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Signicant benets from international cooperation
over marine plastic pollution
Frans de Vries ( frans.devries@abdn.ac.uk )
University of Aberdeen https://orcid.org/0000-0003-0462-5035
Nicola Beaumont
Plymouth Marine Laboratory
Tobias Börger
Berlin School of Economics and Law https://orcid.org/0000-0002-4485-2518
James Clark
Plymouth Marine Laboratory
Nicholas Hanley
University of Glasgow
Robert Johnston
Clark University
Keila Meginnis
Evidera
Christopher Stapenhurst
Budapest University of Technology and Economics
Physical Sciences - Article
Keywords:
Posted Date: November 14th, 2023
DOI: https://doi.org/10.21203/rs.3.rs-3328986/v1
License: This work is licensed under a Creative Commons Attribution 4.0 International License.
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Additional Declarations: There is NO Competing Interest.
1
Significant Benefits from International Cooperation over
Marine Plastic Pollution
Nicola J. Beaumont, Tobias Börger, James R. Clark, Nick Hanley, Robert J. Johnston,
Keila Meginnis, Christopher Stapenhurst & Frans P. de Vries
Plastic pollution in the world’s oceans threatens marine ecosystems and biodiversity, leading to a loss
of well-being for people1,2. The connected nature of the marine environment suggests that coordinated
actions by countries sharing a common ocean border may provide more effective pollution control than
unilateral actions by any one country. However, economic theory and empirical evidence suggest that
countries often fail to cooperate, even when joint welfare would be higher under cooperation3. Here we
provide the first analysis of the potential economic benefits of cooperative marine plastic pollution
(MPP) management in the North Atlantic. An estimated transfer matrix showing how plastics move
across the North Atlantic is combined with game theory and estimates of benefits and costs to derive
the potential net benefits of international cooperation. A fully cooperative outcome across 16 countries
leads to a substantial reduction in MPP, resulting in significant aggregate annual net benefits. However,
MPP reduction burdens are unevenly spread across countries. Constraining the agreement to avoid such
consequences results in both less MPP reduction and lower aggregate benefits. As the United Nations
works on a future global plastic pollution treaty, these results demonstrate that close cooperation will
be a critical determinant of its success.
Beaumont: Plymouth Marine Laboratory, Plymouth, England, UK; Börger: Berlin School of Economics and
Law (HWR Berlin), Badensche Straße 52, 10825 Berlin, Germany; Clark: Plymouth Marine Laboratory,
Plymouth, England, UK; Hanley: School of Biodiversity, One Health and Veterinary Medicine, University of
Glasgow, Scotland, UK; Johnston: George Perkins Marsh Institute, Clark University, Worcester, MA, USA;
Meginnis: Patient-Centered Research, Evidera; School of Biodiversity, One Health and Veterinary Medicine,
University of Glasgow, Scotland, UK; Stapenhurst: Quantitative Social and Management Sciences Research
Centre (QSMS), Faculty of Economics and Social Sciences, Budapest University of Technology and Economics,
Budapest, Hungary; De Vries: Department of Economics, University of Aberdeen Business School, Scotland,
UK.
2
Since the widespread use of plastic for manufacturing and packaging began in the mid twentieth
century, levels of plastic production have risen dramatically to an estimated 390.7 million metric tonnes
(Mt) in 20214. At the same time, inadequate plastic waste disposal and processing systems, combined
with slow rates of degradation, have resulted in plastic becoming a globally ubiquitous pollutant5,6. The
presence of plastic pollution in the marine environment and its impact on marine wildlife is a particular
concern1,7.
It is estimated that between 4.8 and 12.7 Mt of plastic entered the world’s oceans from land in 20108.
Subsequent work has focused on the dominant contribution of rivers as a transport pathway for plastic
waste to the marine environment9–11. Although fewer estimates of marine inputs exist, fishing related
items are frequently reported in marine litter surveys12. The flux of plastic to the oceans is predicted to
increase in the future, with planned interventions unable to prevent ongoing significant accumulation
and associated negative impacts13,14.
A range of international frameworks include instruments to address MPP, including the European Union
(EU) Marine Strategy Framework Directive, the OSPAR Convention, the HELCOM Convention, and
the Barcelona Convention. Most recently, UN Member States voted to establish an Intergovernmental
Negotiating Committee (INC) with the mandate of advancing an international legally binding
instrument on plastic pollution, including the marine environment15. As the marginal benefits and costs
of reducing plastic waste vary between countries, effective and cost-efficient reductions of MPP require
international cooperation16,17.
Achieving such cooperation is challenging, however, due to the fact that any damage reduction to the
marine environment is primarily a public good18. The physical movement of plastic in and across
international waters implies that a substantial proportion of the environmental damages associated with
plastic waste emitted from a given country may be imposed on other countries. Consequently, although
expenditures on MPP reductions from any one country are incurred by that country alone, the benefits
of this unilateral abatement action are experienced by all countries whose territorial waters and
shorelines are impacted. This creates a well-known free-rider problem that dis-incentivises global
cooperation, even when the combined benefits of cooperation could far exceed the costs.
Recognizing this, our objective is to bring new and timely insights to bear on the net benefits of
international cooperation over MPP reductions, and the conditions under which mutually beneficial
coordination can occur. We focus on floating macroplastic (>0.5 cm in size) in the North Atlantic Ocean
that has entered the marine environment via rivers, before being moved within and between each
country’s territorial waters—defined here by their Exclusive Economic Zone (EEZ) (Figure 1a). This
integrated assessment supports a framework for quantifying (1) What abatement policy maximises the
net economic benefits of international cooperation in MPP reduction? (2) How are the benefits of
international cooperation distributed between different countries under the optimal cooperative
3
solution? (3) What is the impact of political economy constraints on these cooperative outcomes, in
terms of both the overall benefits of cooperation, and the reduction in plastics pollution?
The model is implemented using empirical estimates of (i) plastic transfer coefficients between
countries bordering the North Atlantic, and (ii) the economic benefits and costs of reduced MPP for
each country. We combine these elements using an adaptation of the game-theoretic framework in
Mäler19, initially applied to the case of sulphur dioxide (SO2) emissions that contribute to acid rain20.
While the two frameworks share a similar conceptual foundation, the differences between MPP and
SO2 pollution leads to important variations in model structure. Unlike SO2, buoyant macroplastic can
visit and cause damage in multiple locations within the marine environment before settling in a fixed
location or being broken down into micro or nano plastics. Additionally, the potential impacts of MPP
are diverse, causing potentially adverse effects on all marine life including sea birds, fish, and marine
mammals1. Further, citizens of a country may care not just about plastics deposited on their beaches or
found in their coastal waters, but also about plastics floating in the High Seas; i.e., in international
waters beyond the EEZ of countries and thus outside of any state jurisdiction21. The benefits of reducing
plastic pollution in these areas may also differ across regions. All these factors have implications for
identifying the (net) benefits of international cooperation over MPP reductions, how likely such
cooperation is to emerge, and what can be done to encourage it.
Plastic that enters the sea is not a “uniformly mixing” pollutant. Hence, a unit of plastic emitted by a
given country may contribute more or less to the stock of plastic pollution in a specific location than a
unit of plastic emitted by other countries. Plastic can move through the global oceans for many years
before eventually settling on the ocean floor, becoming permanently beached, or being degraded.
During this time, it may become temporarily beached multiple times, thereby causing damage in that
location, before being washed out to sea again. We therefore estimate not only the transition
probabilities of plastic transferred from a given country’s EEZ, but also the contributions of different
countries to the stocks of marine plastic imported into a given EEZ, with the latter used directly within
the economic model.
A particle tracking model22 was used with gridded surface ocean currents and wind data23,24, and annual
estimates of river plastic emissions10. A novel parameterisation of plastic removal was used to account
for the selective loss of buoyant plastic from surface waters to the subsurface and seafloor12, and to
align estimates of plastic inflows with the generally smaller estimates of surface ocean plastic
inventories25,26. This yields a matrix of transfer coefficients, where each value gives the annual average
fractional contribution of each country’s emissions to the stock of plastic in each country’s EEZ (Figure
1). Details about our estimation of these figures are given in Methods and in the Supplementary
Information (SI). The modelled countries in the North Atlantic were Belgium (BE), Canada (CA),
Denmark (DK), Dominican Republic (DO), France (FR), Germany (DE), Haiti (HT), Ireland (IE),
4
Mexico (MX), Morocco (MA), Netherlands (NL), Portugal (PT), Spain (ES), Sweden (SE), United
Kingdom (UK), and United States (US), as explained in the SI. The pathways connecting countries are
illustrated using a network diagram (Figure 2), which shows the fraction of the surface plastic stock
exported to adjoining waters per day, averaged over the final year of the model simulation.
A set of marginal damage cost estimates per unit of plastic emissions in each country’s national waters
and coastline was obtained based on original stated-preference estimates for the US and the UK21,
converted for each of the other 14 nations using a unit-value benefit transfer27, with adjustments for
income and purchasing-power parity (PPP). A country’s marginal benefit from reducing its plastic
emissions by one unit—equivalent to the marginal damage cost of one unit of unabated emissions—is
equal to the economic value of the ecosystem damages in its own coastal waters and beaches that are
avoided due to this reduction in plastic emissions. Unique benefits estimates are provided for MPP
reductions that impact the beaches and coastal waters of each modelled country.
We constructed an economic optimisation model which uses these two sets of parameters (transfer
coefficients and marginal damage costs) to calculate each country’s non-cooperative (selfish) level of
plastic emissions into the ocean, defined as the point at which its domestic marginal abatement costs
are equal to the marginal benefit of damage reductions in that country. These benefits pertain to MPP
reductions on countries’ beaches and coastal waters. This yields a unique, “selfish” or non-cooperative
Nash Equilibrium (NE) level of MPP abatement for each country, reflecting a situation from which no
individual country has an incentive to deviate, given that it will not improve their payoff. We then used
the same model to simulate the vector of abatement levels for each country which, instead, maximises
the net benefits (value of damage reductions minus abatement costs) across all 16 countries combined.
This forms the optimal “full cooperation” scenario which can be compared to the non-cooperative NE,
both for each country individually and when summed across all 16 North Atlantic countries. This full
cooperation outcome characterises the distribution of plastic abatement which maximises net benefits
summed across all 16 countries. It represents a coalition of cooperating nations who all agree to become
members of an International Environmental Agreement (IEA).
RESULTS
We take the sum of the non-cooperative NE to yield zero additional abatement over current (status quo)
emission levels. Countries are assumed to start from this outcome, and all results are then obtained
relative to this equilibrium of national-level marginal benefits and costs. In contrast to this case where
each country maximises its own net benefits unilaterally and independently from other countries’
abatement decisions, the purpose of an IEA is that signatory countries choose an abatement policy that
maximises collective net benefits. This means that each country reduces their plastic emissions up to
the point where their marginal cost of abatement is equal not to their own marginal benefit of abatement,
5
but to the sum of all countries’ marginal benefits. Based on transfer coefficients for the year 2014, this
economically efficient abatement policy results in a fall of 62% in plastic emissions to the North
Atlantic (Figure 3d), as compared to the non-cooperative NE outcome. The net collective benefits equal
around 54% of the total damage caused by MPP to the sample countries (Figure 3b). However, this
benefit is shared unevenly across countries, with the US and Germany receiving a higher share of the
benefit (Figure 3b). Countries tend to benefit more if they have high national income (since this drives
the benefit estimate adjustment for each country) and/or if they receive a large share of the plastic
emissions from other countries.
The largest share of abatement activity in the cooperative solution is allocated to countries who have
the lowest marginal abatement costs and/or are responsible for more MPP transferred beyond their EEZ.
This is explained by the fact that countries who transfer a higher fraction of their plastic pollution (i.e.,
countries with a relatively high transfer coefficient) have less incentive to abate in the absence of an
IEA, hence are required to do relatively more due to the agreement. Countries whose plastic emissions
are transferred to countries with higher gross national income (GNI) implement more abatement in the
optimal cooperative solution than countries whose plastic emissions are transferred to lower GNI
countries. For example, Mexico has higher abatement costs than Canada; yet it is required to conduct
more than three times as much abatement in the economically efficient outcome as Canada because it
has a larger impact on the stock of plastics in the US, which is the highest GNI country and thus
experiences relatively high damage costs. Some countries, such as Dominican Republic and the
Netherlands, are made worse off as a result of this cooperative outcome.
Since the gains from cooperation and abatement responsibility are so unevenly shared in the efficient
solution, we explored alternative scenarios where the cooperative solution is subject to a range of
political-economy constraints. The potential constraints are: (C1) no country is allowed to increase their
plastic emissions relative to the baseline (“positive abatement” scenario); (C2) every country must
derive equal net benefit from the agreement (“equal values” scenario); (C3) every country must agree
to reduce plastic emissions by the same percentage relative to the baseline (“equal abatement” scenario);
(C4) no country is allowed to experience negative benefits from the agreement (“positive values”
scenario).
The outcomes of these four scenarios are compared to the economically efficient cooperative outcome
(Figure 4; Extended data Table 3). When no country is allowed to increase emissions relative to the
baseline (C1), there is a small reduction in the overall economic net benefits, and a small increase in
total plastic abatement from 62% to 63% of current emissions. The equal value scenario (C2) leads to
large losses of potential benefits from international cooperation. When each country is required to cut
emissions by an equal amount (C3), total plastic abatement falls from 62% to 42% of the baseline, and
much lower net benefits are realised. When the policy is constrained to ensure that all countries are
6
better off (C4), the net benefits and the percentage of MPP abatement fall by more than half, from 54%
to 26% and from 62% to 25%, respectively. Thus, the least damaging constraint in terms of both overall
MPP reductions and net economic benefits is that of ensuring that no country is allowed to increase its
baseline emissions (C1).
DISCUSSION
Our modelling work sets out a generalisable framework for analysing the potential gains from
international cooperation when reducing MPP. Empirically, we show that there are large potential,
collective gains from international cooperation over reductions in MPP in the North Atlantic. This is of
particular importance given on-going efforts, led by the UN, to secure a global agreement on tackling
MPP. The optimal “full cooperation” MPP agreement for the North Atlantic, which we identify for the
first time, yields aggregate net benefits across all 16 countries of around $29 billion, and results in an
overall reduction of 62% in baseline emissions. However, countries benefit unequally (and some lose)
from this economically efficient outcome, with particularly large burdens of plastic abatement falling
on a few, low-income countries. Constraining the solution to bar countries from increasing emissions
relative to the baseline turns out to be relatively low cost, and to achieve similar levels of total
abatement. In contrast, an equal burden sharing agreement, where each country agrees to the same
percentage cut in plastic emissions, forgoes many of the benefits of full cooperation, as does an
agreement where each country receives the same net benefit.
When countries lose from a potential IEA, the incentives to participate are reduced or eliminated, unless
some credible side-payment regime can be put in place whereby countries who gain agree to compensate
the countries who lose28. Different damage cost and transfer coefficient values in our model could
clearly result in some countries indeed losing out from cooperation, giving rise to the need for such
side-payments.
Our results likely understate the economic benefits of reducing MPP, since the valuation data which is
used to estimate the benefits of reduced pollution damages for each country relate only to the values
citizens attach to reducing pollution in their own national beaches and coastal waters21. Citizens may
also value pollution reductions in international waters and in third party countries, meaning that the
benefits of abatement will be higher. Furthermore, Börger et al. refer only to reductions in buoyant
macroplastic21, whereas an IEA would also reduce stocks of plastic in the North Atlantic. Moreover,
our assumption that each country starts from a non-cooperative NE in terms of its abatement
expenditures has implications for the size of the net benefits of cooperation, since this assumption
implies that each country has put in place policies to internalise the negative national-level externalities
from MPP. If this is not the case (as seems very likely), benefits of international cooperation are likely
higher.
7
Figures
Figure 1. The area covered in the study, and summary results from the plastic transfer model. a) Map
showing the countries included in the study; the extent of their respective EEZs; their river emissions;
and the major ocean currents influencing the transfer dynamics of surface ocean plastic in the region.
b) Map showing the modelled, annual mean mass concentration of surface ocean macroplastic in the
North Atlantic in the year 2014. c) The annual mean of surface ocean plastic within each EEZ which is
exported per day to the EEZ of a neighbouring country, or to other waters, in the year 2014. d) The
annual mean stock of surface ocean plastic within the EEZ of each country in the year 2014, with colours
indicating the country from which the plastic originated.
8
Figure 2. Network diagram showing the stocks and flows of plastic within and between the EEZs of
countries included in the study. Other Waters (OW), representing international waters and the territorial
waters of all countries not included in the study, are included to highlight their important role in
mediating transfers between geographically separated territories. The relatively large stock for OWs
has been omitted from the diagram to help highlight differences in the stock in each country’s EEZ.
9
Figure 3. Results from the economic optimisation model for the fully cooperative scenario, evaluated
in the years 2012-2014. a) The benefit parameter which has been normalised to allow it to be expressed
in percentage terms. Its conversion to US dollars is accomplished by multiplying through by twice the
WTP to abate all pollution ($54bn) and dividing through by 100. b) The economic value that each
country gains from the policy expressed as a percentage of the total WTP. The vertical red bar highlights
the total value to all countries. c) The percentage of each country’s river emissions that are abated. The
black dashed horizontal line marks zero abatement. The vertical red bar highlights the total percentage
of river emissions abatement when summed across all countries. d) The percentage of the total plastic
stock abated. The vertical red bar highlights the total percentage of all plastic stock abated when
summed across all countries. Associated quantitative data is shown in Extended data Table 1.
10
Figure 4. Results from the economic optimisation model for the year 2014 under a range of political
constraints (see main text for details). a) Value of the policy in percentage terms. In the case of equal
abatement, abatement was equal to 42% for all countries (not shown). The vertical red line is used to
highlight the total value summed across all countries. b) Emissions abated in percentage terms. In the
case of equal value, the value was equal to 0% for all countries (not shown). The vertical red line is
used to highlight the total emissions abated summed across all countries. Associated quantitative data
is shown in Extended data Table 2.
11
Methods
The global public good aspect of the marine plastics problem effectively requires international
cooperation for efficient control and reduce plastics in the oceans16. Since both the marginal costs of
reducing current flows of plastics into the ocean and the marginal damage costs imposed by current
stocks in the sea (and thus the benefits from abatement) are likely to vary across countries sharing an
ocean border, efficient international management is likely to require (i) international cooperation in
reducing emissions and (ii) unequal emission reductions across states. Modelling results reported above
are based on the theoretical structure which we set out here.
Empirical data is used to calibrate a particle tracking model to compute transfer coefficients. Benefit
estimates are derived from a random utility, willingness-to-pay (WTP) space model estimated using
data from a previously published stated-preference choice experiment implemented in the US and the
UK21. These benefit estimates are then extended to all 16 North Atlantic countries using simple benefits
transfer methods based on differences in purchasing-power parity adjusted national income. Finally,
(economic) optimisation techniques are used to compute (i) each country’s selfish, non-cooperative
equilibrium, used here as a baseline; (ii) the abatement levels and net benefits arising in a full
cooperative agreement which maximises aggregate net benefits summed across all 16 countries and (iii)
abatement levels and net benefits in a range of other potential cooperation agreements, referred to as
“political-economy constraints.”
Plastic transfer model
The transboundary nature of the problem is captured by an transfer matrix . The (i,j)th entry of
the transfer matrix denotes the fraction of plastic originating from country i that contributes to the stock
in country j’s waters and coasts. We used the particle tracking model PyLag22 to simulate the movement
of plastic between emitting and receiving countries. The model was configured to read in driving data
from separate Ocean and Atmospheric General Circulation Models, which it used to compute simulated
particle trajectories and associated connectivity metrics.
In the study, we focussed on the surface transfer of buoyant plastic only and did not attempt to simulate
the movement of subsurface plastic or associated subsurface and seafloor inventories. The choice to
focus on the surface ocean only is consistent with its important role in mediating the transfer of plastic
between locations29; and with the areas referred to in questions used to determine respondents’
maximum WTP for plastic abatement, from which benefit estimates were derived21. We used surface
ocean currents and a simple model of leeway30, which combines the effects of windage and Stoke’s
Drift, to simulate the movement of buoyant plastic in the ocean. To facilitate the use of the model
outputs in the economic modelling, we configured it to asymptote toward a steady-state solution for the
12
total inventory of buoyant plastic at the ocean surface. This was achieved by assuming a constant rate
of emissions; and by allowing particle weights — representing the mass of plastic each particle
represents — to decay in time. Particle decay coefficients were pulled from a uniform distribution, with
lower values allowing plastic particles to travel longer distances before their mass at the ocean surface
is reduced to a negligible level (see Extended data Figure 1). In this way, the model was parameterised
to produce a surface ocean inventory and global distribution of floating plastic debris which is consistent
with existing published estimates25,26.
For a simulated particle on the sea surface with position vector , where is
the particle’s initial position vector, trajectories were computed using a Stochastic Differential Equation
(SDE) of the form:
(1)
where is the incremental change in particle’s position in the interval ; is a
velocity term; is the isotropic, horizontal eddy diffusivity; and is an incremental Wiener process
that builds stochasticity into the model. As we only consider motion at the ocean surface, vertical
advection and diffusion are ignored.
The velocity, , is:
,
(2)
where is the Eulerian surface ocean velocity at the location , is the corresponding
surface wind velocity at a height of 10 m above the ocean surface, and is the leeway or wind factor,
which determines an object’s sensitivity to wind forcing. Here, we make the simplifying assumption
that wind forcing drives the particle in a direction parallel to the downwind direction. This assumption
can be contrasted with search and rescue models, which often attempt to account for leeway divergence
using deflection angles derived from the tracks of objects at sea. Deflection angles typically fall in the
range of –30° to +30° and depend on the type of object being modelled30. For the wind factor, we used
a constant value of 0.02. The sensitivity of the model results to this parameter is explored in Extended
data Figure 5.
13
The impact of unresolved motions on particle movement are included through . is derived
from the surface ocean velocity field using the Smagorinsky equation31:
(3)
where C is the Smagorinsky constant, which is set equal to 0.2; and is taken to be the area of the
element in which the particle is located.
We used daily surface ocean current data (for variable ) covering the period 1995–2014, which were
taken from the 1/12° CMEMS Global Ocean Physics Analysis GLORYS12V1 dataset23; and hourly
surface winds (for variable ) covering the same period from the approximately 1/4° ERA5 dataset24.
Using the particle tracking model PyLag22, both grids were decomposed into a set of spherical triangular
elements covering the Earth’s surface, with velocity components defined at element nodes. Interpolation
of velocity components within elements was performed using each particle’s spherical barycentric
coordinates, giving C0 continuity. Gradients in the velocity field within elements, which were required
for calculations of , were computed by first rotating the corresponding Cartesian axes so the positive
z-axis forms an outward normal through the element’s centroid, and the x- and y-axes are locally aligned
with lines of constant longitude and latitude respectively. The element is then projected onto the plane
that lies tangential to the surface of the sphere at the element’s centroid, and gradients in x and y
calculated32.
The model was integrated forward in time by applying separate discrete integral operators for advection
and diffusion. For advection, a fourth-order Runge-Kutta scheme was used with a time step of 3600 s.
A Milstein scheme is used for the stochastic diffusive component, using a time step of 900 s.
In the triangular grid, all land elements were masked. If a particle transitioned into a masked element
during the integration, it was reflected back into the ocean. Thus, the transfer model does not explicitly
resolve beach inventories; rather, these are subsumed within the in-water inventory, and are treated as
one when used with the economic model. This is a pragmatic choice, which is motivated by the current
uncertainty associated with modelling beaching explicitly using coarse global ocean data34.
Plastic decay model
Several studies have noted an apparent mismatch between estimates of plastic emissions into the ocean,
and estimates of surface ocean plastic inventories, as derived from in situ observations and model
simulations25,26. These studies suggest the inventory of floating plastic litter is 1-2 orders of magnitude
less than estimated land-based emissions of plastic to the ocean each year. Many studies have since
14
explored mechanisms to explain the apparent discrepancy. These include, but are not limited to,
accumulation in rivers33, beaching34 and coastal trapping35. The relative importance of these
mechanisms has not been conclusively established.
Our plastic decay model is motivated by the finding that different types of non-buoyant and buoyant
plastic dominate in the coastal and open ocean, and in surface and seafloor environments12; and the
requirement to simulate steady-state conditions for use with the economic model. To allow the system
to approach a near steady-state inventory, each particle was associated with a weighting factor, , with
units of tonnes. Weighting factors were allowed to decay as a function of time, t. The mass of particle i
emitted from river j is then given by:
(4)
where is the mass of plastic emitted by river j each month; (= 100) is the number of particles
released from each river; and , with units of inverse time, is the decay factor for particle i. Each
particle is associated with a decay constant from the set . Extended data
Figure 1 shows how this model allows Belgium’s emissions to transition toward a steady state inventory
over the course of the simulation. Further details on how particle weighting factors are used to compute
plastic stocks and flows can be found in the SI. The sensitivity of plastic stock and flow estimates to
the choice of evaluation year and the value of the wind factor are shown in Extended data Figures 2-5.
Economic model
We adopt the transboundary pollution model of Mäler19. In this model, countries choose how much
pollution abatement to carry out given the national-level costs and benefits of abatement. The gains
from cooperation are given by the difference between a country’s payoffs when they internalise the
impact of their abatement choices on other countries, versus when they ignore them. We formalise and
discuss each of these components in turn. The model was implemented and coded in Mathematica
(version 12.2).
There is a set of countries , with a generic country labelled by . Each country chooses to abate
a percentage of its current (“status quo”) plastic emissions. If , then country continues
to emit its status quo level of polluting emissions; if , then country increases its level of
emissions relative to the status quo. We denote the vector of abatement choices by (we
use notation “” to indicate that the symbol on the left is defined by the expression on the right).
15
The total abatement cost of choice is described by a country-specific function, . We assume
the total abatement cost function satisfies the standard conditions that (i) is increasing and convex;
(ii) there is no additional cost in maintaining the status quo (i.e., ); (iii) the marginal cost of
abating a percentage of pollution tends to infinity as the percentage of abatement tends towards 100
percent (i.e.,
). A simple function satisfying these criteria is defined by:
(5)
where is country ’s cost parameter. The derivative of this function at 0 is , so is
the marginal cost of abatement at the status quo level.
The transboundary nature of the problem is captured by an matrix, (Figure 1d). The th
entry of this matrix denotes the fraction of the stock of buoyant plastic in country ’s waters that
originated from country . We calculate it from the transfer matrix by dividing each th entry by
the sum of the entries in column . If countries commit to a vector of abatement choices, , then the
stock of plastic in country ’s EEZ falls by a fraction . We refer to this as country ’s
“received abatement.” The vector of received abatement is given by . The total
stock of plastic reduces by . This relationship depends on the stock
being in the steady state, as computed using the transfer model.
Country ’s benefit of a percent of abatement is described by a country-specific benefit function,
. Following the literature3,36, we assume that (i) the benefits are quadratic in the percentage of
pollution abated; and (ii) the marginal benefit of full abatement is zero. Moreover, the benefits of the
status quo emissions are normalised to zero. Together, this implies that:
(6)
where is a country-specific damage parameter. Note that , so is country ’s
marginal benefit of abatement at the status quo level. All national-level economic benefits to country i
from abatement relate to damage reductions in the coastal waters and beaches of that country.
Country ’s payoff (“value”) from abatement vector is:
(7)
16
The outcome of abatement vector is the vector of resulting values, , and the total
value is the sum . If country non-cooperatively maximises its own value, then it
chooses to satisfy the first-order condition (FOC)
. In our context, country ’s FOC can be
written as:
(8)
which indicates that the marginal benefit of a unit of pollution abatement to country is equal to the
marginal cost of abatement, given that it can only affect a fraction of their incoming plastic pollution.
A strategy profile is a pure strategy Nash equilibrium if equation (8) holds for all countries .
The corresponding Nash value vector is , and the Nash value is . Existence of this is
guaranteed37 if we make the reasonable assumption that there is a lower bound on how much pollution
each country can abate (or equivalently, an upper bound on how much pollution each country can emit).
Following Mäler19, we assume that the status quo abatement choices are part of a non-cooperative Nash
equilibrium. This means that equation (8) is satisfied for all countries for , i.e.,
for all . This identifies country ’s cost parameter as:
(9)
Mäler19 uses this condition to identify the unknown damage (benefit) parameters, , from his empirical
marginal abatement cost estimates, . We do the opposite: using our assumption that status quo
abatement is a Nash equilibrium, we estimate benefit parameters from the available data (discussed
below) to determine the cost parameters.
The cooperative abatement profile, , is that which maximises net benefits across all countries in the
set aggregated together: . The fact that is concave in and convex in implies that each
is concave in . This subsequently implies that is concave in (and strictly concave so long
as at least one of the benefit or cost parameters is non-zero). Therefore, any solution to the system
of FOCs,
, characterises the unique global maximum. In our case, this condition
simplifies to:
(10)
17
This indicates that each country should abate at the level that sets their marginal cost of reducing
domestic emissions (the left-hand side of equation (10)) equal to the marginal benefits of this reduction
in pollution to all countries impacted by country (the right-hand side). Substituting equation (9) into
(10) yields:
(11)
The strategy profile is the optimal cooperative strategy profile. Equation (11) reveals that it depends
on neither the levels of the damage parameters , nor on the levels of the plastic quantities , but only
on their relative values. The cooperative value vector is , and the cooperative value is
.
For a given Nash equilibrium strategy , the gains from cooperation are equal to the difference
. We assume that status quo abatement is a Nash equilibrium, so , , and thus
the gains from cooperation are equal to exactly
. In any case, we necessarily have
for
all strategies , including any Nash equilibrium , because is the unique maximiser of
. It
follows that the gains from cooperation are always positive. This does not imply that
for each individual country , so it may be the case that some countries are worse off in the cooperative
outcome.
We obtain estimates of the benefit parameters for the UK and the US from a discrete choice
experiment (DCE) data designed to provide estimates of per household willingness to pay (WTP) for
different types of MPP abatement. Methods and data from these DCEs are described by Börger et al.21.
We use a mixed logit model38,39 in WTP space of equation (6) to estimate that the average UK household
is willing to pay $1.510 to abate 1% of buoyant plastic from UK domestic beaches, and $1.559 to abate
1% of buoyant plastic from the UK coastal waters. Models were run in R40 using the ‘Apollo’
package41,42 to produce these estimates (details in SI). Summing these provide a lower-bound
household WTP of $3.069 for abating 1% of MPP from the UK’s EEZ. With 28.535 million households
in the UK43, this national WTP estimate is approximately $88mn. It follows that UK
, such that .
Similarly, for the US we obtain WTP estimates of $1.718 and $1.644 for abating 1% of beach and
coastal pollution, respectively, yielding a total of $3.362 to abate 1% of buoyant plastics from US
waters. There are roughly 128.45 million households in the US44, and following the same routine yields
.
18
Employing international benefit transfers methods45, we use income-adjusted, income- and purchasing
power parity (PPP)-adjusted unit-value benefit transfers to estimate the WTP of the other countries in
the set. If the WTP of a household is known, this benefit transfer technique estimates the WTP of
another household using the relationship WTP
WTP, where and are the households’
respective incomes, and is an estimate of the income elasticity parameter45. Since our primary concern
is on countries rather than households, we adapt this method by estimating country ’s WTP parameter
by
, where and are the Gross National Incomes (GNI) of countries and
respectively. This approach is used because it obviates the need to reconcile estimates of household
numbers across countries in the simulation, as needed for traditional benefit aggregation and transfer.
It should be noted the applied approach will only yield equivalent results to those of a standard income-
and PPP-adjusted unit value benefit transfer45 for the restricted case in which . For all
other cases, the GNI-adjusted benefit transfer will produce comparatively larger benefit estimates for
countries with larger numbers of households when , and smaller benefit estimates when .
The fact that we already have WTP estimates for the UK and the US means that we can use the equality
UK UK
US US to calibrate the income elasticity parameter as UKUS
UKUS.
Substituting the UK and US estimates into this expression, together with purchasing power parity
(PPP) adjusted 2021 GNI estimates46 of $3,327bn and $23,393bn for the UK and US, respectively,
yields an estimate of , which is commensurate with measures found in other studies45.
19
Acknowledgements This work was conducted as part of the project “The Economics of Marine Plastic
Pollution—What are the Benefits of International Cooperation?” funded by the UK Economic and
Social Research Council (ES/S002448/2). The support of the ESRC is gratefully acknowledged. This
work used the ARCHER2 UK National Supercomputing Service (https://www.archer2.ac.uk). The
findings, interpretations and conclusions presented are entirely those of the authors, and any errors
remain those of the authors alone.
Author contributions Idea conceptualisation: NH, FdV; Obtaining original research funding: NB, TB,
JC, NH, RJ, FdV; Design of transfer model simulations: JC, CS, FdV, NH; Estimation transfer
coefficients: JC; Choice experiment design and analyses: TB, NH, RJ, KM; Economic modelling: CS,
FdV; Graphics: JC; Contribution to writing: All authors.
Funding Provided by the UK Economic and Social Research Council (ES/S002448/2).
Competing interests The authors declare no competing interests.
Code availability The particle tracking model PyLag v0.7 is open-source software that can be accessed
at https://github.com/pmlmodelling/pylag/. The online documentation contains tutorials on how to use
the model to perform particle tracking simulations: https://pylag.readthedocs.io/en/latest/.
Configuration and analysis code for both the plastic transfer and economic models can be accessed here:
https://github.com/pmlmodelling/beaumont_et_al_plastics_econ.
Additional Information
Supplementary Information is available for this paper.
Correspondence and requests for materials to Frans P. de Vries.
20
Extended data
Extended data Table 1. List of countries and associated Exclusive Economic Zones (EEZs) included
in the study, and their river plastic emissions as reported by Meijer et al10.
Country name
Country
code
Exclusive Economic
Zones (EEZs)
Number
of rivers
Total plastic
emissions / t yr-
1
Belgium
BE
Belgian EEZ
8
32
Canada
CA
Canadian EEZ
241
237
Denmark
DK
Danish EEZ
22
5
Dominican
Republic (Dom.
Rep.)
DE
Dominican Republic EEZ
178
6027
France
DO
French EEZ
200
234
Germany
FR
German EEZ
67
132
Haiti
HT
Haitian EEZ
231
6929
Ireland
IE
Irish EEZ
80
105
Mexico
MX
Mexican EEZ
420
2218
Morocco
MA
Moroccan EEZ;
Overlapping claim
Western Saharan EEZ
91
1834
Netherlands
NL
Dutch EEZ
46
265
Portugal
PT
Portuguese EEZ;
Portuguese EEZ (Azores);
Portuguese EEZ
(Madeira)
75
75
Spain
ES
Spanish EEZ; Spanish
EEZ (Canary Islands)
154
214
Sweden
SE
Swedish EEZ
48
36
United
Kingdom (UK)
UK
United Kingdom EEZ
416
701
United States
(US)
US
United States EEZ;
United States EEZ
(Alaska), United States
EEZ (Hawaii)
940
2429
21
Extended data Table 2. Results from the fully cooperative solution using plastic transfer coefficients
for the years 2012, 2013 and 2014 (see Figure 3).
Country
code
GNI /
$bn
/ %
/ %
a / %
A / %
/ %
a / %
A / %
/ %
a / %
A / %
2012
2013
2014
BE
688
2.3
0.9
77.2
33.5
0.9
78.8
33
1
68.8
38.6
CA
1976
5.4
-0.2
10.4
3.2
-0.1
12.4
5
0.9
6.8
11.8
DK
390
1.4
0.8
73.5
35.2
0.7
63.8
30.7
0.7
68.6
31.3
DO
216
8.6
4.2
7.2
32.9
4.1
8
32.1
4.4
5.8
33.1
FR
3499
11.4
7.1
-20.8
30.6
6.6
-13.5
29
6.7
-14.8
29.1
DE
4961
0.9
-2.5
87.7
87.5
-2.6
88.5
88.3
-2.7
88.6
87.9
HT
36
0.2
-0.9
98.5
94.3
-0.9
98.5
95
-0.8
98.7
94.2
IE
399
1.4
0.4
55.1
48.4
0.4
53.9
42.1
0.1
40.6
37.2
MX
2501
6.5
4
25.5
60.1
4.4
22.8
62.1
4.5
24.3
63.6
MA
328
1.2
-0.7
50
49.9
-0.5
43.8
44.7
-0.6
47.9
48.4
NL
1110
3.3
-0.9
66.6
48
-1.2
65
49.5
-1.4
69.5
47.1
PT
365
1.3
1
45.3
54.2
1
59.9
56.6
0.9
55.6
49.8
ES
1939
5.3
2.3
43
46.6
2.3
37.5
43.2
2.4
37.3
43.7
SE
636
2.1
1
-19.4
21.2
0.8
-10.2
18.5
0.8
-7.7
19.7
UK
3327
8.2
0.8
28
35.2
1.1
26.6
34.4
0.7
22.4
27
US
23393
40.5
35.9
-14.9
58.5
36.2
-19.1
56.4
37
-25.6
55.8
Total
-
100
53.2
61.8
61.8
53.1
61.4
61.4
54.4
61.6
61.6
Notes: Country codes are listed in the main article. Purchasing power parity (PPP) Gross National
Income (GNI) data is for 2021. It was downloaded in December 2022, and is subject to revision46. is
the benefit parameter, normalised by the WTP to abate all pollution ($54bn), which was calculated for
all countries using equation (6). is the value from the policy, given as a percentage of $54bn. a and A
are the emissions and stocks abated, expressed in percentage terms. The total stock abated excludes
plastic in international waters.
22
Extended data Table 3. Results from the economic optimisation model for the year 2014 under a
range of political economy constraints (see Figure 4).
Country
code
/ %
(C1)
/ %
(C2)
/ %
(C3)
/ %
(C4)
a / %
(C1)
a / %
(C2)
a / %
(C3)
a / %
(C4)
BE
0.96
0
1.3
1.07
67.94
-0.36
42.02
76.98
CA
1.86
0
1.28
1.36
0.55
2.13
42.02
11.83
DK
0.78
0
0.93
0.65
66.62
92.55
42.02
69.89
DO
4.64
0
2.5
3.35
3.86
2.01
42.02
19.05
FR
6.35
0
3.3
5.21
0
4.74
42.02
-7.58
DE
-2.61
0
-0.33
0.1
87.55
0
42.02
10.85
HT
-0.78
0
0.01
0.04
98.62
0.05
42.02
27.74
IE
0.09
0
0.11
0.39
40.25
-0.4
42.02
39.27
MX
4.74
0
1.98
1.74
18.16
0
42.02
55.61
MA
-0.52
0
-0.41
0.21
46.6
0
42.02
17.02
NL
-1.3
0
0.47
1.07
68.14
-0.51
42.02
48.64
PT
0.99
0
0.82
0.44
52.96
0
42.02
83.54
ES
2.53
0.02
2.09
1.59
35.9
0
42.02
48.99
SE
0.92
0
0.75
0.71
0.23
30.32
42.02
-4.39
UK
0.77
0
-1.41
2.01
21.44
-0.56
42.02
27.36
US
34.24
0.04
16.34
14.94
0
0
42.02
18.16
Total
53.66
0.06
29.73
25.5
62.91
0.09
42.02
25.47
Notes: is the value from the policy, given as a percentage of $54bn. a is the percentage of emissions
abated. Results are given for the political-economy constraints C1-C4, as described in the main article.
Extended data Figure 1. The accumulation of surface plastic emitted by a single country (Belgium) as
a function of time. With constant emissions10, the simulated inventory of surface plastic asymptotes
toward an imposed steady state where new inputs are balanced by losses from the surface. Results from
the model are analysed in the years 2012–2014.
23
Extended data Figure 2. Variations in the annual mean mass concentration of plastic in the years 2012
(a), 2013 (b) and 2014 (c).
24
Extended data Figure 3. Variations in the annual mean plastic stock within the EEZ of each country
in the years 2012 (a), 2013 (b) and 2014 (c); with colours indicating the country from which the plastic
originated.
25
Extended data Figure 4. Transfer matrices showing exposure assessed in the years 2012 (a) and 2013
(c), and the difference relative to exposure assessed in the year 2014 (b and d respectively). Receiving
countries with exposures < 10 t d, based on a given country's emissions, have been masked (grey
shading in figures b and d). The calculation of exposure is described in the SI.
26
Extended data Figure 5. Difference plots showing the percentage change in exposure for different
values of the wind factor. Exposure is calculated for a single year of emissions, in which plastic was
released on the 1st of each month in the year 1995. Exposure is calculated over a period that extends
from 1st January 1995 – 31st December 2014. a) Exposure calculated using a model of leeway and
using a wind factor of 1% in the direction of the wind. b) Percentage difference in exposure relative to
the standard run, which uses a wind factor of 2%. c) Exposure calculated using a wind factor of 0%
(i.e., particles are moved by surface ocean currents only). d) Percentage difference in exposure relative
to the standard run. Exposures < 10 t d have been masked (grey cells).
27
Supplementary information
Choice of countries and territories
We limited our study to a selection of countries surrounding the North Atlantic Ocean, where the North
Atlantic and surrounding coastal waters play a dominant role in facilitating the transboundary transfer
of marine plastic debris. The study was further limited to countries for which consistent plastic river
emissions data was available10. The southern boundary of the study was drawn at Mexico and Morocco
on the Western and Eastern sides of the North Atlantic respectively. Given the highly restricted flow of
water between the North Atlantic and the Mediterranean Sea through the Strait of Gibraltar, we
excluded all Mediterranean countries without a coastline facing onto the North Atlantic. Another
notable omission was Norway, for which we lacked consistent data on plastic emissions. Of the complex
set of small island states and overseas territories in the Antilles, only Haiti and the Dominican Republic
were included. Cuba, which is the largest island in the area, was excluded as we lacked plastic emissions
data for it. Lastly, in North Africa, the disputed territory of Western Sahara was joined with Morocco
and included as a single territory for the purpose of the study. In all cases, data on country boundaries
and names were taken from the Natural Earth dataset (https://www.naturalearthdata.com/).
To determine the presence and absence of plastic within the territorial waters of a given country, we
defined the territorial waters of each country by its Exclusive Economic Zone (EEZ). The boundary for
each EEZ was taken from v11 of the Marine Boundaries dataset (https://www.marineregions.org)47.
Within the Marine Boundaries dataset, the boundary of EEZs for some exclave and semi-exclave
regions are entered separately. With a few exceptions, these were combined to give the full EEZ of the
associated country (see Extended data Table 1). Some exclave regions were excluded. In the case of
France, we limited the study to European France, including the island of Corsica; other regions of
France, including French Guiana in South America, were excluded. Although we decided to include the
Pacific facing US states of Alaska and Hawaii, their contribution to inter-country transfers of plastic
was small. If a region was excluded, both its emissions and its associated EEZ were omitted from the
study.
Particle release scenarios
The location of all river mouths was extracted from the Meijer et al (2021) dataset10. River locations
were associated with countries by searching for the nearest country to the river’s geographic coordinates
using country-level shapefile data from the Natural Earth dataset. The dataset was then trimmed so it
only included rivers specific to countries listed in the study. The study was simplified in the sense that
emissions from a given river were, in their entirety, associated with a single country, determined by the
location of the river mouth, irrespective of whether the river’s drainage basin spanned the territory of
multiple countries or not.
28
As the 1/12° ocean model grid on which the sea surface velocity field is defined provides a relatively
poor fit to the global coastline, the exact location around which particles were released into the model
domain were determined by searching for the centroid of the nearest ocean element to the river’s mouth.
These locations were then used as the central coordinates for a set a circular release zones, each of
radius 1 km, and within which 100 particles were randomly scattered. In the Meijer et al dataset10, there
were 3217 rivers associated with the 16 countries included in the study, yielding a total of 3.217 x 105
particles per simulation.
The Meijer et al dataset10 lists the amount of plastic emitted by each river per annum. In our simulations,
we spread the emissions over a year by releasing one set of particles per month, resulting in 12 particle
releases per year. The decision represents a balance between capturing short term variations in currents
and overall computational complexity. In all cases, particles were released at 1200 on the 1st of each
month and their positions saved to file at 1200 on each day of the simulation. In the set of core
simulations, monthly particle releases were started at 1200 on 1st January 2000, and ended with a particle
release at 1200 on 31st December 2014. Each monthly release was run as a separate simulation, yielding
180 simulations involving more than 5.0 x 107 particles in total. All simulations were terminated at
1200 on 1st January 2015. A second set of slightly longer runs were performed to investigate the
sensitivity of the model results to parameter choices and different configuration options. In these
simulations, a set of 12 monthly releases were performed for the year 1995. In all cases, the model runs
were again terminated at 1200 on 1st January 2015.
Calculation of plastic inventories and stocks
The total mass of plastic at time t, , from a single monthly release is calculated using:
(A1)
where NR is the number of rivers. The total amount of plastic in the ocean, , resulting from an
ensemble of releases, is found by further summing equation (A1) over the set of monthly releases, while
the contribution of an individual country to the total inventory is found by limiting the set of rivers, ,
to rivers from that country alone. The stock of plastic in a country’s EEZ is computed by summing the
masses of just those particles that lie within the EEZ at time t (see also next section).
Calculation of plastic fluxes between countries
The flux of plastic moving between countries is calculated based on the presence-absence of plastic
within the EEZs of each country, as determined from particle positions which are defined at discrete
points in time. The flux of plastic, , between two countries k and l, is defined as the annual average
29
daily flux of plastic that flows between the two countries. It is used to compute the export fraction, as
showing in Figure 1c of the main article. For a single simulation in which particles are released at time
, is calculated using:
(A2)
where and correspond, respectively, to the first and last day indices of the target year for
which fluxes are being calculated; is the total number of particles released from all rivers in all
countries; and
and
are discrete variables calculated using case expressions of the form:
which identify whether a particle resides within the EEZ of a country or not – as determined by testing
whether the particle’s point location lies within a polygon (or polygons) that defines the area of the
EEZ. Fluxes are calculated using particle weights defined at the time point, , reflecting the mass
of plastic in the EEZ of receiving country l which was previously in the EEZ of country k. The difference
between the particle’s weight at the two time points, , is the fraction which is assumed
to have sunk away from the sea surface, or to have been removed by other processes not explicitly
represented in the model, as determined by each particle’s decay factor. It should be noted that in this
method, no special attention is given to where the plastic originally came from (i.e., the river and country
from which it was emitted).
In the set of core simulations, monthly releases were repeated at 1200 on the first day of each month,
starting at 1200 on 1st January 2000. While setting equal to the date/time of each monthly particle
release, a single set of fluxes for all members of the ensemble was formed by summing the fluxes
corresponding to each monthly release (equation (A2)) for the given target year.
Calculation of exposure to plastic waste originating from different countries
A second metric called exposure was introduced to further investigate and visualise how each country
was impacted by the emissions from other countries; and to explore model sensitivity. The exposure
metric, , is designed to account for both the mass of surface plastic within the EEZ of country l, and
the amount of time it spends within with the EEZ, following its emission by country k. The metric is
effectively an integral over time, which accounts for changes in the weights of particles in time.
30
Exposure from a single monthly release of particles is calculated from particle positions and weights
using:
(A3)
where the summation is performed for just those particles, , emitted from rivers associated with
country k. Here, the summation in time is done over all time points from the start of the simulation to
some end time index, . Exposure from cumulative monthly particle releases, performed over a single
year, were calculated by further summing equation (A3) over the set of monthly releases.
Choice modelling methodology
The development and application of the discrete choice experiment are described in Börger et al.21. The
specific model to analyse these data differs from that in the paper and is explained in the following. The
choice data were analysed using a mixed multinomial logit model in WTP-space38,39. In this model, the
utility of respondent choosing alternative in choice occasion , , is assumed to
consist of an observable component and an error term :
(A4)
It is further assumed that can be represented by a linear-additive indirect utility function
consisting of the matrix containing the values of all non-monetary attributes of ; , the cost to
the decision-maker of ; as well as and , a conforming parameter vector and scalar to be estimated.
The above model in preference space can be transformed into WTP-space as:
,
(A5)
where
. While equations (A4) and (A5) are behaviourally equivalent, the elements of
in (5) can be interpreted directly as marginal WTP estimates for the changes in the different attributes.
To accommodate possible preference heterogeneity, all parameters are subscripted by to allow them
to vary over decision-makers. In the model in WTP-space, assumptions about the form of the
distribution of the parameters can be made directly for the elements of and ; the former of which
are assumed to follow a normal distribution, the latter of which follows a lognormal distribution with
sign change.
31
Assuming that follows a Type I Extreme Value distribution and that respondent in each choice
situation selects the alternative which maximises their utility, the joint probability of a series
of choices is:
(A6)
Since the mixed multinomial logit model does not have a closed-form solution, simulated maximum
likelihood is used to estimate the parameters in equation (A5). 1,000 Sobol draws are used to simulate
the likelihood function. Models are estimated in R40 using the ‘Apollo’ package41,42. To promote
convergence, both the cost variable and the percentage changes in plastic pollution in are
divided by 100 prior to estimation. Hence, the resulting WTP estimates (
) are directly interpretable
as marginal WTP estimates (in US dollars) for a one-percent change in pollution.
Importantly, in this specification, the level of attribute in one specific choice alterantive is calculated
based on the percentage change in area-specific plastic pollution, , as
. With this
specification, the estimated parameter can be interpreted as the marginal (money-metric) utility of
changing the level of pollution by one percentage point while ensuring that the marginal utility is equal
to when no abatement happens (i.e., ) and at full abatement (i.e., ). The results of
the two mixed multinomial logit models are presented in Table S1.
32
Table S1: Mixed multinomial logit models in WTP-space
UK-US
US-UK
Coefficient
s.e.
Coefficient
s.e.
Mean of random parameters
None
-1.330
***
(0.042)
-1.169
***
(0.097)
Beach
1.510
***
(0.095)
1.718
***
(0.118)
Coastal
1.559
***
(0.245)
1.644
***
(0.232)
International
1.172
***
(0.201)
1.550
***
(0.351)
Foreign
0.628
***
(0.152)
0.521
***
(0.219)
Csplit_25home
-0.091
***
(0.031)
-0.252
***
(0.048)
Csplit_75home
-0.342
***
(0.034)
-0.195
***
(0.039)
Cost
0.552
***
(0.074)
0.404
***
(0.070)
Standard deviation of random parameters
None
3.553
***
(0.121)
4.828
***
(0.300)
Beach
1.515
***
(0.059)
-2.388
***
(0.165)
Coastal
0.004
(0.097)
-1.052
***
(0.237)
International
-2.797
***
(0.215)
4.473
***
(0.530)
Foreign
0.633
***
(0.124)
-1.192
***
(0.204)
Csplit_25home
-0.247
***
(0.017)
0.408
***
(0.144)
Csplit_75home
0.561
***
(0.025)
0.573
***
(0.053)
Cost
1.580
***
(0.113)
1.145
***
(0.102)
Number of respondents
2,014
2,661
Number of choices
10,070
13,305
Log-Likelihood
-7,798
-10,188
Adj. Rho-squared
0.291
0.299
BIC
15,743
20,528
Notes: 1,000 Sobol draws were used to simulate the likelihood; BIC: Bayesian information criterion
33
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