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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
- Beijer International Institute of Ecological Economics, Stockholm, e-mail:
- Department of Economics, Swedish University of Agricultural Sciences, Uppsala, e-mail:
- Prof. Henk Folmer, Department of Economics, Wageningen University, e-mail:
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.
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 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
(2)
Where 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
(3)
We assume that for each region the following expected utility function is maximised
(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
(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
(6)
where E(π2j)=(E(πj))2+Var(πj), which gives E(Uj ) as
(7)
Since Bj(ej) is assumed deterministic, Var(πj)=σj2 is
(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. Formally, the Nash-equilibrium emission vector is found by differentiating (7) with respect to ej, which gives
(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
(10)
If the last term within brackets of (10) is positive, as in the case of multiplicative uncertainty, then emissions for each countryare 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
(11)
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
(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 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.
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.
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 Sea[9]. 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.