DYNAMIC MODELLING OF POLLUTION ABATEMENT IN THE CGE

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DYNAMIC MODELLING OF POLLUTION ABATEMENT IN A CGE
FRAMEWORK
Rob DELLINK, Marjan Hofkes, Ekko van Ierland and Harmen Verbruggen*
Environmental Economics and Natural Resources group
Wageningen University
Hollandseweg 1
6706 KN Wageningen, The Netherlands
tel. +31 317 482009
fax +31 317 484933
email Rob.Dellink@alg.shhk.wag-ur.nl
http://www.sls.wageningen-ur.nl/enr/staff/dellink/dellink.html
ABSTRACT
This paper deals with the specification of pollution abatement in dynamic Computable General
Equilibrium (CGE) models and analyses the dynamic feedback mechanisms between economic
variables and abatement in the context of environmental policy.
A small-open-economy model is presented, in which bottom-up technical and economic
information on abatement techniques is integrated in a top-down CGE-approach. The practical
suitability of the specification is illustrated in the empirical application focusing on climate
change and acidification. Finally, the sensitivity analysis focuses on the impact of the assumptions
underlying the specification of emissions and abatement.
The results show that the specification of the environmental issues is highly relevant for the
calculation of the economic costs of environmental policy. This holds especially for the
specification of climate change abatement options, since controlling the emissions of greenhouse
gasses leads to significant economic costs, which depend largely on the availability of
technological options for emission reduction.
JEL CLASSIFICATION
D58, O41, Q20
*
Rob Dellink and Ekko van Ierland work at Wageningen University (The Netherlands); Marjan Hofkes and
Harmen Verbruggen work at the Institute for Environmental Studies of Vrije Universiteit (The Netherlands).
KEYWORDS
Computable General Equilibrium models, pollution abatement, dynamics, tradable pollution
permits
2
1. INTRODUCTION
In order to make good estimations of the economic costs of environmental policy it is important
how the abatement costs, and of the underlying abatement technologies, are specified. On the one
hand, standard CGE models use smooth, continuous production and utility functions and do not
pay explicit attention to the characteristics of the abatement technologies involved. This is a
common critique by technically oriented scientists on these top-down economic models. On the
other hand, most models that include the technical aspects of changing economic structures do not
model the indirect economic effects of these technologies (i.e. they adopt a partial framework).
The large number of technological options available for pollution reduction complicates the use of
discrete technology modelling in CGE models.
In this paper a different methodology is presented, which combines the advantages of the topdown approach of CGE models with the information on abatement technologies included in the
bottom-up approach (for more details see Dellink, 2000).
The paper deals with different ways in which pollution abatement can be modelled in dynamic
computable general equilibrium (CGE) models. The CGE approach is chosen because it provides
a consistent framework to analyse the economic impacts of environmental policy: it has sound
micro-economic foundations and a complete description of the economy with both direct and
indirect effects of policy changes. There is a growing literature on dynamic CGE models for
environmental policy analysis, including e.g. Jorgenson and Wilcoxen (1990) and Böhringer (1998);
an overview of dynamic CGEs is given in Harrison et al. (2000).
The set-up of this paper is as follows. In Section 2, the main CGE model is described. Section 3
deals with the specification of abatement with an emphasis on the dynamic characteristics of the
abatement processes. Section 4 illustrates the model with a numerical example, analysing the
dynamic impacts of climate change and acidification policies on the Dutch economy. Section 5
concludes. The appendices contain all the model equations (Appendix A1) and a description of
the initial data (Appendix A2).
2. GENERAL DESCRIPTION OF THE MODEL
The model used in this paper is a dynamic computable general equilibrium (CGE) model with
perfect foresight in the Ramsey tradition1. A more detailed description of the basic model is given
in Dellink (2000), where this model specification is compared with other specifications of the
dynamic issues. Here, only a general description of the model is given, focusing on the
assumptions that are needed to build a multi-sectoral (dynamic) applied general equilibrium
1
The forward-looking model has the advantage over recursive-dynamic models that consumers maximise their
utility not only based on the current state of the economy, but also on future welfare (discounted to present
values). This intertemporal aspect lacks in a recursive-dynamic model. Empirical estimates suggest that
consumers in reality do look ahead to some extent, but do not maximise their utility till infinity (Srinivasan, 1982
and Ballard and Goulder, 1985). Intuitively, it is hard to imagine that none of the economic agents in the model
takes a long-term view for his or hers decisions (Solow, 1974).
3
model, including a specification of environmental pollution and abatement activities. The full set
of equations of the model is represented in Appendix A1.
Demand for and supply of produced goods and primary factors, which result from the agents’
optimisation problems, meet each other on the markets. Relative prices adjust such that an
equilibrium is reached simultaneously on all markets (both current and future markets).
Producers (firms) maximise profits under the restriction of their production technology, for given
prices. The nested-CES production function consists of the input of labour and capital and
intermediate deliveries from the other producing sectors. Each producer produces one unique
output from the inputs. As full competition and constant returns to scale are assumed, no excess
profits can be reaped and the maximum-profit-condition diminishes to a least-cost-condition.
The private households are included as the single representative consumer,. The private
households maximise the present value of current and future utility under a budget constraint, for
given prices and given initial endowments. They own the production factors labour and capital
(the endowments) and consume produced goods, for which a CES-type utility function is used.
The budget constraint is only applied to the present value of all periods together and not to
individual periods, so that intertemporal borrowing of funds is assumed possible 2. The annual
labour supply is fixed, but the wage rate is fully flexible; an exogenous growth of the labour
supply in efficiency units is assumed. This growth in the labour supply, which reflects both
increases in the population as well as increases in technological efficiency, drives the growth of
the economy.
In the current version of the model, there is no international trade. This implies that the rate of
return on investments is determined on the domestic market. The capital stock and investment
levels are fully endogenised; households choose to save part of their income until the rate of
return on investments equals the exogenously given interest rate. These savings are in turn used
by the producers as capital investments. The forward-looking behaviour of the agents and the
endogenous savings rate make this model of the Cass-Koopmans-Ramsey type Barro and Sala-iMartin (1995).
The government sector collects taxes on all traded goods (both produced goods and the primary
production factors) and uses the proceeds to finance public consumption of the two produced
goods and pay for a lump-sum transfer to the private household. Furthermore, the assumption is
made that public utility is unaffected by the model simulations, i.e. it stays at the level of the base
projection; this is achieved by proportionately changing the existing tax rates to mitigate changes
in income and/or expenditures of the government3.
Production processes lead to pollution, which is regarded as a necessary (environmental) input for
the production and utility functions. In the policy scenarios, pollution is controlled by the
government by means of annual tradable pollution permits, that the producers and consumers can
2
However, as consumption goods have to be produced, which leads to additional income from the sale of the
primary inputs, and there is not international trade, the income condition is satisfied for each period and
intertemporal borrowing of funds does not occur.
3
This implies that the government budget constraint holds for every period.
4
buy from the government (the proceeds are used to reduce existing taxes) 4. In this way, a market
for pollution permits is created, where, as in all markets in the model, prices are determined
endogenously by equating demand and supply. Polluters have the choice between paying for their
pollution permits or investing in pollution abatement. This choice is endogenous in the model, and
the polluters will always choose the least-cost of the two. A third possibility for producers and
consumers is a reduction of their production and consumption, respectively. This becomes a
sensible option when both the marginal abatement cost and the price of the permits are higher than
the value added foregone in reducing production or utility foregone in reducing consumption.
Environmental quality is not directly included in the utility function, because it is assumed that the
government sets the environmental targets by issuing a restricted number of pollution permits.
Consumers’ environmental expenditures (on pollution rights and abatement) do have an impact on
the maximum consumption and utility level achievable, but environmental stocks and damages
are not taken into account. In policy terms, the model is not used for Pigouvian analyses (Pigou,
1938), where the optimal tax rate is determined by the trade-off between abatement costs and
damage costs, but rather for Baumollian exercises where the cost-effective way to reach a
predetermined policy target is analysed (Baumol, 1977).
3. THE DYNAMIC BEHAVIOUR OF ABATEMENT
3.1. Introduction
As mentioned above, polluters have the choice between paying for pollution permits or paying for
abatement. The calibration of the possibilities and costs of abatement options is important to get a
good estimate of the economic costs of environmental policy. In most literature, the abatement
costs are only implicitly modelled (as profit or utility losses), or modelled through a quadratic
abatement cost curve (e.g. Nordhaus and Yang, 1996). Key exceptions are the detailed energyeconomic models (e.g. Manne et al., 1995) that specify alternative ways to produce energy (a form
of emission abatement). More general specifications of abatement are used by Nestor and Pasurka
(1995), Böhringer (1998) and Hyman (2001). A key feature of the model presented in this paper is
that the expenditures on abatement are specified to capture as much information as possible about
the technical measures underlying the abatement options.
3.2. The static trade-off between pollution and abatement
As a first step in including the technical abatement information in the model, abatement cost
curves have to be constructed for each environmental theme from the raw technical data for the
base year. This step involves making an inventory of all available abatement options (both end-ofpipe and process-integrated options), ranking the measures by cost-effectiveness and solving some
methodological and practical problems (including how to deal with measures that exclude each
other and measures that have to be taken in a fixed order). For details on this first step see Dellink
4
Practical difficulties may lead to a different choice of policy instrument in reality. Nonetheless, the approach
taken here is the cost-effective one and can therefore serve as a reference point for evaluating other policy
instruments.
5
and van der Woerd (1997) and De Boer (2000a,b). Note that the abatement cost curves contain all
known available options to reduce pollution, both end-of-pipe as well as process-integrated
options; amongst others Pasurka (2001) stresses the importance of process-integrated measures.
The abatement cost curves, which describe the marginal abatement costs, are translated for each
environmental theme into a ‘substitution curve’ of pollution and abatement. This means that the
abatement costs are presented as a function of pollution (a downward sloping curve). Then, for
each theme a CES function (the substitution curve) is calibrated to best fit the abatement/pollution
curve. The CES-elasticity thus estimated describes the environmental theme-specific possibilities
to substitute between pollution and abatement (hence the name substitution curve). The technical
potential to reduce pollution through abatement activities provides an absolute upper bound on
abatement in the model. This is a clear advantage over the traditional quadratic abatement cost
curves, where no true upper bound on abatement activities exists (the abatement costs will always
be finite, no matter how much pollution is abated). Dellink (2000) includes more details on this
procedure, that combines the advantages of the CGE approach with technical and economic
information on abatement techniques.
The trade-off between pollution and abatement in mathematical form looks as follows 5:
ESe, j ,t  CES ( EeU, j ,t , CES ( EeA, j ,t , Ae, j ,t ; eA, j );  eES, j ) for each (e,j,t), with  eES, j  0
(1)
where subscript e denotes the environmental theme, j the sector and t the time period. The formula
shows that the total of delivered ‘environmental services’ ( ES e , j ,t )are a nested CES-function. On
the highest level ‘unabatable’ emissions ( EeU, j ,t ) are combined with the aggregate of ‘abatable’
emissions ( EeA, j ,t ) and the expenditures on abatement ( Ae , j ,t ), with a substitution elasticity of zero
A
A
(  eES
, j  0 ). The lower level, CES ( Ee, j ,t , Ae, j ,t ;  e, j ) , brings together the abatable emissions and
expenditures on abatement with a substitution elasticity  eA, j . This latter substitution elasticity is
estimated using the procedure explained above; moreover, the division between abatable and
unabatable emissions is based on the technical potential (expressed as share of total emissions and
labelled eemax
,t ):
U
max
EeA, j ,t  eemax
,t  Ee, j ,t and Ee , j ,t  1  ee ,t   Ee , j ,t
(2)
Figure 1 illustrates the concept of the abatement cost curve and associated substitution curve.
Note that the x-axis gives pollution instead of pollution reduction. In the case of climate change,
emissions in the Netherlands can be reduced from 254 megatons of CO2-equivalents to 164
megatons CO2-equivalents (given the current state of technology) 6. Each mark on the abatement
5
To be precise, the trade-off is between expenditures on pollution rights and expenditures on abatement. A
similar formula applies to the environmental services for the households. The notation
CES ( x, y; xy ) is used
to denote a CES function with two inputs, x and y, that are combined using a substitution elasticity
 xy . See the
footnote in Appendix A1 for more details.
6
The graph and underlying data are based on analysis for 1990 and described in Verbruggen et al. (2001).
6
cost curve gives an individual technical measure; the line without markers shows the estimated
substitution curve.
Figure 1. A substitution curve for greenhouse gasses
4000
Technical potential
Current
emissions
Emission reduction costs
(annual; mln guilders)
3500
3000
2500
2000
1500
1000
Abatement
cost curve
500
Substitution
curve
0
0
50
100
150
200
250
300
emissions (Mtons CO2-equivalents)
Note that in the construction of the abatement cost curves, all costs are transformed into annual
costs, including the capital costs (annuity interest and depreciation payments) of the investments.
In the model, these capital costs of abatement investments are treated similar to ‘conventional’
man-made capital, i.e. the firms pay the capital costs while the households provide the means
necessary for investments (in the form of savings). This means that the order in which the
measures are represented in the abatement cost curve is appropriate to the way the firms decide
upon adoption of a measure. For sake of convenience, the ratio between investment costs and
operational costs are assumed constant over all measures.
3.3. Development of abatement costs over time
When moving from period t to period t+1, several effects take place that have an impact on the
abatement cost curves and especially on the technical potential for emission reduction ( eemax
,t ) and
the curvature of the curve (in model terms, the substitution elasticity  eA, j ).
The first effect that takes place is that some abatement measures are adopted by the polluters
(diffusion of this abatement technology)7. At first glance, this would lead to a reduction of the
technical potential and an increase in average abatement costs (since the least-cost options will be
7
Partial adoption (or diffusion) of a technology is a partial implementation of a measure and leads to a
contraction of the respective point on the curve, with constant cost-effectiveness. Assuming an identical
abatement function for all polluters means that first the most cost-effective measure will be fully taken before the
next measure is partially implemented. The treatment of the abatement cost curve as a continuous function,
instead of as a stepwise function with discrete choices (take the measure or not) implies that partial
implementation of the measure in the economy (partial diffusion) is assumed possible.
7
implemented first). However, what is modelled in the substitution curve is the annual abatement
costs. A polluter has to pay the costs of the same measure each year again; in other words,
adopting a measure in year t does not automatically imply adoption of the same measure in year
t+1: this implies that in the present specification the decision is reversible. Consequently, the
substitution curve does not change due to this effect, as all adopted measures are present again in
A
the following year. The technical potential eemax
,t , the substitution elasticity  e , j and the benchmark
price of abatement PA all remain constant over time.
The second effect is a reduction of the (marginal) costs of all existing measures, presumable at a
higher rate than can be based on labour productivity developments (i.e. labour augmenting
technological change plus other technological progress, like learning effects). This reduction in
abatement costs can be explicitly modelled in the model as a reduction in the price of abatement
coupled with an efficiency improvement in the abatement production process. This effect has no
impact on the technical potential, but might lead to a (small) decrease of the substitution elasticity.
The third effect is that new abatement measures will emerge through innovation (path-dependent,
small innovations are part of the second effect). Though these new measures are presumably more
efficient than existing measures, they are likely to be far from the adoption phase. Hence the
substitution curve will be extended to above and to the left, thereby increasing the technical
potential. The effect of these new measures on the substitution elasticity cannot be predicted
beforehand, but is likely to be very small. Consequently, a constant substitution elasticity may be
assumed.
The fourth effect is that old techniques that are obsolete and have never been implemented are
removed from the curve. This effect counters the third effect, but is likely to be smaller in size.
In the base specification, the technical potential and substitution elasticity are assumed constant
over time and the exogenous efficiency improvements in the abatement sector absent. However,
as a sensitivity analysis, the increase in the technical potential is modelled through a linear growth
function: every period the technical potential grows with g  . A decreasing price of abatement is
captured through exogenous efficiency improvements in the abatement sector ( abeiA,t ), coupled
with decreasing associated prices. It is not unlikely that efficiency improvements in the abatement
sector will not lead to a decrease in the use of inputs, but rather to a decrease in output prices. For
example, increased fuel efficiency in cars has not lead to decreases in fuel use, but rather to larger
cars.
Finally, it should be recalled that the model also contains exogenous technological progress in
environmental efficiency, governed by an autonomous pollution efficiency improvements
( apeie ,t ); this effect is present in both the base specification and the sensitivity analysis.
3.4. The base specification of the abatement sector
In the base specification, abatement is modelled as a separate producer, where ‘abatement goods’
are produced using both produced goods and primary production factors as inputs. This is roughly
in line with Nestor and Pasurka (1995), but there the abatement sector is an implicit part of the
government sector, and hence does not have a specific structure. In the model presented here, a
8
CES production function is calibrated, for which the data are derived from substitution curves: the
inputs in this production function represent the ‘spending effects’ of implementing technical
measures8. It is assumed that these spending effects are homogenous over the complete abatement
cost curve and do not differ between the environmental themes. The model thus includes one
producer (the abatement sector) to represent the abatement activities.
The output of the abatement sector is demanded by the other producers and by consumers, so each
producer and consumer in principle has the same set of abatement technologies available. Each
can, however, have different substitution possibilities between investing in abatement and buying
pollution permits, as they have different initial combinations of abatement costs and pollution
levels and hence start on different points on the curve. Consequently, the costs of abatement will
differ between the producers. The marginal abatement costs will be equalised in the model, as the
resulting equilibrium is characterised by cost-effectiveness. These marginal abatement costs in the
new equilibrium will also equal the price of the pollution permits. Hence, all polluters are
indifferent at the margin between polluting and investing in abatement. The equations for the base
model are represented in Appendix A1.
The model as described above assumes that expenditures on pollution abatement are reversible
over time (see above). In other words, abatement is modelled as a flow variable, i.e. as a nondurable good, and decisions on abatement expenditures are short-term decisions. However, as
capital is needed for production of the abatement goods, the choice of the abatement level is not
entirely reversible (though the capital employed in the abatement sector can be transferred without
costs to other sectors in the economy).
From theory it follows that the price of the abatement goods equal the marginal abatement costs.
In the bottom-up technical description of the abatement measures, annual costs consist of capital
costs, that is the interest and depreciation costs associated with investments, and net operational
costs. Marginal abatement costs are changing over time. Since the abatement sector is a
production sector like the other production sectors, the production costs of abatement goods are
influenced by the general development of labour productivity9. For example, as real labour costs
decrease over time, so do the production costs of abatement. Consequently, if the production
process of abatement is relatively labour-intensive the relative costs of abatement in comparison
to other goods will decrease. Reversibly, if abatement is labour-extensive, the relative costs of
abatement will increase over time10. Not only labour costs, but also the prices of all goods that are
input to the abatement sector will influence the real abatement costs.
8
These spending effects are the increase in the demand for produced goods and primary factors by the abatement
sector.
9
In the model, increases in labour productivity are modelled through an increase in the supply of labour,
measured in efficiency units (i.e. not in number of people). Mathematically, this is equivalent.
10
Empirical data suggest that in the Netherlands abatement is more labour-intensive than the other produced
goods (labour makes up a little less than 50% of abatement costs; Dellink, 2000), and hence real abatement costs
are decreasing over time.
9
4. EMPIRICAL APPLICATION OF THE MODEL
4.1. Introduction
The model specification described above is applied in this section in a numerical example, based
on data for the Netherlands, with 1990 as the base year. Data sources are the national accounts
(Statistics Netherlands, 2001) and environmental data provided by RIVM (2000). GDP is
calibrated to 578 billion guilders and abatement expenditures amount to 360 million guilders
(excluding expenditures on waste management, which are assumed to be part of the services
sector). The full set of data as used in calibrating the model for 1990 is given in Appendix A2. In
interpreting the results one should keep in mind that the description of the economy is kept
simple, with only 3 production sectors and no international trade.11
The benchmark projection
The benchmark projection (the simulation of the model without the environmental policy impulse)
consists of an (autonomous) increase in labour productivity of 2% per year. This leads to a
balanced growth of the economy of 2% per annum. There is an autonomous pollution efficiency
improvement of 1% per year for acidifying emissions and 1.5% for greenhouse gas emissions,
resulting in a growth of emissions of 1% and 0.5%, respectively, per year (values based on
Verbruggen et al., 2001).
All producers have a CES production function for intermediate deliveries and primary factors
with an elasticity of substitution of 0.5. The substitution elasticity between abatement and
pollution is set to 1.26 for climate and 1.4 for acid related emissions respectively (this value is
based on Verbruggen et al., 2001)12. Investments are made up of agricultural and industrial goods
and services in a ratio of 1:83:16. Private consumers have a utility function with a CES elasticity
of 0.5; the corresponding elasticity for the government is set at 0 (Leontief’ utility function). The
intertemporal rate of substitution of consumption is set at 0.75 (only applicable to the private
households). The depreciation rate is set at 5 percent and the interest rate at 4 percent.
The policy impulse
Environmental policy aims at stabilisation of emissions at the 1990-level. As the emissions are
rising in the benchmark projection, the stabilisation policy leads to increasingly large differences
between the number of permits issued and the reference emissions (which can be interpreted as
the base demand for the permits). Figure 2 shows how the issued number of permits deviates from
the benchmark projection13.
11
Though these simplifications make the model results more tractable, the confidence to be placed on the
numerical outcomes is limited. A full empirical analysis is beyond the scope of the current paper.
12
Note that the high APEI, high price, low elasticity and low technical potential for climate change reflects an
abatement curve with a relatively long initial part of very low costs, combined with a steep increase in marginal
abatement costs further in the curve. For acidification, the marginal abatement costs increase more gradually.
13
All results shown in this paper are relative changes compared to the benchmark projection values.
10
2050
2045
2040
2035
2030
2025
2020
2015
2010
2005
2000
1995
1990
Figure 2. Effects of environmental policy on emissions for climate change and acidification
%-change compared to benchmark
0%
-5%
-10%
-15%
-20%
-25%
-30%
-35%
-40%
-45%
-50%
Climate change
Acidification
4.2. Results for the policy scenario using the base specification
It is expected that the environmental policy as discussed above will lead to increasing
expenditures on abatement and a small reduction in GDP. Figure 3 shows the development of the
demand for abatement goods over time. Even though in the base model the decision to adopt
abatement measures is reversible, this does not imply that the substitution possibilities are infinite.
First, there is a finite substitution elasticity between pollution and abatement; and second, there is
a capital input in the abatement production function. This prevents a situation where extremely
large fluctuations in the demand for abatement occurs.
The results confirm that the demand for abatement goods is relatively stable over time. For all
polluting sectors, the demand for abatement increases rapidly and even at an increasing rate. The
increasing rate at which the demand for abatement grows cannot be directly explained by the
development in pollution levels (compare Figure 3 with Figure 2). The more than proportionate
increase of abatement over time can be attributed to the decreasing unit abatement costs over time
(caused by the increases in labour productivity). Abatement expenditures increase by a factor 10
as compared to the benchmark projection in 2050.
11
Figure 3. Effects of environmental policy on the sectoral demand for abatement goods
%-change compared to benchmark
1100%
1000%
900%
800%
700%
600%
500%
400%
300%
200%
100%
Agriculture
Industry
Services
2050
2045
2040
2035
2030
2025
2020
2015
2010
2005
2000
1995
1990
0%
Private households
The reduction in abatable emissions is substantial; in the later period, up to two-thirds of the
abatable emissions are abated (see the left panel in Figure 4). For the unabatable emissions, the
reduction is of course much smaller; it is slightly larger than the reduction in GDP (see the right
panel in Figure 4). This clearly shows the shift in the economy from relatively dirty production to
cleaner sectors. Note that though the development of both abatable and unabatable emissions are
very similar for climate change and acidification, the share of abatable emissions in total
emissions is smaller for climate change. Consequently, the reduction in total emissions is much
smaller for climate change than for acidification (see also Figure 2). The reduction in unabatable
emissions also shows that the marginal costs of abatement are becoming so high at higher rates of
abatement that it becomes cheaper to reduce economic activity.
Figure 4. Development of abatable and unabatable emissions
0%
-10%
-20%
-30%
-40%
-50%
-60%
-70%
-80%
C l i m a te c h a n g e
2050
2045
2040
2035
2030
0 .0 %
- 0 .5 %
- 1 .0 %
- 1 .5 %
- 2 .0 %
- 2 .5 %
- 3 .0 %
C l i m a te c h a n g e
A c i d i fi c a ti o n
2025
2020
2015
2010
2005
2000
1995
1990
2050
2045
2040
2035
2030
2025
2020
2015
2010
2005
2000
1995
U n a b a ta b le e m is s io n s
%-change com pared to benchm ark
%-change com par e d to be nchm ar k
1990
Ab a ta b le e m is s io n s
A c i d i fi c a ti o n
Given the limited size of the abatement sector in the benchmark, the effects on the rest of the
economy are expected to be limited. Table 1 shows that this is indeed the case in the short run, but
12
in the longer run the negative impact on GDP is above one percent. Apparently, the (indirect)
positive impact of the increased abatement expenditures is too small to fully mitigate the negative
direct impact of the environmental policy. Note that the long run decrease of GDP of between 1
and 2 percent is still moderate given the large decreases in emission levels. For example Tol
(1997) shows that the world average estimate of GDP-loss of stabilising CO2 emissions in 2010 is
0.4%.
In 2050, the agricultural sector is most negatively affected by the environmental policy, primarily
due to the significantly decreasing consumption of agricultural goods (see Table 1 below)14. The
agricultural sector is relatively worse off on the one hand due to the relatively high pollution
intensities in this sector, and on the other hand due to the absence of the positive indirect effect of
higher demand for products by the abatement sector. The least hurt by the environmental policy is
the relatively clean and profitable services sector, though the general slowdown of the economy
also generates a negative net impact on this sector from 2010 onwards.
Table 1. Changes in main variables in the non-durable good case
(%-change
in
volumes
compared
to
1990
2000
2010
2025
2050
0.00%
-0.11%
-0.24%
-0.56%
-1.64%
-0.22%
-0.58%
-1.03%
-2.16%
-6.81%
Private consumption of Industrial goods
0.05%
-0.13%
-0.32%
-0.78%
-2.95%
Private consumption of Services
0.20%
0.13%
0.10%
Sectoral production Agriculture
-0.17%
-0.37%
-0.65%
-1.34%
-3.77%
Sectoral production Industry
-0.14%
-0.28%
-0.47%
-0.95%
-2.33%
Sectoral production Services
0.10%
benchmark)
GDP
Private consumption of Agricultural goods
0.03% -0.03%
-0.77%
0.06% -0.33%
-0.13% -0.60%
Capital investment
-0.31%
-0.49%
-1.52%
-3.38%
Abatement expenditures
-0.33%
42.14% 107.37% 274.39% 922.06%
Greenhouse gas emissions
0.00%
-4.86%
-9.49% -16.02% -25.87%
Acidifying emissions
0.00%
-9.47% -18.05% -29.41% -44.96%
Capital investments drop in the first period to allow the households to have a higher level of
consumption in the first period. This has a large positive impact on utility, while the resulting
lower consumption levels in later periods (as the lower investments slowdown economic growth)
have less impact on utility in present values, given the positive discount factor. The consumers
foresee that they will be confronted with increasingly strict environmental policy and choose to
adapt to that by slowing down the rate of economic growth and increasing current consumption.
14
The income elasticities of all goods are implicitly assumed to be equal to one, given the CES-structure of the
utility function. This may be changed by introducing a Linear Expenditure System. Such an extension of the
model is expected to have only a minor effect on the general outcomes of the model.
13
The impact of the environmental policy on the development of GDP, the income of private
households and investments is shown graphically in Figure 5. Over time, the gap between the
policy-GDP and the benchmark projection gets larger and larger. This mirrors the strictness of
environmental policy, at least in qualitative terms. The impacts on GDP are relatively small, so
that in absolute terms GDP keeps growing even with stabilisation of emissions. In other words, a
decoupling between economic growth and environmental pressure related to climate change and
acidification is achievable.
2050
2045
2040
2035
2030
2025
2020
2015
2010
2005
2000
1995
1990
Figure 5. Impact of environmental policy on GDP and private household income
%-change compared to benchmark
0.5%
0.0%
-0.5%
-1.0%
-1.5%
-2.0%
-2.5%
-3.0%
-3.5%
-4.0%
GDP
Income Private Households
Investment
4.3. Results of sensitivity analysis
4.3.1. Exogenous developments in abatement technology
In this first sensitivity analysis, the technical potential for emission reduction techniques increases
with 1 percent-point every eight years (i.e. g  ,e equals 0.00125). Consequently, the share of
abatable greenhouse gas emissions is 41% in 1990 and slowly increases to 48.5% in 2050.
This increase in the technical potential is combined with increasing efficiency in the abatement
sector. An autonomous abatement efficiency improvement parameter ( abeiA,t ) of 1% per year is
introduced, leading to decreasing abatement costs and a decreasing output price of the abatement
sector.
14
Table 2. Main results of sensitivity analysis on abatement technology
alternative specifications
base incl. abatement
(volumes;
bln.
only technical
only efficiency
technology potential effect
effect
benchmark
specification
0
-0.76%
-0.61%
-0.61%
-0.76%
GDP 1990
578
578
578
578
578
GDP 2020
1047
1043
1043
1043
1043
GDP 2050
1897
1866
1871
1871
1866
Abatement 1990
0.36
0.36
0.36
0.36
0.36
Abatement 2020
0.65
2.00
2.63
1.96
2.68
Abatement 2050
1.18
12.07
18.85
10.50
21.68
15
NLG )
Equivalent Variation
Table 2 shows the outcomes of this change in model specification for the equivalent variation,
GDP and abatement expenditures. The different columns give the benchmark projection, the result
for the base specification and the results of the sensitivity analysis on abatement technology.
These alternative specifications are split into three parts: (i) including the increase in the technical
potential over time, combined with increasing abatement efficiency; (ii) only the increase in
technical potential; and (iii) only the increase in abatement efficiency. For the details of these
alternative specifications see Section 3.3. above.
The most striking result is an increase in abatement activity: in 2050, the increase in abatement is
almost 1500 percent or an absolute level of 18.85 billion NLG, as shown in Table 2. In the base
specification, the increase is 922 percent, leading to abatement expenditures of 12.07 billion NLG.
This increase is in line with expectations, as both the increasing technical potential and the
increased abatement efficiency lead to lower abatement costs relative to the price of the emission
permits.
The abatement efficiency improvement leads purely to a lower price of abatement, which is offset
by an increase in the abatement volume, so that total expenditures on abatement remain constant.
Consequently, there is no impact of the abatement efficiency improvement on the rest of the
economy.
The increase in the technical potential does have an impact on the rest of the economy, as it
allows for more abatement and less emission reduction through economic restructuring. The
perverse situation arises that the larger technical potential leads to a smaller increase in abatement
than in the base specification. This can be explained by the fact that a larger share of abatable
emissions means that the marginal abatement costs are lower. In other words, the starting point for
substitution between abatable emissions and abatement shifts towards relatively more emissions
and less abatement. Given the constant elasticity of substitution, this implies lower abatement
costs.
15
NLG stands for Dutch guilders; 1 NLG = 0.45378 Euro.
15
4.3.2. Changing emission-abatement substitution elasticity
Another assumption that is clearly relevant for the outcomes is the substitution elasticity between
abatable emissions and abatement. In the base specification, this elasticity is calibrated to 1.26 for
climate change and 1.41 for acidification, and assumed constant over time. The results of three
sensitivity analyses are presented in Table 3. In the third column, both elasticities are decreasing
with 0.01 per decade (so after 60 years they are 1.2 and 1.35, respectively). In the fourth column,
they are assumed to be increasing at the same speed (and consequently in 2050 they equal 1.32
and 1.47, respectively). In the last column, the increase in this elasticity is assumed to apply only
to climate change. This latter sensitivity analysis is added to show to what extent climate change
causes the changes in the model results. The expected outcome is that a lower elasticity leads to a
more negative economic impact, as marginal abatement costs are increasing more rapidly.
Table 3. Main results of sensitivity analysis on emission-abatement substitution elasticity
alternative specifications
base lower elasticity higher elasticity higher elasticity
(volumes;
bln.
benchmark
specification
NLG)
Equivalent Variation
for both
for both
climate ch.
themes
themes
only
0
-0.76%
-0.96%
-0.64%
-0.64%
GDP 1990
578
578
578
578
578
GDP 2020
1047
1043
1042
1043
1043
GDP 2050
1897
1866
1859
1870
1870
Abatement 1990
0.36
0.36
0.36
0.36
0.36
Abatement 2020
0.65
2.00
2.04
1.97
1.97
Abatement 2050
1.18
12.07
13.75
10.75
10.78
The results shown in Table 3 confirm the expectations: a lower substitution elasticity between
abatable emissions and abatement causes lower levels of GDP and consumption (and hence EV)
in the long run. The abatement levels are higher, but not dramatically. The polluters are
confronted with higher abatement cots than in the base specification, but they have no real
alternative, as the costs of reducing unabatable emissions through a reduction of output are also
very costly.
For larger assumed substitution possibilities between abatable emissions and abatement the effects
are opposite. Emissions are more easily reduced by abatement, as is reflected by the lower price of
permits, and hence the economic costs of environmental policy are lower. But again, the impact is
only small, especially in the earlier periods.
As can be seen in the last column, the differences with the results of the base specification are
completely due to the environmental theme of climate change. Clearly, the specification of
substitution elasticity for climate change is relevant for the model outcomes, but the elasticity for
acidification is not. This shows that climate change is the binding environmental theme, and that
the influence of acidification is much smaller. This is not surprising, given the differences in the
16
abatement cost curves: the reduction possibilities for acidifying emissions are more favourable
(compare the technical potential, initial permit price and substitution elasticity for both themes).
4.3.3. Changes in autonomous pollution efficiency improvements
The final sensitivity analysis carried out is on the specification of the autonomous pollution
efficiency parameter. In the base specification, emissions grow at a slower speed than economic
production, due to increasing efficiency in the use of environmental resources; in terms of
emissions this means that the emissions associated with one unit of production or consumption
decrease over time.
Table 4. Main results of sensitivity analysis on pollution efficiency improvements
alternative specifications
base lower efficiency
(volumes;
bln.
benchmark
specification
NLG)
higher
higher
for both
efficiency for
efficiency
themes
both themes
climate ch.
only
Equivalent Variation
0
-0.76%
-6.25%
-0.03%
-0.06%
GDP 1990
578
578
578
578
578
GDP 2020
1047
1043
1028
1046
1046
GDP 2050
1897
1866
1633
1894
1894
Abatement 1990
0.36
0.36
0.36
0.36
0.36
Abatement 2020
0.65
2.00
6.14
0.74
0.85
Abatement 2050
1.18
12.07
47.43
1.55
2.12
As a sensitivity analysis, the autonomous pollution efficiency parameter is lowered and increased
with 0.5 percent-points per year. Table 4 shows how important this parameter is in the long run. If
emissions follow economic growth more closely, the required emission reduction to achieve the
environmental policy target increase. More emissions have to be abated, both abatable and
unabatable. Abatement levels are much higher, and GDP is much lower, not in the last place
because of the high price of pollution permits. The equivalent variation, which indicates the
development of consumption over time, goes from –0.76% in the base specification to –6.25% if
pollution efficiency improvements are smaller.
The sensitivity analysis with higher pollution efficiency effectively removes the environmental
policy for climate change: the benchmark emissions of greenhouse gasses are constant over time
and hence no further reductions are required to keep to the policy target. For acidification still
some emission reductions are required. Consequently, there are still some economic costs from
environmental policy and there is still some abatement, but much less than in the base
specification. The price of climate change permits does not drop to zero, as the number of permits
is still restricted; the price of these permits are however roughly comparable to the price in the
benchmark and much lower than in the base specification.
17
Comparing the last two columns shows that the economic costs of the acidification policy are
small at either rate of pollution efficiency improvements. Again, the results show that climate
change is the dominant environmental theme.
5. CONCLUDING REMARKS
This paper shows how important characteristics of pollution abatement can be captured in a CGE
framework. The extended calibration of the abatement possibilities is important, as it has
significant effects on the estimation of the (sectoral) economic costs of environmental policies.
When environmental policy remains limited in size, there are cheap abatement options available,
and the effect on the rest of the economy is minor. However, the more strict environmental policy
becomes, the more significant it is to get the best possible representation of abatement
possibilities. The macro-economic impacts of high marginal abatement costs can be significant.
The sensitivity analysis shows that the specification of environmental issues is highly relevant for
climate change, as this is the binding environmental theme, but not so much for acidification.
Increasing abatement efficiency will have an impact on the abatement levels and price, but not on
the rest of the economy. Changes in the technical potential for emission reduction are however
relevant for the economic impacts of environmental policy, but do not influence abatement levels
as much.
It should be noted that many improvements to the model can be made, both in the specification of
the model and in the calibration for empirical analysis. One major issue to be investigated in more
detail is the possibility to capture endogenous technology. Clearly, price induced technological
change is of the highest importance when one wants to specify pollution abatement as realistic as
possible16. The durable goods specification of abatement as presented in this paper provides
endogenous balancing of investments in abatement capital and other capital and thus captures
price-induced technological progress in a rudimentary way. However, it is beyond the scope of the
current paper to capture these issues in all detail.
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16
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18
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19
APPENDIX A1. SPECIFICATION OF THE RELEVANT EQUATIONS FOR THE BASE
MODEL
Producers
Goods production functions:
Yj ,t  CES (Y1,IDj ,t ,..., YJID, j ,t , K j ,t , L j ,t , ES1, j ,t ,..., ESE , j ,t ; 1j ,...,  Vj ) for each (j,t)17
(1)
Zero profit conditions:
0   j ,t 
J
p j ,t  Y j ,t   (1   jj , j )  p jj ,t  Y jjID, j ,t  (1   A, j )  pA,t  YAID, j ,t
jj 1
for each (j,t)
(2)
ESe, jh,t  CES ( EeU, jh,t , CES ( EeA, jh,t , Ae, jh,t ; eA, jh ); eES, jh ) for each (e,jh,t), with  eES, jh  0
(3)
E
(1   L , j )  pL ,t  L j ,t  (1   K , j )  rK ,t  K j ,t   pe ,t  Ee , j ,t
e 1
Environmental services ‘production’ functions:
Other environmental equations
E
Y j ,t 1   (1  apeie,t 1 )   EeA, j ,t Y j ,t  for each (e,j,t)
(4)
E
Y j ,t 1   (1  apeie,t 1 )   EeU, j ,t Y j ,t  for each (e,j,t)
(5)
E
Wh ,t 1   (1  apeie,t 1 )   EeA,h ,t Wh ,t  for each (e,h,t)
(6)
E
Wh ,t 1   (1  apeie,t 1 )   EeU,h ,t Wh ,t  for each (e,h,t)
(7)
A
e , j ,t 1
U
e , j ,t 1
A
e , h ,t 1
U
e , h ,t 1
In the benchmark projection the division of abatable and unabatable emissions is given by 18:
EeA, jh ,t
17
E
A
e , jh ,t
 EeU, jh,t   e, jh,t for each (e,jh,t)
(8)
As usual, ‘…’ is used to indicate all items within the range as given by the items listed before and after.
A general nested CES production function with for example 4 inputs and 2 levels can be written as:
Y = (a1X1+ a2X2+ a34X34)1/ , and X34 = (a3X3+ a4X4)1/ for some parameters a1, a2, a34, a3, a4, where
=(-1)/ and =(-1)/. A convenient notation is: Y = CES(X1, X2, X34; ); X34 = CES(X3, X4; ).
18
Note that this division of emissions may be different in the policy simulations, as both parts are endogenously
determined in the model.
20
Consumers
Utility functions:
Wh,t  CES (C1,h,t ,..., CJ ,h,t , ES1,h,t ,..., ESE ,h,t ;  h1 ,...,  hV ) for each (h,t)
U h  CES (Wh,1 ,...,Wh,T ; hUtil ) for each h
(9)
(10)
Income balances – expenditures side:
J
E
j 1
e 1
phW,t Wh,t   (1   j ,h t )  p j ,t  C j ,h,t  pA,t  Ae,h,t   pe,t  Ee,h,t for each (h,t)
(11)
Income balances – income side:
T
 phW,t Wh,t  pK ,T  K h,T  (1   K ,h t )  pK ,1 
t 1
T
K h ,1
(r   )
E
T
  pe,t  Ee ,h ,t   
t 1 e 1
t 1
LS
h
T
  (1   L ,h   t )  pL ,t  Lh,t
t 1

T
LS
t
for each h
  TRh ,t
t 1
(12)
Capital accumulation (as the volume of capital is free, the equation is written for the associated
prices):
pK ,t  (1   K ) pK ,t 1  rK ,t for each t
(13)
Terminal condition on capital (transversality condition):
H
K
h 1
H
h ,T
 (1  g L )   K h ,T 1
(14)
h 1
Demographic developments:
Lh,t 1  Lh,t  (1  gL ) for each (h,t)
(15)
Rule for development in government expenditures:
W' govt ',t  W' govt ',t determines  t and  tLS
(16)
Market clearance
Goods markets balance:
J
H
jj 1
h 1
ID
Y j ,t  Y jID
, jj , t  Y j , A, t  I j , t   C j , h , t for each (j,t); determines p j ,t
(17)
Capital markets balance:
J
H
j 1
h 1
 K j ,t  K A,t   Kh,t for each t; determines rK ,t
(18)
Labour markets balance:
J
H
j 1
h 1
 L j ,t  LA,t   Lh,t for each t; determines p L,t
21
(19)
Pollution permits markets balance:
JH
JH
H
jh 1
jh 1
h 1
 EeU, jh,t   EeA, jh,t  EeU, A,t  EeA, A,t   Ee,h,t for each (e,t)
(20)
determines p e ,t .
Savings/investments balance:
H
S
h 1
J
h ,t
  p j ,t  I j ,t for each t
(21)
j 1
Indices
Label
Entries
Description
j and jj
1,…,J,A
Production sectors, including Abatement sector (A)
j={Agriculture, Industry, Services, Abatement sector}
h
1,…,H
Consumer groups
h={Private households, Government}
jh
(JxH)
Combination of production sectors and households
e
1,…,E
Environmental themes
e={Climate change, Acidification}
vJ
1,…,VJ
‘CES-knots’ in production functions
vJ={Economic inputs, Environmental inputs, Production}
vH
1,…,VH
‘CES-knots’ in utility functions
vH={Goods, Environmental inputs, Consumption}
t
1,…,T
Time periods
t={1998,1999,…,2030}
Parameters
Symbol
Description
gL
Exogenous growth rate of labour supply
apeie ,t
Autonomous pollution efficiency improvement; assumed equal across all agents
e, jh,t
Benchmark share of abatable emissions in total emissions for environmental
theme e by production sector j / consumer h in period t
K
Depreciation rate
r
Steady-state interest rate
IS
Benchmark level investments (calibrated to steady-state)
KS
Benchmark level capital stock (calibrated to steady-state)
Lh,t
Exogenous labour supply by consumer h in period t
Ee,h,t
Endowments of pollution permits for environmental theme e by consumer h in
period t
22
Symbol
Description
W' govt ',t
Benchmark size of government sector in period t
j
Input share of good j for investments (by origin)
K, j
Tax rate on capital demand by sector j
 L, j
Tax rate on labour demand by sector j
 jj, j
Tax rate on input of good jj by sector j
 j, h
Tax rate on consumption of good j by consumer h
 K ,h
Tax rate on the supply of capital by consumer h
 L, h
Tax rate on the supply of labour by consumer h
 hLS
Lumpsum transfer from government to consumer h,
H
with
  hLS  0 and
h 1
H

h 1
LS
h
  tLS  0
 SUB
Lumpsum transfer from (excess) private households to the subsistence consumer
 vj
Substitution elasticities between inputs combined in knot vJ in production function
for sector j
 e,A j
Substitution elasticities between pollution and abatement for environmental theme
e in production function for sector j
 hv
Substitution elasticities between consumption goods combined in knot vH in utility
function for consumer h (within same time period)
 e,Ah
Substitution elasticities between pollution and abatement for environmental theme
e in utility function for consumer h
 hUtil
Intertemporal substitution elasticities in utility function for consumer h (between
time periods)
Variables
Symbol
Description
Y j ,t
Production quantity of sector j in period t
Y jjID, j ,t
Demand for input jj by sector j in period t
L j ,t
Labour demand by sector j in period t
K j ,t
Capital demand by sector j in period t
I j ,t
Investment originating in sector j in period t
I h ,t
Investment by consumer h in period t
 j,t
(Net) profits in sector j in period t (equal to zero)
23
Symbol
Description
EeU, jh,t
‘Unabatable’ emissions of environmental theme e by sector j / consumer h in period t
EeA, jh,t
‘Abatable’ emissions of environmental theme e by sector j / consumer h in period t
Ae, jh,t
Expenditures on abatement of environmental theme e by sector j / consumer h in
period t
E
{note that
 Ae, j ,t  YAID, j ,t and
e 1
E
A
e 1
e , h ,t
 C A , h ,t }
ESe, jh,t
Emission services of environmental theme e by sector j / consumer h in period t
Wh , t
Welfare level of consumer h in period t
Uh
Total welfare of consumer h over all periods
C j , h ,t
Consumption of good j by consumer h in period t
Sh,t
Savings by consumer h in period t
K h ,t
Capital supply by consumer h in period t (in ‘flow’ terms: capital services)
p j ,t
Equilibrium market price of good j (including A) in period t
rK , t
Equilibrium market rental price of capital in period t
pL ,t
Equilibrium market wage rate in period t
pe ,t
Equilibrium market price of pollution permits for environmental theme e in period t
p hW,t
Equilibrium price of the ‘utility good’ (consumption bundle)
t
Endogenous change in existing tax rates to offset government income from sale of
pollution permits in period t
 tLS
Endogenous change in lumpsum transfers to offset government income from sale of
pollution permits in period t
TRh ,t
Endogenous tax revenues for consumer h in period t (only nonzero for Government)
24
APPENDIX A2. DATA FOR THE BASE MODEL
Table SAM(*,*) Benchmark accounting matrix (billion NLG)
Agri.
Indu.
Serv.
Abat. Priv.hh.
Agri.
51.08
-32
-1
0
-18.08
Indu.
-12
273.14
-67
-0.09 -194.05
Serv.
-5
-45
415.98
-0.07 -315.91
Abat.
-0.08
-0.14
-0.09
0.36
-0.05
Labour
-8
-99
-176
-0.09
283.09
Capital
-23
-74 -127.89
-0.11
225
lab.tax
-1.5
-18
-35
0
0
cap.tax
-1.5
-5
-9
0
0
Lumpsum
0
0
0
0
20
Rowsum
0
0
0
0
0
Table Y_DATA(*,J) Producer data
Agri.
Indu.
Substit. elast.
0.5
0.5
Climate emis.
0.17
0.44
Acid emis.
0.43
0.26
Serv.
0.5
0.25
0.22
Govt
0
0
-50
0
0
0
54.5
15.5
-20
0
colsum
0
0
0
0
0
0
0
0
0
0
Abat.
0.5
0
0
Table HH_DATA(*,H) Household data
Priv.hh.
Govt
Savings
1
0
Substit. elast.
0.5
0
Intertemp. elast.
0.75
0
Climate emis.
0.14
0
Acid emis.
0.09
0
Table E_DATA(*,E) Environmental data
Climate
Acid
Substit. elast.
1.26
1.4
Price
1.89
0.32
APEI
0.015
0.01
Abatable share
0.41
0.66
Tot. emis.
254
40
Note that the column in SAM for the consumers contains not just the consumption expenditures,
but also the investments. Investments are calculated as Invsh j  I 0 , where I 0  ( g   )  K0 , and
multiplied by Savshh for distribution over the consumers. Consumption expenditures can then be
calculated as the residual of the total consumer’s expenditures.
25
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