COOPERATION VERSUS NON-COOPERATION IN CLEANING OF AN
INTERNATIONAL WATER BODY WITH STOCHASTIC ENVIRONMENTAL
DAMAGE : THE CASE OF THE BALTIC SEA
Ing-Marie Gren2,3 and Henk Folmer1
This paper develops a simple model that accounts for uncertainty in degradation of water
quality from emission from countries surrounding an international waterbody. Theoretical
analysis of the cooperative and noncooperative solutions shows that the inclusion of risk
and risk aversion can either increase or decrease the differences between the two solution
concepts. An application to the Baltic Sea shows that the higher risk aversion, the larger
abatement and the smaller the net benefits of abatement. This result was found to hold for
both the cooperative and the noncooperative solution, though less for the latter than for the
former.
Key words: international water pollution, stochastic damage, cooperation, noncooperation,
Baltic Sea
JEL classification: D61, Q25
1. Beijer International Institute of Ecological Economics, Stockholm, e-mail:
ing@beijer.kva.se
2. Department of Economics, Swedish University of Agricultural Sciences, Uppsala, email: Ing-Marie.Gren@ekon.slu.se
3. Prof. Henk Folmer, Department of Economics, Wageningen University, e-mail:
Henk.Folmer@alg.SNNK.WAU.NL
1
1. Introduction
Like for many sea and lake common properties, the use of Baltic Sea as a nitrogen sink has
been one of the most important reasons for the current ecological damages from
eutrophication. Damages occur if either of the growth limiting nutrients, nitrogen or
phosphorus, increase. This implies higher production of algae, which, when decomposed,
demand oxygen. The resulting decrease in oxygen may then generate sea bottom areas with
reduced biological life. Furthermore, there is a change in the composition of fish species. In
the case of the Baltic Sea, decreases in the production of commercial fish species have
occurred frequently and there are large sea bottom areas without life (Wulff and Niemi,
1992). It is regarded that excessive loads of nitrogen is the main source of damages from
eutrophication of the Baltic Sea
Another feature of the Baltic Sea is that it is bordered by nine countries - Finland, Estonia,
Latvia, Lithuania, Russia, Poland, Germany, Denmark, and Sweden. Each of these
countries contributes to the eutrophication of the Baltic. This implies that effective and
efficient nitrogen reduction requires joint action. Unilateral abatement efforts or actions by
a few of these countries are likely to be insufficient to reduce eutrophication because the
emissions produced by the individual countries are small proportions of total emissions.
Moreover, efficiency requires that the marginal abatement costs are the same across the
polluting countries, which implies that policy coordination is required for the states
bordering the Baltic Sea. (For further details see amongst others Folmer and de Zeeuw
(2000).)
The early concern for the ecological conditions of the Baltic Sea has resulted in a lot of
natural science research. The 20 years period of this kind of research has generated much
data on biological conditions of parts of the Sea and nutrient transports between different
water basins [see e.g. Edler (1979), Granéli et al. (1990), Larsson et al. (1985), Wulff et al.
(1990), and Wulff and Niemi (1992)]. Furthermore, cost benefit analyses of improvement
of the Sea corresponding to its ‘healthy’ conditions prevailing prior to the 1960s, have been
carried out [Markowska and Zylics (1996), Söderqvist (1996) and (1998), and Gren
(2001)]. However, in spite of these studies, difficulties remain with respect to the
development of an effective and efficient abatement scheme and its implementation. These
difficulties relate to amongst others uncertainty inherent to nitrogen pollution and
international cooperation.
2
In much of the economic literature on water management, pollution abatement has been
analysed within a deterministic framework [see for instance Johnsson et al. (1991), Helfand
and House (1995), Wu and Segerson (1995), and Gren (2001)]. However, environmental
damages from water pollution (like virtually any other damages from pollution) are
characterised by conditions of uncertainty. For nitrogen, uncertainty in the water recipient
and its catchment region is related to:
-the diffusion of pollutants in the drainage basins to the coastal water;
-coastal and marine transports of the deposited nitrogen and
-ecological damages from the remaining nitrogen.
Adequate abatement of environmental damages caused by stochastic pollution thus requires
consideration of the probability distribution of pollution loads to the recipient. (See amongst
others, Malik et al., 1993; McSweeny and Shortle, 1990; Shortle, 1990; Mapp et al., 1994;
Byström et al., 2000.) These studies show that pollution abatement allocation and costs are
affected by the introduction of reliability constraints in addition to a standard deterministic
pollution constraint.
There is a large literature, mainly theoretical, with the focus on efficient provision of an
international environmental public good [see e.g., Barrett (1990), Mäler (1991) and (1993),
Hoel (1992), and Kaitala et al.(1995), Folmer and van Mouche (2000), Gren (2001), and
Folmer and van Mouche (2002).]. However, only a few of these studies contain empirical
analyses of concrete international environmental concerns [e.g Mäler (1991) and (1993),
Kaitala et al. (1995), and Gren (2001)]. Except for Gren (2001), common to these case
studies is their application to environmental damages from sulphur emissions under
deterministic conditions. To our best knowledge, however, there exist no case studies
relating to stochastic pollutants and international water bodies.1
Another important feature of this paper is that it makes use of benefit data, based on
estimated willingness to pay for an improved Baltic Sea. This is in contrast to most other
international studies, which overcome the problem of lacking information on the benefits of
pollution reduction by assuming revealed preferences. The assumption adopted is then that
1
We observe that this study is inspired by Gren (2001), the main differences being the consideration of a
stochastic rather than a deterministic pollutant, and the simplification made by disregarding transboundary air
pollution of nitrogen oxides and ammonium.
3
marginal
environmental
damage
equals marginal abatement cost at the actual level of
abatement (see amongst others Kaitala et al (1995) for an example) .
The paper is organised as follows. First, in section 2 we present the theoretical model
underlying the case study. We discuss the non-cooperative or Nash solution as well as the
cooperative solution to transboundary pollution in a stochastic framework. Next the case
study relating to the Baltic Sea is presented in sections 3 and 4. Section 3 presents the data
ant the assumptions whereas in section 4 the main results are discussed. The paper ends
with a brief summary and discussion of the results.
2. Uncertainty, the Nash equilibrium and the full cooperative solution
Consider N countries denoted by subscripts j=1, 2, …., N. Let E be the set of country j's
emissions with elements ej. Country j's gross benefit function reads as
Bj=Bj(ej) , j= 1,2,…, N
(1)
We assume that Bj is continuous, twice continuously differentiable, that B'j>0 and B"j<0.
Let Q be the set of country j's depositions with elements qj. Deposition at receptor j is given
by
N
q j   T jiei  q j ,
(2)
i 1
Where q j , are background depositions, Tji are the transportation coefficients, i.e. the
proportion of pollution generated in country i and deposited in country j.
Damages from emissions in country j, Dj, depend on depositions and ecological functioning
at the receptor. In order to take uncertainty into account, depositions at each receptor j are
regarded stochastic. We assume that Dj is continuous, twice continuously differentiable with
respect to emissions and that Dj'>0 and Dj">0.
Taking (1) and (3) together net benefits in country j, πj, are given by
 j  B j (e j )  D j ( q j )
(3)
4
We assume that for each region the following expected utility function is maximised

E (U j ( j ))  E U ( B j (e j )  D j (q j ))

(4)
where U'>0, and U"≤0.
In order to relate expected profits to risk, as measured by the variance in profits, we specify
a quadratic utility function as follows
U j  j  b j 2j
(5)
Equation (5) implies that the larger bj, the higher risk aversion. Moreover, for bj =0 we have
risk neutrality. The restriction (1-2bjπj)>0 is imposed due to the assumption of U’>0.
Expected utility for (5) is
EU j  E j  bE( 2j )
(6)
where E(π2j)=(E(πj))2+Var(πj), which gives E(Uj ) as


EU  j  E j  b ( E( j )) 2  Var( j )
(7)
Since Bj(ej) is assumed deterministic, Var(πj)=σj2 is
N
N
i 1
i 1
 2j  Var ( j ) Var ( D j )  Var (q j )  Var (Tij ei )   (Var (Tijei )  2Cov(Tijei , T jie j )) (8)
Depending on the signs of the covariances, country j’s risk may be larger or lower than the
sum of the variances in the countries’ depositions of pollutants at recipient j. For negative
covariances, country j’s risk is reduced, and can, in the extreme case, approach zero.
If the N countries behave non-cooperatively, country j maximizes (7) with respect to its own
emissions, taking emissions from other countries and background depositions as given.
5
Formally, the Nash-equilibrium emission vector Q jN is found by differentiating (7)
with respect to ej, which gives
U j
e j
 (1  2b j E j ) E ( B  T jj D )  b j
'
j
'
j
 2j
e j
0
(9)
It follows from (9) that when the variance is increasing (decreasing) in ej, emission is lower
(higher) under risk aversion than under risk neutrality.2
In contrast to (9), in the case of the full co-operative approach country j does not only take
its own marginal benefits and marginal damage into account but the marginal damage of its
emissions in other countries as well. The co-operative solution implies that ΣjEUj ≡EU is
maximized, which gives
 2j N 
EU
 2 
 (1  2b j E j ) E ( B 'j  T jj D 'j )  b j
  (1  2bi E i )T ji EDi'  bi i   0
e j
e j i  j 
e j 
(10)
If the last term within brackets of (10) is positive, as in the case of multiplicative
uncertainty, then emissions for each country are lower than under the Nash solution (9).3
The role of variance in (10) is similar to that in (9).
Another difference between the Nash and the cooperative solution is that the latter offers an
additional instrument for the allocation of risk. 4 This can be seen from (10), which can be
written as
N
N
i
i
(1  2b j E j )( B'j  T ji EDi' )   bi
 i2
e j
(11)
For a multiplicative specification of uncertainty such as Var(Tjjej)=(Tjjejj)2Var(εj), the variance is increasing
in emissions: ∂Var(Tjjejεj)/∂ej=2(Tjjej)Var(εj )>0 where  represents a stochastic error term. Hence, emissions
are lower under risk aversion than under risk neutrality in the case of a multiplicative specification.
3
For details about the relationship between the Nash equilibrium and the full cooperative solution see Folmer
and van Mouche (2000) and Folmer and van Mouche (2002).
4 We observe that if only one abatement measure is available for each country, then there is no portfolio
choice for the Nash solution. The cooperative solution on the other hand does allow for a choice of different
abatement levels in different countries and thus does offer a portfolio choice. For an application of efficient
portfolio choice of risky biodiversity assets, see Xepapadeas (2001).
2
6
The left-hand side reflects the utility from a marginal change in expected net return,
which consists of the marginal gross return from emissions in country j minus the costs of
marginal environmental damages in all countries from the marginal change in country j’s
emissions. The right hand side shows the impact on utility in all countries from an increase
in risk associated with a marginal change in j’s emission. The efficient allocation of risky
emissions between any two countries, j and k, thus occurs where
N
N
(1  2b j E j )( B   T ji ED )
'
j
'
i
i
N
(1  2bk E k )( B   Tki ED )
'
k
'
i
i

 bi
i
 i2
e j
 i2
b
i i e
k
N
(12)
That is, the efficient allocation of risk between countries is determined by the equality of the
ratio of utility from expected net returns and the ratio of marginal utility of risk (see e.g.
Elton and Gruber, 1991). If the utility function is the same for all countries, (12) reveals that
the emission level of a country with relatively high marginal impact on risk, should be
relatively low.
3. Benefits, costs, and risk estimates of nitrogen load changes
In this section we describe the data requirements to apply the theoretical framework
outlined in the previous section to determine the full cooperative and the non-cooperative
solution to the reduction of nitrogen emissions in the Baltic Sea taking into account the
stochastic nature of depositions at each receptor. The empirical analysis requires data on the
costs and benefits of emission reductions per country or region bordering the Baltic Sea. By
emission reduction we mean decreases in nitrogen loads in the coastal waters. This means
that estimation of the costs of nitrogen load reductions requires information on nitrogen
transports in the drainage basins because during transport part of the emissions is
transformed into harmless nitrogen gas. Finally, information is needed on nitrogen
transports in the Baltic because emissions entering the sea at one location are dispersed over
several regions.
The above mentioned data requirements have implications for the regional division of the
drainage basins. Particularly, data is needed on both economic parameters as well as on
nitrogen transport. Since data on costs and benefits of abatement are available on another
spatial scale than hydrological and biogeochemial information, the regional division of the
7
Baltic Sea drainage basin used here is based on the least common denominator for both
types of data sets (see Elofsson 2000 for further details). This has resulted in 19 different
drainage basins with different nitrogen transport parameters.5
The benefits from nitrogen emission reduction are derived from Gren (2001), which
transfers benefit estimates of an improvement of the Baltic Sea in Poland and Sweden to the
other Baltic S ea countries [Söderqvist (1996), (1998), and Markowska and Zylics (1996)].
In order to obtain benefit estimates for the entire drainage basin, the Swedish results were
transferred to Finland, Germany, and Denmark and the Polish results to Estonia, Latvia,
Lithuania and Russia. The transfer mechanism applied was GDP per capita.6 The valuation
scenario used was a change from the current status of the Baltic Sea to ecological conditions
corresponding to those prevailing in the 1960s before the large increase in the nutrient loads
took place (Wulf and Niemi, 1992).
From the benefit transfer analysis it follows that in total the 80 million inhabitants of the
Baltic Sea drainage basin would be willing to pay 31,000 millions SEK for this change in
ecological conditions of the Baltic Sea (1 Euro=9.31 SEK, July 9, 2001).7
The calculation of efficient nitrogen abatement under the cooperative and Nash solutions
requires amongst others information on the relationship between damage and nitrogen load.
We start by observing that we assume a linear damage function which implies constant
marginal damage. In terms of abatement this implies constant marginal benefits of
abatement. According to Wulff and Niemi (1992), the above mentioned ecological change
in the valuation scenario would require a total nitrogen reduction of at least 50 per cent,
which corresponds to 550 000 tons of N (Gren et al 1997). A constant marginal benefit
estimate is then obtained by dividing the estimated total willingness to pay of SEK 31,000
millions by the 550 000 tons of N. The calculated uniform marginal benefit of reduction is
then equal to 62/kg N. Thus, a nitrogen emission decrease by 1 kg to the Baltic Sea implies
a value increase of SEK 62 for all countries.
5
For a map see Figure A1 in the appendix
That is, the estimates for e.g. Estonia are the estimates available for Poland, after correction for the difference
in GDP per capita between both countries. For details see Söderqvist (2000) and Markowska and Zylics
(2000).
7
It is interesting to note that after adjustment for differences in GDP per capita WTP in Sweden and Poland
were approximately the same.
6
8
In the context of nitrogen reduction measures we distinguish between direct abatement
measures and land use measures. The former include: increased nutrient cleaning capacity at
sewage treatment plants, catalysts in cars and ships, scrubbers in stationary combustion
sources, and reductions in the use of fertilisers and manure in agriculture. Land use
measures include: change in spreading time of manure from autumn to spring, cultivation of
so called catch crops such as energy forests and ley grass, and creation of wetlands.8
Calculations of nitrogen abatement costs are based on econometric estimates for sewage
treatment plants, fertiliser reductions, reduction in nitrogen oxides from reduced use of gas
and oil, and wetland creation (for details, see Gren et al, 1997, and references therein).
Abatement costs of all other measures are obtained from engineering data. Marginal
reduction costs have been obtained from Gren et al. (1997a) and are presented in Table 1.
The marginal costs refer to the cost of a unit nitrogen reduction to the coastal waters. The
marginal costs vary according to type of abatement measures used and abatement level, as
well as the location of abatement measures. Measures implemented remote from the coastal
zones have smaller impacts, and hence, higher costs for achieving a unit reduction at the
coastal waters. Hence, the variation in marginal abatement costs in Table 1.
The impact of location on marginal abatement costs is explained by the nature of nitrogen
transport in the Baltic Sea catchments. In order to relate nitrogen emissions from sources in
the catchment areas to loads in the coastal waters, data is needed on nitrogen transformation
during transport from the source to the coastal waters. These transports are determined by
hydrological, climatic, and biogeochemical conditions, and vary for the 19 regions of the
Baltic Sea catchment. A simplification is made, however, by assuming a linear relationship
between emission generation at the source and deposition in the own coastal waters. That is,
for each source a constant fraction, less than unity, of upstream emissions was assumed to
reach the coastal water. The smaller load to the coast than emissions at the source is mainly
due to the transformation of nitrogen into harmless nitrogen gas during transport. The
magnitude of the fractions of emission reaching the coastal loads is determined by climatic
and biogeochemical parameters and differ for different regions of the Baltic Sea. For a
further description of the derivation of the transport parameters, see Elofsson in this issue.
8
Change of spreading time from autumn to spring implies less leaching due to the fact that, in spring, the
crops are growing making use of the nutrients. Catch crops refer to certain grass crops which are sown at the
same time as ordinary spring crops but start to grow, thereby making use of remaining nutrients in the soil,
when the ordinary crop is harvested.
9
Based on these assumptions, calculated emissions to the coastal waters are as
presented in Table 1. It follows that in total almost 900 thousand kton of N is deposited at
the Baltic Sea coasts from the nine countries bordering the Baltic Sea9. Poland is the largest
emitter, accounting for about 27 per cent of total emissions. Latvia and Sweden account for
approximately 14 per cent each.
In addition to information on transport in the drainage basin information is needed on
the dispersion of pollution among countries , i.e. the matrix of transport coefficients T. The
dispersion matrix is determined by several factors such as vertical circulation, temperature,
and salinity in different parts of the Sea, and total inflow to the Sea of oxygen supply (see
Wulff et al 2001 for further details). The depositions on the own coast of a country’s
nitrogen emission depends on these factors and also on the vegetation in coastal regions.
The more vegetation, the higher is the damage from oxygen depletion on the own coast.10
Data on transport coefficients are obtained from large scale modelling exercises for the
Baltic Sea (Wulff and Niemi (1992) and Gren (2001) for further details). However, these
modelling results give no information on transport among countries but among Baltic Sea
basins. Therefore, we assume that transports coefficients are the same for regions sharing
the same Baltic Sea basin. (See the transport matrix in Appendix 1.) Table 1 shows the
impact on the own coast from the region’s emission, and also total deposition including
transports from other regions.
In order to take risk into account we assume a quadratic utility function. Numerical
operationalization of risk, (i.e. the variance), is obtained by means of coefficients of
variations of nutrient concentration ratios measured at river mouths along the Baltic Sea
coasts (Stålnacke, 2000). In order to simplify the numerical optimisation, co-variances
among concentration ratios at different locations are disregarded. The reason is that the
variance-covariance matrix is not positive semi-definite. Depending on the magnitude of the
co-variances the marginal impact of a risk reducing abatement measure as expressed by eqs.
(10) and (12) is either increased or decreased. As shown by Elofsson in this issue, inclusion
of covariation increases overall risk. The coefficients of variation are displayed in Table 1.
9
The total load is higher due to emissions of nitrogen oxides from countries outside the Baltic Sea drainage
basin.
10
It should be observed that the less vegetation, the larger offshore transport of nitrogen. On the other hand,
vegetation in coastal regions takes up part of the nitrogen deposited. Hence, the more vegetation, the higher is
the damage from oxygen depletetion on the own coast assumed to be.
10
Table 1: Nitrogen loads, own national impacts per unit of nitrogen load,
marginal costs, and coefficient of variation in measured nitrogen
concentration.
We observe that the coefficients of variation vary between 0.17 and 0.39, being highest for
Kaliningrad.11
Finally, we turn to risk attitude. In the expected utility function, the value of the coefficient
bj is bounded by the requirement of U’j>0, but can otherwise take any positive value
depending on risk attitudes. Unfortunately, there is no information on risk attitudes for the
different countries. Therefore, we adopt the following assumptions. First, the case of risk
neutrality, bj=0, is used as a reference case. Next, we consider a relatively high and a
relatively low value of b: bj=0.001 and bj=0.0001.12
4. Maximum net benefits
The program code to calculate the cooperative and nocooperative solutionfollows the
structure of the equations presented in Section 2, except for the profit function specified in
(3). In order to facilitate the numerical calculations, we solve for the "dual" of (3) which
specifies net benefits as benefits from emission abatement minus abatement costs. The
optimisation solver used is GAMS (Brooke et al. 1998).
Appropriate calculations of the Nash solution would require reaction functions for each
country showing responses from other countries on its nitrogen reduction levels. However,
this considerably complicates calculations. Therefore, Nash solutions are calculated by
assuming other countries' emissions fixed at the uncontrolled level. This implies an
underestimation of net benefits from a country’s emission reductions (since other countries’
emission reductions are excluded), and consequently an overestimation of the emission
reduction (due to the decreasing utility in net benefits).
Table 2: Maximum net benefits (mill SEK per year) and nitrogen reductions
( in %) under cooperative solutions for risk neutrality and risk aversion
11
We observe that relatively large risk may be an important incentive to reduce emission and counteract
possible low reduction incentives due to small own marginal benefits. Due to the absence of positive
covariances risk is underestimated.
12
We observe that these values for b are arbitrary. We are not aware of any reference values that have been
used in empirical research in this aera.
11
The results presented in Table 2 show that there is no change in total nitrogen reductions
when b increases from b=0 to b=0.0001. Moreover the reductions are constant for all
countries except for Finland, Poland and Estonia. Total net benefits decrease from SEK
18612 million to 16296 million. All countries, except Poland, experience a decrease in net
benefits with the highest relative decrease for Estonia (33 %). The reason for the increase in
net benefits for Poland is cost savings from less nitrogen abatement. This, in turn, is a result
from the larger change in marginal utility of net benefits than in marginal utility of risk at
the relatively high Polish abatement level. The opposite is true for Estonia, which also faces
relatively low abatement costs
A further increase of b to b=0.001 leads to an increase in overall abatement from 45% to 50
%. All countries increase their abatement as compared to when b=0.0001. The increase in b
causes substantial decreases in net benefits, which turn into net losses for Denmark and
Estonia. Total net benefits drop from SEK18612 million to SK2071 million. Sweden and
Estonia experience decreases in net benefits of similar orders of magnitude. These results
show that the higher risk aversion, the larger abatement and the smaller net benefits.13
Table 3 displays abatement and maximum net benefits under the Nash solution. We observe
that total abatement is constant for an increase of b from b=0 to b=.0001 and only slightly
increases when b increases from b=0.0001 to b=0.001. Similar results hold for the
individual countries. The most striking result is the increase for Germany from zero
abatement for b=0 and b=0.0001 to 13% for b=0.001. Total net benefits as well as net
benefits per country decrease slightly when b increases from b=0 to b=0.0001. When b
increases further to b=0.001 total net benefits drop from Sk 1755 million to Sk 963 million.
For the individual countries the decrease in net benefits is also relatively large. Moreover,
for Denmark, Germany and Poland the net benefits turn negative. These results further
illustrate, though less clearly, that the higher risk aversion, the larger abatement and the
smaller net benefits. Since under the Nash countries only take their own impacts into
account, the results are less outspoken.
Table 3: Maximum net benefits (mill SEK per year) and nitrogen reductions
( in %) under Nash solutions for risk neutrality and risk aversion
13
The decrease of net benefits is the "price" of risk aversion.
12
Comparison of Table 2 and Table 3 shows the familiar result that under the full
cooperative approach total abatement and total net benefits are substantially higher than
under the Nash. Similar results hold for the individual countries.
An interesting result is that all countries benefit from cooperation and that there are no
countries that incur a net loss under cooperation, except Denmark and Estonia for b=0.001.
The virtual absence of losses is due to the absence of strong asymmetries in the diffusion of
nitrogen emissions in the Baltic and also the assumed uniform marginal benefits of nutrient
reduction. An important consequence is that there is no need to compensate countries for
their losses and to induce them to accept the co-operative solution when b=0 and b=0.0001.
However, the increase in net benefits for Sweden, Germany, Finland, Poland and Russia
under the full cooperative solution compared to the Nash is substantially larger than for
Estonia, Latvia, Lithuania and Denmark. Therefore, in order to achieve a “fair sharing” of
the net benefits from cooperation side payments may be needed. Several fair sharing
schemes could be thought of, the most simple one being an equal split between the
countries. Other possible schemes are the proportional rule and the Shapley value. Roughly
speaking, these redistribution schemes take into account how valuable a country's abatement
is to the net benefits of the other countries (e.g. Pham et al., 2001 and the references
therein).
5. Summary and conclusions
In this paper we have addressed the problem of efficient cleaning of an international water
body with stochastic environmental damage. A standard net benefit function was embedded
in a quadratic utility function framework which, in its turn, was used to derive the noncooperative outcome or Nash equilibrium emission vector as well as the full cooperative
solution. For both outcomes we showed that if risk (measured as variance) is increasing
(decreasing) in emissions, the level of emission is decreasing (increasing) under risk
aversion relative to risk neutrality.
The model was applied to nitrogen reduction in the Baltic See which is surrounded by 9
countries. The application was hampered by data limitations. The benefits from nitrogen
reduction per country surrounding the Baltic Sea were obtained by means of benefit transfer
which made it possible to circumvent the usual assumption that marginal environmental
damage equals marginal abatement costs at the actual levels of pollution abatement. With
13
respect to the transport of pollution from its source to the coastal waters, transformation
of nitrogen into harmless nitrogen gas was taken into account. The dispersion of pollution
among countries was modelled by means of a dispersion matrix, taking into account several
ecological system factors, such as vertical circulation, temperature, salinity and coastal
structure.
A variety of abatement measures consisting of direct measure and land use measures were
used to derive the marginal abatement costs per country. The empirical results for the Baltic
Sea confirm the theoretical results mentioned above. In addition to the well-known result
that, ceteris paribus, abatement is higher under the cooperative than under the noncooperative approach, we found that the higher risk aversion, the larger abatement and the
smaller net benefits. This was found to hold for both approaches, though less for the Nash
because in this case countries only take their own impacts into account.
Another important result is that for risk neutrality and low risk aversion the net benefits are
positive for each country under the full cooperative outcome and the Nash solution (except
Germany under low risk aversion). This implies first of all a major incentive for nitrogen
abatement: no country will incur a loss from cleaning up its act. However, the net benefits
under the full cooperative approach strongly outweigh the net benefits under the Nash
which makes the former preferable to the latter. Although no country will incur a loss under
the former, some countries will benefit more than others which may necessitate the
implementation of a redistribution scheme of the increase of the net benefits due to
cooperation.
It is important to note that these estimates are sensitive to several assumptions. For example,
sensitivity analysis in Gren et al. (1997) shows that total costs of nitrogen may double when
a reduced capacity of low cost measures is assumed. Another crucial assumption concerns
the linkage of nitrogen reductions to benefits as measured in monetary terms. Moreover,
diversifying the (assumed) constant marginal benefits may further impact on the results
including the differences between the cooperative and Nash solution (seeGren, 2001).
Recall also the arbitrary measurement of marine nitrogen transports between countries. A
change in these transport parameters might result in considerable changes in allocations of
nitrogen reductions and net benefits. Another strong assumption relates to the shape of the
utility function and, in particular, the influence of risk on utility. Except for restrictions
imposed by positive marginal utility from damage reductions, we could not find any support
14
in the literature for the values of the parameter b. Since our results indicate
significant implications of differences in risk attitudes, this is a fruitful area of further
research.
The results are, by all likelihood, not only affected by difficulties of measuring included
parameters, but also by excluded factors. One such factor is the negligence of all other
environmental benefits than those associated with eutrophication reductions in the Baltic
Sea. For example, the construction of wetlands implies further environmental benefits by
the provision of biodiversity and may also contribute to recreational values. The inclusions
of such “extra” environmental benefits would increase nitrogen reductions for all regions
where these benefits are positive.
Another important issue is related to the concept of cost of nitrogen reductions applied in
this study. It would be more appropriate to include not only the direct costs of the reduction
activities, but also their general equilibrium impacts. As shown in Johannesson and Randås
(1996), structural impacts of nitrogen reduction policies can be large but the net impact on
GDP is small. Further, costs of enforcing nitrogen reduction are not included. Since there
are large differences in institutions affecting environmental policies among the countries,
enforcement costs are likely to differ much, being highest in the Baltic states and Poland
(Eckerberg et al., 1996). The inclusion of enforcement costs would thus effect, not only
total net benefits, but also the allocation of nitrogen reductions among countries.
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17
Table 1: Nitrogen loads, own national impacts per unit of nitrogen load,
marginal costs, and coefficient of variation in measured nitrogen
concentration.
Nitrogen
National
Deposition
Marginal costs Coefficient
Regions
emission
own impact, on coast,
,
of variation
1000 kton Tjj
iTijeI
SEK1/kg
N
N, ej
reduction
Finland
Bothnian Bay
Bothnian Sea
Gulf of Finland
Sweden:
31
25
19
0.2
0.2
0.3
42
42
47
0 – 1677
0 – 1968
0 – 3645
0.21
0.25
0.24
Bothnian Bay
Bothnian Sea
North
Baltic
Proper
South
Baltic
Proper
Sound
Kattegat
Denmark
19
33
20
0.2
0.2
0.3
42
42
46
0 – 1516
0 – 1780
0 – 1404
0.17
0.20
0.27
18
0.3
45
0 – 1404
0.35
7
39
85
0.3
0.3
0.3
42
42
70
0 – 703
0 – 421
0 – 986
0.33
0.21
0.25
Germany
37
0.3
52
0 – 2977
0.20
Vistula
Oder
Polish coast
Lithuania
145
84
28
60
0.15
0.15
0.15
0.15
54
48
43
46
0 –2233
0 – 2232
0 – 1116
0 – 715
0.29
0.27
0.18
0.16
Latvia
131
0.15
52
0 – 818
0.20
Estonia
59
0.15
65
0 – 838
0.18
90
20
952
0.3
0.15
58
43
9212
0 – 528
0 – 747
0 – 2 977
0.17
0.39
Poland:
Russia:
S:t Petersburg
Kaliningrad
Total
Sources: Elofsson (2000), Gren et al (1997), and Gren (2001)
1) 1 Euro = 9.3 SEK (July 9, 2001)
2) Total deposition is lower than total emission since part of emission from Denmark and
Kattegatt enters Skagerack
18
Table 2: Maximum net benefits (mill SEK
per year) and nitrogen reductions
( in %) under cooperative solutions for risk neutrality and risk aversion
Country
b=0
b=0.0001
b=0.001
Red.

Red.

Red.

Denmark
35
981
35
841
41
-72
Finland
36
2870
37
2568
43
419
Germany
33
1143
33
998
51
155
Poland
48
1267
46
1435
47
289
Sweden
33
6041
33
5318
47
764
Estonia
47
1781
59
1164
63
-23
Latvia
58
1066
58
940
61
162
Lithuania
57
986
57
881
60
204
Russia
43
2475
43
2147
49
172
Total
45
18612
45
16296
50
2071
Table 3: Maximum net benefits (mill SEK per year) and nitrogen reductions
( in %) under Nash solutions for risk neutrality and risk aversion
Country
b=0
b=0.0001
B=0.001
Red.

Red.

Red.
Denmark
11
129
11
114
11
Finland
23
185
23
179
23
Germany
0
0
0
-2
13
Poland
5
48
4
39
4
Sweden
16
249
15
237
17
Estonia
46
282
46
274
46
Latvia
44
481
44
455
44
Lithuania
6
21
6
20
6
Russia
35
464
35
439
37
Total
21
1859
21
1755
22

-12
131
-16
-38
137
197
231
17
316
963
19
Appendix: Table
Table A1: Matrice of transport coefficients among Baltic Sea catchments
DENMARK
FIBB
FIBS
FIFV
GERMANY
VIST
ODER
POLCOS
SEBB
SEBS
SEBANO
SEBAP
SESO
SEKA
ESTONIA
LATVIA
LITHUANIA
SUKAL
SUPET
DENMARK
FIBB
FIBS
FIFV
GERMANY
VIST
ODER
POLCOS
SEBB
SEBS
SEBANO
SEBAP
SESO
SEKA
ESTONIA
LATVIA
LITHUANIA
SUKAL
SUPET
DENMARK FIBB
0.3
0
0.01
0.3
0.01
0.3
0.01
0
0.05
0
0.03
0
0.03
0
0.03
0
0.01
0.2
0.01
0.2
0.03
0
0.03
0
0.03
0
0.10
0
0.02
0
0.03
0
0.03
0
0.03
0
0.01
0
FIBS
0
0.3
0.3
0
0
0
0
0
0.2
0.2
0
0
0
0
0
0
0
0
0
FIFV
0.01
0.02
0.02
0.3
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.01
0.2
0.02
0.02
0.02
0.2
GERMANY
0.05
0.02
0.02
0.03
0.3
0.05
0.05
0.05
0.02
0.02
0.05
0.05
0.05
0.02
0.05
0.05
0.05
0.05
0.03
VIST
0.06
0.02
0.02
0.03
0.06
0.15
0.06
0.06
0.02
0.02
0.06
0.06
0.06
0.04
0.06
0.06
0.06
0.06
0.04
ODER POLCOS
0.06
0.06
0.02
0.02
0.02
0.02
0.03
0.03
0.06
0.06
0.06
0.06
0.15
0.06
0.06
0.15
0.02
0.02
0.02
0.02
0.06
0.06
0.06
0.06
0.06
0.06
0.04
0.04
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.04
0.04
SEBB
SEBS
SEBANO
SEBAP
SESO
SEKA
ESTONIA
0
0.2
0.2
0
0
0
0
0
0.3
0.3
0
0
0
0
0
0
0
0
0
0
0.2
0.2
0
0
0
0
0
0.3
0.3
0
0
0
0
0
0
0
0
0
0.05
0.02
0.02
0.03
0.05
0.05
0.05
0.05
0.02
0.02
0.3
0.05
0.05
0.02
0.05
0.05
0.05
0.05
0.03
0.05
0.02
0.02
0.03
0.05
0.05
0.05
0.05
0.02
0.02
0.05
0.3
0.05
0.02
0.05
0.05
0.05
0.05
0.03
0.05
0.02
0.02
0.03
0.05
0.05
0.05
0.05
0.02
0.02
0.05
0.05
0.3
0.02
0.05
0.05
0.05
0.05
0.03
0.2
0.0
0.0
0.0
0.01
0.01
0.01
0.01
0
0
0.01
0.01
0.01
0.3
0.01
0.01
0.01
0.01
0.01
0.05
0.02
0.02
0.1
0.05
0.05
0.05
0.05
0.02
0.02
0.05
0.05
0.05
0.01
0.15
0.05
0.05
0.05
0.1
20
LATVIA
DENMARK
FIBB
FIBS
FIFV
GERMANY
VIST
ODER
POLCOS
SEBB
SEBS
SEBANO
SEBAP
SESO
SEKA
ESTONIA
LATVIA
LITHUANIA
SUKAL
SUPET
0.06
0.02
0.02
0.03
0.06
0.06
0.06
0.06
0.02
0.02
0.06
0.06
0.06
0.04
0.06
0.15
0.06
0.06
0.04
LITHUANIA
0.06
0.02
0.02
0.03
0.06
0.06
0.06
0.06
0.02
0.02
0.06
0.06
0.06
0.04
0.06
0.06
0.15
0.06
0.04
SUKAL
SUPET
0.06
0.02
0.02
0.03
0.06
0.06
0.06
0.06
0.02
0.02
0.06
0.06
0.06
0.04
0.06
0.06
0.06
0.15
0.04
0.01
0.02
0.02
0.2
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.01
0.2
0.02
0.02
0.02
0.3;
Baltic Proper: Denmark, Germany, Vistula (Vist), Oder, Polish coast (Polcos), North Baltic
Proper (Sebano), South Baltic Proper (Sebap), Swedish sound (Seso), Estonia, Latvia,
Lithuania, Kaliningrad (Sukal).
Bothnian Bay: Finnish and Swedish Bothnian Bay (Fibb and Sebb)
Bothnian Sea: Finnish and Swedish Bothnian Sea (Fibs and Sebs)
Gulf of Finland: Finland (Fifv), S:t Petersburg, (Supet), and Estonia
Kattegatt: Sweden (Seka) and Denmark
21
Fig.A1 The Baltic Sea Drainage Basin..