The Allocation of Greenhouse Gas Emission in European Union through Applying the Claims Problems Approach

By inergency On Mar 8, 2024

1. Introduction

The EU has a significant impact on the context of global warming. This region is the fourth global GHG emitter [1]. Nonetheless, the EU has always played the role of a leader to navigate activities for diminishing GHG emission [2].

The most prominent role of the EU is its proposal to limit the global temperature increase up to 2

^{\circ}

C above the pre-industrial level in 1996 [3]. This proposal has been the main target of all climate changes protocols and agreements [4]. After this, we can mention the Paris Agreement as a landmark in the EU’s leading role to accelerate emission mitigation [5]. To achieve the targets of the Paris Agreement, the EU believes countries’ efforts should be clear and quantifiable [6]. Therefore, the EU itself set three objectives: a 20% reduction in GHG emissions by 2020, a 55% reduction by 2030 (compared with the 1990 level), and reaching net zero emissions by 2050. Member states have succeeded in starting a decreasing trend from 1990 onwards. This diminishing path has led to the target of 2020 being overachieved (32% emission reduction in 2020 compared with 1990 [7]).

Nevertheless, countries’ emission projections for the period of 2021 to 2030 indicate that this achievement is temporary. The member states’ aggregate emission projections show that, in the best condition, their emission reduction is 41% less than 1990 [7]. Thereby, the countries’ national efforts are not sufficient in following the EU targets.

Several studies have tried to solve this problem. References [8,9] define different emission budget scenarios aligned with the Paris Agreement and allocate them among countries. The allocation each country receives can work as a criterion to limit their national emissions [10]. The studies allocate the emission budget based on some equity principles. For instance, countries with larger historical emissions and/or a larger Gross Domestic Product (GDP) per capita should diminish more GHG emissions. Reference [11] considers the equity principle and compromises it with the efficiency principle. The efficiency principle focuses on the economic benefit and minimizing the cost of emission reduction. They define population size, economic development, and historical emissions as the indicators that are utilized for an equitable allocation. Regions with higher population size, GDP, and historical emissions should take more responsibility for GHG emissions reduction. To evaluate the efficiency, they use a model called Super-SBM. Capital, labor, and energy are the inputs of this model and the output is GDP and GHG emissions. The regions with higher efficiency are assigned higher emission allocations. Reference [12] discusses that the eventual allowable emission level that countries can emit is the difference between the target emission budget and countries’ historical emissions. They proposed to allocate this allowable budget based on equal per capita or equal per countries’ current and future emissions. They also propose to enter the factor of historical emission into the aforementioned allocation methods.

However, the division of emission reduction responsibility is one method to abate the total GHG emission; another way is to sink and capture the cumulative GHG from the atmosphere. References [13,14,15] focus on this issue rather than studying the emission reduction actions. They divide Carbon Dioxide Removal (CDR) responsibilities fairly among countries. Based on their results, countries with larger GDPs and larger cumulative emissions per person will take a greater portion of CDR.

If we return to the solution of the GHG emission reduction through assigning a target emission budget to countries, reference [16] provides a new approach to do that which is the application of the claims problems approach. Claims problems [17] distribute a limited resource in situations where the total needs of parties in a dispute are more than the available resource. Reference [18] studies the distribution of the GHG emission budget between five main groups of countries by applying the claims problems approach. This method is used in a variety of resource allocation fields. Recently, reference [19] implemented claims problems to distribute the European Structural and Investment Fund to different regions throughout the EU.

The case of GHG mitigation in the EU can evidently be defined as a claims problem. We estimate the total amount of GHG that member states must emit from 2021 to 2030 in the framework of the EU 2030 target and compared it with the member states’ aggregate emission projections in this period. We observe that the aggregate projections exceed the desirable emission level and the claims problems approach is applicable. We apply several allocation rules which are well-known in the claims problems literature and study their behavior. The allocation each member state receives by these rules tells how much they should abate their emission in the ten years to reach the target of 55% reduction by 2030 and obliges countries to adjust their emission projections to be more compatible with that target.

Here, the question rises: how countries should adjust the projection? We propose to look at this issue in a more dynamic way by applying the claims problem in each year. Now, countries can adjust their projections step by step according to the annual ceiling which is determined by the claims problems. The annual allocation is conducted as follows: in 2021, we allocate the permitted emission budget for this year to the projections of the year. As the aggregate projection is more than the emission budget, countries’ projections cannot be fully satisfied, and part of them will be lost. These losses are added to the projections for 2022 and then we divide the 2022 emission budget based on these revised projections and so on. This method is an opportunity for member states to adjust their annual projections by considering the losses and can accelerate the process of GHG mitigation. If member states define their annual projections without taking into account the losses, they will face large projections when the losses are added. We will see that some division rules extremely penalize these countries by satisfying a slight portion of their projection, which means more loss for countries.

In the claims problems approach, countries are allowed to announce their demands and the claims problems allocates the emission budget on the basis of these demands. In addition, countries’ final GHG emissions are limited to the amount that the claims problems assigns to them. Since, in the claims problems, no country can receive more than her claim (i.e., her need to emit), there is no chance for trading the emission allowances. Indeed, the claims problems establishes a strong limitation for rich countries to buy other countries’ exceeded emission allowances.

This paper is organized in this order: Section 2 defines the claims problems approach and the division rules we apply to allocate the emission budget. This chapter also mentions the conditions and principles the division rules should satisfy. Section 3 discusses the implementation of division rules. In Section 4, the conclusions are provided.

2. Materials and Methods

Formally, we can define the claims problems as a set of agents $N = \{1, 2, . . ., n\}$ and an amount $E \in R_{+}$ the endowment that has to be allocated among them. Each agent has a claim, $c_{i} \in R_{+}$ on it. Let c $\equiv {(c_{i})}_{i \in N}$ be the claims vector.

Then, a claims problems [17] is a pair

(E, c)

with

C = \underset{i = 1}{\sum^{n}} c_{i} > E

Without loss of generality, we increasingly order the agents according to their claims, $c_{1} \leq c_{2} \leq$ … $\leq c_{n}$ , and we denote by $B$ the set of all claims problems.

We define the EU member states as the agents. To define the against’ claims, we use countries’ national projections of anthropogenic GHG emissions. The projections are the countries’ estimations about their future GHG emissions in different sources and GHG removals for the period 2021 to 2030. The projections are prepared in two scenarios: ‘with existing measures’ (WEM) and ‘with additional measures’ (WAM).

In WEM scenario, projections reflect the effects of all adopted and implemented measures at the time the projections are prepared. These measures embrace all mitigation actions and instruments which are the yield of governments’ official decisions. Measures are supported by assigning adequate financial and human resources and the process of implementation of these measures are guaranteed. In WAM scenario, projections consider all adopted and implemented measures and the measures are at the planning stage at the time the projections are prepared. Although these planned measures are under review when the projections are submitted, they have a realistic chance to be adopted and implemented in the future [20].

The member states are obliged to report their national measures and projections every two years to the Monitoring Mechanism Regulation (MMR). These reports are used to monitor the member states’ national mitigation efforts and assess the capability of the current measures to serve the GHG emission mitigation [21]. These measures are mainly implemented in industrial and agricultural sectors, energy supply (i.e., fuel extraction, distribution, and storage), and, energy consumption (i.e., consumption of fuels and electricity by households, services, industry, and agriculture). These measures appear in different forms such as economic incentives to reduce GHG, setting taxes on GHG emissions, building standard regulations, training programs, and research programs [21].

Afterward, we need to define the emission budget in line with the target of a 55% reduction by 2030. For this purpose, we assume a constant decreasing trend from the countries’ last absolute emission to the desirable emission in 2030. According to the EU database (Eurostat), the latest absolute emission released hitherto belongs to 2020 which is 3124.59 Megatonnes (Mt). The desirable emission in 2030 is 2109.36 Mt which represents a 55% reduction compared with emissions in 1990. Let us show the emission in 2020 by

e^{2020}

and desirable emission in 2030 by

e^{2030}

and let us

d = \frac{e^{2020} - e^{2030}}{10}

where 10 is the period in which the countries are diminishing the emission reduction (i.e., the number of years from 2021 to 2030). To achieve the constant decrease from 2021 and meet the desirable emission in 2030, the emission of EU in each year is the emission of the previous year minus d. Table 1 shows the total of this emission budget for 2021–2030 and the total of projections (in two scenarios) for these years.

As Table 1 depicts the emission budget is not sufficient to satisfy the projections. There is a variety of division rules in the claims problems that each proposes a particular way to divide the emission budget. A division rule is a single-valued function

φ : B \to R_{+}^{n}

, such that

φ_{i} (E, c) \geq 0

. We use division rules which were already implemented in the context of CO₂ emission right by [16,18], these rules include Proportional, Constrained Equal Award, Constrained Equal Losses, Talmud, Adjusted Proportional, and

α - m i n i m a l

The Proportional (P) [22] divides the emission budget proportionally among countries according to their projections. In this rule for each

(E, c) \in B

and each

i \in N

P_{i} (E, c) \equiv λ c_{i},

where

λ = E / \sum_{i \in N} c_{i} .

The Constrained Equal Award (CEA) [22] divides the emission budget equally to all countries’ provided that none of them receive more than their projections. The process is as follows: If the average emission budget exceeds the projection of one country, the rule fully satisfies the country’s projection, excludes this country from the allocation process, and continues to allocate the remaining emission budget equally to the rest of the countries.

For each $(E, c)$ $\in B$ and each $i \in N,$ $C E A_{i} (E, c) \equiv min \{c_{i}, μ\},$ where $μ$ is such that $\sum_{i \in N} min \{c_{i}, μ\} = E .$ However, this rule neglects the differences between projections of countries.

The Constrained Equal Losses (CEL) [22] proposes to divide the loss (difference between aggregate projections and emission budget) equally to all countries given that no country receives a negative amount. The allocation each country receives is the difference between her projection and the loss which is divided by

C E L

. If this difference is negative for a country, the country’s allocation will be zero and she leaves the allocation process.

C E L

divides the loss equal to the remaining countries.

For each $(E, c)$ $\in B$ and each $i \in N,$ $C E L_{i} (E, c) \equiv max \{0, c_{i} - μ\},$ where $μ$ is such that $\sum_{i \in N} max \{0, c_{i} - μ\} = E .$

Talmud (T) [23] proposes a combination of CEA and CEL. This rule focuses on the half-sum of aggregate projections. If the emission budget is less than or equal to the half-sum of projections, CEA is applied. Countries receive the average emission budget or half of their projection (if the average emission budget is greater than half of the projection). If the emission budget is greater than the half-sum of projections, the following process is conducted: countries receive half of their projections. The projections and emission budget are revised down by these initial allocations and CEL is applied to these revised amounts.

For each $(E, c)$ $\in B$ and each $i \in N,$ $T_{i} (E, c) \equiv C E A_{i} (E, c / 2)$ if $E \leq c / 2;$ or $T_{i} (E, c) \equiv c_{i} / 2 + C E L_{i} (E - c / 2, c / 2)$ , otherwise.

The Adjusted Proportional (AP) [24] has been introduced in two steps. In the first step, AP assigns to each country a minimal right (

m_{i}

). This minimal right is the remaining emission budget when the projections of the rest countries have been satisfied, with respect to the condition of

m_{i} (E, c) = max \{0, E - \sum_{j \neq i} c_{j}\}

. In the second step, the projections are revised down by the minimal rights. Then the remaining emission budget is assigned proportionally among countries based on their revised projections.

For each $(E, c)$ $\in B$ and each $i \in N,$ $A P_{i} (E, c) = m_{i} (E, c) + P (E - \sum_{i \in N} m_{i} (E, c), c - m (E, c))$

The $α$ -minimal ( $α$ -min) [25] proposes to give each country a minimal amount equal to the lowest projection, in the case that the emission budget is enough. After revising down the projections by minimal amounts, the rule distributes the remaining emission budget proportionally among countries according to their revised projections. However, if the emission budget is not sufficient to give all countries the minimal amount, this rule recommends dividing the emission budget equally among countries.

For each $(E, c)$ $\in B$ and each $i \in N,$ if $c_{1} > E / n$ then $α - m i n_{i} (E, c) = E / n$ and if $c_{1} < E / n$ then $α - m i n_{i} (E, c) = c_{1} + P (E - n c_{1}, c - c_{1}) .$

All these rules must satisfy three basic requirements. First, the minimum amount countries receive by applying the rules is 0 (non-negativity), $φ_{i} (E, c) \geq 0$ , for all $i \in N$ . Second, countries cannot receive more than their projections (claim-boundedness), $φ_{i} (E, c) \leq c_{i}$ , for all $i \in N$ . Third, the whole emission budget should be divided among countries. (efficiency) $\sum_{i \in N} φ_{i} (E, c) = E$ .

We also introduce some well-known properties in the context of resource distribution. These principles examine the characteristic of each division rule and assist us to select an optimal one.

Equal treatment of equals states that countries with the same projections should receive an equal amount of emission budget. For each $(E, c) \in β$ and $i, j \subseteq N$ , if $c_{i} = c_{j}$ then $φ_{i} (E, c) = φ_{j} (E, c)$ .

Anonymity says the allocation of emission budget exclusively depends on countries’ projections. Other factors such as the identity of the countries cannot affect the emission allocation. For each $(E, c) \in β$ each $π \in \prod^{N}$ and each $i \in N$ , $φ_{π (i)} (E, {(c_{π (i)})}_{i \in N}) = φ (E, c)$ , where $\prod^{N}$ is the permutations of N.

Order preservation [23] means the emission allocation assigned to countries with larger projections cannot be smaller than the emission allocation of countries with lower projections. For each

(E, c) \in β

and each

i, j \in N

such that

c_{i} \geq c_{j}

, then

φ_{i} (E, c) \geq φ_{j} (E, c)

. Likewise, countries with larger projections bear an equal or larger amount of loss than countries with lower projections.

c_{i} - φ_{i} (E, c) \geq c_{j} - φ_{j} (E, c)

Claims monotonicity states if a country increases its projection, the allocation assigned to this country cannot be less than the initial amount. For each $(E, c) \in β$ , $i \in N$ and each $c_{i}^{'} > c_{i}$ we have $φ_{i} (E, c_{i}^{'}, c_{- i}) \geq φ_{i} (E, c)$ .

Composition down [26] is a property for situations in which the emission budget is reduced after allocation due to re-evaluation of the emission budget or setting more strict emission reduction rules. For instance, the EU decides to increase the percentage of emission reduction by 2030 to more than 55%, while the emission budget of 55% reduction has been allocated before this announcement. In this case, we have two choices: First, we cancel the initial emission budget allocation and reallocate the new amount of the emission budget. Second, we consider the initial emission allocation assigned to each country as their claims (rather than considering the projections) and divide the new emission budget by these new claims. for each

(E, c) \in B,

each

i \in N

, and each

0 \leq E^{'} \leq E,

φ_{i} (E^{'}, c) = φ_{i} (E^{'}, φ (E, c))

Invariance under claims truncation [27] imposes an upper bound to countries’ projections. If a country’s projection is greater than the emission budget, the exceeding part will be ignored. This property says that countries cannot request more than the available emission budget. For each

(E, c) \in β

and each

i \in N

φ_{i} (E, c) = φ_{i} (E, {(m i n c_{i}, E)}_{i \in N})

Table 2 shows the division rules and the properties which are satisfied by them. The constrained Equal Awards (CEA) rule satisfies all these basic properties.