Emission Permit Trading for Air Pollution Hot Spots
By Werner Antweiler∗
A conventional emission permit market is inefficient for nonuniformly mixed pollutants that create geographic ‘hot spots’ of different ambient emission concentrations and environmental hazard.
Economically efficient ambient concentration markets involve difficult interactions among multiple markets that makes them practically infeasible. This paper advances a novel type of single permit market with a hybrid price-quantity instrument that addresses
the dual heterogeneity of firm-specific abatement costs and regional
varation in hazard. An empirical measure of plant centrality is introduced that captures each plant’s strategic interaction potential.
Analytic solutions and simulation results demonstrate the feasibility of the market concept, which is then applied to analyze emissions of metallic air toxics (in particular mercury) in Canada.
JEL: Q53,Q58
Keywords: emission permits; permit markets; air pollution; pollution hot spots; environmental policy
While emission permit trading systems have grown in use over the last number
of years, their application potential remains somewhat limited because such trading systems work well only for uniformly mixed pollutants such as greenhouse
gases or widely dispersed pollutants such as sulfur dioxide. However, conventional emission permits for non-uniformly mixed pollutants such as air toxics are
∗ Sauder School of Business, University of British Columbia, 2053 Main Mall, Vancouver, BC,
V6T 1Z2, Canada. Phone: 604-822-8484. E-mail: werner.antweiler@ubc.ca. An earlier version of
this paper was entitled ‘Smart Emission Trading for Toxics: Spatial Heterogeneity and Hybrid Regimes.’
This paper has benefited hugely from presentations at the University of British Columbia, the University
of Kiel, the University of Cologne, York University, the University of Maryland, as well as the Canadian
Economics Association conference in 2007. I am grateful to all the audiences and individuals who have
provided feedback and comments. Special thanks to Till Requate for helping me appreciate the merits
of hybrid policy instruments.
1
inefficient. Since the work of Montgomery (1972) it is known that the theoretically ideal alternative employs “ambient concentration contribution permits” in
which permits are contracted in fractions of emission concentrations; see Tietenberg (2006, chap. 4) for an extensive discussion. In the presence of strong spatial
heterogeneity, defined by the location of emission points (plants) and receptor
points (people), ambient concentration permit markets suffer from practical limitations. Most importantly, such a system requires a large number of markets to
work efficiently. As Atkinson and Tietenberg (1987, p. 372) point out:
An ambient permit market is complex, because it involves a separate permit for each monitored receptor where air quality equals the
standard. Any source seeking to increase its emissions would have
to purchase sufficient permits from each of these monitored receptors.
Since the source’s emissions would affect air quality differently in each
of these markets, the interdependence of its decisions in these multiple
markets creates a rather complex pattern of transactions.
The multiplicity of markets implies high transaction cost and low liquidity of the
traded permits. A further problem is the nature of the permit contracts. Unlike
emission permits, ambient concentration contribution permits may be difficult to
monitor and enforce as additional contributions to emission concentrations at a
given receptor location may be subject to large stochastic variation. It is much
easier to monitor emissions at the source.
In the presence of these challenges, finding suitable practicable alternatives to
implement a market solution for non-uniformly mixed pollutants has been elusive.
Many of the alternatives suggested in the literature appear to offer very complex
solutions. The key to a practicable alternative is simplicity and objectivity. A
trading system is simple if it keeps transaction costs low, and offers verifiable and
enforceable contracts. It strives for objectivity by basing any firm-specific rules
on measurable quantities that are relatively immune to challenge or lobbying.
In an UNCTAD report Tietenberg et al. (1999, pp. 105-7) comment on design
2
principles for a permit trading system:
The emissions trading system should be designed to be as simple as
possible. The historic evidence is very clear that simple emissions
trading systems work much better than severely constrained ones.
The transaction costs associated with implementing and administering an emissions trading system rise with the number of constraints
imposed, and as transactions costs rise, the number of trades falls.
As the number of trades falls, the cost savings achieved by the programme also decline. [...] Transaction costs play a key role in the
success or failure of an emissions trading system. In the past, only
emissions trading programmes with low transaction costs have succeeded in substantially lowering the cost of compliance.
This paper proposes a new practicable emission trading system for non-uniformly
mixed pollutants. It involves a single emission permit market with permits based
on firms’ actual emissions. However, to provide the economically-efficient incentive for reducing emissions more aggressively in air pollution ‘hot spots,’ firms
contributing emissions to ‘hot spots’ must face a higher effective permit price
than firms outside these ‘hot spots.’ On the other hand, a unified permit market
only has a single market-clearing price. The key insight to facilitate this effective price differentiation is to require firms to buy a number of permits that is
proportional to their emissions rather than exactly equal to their emissions. The
implicit adjustment factor reflects the firm’s contribution to the environmental
hazard. For example, a firm contributing pollution to a hot spot may have to buy
twice as many permits as their actual emissions, while firms outside the hot spot
may have to buy permits for only half of their actual emissions. This adjustment
factor, henceforth referred to as the hazard factor, can be determined scientifically
and attributed to each firm prior to trading. With this adjustment in place, an
individual firm faces an effective permit price per unit of emissions that is equal
to the product of the market permit price and the hazard factor. Each firm buys
3
emission permits equal to the product of its emissions times its hazard factor at
the prevailing permit market price.
The intuition behind this simple concept is that price and quantity signals are
both economically efficient (at least without uncertainty), and that both signals
can be mixed in a hybrid fashion. Policy hybridization plays an important role in
environmental policy discussions since the seminal work by Roberts and Spence
(1976). In their work, price floors and price ceilings can improve the overall
efficiency of the system by ensuring sufficient dynamic incentives to innovate (price
floor) and relief from sudden price spikes (price ceiling, or allowance reserve). A
hybrid price-quantity system is envisioned in this paper to overcome limitations
of previously-proposed emission permit markets for ‘hot spots.’ While the use
of multiple (hybrid) policy instruments has been considered extensively (e.g.,
Bennear and Stavins, 2007) in particular with respect to second-best approaches,
the hybrid price-quantity mechanism proosed here aims at achieving first-best
optimality, albeit sequentially rather than instantaneously.
This paper also introduces a novel concept of ‘plant centrality’ that captures the
potential for spatial interaction among firms. This measure is useful for identifying
the potential usefulness of a hot-spot permit market that involves intra-regional
as well as inter-regional trade-offs. The feasibility of the market concept is further
explored in the context of metallic air toxics in Canada, in particular mercury.
I.
The ‘Hot Spot’ Problem in Environmental Economics
With non-uniformly mixed pollutants, emission concentrations vary strongly
across receptor locations. ‘Hot spots’ are localized areas with high concentrations
of the pollutant. The efficacy of any policy intervention depends crucially on how
it targets these ‘hot spots.’ The more localized these hot spots, the more localized
the intervention needs to be, as the largest environmental benefits are generated
by reducing the ambient concentrations in these hot spots.
In the presence of information asymmetries between regulator and firms, emis4
sion permit trading systems (as well as pollution taxes) are demonstrably more efficient than conventional command-and-control regulation through emission standards. For non-uniformly mixed pollutants, ambient concentration permits are
more efficient than simple emission permits. Nevertheless, the efficiency rank
order of these regulatory interventions may be greatly affected by large differences in transaction costs. Stavins (1995) notes that even complicated trading
systems with relatively high transaction costs will likely dominate command-andcontrol regulation because there is substantial heterogeneity in abatement cost
(i.e., abatement technology) across plants. A trading system provides flexibility
to plants in choosing the pollution abatement technology that is best suited for
their particular environment.
Transaction costs for permit trading systems consist of a variety of specific costs,
which in turn are driven by particular economic factors (Egenhofer, 2003). Search
costs, the cost of matching buyer and seller, are greatly reduced through organized
exchanges, but crucially depend on the liquidity and transparency of the market.
Negotiation costs arise from contracting and standardization of contracts through
permit exchanges. These depend on the clarity of the property rights assigned
by the contracts. Monitoring costs arise through verification of compliance, but
are typically borne by the regulator. Similarly, enforcement costs arise in the
case of non-compliance when the regulator needs to enforce compliance or fine
violators. For individual firms there are also numerous types of information costs,
for example the cost of monitoring permit markets, and the cost of involuntary
disclosure of confidential technical information. Firms may also incur insurance
costs to allow for the technical risk of accidental non-compliance (e.g., unpredictable leaks, spills, or accidents). While some of these transaction costs are
similar across different types of regulatory intervention, different types of emission permit markets differ most strongly with respect to search and information
costs. Potential illiquidity of the market may reduce trading opportunities, and
in the extreme case may turn such a market into bilateral bargaining.
5
Trading costs, combined with market and regulatory uncertainty, may reduce
the efficiency of permit trading systems. Montero (1997) shows that these frictions can have a non-negligible impact on abatement outcomes: trade volume decreases, and total compliance cost increases. They also find that in the presence
of transaction costs the initial allocation is not neutral with respect to efficiency.
Gangadharan (2000) considers a variety of the aforementioned transaction costs
in the context of the RECLAIM market in the Los Angeles basin. Transaction
costs influences the participation decision of plants; various types of transaction
costs can be identified as the reason for an overall 32% reduction in the probability
of trading in the RECLAIM market in 1995.
A multiplicity of markets would be costly. This makes the Montgomery (1972)
ambient-concentration markets highly impractical, as well as numerous alternatives that have been proposed in the past; see Atkinson and Tietenberg (1982)
for a discussion. Among the most advanced second-best models that have been
proposed are trading zones with a limited number of markets. Among the most
prominent examples are Førsund and Nævdal (1998), who propose a zonal system with inter-zone exchange rates, and more recently Krysiak and Schweitzer
(2010), who derive the optimal size of zonal permit markets in the presence of
informational constraints.
To make emission permit trading work for ‘hot spots,’ the trading system has
to be as simple and transparent as the conventional cap-and-trade system for
uniformly-mixed pollutants. The model proposed in this paper is appealing because it relies on a single integrated market, although one combined with plantspecific ‘hazard factors’ that are based on observables and which can be updated
easily by the regulator prior to each trading period. This set up is able to achieve
the first-best economically-efficient solution.
6
II.
A.
Model
Regulator’s Objective
Consider the regulator’s problem of controlling the ecosystem hazard emanating
from emissions generated by plants i = 1, .., n. The regulator is concerned about
the total ecosystem hazard Hj for regions j = 1, .., m. Ecosystem hazard includes
the health risk of the population directly exposed to the emissions but may also
include the negative impact on animals and plants, which (in addition to their
intrinsic value) have an indirect effect on the health of the population through
the food chain. Let Pj denote appropriate ecosystem weights (‘population’) for
region j and define regions sufficiently small that emission concentrations can be
thought of as homogeneous within that area. Let Aj denote measured ambient
pollution concentration in region j in a reference period. As in Hoel and Portier
(1994) and in line with Krysiak and Schweitzer (2010), hazard typically follows
a quadratic dose-response function.1 The ecosystem hazard in region j can be
defined as
"
(1)
Hj = Pj Aj A
j +ω
n
X
#
dij Ei ≈ Pj A2j
i=1
where Ei is the emission from plant i and dij is the dispersion factor between firm
i and location j (the fraction of firm i’s emissions deposited in region j) such that
P
j dij = 1. Aj captures ambient concentrations from natural or transboundary
sources, and ω converts emission deposits into emission concentrations.
1 The
P
underlying structure of the model is quadratic in emission concentrations, that is j A2j . In a
linear model inter-regional trade-offs between regions i and j would be ∂Aj /∂Ai = −1, suggesting that
reducing emission concentrations in a ‘benign’ region i while letting them increase in a ‘hot spot’ j by
the same amount would leave total hazard unchanged. By comparison, with a quadratic function the
inter-regional trade-off is ∂Aj /∂Ai = −Ai /Aj . This means that to keep total hazard unchanged, an
increase in ambient concentrations in ‘benign’ region i would only offset a smaller ambient concentration
increase in ‘hot spot’ j to leave total hazard unchanged. As j is a ‘hot spot’ and thus Ai < Aj , the
ratio Ai /Aj < 1. Earlier work on emission hot spots often posits a constrained optimization problem so
that ∀j : Aj ≤ Ā. This set-up rules out any inter-regional trade-offs and implies ∂Aj /∂Ai = ∞, a very
strong Rawlsian view of the world. I argue that the utilitarian approach with a weighted quadratic loss
function that allows inter-regional trade-offs is more intuitive.
7
An important innovation in this model is that the non-linear dose-response
function is captured through the product of an ex-ante (observed) emission concentration Aj and an ex-post (incentivized) emission concentration captured by
the term in square brackets; thus Hj may be thought of as Pj,t−1 Aj,t−1 Aj,t for
successive time periods t. Applying this temporal logic allows for a loss function
quadratic in Aj while keeping the model effectively linear.2
The above hazard model (1) generalizes the existing literature on ambient emission level control. The total ecosystem hazard is not merely a function of ambient
concentrations, but also a function of the number of people, plants, and animals
that are exposed to the concentration. This implies a trade-off between higher
ambient concentrations in losely populated areas against lower concentrations
in densely populated areas. Different regulators may therefore rely on different
weights Pj . For example, Pj could simply denote population, or it could capture
pollution-related health care costs.
The regulator is also concerned about the (expected) abatement cost B =
P
i Bi
incurred by firms in meeting the desired environmental footprint. The regulator’s
objective then is to minimize the expected ‘welfare loss’ L from ecosystem hazard
H and abatement cost B
(2)
L=
n
X
Bi + γ
i=1
J
X
Hj
j=1
where γ represents the marginal damage of a unit of ecosystem hazard. Alternatively, γ may also be thought of as a political preference parameter indicating the
regulator’s weight on ecosystem hazard. Importantly, hazards are additive over
regions, allowing inter-regional hazard trade-offs.
2 This property entails that the welfare loss is minimized only over time, not instantaneously. If
one used a one-period instantaneous quadratic loss function instead, the resulting model becomes very
complex because the optimal solution for firm i depends on the optimal solution for all other firms.
This requires solving a system of n first-order conditions in n unknowns, rather than solving n firstorder conditions directly. Using temporal logic to linearize the economic decision problem comes at little
economic cost because a regulator will phase in a cap-and-trade system gradually to allow firms to adjust.
8
The permit market is structured as follows. The regulator issues permits equal
P
to the targeted total amount of emissions Ē ≡ i Ei . Market participants then
determine the market price τ for these permits. Individual firms buy φi Ei permits,
P
and therefore Ē = i φi Ei must hold as well.
B.
The Plant
Each plant i’s emissions affect the neighboring regions j through the dispersion
P
factor dij so that j dij = 1. These dispersion factors are determined by measurement or modeling of atmospheric disperson processes. Each plant has final
emissions Ei and is required to purchase φi Ei emission permits at market price
τ , where φi > 0 is each plant’s hazard factor as determined by the environmental
regulator at the beginning of each trading period. Consequently, firm i faces an
effective unit price for its emissions Ei equal to φi τ .
Plant i’s final emissions are a function of its abatement effort θi ∈ [0, 1[ so that
(3)
Ei = (1 − θi )Ei0
with Ei0 denoting the original unabated emission level of plant i. The scale
(output) of the firm is assumed to be fixed.3
It is useful to impose a specific and plausible single-parameter abatement cost
function, in particular for the purpose of facilitating simulations later on. Abatement costs are given by the function
(4)
Bi = bi [− ln(1 − θi )]Ei0
with cost factor bi . The crucial information asymmetry between regulator and
firm is that the regulator cannot observe bi ; the firm knows its true bi but not
3 This simplification rules out quantity adjustment in response to environmental price signals. This
is a useful and plausible approximation when abatement costs play only a small part in the overall cost
structure of a firm.
9
the regulator. Abatement cost function (4) has several desirable properties. As
θ → 1 (complete abatement), abatement costs rise to infinity, which implies that
plants are unable to ever completely abate emissions. Furthermore, B 0 (θ) > 0
and B 00 (θ) > 0 imply that abatement costs are increasing in abatement effort at
an accelerating rate: abatement effort becomes increasingly costly. At low levels
of effort, the cost function is almost linear, but as the effort level approaches total
elimination of emissions, abatement cost starts to rise steeply. Abatement costs
rise proportional with output, and there are no increasing or decreasing returns
to scale in abatement activity.
The firm’s objective is to minimize its environment-related costs
(5)
Ci = min {Bi + τ φi Ei }
θi
by choosing the optimal abatement effort θi in response to the effective price τ φi
for buying permits for its (post-abatement) emissions Ei . Using (3) and (4) and
solving the minimization problem (5) yields the optimal abatement effort θi∗ =
1 − bi /(τ φi ), which in turn implies Bi∗ = bi ln(τ φi /bi )Ei0 and Ei∗ = Ei0 bi /(τ φi ).
(Star superscripts indicate the optimum solution.) After abatement, the firm
buys φi Ei∗ = Ei0 bi /τ permits at price τ and thus overall expense Ei0 bi . As the
P
P
regulator issues exactly Ē = Ei permits, it must hold that i φi Ei = Ē.
Optimal abatement effort is conditioned on a participation constraint. The
permit price needs to be sufficiently high (τ φi > bi ) to induce firms to engage
in abatement effort. If a firm’s available abatement technology is too costly, it
will rather buy permits than engage in any abatement effort. If the empirical
distribution of bi is wide, non-abatement cases where bi ≥ τ φi may account for
a significant share of firms. In numerical simulations it is important to allow for
cases of non-abatement, in which case Ei∗ = Ei0 and the firm’s environment-related
costs are the expense for buying sufficient permits Bi∗ = τ φi Ei0 . The participation
constraint is conceptually equivalent to a fixed abatement cost, which would also
10
impose a participation threshold.
C.
Optimal Intervention
With the above results the regulator’s consolidated objective function becomes
(6)
L=
X
bi Ei0 ln
i
"
τ φi
bi
+γ
X
P j Aj
A
j
+ω
j
X
i
bi Ei0
dij
τ φi
#
The regulator’s problem is finding the optimal intervention that minimizes (6).
Knowing the hazard factors φi with certainty then solves the ‘hot spot’ problem
implicitly. The optimal intervention involves minimizing L with respect to an
individual price for each plant, τi ≡ τ φi . This optimization yields prices
τi∗ = γω
(7)
X
Pj Aj dij = γQi
j
where Qi ≡ ω
P
j
Pj Aj dij are hazard weights for plant i, and thus plant-specific
hazard contribution is Hi ≡ Qi Ei . The next step is demonstrating that finding
a single permit price τ replicates the first-best intervention (7). The first-order
condition for minimizing (6) with respect to a single permit price τ , given hazard
factors φi , yields
P
Hi
H
τ = γP i
=γ
E
i Ei φi
∗
(8)
where Q̄ ≡ H/E =
(9)
P
i Qi Ei /
P
i Ei .
Now consider the solution
φi =
Hi /H
Qi
=
Ei /E
Q̄
which defines the hazard factor as the ratio of hazard share to actual (postabatement) emission share. From this it follows immediately that τ ∗ = γ, and
11
thus τi∗ /τ ∗ = Qi /Q̄. As long as the regulator is able to determine φi = Qi /Q̄
reliably, the enhanced version of the permit market is able to obtain the firstbest solution for emission reduction. The simple modification that leads to this
crucial result is to require firms to buy φi Ei permits instead of merely Ei as in
a conventional cap-and-trade market. Thus, the ‘cap’ is effectively on hazard
despite being nominally on emissions (Ē).
D.
Limiting Cases
The emission permit market with hazard factors φi entails two limiting cases.
First, setting φi = 1 replicates a conventional cap-and-trade market. This is
a useful benchmark against which one can compare the benefits of introducing
plant-specific hazard factors. This limiting case is also approached when the
number of regions drops to m = 1, which implies that the world is a single ‘hot
spot.’
The second limiting case involves plant-specific hot spots without interaction
among firms. In this case there are as many regions as plants (n = m) with dij = 1
for i = j and dij = 0 for all i 6= j.4 The limiting case simplifies Qi = ωPj=i Aj=i
but does not change the overall optimality of the market design. The hazard
contribution factor Qi (and thus φi ) simply captures each plant’s unique impact
on the surrounding environment. There are no strategic interactions among firms.
Thus the permit market facilitates inter-regional trade-offs in emission and hazard
reduction, rather than intra-regional trade-offs. Even in this limiting case the
permit market with hazard factors accomplishes its goal of targeting hot spots
because the effective permit prices φi τ equate marginal abatement cost to the
marginal damage from environmental hazard (specific to each hot spot).
4 Without loss of generality, smaller regions within each hot spot can be suitably aggregated to allow
for ambient concentration variations within each hot spot.
12
E.
Hazard Factor Determination
Precise knowledge of dispersion factors dij is essential for any regulatory intervention that involves non-uniformly mixed pollutants. While pollutant concentrations can be measured at receptor locations, an atmospheric dispersion model
is required to link emissions to emission concentrations. The widely-used model
by Turner (1994) captures atmospheric dispersion through the equation (consolidated for expositional clarity)
(10)
F
1
x
A(x) =
exp −
ζS(x)U
2 S(x)
where A is the downwind concentration at ground level (g/m3 ), F is the emission
flow rate of the pollutant (g/s), x is the distance from the plant (m), S(x) the
plume standard deviation (m), U the wind speed (m/s), and ζ contains other
plant-specfic information (m) based on stack height and vertical plume standard
deviation.
Attenuation over distance follows predictable patterns. Given distance x(i, j)
between plant i and region (measurement station) j, it is possible to compute
dispersion factors dij by integrating over suitable spatial areas. Conversely, it
is possible to observe ambient concentrations Aj at measurement stations and
concurrent emissions Ei at nearby plants, and use the data to estimate dispersion
factors dij as a multi-parameter function of x(i, j).
Spatial disaggregation identifies ‘hot spots.’ The granularity of this disaggregation matters. Enlarging the number of observation regions m increases the
accuracy of the underlying hazard model. On the other hand, the limiting case
m → 1 with a single hazard region reverts the proposed model to the conventional
cap-and-trade model.
The regulator’s main function in overseeing the permit market is to announce
new φi,t = Qi,t /Q̄i,t at the beginning of each trading period t, based on measure13
ments from the previous period. It is useful to recall how Qi depends on emissions
from neighbouring plants. As ambient concentrations Aj depend on contributions
from all plants, the hazard summation factor Qi can be written as
(11)
Qi,t = ω
X
Pj Aj,t−1 dij = ω 2
j
X
Pj dij
j
X
dkj Ek,t−1
k
Equation (11) shows how emissions from other plants affect plant i through the
network of dispersion coefficients dij . Scientifically accurate modeling of these
coefficients is therefore critical to implementing the permit market.
F.
Plant Centrality
Through equation (11), firms are interconnected participants in the permit
market where actions by one firm such as increasing or decreasing emissions may
influence neighbouring plants by raising or lowering their particular hazard factor
φi . It is possible to capture the degree of interconnectedness through empirical
measures of centrality, specifically eigenvector centrality. Equation (11) can be
expressed in matrix notation as
(12)
Q = ω 2 DPDT E
where Q and E are n×1 vectors of each plant’s (non-normalized) hazard factor
and emission level, D is an n×m matrix of dispersion coefficients, P is an m×m
diagonal matrix with region factors Pj , and the T superscript indicates the matrix
transpose. S ≡ DPDT is a symmetric n×n matrix that captures the inter-firm
influences weighted by P. Matrix S can be normalized through the transformation
U ≡ RSR − I where R = [diag(S)]−1/2 and I is the identity matrix.5 Thus, all
elements in matrix U identify the relative impact of one plant on another, scaled
5 This transformation is the same procedure that is used to compute a Pearson correlation matrix
from a variance-covariance matrix.
14
to the range [0, 1[. Subtracting I ensures that the diagonal elements in U are all
zero, as is required for adjacency matrices that are used to analyze networks.
The influence of an individual plant in the emission market network can be
captured by eigenvector centrality. First proposed by Bonacich (1972), the largest
eigenvalue λ̄ that solves the eigenvector equation Uv = λv is associated with
the principal eigenvector v̄, which can be obtained numerically through power
iteration even for very large matrices. The centrality measure can be suitably
disaggregated into plants with zero or postive centrality. For the n+ ≤ n firms
with positive centrality, rescaling makes the measures easier to interpret. Let
P
χi ≡ (v̄i / k v̄k )/(1/n+ ) denote plant centrality with an average of 1. Values
larger than 1 indicate above-average centrality, and values below 1 indicae belowaverage centrality.
The plant-specific hazard factors φi will be strongly rank-correlated with the
centrality measures χi . The firm centrality measure is useful in the context of
spatially-interacting plants because it readily identifies which plants affect their
neighbours more, and which less. For example, a centrality measure of χi = 1.5
suggests that plant i has 50% stronger influence on neighbouring plants than
the average plant. By comparison, a plant with χi = 0.5 is much less spatially
connected, influencing other firms 50% less than average. Plants that are far from
any other plants have a χi equal or close to zero.
For a hot-spot permit market to be effective, having a sufficient number of
firms with inter-regional interaction is important. This means that regardless of
their emission size, a sufficient number of firms need to have non-zero centrality.
This in turn depends crucially on the average dispersion radius of the pollutant.
Centrality can thus be used to gauge the interconnectedness of potential market
participants, ignoring actual emission size, in oder to determine the feasibility of
an emission market with plant-specific hazard factors.
15
G.
Numerical Illustration
A simple numerical simulation can help illustrate the key concepts in this paper.
Table 1 provides a ‘sandbox’ for exploring the model with five firms (1–5) and
four regions (a–d). Region (a) is densely populated and industrial, region (b)
more suburban, region (c) large and rural, and region (d) a small industrial town.
Parameter values for abatement costs bi and initial emissions Ei0 are given along
with dispersion factors dij and regional weights Pj . The table also shows the
initial ambient concentrations (prior to abatement) Aj and the corresponding
hazard γHj , expressed in monetary terms using a hazard cost factor of γ = 1/200.
Regions (a) and (d) are ‘hot spots’ as their initial ambient emission concentration
is two or three times that of the neighbouring regions (b) and (c), and thus the
regulator’s assessment of total hazard of regions (a) and (d) is about five times
that of regions (b) and (c). The spatial interconnections among the five firms can
be expressed through the centrality measure χi ; firms 1–3 have above-average
centrality and firms 4 and 5 have below-average centrality.
Table 2 shows the results of a market simulation where the number of emission
permits is gradually lowered from 700 until the regulator’s loss function reaches a
minimum. The first row shows the baseline (zero market price τ ) and intermediate
steps are shown for ‘round’ permit prices. The final permit price turns out to be
τ = 12.85, and the last row ∆[%] shows percentage changes of the optimal result
against the baseline.
While total emissions E are reduced by 36%, total environmental hazard is
reduced by about 68%. The columns φ1 –φ5 show how the hazard factors evolve.
In part, the changes are driven by neighbouring plants commencing abatement
activity as the permit price reaches their participation constraint τ φi > bi , which
is visible in the bottom right segment of the table for abatement effort θ1 –θ5 .
Plant 3 has the lowest abatement cost and eventually reduces 73% of its emissions,
whereas other plants only reach an abatement effort of between 12% and 60%.
The hazard factors only evolve slowly.
16
Table 1—Numerical Illustration: Parameters
Firm
i bi Ei0
1 10 150
2
7
70
3
5 100
4
8 130
5
9 250
Weight Pj
Initial Aj
Initial γHj
Region
a
b
0.7 0.2
0.6 0.3
0.5 0.1
0.1 0.0
0.0 0.1
24
18
210
86
5,292 666
j (dij )
c
d
0.1
0.0
0.0
0.1
0.1
0.5
0.3
0.6
0.2
0.7
8
5
114
310
520 2,403
P
j
1.0
1.0
1.0
1.0
1.0
30
—
8,880
χi
1.656
1.500
1.259
0.370
0.215
Table 2—Numerical Illustration: Simulation
τ
0.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
12.85
∆[%]
τ
0.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
12.85
∆[%]
B
0
179.1
378.1
659.4
967.4
1,228
1,516
1,842
2,266
2,662
Aa
210.0
194.8
180.8
163.3
145.9
132.8
121.6
111.6
102.7
95.88
-54.3
H
8,880
8,346
7,022
6,131
5,346
4,806
4,312
3,835
3,311
2,887
-67.5
Ab
86.00
82.64
77.68
72.04
66.65
62.58
59.30
56.57
52.75
49.26
-42.7
L
8,880
8,525
7,400
6,791
6,313
6,034
5,828
5,677
5,577
5,549
-37.5
Ac
114.0
111.2
109.8
107.7
105.5
103.9
100.5
95.45
88.89
83.01
-27.2
E
700.0
669.9
644.4
615.7
588.2
567.6
543.9
517.1
481.7
449.8
-35.7
Ad
310.0
295.6
287.7
282.5
278.7
275.8
269.3
259.7
243.1
227.0
-26.8
φ1
1.379
1.549
1.563
1.552
1.529
1.501
1.475
1.454
1.446
1.446
4.81
θ1
0
0
0
0.080
0.182
0.260
0.322
0.375
0.424
0.462
φ2
1.279
1.436
1.454
1.448
1.432
1.411
1.393
1.378
1.372
1.372
7.27
θ2
0
0.025
0.198
0.309
0.389
0.449
0.497
0.538
0.575
0.603
φ3
1.243
1.396
1.431
1.448
1.460
1.465
1.464
1.461
1.460
1.460
17.46
θ3
0
0.283
0.418
0.507
0.572
0.621
0.659
0.689
0.715
0.734
φ4
0.599
0.673
0.716
0.752
0.792
0.824
0.846
0.861
0.865
0.865
44.38
θ4
0
0
0
0
0
0
0.055
0.155
0.230
0.281
φ5
0.499
0.561
0.607
0.648
0.696
0.735
0.763
0.785
0.792
0.792
58.62
θ5
0
0
0
0
0
0
0
0
0.053
0.116
Table 3—Comparison with Conventional Cap-and-Trade
τ
14.25
∆[%]
B
3,038
H
2,887
-67.5
L
5,925
-33.3
E
405.6
-42.1
θ1
0.298
17
θ2
0.509
θ3
0.649
θ4
0.439
θ5
0.368
Ambient emission concentrations in the four regions drop between 27% (regions
c and d) and 54% (region a). This illustrates that the market helps reduce hazard more in the more populous regions (a) and (b), whereas region (d) with the
highest original emission concentration has much smaller population, and consequently sees a lesser reduction. Of course, it also matters whether plants close
to this region have affordable abatement ability. In the example, plants 4 and 5
contribute much to region (d) but have relatively high abatement costs.
Table 3 provides a comparison to a conventional cap-and-trade market in which
φi = 1. At its optimum level, the permit price is higher (14.25 versus 12.85) for
a larger reduction in emissions (42% versus 36%) but about the same reduction
in overall hazard. Comparing total losses (33.3% versus 37.5%), the conventional
cap-and-trade market underperforms as expected, and generates a comparable
level of hazard reduction at 15% higher cost.
III.
Practical Considerations
A.
Multiple Pollutants
Environmental regulators have identified classes of toxic substances. For example, under the United States Clean Air Act of 1990, 188 substances were identified
as hazardous air pollutants (HAPs) with the potential for causing adverse health
effects, such as cancer, reproductive and neurological effects, immune system damage and birth defects. This list also includes the metallic air toxics that are a
specific target in this paper.
An emission permit market has the potential to target multiple pollutants rather
than just one. For example, greenhouse gas permit markets target carbon dioxide
as well as methane and chlorofluorocarbons using equivalency factors. A metallic
air toxics market could include a list of substances with similar characteristics.
Including multiple pollutants in a single market can be very desirable when pollutants are substitutes for each other. Regulating only one pollutant may cause
18
undesirable substitution effects by shifting production to methods that use the
unregulated pollutant. An emission permit system can be designed easily to cover
multiple pollutants by assigning fixed toxicity factors to each pollutant. The USEPA’s (2004) Risk-Screening Environmental Indicators (RSEI) of Chronic Human
Health provide suitable equivalence factors.
Another important reason to consider a multiple pollutant permit market is
that many toxics are only emitted by a small number of plants, and thus a single
pollutant permit market would face relatively low liquidity. By covering multiple
pollutants, more plants and firms will participate in the market, thus increasing
liquidity and efficiency of the market. Different pollutants may disperse differently
over distance. Thus a practical limitation for grouping air toxics is their similarity
with respect to dispersion factors dij .
B.
Bioaccumulation and Biomagnification
Many toxics have the tendency to bioaccumulate and biomagnify.6 For example,
lead, mercury and cadmimum emissions from a smelter in a sparsely populated
area may expose a much larger population far away if these air toxics find their
way into the food supply through nearby agricultural production or fish habitat.
It is possible to design ecosystem weights Pj for each region that allow for health
hazards ‘imported’ from other regions. However, spatial models that take these
types of second-order effects into account have not been widely developed yet.
Nevertheless, the emission permit market envisioned in this paper is able to deal
with such extensions because the regulator can calculate appropriate Pj , which
are then imputed into specific hazard factors φi for individual firms.
6 Bioaccumulation is the process by which chemical compounds accumulate or build up in an organism
at a rate faster than they can be broken down. More concisely, environmental scientists draw a distinction
between bioaccumulation and biomagnification. Bioaccumulation occurs within a trophic (food chain)
level in an ecosystem and captures the increase in concentration of a substance in an individual’s tissues
due to ambient exposure to the substance. Biomagnification occurs across trophic levels and captures
the increase in concentration of a substance when the substance moves from one trophic level to the next.
19
C.
Transboundary Pollution
A further complication arises from the problem that pollutants travel easily
across national boundaries. Yap et al. (2005), a study commissioned by the
Ontario Ministry of the Environment, concluded that of the estimated $9.6 billion
in health and environmental damages from ground-level ozone and fine particulate
matter in Ontario in 2003, 55 per cent is attributable to U.S. emissions.
Transboundary pollution, which in the model is captured through A
j , is a
spatial fixed effect that does not impact the design of the permit market. The term
drops out in the first-order conditions of the model. It only matters insofar as the
regulator sets more aggressive emission reduction goals in order to compensate
for the transboundary pollution, in which case local firms bear the burdern of
abatement that more efficiently could be borne by firms across the border.
D.
Initial Allocation: Grandfathering or Auctions?
The method of allocating permits does not affect efficiency, except when transaction costs are significant and marginal transaction costs are decreasing in the
volume of trades. However, whether permits are grandfathered or auctioned has
important distributional effects that also touch upon the political feasibility of
the permit system. Grandfathering, which allocates permits to existing polluters
based on some formula, is often considered politically less onerous than an auction, which generates government revenue and looks more like taxation. On the
other hand, grandfathering tends to lead to larger trading volume than auctions
because the regulator’s formula for allocating permits will tend to be biased. Consequently, allocating permits through auctions implies lower transaction costs.
E.
Permit Banking and Borrowing
Emissions of air toxics are often more variable over time than fundamental
indicators of operational size, such as plant employment or value added. The
20
spatial ‘hot spot’ problem may thus get aggravated through temporal clustering.
Permit banking and borrowing are methods to address temporal variability in
emissions; see Rubin (1996), Cronshaw and Kruse (1996) and Schennach (2000).
A permit system that is defined in terms of ambient concentrations cannot easily accommodate banking or borrowing because of potential temporal clustering
of emissions. Temporal clustering would intensify ‘hot spots’ of very high peak
concentrations, posing a significant health risk. The economic rationale for banking and borrowing is compelling: greater flexibility across time provides for a
better allocation of abatement investments over time. Allowing consolidation of
permits over a longer time horizon may contribute to intertemporal efficiency in
the presence of high emission variability across years.
F.
Plant Entry, Exit, and Relocation
In a permit market with differentiated hazard factors φi , the spatial dimension
of firm entry and exit matters. The closer plants are located to each other,
the more they care about each others’ actions. Entry of a new plant creates a
negative externality on surrounding plants, while exit creates a corresponding
positive externality. New entrants can aggravate the ‘hot spot’ problem through
increased emissions. Concretely, a new entrant will contribute more emissions and
larger hazard, which will be reflected in the reference period in an increase in Aj .
As is visible in equation (11), this increases the φi that the regulator announces
for firm i in the next period. The total effect is inversely related to firm centrality.
An effective permit system may also help bring about beneficial relocation, as
some firms may find relocation cheaper than abating emissions or buying emission
permits. While relocating a plant does not reduce emissions, it can significantly
reduce environmental hazard if the plant is moved out of a pollution ‘hot spot.’
21
G.
Constrained Hazard Factors
The emission permit market with hazard factors introduced in this paper may
involve a wide range of hazard factors. Firms that face a high φi would bear
a large share of the financial burden of pollution abatement. This may not always be politically feasible. The hazard factors can be suitably constrained to an
interval [φ, φ] that the regulator finds politically expedient with respect to distributional equity considerations. In particular, capping φi at a particular φ may
help convince participating firms that the abatement burden is not distributed
too unequally and thus may safeguard against distortions of their competitive
position. A permit market with constrained hazard factors diminishes its costeffectiveness with respect to lowering environmental hazard, but this suboptimal
solution may still be preferable if the alternative is either no regulation or economically inefficient command-and-control regulation.
IV.
Metallic Air Toxics in Canada
How does an emission permit market with hazard factors work out in practice?
Concretely, what hazard factors can one expect in a typical application to local
pollutants with short dispersion range? This section explores the feasibility of a
permit market for metallic air toxics, in particular mercury. The dispersion range
around plants is varied extensively in order to understand how such differences
affect the empirical hazard factors. Canada makes a good test case for probing
the limits of feasibility for a mercury permit market with hazard factors. The
country’s spatial expanse and mid-sized industrial base produce a mix of sites near
densely populated areas as well as geographically more isolated areas. Countries
with denser geographic and industrial activitiy (the United States, Japan, and
European Union countries) will likely be better candidates for an emission permit
market with hazard factors.
Metallic air toxics account for some of the most significant airborne health haz22
ards. These substances are considered developmental and reproductive toxicants.
Among the most important substances in this category are mercury (Hg), lead
(Pb), and cadmium (Cd), which are listed as toxic substances on Schedule 1 of
the Canadian Environmental Protection Act (CEPA) of 1999.
Exposures to mercury can affect the human nervous system and harm the brain,
heart, kidneys, lungs, and immune system. Mercury in the air eventually settles
into water or onto land where it can be washed into water. Once deposited, certain
microorganisms can change it into methylmercury, a highly toxic form that builds
up in fish, shellfish and animals that eat fish. Mercury remains a substance of
great concern for regulators because it is emitted largely in the gaseous state and
does not adhere to fine particles in emission streams to the extent that other
heavy metals do. Due to its long atmospheric residence time, mercury is more
mobile than most other heavy metals and can be deposited far from the source.
Mercury emissions can be reduced with increasing efficiency. Sundseth et al.
(2010) report a 2005 estimate of the U.S. Environmental Protection Agency of an
abatement cost of about US$ 150,000 per kg of mercury to achieve a 90% control
level using sorbent injection. More recent innovations have lowered this number
to about $22,000 per kg using novel echologies. The Sundseth et al. (2010) study
also reports estimates of the health and environmental cost of mercury exposures.
Lead emissions have declined immensely over the last decades as a result of
removing lead from gasoline. Industrial lead emissions are associated primarily
with metals processing and waste incineration. Lead is persistent in the environment and accumulates in soils and sediments through deposition from air sources.
Lead exposure has been linked to neurological effects in children and cardiovascular effects in adults.
Cadmium emissions are associated with the burning of fossil fuels and the incineration of municipal waste. Inhalation exposure is linked to acute effects such
as pulmonary irritation, while chronic inhalation or oral exposure to cadmium
leads to a build-up of cadmium in the kidneys that can cause kidney disease.
23
Table 4—Sectoral Composition of Emissions of Mercury (Hg), Lead (Pb), and Cadmium (Cd)
in Canada 2009-2010
3314
3315
2122
3311
2211
3221
2111
3273
3241
5622
2123
2213
Industry (NAICS-4)
Non-Ferrous (exc. Al) Production & Processing
Foundries
Metal Ore Mining
Iron & Steel Mills & Ferro-Alloy Mfg.
Electricity Generation, Transmission & Dist.
Pulp, Paper & Paperboard Mills
Oil & Gas Extraction
Cement & Concrete Product Mfg.
Petroleum & Coal Products Mfg.
Waste Treatment & Disposal
Non-Metallic Mineral Mining & Quarrying
Water, Sewage & Other Systems
All Other Sectors
Facilities
Total Emissions
Average Emission
Median Emission
Concentration Index
Toxicity [Hg equiv.]
%
%
%
%
%
%
%
%
%
%
%
%
%
Hg
17.0
1.0
4.1
9.6
44.7
1.6
2.0
7.6
1.6
5.3
1.5
2.4
1.6
Pb
48.9
34.0
9.6
2.7
1.2
0.8
0.4
0.2
0.2
0.1
0.1
0.0
1.7
Cd
79.5
5.9
5.8
1.5
1.5
2.5
0.8
0.1
0.7
0.1
1.3
0.1
0.2
Load
48.8
33.3
9.5
2.8
1.7
0.9
0.4
0.3
0.3
0.1
0.1
0.1
1.7
—
ton
kg
kg
—
—
209
7.119
34.1
5.1
.0437
1.000
415
389.9
939.6
6.6
.1825
1.467
258
34.46
133.6
2.0
.3639
0.167
507
584.7
1153.3
7.1
.1791
Note: Load is the sum of emissions across substances, adjusted for US-EPA (2004) toxicity scores (oral
intake). Toxicity is expressed in mercury-equivalent units. Concentration is measured through the
Herfindahl-Hirschman index.
Table 4 shows the sectoral composition of emissions across the three air toxics.
The key sector that accounts for most emissions is the non-ferrous/non-aluminium
production and processing sector. Foundries also account for a significant share
of lead emissions, and power plants account for the largest share of mercury
emissions. Iron and steel mills, cement production, and waste incineration also
contribute significantly to mercury emissions. Overall, mercury emissions are
much less concentrated sectorally than either lead or cadmium. 80% of emissions
are attributable to two sectors for lead, and one sector for cadmium.
The total toxic load is calculated using US-EPA (2004) toxicity scores and
closely follows the sectoral composition of lead due to the overall emission volume
and the highest among the three toxicity scores. Emissions are also concentrated
among a few large emitters; for all three substances, the mean emission per facility
is much larger than the median emission per facility.
24
Based on these data it is possible to contemplate individual or joint emission
permit markets. There are about 200 facilities emitting mercury, and just over
500 facilities Canada-wide emitting at least one of the three substances.7
A.
Spatial Distribution and Hot Spots
Emission dispersion can be modeled by projecting emissions from individual
plants into air concentration plumes that decrease in intensity from the point of
origin. Dispersion modeling was discussed earlier in section II.E. Here, the modeling is intended to establish the typical range and properties of hazard factors
φi that are used in the proposed emission permit market. For this purpose it is
sufficient to use a relatively unsophisticated approach with a symmetric radial
exponential air plume, which requires a single parameter r (the mean travel distance of pollution particles).8 This simplified approach is purposefully trading off
a degree of realism for the benefit of modeling how variation in dispersion distance
affects the empirical distribution of the hazard factor. Al Razi and Hiroshi (2012)
7 In Canada, environmental matters are a joint federal-provincial responsibility with overlapping jurisdiction. Establishing a federal market is possible, although the provinces have often exercised leadership
on environmental issues in many instances. Interprovincial coordination through the Canadian Council
of Ministers of the Environment (CCME) has led to the establishment of several cross-country environmental standards, including ambient air pollution standards for mecury. CCME policies for mercury were
adopted in June 2000 and again in October 2006. Whereas the 2000 accord targeted base metal smelting
and waste incineration, the 2006 accord set provincial caps on mercury emissions from existing coal-fired
electric power generation plants by 2010. Both accords were without participation from the province of
Quebec, which has endorsed neither the Canada-wide Accord on Environmental Harmonization nor the
Canada-wide Environmental Standards Subagreement. Standards for incineration are typically maximum emission concentrations in exhaust gases (20-70µg/m3 ), and for base metal smelting the standard
is defined in grams of mercury emissions per tonne of finished metal, with variations for existing versus
new/expanding facilities and for different types of finished metal.
8 The following spatial integration method is used. Let r be the mean distance for pollutants to be
carried through the air. A given emission load v can be allocated to grid cells or polygons by splitting
the load v into w ≥ 10, 000 partial loads of weight v/w, and then distributing these partial loads at
impact locations drawn from a suitable dispersion distribution, described below. Partial loads v/w are
added up within each grid cell or polygon. To determine depositions by grid cell or polygon, a pair
of random numbers (ω, d) is drawn comprised of compass angle ω (clockwise from North) and distance
d, given average radial dispersion of r. Angle ω is drawn from the uniform distribution [0◦ , 360◦ [, and
distance d is drawn from the exponential distribution with cumulative distribution function Ω(d) =
1.0 − exp(−d/r). The exponential distribution function has mean r, the average impact distance. The
median impact distance is ln(2)r. In practical terms the distance d can be generated by first drawing z
from a uniform [0, 1[ distribution and then transforming z through the inverse cumulative distribution
function d = −r ln(1 − z). Given (ω, d) and the location of the emission source (φ0 , λ0 ) of latitude φ0 and
longitude λ0 , the impact location (φ1 , λ1 ) can be calculated through loxodrome approximation, which is
sufficiently accurate for small distances as φ1 = arcsin (sin(φ0 ) cos(d/D) + cos(φ0 ) sin(d/D) cos(ω)) and
λ1 = λ0 + arcsin (sin(ω) sin(d/D)/ cos(φ0 )), where D is the earth radius of 6371km.
25
Figure 1. Pollution Concentration Plumes by Latitude-Longitude Squares for Mercury Emissions, Western Canada
58°
57°
56°
55°
54°
Prince George
Edmonton
53°
Red Deer
52°
<0.1
<0.2
<0.5
<1
<2
<5
<10
<20
<50
Saskatoon
Calgary
51°
Kamloops
50°
Regina
Medicine Hat
Lethbridge
Kelowna
Winnipeg
Vancouver
49°
Victoria
48°
130°
Thunder Bay
125°
120°
115°
110°
105°
100°
95°
90°
85°
80°
Figure 2. Pollution Concentration Plumes by Latitude-Longitude Squares for Mercury Emissions, Eastern Canada
50°
49°
48°
47°
Quebec
Sault Sainte Marie
Sudbury
Trois−Rivières
North Bay
46°
Drummondville
Montreal
Ottawa
Granby Sherbrooke
45°
Barrie
Peterborough
Belleville
44°
Kingston
Oshawa
Toronto
Guelph
Waterloo
Kitchener
Hamilton
Brantford
43°
Sarnia
London
<0.1
<0.2
<0.5
<1
<2
<5
<10
Windsor
42°
85°
84°
83°
82°
81°
80°
79°
78°
77°
76°
75°
74°
73°
72°
71°
70°
Note: Air pollution concentration plumes are computed using Gaussian plumes with mean dispersion
range of 60 km.
26
Figure 3. Population-Adjusted Hazard by Latitude-Longitude Squares for Mercury Emissions,
Western Canada
58°
57°
<1
<2
<5
<10
<20
<50
<100
<200
<500
<1,000
<2,000
<5,000
<10,000
<20,000
<50,000
<100,000
<200,000
56°
55°
54°
Prince George
Edmonton
53°
Red Deer
52°
Saskatoon
Calgary
51°
Kamloops
50°
Regina
Medicine Hat
Lethbridge
Kelowna
Winnipeg
Vancouver
49°
Victoria
48°
130°
Thunder Bay
125°
120°
115°
110°
105°
100°
95°
90°
85°
80°
Figure 4. Pollution Concentration Plumes by Latitude-Longitude Squares for Mercury Emissions, Eastern Canada
50°
49°
48°
47°
Quebec
Sault Sainte Marie
Sudbury
Trois−Rivières
North Bay
46°
Drummondville
Montreal
Ottawa
Granby Sherbrooke
45°
Barrie
Peterborough
Belleville
44°
<1
<2
<5
<10
<20
<50
<100
<200
<500
<1,000
<2,000
<5,000
<10,000
<20,000
<50,000
<100,000
Kingston
Oshawa
Toronto
Guelph
Waterloo
Kitchener
Hamilton
Brantford
43°
Sarnia
London
Windsor
42°
85°
84°
83°
82°
81°
80°
79°
78°
77°
76°
75°
74°
73°
72°
71°
70°
Note: Population figures in absolute numbers based on year 2000 reference data. Source: CIESIN (2005).
Hazard (exposure risk) is calculated using equation (1) and utilizing the population and emission data
as shown in figures (1) and (2).
27
provide a recent example of a sophisticated approach to modelling atmospheric
mercury dispersion around coal-fired power stations in Japan. Cohen et al. (2004)
estimates the transport and fate of mercury emissions in North America, and in
particular the Great Lakes Region. That paper also discusses state-of-the-art
modelling approaches. The U.S. Environmental Protection Agency employs a
number of sophisticated atmospheric dispersion models. The Community Multiscale Air Quality (CMAQ) model is used to simulate the dispersion of air pollutants and has been widely adopted by other environmental agencies. The main
application of CMAQ is to track multiple pollutants simultaneously across regions
by projecting air plumes from multiple point sources on a spatial grid.
A suitable geographic grid for modeling air toxics is provided by the CIESIN
(2005) database of the Gridded Population of the World (version 3), which projects
the population of the world into grid squares of 2.5 arc minutes of longitude and
latitude. At 45◦ latitude, a typical grid cell covers about 15 square kilometers.
Figures 1 and 2 show the result of dispersing mercury emissions from plants as
reported to Canada’s National Pollutant Release Inventory for the years 2009-10,
using r =60 km. Dispersion does not account for differences in stack heights, wind
direction and other relevant factors. On the logarithmic scale that is used to depict
ambient concentrations, the green areas indicate low emission concentrations, and
the brown areas indicate high concentrations. While some of the plants are near
heavily-populated urban areas (especially in Ontario and Quebec), several others
are located in small industrial towns.9
Figures 3 and 4 show how ambient concentrations are mapped into hazard
using the loss function Pj A2j that is quadratic in concentrations Aj and adjusted
by the factor Pj , which here is taken as population. For loosely-populated grid
cells a minimum population of 1,000 is assumed to account for other ecosystem
characteristics. What is immediately apparent is that the hazard potential is
9 One 80-year old copper smelter in Flin Flon, Manitoba, that shows up on the maps has subsequently
been shut down.
28
highly locally concentrated around major urban areas (the greater Montreal area
and the ‘golden horseshoe’ of Southern Ontario) and a few select other hot spots
in Western Canada.
B.
Centrality
The centrality measure χi identifies a firm’s potential for strategic interaction
with other firms independent of its emission size. Table 5 provides counts of
plants for different levels of centrality based on different mean dispersion ranges,
varied in approximate logarithmic steps from 2 km to 200 km.
Table 5—Plant Centrality and Dispersion Range
Dispersion
Radius
2
5
10
20
50
100
200
=0
190
189
185
179
173
167
161
Facilities count for χi by range
>0
]0, 0.2[
[0.2, 1[
5
1
1
6
1
2
10
5
1
16
9
2
22
10
6
28
11
10
34
15
11
≥1
3
3
4
5
6
7
8
The data in table 5 reveals clearly that the potential for firm-level externalities
(and thus strategic interactions) among firms is very small when the dispersion
range is low. At 2 km mean dispersion, only 5 out of 195 firms interact strategically at all. At 200 km mean dispersion, the number of strategically-interacting
firms has risen to 34, but this amounts to less than 18% of the total. Among the
firms with positive χi , a group of six plants in the Montreal area stand out as
those with very high centrality.10
A simple regression analysis of the simulation data shows that among the plants
with non-zero centrality, log centrality can be approximated closely (with an R2
10 These are the Raffinerie de Montréal-Est, Station d’épuration des eaux usées Montréal, Raffinerie
de Montreal, Affinerie CCR de Montréal-Est, Anachemia Canada in Lachine, and the Centre d’épuration
Rive-Sud in Longueuil.
29
of 0.81) by the log rank of centrality (coefficient –1.813) and the log dispersion
range (coefficient +0.657). This suggests strongly that centrality follows a power
law distribution, a feature that has also been observed for a variety of centrality
measures in applications in different domains.
C.
Empirical Hazard Factors
The discussion of centrality has shown that an emission permit market with
hazard may be dominated by a small group of plants with high interaction potential. Combining the dispersion data with emission data using equations (9) and
(11) confirms that a mercury market in Canada would concentrate abatement
activity on a small number of plants in proximity to urban areas.
Table 6—Plant Counts by Hazard Factor Range
Dispersion
Radius
2
5
10
20
50
100
200
500
φi for Pj =population
= 0 ]0, 0.2[ [0.2, 1[ ≥ 1
96
80
14
5
91
84
14
6
86
86
17
6
74
97
18
6
56
106
26
7
31
125
28
11
12
139
33
11
2
134
47
12
=0
105
95
91
83
64
39
17
2
φi for Pj =1
]0, 0.2[ [0.2, 1[
80
8
90
8
95
6
101
8
118
10
142
9
164
11
176
13
≥1
2
2
3
3
3
5
3
4
Table 6 provides plants counts for the empirical distribution of hazard factors
where the dispersion range is varied from 2 to 500 km. This variation sheds light
on the effect of dispersion range on hazard factors. The first group of columns
shows results for the assumption that Pj captures population, while the second
group of columns shows results for the assumption of neutral weights (Pj = 1).
A value of less than 10−3 is assumed to be effectively zero. The majority of
plants fall into that category when the dispersion range is small, and this shifts
gradually as the dispersion range increases. The group of firms with a φi in excess
30
of 1 remains relatively small: it increases from five at 2 km mean dispersion to
twelve at 500 km dispersion.
Figure 5. Plant-Specific Hazard Factors (Dispersion Range 50 km)
Plant−specific Hazard Factor (φi)
.01 .02 .05 .1 .2
.5 1
2
Plant−specific Hazard Factor (φi)
.005 .01 .02 .05 .1 .2
.5 1
2
5
Plants with zero centrality (χi=0)
5
Plants with positive centrality (χi>0)
.02
.05
.1
.2
.5
1
Plant Centrality (χi)
2
5
.2
.5
1 2
5 10 20 50 100 200 500
0
Plant Emissions [kg Hg] (E i)
Figure 5 illustrates how the hazard factors vary across two key dimensions for
a dispersion range of 50 km.11 The left panel shows only plants with positive
centrality (χi > 0), and it is apparent that plant centrality largely explains the
magnitude of the hazard factors. The right panel shows plants with zero centrality
(χi = 0), which thus do not interact spatially. In this case, emission size weakly
correlates with hazard factors. This visual inspection of the data is confirmed by
a more systematic analysis of the simulated data across all dispersion ranges.
Results from an ordinary least squares regression of ln(φi ) on logarithms of
centrality, emissions, and dispersion radisus are shown in table 7. When centrality
is positive, centrality explains most of the variation in the data. The elasticity of
φi with respect to centrality is 0.851, whereas the corresponding elasticity with
11 Airborne mercury is considered a phenomenon on global, regional, and local scales, depending on
the particular speciation of Hg; see Schroeder and Munthe (1998). Elemental water-insoluble Hg◦ can be
transported for very long distances (tens of thousands of kilometers), while gaseous water-soluble Hg2+
and particulate mercury Hgp compounds are typically removed in the vicinity of a few tens to a few
hundreds of kilometers.
31
Table 7—Regression Analysis of ln(φi ) for φi > 0
Variable
intercept
log centrality
log emissions
log dispersion range
Observations
R2
χi > 0
Estimate
T value
–1.607∗∗∗ (10.32)
0.851∗∗∗ (29.92)
0.115∗∗∗ (6.11)
0.035
(1.00)
120
0.901
χi = 0
Estimate
T value
–4.366∗∗∗ (25.47)
0.228∗∗∗
0.182∗∗∗
918
0.112
(10.53)
(4.23)
respect to emissions is only 0.115. Clearly, centrality has a much greater influence
on hazard factors then emission size, while the dispersion range has no statistically
significant effect on the hazard factor. When centrality is zero, however, emission
size explains a larger share of the variation in hazard factors, and the dispersion
range also has a positive effect on hazard factors. The latter is not a result from
spatial interactions among firms (as centrality is zero), but instead reflects the
fact that larger dispersion likely reaches more populated areas (and thus includes
more regions with a higher Pj ). As figure 5 shows, the plants with the highest
hazard factors are all plants with zero centrality; most high emission plants are
spatially isolated.
The above discussion reveals that an emission permit market with hazard factors would likely identify a relatively small group of ‘active’ participants with
reasonably high hazard factors, while a large number of plants could be excluded
from participation if they have small emissions or small centrality.
Repeating the above simulations for lead and cadmium reveals that they are
less likely candidates for a permit market with hazard factors. The hazard factors would single out a much smaller number of participants. This reflects the
significantly higher concentration of emission volumes (second last row, table 4)
for lead and cadmium compared to mecury.
32
V.
Conclusion
Emission permit trading for air toxics is made difficult by the fact that the
dispersion of these toxics is geographically confined and impacts regions of varying
population density or ecosystem importance. This is known as the ‘hot spot’
problem, and addressing it has remained a formidable challenge for market-based
instruments. High transaction costs make it infeasible to operate a large number
of regional ambient concentration contribution permit markets as envisioned in
the pioneering work of Montgomery (1972). While numerous alternatives have
been explored, a solution that is sufficiently simple and involves only a single
market has been elusive.
The permit market proposed in this paper has the desirable property of achieving the first-best economic outcome by way of introducing firm-specfic hazard
factors. Firms buy permits in proportion to their emissions and their specific
hazard factors. This amounts to a hybrid price-quantity instrument in which
firms face an effective price per unit of emission that varies along with their specific hazard factor, while on a practical level they purchase and trade permits in
a (liquid) market with a single price. This novel hybrid policy instrument has not
been considered previously, and its simplicity is appealing.
Determining the firm-specific hazard factors is feasible and practical using established methods of modelling the spatial disperson of air pollutants. Furthermore, the underlying model of environmental hazard generalizes ambient concentration targets by specifically allowing for population density or other ecosystem
charateristics. Rather than targeting maximum ambient concentrations alone, the
proposed system is sufficiently flexible to allow for the consideration of a variety
of region-specific factors.
A further contribution of this paper is the introduction of a centrality measure
that captures the potential for externalities among neighbouring firms (regardless of emission size), and thus the magnitude of strategic interactions through
an emission permit market. The prevalance of positive centrality also identifies
33
the importance of intra-region interaction among plants relative to inter-region
interaction among plants.
A numerical example and the application of the proposed emission permit system to the case of air toxics in Canada illustrates its practical feasibility. The
benefits of the proposed market increase with the dispersion range of the pollutant, as wider dispersion increases the centrality of plants, which in turn allows for
larger economic benefits from exploiting the abatement cost heterogeneity among
firms. Countries in which emission sites are in close proximity, and thus exhibit
high levels of plant centrality, will stand to benefit the most from applying an
emission permit market with hazard factors.
34
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