measurement of the net value in all uses. The purpose of this paper is to analyse and estimate
the value of land as a pollutant sink under differ- ent decision contexts and objectives.
When we regard an ecosystem’s capacity to reduce leaching of pollutants as an input for the
production of water quality its value can be calcu- lated as associated impacts on net welfare by
means of the production function approach Ma¨ler, 1991a; Barbier, 1994, 1997; Gren, 1995;
Bystro¨m, 1999. The value of the pollutant sink functioning is then determined by the valuation of
water quality, the effectiveness in producing water quality, and the cost as compared to other pollu-
tant reduction measures. The optimal choices of inputs and water quality are, in turn, determined
by type of decision framework. In this paper, two classes of decision contexts and objectives are
identified for the management of international waters. The alternative decision contexts are coor-
dinated and uncoordinated choices of water qual- ity improvement options, and the objectives to be
achieved are formulated either as maximization of net benefits or as minimization of costs for achiev-
ing a certain water quality target.
As demonstrated in Barbier 1997 and Free- man 1991, the design of property rights for a
common property resource and associated deci- sion context affects the value of an ecosystem as
an input into the production of a common prop- erty resource. The difference with this paper as
compared to the approach of Barbier and Free- man is the large-scale international aspect. There
is a relatively large literature on net benefits from emission reductions under different international
cooperative frameworks Barett, 1990; Kaitala et al., 1991; Ma¨ler, 1991b; Hoel, 1992. There are
also numerous studies on the valuation of ecosys- tem life support values, especially wetland valua-
tion see Gren and So¨derqvist, 1994, for a survey. However, the combination of ecosystem valuation
and transboundary environmental impacts, which is the approach applied in this study, is rare.
The paper is organized as follows. The first two sections contain an analytical decomposition of
factors affecting the value of land as a pollution abatement option. Next, the approach is applied
to the valuation of Baltic Sea coastal wetlands as nitrogen sinks. The paper ends with a brief sum-
mary and some concluding comments.
2. Basic model and decision framework
This paper contains two basic components for the analysis and calculation of the value of land
as a pollutant sink. One is a description of pollu- tant transports among the countries sharing the
common water body. The other is modelling of alternative decision contexts and objectives. In the
following, the construction of simple models of pollutant transports and decision frameworks are
presented. By means of these models, the value of land as a pollutant sink in a country is calculated
as the impact on net benefits or abatement costs from a marginal increase in the current area of
pollutant sink. Land as a pollutant sink is here interpreted as the area of land with relatively low
pollutant leaching. A switch in the area of land from high to low leaching then implies a net
decrease in pollutant leaching, the effectiveness of which, as measured in tons of pollutant reduc-
tions to the water body, depends on the difference in leaching between the high and low leaching
land covers.
2
.
1
. Pollutant transport modelling If there were no pollutant transports between
countries, there would be no difference in out- comes between coordinated and uncoordinated
pollution abatement policies. However, in the case of international waters we have to deal with two
types of transboundary pollutants: air and water streams. Simplified models for these transports
are presented in this section.
For each country i, where i = 1,…,N different countries, there are two types of pollutant path-
ways to the water body under study: direct, E
i
, and indirect deposition, P
i
. Direct deposition is defined as the pollutant emissions in region, E
i
, which are transported directly into the water
body. It is assumed that this direct deposition can be calculated as a share of total emissions from
the region, a
i
E
i
. Total pollutant load from a country i to the common water body, L
i
, is then written as
L
i
= P
i
+ a
i
E
i
1 Indirect deposition, P
i
, refers to the pollutants deposited on land and further transported by
water streams to the international water body. The total deposition on land within a country is
determined by the emissions from all countries, which are deposited on land within the country. It
is assumed that these transboundary air pollutants can be described by a matrix where each element
a
ji
measures that share of country j’s emissions that is transported to country i. When a
ii
=
1
− a
i
there are
no transboundary
pollutant transports.
Total pollutant deposited on land within the territory of each country, S
j
a
ji
E
j
, is subjected to transformation during the transport from the de-
position localization to the water body under study. The level of P
i
is then dependent, not only on the pollutant deposition within the regions, but
on other factors, such as the composition of land, climate, geology and hydrology. For example,
there is a great difference in nutrient leaching between forest areas and bare arable land. An-
other simplification of the model is the discrimi- nation between only two types of land, relatively
high leaching land, A
Hi
, and low leaching land, A
Li
, or land covered by pollutant sink. The indi- rect deposition of pollutants from country i to the
water body, P
i
, is then written as P
i
= P
i
A
Li
, A
Hi
, S
j
e
ji
E
j
2 where A
Li
+
A
Hi
= A
Ti
and A
Ti
is the total area of land in region i. In principle we expect P
i
to be increasing in E
j
and A
Hi
and decreasing in A
Li
. The simplification of pollutant transports made in
Eq. 2 occurs for at least two reasons. One is that the spatial distribution of different land cover
types within a drainage basin affects the pollutant load to the water body. For example, high leach-
ing land located close to the water body implies larger P
i
than if the same land is located upstream in the drainage basin. The reason is the transfor-
mation of pollutants during the water and soil transports from the pollutant source to the water
body. The second reason is the complex dynamic relation between surface and subsurface transport
of pollutants. However, the consideration of these factors would not alter the principal analytical
results in this section, although they will probably have a strong empirical importance. Therefore, in
order to focus on the role of institutional and informational settings, these dynamic and spatial
factors are excluded from the analysis.
The transboundary dispersion of water quality impacts is determined by the water streams. It is
assumed that these transports between surround- ing regions can be described by a matrix where
each element, e
ji
, denotes the fraction of pollutant load from region j, L
j
, which affects region i. The water quality for a region, W
i
, can then be writ- ten as
W
i
= W
i
S
j
e
ji
L
j
3 Water quality is assumed to be measured so that
a higher W
i
implies improved water quality. It is then expected that W
i
is decreasing in L
j
.
2
.
2
. Decision contexts and objecti6es Based on the above description of pollutant
transports, we can identify two types of options for improving the water quality: emission-oriented
abatement measures, R
i
, and land use-oriented options increasing the area of low leaching land,
A
Li
, or pollutant sinks. Pollutant emission from a country i is then initial emission, E
io
, which could be measured at a certain base year, minus R
i
, or E
i
= E
io
− R
i
. Common to all decision contexts and objectives is the choice of these two pollutant
load reduction measures. Another common fea- ture for all types of decisions is that the value of
land as a pollutant sink is calculated as a mar- ginal increase in the current area of pollutant sink
in each country i, A
Li
. In an international context there are no super
national authorities who are able to enforce con- tracts on cooperation between regions. Countries
or regions will then cooperate only if they make gains as compared to a situation where they act
on their own. It is therefore of interest to calculate and compare the outcomes when countries coor-
dinate their policies with the outcomes from single country decisions. Two types of international in-
stitutional frameworks are therefore analysed. One is where all regions coordinate their choices
of R
i
and A
Li
for obtaining a common objective. The other is the uncoordinated case where each
country makes its own choice taking other coun- tries’ decisions as given.
Ideally, when sufficient information is available, we would solve for the efficient choices of R
i
and A
Li
by maximizing net benefits under the two institutional
settings. However,
estimating changes in the supply of public goods in monetary
terms is far from a trivial matter. In the case of water quality improvements this implies the trans-
lation of water quality changes, such as pollutant concentration ratios, into welfare terms. For ex-
ample, changes in pollutant loads affect reproduc- tion of commercial fish and bathing water quality.
We thus have to deal with multi-attribute valua- tion, which is a relatively recent research area e.g.
Dale et al., 1996. It is therefore likely that benefit estimates of water quality impacts are not avail-
able. Further, we might not even obtain informa- tion on water quality impacts from pollutant
transports in biological terms. The reason is the lack of data on marine pollutant transports for
large international water bodies Gren et al., 1997. Therefore, two types of decision objectives
are identified depending on the availability of marine pollutant transports and benefits esti-
mates. In the case of information availability, net benefits are maximized. When sufficient informa-
tion does not exist, the cost effectiveness decision rule is applied. The decision is then formulated as
achieving a certain reduction in the pollutant load to the water body at minimum cost.
We thus have four different combinations of institutional and informational settings: coordi-
nated and uncoordinated choices of R
i
and A
Li
where either net benefits are maximised or costs are minimized for a certain target in the load of
pollutants to the water body. Under all four situations it is assumed that there exists cost
functions for each type of measure, C
iR
and C
iA
, which are increasing and convex in R
i
and A
Li
respectively. When maximizing net benefits, valu- ation functions are assumed to exist for each
country, V
i
W
i
which are increasing and concave in W
i
. The four different decision models and the associated first-order conditions with respect to
the optimal choice of A
Li
are written as presented in the following.
Coordinated maximization of total net benefits IB
, implies that total net benefits for all coun- tries are maximized, which gives
Max S
i
[V
i
W
i
− C
iR
R
i
− C
iA
A
Li
] R
i
, A
Li
, s.t. 1 − 3
A
Li
5 A
Li
4 The associated first-order conditions for an opti-
mum read S
j
[V
W
j
j
W
L
j
j
e
ij
P
R
i
a
i
+ S
j
V
W
j
W
L
j
j
L
P
j
e
ji
P
R
j
a
ij
] =
C
R
i
i
5 S
j
V
W
j
W
L
j
j
e
ij
P
A
Li
i
− C
A
Li
i
= a
iIB
6 where subindexes denote partial derivatives, j =
i = 1,…,N different countries, and a
iIB
is the La- grangian multiplier of the constraints on the area
of pollutant sinks, which is positive when the constraint is binding. This multiplier is interpreted
as the value of a marginal increase in A
i
, which constitutes our measurement of the pollutant sink
value of land in country i. From Eq. 6 we can see that its magnitude is determined by the differ-
ence in marginal benefits minus marginal costs. When A
Li
does not bind at the actual area of pollutant sinks, there is no marginal pollutant
sink value. The first-order condition Eq. 5 also reveals
two types of international spillover impacts from a marginal change in pollutant emissions in coun-
try i. The first term within brackets in Eq. 5 disregards the transboundary air transports but
includes the dispersion of water quality impacts to other countries by the marine transport coeffi-
cients e
ij
. The second term shows somewhat more complicated spillover effects by considering trans-
boundary air and water pollution. First, the emis- sion reduction in country i gives rise to a
deposition and leaching reduction in other coun- tries through
P
j
R
j
a
ij
. Then, the pollutant load reduction in each country j generates disper-
sion of water quality impacts to all other coun- tries through the marine transport coefficients e
ji
.
In Gren 1997 it is shown that the consideration of these two spillover effects, instead of only one
as in most papers on transboundary pollutants, is likely to reduce the difference between outcomes
from coordinated and uncoordinated policies. However, in this paper we are mainly concerned
with the comparison of the value of marginal changes in the area of pollutant sinks. In subse-
quent analysis we will therefore abolish the first- order conditions for optimal choices of emission
reduction measures.
Coordinated minimization of total costs IC
for achieving a certain maximum pollutant load
target, L, is written as Min S
i N
[C
iR
R
i
+ C
iA
A
Li
] R
i
, A
Li
s.t. 1 − 2 S
i N
L
i
5 L
A
Li
5 A
Li
7 and the first-order conditions with respect to the
optimal choice of A
Li
is l
P
A
Li
i
− C
A
Li
i
= a
iIC
8 where l ] 0 is the Lagrange multiplier on the
pollutant load restriction, which measures the change in total costs from a marginal change in
the pollutant load restriction. Whether or not a
iIC
is positive depends on the cost and effectiveness of land as a pollutant sink as compared to abate-
ment options in all countries. The corresponding decision problems under na-
tional policies is written in the same way as Eqs. 6 and 7, except for the absence of summation
over all countries in the objective function. Under national minimization of costs, a restriction is
imposed only on the country’s pollutant load to the water body. The associated first-order condi-
tions under National maximization of net benefits
NB , is then written as
V
W
i
i
W
L
i
i
e
ii
P
A
Li
i
− C
A
Li
i
= a
iNB
9 The corresponding condition under National min-
imization of costs NC
is l
i
P
A
Li
i
− C
A
Li
i
= a
iNC
10 where the Lagrange multiplier, l
i
, measures the change in costs from a marginal change in the
pollution requirement L
i
which considers only the reduction options in the country. The multi-
plier on the overall reduction target, l, measures changes in total costs from a marginal change in
L where reduction options in all countries are taken into account.
3. Comparison of pollutant sink values
