Emissions Trading To Reduce Urban Ozone: The Chicago Area ERMS Program
Richard F. Kosobud, Houston H. Stokes, and Carol D. Tallarico, Dept. of Economics,
University of Illinois at Chicago.
Contents
1 Introduction
2 Summary of Results
3 Outline of the Study
4 How the ERMS Cap-and Trade Market Works
5 The Theory of Cap-and-Trade Market Incentives Applied to the Urban Scene
Figure 1a Price determination and cost savings with a homogenous pollutant
Figure 1b Price determination and cost savings with heterogeneous pollutants
6 Modeling Spatially Heterogeneous Pollutants
7 The Required Databases
8 Empirical Implementation of the Model
9 The Performance of the ERMS Cap-and-Trade Market
Table 1 Prices, Trades, and Cost Savings for Varying VOM Reduction Rates
Figure 2a Rates of Reduction, Cost Savings, and Trades Plotted
Figure 2b Variance of Costs, Trades, and Cost Savings Plotted
Table 2 Changes in Control Costs, Trades, and Cost Savings
Table 3 Transactions Costs, Trades, and Cost Savings
Table 4 Prices, Trades, and Cost Savings in an Auction Market Variant
Figure 3a Individual Firm Trades Under Free Allocation
Figure 3b Individual Firm Trades Under an Auction Market
Table 5 Affects of Spatial Restrictions on Market Trading
10 Conclusion and Research Directions
Appendix A. Implementation Procedures for the Model
References
1
1. Introduction
The government is confronted with difficult regulatory choices in controlling numerous
air pollutants, ranging from volatile organic compounds to particulates and sulfur
dioxide. Difficulties arise in devising control policies because these pollutants differ in
the harms they cause and the costs of their control. Difficulties are compounded because
air pollutants also differ by location of their emissions giving rise to varying exposures to
sensitive populations. The regulator cannot rely on established estimates of marginal
benefits and costs of reduction for optimal control of each and every emission, wherever
it occurs, because these estimates are unavailable in the great majority of cases, or not
permitted by legislation. These constraints are not likely to change in the foreseeable
future.
However, there is no escaping government responsibility for control of numerous air
pollutants as the prevalent belief is that poor air quality comes as close as one can find to
a pure public good with an army of polluters and a host of sufferers. One approach, at the
policy level, is to establish a politically determined cap on pollutant emissions rather than
attempt an estimate, based on limited or nonexistent data, of the benefit-cost level of
emissions. In this approach emitters of pollutants are delegated the specific control
decisions to be made under economic incentives while the government retains the right to
set the cap, allocated tradable credits, and monitor the market.
This study investigates this approach in the case of a pioneering application of a cap-andtrade market variant of emissions trading that has been designed as one of the measures
to reduce urban ozone in the Chicago region. Our method of investigation is to model the
cost-minimizing responses of stationary source emitters of volatile organic compounds or
material (VOM) to market incentives given an aggregate cap on emissions in an effort to
compare the cost-effectiveness of emissions trading as an alternative to traditional
regulation. The region is a severe non-attainment area with respect to nationally
established ozone standards, which means that Chicago’s air has found to be below these
standards during prior summer seasons.
The model is developed based upon existing rules of the cap-and-trade market, upon prior
studies of actual marginal control costs for emitters, and upon actual allocations of
tradable credits and historic emissions. The model then simulates or predicts transactions
based upon the key assumption of cost minimizing behavior in an ideal market setting.
Observed transactions to test the model are unlikely to become available for several years
after the start-up date of the year 2000. Furthermore, the market may be operating below
its potential for an even longer period for reasons to be explained shortly. Consequently,
the objectives of this study are to:
a. Estimate, within the model confines, the cost-effectiveness of emissions trading
compared with traditional regulation in this innovative market incentive system;
b. Prepare a model framework for future comparisons, or tests, with observed data;
c. And, highlight critical areas deserving more research if the model’s predictions
diverge from observed data.
2
Note it may not be a matter of judging the model right or wrong, but of evaluating
reasons why the observed transactions differ from predicted. Such reasons could include
learning behavior, concern about public acceptance of pollutant trading, transactions
costs, and the like. A carefully prepared framework can advance later study of these
issues. We also will indicate how this framework could be extended to consider issues of
environmental justice.
Research on emissions trading has burgeoned in recent years as applications of this
incentive scheme have increased. Stavins (1995) has introduced transactions costs into
the emissions trading framework; Montero (1997) has considered transactions costs and
uncertainty with respect to regulatory approval of trades; and Mendelsohn (1986) has
analyzed spatial emissions of sulfur dioxide in a trading setting. Tolley et al. (1993) have
studied reasons for caution in applying emissions trading to urban ozone control. This
study is the first we know of that develops a model to analyze a specific application of
emissions trading to control of volatile organic compounds, a precursor of urban ozone
control.
We now proceed to a brief presentation of the results achieved, then to a brief description
of the features of this innovative market incentive scheme, and next to an explanation of
the specification of the model. This is followed by a description of the key databases, an
account of the quantitative methods used to obtain empirical results, a more detailed
explanation of the results, and finally a discussion of further research open up by this
study.
2. Summary of Results
We first assume emissions to become uniformly mixed concentrations over an
unconstrained urban market area with resulting uniform harms to the population. In this
case the model generates, with a cap-and-trade market in place, substantial cost savings
that could be realized under unrestricted emissions trading compared with traditional or
command-and-control (CAC) regulation. An advantage of our flexible model is that it
enables us to carry out scenario experiments with alternate parameter values and emission
targets to gauge the outcomes on the prices and quantities of trades, and on cost savings.
Some of these scenarios would be very difficult, if not politically impossible, to carry out
as trial runs.
Our first finding is that the present program could achieve, in a well-functioning market,
up to one million dollars in savings per year compared with CAC regulation. These
savings free resources for alternative uses by government or the private sectors. Our
model assumes cost-minimizing behavior on the part of emitters, flexibility of choice
about control options, full information about control and trading opportunities, no
uncertainty about trades and their public reception, and no transactions costs. The model
results provide a benchmark for appraising actual market prices and transactions that may
fall short of the potential if one or more of these assumptions fail to be appropriate.
We then ask how changing the slopes of marginal cost control curves affect the results.
Our motivation in this experiment is to explore how market incentives might stimulate
innovations and reduce slopes, or how unforeseen events might hinder control measures
and increase slopes. We find that changing all slopes by an equal percentage leads to
3
proportionate changes in the same direction of tradable credit prices and cost savings.
This reduction in control cost slopes reduces tradable credit prices and reduces the
variance among emitter costs compared with an increase in slopes that increases the
prices and variance. In simple language, reducing costs of control and cost differences
among emitters, advantageous as that is, reduces the gains from trade, whereas increasing
costs and differences leads to greater savings.
We introduce a simple form of transactions costs to estimate the impact on market
variables. Higher transactions costs increase tradable credit prices, reduce trading, and
reduce cost savings. Finally, to show the flexibility of the model, we reduce the policy
cap on emissions, that is, reduce allowable emissions, and find that at the new
equilibriums there is an increase in tradable credit prices, volumes traded, and cost
savings.
Environmental justice concerns have been raised about the spatial redistribution of
emissions after trading. The issue is whether all neighborhoods have benefited by a
market extending over the urban region. We have incorporated into the model
sophisticated mapping software that can portray before and after spatial emission
patterns. Differences in these spatial or neighborhood patterns could be an indicator or
flag of possible spatial environmental equity concerns. The model can thus provide for a
wide variety of mapping specifications as desired by the user including zip code, census
tract, or neighborhood mappings of volatile organic compound or material (VOM) and
HAP (hazardous air pollutants) emissions as affected by emissions trading.
We shall report in later research on this complex matter after detailed reports by emitters
on VOM and HAP emissions become available. It seems prudent in view of the general
interest about neighborhood concerns to ask a question about the loss in cost savings if
spatial market constraints are applied. We provide at this stage one kind of answer by
arbitrarily limiting trading in certain areas and directions and assess the outcome in terms
of the volume of trades, tradable credit prices, and control cost savings.
3. How the ERMS Cap-and-Trade Market Works
Not only is emissions trading a new regulatory tool, but also the cap-and-trade variant
was an untried approach to controlling urban ozone until the Illinois EPA (IEPA)
launched the Emissions Market Reduction System, or ERMS, in 2000, for control of
stationary source VOM emissions in the Chicago region.
3.1 How Government and Emitter Firms Share Key Decisions Under ERMS
The target was set in the ERMS program for a further aggregate reduction of 12% of
VOM emissions from stationary sources in the non-attainment area. It was estimated that
this cap of 88% of historical emissions would contribute to the region’s attainment of
national air quality standards that had not been reached by former reductions under CAC
regulation. These stationary sources comprise about 20% of all seasonal VOM emissions
in the region, transportation and smaller area sources under different regulatory control
making up the rest.
4
The tradable credit was defined as a dated Allotment Trading Unit (ATU) good for 200
pounds of seasonal VOM emissions and transferable one-for-one anywhere in the region.
The ATUs were not denominated in those HAPs that are a subset of VOMs nor identified
or restricted by location. Thus, the decision was to have a unified regional or spatial
market for VOM emissions. After devising a rule for allocation of ATUs to individual
emitters, a rule requiring a properly dated ATU to be returned to the IEPA for every 200
pounds of emissions during the specific five month ozone season, and rules establishing
record keeping, monitoring, and enforcement procedures, the IEPA turned over key
implementation decisions to the regulated community.
At the time of this study we had data on 179 major stationary sources that were each
allocated free of charge 88% of their average 1994 to 1996 emissions (with some
adjustments for unusual circumstances). These ATU allocations were made initially for
the year 2000 ozone season. The allocations were to be renewed each year in the future
generating an intertemporal stream of ATUs. Unlike traditional regulation that required
specific control technologies or specified rates of emissions dependent upon
technologies, the emitter firms were now free to compare reduction control options, and
their costs, with trading in a market where ATU prices were revealed or negotiated.
Emitters were expected to choose trading or control or a combination of the two in an
effort to minimize control costs. Those emitters with the lowest control costs were
expected to reduce more than 12% and sell ATUs to those emitters with higher costs
until marginal control costs were equal to ATU prices across all emitters, thus achieving
savings compared to traditional regulation. ATUs could be banked for one year only
preventing a build-up of unused credits that could lead to seasonal spikes in emissions1.
Stationary sources in this cap-and-trade market range over 23 SIC classifications
including painting, plating, refining, manufacturing, publishing, and other industries.
These industries vary by an order of magnitude in their seasonal emissions. They also
vary widely in the control measures available to firms in different industries. Control
measures could include changing the output level, the product, inputs into processes, or
installing control equipment such as catalytic incinerators or other afterburners of various
types (DePriest 2000).
Such diversity in control options suggests a range of marginal control costs, which augurs
well for cost savings from trading. However, such diversity of emitter industries scattered
about the region also results in a multiplicity of different hydrocarbon and hazardous air
pollutant emissions that constitute VOMs.
3.2 Addressing Non-uniform Mixing or Heterogeneity of VOM Pollutants in the Model
Urban air is filled with an enormous variety of substances that move about and interact in
ways not yet thoroughly understood. A few aspects bear on our study of spatial patterns.
VOMs react with nitrogen oxides (NOx) and climate conditions to generate low-level
ozone, which can impair lung function and contribute to other problems like the reduction
in visibility. NOx moves about over larger areas than do most VOMs so that current
1
Additional details on the features of this cap-and-trade market with a comparison of the national sulfur
dioxide version and the local Los Angeles cap-and-trade markets for sulfur dioxide and nitrogen oxides are
available in Chapter 1 of Kosobud (2000).
5
policy efforts are directed toward larger regional control of NOx emissions while VOM
controls are more directed toward local action like the cap-and-trade market subject of
this study.
Not only ozone but also aggregate and individual VOMs can have harmful impacts on
human health and the environment. HAPs that are VOMs include benzene, toluene, the
xylenes and other carcinogens. VOMs as they diffuse over space can also be transformed
chemically into, generally, less harmful substances. Almost all of them tend to be fund
rather than stock pollutants and dissipate over time so that control over the summer
season seems appropriate.
The regulatory agency understands this heterogeneity of pollutants by type and location,
but made the implicit assumption that pollutants are sufficiently fixed in proportion from
each emission source, and wafted approximately uniformly about the region so that the
decision to create one market and one tradable credit, with attendant advantages, was
defensible. The further implicit assumption was made that an aggregate emissions target
or cap on stationary sources could represent their contribution toward meeting air quality
standards. The objective was then to provide incentives for firms to minimize the costs
while staying within the aggregate cap. The alternative was to define many spatially
specific credits, and hence many markets, with possibly significant losses in market
effectiveness. One aspect of our model was developed to help evaluate these
assumptions by permitting a comparison of the performance of the unified market and a
spatially subdivided market.
It is important to note that existing traditional regulation of VOMs and HAPs remains in
force underlying the emissions trading. That is, emitters cannot exceed existing
traditional regulation levels; it is only the 12% reduction from those levels that is subject
to trading opportunities. Therefore, it would appear that the worst that could happen is
that neighborhoods would experience different percentage decreases in VOM and HAP
emissions. The environmental equity issue would then be whether every neighborhood
enjoys about the same percentage decrease. This conclusion must be modified for several
contingencies.
ATUs are allocated to the firm not the emission units or processes at the firm’s address.
Those firms with more than one emission unit at one address may decrease one process
and increase another with no change in VOMs, or required purchase of ATUs, but with a
change in HAPs. Or a firm with a high proportion of HAPs per unit VOM emissions
could buy ATUs from a firm with a low proportion. Therefore, HAP emissions could
increase in a neighborhood. Similarly, new firms could enter the region or existing firms
could decide on a major expansion. In each such case, the firm must acquire ATUs from
the existing stockpile (no new ones are created for these firms), but neighborhoods in
which they are located may experience a net increase in emissions over historical
emissions while other neighborhoods enjoy a larger decrease.
These cases and the general issues of environmental equity will require more data for
their resolution, especially additional HAP emission reports from each participant
emitter. The manner of collecting these data by individual ERMS participant remains to
be worked out and may yet be several years away. The advantages of specifying and
6
testing the empirical base for such a model in preparation for this later study seem
compelling to us.
7
4. The Theory of Cap-and-Trade Market Incentives
4.1 Overview of the Study’s Theoretical Framework
We sketch just those theoretical aspects of cost minimizing behavior of emitter firms that
guide our empirical work.
Emitter firms with their allocated portfolio of dated ATUs are assumed to know their
marginal control costs and those of others in the market. Knowing these costs, their
endowments of ATUs, and the exogenous ATU price, the firm’s objective is to make
joint cost-minimizing decisions about the degree of reduction of emissions by control
measures and trading.
The aggregate cap is a key decision of government policy. Our discussion in this section
is based on the ERMS cap of 88%, but the theory holds for hypothetical alternate caps,
say reducing the cap to lower levels like 76%. We illustrate the consequences of these
changes in hypothetical scenarios in the results section.
We shall assume in this first case, consistent with the ERMS program, that air pollutants
are uniformly mixed over the region and ATUs trade one-for-one everywhere. We shall
simplify this study by concentrating on the currently dated credits and leave for later
work the issue of optimal intertemporal trading.
4.2 The Model Guiding Our Empirical Results
Because of the fundamental rule that an ATU must be returned to the government for
every 200 pounds of VOM emissions during the season by an emitter, the following
identity holds:
(1) hi  qi  ri  ti
i  1,
,179
emitters.
h i refers to the historical or benchmark emissions of the ith firm, q i is the allocation of
currently dated ATUs for the ith firm, ri is the reduction in emissions during the season
for the ith firm, and t i is the number of ATUs bought (if negative) or sold (if positive)
during the season for the ith firm. We shall consider ATUs that are banked for one year
as a self-sale and include them in t i . ATUs may not be bought or borrowed from the
future for current use. All variables are measured in 200-pound units of VOMs.
Under traditional regulation, t i  0 and equation (1) reduces to ri  hi  qi where all
values of the variables are determined by the government. Under emissions trading,
equation (1) holds where ri and t i are now decision variables of the firm. We show later
that the optimal value of one determines the optimal value of the other.
8
The emitter’s objective function under trading is to minimize reduction and trading costs
knowing the control cost function, cr i (ri ) , which is increasing in r and differentiable, and
the trading cost function, ct i (ti ) , or
(2) Min cr i (ri )  ct i (ti ),
(3)
Subject to ri  0.0.
Knowing that ct i (ti )  pti because p is the exogenous ATU price, and also knowing that
ti / ri  1 because of (1), we can write the equilibrium conditions as
(4) cr i (ri ) / ri  p  0,
(5) ri [cr i (ri ) / ri  p]  0,
(6) ri  0.
The solution to (4), (5), and (6) yields the firm’s optimal reduction, ri* , and therefore the
optimal trades, ti* . Note that ri* could be zero or equal to hi , and ti* could be positive or
negative or zero. Marginal costs are equated to p for every firm deciding to reduce
emissions, a requirement for minimum aggregate control costs.
The optimal values for the firm’s reductions and trades may be used to obtain a measure,
S, of the aggregate cost savings of trading compared with command-and-control (CAC).
We may estimate S as the difference in aggregate control costs between regulatory
regimes, or
m
m
m
i 1
i 1
i 1
(7) S   ci (hi  qi )   cr i (ri* )   ct i (ti* ) .
The first term is aggregate control costs under CAC, the middle term is aggregate control
costs under trading, and the last term is the sum of equilibrium purchases and sales of
ATUs. Except in the unusual case of equal marginal control costs functions and equal
historical emissions for all firms, S is expected to be positive; that is, emissions trading
leads to cost savings. We also hypothesize that the greater the variance of control cost
functions, the greater the aggregate cost savings.
Demand and supply curves for ATUs may be derived from the marginal control cost
schedules of firms. Since we know the marginal cost functions of the 179 emitter firms,
we may simulate demand and supply trading in the market under the ERMS cap by trying
out varying prices until sales equal purchases, or, equivalently, until the last term in (7) is
zero. This approach may also be used to determine equilibrium ATU prices when model
constraints, parameters, and emissions targets are changed. A geometric description of
this procedure is provided in the next section.
An implication of emissions trading theory in a competitive market is that any change in
the allocation will not affect the ATU price and cost savings (Montgomery 1975). Under
ERMS rules, the firm’s allocation, free of charge, is determined by the equation
9
qi  (1   )hi where lambda is the fraction reduction (.12) of the firm’s historical
emissions. One interesting alternative allocation could be determined by an auction of
the same number of ATUs as were allocated free. We devise a Vickery- type auction as
one way to test whether the price and aggregate savings are the same in the auction as
they are in the free allocation. We find the ATU price, quantity of trades, and cost
savings to be the same. The difference is that under the free allocation emitter firms
receive a significant transfer of wealth whereas under the auction the government
receives the wealth in the form of revenues. These results hold for the ERMS cap and
also for hypothetically tightened caps.
4.3 The Geometry of Emissions Trading and CAC Regulation with a Homogeneous Air
Pollutant
In figure 1a we illustrate our method of estimating the equilibrium price of an ATU and
calculating the cost savings from emissions trading in this case. The increasing and
linear approximation to the marginal cost schedules of two emitter firms, i and j, are
drawn under the assumption that 0 r, measured in 200 pound units, reflects the total
possible reductions of both. For ease of visualization, we assume the government
allocates r r0 ATUs to both for a 40% cap or an equivalent 60% emission reduction.
Under CAC regulation each firm would reduce by 0 r0 with total control costs measured
by the triangles  0 r0b   0r0 a .
Allowing the firms to trade opens up new possibilities. Assume an independent
auctioneer calling out trial prices and not allowing a transaction until the number desired
to be bought equals the number desired to be sold. Assume initially only two firms.
Given our schedules and cost minimizing behavior, a unique equilibrium price of 0 p1
exists. Emitter j sells r0 rj* ATUs and reduces by the amount 0 rj* . Emitter i buys an
amount r0 ri* where r0ri*  r0rj* , and reduces by 0ri* . Total control costs under trading are
measured by the triangles 0ri*d  0rj*c and net savings compared with CAC regulation
are ri* r0 b d  r0 rj*c a , clearly a positive number measured by dfb  fac . The argument
generalizes to more than two firms and to integrals under nonlinear cost functions.
A spatial inequity possibility emerges if emitter j is located in one neighborhood and
emitter i in another. Both emitters have reduced emissions from the origin, but emitter j
by more than i. To the extent that emissions have neighborhood rather than regional
effects, they become spatially heterogeneous and a flag is raised concerning an
environmental inequity.
10
p
MCCi
b
d
c MCCj
f
p1
a
e
ri*
0
r0
r
rj*
Figure 1a. Price determination and cost savings with a homogenous pollutant.
p = $ per 200 pounds of VOM. r = reduction in 200 lb VOM units.
In this figure the assumed firm cap is about 40% given by r0 r .
p
MSDi
MCCi
b
d
p1
c MCCj
f
a
MSDj
e
rj
0
ri
r0
rj ri
r
Figure 1b. Price determination and cost savings with heterogeneous pollutants.
p = $ per 200 pounds of VOM. r = reduction in 200 lb VOM units.
In this figure the assumed firm cap is about 40% given by r0 r .
5. Modeling Spatially Heterogeneous Pollutants: Issues and Choices
5.1 The Heterogeneity Issue
Any attempt to track the contribution that one unit of emission from firm i at one location
makes to pollutant concentrations at another location j, poses difficult problems for
analysis (Tietenberg 1995). An estimate of the associated health impacts by location are
even more difficult to make. Yet knowing that some VOMs are HAPs, and that speciated
HAPs differ in toxicity, and that HAPs detoxify differently, motivates us to devise
provisional yet tractable concepts of heterogeneity of pollutants. We have already
indicated the simplification that the regulating community has made by treating pollutant
emissions as homogeneous throughout the region when establishing a reduction target
and defining ATUs as undifferentiated by location.
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If the spatial distribution of all types of emissions changes little under trading and
therefore all neighborhoods enjoy about the same emissions reduction, then the concern
about environmental equity of trading may be eased. If, on the other hand,
neighborhoods vary in the extent of particular reductions, this result raises a flag for
further study of environmental inequity although no conclusive proof is obtained. We
may look for these flags by tracking the local emissions, and changed emission spatial
patterns after trading of aggregate VOMs and HAPs, and of speciated selected HAPs. A
geometric description of some of the problems raised by heterogeneity of pollutants is
provided in figure 1b, which may be usefully compared with figure 1a.
5.2 The Geometry of Emissions Trading Under Heterogeneous Pollutants
In figure 1b we reproduce the schedules, price, and trading volume of figure 1a but we
now assume that firm i emits hazardous VOMs that are HAPs and firm j emits nonhazardous VOMs. We illustrate that fact by assuming initially that we know the marginal
social damage function for both types of emissions, and draw the function for firm i
higher than for firm j. To maximize welfare we should require firm i to reduce by 0ri and
firm j by 0ri thus equating benefits and costs rather than setting a common target level.
Note that cost-minimizing behavior is assumed in this situation as in Figure 1a.
If we incorrectly assume spatial homogeneity of pollutants, thinking that Figure 1a
applies, we will reduce emissions from emitter i insufficiently, by ri ri , and emissions
from firm j too much, by rj rj . If we knew the entire damage functions, the welfare loss
could be calculated as the net areas under the damage curves. Even a glance indicates
that these welfare losses could be important.
Figure 1b highlights several problems. We do not have even a reasonable grasp of the
spatial damage functions for HAPs, or for non-hazardous VOMs, singly or aggregated.
In order to make progress in this area, it seems reasonable to both aggregate and
distinguish speciated HAPs from other hydrocarbon VOMs because of their different
capacities to harm. It also seems reasonable to test a hypothesis of a spatial emissions
surrogate for the damage function; that is, changes in local or neighborhood emissions
could have a bearing on the associated exposures and risks of the local or neighborhood
population. This spatial dimension to heterogeneity could be changed by later research.
We propose for later work a provisional definition of heterogeneous emissions that is
relevant to the analysis of the ERMS program impacts on local areas. The first aspect of
the definition treats aggregate and speciated HAP emissions differently from aggregate
non-hazardous VOM emissions. The second aspect treats HAPs and non-HAP VOMs by
location of emissions. A decline in aggregate or speciated HAPs observed in the region
as a whole may occur at the same time that these pollutants increase in one or more
neighborhoods. Hence, changes in emissions of varied types among neighborhoods after
trading require separate analysis and a detailed database not yet available.
With these distinctions in mind we could raise, or lower, flags of concern about
environmental equity impacts of emissions trading. If all neighborhoods or zip codes
enjoy the same reduction in VOM and HAP emissions because of trading, then no flags
of concern appear to be flying. However, if one or more neighborhoods experience
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different changes in aggregate VOM or HAP emissions, or a speciated HAP emission
because of trading, then flags are set flying for a more detailed investigation.
Figure 1b offers a way of illuminating this line of attack. Suppose firm i emits a greater
proportion of HAPs per unit VOM than firm j. Suppose firm i is located in one
neighborhood, firm j in another. Suppose that firm i, after trading (as in the figure),
reduces emissions by less than firm j. We may conclude after this long list of
suppositions that the flag of a possible environmental inequity in HAP reductions has
been raised in firm i’s neighborhood. Whether these spatial patterns of HAP and other
VOM emissions change after trading, raising or lowering possible flags of environmental
equity in each case, are now empirical questions demanding data for empirical answers.
We raise these environmental justice issues at this stage to indicate the kinds of data that
will be needed to facilitate later research.
6. The Required Databases
To measure the variables we have described requires detailed information on individual
emitter locations, data on their marginal control costs, their ATU allocations and trades,
and their VOM and HAP emissions before and after trading. Some of th4ese data are
available for this study. We shall assume perfect and symmetric information in the
regulated and regulating communities in order to focus on the issues of this study.
Imperfect and asymmetric information are important topics for further research.
6.1 Location
Street addresses of individual emitters are publicly available. If their emission or process
units are at separate addresses, each address receives an allotment of ATUs. Zip codes
offer an attractive local area designation because codes can be made more visible by
different markings than the smaller census tract. Zip codes can be aggregated into larger
neighborhoods, if desired.
6.2 Marginal Control Cost Schedules
For this critical information we rely on a large study carried out by the IEPA that
surveyed the numerous control measures for emission reduction available to participants
in the market (IEPA, Technical Support Document, 1996). The survey estimated the
costs at about the 12% emission reduction level for a number of emitters making use of
engineering data and U.S. EPA estimates of the costs of Reasonably Available Control
Technologies (RACT). These estimates were then extended to other emitters in the same
SIC classification. Capital and operating costs were estimated in the study in present
value terms.
We are aware that questions of imperfect and asymmetric information may be most
significant in this area. We temporarily set them aside for later work noting that a small
survey of experts in this area does not reveal major problems in our cost estimates.
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6.3 ATU Allocations and Trades
Information on actual ATU allocations is available before the start of each season, but
information on actual aggregate and individual trades and average ATU prices will
become available only after the December 31 reconciliation periods when the IEPA will
report on these variables. The model of this study makes use of actual ATU allocations
but makes predictions before the end of the reconciliation date of the first year of trades
and average ATU prices. The appropriate test of the model will be a comparison of the
actual to the predicted trades and prices. However, several cautionary notes are in order.
The model predicts the potential performance of the ERMS program to realize control
cost savings. The predicted ATU trades and prices are for a fully functioning market.
Because firms may exhibit learning behavior that restricts trades, or limit trading until
they can gauge public acceptance of the program, the market may not be fully
functioning in the first few years. Another feature of the market is the wide variation in
size and industry of participants. It may take some time for all participants to learn about
and take full advantage of the market’s opportunities. The sulfur dioxide program
experienced such a lack of expected trading in its first few years.
Therefore, the results of the model may be of value in providing a yardstick against
which the actual performance of the market may be measured over time. And, of course,
the model is used in this inquiry to simulate hypothetical scenarios including policy
changes that cannot be tested by actual data from the current program, but do reveal
properties of the cap-and-trade market.
6.4 VOM and HAP Emissions
VOM emissions data available at the time of this study include the firm’s historical
emissions and annual emissions since the 1994-1996 period. HAP emissions reported
under Most Achievable Control Technology (MACT) and under Toxic Release Inventory
(TRI) rules are accessible for prior years but these reports do not cover all HAPs, some of
which are in the process of regulatory development.
After the 2000 ozone season, participant firms will report their aggregate VOM emissions
for the season and year, and the proposal is to participant firms report their aggregate and
speciated HAP emissions after the year 2001 season. These reported emissions will take
on more significance as the program evolves beyond the learning period. They will
become essential information for later testing of the model’s predictions.
7. Empirical Implementation of the Model
The underlying structural relationships of the model are the marginal control cost curves
that were fitted for each firm by passing the curve through the origin and the 12%
emission reduction cost value. These costs may be viewed as incremental to the control
costs necessitated by prior traditional regulations that remain in effect. They are
understood to be linear approximations to marginal costs over the relevant range.
14
Based on these structural relationships, the estimates of ATU equilibrium prices and of
control costs under trading and under CAC regulation at equilibrium output levels were
obtained by use of both a specially written optimization program that was built using the
B34S® matrix programming language and an Excel® spread sheet program. Different
approaches give us independent checks on the results.
Basic to both approaches was the specification of the excess demand functions. These
depend upon the desired targeted level of reduction, which was 12% in the case of
ERMS. Summing the excess demand functions for all the firms and selecting the price
that made this sum equal to zero determined the equilibrium price. In other words, at
equilibrium the number of ATUs sold must equal the number of ATUs bought as
demonstrated in figure 1a. Using Excel®, the price was manually moved until this sum
was as close to zero as possible. Using the B34S® matrix command, the price was
restricted to be greater than or equal to zero in the model specification and the
optimization routine determined the solution of equilibrium price where the sum of
excess demands were zero.
An advantage of the optimization approach is that it allows the user to easily change
constraints, parameters, and emissions targets or caps in the model and observe the
results. Most important for our purposes is the inclusion of spatial constraints in the
optimization model. For example, it is possible to restrict purchases of ATUs within a
certain zip code, or group of them. The model enables us to gauge the effects of such
proposed changes on both prices and the distribution of pollution. Mapping of these
emission patterns provides a means of evaluating these changes in distribution and can be
implemented by use of an advanced software routine. The optimization approach also
enables us to highlight the flexibility of the model by changing the emissions reduction
targets and reporting the consequences. A more explicit account of these implementation
methodologies is given in Appendix A.
8
The Performance of the Cap-and-Trade Market With and Without Equity
Constraints
To recapitulate, the cap-and trade variant of emissions trading is often said to be costeffective, flexible, and non-confrontational. We are able to report detailed results on the
first and second mentioned performance features. We consider first the situation where
pollutants diffuse uniformly over the region independent of the location of emissions, the
homogeneous case, and then we consider the situation where spatial constraints are
placed on trading.
8.1 Emission Trading Results when Pollutants are Uniformly Mixed Over Space
Establishing the cap or emissions reduction target may be viewed as the government
acting as the citizen’s purchasing agent for air quality. The cap or target may change
from time to time as new information comes to light or new citizen pressure comes to
bear on air quality. Similarly the choice of a regulatory instrument may be viewed as the
purchasing agent’s efforts to obtain the desired air quality in the most cost-effective way.
Our model presents a methodology to evaluate the agent’s policy options and their
consequences.
15
In table 1 we present the equilibrium ATU price, volume of ATU trades, the control costs
under emissions trading compared with CAC regulation, and the cost savings to be
realized by using market incentives for the present ERMS program reduction rate of 12%
from the historical benchmark. We present additional results for hypothetically increased
reduction rates on up to 36%, both as a test of the model and as a relevant exercise in
view of the current policy debate on reducing acceptable urban ozone levels.
The results are as expected from emissions trading theory. ATU prices increase as the
cap tightens. Decentralizing control decisions in the cap-and trade market at the 12%
ERMS reduction rate can bring about a million dollars in saving per year compared with
CAC regulation. These savings increase to 9 million dollars as the emissions target rate
of reduction increases to 36% implying that, as the number of ATUs allocated decrease
and prices increase, the incentives to trade strengthen with the consequence of a more
than proportionate increase in savings.
Our approach enables us to report the number of ATUs traded at each reduction rate, as
in the last column of Table 1. Recall that the reductions in emissions are obtained by
issuing tradable credits to pollute in amounts below the benchmark or historical emission
level. The benchmark emissions utilized in the ERMS program were equivalent to
109,211 ATUs; thus, to achieve the 12% reduction required that 96,106 ATUs be
allocated for the year 2000 season.2 The amounts allocated decrease as the desired
reduction rate increases so that 69,895 ATUs would have to be allocated to achieve a
36% decrease in emissions.
The number of ATUs traded in the 12% scenario is 3,743, about 4% of those allocated in
that case. The number of ATUs to be traded if the reduction rate were set to 36%
increases to 11,229, a little over 16% of the total allocated in that scenario. These results
confirm our expectations, based on rising marginal control cost schedules, that as
reduction rates increase and ATUs allocations decrease, cost-saving trading opportunities
increase even more rapidly. Figure 2a depicts the relationships between reduction rates
and cost savings and ATUs traded.
2
In order to create a backstop to the market, the IEPA set aside 1% of these ATUs in an Alternative
Compliance Market Account. As these credits are available at a price in the market, we believe that
ignoring this set-aside will have negligible effects on our results.
16
Table 1
Estimates of ATU Equilibrium Price, Number of ATUs Traded, and Emissions Trading
Cost Savings under ERMS for different VOM Emission Reduction Rates
(year 2000 trading season)
[1]
[2]
[3]
[4]
[5]
[6]
VOM Reduction ATU Equilibrium Control Cost Control Cost Control Cost Number of
Rate
Price
Under CAC Under ERMS Savings (3-4) ATUs Traded
($)
(x $1000)
(x $1000)
(x $1000)
0.12
258
2,749
1,687
1,061
3,743
0.14
300
3,741
2,297
1,444
4,367
0.16
343
4,886
3,000
1,887
4,991
0.18
386
6,184
3,797
2,388
5,615
0.20
429
7,635
4,687
2,948
6,238
0.22
472
9,238
5,671
3,567
6,862
0.24
515
10,994
6,749
4,245
7,486
0.26
558
12,903
7,921
4,982
8,110
0.28
601
14,964
9,187
5,778
8,734
0.30
644
17,179
10,546
6,633
9,358
0.32
687
19,545
11,999
7,546
9,981
0.34
730
22,065
13,546
8,519
10,605
0.36
773
24,737
15,186
9,551
11,229
Note: There are 179 emitters included in the ERMS – UIC model. The number of
ATUs allocated depends upon the VOM reduction policy goals. For the current
12% reduction, 96,106 ATUs were issued to these emitters for the ozone-trading
season May through September 2000. Prices and cost estimates are in current
(2000) dollars.
Source of estimates: Simulations with the ERMS – UIC model.
17
Guided by another implication of emissions trading theory, we expect that the greater the
spread in marginal control cost slopes among emitters, the greater the opportunities for
savings and the higher the ATU price. To check these beliefs, we have changed the
absolute spread among emitter slopes by varying percentages up and down with a
consequent change in the variance among these slope coefficients. The confirming
results are presented in Table 2 for the ERMS reduction rate of 12%. The equilibrium
price increases as the absolute spread increases as do cost savings indicative of the
increase in savings opportunities from trading. Figure 2b depicts the relationships
between the variance and cost savings and ATU prices.
Note as we increase or narrow the spread of all slopes by the same percentage, while
holding the reduction rate constant, the number of ATUs that emitters find it
advantageous to trade does not change even though the gains from each trade increase as
the variance increases.
Introducing transactions costs into the emissions trading section of the model is expected
to decrease cost savings, increase ATU prices, and decrease the number of trades. In
essence, they drive a wedge between sale and purchase price compared with the price in a
frictionless or transaction cost-free market. These costs were introduced into the model
in the case of the ERMS cap with both seller and buyer paying the same amount indicated
in table 3. The results are as expected. Savings from trading and the number of trades
decline appreciably in these extreme cases.
The IEPA has attempted to reduce transactions costs by maintaining a free electronic
bulletin board of offers and bids. These transactions costs to the emitter typically include
search and negotiation expenditures, but they may also include anticipated emitter
expenditures for legal and public relations assistance in the case of regulator challenges
to trades, or public disapproval of trades.
18
N T RA D ED
11000
Cost savings (x $1000) and num ber of A T Us traded
10000
COST SA VE
9000
8000
7000
6000
5000
4000
3000
2000
.12
.14
.16
.18
.20
.22
.24
.26
.28
Rate of reduction of VOM em issions
.30
.32
.34
.36
Figure 2a. The relationships between the rate of reduction of emissions and cost savings
and number of ATUs traded. Note that the ERMS reduction rate of 12% results in cost
savings of about $1,000,000.
COST SA VE
A T U Price and Cost Savings (x $1000)
1400
1200
1000
800
600
400
A T UPRI CE
200
40
60
80
100
120
140
160
Variance of m arginal cost curv e slopes (000)
180
200
Figure 2b. The relationships between the variance of emitter marginal cost slopes and
cost savings and ATU prices when the aggregate target rate of reduction is 12%.
19
Table 2
Effects of Changes in Control Costs on ATU Prices, Number of ATUs Traded, and
Emission Trading Cost Savings
(12% Reduction: Year 2000 trading season)
[1]
[2]
Percent of Original
ATU Equilibrium
Slopes of Marginal
Price in $
Control Cost Curves
Variance ( ) (x $1000)
50 (23)
55 (28)
60 (34)
65 (39)
70 (46)
75 (52)
80 (60)
85 (67)
90 (76)
95 (84)
100 (93)
105 (103)
110 (113)
115 (123)
120 (134)
125 (146)
130 (158)
135 (170)
140 (183)
145 (196)
150 (210)
129
142
155
167
180
193
206
219
232
245
258
270
283
296
309
322
335
348
361
373
386
[3]
Control Costs
Under CAC
[4]
Control Costs
Under ERMS
[6]
Number of ATUs
Traded
(x $1000)
[5]
Control Costs
Savings
(3-4)
(x $1000)
(x $1000)
1,374
1,512
1,649
1,787
1,924
2,061
2,199
2,336
2,474
2,611
2,749
2,886
3,023
3,161
3,298
3,436
3,573
3,711
3,848
3,985
4,123
844
928
1,012
1,097
1,181
1,266
1,350
1,434
1,519
1,603
1,687
1,772
1,856
1,940
2,025
2,109
2,194
2,278
2,362
2,447
2,531
531
584
637
690
743
796
849
902
955
1,008
1,061
1,114
1,167
1,220
1,273
1,327
1,380
1,433
1,486
1,539
1,592
3,743
3,743
3,743
3,743
3,743
3,743
3,743
3,743
3,743
3,743
3,743
3,743
3,743
3,743
3,743
3,743
3,743
3,743
3,743
3,743
3,743
Notes: The downward and upward shifts in the marginal control cost slopes maintain
relative differences across emitters but do not change the advantages of trading,
which is why the numbers of ATUs remains constant. Column 1 contains the
percent by which original marginal cost curve slopes were shifted with the
variance of all slopes in parentheses times $1,000. Note a 50% change means a
decrease of 50% for each slope. The shifts change the gains from trading which is
why the ATU price and control cost columns change.
Source of Estimates: Simulations with the ERMS – UIC model.
20
Table 3
Effects of Transactions Cost Changes on ATU Equilibrium Price, Number of ATUs
Traded, and Emissions Trading Cost Savings
(12% Reduction: Year 2000 Trading Season)
[1]
Transaction Costs
[2]
Equilibrium Price
[3]
Control Costs
Under CAC
[4]
Control Costs
Under ERMS
[6]
Number of ATUs
Traded
(x $1000)
[5]
Control Cost
Savings
(3-4)
(x $1000)
($)
($)
(x $1000)
No transaction costs
258
2,749
1,687
1,061
3,743
10
264
2,749
1,728
1,020
2,588
20
270
2,749
1,769
979
2,422
30
276
2,749
1,810
938
3,278
40
283
2,749
1,851
897
3,123
50
289
2,749
1,892
856
2,968
60
295
2,749
1,933
815
2,813
70
301
2,749
1,974
774
2,658
100
320
2,749
2,097
651
2,194
200
375
2,749
2,627
126
765
250
419
2,749
2,747
2
594
Notes: Transaction costs are considered to include a component for search, negotiation
and bargaining expenditures required for trades. Broker fees may approximate
part of these expenditures. Any extra expenditures by emitters for special
reporting and management required by the ERMS program could also be included
as well as anticipated expenditures for public relations or legal services.
Source of Estimates:
Simulations with the ERMS – UIC model.
21
A powerful implication of emissions trading theory is that changes in the allocation of
ATUs among emitters ought not to affect prices or quantities, and hence savings,
presuming that the market remains competitive and free of uncertainties and transactions
costs. As discussed in the theory section, we simulate a Vickery-type auction in which
the final equilibrium price balances the given supply with the demand schedules
derivable from the marginal cost schedules. To dramatize this result, we show the
auction results should the cap or reduction rate be changed. The results in Table 4
confirm the implications: the equilibrium ATU prices and cost savings are the same
under both a government auction and a free allocation as a comparison of tables 1 and 4
discloses.
What is different in these two markets is the transfer of wealth. Under the free allocation,
the value of the ATU is transferred to the emitter; under the auction the revenues go to
the government. We may estimate these transfers by multiplying the number of ATUs
auctioned by the price. The wealth transfers amount to about 25 million dollars per year
in the 12% scenario increasing to 54 million dollars in the 36% case.
What also is different in these two markets is the individual firm purchases and sales of
ATUs. We have arrayed emitter firms from low to high marginal costs in figure 3a and
plotted their purchases and sales in the free-allocation and 12% reduction scenario. In
figure 3b we array emitter firms in the same way but plot their purchases in the auction
market again in the 12% scenario. In both markets, it will be recalled, emitters are
equating their marginal costs to the ATU price. Total purchases for each emitter in the
auction market are the algebraic sum of what they would have gotten under free
allocations plus their purchases or minus their sales. Emitter control costs are the same in
both markets but not their balance sheets.
22
Table 4
Estimates of ATU Equilibrium Price, Number of ATUs Traded, and Emissions Trading
Cost Savings Under ERMS as an Auction Market.
[1]
VOM Reduction
Rates
[2]
ATU Cap: Number
of ATUs Auctioned
[3]
[4]
[5]
ATU Equilibrium Control Cost Under Control Cost for
Price
CAC
VOM Reductions
Under ERMS
$
(x $1000)
(x $1000)
[6]
Control Cost
Savings
(4-5)
(x $1000)
.12
.14
96,106
93,922
258
300
2,749
3,741
1,687
2,297
1,061
1,444
.16
.18
91,738
89,553
343
386
4,886
6,184
3,000
3,797
1,887
2,388
.20
.22
87,369
85,185
429
472
7,635
9,238
4,687
5,671
2,948
3,567
.24
.26
83,001
80,816
515
558
10,994
12,903
6,749
7,921
4,245
4,982
.28
.30
.32
.34
.36
78,632
76,448
74,264
72,080
69,895
601
644
687
730
773
14,964
17,179
19,545
22,065
24,737
9,187
10,546
11,999
13,546
15,186
5,778
6,633
7,546
8,519
9,551
Notes: The ATU cap for the auction is determined by multiplying the historical
emissions of all emitters by 1 minus the desired rate of reduction of VOM
emissions (or .88 in the case of the first row). Source of Estimates: Simulation
with the ERMS-UIC model.
23
1000
Purchases (-) and sales (+) of A T U contracts
800
600
400
200
0
-200
-400
20
40
60
80
100
120
140
I ndi vidual em itter f irm s array ed f rom low to high M C curv e slopes
160
Figure 3a. Individual emitter purchases and sales of ATUs at a VOM reduction rate of
.12, an ATU equilibrium price of $258, and a free allocation of ATUs. The ordinate
values are ATU sales if positive and purchases if negative. The abscissa values are 179
individual emitters arrayed from lowest marginal control cost slope value on the left to
the highest on the right.
Purchases (-) and sales (+) of A T U contracts
-1000
-2000
-3000
-4000
-5000
-6000
-7000
-8000
-9000
20
40
60
80
100
120
140
I ndi vidual em itter f irm s array ed f rom low to high M C curv e slopes
160
Figure 3b. Individual emitter purchases of ATUs at a reduction rate of .12 and ATU
equilibrium price of $258 assuming the government auctions the ATUs.
24
8.2 Emission Trading Results When Pollutants are Not Uniformly Mixed Over Space
Changes in VOM emissions in particular zip codes, and clusters of them due to trading,
can be among our indicators of spatial equity concerns, as we have mentioned3. We
launch our investigation into environmental equity concerns by first experimenting with
constraints on trading in certain zip codes that are selected at random and not for their
welfare significance. We begin in this way to bring out two important consequences of
spatial restrictions. First, restricting the emitters from buying ATUs in certain
neighborhoods, frequently mentioned as the way to reduce importing emissions into these
areas, has the immediate effect of reducing the demand for ATUs. This translates into
lower equilibrium prices, fewer trades, and decreased cost savings. These effects must be
balanced against the welfare gains of these spatial restrictions.
There is a second, more subtle, consequence of spatial constraints. Restrictions in one
neighborhood mean increased emissions in others. Total emissions remain capped, of
course, but the decline in ATU price caused by spatial constraints leads other emitters to
reduce emissions less by control measures and buy more ATUs, hence emit more. Only a
careful spatial analysis can reveal the changing emission patterns that result.
The first consequence can be explored in the abstract by starting with the 98 zip codes in
which emitters are located and randomly eliminating first about 10% of the codes, then
20% on up to 40%. The results in table 5 reveal that ATU prices, trades, and cost savings
decrease as expected. Spatial restrictions on the market’s workings can have significant
effects that must be kept in mind when evaluating the environmental equity benefits of
such restrictions. The results of Table 5 are based on one random pattern of zip code
elimination.
3
Several simple spatial restrictions have characterized existing trading programs to date in an effort to
allay equity concerns. The Los Angeles Regional Clean Air Incentive Market (RECLAIM) program
prohibits sales of SOx and NOx credits from the inland area to the coastal area because of the prevailing
winds (Lents 2000). In the national SO2 control program, the state of New York has recently prohibited
electric utilities from selling credits to the west of the state due to concern about prevailing winds and acid
rain deposition (Ellerman et al. 2000).
25
Table 5
Effects of ERMS Sub-area Restrictions on ATU Equilibrium Prices, Number of ATUs
Traded, and Emission Trading Cost Savings
(12% Reduction: Year 2000 trading season)
[1]
[2]
Restrictions on ATU ATU Equilibrium
Purchases in Selected
Price
ZIP Codes
[3]
Control Costs
Under CAC
[4]
Control Costs
Under ERMS
[6]
Number of ATUs
Traded
(x $1000)
[5]
Control Cost
Savings
(3-4)
(x $1000)
(x $1000)
No special restrictions
(12 % reduction)
258
2,749
1,687
1,061
3,743
Restrictions on
purchases in 10 zip
Codes
238
2,749
1,964
784
2,942
Restrictions on
Purchases in 20 zip
Codes
(including first 10)
230
2,749
2,047
702
2,597
Restrictions on
Purchases in 30 zip
Codes
(including above 20)
213
2,749
2,242
507
1,917
Restrictions on
Purchases in 40 zip
codes
(including above 30)
208
2,749
2,289
460
1,709
Notes: There are 98 zip codes in the non-attainment area in which emitters are located.
Codes were chosen for restrictions on buying ATUs in a random manner.
Emitters not allowed to buy ATUs must meet the requirement of covering their
seasonal emissions with ATUs allocated but not sold. All dollar values are in
current (2000) prices.
Sources of Estimates: Simulations with the ERMS – UIC model.
26
9
Conclusions and Research Directions
Emissions trading compared with traditional control compels us to take a fresh look at
and ask different questions about the workings and impacts of environmental regulation.
The government makes new key policy decisions about the cap and devises general
market rules and appraisal procedures subject to the scrutiny and comment of the
regulated community and public interest groups. The regulated community in turn makes
new decisions about the choice of control options, the search for new options, and the
management of the ATU portfolio.
Our model provides one means for taking this fresh look. It can help reveal the potential
of emissions trading under a variety of assumptions about the parameters of relationships
and changes in emission targets or goals. The model can become a guide to the workings
of the ERMS program before the learning and break-in period is complete. As recorded
data become available, the model can be tested and adjusted for future research.
Our first results indicate that the present ERMS program can bring about significant cost
savings, up to one million dollars per period, compared with CAC regulation. This result
can be achieved with trading of about 4% of all ATUs allocated. An equilibrium price of
$258 is generated by the model’s trading simulation. The actual observed price may be
lower due to the fact that marginal cost functions were estimated on the basis of a 1996
study and participants may have introduced new cheaper control actions since then—just
what market incentives are suppose to encourage them to do. Actual observed prices and
trades also may be lower than the model predictions due to learning behavior or concern
about public acceptance of emissions trading. Careful further research is required here.
The model enables us to simulate emitter decisions when changes in marginal control
cost (slopes) are introduced. Decreasing the spread of these slopes decreases ATU
prices, trades, and savings, as trades become financially less attractive. Increasing them
does the opposite. If emitters confront transactions costs in the market, the model enables
us to demonstrate that the higher these costs the lower the ATU price, the fewer the
trades, and the lower the cost savings. Study of participant perceived transactions costs is
also a serious research priority.
The model enables us to simulate government changes in policy objectives such as
tightening the cap. Allocating fewer aggregate ATUs in this case causes higher prices,
more trades, and greater cost savings compared with traditional regulation. If the
government chose to change the free allocation of ATUs, the model enables us to show
that, in a competitive market, there would be no change in ATU equilibrium price or cost
savings, but there would be a change in the transfer of wealth. We prove this by having
the government auction ATUs and solving for ATU price and quantity traded.
The model can show its versatility by providing the input data for software mapping of
emissions patterns that can help evaluate issues of environmental equity. In anticipation
of future research based on detailed emitter data, we illustrate the reduction of market
performance when arbitrary spatial restrictions are implemented.
27
Appendix A: Implementation Methodology
Specification of the Excess Demand Function in the Case of an ERMS 12% Emission
Reduction Goal.
The key variables in our dataset of 179 firms are:
cri (ri ) = the marginal cost of reduction of emission reduction for firm i.
0
= the reduction goal of 12%. The cap then becomes 88% of historic
emissions.
hi and qi as given by prior recorded emissions and government policy where
qi  (1   0 )hi .
In words, if the firm reported historic emissions of 100 units of VOM emissions as an
average during 1994-1996, the firm was then allocated 88 ATUs for the ozone season.
The next task is to estimate the marginal control cost based upon reported values (IEPA
Technical Support Document 1996) at a 12% reduction. One assumption would have
been to assume constant marginal costs. We rejected this approach as not realistic in
favor of the increasing marginal cost case. The question then becomes, are the costs
increasing at an increasing rate, at a constant rate or a decreasing rate? In our preliminary
model we assumed the constant increase rate case where the cost curve was fitted to the
12% reduction value and the origin. As more detailed data on costs becomes available,
other cost functions can be employed in the model.
These estimated marginal cost curves underlie our excess demand and enable us to
generate equilibrium prices, quantities of ATUs traded, and control costs under both CAC
and ERMS regulation. We show how we derive these values in the next section where we
illustrate the flexibility of the model by explaining the implications of varying emission
caps or emission reductions.
Specification of the Excess Demand Functions in the Case of Varying Reduction Goals.
Assume 0  base reduction rate (.12 ) and  j  the reduction rate mandated in period j
then
(A1) cr i (ri ,  j )  cr i (ri ,  0 )[ j /  0].
where we introduce  j to indicate that we are comparing the cost value of a different cap
point along the curve, although the slope remains the same. In words, if the marginal
costs of reducing emissions was $200 assuming the base reduction was 12%
( cr i (ri ,.12)  $200 ) and the reduction rate was mandated to increase to 16%, then
marginal costs will rise to $266.67 [cr i (ri ,.16)  $200*(.16 / .12)  $266.67] .
The decision for a firm to sell or buy is limited by various constraints. Clearly the firm
cannot sell more than it has been allocated. Nor will it buy more than it needs to reduce.
Define ri ( ) as the amount of emissions that firm i needs to reduce given any  . As
28
explained in section 5, the relation ri  hi  qi holds if there is no trading under traditional
regulation. When trading is permitted ri  hi  qi  ti . Define ti ( , p) the amount firm i
sells (if positive) or buys (if negative) given the required reduction  and the market
price of an ATU p . We will show later that the price of an ATU, p , is an increasing
function of  , or the required reduction percentage. Equations (A2) and (A3) explain
how we calculated the optimal trading for the firm; that is, how we determined ti ( , P)
given the allocation of ATUs and the marginal control cost.
(A2) For p  cr i (ri ,  ) ti ( , p)  min(( p  cr i (ri ,  )(ri ( ) / cri (ri ,  )), qi ( )).
(A3) For p  cr i (ri ,  ) ti ( , p)  max(( p  cr i (ri ,  )(ri ( ) / cri (ri ,  )), hi  qi ( )).
Note that (A2) limits the maximum sales to the amount the firm has been allocated qi ( )
while (A3) limits the amount bought to what they need or their historic emissions minus
the ATUs they have been given. The optimization problem is to find p such that
179
 t ( , p)  0 for a 
i 1
i
j
j
value. Given p1 is the equilibrium price, our empirical work
shows that, everything else equal, p1 /   0 or the greater the required rate of
reduction, the higher the price of the ATU. The higher price results in more ATUs traded
due to the increased incentive to acquire ATUs as marginal control costs mount. It also
revealed that cost savings of trading increase compared to CAC regulation.
More specialized cases can easily be solved if for an individual firm i we place a cap 
on the amount it can buy (ti ( , p)   ) or in fact restrict the firm to only selling ATUs
(ti ( , p)  0.0 .4 In summary, our model allows much more specialized excess demand
functions whose implications are a task for future research.
Solving for a Government Auction of ATUs
The above analysis assumes that each firm was given an allocation of ATUs, qi ( ) and
that some firms would buy ATUs and some firms would sell ATUs depending on their
individual cost functions. In the assumed auction case, we do not allocate any ATUs to
firms. Instead each firm must either reduce all emissions or buy ATUs from the
government to cover emissions at a Vickery-type auction where the single price clears the
market. As in the free allocation case, the market clears when all ATUs offered by the
government are sold and excess demands equal zero. Our approach to estimating prices,
quantities traded and costs are the same in both auction and free allocation scenarios. It
will be noted that both scenarios yield the same prices, same number of ATUs traded, and
same cost savings, although the transfer of wealth is different. This turns out to be an
application of the Coase theorem (Coase 1960).
4
Note that the cap is inserted as a negative number.
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In all cases command and control costs have been calculated as ri ( ) cr i (ri ,  ) / 2 and
trading costs as (ri* ( )  ti ( , p)) 2 (cr i (ri ,  ) / 2ri* ( )) in keeping with figure 1a and 1b in
section 5. The gain from trading for firm i becomes
(A4)
(cr i (ri ,  )ri ( )) / 2  (( ri* ( )  ti ( , p)) 2 (cr i ( ri ,  ) / 2 ri* ( ))).
The percent reduction of the firm becomes (ri* ( )  ti (, p)) / hi which suggests that the
more a firm sells (buys) ATUs the more (less) it reduces its emissions.
Concluding Comments on the Model
Because we have been using a general nonlinear optimizer to solve our model, it is
possible to add other parameters to the model and place complex nonlinear constraints on
the solution.5 What would be the nature of these constraints is left to further research. Our
model has been designed to highlight both the price and spatial effects of such changes.
5
The B34S (Stokes 1997) contains a nonlinear programming with nonlinear constraints function. This was
not needed in this preliminary analysis since the only constrained placed on the solution that p must be
greater than or equal to zero.
30
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