Emission Permits Allocation, Market Power and
Cost-effectiveness of ETS— A Theoretical Analysis
Mei Wang, PhD Student,
College of Economics and Management, Nanjing University of Aeronautics and Astronautics,
29 Jiangjun Avenue, Nanjing 211106, China,
Phone +86 15195840282, Fax: +86 25 84892751, E-mail: [email protected]
Peng Zhou, Professor,
College of Economics and Management, Nanjing University of Aeronautics and Astronautics,
29 Jiangjun Avenue, Nanjing 211106, China,
Phone +86 25 84893751, Fax: +86 25 84892751, E-mail: [email protected]
Abstract
Emission trading system (ETS) plays an important role in achieving the emission reduction
targets cost-efficiently. The presence of market power in the carbon market can affect the
cost-effectiveness of ETS. Since the market power depends critically on the initial allocation, this
paper theoretically explores the impact of CO2 emission permits allocation methods on the
cost-effectiveness of ETS from the perspective of market power. By using Stackelberg model in ETS,
we find CO2 emission permits allocation method affects the cost-effectiveness of ETS if market power
exists. When the emission permits are allocated by grandfathering, the more the initial allocation of
dominant firm deviates from its emissions, the more the efficiency loss occurs in the carbon market. If
benchmarking is adopted, the carbon price is even more than that by grandfathering. Given proper
carbon price, the auctioning is the most efficient allocation method.
Keywords: Market Power, Emission permit allocation, Stackelberg model
1. Introduction
Emissions trading system (ETS) has become an important policy instrument in the
post-Kyoto period of climate change (González-Eguino, 2011). Many countries/regions have
gradually launched their ETS since 2005, such as the European Union (EU) (comprising 31
countries), New Zealand, Australia, Korea and China (seven provinces and cities). In addition,
countries such as Canada, Ukraine, Brazil and Russia are developing or to be developing their
ETS. China's National Development and Reform Commission has explicitly stated national
carbon market is to be established in 2017.
Most of the current carbon markets proved to be successful in helping the
corresponding countries and regions reduce CO2 in a cost-efficient way (Hahn and Stavins,
2011), while problems were also observed in the existing carbon markets. For example, the
carbon price in the first period of EU ETS experienced high fluctuation, consequently the
carbon price fell to zero in 2007. And the pilot carbon markets in China emerged market
downturn to certain degree with big variation of carbon price (4.2-123 Yuan/ton) and low
liquidity in trading market (Only about 2% of the allowances were traded).
Many studies have been devoted to study the possible reasons for high fluctuation and
variation of carbon price in carbon markets. The main reasons include over-allocation and
market power in carbon market (Ellerman and Buchner, 2008). The over-allocation helps
explain why the carbon price fell to zero in the end of the first period of EU ETS. The market
power could be the reason why the carbon price was not zero at the beginning of the EU ETS
(Hintermann, 2011).
The presence of market power in the carbon market can deviate the carbon price from the
cost efficient equilibrium price (Hahn, 1984; Westskog, 1996). If a firm with market power is
a likely allowance seller, it has an incentive to act as a monopolist and hold back allowances
from the market to drive up allowances prices (Malik, 2002), and if it is a likely allowance
buyer, it has an incentive to act as a monopsonist and buy fewer allowances to keep the price
lower (Hahn 1984).
Hahn (1984) firstly proposes the idea that market power in permit market can lead to
efficiency loss which is dependent on initial allocation of permits. In this paper, Hahn (1984)
only considers market power in permit market, which is suitable in many cases. Maeda (2003)
derives formulae that estimate the degree of market distortion and shows the existence of a
threshold for effective market power. Again, market power is set to be present only in the
permit market. Assuming market power exists both in the carbon market and production
market, Eshel (2005) analyzes the effect of the initial distribution of tradable rights on the
firms’ abatement and production and proposes an efficient criterion for the allocation of
permits among firms. Hintermann (2011) examines the effect of free allocation on price
manipulation with market power in both product and permit market from theory and practice
point of view. Hintermann (2017) shows that some firms’ excess allowance holdings were
consistent with strategic price manipulation even if the dominant firm perceives market power
in the permit market alone.
Since the market power depends critically on the initial allocation, it is possible that the
allocation method affects the carbon price and allowance trading quantity. The main purpose
of this paper is to theoretically analyze the impact of CO2 emission permits allocation
methods on the cost-effectiveness of ETS from the perspective of market power.
The paper is organized as follows: After the introduction, we describe the CO2 emission
permits allocation methods (grandfathering, benchmarking and auctioning). Then we present
a Stackelberg model in carbon market when a single firm has market power and the rest of the
firms in the market are price taker. The third section provides the results, including the
efficiency loss in the carbon market under different CO2 emission permits allocation methods.
Policy suggestions are provided in the final section.
2. Method
2.1 CO2 emission permit allocation methods
CO2 emission permit allocation methods at macro level include indicator approach,
optimization approach, game theoretic approach and hybrid approach in theory, while at
micro level they are mainly grandfathering, benchmarking and auctioning in ETS (Zhou and
Wang, 2016).
Grandfathering is the most widely used CO2 emission permit allocation method,
probably due to its simplicity, wide acceptability and potential for reducing carbon leakage
(Schmidt and Heitzig, 2014). Grandfathering refers to the free allocation of emission permits
in proportion to historical emissions of the firm (Zetterberg et al., 2012). Let 𝑒̅𝑖 be the free
allocation of CO2 emission permits of firm 𝑖. 𝑓 is the CO2 emission allocation coefficient or
reduction rate. 𝑒0 is the CO2 emission amount in the base year. The CO2 emission allocation
coefficient and the base year are determined by the government. The initial CO2 emission
permits allocated by grandfathering method equal the product of the CO2 emission allocation
coefficient and the CO2 emission amount in the base year, as Eq. (1)
𝑒̅𝑖 = 𝑓𝑒0
(1)
Benchmarking refers to freely allocating CO2 emission permits based on the reference
emission level per product and the amount of production, which is often called output-based
allocation (Groenenberg and Blok, 2002). Compared to grandfathering, the benchmarking
allocation rule avoids rewarding carbon inefficient firms and punishing rapidly growing firms,
which makes it be more acceptable by carbon efficient firms (Zetterberg et al., 2012).
Let 𝑞𝑖 refer to the amount of production of firm 𝑖. 𝑒𝑏𝑖 refers to the benchmark setting, i.e.
reference emission level per product, which is assigned by the government. Generally the
government sets different benchmark for different industries. The initial CO2 emission permits
allocated by benchmarking method equal the benchmark setting multiplies the amount of
production, as shown by Eq. (2)
𝑒̅𝑖 = 𝑒𝑏𝑖 𝑞𝑖
(2)
Many scholars argue auctioning with revenue recycling is the preferable CO2 emission
permit allocation method (Cramton and Kerr, 2002; Zetterberg et al., 2012). It best complies
with the Polluter Pays Principle and avoids giving windfall profits to certain sectors that pass
on the notional cost of allowances to their customers despite receiving them for free
(European Commission 2008). According to Zhang et al. (2015), when auctioning is used, all
the CO2 emission permits should be bought from the carbon market, and the initial CO2
emission permits are as Eq. (3)
𝑒̅𝑖 = 0
(3)
2.2 Stackelberg model in ETS
According to “Coase Theorem”, under certain conditions, the market equilibrium in an
ETS will be cost-effective and independent of the emission permits allocation methods. That
is, the overall cost of achieving a given aggregate emission reduction will be minimized, and
the final allocation of emission permits will be independent of the initial allocation.
If there is no market power in carbon market, the market is considered to be competitive,
then the firms are all price takers. In this section, we explore the impact of CO2 emission
permits allocation methods on the cost-effectiveness of ETS in a carbon market with market
power. Following Hahn (1984), we assume a single firm has market power and the rest of the
firms in carbon market are price taker.
Consider the case of n firms in an industry covered in ETS, among which the firm 1 is
set to be the firm with market power. The total CO2 emission permits allocated to the firms in
̅. Firms are allowed to trade CO2 emission permits in the carbon market. The
this industry is E
number of CO2 emission permits the ith firm has after trading is set to be ei. All firms except
the firm with market power are assumed to have download sloping inverse demand functions
for CO2 emission permits of the form Pi(ei) over the region [0, E]. 𝑃𝑐 is CO2 emission permit
price in carbon market, which is determined by firm 1. All CO2 emission permit trades in the
market are constrained to take place at a single equilibrium carbon price 𝑃𝑐 . Let Ci(ei) be the
abatement cost associated with emitting ei units of firm i. Marginal abatement costs, -C', are
assumed to be positive and increasing, which implies that C' < 0 and C"> 0 for i = 2, …, n.
All price-taking firms attempt to minimize the sum of abatement costs and CO2 emission
permit buying costs.
2.2.1 Grandfathering
We first consider the case when the CO2 emissions permits are allocated by
grandfathering. Price takers solve the following optimization problem:
Minimize
𝐶𝑖 (𝑒𝑖 ) + 𝑃𝑐 (𝑒𝑖 − 𝑒̅)
𝑖
The first-order condition for an interior solution is
(i = 2, …, n)
(4)
𝐶′𝑖 (𝑒𝑖 ) + 𝑃𝑐 = 0
(5)
This means the price takers will adjust the CO2 emissions until the marginal abatement
cost is equal to equilibrium carbon price 𝑃𝑐 . Equation (5) implicitly defines a demand
function 𝑒𝑖 (𝑃𝑐 ), which is downward sloping on [0, E] for i = 2, …, n. Furthermore, we can
observe that the number of CO2 emissions permits the ith price-taking firm will use is
independent of its initial allocation of permits under the allocation rule of grandfathering.
Firm 1 has the power to determine the carbon price that will minimize its cost from
abatement costs and CO2 emissions permits buying cost. The CO2 emissions permits required
are subject to the constraint that the market clear.
Minimize 𝐶1 (𝑒1 ) + 𝑃𝑐 (𝑒1 − 𝑒̅1 )
(6)
Subject to 𝑒1 = 𝐸 − ∑𝑛𝑖=2 𝑒𝑖 (𝑃𝑐 )
(7)
Substituting the constraint into the objective function and differentiating yield the
following first-order condition for an interior minimum.
𝑛
(−𝐶′1 − 𝑃𝑐 ) ∑
𝑛
𝑒′𝑖 + (E − ∑
𝑖=2
𝑒𝑖 (𝑃𝑐 ) − 𝑒̅1 ) = 0
𝑖=2
(8)
𝑛
(−𝐶′1 − 𝑃𝑐 ) ∑
𝑒′𝑖 + (𝑒1 − 𝑒̅1 ) = 0
𝑖=2
Equation (8) reveals that the only case in which the marginal cost of abatement −𝐶′1
will equal the equilibrium carbon price is when firm l's allocation of CO2 emissions permits
just equals the amount it chooses to emit. That is the only way to achieve a cost-effective
solution is to pick an initial allocation of CO2 emissions permits for firm 1 which coincides
with the cost-minimizing solution (Hahn, 1984).
𝑃𝑐 =
(𝑒1 − 𝑒̅1 )
− 𝐶′1
∑𝑛𝑖=2 𝑒′𝑖
(9)
Equation (9) means that the carbon price is dependent on initial allocation of emission
permits of dominant firm. Since 𝑒′𝑖 < 0, the more the initial allocation of firm 1, the higher
the carbon price is. If the firm 1 is a seller of carbon emission permits, i.e. 𝑒1 − 𝑒̅1 < 0, then
the firm 1 will set 𝑃𝑐 > 𝐶′1 to reach the minimum total cost. If the firm 1 is a buyer in the
carbon market, i.e. 𝑒1 − 𝑒̅1 > 0, then the firm 1 will lower the carbon price to decrease the
total cost.
𝑔𝑎𝑝𝑔 = 𝐶′1 − 𝐶 ′ 𝑖 (𝑒𝑖 ) = 𝐶′1 + 𝑃𝑐 =
(𝑒1 − 𝑒̅1 )
∑𝑛𝑖=2 𝑒′𝑖
(10)
The marginal inefficiency in the carbon market can be described as the gap between the
marginal abatement cost of dominant firm and fringe firms (Eshel, 2005; Hagem and
Westskog, 2009). When the carbon emission permits are allocated by grandfathering, the
marginal abatement cost of the price takers is equal to equilibrium carbon price 𝑃𝑐 , thus the
marginal inefficiency in the carbon market is equal to the gap between the marginal abatement
cost of dominant firm 1 and carbon price 𝑃𝑐 , as shown in equation (10). It can be observed
that the inefficiency in abatement is dependent on the net volume of emission permits traded
by firm 1. The more the emission permits allocation of firm 1 deviates from its emissions, the
more the efficiency loss occurs in the carbon market.
2.2.2 Benchmarking
If benchmarking is applied in CO2 emissions permits allocation, for the price takers, the
first-order condition for an interior solution to the cost optimization problem is:
𝐶 ′ 𝑖 (𝑒𝑖 ) + 𝑃𝑐 (1 − 𝑒𝑏𝑖 /𝑒𝜌𝑖 ) = 0
𝑃𝑐 = −𝐶 ′ 𝑖 (𝑒𝑖 )/(1 − 𝑒𝑏𝑖 /𝑒𝜌𝑖 )
(11)
𝑒𝜌𝑖 is the CO2 emission coefficient (CO2 emissions per unit of product) and 𝑒𝜌𝑖 > 0.
𝑒𝜌𝑖 is assumed to be constant in a short period of time. Generally, 𝑒𝑏𝑖 is set at the range of (0,
𝑒𝜌𝑖 ], then 0 ≤ (1 − 𝑒𝑏𝑖 /𝑒𝜌𝑖 ) < 1. Equation (11) implicates that under the benchmarking
allocation rule, the equilibrium carbon price is probably more than −𝐶 ′ 𝑖 (𝑒𝑖 ). Thus, in theory,
when the percentage of application of benchmarking is increased, the carbon price is likely
increased. This idea is proved by Takeda et al. (2014) in the Japanese ETS.
For the firm 1 with market power, we get the first-order condition for an interior
solution.
𝑛
−(𝐶′1 + (1 − 𝑒𝑏1 /𝑒𝜌1 ) 𝑃𝑐 ) ∑
𝑛
𝑒′𝑖 + (1 − 𝑒𝑏1 /𝑒𝜌1 ) (E − ∑
𝑖=2
𝑒𝑖 (𝑃𝑐 )) = 0
𝑖=2
(12)
According to equation (12), we can get the equilibrium carbon price,
𝑃𝑐 =
𝑒1
𝑛
∑𝑖=2 𝑒 ′ 𝑖
−
𝐶′1
(1 − 𝑒𝑏1 /𝑒𝜌1 )
(13)
Equation (13) shows that the equilibrium carbon price is dependent on the value of the
benchmark the government sets for the firm with market power. Since 𝑒1 ≥ 0, 𝑒′𝑖 ≤ 0, and
0 ≤ (1 − 𝑒𝑏𝑖 /𝑒𝜌𝑖 ) < 1 , then the relationship between carbon price ( 𝑃𝑐 ) and marginal
abatement cost (−𝐶′1) is uncertain.
−𝐶 ′ 𝑖 (𝑒𝑖 ) = (1 −
𝑒𝑏𝑖
𝑒1
𝐶 ′1
)( 𝑛 ′ −
)
𝑒𝜌𝑖 ∑𝑖=2 𝑒 𝑖 (1 − 𝑒𝑏1 )
(14)
𝑒𝜌1
Equation (14) reveals that the only case in which the marginal abatement cost of firm 1
−𝐶′1 will equal marginal abatement cost of other firms −𝐶 ′ 𝑖 is when 𝑒𝑏𝑖 = 𝑒𝜌𝑖 in every
industry. That is the only way to achieve a cost-effective solution, is to make the benchmark is
set close to the emission intensity of the firm. Since 𝑒𝜌𝑖 is always different among firms in
every industry, 𝑒𝑏𝑖 = 𝑒𝜌𝑖 is impossible to be realized. Thus, benchmarking rule can easily
result in market distortion when market power exists in carbon market.
2.2.3 Auctioning
Under the allocation rule of auctioning, we consider two kinds of auctioning. One is
when firm 1 has the market power to set carbon price (Auctioning 1). The other one is when
the carbon price is set firstly by the government (Auctioning 2). In any case, the price takers
determine the emissions by 𝐶′𝑖 (𝑒𝑖 ) = −𝑃𝑐 .
By Auctioning 1, for the firm 1 with market power, we get the first-order condition for an
interior solution.
𝑛
(−𝐶′1 − 𝑃𝑐 ) ∑
𝑛
𝑒′𝑖 + (E − ∑
𝑖=2
𝑒𝑖 (𝑃𝑐 )) = 0
𝑖=2
(15)
Then the carbon price is
𝑃𝑐 =
𝑒1
𝑛
∑𝑖=2 𝑒′𝑖
− 𝐶′1
(16)
Since 𝑒1 ≥ 0 and 𝑒′𝑖 ≤ 0, then 𝑃𝑐 ≤ −𝐶′1 . It means that the firm 1 who has the
market power sets the carbon price lower than its marginal abatement cost. Since firm 1 can
be seen as an emission permits buyer, it makes sense for firm 1 to set carbon price lower to
reduce its whole cost. From the equation (16), we can see that the more the dominant firm
emits, the lower the carbon price it will set.
Thus the gap between the marginal abatement cost of dominant firm and fringe firms is
𝑔𝑎𝑝𝑎 = 𝐶′1 − 𝐶 ′ 𝑖 (𝑒𝑖 ) = 𝐶′1 + 𝑃𝑐 =
𝑒1
𝑛
∑𝑖=2 𝑒′𝑖
(17)
Equation (17) shows the marginal inefficiency in the carbon market when emission
permits are allocated by auctioning 1. In this case, the −𝐶′𝑖 = 𝑃𝑐 ≤ −𝐶′1 , thus the
cost-effectiveness of ETS cannot be reached. It can be observed that the inefficiency in
abatement is dependent on the net volume of emission permits traded by firm 1. The more
firm 1 emits, the more the efficiency loss occurs in the carbon market.
By Auctioning 2, all the firms are carbon price takers. Thus, for every firm in carbon
market, we get the first-order condition for an interior solution.
𝐶′𝑖 (𝑒𝑖 ) + 𝑃𝑐 = 0
(18)
According to equation (18), under auctioning, the cost-efficiency in carbon market can
be achieved, given the proper carbon price set by the government.
3. Discussions and implications
First, market power plays an important role in the cost-effectiveness of ETS. The firms
with market power in the carbon market can deviate the carbon price from the cost efficient
equilibrium price.
Second, the market power is highly dependent on the initial allocation permits when the
emission permits are allocated by grandfathering. The more the initial emission permits
allocation of dominant firm deviates from its emissions, the more the efficiency loss occurs in
the carbon market.
Third, when benchmarking is adopted in emission permits allocation, only the
benchmark is set close to the emission intensity of the firm, the cost-effectiveness of ETS can
be approached. Since it is impossible, the application of benchmarking rule would affect the
cost-effectiveness of ETS.
Fourth, if the government sets the proper carbon price at firstly, the market equilibrium
in a cap-and-trade system will be cost-effective.
4. Conclusions
This paper is to theoretically analyze the impact of CO2 emission permits allocation
methods on the cost-effectiveness of ETS from the perspective of market power.
Under some assumptions in Stackelberg model, we find some interesting and meaningful
results. CO2 emission permits allocation method plays an important role in the
cost-effectiveness of ETS from the perspective of market power. The more the initial emission
permits allocation of dominant firm deviates from its emissions, the more the efficiency loss
occurs in the carbon market when the emission permits are allocated by grandfathering. When
benchmarking is adopted in emission permits allocation, only the benchmark is set close to
the emission intensity of the firm, the cost-effectiveness of ETS can be approached. And if
benchmarking is adopted, the carbon price is even more than that by grandfathering. Given the
proper carbon price set by the government, the market equilibrium in a cap-and-trade system
will be cost-effective.
Our results suggest that compared to benchmarking, grandfathering rule is a better
choice, when the policy makers want to adopt one kind of free allocation method to attract
firms to participate in the ETS at the early time. And the policy makers should identify the
firms with market power, in order to distribute them corresponding emission permits they
need. Auctioning rule would be suggested when the ETS is well developed and proper carbon
price should be set firstly.
References
1.
Cramton, P., Kerr, S., 2002. Tradeable carbon permit auctions: how and why to auction not grandfather.
Energy Policy 30, 333–345.
2.
Eshel D.M.D., 2005. Optimal allocation of tradable pollution rights and market structures. Journal of
Regulatory Economics 28(2), 205-223.
3.
Ellerman, A.D., Buchner, B.K. 2008. Over-allocation or abatement? A preliminary analysis of the EU ETS
based on the 2005-06 emissions data. Environmental and Resource Economics 41(2), 267-287.
4.
European Commission. (2008). MEMO/08/35, Brussels, 23 January 2008. Questions and answers on the
commission’s proposal to revise the EU emissions trading system.
5.
González-Eguino, M., 2011. The importance of the design of market-based instruments for CO2 mitigation:
An AGE analysis for Spain. Ecological Economics 70(12), 2292-2302.
6.
Groenenberg, H., Blok, K., 2002. Benchmark-based emission allocation in a cap-and trade system. Climate
Policy 2, 105-109.
7.
Hahn, R.W., 1984. Market Power and Transferable Property Rights. Quarterly Journal of Economics 99:
753-765.
8.
Hahn, R.W., Stavins, R.N., 2011. The Effect of Allowance Allocations on Cap-and-Trade System
Performance. The Journal of Law and Economics 54(S4), S267-S294.
9.
Hagem, C., Westskog, H., 2009. Allocating tradable permits on the basis of market price to achieve cost
effectiveness. Environmental and Resource Economics 42(2), 139-149.
10. Hintermann, B., 2011. Market power, permit allocation and efficiency in emission permit markets.
Environmental and Resource Economics 49(3), 327-349.
11. Hintermann, B., 2017. Market power in emission permit markets: theory and evidence from the EU ETS.
Environmental and Resource Economics 66, 1-24.
12. Maeda A., 2003. The emergence of market power in emission rights markets: The role of initial permit
distribution. Journal of Regulatory Economics 24(3), 293-314.
13. Malik, A., 2002. Further Results on Permit Markets with Market Power and Cheating. Journal of
Environmental Economics and Management 44:371-390.
14. Schmidt, R.C., Heitzig, J., (2014). Carbon leakage: grandfathering as an incentive device to avert firm
relocation. Journal of Environmental Economics and Management 67(2), 209-223.
15. Takeda, S., Arimura, T.H., Tamechika, H., Fischer, C., Fox, A.K., 2014. Output-based allocation of
emissions permits for mitigating the leakage and competitiveness issues for the Japanese economy.
Environmental Economics and Policy Studies 16(1), 89-110.
16. Westskog, H., 1996. Market Power in a System of Tradeable CO2 Quotas. The Energy Journal 17, 85-103.
17. Zetterberg, L., Wråke, M., Sterner, T., Fischer, C., Burtraw, D., (2012). Short-run allocation of emissions
allowances and long-term goals for climate policy. Ambio 41(1), 23-32.
18. Zhang, Y.J., Wang, A.D., Tan, W., 2015. The impact of china's carbon allowance allocation rules on the
product prices and emission reduction behaviors of ETS-covered enterprises. Energy Policy 86(1), 176-185.