, & J. M. Poterba (Eds.) Global Warming: Economic Policy Responses.
Cambridge, Massachusetts: MIT Press.
Wing, I. S. (2008). Explaining the declining energy intensity of the U.S. economy. Resource and Energy Economics, 30 , 21–49.
World Bank (n.d.). World development indicators. Retrived on May18, 2013 from http:
//data.worldbank.org/data-catalog/world-development-indicators.
Zhang, Z. (1998). Macro-economic and sectoral effects of carbon taxes: A general equilibrium analysis for China. Economic Systems Research, 10 (2), 135–159.
28