1
Breakdown of the Equi-Marginal Principle in Permit Markets
2
Involving Multiple Pollutants and Exogenous Caps
3
Abstract Interest in expanding market-based approaches involving intra-pollutant trading
4
(trading “like” pollutants) to allow inter-pollutant trading (trading “dis-similar” pollutants) is
5
growing. We examine the optimal choices of inter- and intra-pollutant trade ratios when some
6
firms generate multiple pollutants affecting different media and when the ratios are set
7
independent of permit caps, which are exogenously-specified by prior regulations. We find that
8
optimal intra-pollutant trade ratios generally fail to satisfy the equi-marginal principle because
9
there are insufficient policy instruments under exogenous caps (the Tinbergen rule is violated).
10
Inter-pollutant trading enhances efficiency by offering an additional policy instrument: the inter-
11
pollutant trade ratio. We also find realistic cases where inter-pollutant trading may universally
12
improves environmental quality, in contrast to concerns that trading across environmental media
13
may improve one medium at the expense of another. An example of nitrogen trading in the
14
Susquehanna River Basin in Pennsylvania illustrates our results.
15
Keywords equi-marginal principle; instrument design; multi-pollutant markets; pollution permit
16
markets; second-best
17
1. Introduction
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Pollution permit trading offers the potential to improve the efficiency of pollution control by
19
reallocating abatement effort towards more efficient abaters. Markets can also be useful in
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expanding the scope of environmental regulation. In the U.S., for example, many nonpoint
21
sources of water or air pollutants (e.g., agricultural sources) are generally only regulated on a
1
22
voluntary basis.1 Pollution offset markets are seen as a way of voluntarily bringing these sources
23
under the umbrella of regulation. Emissions markets have been successfully applied to manage
24
various air pollutants (Burtraw et al. 2005), and efforts to apply markets to water are increasing
25
(Fisher-Vanden and Olmstead 2013).2
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While programs have historically focused on individual pollutants, many problems
27
involve multiple, linked pollutants (US EPA 2015, 2011; NRC 2004). For example, coal-fired
28
power plants typically release SO2, NOX, and CO2 as joint outputs from energy production (Agee
29
et al. 2014). These pollutants generate myriad damages across multiple environmental media,
30
including acidification of surface waters (SO2), local air quality degradation (SO2 and NOX), and
31
global warming (NOX and CO2). Likewise, agricultural nitrogen fertilizer use contributes
32
simultaneously to global warming via N2O emissions and to water quality impairment via
33
nutrient loadings to waterways (Galloway et al. 2003).
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The presence of pollutant linkages implies potential benefits from developing multi-
35
pollutant strategies that take a more comprehensive approach to management (NRC 2004; Lutter
36
and Burtraw 2002), including multi-media efforts to protect both air and water (Gray and
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Shadbegian 2015; Aillery et al. 2005). Indeed, multi-pollutant management is considered to be a
38
key facet of next-generation pollution control efforts, with market-based approaches offering an
39
important mechanism for implementation (US EPA 2011; NRC 2004). For instance, the U.S.
1
In the case of water pollution, section 319 of the Clean Water Act delegates the regulation of nonpoint sources to
states, who have largely implemented control programs on a voluntary basis. Moreover, for both air and water
pollutants, there are technical difficulties associated with nonpoint regulations due to the diffuse and largely
unobservable nature of these emissions, and there is little political will for regulating agricultural sources (Shortle et
al. 2012; Ribaudo 2009; Ribaudo et al. 1999).
2
In the U.S., for example, atmospheric emissions of NOX and SO2 have been regulated via separate pollution trading
markets under the Acid Rain Program and Cross-State Air Pollution Rule. Greenhouse gas emissions are governed
in some regions by carbon trading programs, including California’s Cap and Trade Program (GWSA 2006) and the
Regional Greenhouse Gas Initiative in nine northeastern states. In the case of water markets, the focus has largely
been on point-nonpoint nutrient trading whereby high-cost point source abatement is exchanged for low-cost
nonpoint source abatement.
2
40
Cross-State Air Pollution Rule is a multi-pollutant approach, albeit based on distinct markets for
41
each pollutant. The European Union Emissions Trading System (EU ETS) allows trades among
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CO2, nitrous oxide (N2O), and perfluorocarbons (PFCs) by converting all pollutants into CO2
43
equivalents (EC 2013). There have been calls for expanding market-based approaches that
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traditionally involve intra-pollutant trading, or trading “like” pollutants, to allow inter-pollutant
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trading, or trading across imperfectly substitutable pollutants that cannot easily be converted into
46
equivalent units (e.g., due to heterogeneous and nonlinear environmental impacts) (NRC 2004;
47
US EPA 2011). However, realizing the gains from multi-pollutant management requires careful
48
policy design.
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There is no reason to consider inter-pollutant trading in settings where efficiency is
50
attainable; distinct markets for each pollutant can be constructed to be efficient or first-best,
51
provided regulators can coordinate on the efficient permit caps and trading ratios (i.e., the rate at
52
which abatement requirements can be traded among different sources) for the two markets. It is
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an open question whether gains may arise from allowing both intra- and inter-pollutant trading in
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cases where efficiency is unattainable, for instance due to existing regulations or other
55
institutional constraints. Such settings are relevant because permit caps are typically not chosen
56
based on cost-benefit analysis and therefore are unlikely to reflect the efficient level of emissions
57
(Tietenberg 2005). Moreover, policy tools for managing pollutants are often designed using a
58
piecemeal approach (Yaffee 1997; Lutter and Burtraw 2002). Trading ratios and other trade rules
59
may be established after–– rather than jointly with––pollution regulations, as is the case for the
60
offset programs used to address nonpoint source water pollution and carbon emissions
61
(Woodward 2011). These programs allow previously-regulated point sources to purchase offsets
62
from nonpoint sources to improve the cost-effectiveness of water quality management (Wainger
3
63
and Shortle 2013; Ribaudo and Nickerson 2009; Fisher-Vanden and Olmstead 2013) or
64
greenhouse gas emissions (GWSA 2006).
65
We examine the optimal design of both inter- and intra-pollutant trades when some
66
polluters generate multiple pollutants, with a particular focus on cases where permit caps are
67
inefficient. The impact of inefficient caps on the design of both inter- and intra-pollutant trading
68
ratios has yet to be addressed. Lutter and Burtraw (2002) examine inter-pollutant trading using
69
an ad hoc trade ratio. Others explore separate pollutant markets, with no inter-pollutant trading,
70
when there is jointness in the production of multiple pollutants (e.g., Woodward 2011; Stranlund
71
and Son 2015). These studies investigate the choice of emissions caps when intra-pollutant
72
trading ratios are set at a fixed one-to-one rate due to uniform mixing of emissions for each class
73
of pollutants. Woodward (2011) also considers whether it is more efficient to allow previously
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unregulated firms to sell abatement of different pollutants in only one or several distinct or
75
separate pollution offset markets.
76
In the context of a single-pollutant problem, Horan and Shortle (2005) examine the
77
design of second-best intra-pollutant trading ratios when permit caps are inefficient. They show
78
that the trading ratio only has to manage relative emissions prices in the first-best case, whereas
79
in the second-best case it has to manage both relative prices and effective permit endowments
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(i.e., the number of credits a polluter can generate through trades, which depends on the
81
inefficient caps and the trade ratio). The second-best ratio is adjusted to address these dual tasks,
82
but it can do neither efficiently and so market performance declines.
83
We extend Horan and Shortle’s (2005) analysis to the case of multiple pollutants and find
84
inter-pollutant trading produces gains when permit caps are inefficient. These gains arise because
85
the inter-pollutant trading ratio serves as an added tool for managing abatement allocations more
4
86
efficiently. This result is rooted in the so-called “Tinbergen Rule” that one instrument is
87
generally needed to address each externality (Tinbergen 1956). As problems involving inefficient
88
caps are characterized by too few instruments, adopting an additional instrument––the inter-
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pollutant trade ratio, which integrates markets by facilitating inter-pollutant trading––enhances
90
efficiency relative to distinct markets that do not involve inter-pollutant trading.
91
We also find that the equi-marginal principle breaks down—so that effective marginal
92
abatement costs are not equated across polluters—in both integrated and distinct markets that are
93
designed optimally except for inefficient permit caps. This result stems from the types of second-
94
best trade ratio adjustments that Horan and Shortle (2005) identified but did not explore
95
analytically or numerically. Here, we find additional intra-pollutant trade ratio adjustments are
96
required––for either distinct or integrated markets involving inefficient caps––to account for the
97
joint production of emissions. The additional adjustments arising in the multi-pollutant case can
98
create greater violations of the equi-marginal principle. The notion that markets should be
99
designed to violate the equi-marginal principle is in contrast to textbook markets that promote
100
efficiency by replicating the equi-marginal principle, and it is in contrast to prior work on inter-
101
pollutant trading that simply imposes the equi-marginal principle, e.g., by applying one-to-one
102
trade ratios for uniformly mixed emissions. Our numerical analysis shows there may be
103
significant inefficiencies to imposing this principle when permit caps are inefficient.
104
We develop a model of multi-pollutant abatement in the next section. Section 3 derives
105
conditions for efficient abatement, and Section 4 explores the outcome of several pollution
106
permit trading scenarios. We highlight our analytical results using a numerical example of
107
nitrogen trading in the Susquehanna River Basin (SRB) in Section 5. Section 6 concludes.
5
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2. A Model of Multi-Pollutant Abatement
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Consider a pollution problem whereby two environmental media (air and water) are harmed by
110
two pollutants. For expositional purposes, we focus on two different forms of nitrogen pollution:
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nitrous oxide emissions (N2O) that contribute to atmospheric pollution, and total nitrogen
112
loadings, defined as the quantity of nitrogen delivered to a particular water body. This pollution
113
is produced in three sectors: an industrial sector (indexed by I) that produces point source
114
emissions, denoted eI; a wastewater treatment sector (indexed by W) that produces point source
115
loadings, rW; and an agricultural sector (indexed by A) that contributes nonpoint pollution to both
116
media: air emissions, eA, and water loadings, rA.
117
Our definitions of emissions and loadings account for the effect of spatial heterogeneity
118
on local air and water quality, which means we can consider emissions and loadings from the
119
various sources to be uniformly mixed within an environmental media and therefore perfect
120
substitutes in creating environmental damages. We also assume emissions and loadings from
121
each source are deterministic. These assumptions allow us to focus on aggregate decisions at the
122
sector level rather than focusing on individual firms within each sector. More importantly, these
123
assumptions allow us to illustrate how the multi-pollutant case differs from textbook models that
124
focus on a single pollutant involving deterministic and uniformly-mixed emissions.3
125
Moving forward, it will be simpler to work with abatement rather than pollution levels.
126
Define the industrial sector’s abatement as aeI = eI0 – eI, where the subscript “0” denotes initial
3
We concentrate on optimal market design under somewhat pristine conditions (apart from exogenous permit caps)
and ignore factors (e.g., uncertainty) discussed in prior work that complicate the analysis but do not help illustrate
the present findings. Making the more realistic assumption that agricultural emissions are stochastic makes it more
difficult to parse out the effects of multiple pollutants. This is because permit markets in such settings (based on
trades of estimated or mean agricultural emissions) can only be second-best when damages are nonlinear, and
generally involve a number of complex design elements (e.g., uncertainty trading ratios to adjust for risk) that
significantly alter these markets relative to textbook markets (Shortle and Horan 2001). Our focus on the effects of
multiple pollutants when emissions are deterministic offers a clearer comparison to textbook markets. The potential
impact of stochastic agricultural pollution is described in the Discussion section.
6
127
emissions prior to abatement. The industrial abatement cost function is CI (aeI), where CI (0) = 0
128
and CIʹ , CIʹʹ > 0 . Likewise, wastewater treatment sector abatement is arW = rW0 – rW, with the
129
increasing, convex abatement cost function CW (arW), where CW (0) = 0. Finally, agricultural
130
emissions and loadings abatement are aeA = eA0 – eA and arA = rA0 – rA, respectively, with the
131
increasing, convex abatement cost function CA(aeA,arA), where CA (0,0) = 0.4
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Finally, abatement reduces economic damage that depends on the ambient concentration
133
of each pollutant. Let Ee = Ee0 – aeI – aeA and Er = Er0 – arW – arA be ambient air and water
134
pollution, respectively, where Ee0 = eI0 + eA0 and Er = rW0 + rA0 are ambient pollution prior to
135
abatement. Let Ds(Es) be economic damages from pollutant s ∈ {e,r}, with Dsʹ, Dsʺ> 0.
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Emissions abatement benefits are then avoided economic damage, denoted Be(aeI + aeA) ≡ De(Ee0)
137
– De(Ee), with Bʹe (⋅) > 0 and Bʺe (⋅) < 0; loadings abatement benefits, Br(arW + arA), are analogous.
138
Under the framework presented here, the only potential linkage between the air and water
139
pollution problems arises through agricultural abatement costs. Assume agricultural abatement
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costs are not linearly separable, i.e., ∂2CA/(∂aeA∂arA) ≠ 0, to ensure the problems are linked.
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Otherwise, the pollution management problem could be treated as two independent problems—
142
one for each environmental medium.5
4
Abatement costs are defined as the minimum reduction in profits required to attain a particular abatement level.
Let πi(zi) be profits for sector i ∈{I, W, A}, gsi(zi) be the sector’s emissions or loadings of pollutant s ∈{e,r}, and zi
be a vector of the sector’s production and pollution control choices. Absent abatement activity, sector i’s profitmaximizing choice vector is zi0. The abatement cost function for point source sector i ∈ {I,W}, Ci(ais), is obtained by
choosing zi to minimize πi(zi0) – πi(zi) subject to asi ≤ gsi(zi0) – gsi(zi). Agriculture’s abatement cost function CA(aeA,
arA) is obtained by choosing zi to minimize πi(zi0) – πi(zi) subject to aeA ≤ geA(zi0) – geA(zi) and arA ≤ grA(zi0) – grA(zi).
5
Air and water pollution linkages could also arise through the damage function D(⋅) if, for example, a fraction of all
air emissions are deposited into the water resource rather than contributing only to Ee. This type of behavior is
especially common among different types of nitrogen pollution (e.g., NO3 or NOX; Galloway et al. 2003). We do not
analyze such linkages here, but note that doing so requires only a simple extension of our model. Using the example
of atmospheric nitrogen deposition, we could rewrite aggregate loadings as Er(arW, arA, aeI , aeA) = rW0 – arW + rA0 –
arA + η[eI0 – aeI + eA0 – aeA], where η is the proportion of atmospheric N emissions deposited to aquatic systems. The
benefits from emissions abatement would then be Br(arW, arA, aeI , aeA) = Dr(Er0) – Dr(Er0 – Er(arW, arA, aeI , aeA)). The
only difference with our current model would be an additional marginal benefit term in equations (2) and (4).
7
143
3. First-Best Control
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We first characterize the efficient, or first-best, allocation of pollution control effort as a
145
benchmark for comparison with market outcomes. The efficient outcome is defined as an
146
allocation of pollution control effort that maximizes social net benefits
147
(1)
148
Assuming an interior solution, the first-order conditions (FOCs) for problem (1) are
149
(2)
∂V
= 0 ⇒ C Iʹ = Beʹ ,
∂aeI
150
(3)
∂V
= 0 ⇒ CWʹ = Brʹ ,
∂a rW
151
(4)
∂V
∂C A
=0⇒
= Beʹ ,
∂aeA
∂aeA
152
(5)
∂V
∂C
= 0 ⇒ A = Brʹ .
∂a rA
∂a rA
153
The FOCs (2)–(5) state the familiar result that, at the first-best abatement levels a*eI, a*rW, a*eA, and
154
a*rA, each sector’s marginal abatement costs equal the marginal benefits from abatement.
155
max
aeI ,arW ,aeA ,arA
V = Be (aeI + aeA ) + Br (arW + arA ) − CI (aeI ) − CW (arW ) − C A (aeA , arA ).
Additional insight is obtained by manipulating (2)–(5) to yield the following modified
156
equi-marginal condition,
157
(6)
158
so that the effective marginal cost of abatement—measured by the marginal cost normalized by
159
the marginal avoided damages from abatement—is equalized across all sources under the
160
efficient outcome. The first and third equalities in (6) imply the conventional equi-marginal
161
condition: marginal abatement costs should be equated within each environmental medium. The
C Iʹ ∂C A / ∂aeA CWʹ ∂C A / ∂a rA
=
=
=
= 1,
Beʹ
Beʹ
Brʹ
Brʹ
8
162
second equality extends the equi-marginal principle across media by normalizing costs in a way
163
that treats abatement benefits in the different media as fungible or perfectly substitutable. The
164
final equality indicates marginal costs equal marginal benefits in each case. While not a
165
surprising result, this modification contrasts with current regulatory approaches (e.g., distinct
166
markets for different pollutants) that treat abatement of distinct pollutants as non-substitutable
167
even when those pollutants arise from the same source.
168
4. Market Trading Scenarios
169
We now consider the outcome under various trading scenarios that differ along two dimensions.
170
First, pollution trading can occur either in distinct markets for each pollutant that allow only
171
intra-pollutant trading (reflecting current market-based approaches) or in an integrated, multi-
172
pollutant market that allows both intra- and inter-pollutant trading. Second, point source
173
pollutant caps can either be chosen optimally in conjunction with trading ratios, or they can be
174
set exogenously relative to trading ratios. We begin by defining the market responses in a general
175
model of trading, as these responses will be used to construct the various trading scenarios.
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4.1. Market Responses in a General Model of Pollution Trading
177
We adopt a general model of trading by defining sector-specific permits for each pollutant.
178
Agricultural permits are denoted êA and r̂ A, with initial allocations êA0 and r̂ A0 and permit prices
179
peA and prA. The agricultural sector is not initially regulated, i.e., êA0 = eA0 and r̂ A0 = rA0, and so
180
farmers have initial rights to pollute. Point source permits are denoted êI and r̂ W, with associated
181
initial allocations or permit caps êI0 and r̂ W0 and permit prices peI and prW. Point sources initially
182
face binding regulations, i.e., êI0 < eI0 and r̂ W0 < rW0 but they may purchase permits (or offsets)
183
from other sources to pollute more and reduce abatement costs.
9
184
We examine two types of market structures. First is an integrated market that allows both
185
intra- and inter-pollutant trading. Industrial emissions are defined as the numeraire pollutant, and
186
trades are guided by trading ratios that define the number of permits that must be purchased for
187
an industrial source to increase emissions by one unit. Three ratios are required: an intra-
188
pollutant ratio for emissions, τeA,eI = | dêA/dêI |, and two inter-pollutant ratios, τrA,eI = | dr̂ A/dêI | and
189
τrW,eI = | dr̂ W/dêI |. These ratios can be used to define the trade ratios for the other potential trades:
190
an intra-pollutant ratio for loadings, τrA,rW = | dr̂ A/dr̂ W |= τrA,eI /τrW,eI, and the two remaining inter-
191
pollutant ratios, τrA,eA = | dr̂ A/dêA | = τrA,eI /τeA,eI and τeA,rW = | dêA/dr̂ W | = τeA,eI /τrW,eI. The market
192
clearing condition for this case is
193
(7a)
eˆI 0 + eˆ A0 / τ eA,eI + rˆW 0 / τ rW ,eI + rˆA0 / τ rA,eI = ( eI 0 − aeI ) + ( e A0 − aeA ) / τ eA,eI
$!!!!!!
!#!!!!!!!
"
Q
+ ( rW 0 − a rW ) / τ rW ,eI + ( rA0 − a rA ) / τ rA,eI
194
where the left hand side (LHS), denoted Q, is the effective aggregate permit cap denominated in
195
terms of industrial emissions. Notice the effective cap or endowment depends on the trade ratios.
196
Now consider the case of distinct markets, defined as an emissions market and a loadings
197
market in which no inter-pollutant trades are allowed––only intra-pollutant trading occurs within
198
each market. Point source permits serve as a numeraire in their respective markets, with one
199
intra-pollutant trade ratio required for each market: τeA,eI = | dêA/dêI | and τrA,rW = | dr̂ A/dr̂ W |. There
200
is also a distinct market-clearing condition for each market:
201
(7b)
eˆ
(e − a )
rˆ
( r − arA )
.
eˆI 0 + A0 = (eI 0 − aeI ) + A0 eA and rˆW 0 + A0 = ( rW 0 − arW ) + A0
τ eA,eI
τ eA,eI
τ rA,rW
τ rA,rW
$!#!"
$!#!"
Qe
202
203
204
Qr
where Qe and Qr represent the effective aggregate permit caps for each market.
Now consider each sector’s decisions. Each sector chooses abatement to minimize
abatement costs plus the cost of purchasing permits. We show in the Appendix that these
10
205
problems can be written as follows, regardless of whether the markets are integrated or distinct:
206
(8)
min CI (aeI ) + peI [eI 0 − aeI − eˆI 0 ]
207
(9)
min CW (arW ) + prW [rW 0 − arW − rˆW 0 ]
208
(10)
209
with the following FOCs for interior solutions
210
(11)
CIʹ = peI
211
(12)
CWʹ = prW
212
(13)
∂C A
= peA
∂aeA
213
(14)
∂C A
= prA .
∂arA
214
Conditions (11)–(14) simply state that, at the optimum, each sector’s marginal abatement cost
215
equals the permit price of the abated pollutant. Further, we show in the Appendix that additional
216
market equilibrium conditions relate the trade ratios to permit price ratios, consistent with prior
217
work on markets for a single pollutant (e.g., Malik et al. 1993). Using these relations from the
218
Appendix, along with (11)–(14), the market equilibrium conditions for an integrated market are:
219
(15a)
220
The market equilibrium conditions for distinct markets are
221
(15b) τ eA,eI =
222
223
aeI
arW
min CA (aeA , arA ) + peA [eA0 − aeA − eˆA0 ] + prA[rA0 − arA − rˆA0 ]
aeA ,arA
τ eA,eI =
peI
CIʹ
=
,
peA ∂C A / ∂aeA
peI
CIʹ
=
,
peA ∂C A / ∂aeA
τ rA,eI =
peI
C Iʹ
=
,
prA ∂C A / ∂arA
τ rA,rW =
τ rW ,eI =
peI
Cʹ
= I .
prW CWʹ
prW
CWʹ
.
=
prA ∂C A / ∂arA
The abatement choices that solve the relevant market equilibrium conditions (15) and the
relevant market-clearing condition (7) can be expressed as responses to the policy variables,
11
224
aeI (τ,ê), aeA (τ,ê), arA (τ,ê), and arW (τ,ê), where τ = [τrA,eI τrW,eI τeA,eI] in the integrated market
225
scenario and τ = [τeA,eI τrA,rW] in the distinct markets scenario, whereas ê = [êI0 r̂ W0] in both
226
scenarios. Note that each sector’s behavior depends on the policy variables associated with both
227
air and water pollution. It is obvious that this should be the case for an integrated market, but it is
228
also true for distinct markets due to the agricultural source participating in both markets; its non-
229
separable abatement costs imply its decisions are dependent across markets. It is analytically
230
intractable to identify the signs of the comparative statics results for the abatement response
231
functions (which stem from applying Cramer’s Rule to a 4 × 4 matrix). However, prior work on
232
trading a single pollutant across two sectors indicates that a larger ratio τy,z generally makes it
233
more expensive for sector z to trade to reduce abatement (Horan and Shortle 2015).
234
4.2. Market Design with Endogenous Permit Caps: First-Best Markets
235
We begin our analysis of optimal permit market design with the case where permit caps are
236
endogenously chosen. We start with this case because it most directly relates to prior work on
237
market design (e.g., Montero 2001) and because prior work has not formally examined the
238
optimal choices of intra-pollutant trade ratios in a multi-pollutant setting. The planner’s problem,
239
after substituting the behavioral responses into V, is
240
(16)
241
Problem (16) is written generally to reflect both market scenarios. The FOC for any relevant
242
policy parameter u, defined as a scalar element of the policy vectors, is
243
(17)
244
Comparing (17) with the efficiency conditions (2)–(5), it is clear that an efficient market design
maxV = Be (aeI ( τ, eˆ ) + aeA ( τ, eˆ ) ) + Br (arW ( τ, eˆ ) + arA ( τ, eˆ ) )
τ ,eˆ
− C I (aeI ( τ, eˆ ) ) − CW (arW ( τ, eˆ ) ) − C A (aeA ( τ, eˆ ), arA ( τ, eˆ ) )
⎡
⎡
∂a
∂a
∂C ⎤ ∂a
∂C ⎤ ∂a
∂V
= [ Beʹ − C Iʹ ] eI + ⎢ Beʹ − A ⎥ eA + [ Brʹ − CWʹ ] rW + ⎢ Brʹ − A ⎥ rA = 0 ∀u.
∂u
∂u ⎣
∂a eA ⎦ ∂u
∂u ⎣
∂a rA ⎦ ∂u
12
245
causes each of the four bracketed terms in (17) to vanish. Ensuring such an outcome generally
246
requires four instruments––one instrument for each externality, consistent with the Tinbergen
247
rule (Tinbergen 1956). Note that four instruments are available in both the integrated and distinct
248
market scenarios.6
249
For the integrated market scenario, FOC (17) can be written in terms of three trading
250
ratios by using the sectors’ FOCs along with the market equilibrium relations (15a):
251
(18a) [ Beʹ − peI ]
252
The bracketed terms in (18a), and hence in (17), will vanish to yield an efficient outcome when
⎡
⎡
∂aeI ⎡
p ⎤ ∂a
p ⎤ ∂a
p ⎤ ∂a
+ ⎢ Beʹ − eI ⎥ eA + ⎢ Brʹ − eI ⎥ rW + ⎢ Brʹ − eI ⎥ rA = 0 ∀u.
∂u ⎣
τ eA,eI ⎦ ∂u ⎣
τ rW ,eI ⎦ ∂u ⎣
τ rA,eI ⎦ ∂u
*
*
Bʹ
Bʹ
*
= e* and τ eA,eI = e* = 1 and ê is set such that peI = Beʹ (see footnote 6). Using
Brʹ
Beʹ
253
τ rW ,eI = τ rA,eI
254
the market equilibrium conditions, we can use the trading ratio results to derive the remaining
255
equilibrium prices prW =
256
ensures one-to-one intra-pollutant trading for emissions, τ*eA,eI = peI / peA = 1, and loadings,
257
τ*rA,rW = prW / prA = 1, as well as equivalent inter-pollutant trading ratios, τ* = τ*rA,eI = τ*rW ,eA =
258
*
*
Beʹ / Brʹ . One-to-one intra-pollutant trading is consistent with current approaches for uniformly-
peI
τ rW ,eI
*
= Brʹ , peA =
peI
τ eA,eI
*
= Beʹ , and prA =
peI
*
= Brʹ . This solution
τ rA,eI
259
mixed pollutants. The optimal inter-pollutant trade ratio, based on relative economic benefits,
260
contrasts with the standard approach in current multi-pollutant markets of setting the ratio
6
As depicted in problem (16), the integrated market scenario involves five policy choices to manage four abatement
levels. In this case it is equivalent to transform the problem slightly by treating Q from the market clearing
condition (7a) as the policy variable rather than individual permit levels. Then the abatement response functions
would take the form aeI(τ,Q), aeA(τ,Q), arW(τ,Q), and arA(τ,Q), and the choice of Q along with the three trading ratios
would be sufficient to manage the four abatement levels. Optimizing (16) with respect to Q and τ yields the firstbest levels Q* and τ* . Then the initial permit allocation êI0 and r̂ W0 may be set at any combination to satisfy Q* = êI0
+ êA0/τ*eA,eI + r̂ W0/τ*rW,eI + r̂ A0/τ*rA,eI.
13
261
according to the pollutants’ relative physical or chemical qualities.7 However, the efficient ratio
262
is consistent with prior economic research that says efficient trades should occur at the marginal
263
rate of substitution of damages (e.g., Schmalensee 1993; Lutter and Burtraw 2002).
264
For the distinct markets scenario, FOC (17) can be written in terms of two trading ratios
265
by using the sectors’ FOCs along with the market equilibrium relations (15b):
266
(18b)
267
The bracketed terms in (18b), and hence in (17), will vanish to yield an efficient outcome when
[Beʹ − peI ] ∂aeI
⎡
⎡
p ⎤ ∂a
∂a
p ⎤ ∂a
+ ⎢ Beʹ − eI ⎥ eA + [Brʹ − prW ] rW + ⎢ Brʹ − rW ⎥ rA = 0 ∀u
∂u ⎣
τ eA,eI ⎦ ∂u
∂u ⎣
τ rA,rW ⎦ ∂u
*
*
Bʹ
Bʹ
*
*
= e* = 1 , τ rA,rW = r * = 1, eˆ*I 0 is set such that peI = Beʹ , and rˆW* 0 is set such that prW = Brʹ .
Beʹ
Brʹ
268
τ eA,eI
269
Using the market equilibrium conditions, we can use the trading ratio results to derive the
270
remaining equilibrium prices peA =
271
point-nonpoint emissions and loadings trading ratios are τ*eA,eI = τ*rA,rW = 1 .
272
peI
τ eA,eI
*
= Beʹ and prA =
prW
*
= Brʹ . This solution ensures the
τ rA,rW
There is one important caveat to these results for both the integrated market and the
273
distinct markets. Let Ee* = Ee0 – a*eI – a*eA and Er* = Er0 – a*rW – a*rA be the efficient levels of total
274
emissions and loadings, respectively. Assuming agricultural sources are not initially regulated so
275
that they have implicit initial permit caps of eA0 and rA0, then the efficient permit caps for the
276
emissions and loadings by the industrial and wastewater treatment sectors, respectively, are
277
eˆ*I 0 = Ee* − eA0 and rˆW* 0 = Er* − rA0 . Note that eˆA0 ≤ Ee* and rˆA0 ≤ Er* are required to obtain the
278
efficient outcome with êA0 = eA0 and r̂ A0 = rA0; in other words, initial nonpoint source emissions
279
and loadings must not exceed efficient levels. Otherwise, initial nonpoint source emissions
7
For example, different types of GHGs are traded based on their global warming potential, denominated in units of
“carbon dioxide equivalents.” Trades governed by these types of trade ratios are unlikely to be cost-effective as they
ignore the economic characteristics of pollution that vary across pollutants (Schmalensee 1993; Muller 2012).
14
280
and/or loadings are so large that the first-best outcome cannot be attained simply by regulating
281
point source emissions and loadings. In such instances, agriculture must be regulated, êA0 < eA0
282
and/or r̂ A0 < rA0, to obtain the first-best outcome. Otherwise, the permit levels are effectively
283
constrained as in the exogenous permit cap scenarios described in section 4.3 below.
284
The two market scenarios imply the following result:
285
Result 1. Suppose point source permit caps are endogenously chosen while nonpoint source caps
286
are essentially set at unregulated levels. Either integrated or distinct markets can be efficient
287
(provided unregulated agricultural pollution is not too great) because the tradeable permit
288
markets can replicate the first-best equi-marginal principle. Moreover, one-to-one trading is
289
optimal for intra-pollutant trades involving uniformly-mixed pollutants, consistent with the
290
traditional equi-marginal principle.
291
Result 1 indicates we could obtain an efficient outcome by integrating permit markets, but there
292
is no need for this integration provided point source permit caps are chosen optimally to reflect
293
the linkages created by the agricultural sector (or, more generally, any sector that pollutes in
294
multiple markets). Moreover, neither the linkages nor decisions on market integration affect the
295
standard result of one-to-one intra-pollutant trades for uniformly-mixed pollutants.
296
In practice, market caps are not typically chosen efficiently, but instead are set outside the
297
market to meet environmental or human health standards. We now turn to the more realistic case
298
of exogenously-defined pollution caps to examine trading in a second-best setting.
299
4.3. Market Design with Exogenous Permit Caps
300
Consider the optimal choice of τ given that ê has already been exogenously specified, likely at a
15
301
sub-optimal value. The objective function for this new problem, in which we simplify the
302
notation by suppressing ê, is
303
(19)
304
The first order conditions are analytically equivalent to (17), but now u is only defined as a scalar
305
element of the vector τ. This means there are no longer four policy instruments—in either type of
306
market—to ensure that each of the bracketed terms in (17) vanishes to produce the efficient
307
outcome; the Tinbergen rule is violated and the resulting market solutions cannot be first-best.
308
309
maxV = Be (aeI ( τ) + aeA ( τ) ) + Br (arW ( τ) + arA ( τ) )
τ
− CI (aeI ( τ) ) − CW (arW ( τ) ) − C A (aeA ( τ), arA ( τ) )
First consider the case of integrated markets. We show in the Appendix that the optimal
trading ratios are defined implicitly by the following relations:
2nd best
efficiency
loss
310
(20a)
τ rW , eI
$
!#!
"
$!!!!!#!!!!!
"
$!#!"
Beʹ [Brʹ − CWʹ ]ρ rW , rW , eI ( τ) Beʹ [(ρeI , rW , eI ( τ) − 1) + ρeA, rW , eI ( τ)] Brʹ ρrA, rW , eI ( τ)
=
+
+
+
CWʹ
CWʹ
CWʹ
CWʹ
2nd best
311
(20b) τ eA,eI =
312
(20c)
Bʹ
e
∂C A
∂aeA
+
efficiency loss
$!
!#!!"
[Beʹ − ∂C A / ∂aeA ]ρ eA,eA,eI ( τ)
∂C A
∂aeA
2nd best
Beʹ
efficiency loss
$!
!#!!"
[Brʹ − ∂C A / ∂arA ]ρ rA,rA,eI ( τ)
313
τ rA,eI =
314
where ρ j , y ,z ( τ) =
∂C A
∂arA
+
Behavioral
spillovers
from ag loadings
Behavioral spillovers in
emissions sectors
∂C A
∂arA
(∂a j / ∂τ y ,z ) / τ j , z
∑ (∂a
k
/ ∂τ y ,z ) / τ k ,z
Behavioral spillovers
from industrial emissions
+
$!!#!!
"
Beʹ [ρ eI ,eA,eI ( τ) − 1]
∂C A
∂aeA
Behavioral spillovers in
+
$!!loadings
!!#sectors
!!!!
"
Brʹ [ρ rW ,eA,eI ( τ) + ρ rA,eA,eI ( τ)]
∂C A
∂aeA
Behavioral spillovers
+
in emissions sectors
$!!!
!
!#!!!!!
"
Beʹ [(ρ eI ,rA,eI ( τ) − 1) + ρ eA,rA,eI ( τ)]
∂C A
∂arA
Behavioral spillover
from WWT
+
$!#!"
Brʹ ρ rW ,rA,eI ( τ)
∂C A
∂arA
τ j ,z (for j,y,z ∈ {eI, eA, rW, rA} and τy,y = 1) is the marginal
k≠y
315
abatement response of sector j to trade ratio τy,z, relative to the marginal responses in all other
316
sectors (with all effects denominated in terms of sector z’s permits). The first RHS term in (20) is
16
317
the ratio of marginal benefits of abatement in sector z relative to the marginal cost of abatement
318
in sector y. This term is of the same form as the first-best trade ratio τy,z presented above, given
319
that the first-best outcome equates sector y’s marginal benefits and marginal costs of abatement.
320
The remaining RHS terms in (20) are adjustments to address inefficiencies from having
321
too few instruments to perfectly control each sector’s abatement. Recall from the market
322
equilibrium condition (15) that trade ratios determine relative permit prices, and from the market
323
clearing condition (7) that they determine effective permit endowments. Trade ratios only have
324
to manage relative prices when permit levels are chosen optimally to manage endowments. But if
325
permits levels are exogenous, then trade ratios must perform both tasks, in which case neither
326
task is performed efficiently. The second RHS term in (20) reflects an inefficient deviation in the
327
marginal benefits and marginal costs of abatement in sector y, arising from an inability to adjust
328
permit endowments to equate these values. We expect ρy,y,z(τ) to be negative, which means τy,z is
329
optimally decreased (increased) to incentivize more (less) abatement in sector y whenever the
330
inefficiencies increase (decrease) the marginal benefits of abatement in sector y relative to the
331
marginal abatement costs. This term was identified by Shortle and Horan (2005) and described
332
as a trade ratio modification to move the trading equilibrium “close” to the first-best optimum.
333
Two additional terms arise here due to the multi-pollutant nature of the current problem.
334
Specifically, the third and fourth terms in (20) reflect the economic impacts of inefficient
335
behavioral responses to τy,z outside of sector y, as manifested through the ρj,y,z(τ) terms. In other
336
words, trying to adjust the effective endowment in one sector causes an inefficient behavioral
337
response in the other sector due to the markets being linked.8
338
A key result from equation (20) is that intra-pollutant trading at a one-to-one rate (i.e.,
8
Note that the first-best trade ratios (18) arise as a special case of (20) when permit levels are set to ensure the
behavioral responses yield ρj,y,z(τ) = 0 ∀j ≠ z,y , such that ρz,y,z(τ) = 1 (i.e., at the margin, a change in τy,z for y ≠ z
only guides trades between sectors y and z, with no effect on other sectors’ abatement), and ρy,y,z(τ) = – τy,z ∀j ≠ z,y.
17
339
τeA,eI = 1; τrA,rW = τrA,eI/τrW,eI = 1) is unlikely to be optimal, even though pollution is uniformly
340
mixed within each environmental medium. More generally, standard notions of the equi-
341
marginal principle break down. Note that this result holds even in the special case where
342
agricultural abatement costs are linearly separable due to the fact that the integrated market links
343
behaviors affecting both environmental media.
344
Now consider the case of distinct markets. We begin by noting this scenario has one less
345
policy tool than the integrated market scenario (two ratios here versus three in the integrated
346
market).9 This means the distinct market scenario cannot yield larger net benefits than the
347
integrated market case by Le Châtelier’s Principle (Samuelson 1947), and so it may be more apt
348
to describe this scenario as third best.10 Even so, the optimality conditions are still given by (17).
349
Following the same approach used above, the optimal trade ratios for this case are (20b) and
2nd best
Bʹ
efficiency loss
$!
!#!!"
[Brʹ − ∂C A / ∂arA ]ρ rA,rA,rW ( τ)
Behavioral spillovers
WWT loadings
$from
!!
#!!"
Brʹ [ρ rW ,rA,rW ( τ) − 1]
Behavioral spillovers in
$!!emissions
!!#sectors
!!!!
"
Beʹ [ρ eI ,rA,rW ( τ) + ρ eA,rA,rW ( τ)]
350
(20d) τ rA,rW =
351
The interpretation of this intra-pollutant ratio is the same as above, as is the result that intra-
352
pollutant trading at a one-to-one rate is unlikely to be optimal. Note that the third and fourth RHS
353
terms in (20b) and (20d) do not vanish, even though there are no explicit market linkages in the
354
present case of distinct markets. The reason is that agricultural abatement costs are not linearly
355
separable, so that incentives in one market affect agricultural choices in the other market. If
356
agricultural abatement costs were linearly separable, such that the markets were truly separate
r
∂C A
∂arA
+
∂C A
∂arA
+
9
∂C A
∂arA
+
∂C A
∂aer
Recall this was also true when permit levels were endogenous, although there were no efficiency implications in
that case since there were sufficient numbers of controls in each market scenario to attain a first-best outcome (see
footnote 6). Making permit levels exogenous results in two fewer controls in each market scenario, imposing
efficiency-reducing restrictions for each scenario.
10
Beavis and Walker (1983) use the terminology “third-best” to describe a pollution control strategy that optimizes
economic welfare in the face of constraints on the design or implementation of the strategy that prevent the solution
from even being second-best.
18
357
with ρz,y,z(τ) = 1, ρy,y,z(τ) = –τy,z, and ρj,y,z(τ) = 0 ∀j ≠ z,y, then setting τeA,eI = τrA,rW = 1 yields the
358
least-cost allocation associated with the chosen permit levels.
359
The results of this section are summarized as follows:
360
Result 2. Suppose point source permit caps and nonpoint source caps are set exogenously
361
relative to the trading program. We find one-to-one intra-pollutant trading is sub-optimal in this
362
case, even when pollutants within a particular medium are uniformly-mixed. More generally, the
363
equi-marginal principle does not apply when caps are exogenous. Finally, whereas integrated
364
markets can only be second best, distinct markets are likely to be even less efficient.
365
In practice, caps are set exogenously for individual pollutants, and then distinct markets are
366
implemented with trading occurring on a one-to-one basis for uniformly mixed pollutants. Result
367
2 indicates that such a market design is not even third-best.
368
5. Numerical Model: Multi-Pollutant Trading in the Susquehanna River Basin
369
We now illustrate the theory using a model of multi-pollutant trading in the Pennsylvania portion
370
of the SRB (Figure 1). The SRB is the Chesapeake Bay’s largest drainage basin, contributing
371
about 60 percent of the total streamflow and nearly 46 percent of the nitrogen loads to the Bay
372
(US EPA 2010). Most of the SRB is in Pennsylvania, which is the major source of the SRB’s
373
nutrient inputs. Pennsylvania established a nutrient water quality trading program in 2005 under
374
its 2004 Chesapeake Bay Tributary Strategy (Shortle 2012). Trading activity, while sparse
375
initially, has recently increased due to stringent new caps imposed by the 2010 Chesapeake Bay
376
Total Maximum Daily Load (TMDL). The Pennsylvania portion of the SRB also features
377
numerous point and nonpoint sources of greenhouse gases (GHGs). Pollution in the form of
19
378
GHG emissions and water quality loadings poses a major threat to environmental quality and
379
economic activities in the Chesapeake Bay and the surrounding airshed (Birch et al. 2011).
380
5.1. Model Specification and Calibration
381
We begin by specifying and calibrating a numerical model of abatement costs and benefits for
382
the SRB. The emissions data used to calibrate our model is expressed in metric tons of carbon
383
equivalents (mtCO2e), and the loadings data is expressed in pounds of N. We use these original
384
units when calibrating our model, then scale the parameters so that emissions are expressed in
385
millions of mtCO2e and loadings are expressed in thousands of metric tons of N (mtN). The
386
scaled parameters are reported in Table 1.
387
Let CI ( aeI ) = ( ψ / 3)aeI3 be the industrial sector’s abatement cost so that marginal
388
abatement costs are C Iʹ ( aeI ) = ψaeI2 . Assuming a marginal abatement cost of $35 at an abatement
389
level of aeI = 19.8 million mtCO2e (RGGI 2014; US EPA 2013), we solve for ψ = 8.9×104.
390
3
Similarly, let CW ( arW ) = (φ / 3)arW
be the wastewater treatment sector’s abatement costs
391
2
so that marginal abatement costs are CWʹ ( arW ) = φarW
. Kaufman et al. (2014) estimate the
392
marginal abatement cost for point sources in the Pennsylvania portion of the SRB to be $15 at an
393
abatement level arW = 4.99×106 lbN. Substituting this information into the marginal abatement
394
cost relation and solving yields φ = 6.42×106.
395
396
3
3
Finally, let C A ( aeA , arA ) = (α / 3)aeA
+ (β / 3)arA
− γaeAarA be the agricultural sources’
abatement cost function. Following Woodward (2011), we assume agricultural emissions and
20
397
loadings abatement are complements, with γ > 0 representing the degree of complementarity.11
398
We are unaware of any empirical measurement of the complementarity between agricultural
399
emissions and loadings abatement, so we assume γ = 1.1×107. This is small enough that marginal
400
abatement costs do not become negative over reasonable ranges of abatement.12 The parameters
401
α and β are calibrated by substituting values for marginal abatement costs and abatement levels
402
into the marginal cost relations. For loadings, we use Kaufmann et al.’s (2014) marginal
403
abatement cost value of $11.58/lbN at an abatement level of 20,955,000 lbN. Using these values
404
2
in the marginal abatement cost relation ∂C A / ∂a rA = βa rA
− γa eA , we solve for β = 3.7×105.
405
We use the agricultural loadings abatement value to determine the corresponding level of
406
emissions abatement of aeA = 734,451 mtCO2e.13 Assuming a marginal abatement cost of $10
407
2
(Golub et al. 2009), we use the relation ∂C A / ∂a eA = αa eA
− γa rA to solve for α = 2.08×108.
408
We assume the damage function for emissions takes the form De(Ee) = εEe since GHGs
409
are a globally mixed pollutant and the emissions from the Pennsylvania portion of the SRB
410
represent a small portion of the world’s GHG emissions. We set ε = 1.4×107 in accordance with
411
Tol’s (2005) median estimate of the marginal damage value of CO2 emissions.
Finally, damages from loadings take the form Dr ( Er ) = ( ν / 2) Er2 , so that Drʹ ( Er ) = νEr
412
413
where ν > 0 is a parameter. Kaufman et al. (2014) estimate marginal damages for total N
414
loadings in the Chesapeake Bay to be $3.37 at an aggregate emissions level of Er = 9.9×107 lbN.
415
Substituting these values into the marginal damage relation, we solve for ν = 1.65×105.
11
In other settings, agricultural abatement of the linked pollutants may be substitute. For example, no-till farming
can reduce N loss from farm fields, but increased weed pressure may result in increased herbicide use, and hence
increase herbicide loadings to waterways (Soane et al. 2012).
12
We performed sensitivity analysis and found that our numerical results are largely insensitive to γ.
13
Specifically, we used the initial loadings abatement value along with transport coefficients from the USGS
SPARROW model (Ator et al. 2011) to calculate the average change in applied nitrogen for cropland in the SRB,
assuming all abatement was due to changes in nitrogen application. We then follow the approach of Reeling and
Gramig (2012) of using the DAYCENT model (NREL 2011) to estimate emissions abatement associated with this
change in nitrogen applications.
21
416
5.2. Simulation Results
417
We simulate a variety of trading scenarios for the SRB using MATLAB (Mathworks, Inc. 2016);
418
the results are presented in Table 2. In each scenario, the inter-pollutant trade ratio denotes trades
419
involving equivalent units (e.g., metric tons-for-metric tons).14 Scenario 1, or the efficient
420
scenario, represents a first-best or efficiently designed integrated pollution market. Although not
421
reported in Table 2, the initial emissions and loading caps, êI0 and r̂ W0, are chosen to ensure
422
*
*
peI = peA = Beʹ and prW = prA = Brʹ in the market outcome, given that nonpoint sources have an
423
implicit right to pollute. A distinct market with the same intra-pollutant trade ratios can also yield
424
the efficient outcome, provided the caps are adjusted to account for no inter-pollutant trading.
425
The first-best results indicate industry is the least cost source of emissions abatement, as
426
evidenced by the large relative abatement allocation to industry, whereas agriculture is the least
427
cost source of loadings abatement. These results are due to agriculture’s relatively high marginal
428
cost of abating emissions, but relatively low marginal cost of abating loadings. The efficient
429
inter-pollutant trade ratio is less than one to encourage more abatement in the loadings sector at
430
the margin, due to convex damages from loadings (whereas marginal damages from the SRB’s
431
emissions are constant). The efficient intra-pollutant trade ratios are unity, as is expected.
432
We compare the efficient outcome to the more realistic integrated and distinct market
433
scenarios in which the initial permit caps for each pollutant have been set exogenously and sub-
434
optimally, e.g., by different agencies regulating point sources in each sector. These sub-optimal
435
point source permit caps represent the only differences in initial regulations relative to the
436
efficient outcome, as we have assumed the agricultural sector is not initially regulated in either
14
Notice that three trade ratios are presented for each scenario: one inter-pollutant trade ratio and two intra-pollutant
trade ratios. In the analytical section above, we optimized over the inter-pollutant ratio τrA,eI rather than the intrapollutant ratio τrA,rW. This is of no consequence, since any three ratios give rise to all other ratios. We focus on the
intra-pollutant ratio in our numerical results to make comparisons with the case in which one-to-one intra-pollutant
trade ratios are imposed exogenously.
22
437
case. Therefore, to facilitate comparison with the first-best case, let the point source permit caps
438
be eˆI 0 = ζ e eˆ*I 0 and rˆW 0 = ζ r rˆW* 0 , where ζs (for s ∈ {e, r}) is a parameter indicating the degree of
439
regulation relative to the efficient case. A value of ζs = 1 represents an efficient cap on point
440
sources of pollutant s, whereas ζs < 1 (> 1) implies an inefficiently strict (lax) cap. Note that an
441
efficient cap in only one sector (e.g., ζe = 1, ζe ≠ 1 or vice versa) will not yield an efficient
442
allocation of either type of pollutant since agricultural choices respond to incentives in both
443
markets. Efficiency is only obtained when ζe = ζr = 1. We set ζe = ζr = ζ in Table 2 because our
444
interest is in highlighting how traditional results change when caps are set exogenously, rather
445
than in exploring every qualitative combination of ζe and ζr relative to unity.
446
Table 2 illustrates results for ζ = 0.95 (a strict cap) and ζ = 1.05 (a lax cap), with three
447
scenarios examined for each value of ζ. The first scenario involves no trading, whereby point
448
sources must satisfy the caps on their own while nonpoint sources remain unregulated. The no-
449
trading scenarios are insightful because comparing these to the various trading scenarios
450
illustrates the economic and ecological performance of trading. The second scenario considered
451
involves optimally chosen trade ratios, whereby all trading ratios are optimally chosen to satisfy
452
the cap given the type of market being considered (integrated versus distinct). The third scenario
453
considered involves one-to-one intra-pollutant ratios, whereby all intra-pollutant ratios are
454
exogenously set equal to one. Both integrated and distinct markets are considered for each of the
455
trading scenarios.
456
First consider the no-trading scenarios 2 and 7. Social net benefits are negative for both ζ
457
= 0.95 and ζ = 1.05 because the cost of point sources satisfying the abatement requirements on
458
their own greatly exceeds the social benefits. The costs are particularly large under the case of
459
strict caps, with industry abating 61 percent more and wastewater treatment plants abating 649
23
460
percent more than in the efficient outcome. This means abatement costs increase significantly for
461
all point sources, with wastewater treatment plants bearing the greatest costs of over-regulation
462
absent trading.
463
The environmental performance of the no-trading scenarios is measured by the aggregate
464
pollutant levels arising in these scenarios, which equals the sum of the point source emissions
465
cap and the nonpoint source’s unregulated pollution. For each ζ, these aggregate pollutant levels
466
can be interpreted as the imputed aggregate cap for each pollutant: these are the levels that would
467
arise when trading is not allowed. The imputed caps are presented in Table 3 for each value of ζ.
468
Comparing these values to the aggregate pollutant outcomes under various trading scenarios
469
allows us to examine whether trading causes the imputed cap to be violated. The political
470
viability of inter-pollutant trading could be in question if inter-pollutant trading increases
471
pollutants in one medium relative to the no-trading outcome.
472
We now turn to the trading scenarios, starting with excessively strict caps (ζ = 0.95).
473
Consider the case of an integrated market with optimally-chosen intra-pollutant trading ratios
474
(scenario 3). This scenario results in social net benefits that are 5 percent smaller than those in
475
the efficient scenario due to over-regulation in scenario 3. Wastewater treatment plants bear the
476
greatest costs of over-regulation. To offset these additional costs, the optimal inter-pollutant
477
trade ratio (τrW,eI = 0.014) for scenario 3 is larger than the efficient ratio, reducing the incentives
478
to reallocate abatement from industry to wastewater treatment facilities. Additionally, the intra-
479
pollutant ratios (τeA,eI = 0.318 and τrA,rW = 0.089) are considerably smaller than the efficient
480
values so that more abatement is allocated to nonpoint sources––including more exchange of
481
industrial emissions for nonpoint loadings abatement. This further alleviates the burden of over-
482
regulation on point sources and takes advantage of the complementarities in agricultural
24
483
abatement costs. The result is that agricultural abatement of both emissions and loadings
484
increases by 26 percent relative to the efficient scenario, while point source abatement decreases
485
relative to the efficient outcome. Relative to scenario 2, it is clear that the greatest reallocation of
486
abatement responsibilities are from industrial emissions to agricultural loadings. Indeed, Table 3
487
indicates the implied loadings cap is satisfied for scenario 3, which stems from the significant
488
increase in agricultural loadings abatement. However, the implied emissions cap is violated;
489
since industry is by far the largest contributor of emissions, the 2 percent decrease in industry
490
abatement in this case yields a significant increase in emissions. The intuitive reason for the
491
imputed cap being violated is that the optimal market design is trying to move the system
492
towards the efficient outcome, which involves greater pollutant levels in each sector.
493
Optimally-designed distinct markets under strict caps (scenario 4) are 5 percent less
494
efficient than the corresponding integrated market (scenario 3) because distinct markets offer
495
fewer instruments to reallocate abatement responsibilities. In particular, without the ability to
496
directly exchange industrial emissions abatement for agricultural loadings abatement (the
497
dominant form of exchange in scenario 3), the next best option is to reallocate emissions
498
abatement from industrial sources to agricultural sources. This explains the intra-pollutant
499
trading ratio for emissions being significantly smaller than in the integrated market scenario. The
500
reallocation of emissions abatement to agricultural sources also results in significant loadings
501
abatement by agricultural sources due to abatement cost complementarities, benefitting
502
wastewater treatment plants. The intra-pollutant trading ratio for loadings increases in the
503
distinct markets case to offset this effect. As with the case of integrated markets, the implied
504
loadings cap is satisfied, whereas the implied emissions cap is violated (Table 3).
25
505
Further insight is obtained by examining the case where one-to-one intra-pollutant trade
506
ratios are imposed. Consider first the integrated market scenario under strict caps (scenario 5).
507
Social net benefits decline by 19 percent relative to scenario 3 because scenario 5 restricts the
508
available tools for efficiently reallocating abatement responsibilities. The inter-pollutant trade
509
ratio (τrW,eI = τrA,eI = 0.0005) is smaller than any of the other ratios examined thus far, as this is
510
now the only mechanism for reallocating abatement to the loadings sector. But note that, unlike
511
the case with differentiated ratios, it is no longer possible to target reallocations towards
512
abatement in agricultural loadings. Instead, the small inter-pollutant trade ratio encourages more
513
loadings abatement by both agriculture and wastewater treatment plants. The result is greater
514
control costs than in scenario 3. The imputed loadings cap is satisfied for this case, but the
515
imputed emissions cap is violated.
516
The distinct market scenario 6 is even more limited in reallocating abatement efforts
517
when the intra-pollutant ratios are fixed at unity because now policy makers have no tools
518
available to guide the market. Consequently, this is the least efficient outcome overall. Social net
519
benefits decline by 22 percent relative to scenario 5, which is a greater efficiency loss relative to
520
the case when intra-pollutant trade ratios are chosen optimally; the inefficiency of eliminating
521
inter-pollutant trading is compounded when the intra-pollutant trade ratios are restricted.
522
However, neither imputed cap is violated in this case due to the difficulty in encouraging
523
reallocations across sectors.
524
The welfare rankings for the various scenarios involving excessively lax caps (ζ = 1.05)
525
are the same as those for overly strict caps, whereas the optimal choices of trade ratios––and
526
hence the allocation of abatement efforts––are largely opposite (Table 2), as might be expected.
527
In contrast to trading under strict caps (scenarios 3–6), the imputed caps are not violated under
26
528
any scenario involving lax caps. The intuitive reason is that the optimal market design is trying
529
to move the system towards the efficient outcome, which involves smaller pollutant levels in
530
each sector. This result illustrates that trading––particularly inter-pollutant trading––is capable of
531
both reducing aggregate abatement costs and emissions relative to cases where trading is not
532
allowed. The importance of this result is magnified once we recognize that lax caps are more
533
likely to be applied in practice than strict caps.
534
Finally, Figure 2 illustrates social net benefits under each of the trading scenarios
535
described above over multiple values of ζ. The figure shows the ranking of trade scenarios is
536
mostly preserved for other values of ζ, with the welfare deviation expanding the further is ζ from
537
unity, which is the point where all scenarios converge at the efficient outcome. The only
538
exception is the integrated market with one-to-one inter-pollutant trading, which outperforms the
539
distinct markets with optimal inter-pollutant trading for large values of ζ. Trading does not occur
540
in the emissions market for ζ > 1.04; complementary emissions abatement by agriculture––
541
combined with industry’s own abatement––satisfies the emissions cap without need for trading.
542
6. Discussion and Conclusion
543
Growing recognition of the linkages between multiple pollutants has led economists and
544
regulatory agencies to consider multi-pollutant markets as a means to reduce the social cost of
545
environmental policies and improve efficiency (Lutter and Burtraw 2002; US EPA 2011). By
546
allowing trade across pollutants, multi-pollutant markets can exploit complementarities in
547
pollution abatement costs and the linkages between pollutant marginal damages, e.g., due to
548
cross-media damages.
549
550
Our findings reveal that in a world with no previous regulation in place and no
institutional constraints relative to setting the aggregate pollution cap, multi-pollutant markets for
27
551
uniformly mixed pollutants perform identically to distinct markets and replicate the first-best
552
outcome in the absence of uncertainty. Hence, integrated markets for linked pollutants do not
553
improve efficiency when caps can be set efficiently.
554
In practice, environmental managers engaged in permit market design decisions may face
555
many practical constraints, including prior regulations that prevent permit caps from being set
556
efficiently as a joint decision with the trade ratios. We demonstrate that such constraints have
557
important consequences for market design choices in the context of multi-pollutant problems. In
558
particular, it becomes optimal to choose trade ratios that cause the equi-marginal principle to
559
break down in the permit market. This result contrasts with one basic tenet of environmental
560
economics—that pollution markets minimize social costs by reallocating abatement effort to
561
equate effective marginal abatement costs across sectors. Yet, the result stems from another basic
562
tenet—the Tinbergen rule that one instrument is required for each externality. Specifically, the
563
inability to set permit levels efficiently means that adjustments to the trade ratios, and an
564
abandonment of the equi-marginal principle, are warranted to improve efficiency. This result
565
holds even in the case of distinct markets when no inter-pollutant trading is allowed. However,
566
as integrated markets involve an additional policy instrument that can ameliorate the efficiency
567
losses from the permit restrictions (i.e., the inter-pollutant trade ratio), we find that integrated
568
markets can be more efficient than distinct markets.
569
An important concern over integrated markets is that reallocating abatement effort across
570
environmental media could, in principle, violate current environmental standards governing a
571
particular medium. We find this is likely to be a concern when existing regulations are overly
572
strict. However, in the more likely case that existing requirements are too lax relative to the
573
efficient outcome (e.g., Muller and Mendelsohn 2009), we find that cross-media reallocations
28
574
can reduce social costs and improve environmental quality within each environmental medium.
575
This is because trading ratios are optimally chosen to generate abatement closer to efficient
576
levels. In cases where inter-pollutant trading does not reduce pollution universally, our results
577
indicate that pollution is likely to decline for some media. More importantly, the overall
578
economic efficiency of the solution will improve. Prior studies on air pollution (e.g., Lutter and
579
Burtraw 2002) have argued for a need to focus on the efficiency gains arising from multi-
580
pollutant trading, rather than focusing on whether suboptimal environmental standards are
581
always satisfied.
582
A practical concern regarding multi-pollutant markets is the amount of information
583
required to implement them. However, the only additional piece of information required relative
584
to distinct markets is some measure of the complementarity in marginal abatement costs for
585
linked pollutants, or the linkages in marginal damages across multiple media for pollutants
586
affecting multiple media. Prior work empirically measures the joint production of multiple
587
pollutants in the electrical utility industry (e.g., Agee et al. 2014), and doing so for other sectors
588
is likely to be straightforward. It is more challenging to obtain estimates of the complementarity
589
in marginal damages since, in many cases, the biogeochemical relationships between pollutants
590
may not be well-known. However, as our understanding of the linkages between pollutants
591
increases, so too will our ability to effectively manage them.
592
Finally, an important caveat of our results is that uncertainties stemming from stochastic
593
emissions and uncertain abatement effectiveness, which are often characteristic of nonpoint
594
pollution problems, were ignored here so that we could focus on the core issue of inter-pollutant
595
trading. Incorporating these uncertainties into the analysis would be straightforward, however,
596
and would mainly involve further modifications to the trade ratios. Recent numerical work on
29
597
nutrient water quality problems in the SRB (Horan and Shortle 2015) suggests that the
598
modifications could be positive or negative, depending on which type of uncertainty
599
(stochasticity, abatement effectiveness) dominates in the market equilibrium. We have also
600
ignored cost uncertainty, but including this feature would be unlikely to affect our qualitative
601
results since we compare market designs within a pollution permit trading framework rather than
602
compare different policy instruments (e.g., price and quantity instruments).
603
Appendix
604
Deriving Sector-Level Cost Minimization Problems
605
Consider the case of an integrated market. Following the approach of Horan and Shortle (2005),
606
suppose the wastewater sector may hold permits sold by any other sector. This sector’s initial
607
emissions permit holdings are rˆW 0 , and denote its purchases of permits from other sources by
608
êWI , êWA , and r̂WA . The sector’s costs of abatement and permit purchases are CW(arW) + peIêWI +
609
peAêWA + prAr̂ WA. Moreover, this sector is constrained in that its total emissions cannot be greater
610
than its permit holdings, rW ≤ rˆW 0 + eˆWI / τ eI ,rW + eˆWA / τ eA,rW + rˆWA / τ rA,rW , where the final three
611
RHS terms represent the emissions that the wastewater treatment sector can generate based on
612
permits obtained from other sectors. Assuming the emissions constraint is satisfied as an
613
equality, then r̂WA can be eliminated as a choice variable so that total costs are
614
(A1)
615
Here, the choice variables are a rW , êWI , and êWA. The FOCs associated with êWI , and êWA are
616
(A2)
CW (arW ) + prAτ rA, rW [rW − rˆW 0 − eˆWI / τ eI , rW − eˆWA / τ eA, rW ] + peI eˆWI + peAeˆWA
= CW (arW ) + prAτ rA, rW [rW 0 − arW − rˆW 0 − eˆWI / τ eI , rW − eˆWA / τ eA, rW ] + peI eˆWI + peAeˆWA
peI = p rA
τ rA,rW
τ eI ,rW
30
peA = prA
τ rA,rW
617
(A3)
618
where the equalities in equations (A2)–(A3) emerge in a competitive market equilibrium. Divide
619
(A2) by (A3) to yield
620
(A4)
621
The cost minimization problems for the other sectors are analogous, with FOCs ultimately
622
yielding the other two primary trade ratios
623
(A5)
τ rA,eI =
624
(A6)
τ rW ,eI =
625
Given these relations, the ê terms in (A1) cancel, so we can write the cost function for a
626
particular sector restricted on only that sector’s pollution: C I (aeI ) + peI [rI 0 − aeI − eˆ I 0 ],
627
CW (a rW ) + prW [rW 0 − a rW − rˆW 0 ] , and C A (aeA , a rA ) + peA [e A0 − aeA − eˆ A0 ] + prA [rA0 − a rA − rˆA0 ] .
628
Deriving Second-Best Trade Ratios
629
Consider the integrated market, with the first-order conditions given by (17). In particular, the
630
condition for the choice of τ rW ,eI is
631
632
τ eA,rW
,
peI τ eA,rW deˆ A
=
=
= τ eA,eI .
peA τ eI ,rW
deˆ I
peI
p rA
p eI
.
p rW
[Beʹ − C Iʹ ]
⎡
⎡
∂a eI
∂a
∂C ⎤ ∂a eA
∂C ⎤ ∂a rA
+ ⎢ Beʹ − A ⎥
+ [Brʹ − CWʹ ] rW + ⎢ Brʹ − A ⎥
=0
∂τ rW ,eI ⎣
∂a eA ⎦ ∂τ rW ,eI
∂τ rW ,eI ⎣
∂a rA ⎦ ∂τ rW ,eI
which can be rearranged and written as
31
⎡ ∂a eI
⎡ ∂a rW
∂a eA ⎤
∂a rA ⎤
Beʹ ⎢
+
+
⎥ + Brʹ ⎢
⎥
⎣ ∂τ rW ,eI ∂τ rW ,eI ⎦
⎣ ∂τ rW ,eI ∂τ rW ,eI ⎦
∂a eI
∂a rW
∂C A ∂a eA
∂C ∂a rA
= C Iʹ
+
+ CWʹ
+ A
∂τ rW ,eI ∂a eA ∂τ rW ,eI
∂τ rW ,eI ∂a rA ∂τ rW ,eI
633
(A7)
634
Next, use the market equilibrium conditions (15) to write (A7) as
635
(A8)
⎡ ∂aeI
⎡ ∂arW
∂aeA ⎤
∂arA ⎤
Beʹ ⎢
+
+
⎥ + Brʹ ⎢
⎥
⎣ ∂τ rW , eI ∂τ rW , eI ⎦
⎣ ∂τ rW , eI ∂τ rW , eI ⎦
∂aeI
C ʹ ∂aeA
C ʹ ∂arA
∂arW
= CIʹ
+ I
+ I
+ CWʹ
∂τ rW , eI τ eA, eI ∂τ rW , eI τ rA, eI ∂τ rW , eI
∂τ rW , eI
⎡ ∂aeI
1 ∂aeA
1 ∂arA ⎤
∂arW
= CIʹ ⎢
+
+
.
⎥ + CWʹ
∂τ rW , eI
⎣ ∂τ rW , eI τ eA, eI ∂τ rW , eI τ rA, eI ∂τ rW , eI ⎦
636
We can solve (A8) for
637
(A9)
638
where the first equality stems from the polluters’ market equilibrium condition (15a), and where
639
ρ j (τ y ,z ) =
τ rW ,eI =
[Bʹ − CWʹ ]ρ ( τ ) + Brʹ ρ ( τ )
C Iʹ Beʹ
[
=
ρ eI ( τ rW ,eI ) + ρ eA ( τ rW ,eI )]+ r
rW
rW ,eI
rA
rW ,eI
CWʹ CWʹ
CWʹ
CWʹ
(∂a j / ∂τ y , z ) / τ j , z
∑ (∂a
k
/ ∂τ y , z ) / τ k , z
τ j , z , for y,z ∈ {eI, eA, rW, rA} and τy,y = 1. The term ρ j ( τ y ,z ) is
k≠y
640
indicated to be a function of τ y , z to reflect the derivatives arising within this term, but actually
641
the term depends on all trade ratios. Likewise, we can derive
τ eA,eI =
642
(A10)
τ rA,eI =
643
(A11)
[B ʹ − ∂C A / ∂a eA ]ρ ( τ )
Beʹ
ρ eI ( τ eA,eI ) + e
eA
eA ,eI
∂C A / ∂a eA
∂C A / ∂a eA
Brʹ
[ρ rW (τ eA,eI ) + ρ rA (τ eA,eI )]
+
∂C A / ∂a eA
Beʹ
[ρ eI ( τ rA,eI ) + ρ eA ( τ rA,eI )]+ [Brʹ − ∂C A / ∂aeA ]ρ rA (τ rA,eI )
∂C A / ∂a eA
∂C A / ∂a eA
Brʹ
+
ρ rW ( τ rA,eI )
∂C A / ∂a eA
32
644
645
Now consider the case of distinct markets. The optimality conditions (17) still hold.
Using a process analogous to that described above, the optimal trade ratios are (A10) and
τ rA,rW =
[B ʹ − ∂C A / ∂a rA ]ρ ( τ )
Brʹ
ρ rW ( τ rA,rW ) + r
rA
rA, rW
∂C A / ∂a rA
∂C A / ∂a rA
.
Beʹ
[ρ eI (τ rA,rW ) + ρ eA ( τ rA,rW )]
+
∂C A / ∂a rA
646
(A12)
647
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37
Table 1. Simulation Parameters
Sector
Industrial
Wastewater
Parameter Description
ψ
Marginal cost parameter,
industrial sector
eI0
Initial industrial emissions
(million mtCO2e)
Value
8.93×104
ϕ
Marginal cost parameter,
wastewater treatment sector
Initial wastewater treatment
loadings (thousand mtN)
6.4×106
Marginal cost parameter,
agricultural sector
Marginal cost parameter,
agricultural sector
Complementarity parameter,
agricultural sector
Initial agricultural emissions
(million mtCO2e)
Initial agricultural loadings
(thousand mtN)
2.08×108
Marginal damage from emissions
Marginal damage from loadings
1.4×107
1.65×105
rW0
Agricultural
α
β
γ
eA0
rA0
Damages
ε
ν
38
153.5
12
3.71×105
1.1×107
5.54
28
Scenarios
1. Efficient (first-best)
Table 2. Simulation Results from Pollutant Trading Scenarios
Emissions abatement
Trading ratios
(million mtCO2e)
IntraIntraSocial
Interpollutant
pollutant
net benefits
pollutant (emissions) (loadings)
($ million)
τrW,eI
τeA,eI
τrA,rW
Industry Agriculture
163.4
0.0025
1
1
12.52
0.61
Loadings abatement
(1,000 mtN)
WWTa
0.92
Agriculture
5.73
Exogenous caps: strict (ζ = 0.95)
2. No trading
–630.7
——
——
——
20.15
——
6.93
——
Optimally chosen trade ratios
3. Integrated market
4. Distinct markets
155.8
148.6
0.014
——
0.318
0.116
0.089
1.012
12.29
12.11
0.77
0.93
0.39
0.80
7.24
6.21
One-to-one intra-pollutant ratios
5. Integrated market
6. Distinct markets
126.5
98.9
0.0005
——
1
1
1
1
11.83
19.46
0.74
0.69
1.89
0.94
9.16
5.99
Exogenous caps: lax (ζ = 1.05)
7. No trading
–441.3
——
——
——
6.11
——
6.39
——
Optimally chosen trade ratios
8. Integrated markets
9. Distinct markets
157.3
125.3
0.0007
——
2.265
N/Ab
4.692
1.000
11.22
6.11
0.54
0.61
1.58
0.92
5.02
5.73
One-to-one intra-pollutant ratios
10. Integrated market
11. Distinct markets
125.3
118.9
0.0012
——
1
1
1
1
6.30
5.56
0.52
0.55
0.69
0.89
4.87
5.50
a
b
WWT = Wastewater treatment sector.
Emissions trading breaks down for a lax cap.
39
Table 3. Imputed Caps and Pollutant Levels by Trading Scenario
Emissions (million mtCO2e)
Loadings (thousand mtN)
Scenarios
Imputed cap Total emissions
Imputed cap Total loadings
Exogenous caps: strict (ζ = 0.95)
138.89
33.07
Optimally chosen trade ratios
3. Integrated market
145.98
32.37a
4. Distinct markets
146.0
32.99
One-to-one intra-pollutant ratios
5. Integrated market
6. Distinct markets
Exogenous caps: lax (ζ = 1.05)
Optimally chosen trade ratios
8. Integrated market
9. Distinct markets
146.47
138.89
152.93
33.61
One-to-one intra-pollutant ratios
10. Integrated market
11. Distinct markets
a
28.95
33.07
147.28
152.32
33.4
33.35
152.22
152.93
34.44
33.61
Shaded cells highlight trading scenarios that do not violate the imputed cap.
40
Figure 1. The Susquehanna River Basin
41
Figure 2. Social net benefits from abatement in the SRB under separate and integrated
markets when permit caps set exogenously at the fraction ζr = ζe = ζ of efficient levels.
42