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李, 倩
http://hdl.handle.net/2324/4474924
出版情報：Kyushu University, 2020, 博士（経済学）, 課程博士 バージョン：
権利関係：
International Environmental Agreements under Heterogeneity
A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy
Department of Economic Engineering Graduate School of Economics
Kyushu University
by
Qian Li
January 2021
Abstract
With the development of economics and technologies, environment has deteriorated in the past centuries. Forming International Environmental Agreements (hereafter IEAs), which requires countries’ voluntary participations and stipulates these participants’ abatement responsibilities, is a promising way to combat for global environmental degradation. Based on the rules of IEAs, member countries coordinate their actions so as to reach a common goal.
Specifically, such actions include: decrease or avoid emission activities; financially support other countries to abate pollutants and so on.
Previous studies employing one shot game to model the formation of IEAs assume that countries are symmetric, in terms of the benefits and costs from abatement of pollutant emissions. Nevertheless, such assumption is unreasonable since countries differ in the technology levels and geographic location. Therefore, in this doctoral thesis, we choose three representative IEAs that solve different transboundary pollutant problems and reexamine their efficiency considering asymmetric countries. This thesis includes five chapters.
The first chapter explains the research background. After reviewing some former literature, we also briefly introduce the motivations and objectives to show the importance of this thesis.
In the second chapter, we compare the effectiveness of internal and external transfers in multilateral IEAs with two types of countries and two-sided strong asymmetry. To make it clear, developed countries have sufficiently larger abatement benefit and abatement cost parameters than developing ones. The game modelling IEAs with internal transfers requires all member countries to reallocate their welfare while that modelling IEAs with external transfers requires some free riders to transfer welfare to countries that will later become IEA
members. Our results show that both transfers are effective to enlarge the size of IEAs and to increase all countries’ social welfare. What’s more, external transfers are always preferred.
The third chapter explores the efficiency of uniform abatement level and uniform emission tax in multilateral IEAs with unlimited types of asymmetric countries. Rather than maximizing coalition welfare, member countries decide the uniform abatement level and uniform emission tax via pairwise majority voting. We find that IEAs under neither of the above-mentioned uniform regulatory policy can include more than two asymmetric countries.
However, if an internal transfer scheme is well designed, the larger IEA is possible.
In the fourth chapter, we investigate the efficiency of bilateral IEAs formed by two asymmetric countries in the context of strategic delegation. We assume that the developed country has higher abatement cost than the developing counterpart and its households also value environment more than that of the latter. Allowing households of each country to elect the government via pairwise majority voting, which is the so-called strategic delegation, our result confirms the existence of incentives to choose a less green government in the cooperative case. Moreover, cooperation is conducive because both the total payoff of all households and the aggregate abatement levels are increased, comparing with the situation when no cooperation is allowed.
The last chapter concludes this doctoral thesis. Our main contributions are as follows.
First, external transfers are more effective than internal transfers when assuming two types of countries with strong asymmetry. Second, neither uniform abatement level nor uniform emission tax is an useful instrument to induce the large stable IEAs when assuming unlimited types of countries. Therefore, it is necessary to employ transfers among member countries to achieve efficient result. Third, when considering domestic politics in the bilateral environmental agreements with two asymmetric countries, cooperation is effective even though households in both countries elect less green governments. Overall, this doctoral thesis
fills the research gap for theoretical studies in IEAs using one shot game, since there are few work considering heterogeneity among countries.
Acknowledgement
To my supervisor Prof. Toshiyuki Fujita I owe the greatest debt for making this dissertation possible, first in the living of it, then in the writing of it. He was patient, talented and knowledgeable. As an expert in theoretical study of international environmental agreements, he gave lots of excellent advices over this thesis and the joint work. In the past five and a half years, I learned much about research and education from him.
Prof. Taro Takimoto and Prof. Kunio Urakawa in particular were generous with their time reading multiple drafts and attending the research workshops. Their insightful comments have helped to improve this thesis.
Special gratitude to Prof. Shigemi Kagawa for his encouragement and recommendation. I also like to thank Prof. Hsiao-chi Chen for her advices over how to become independent researcher.
My appreciation also goes to the participants of the 4th World Social Science Forum, the participants of the 8th Congress of the East Asian Association of Environmental and Resource Economics, the anonymous reviewers of Applied Economics Letters and Applied Economics for their insightful comments that have contributed much to my research.
I am grateful to Kyushu University: first, it gave me chance to study in Japan and financially supported my research; second, in the beautiful campus, I met many interesting and nice people; last but not the least, supports from the staff have helped me to develop the research smoothly.
The financial supports for international students from Ministry of Education, Culture, Sports, Science and Technology-Japan in years 2015, 2017 and 2020 also contribute to this study.
Finally, thanks my parents and friends for their encouragements, understanding and company.
Contents
Abstract ... ii
Acknowledgement ... v
1 Introduction ... 1
1.1. Research Background ... 1
1.2. Literature Review ... 5
1.2.1 International Environmental Agreements ... 5
1.2.2 Emission tax ... 17
1.3. Objectives... 20
1.4. Thesis structure ... 22
2 Transfers in International Environmental Agreements under Heterogeneity ... 25
2.1. Introduction ... 25
2.2. International environmental agreements without transfers ... 27
2.2.1 The model ... 27
2.2.2 Choice of abatement ... 29
2.2.3 Self-enforcing agreements ... 30
2.3. International environmental agreements with internal transfers ... 33
2.4. International environmental agreements with external transfers... 35
2.5. Comparison of internal and external transfers ... 43
2.6. Conclusions ... 44
3 Uniform Regulation in International Environmental Agreements under Heterogeneity ... 47
3.1. Introduction ... 47
3.2. The model ... 50
3.3. Uniform abatement level in international environmental agreements ... 52
3.4. Uniform emission tax in international environmental agreements ... 55
3.5. Multilateral compensation scheme ... 58
3.6. Conclusions ... 59
4 Strategic Delegation in International Environmental Agreements under
Heterogeneity ... 62
4.1. Introduction ... 62
4.2. The model setting ... 64
4.3. Cooperative environmental policies ... 66
4.3.1 When bargain fails ... 66
4.3.2 Nash bargaining solution with transfers... 67
4.4. Isolationism in environmental policies ... 70
4.5. Comparison of the cooperative and isolationism environmental policies... 71
4.6. Conclusions ... 72
5 Conclusions ... 74
Appendices ... 76
Appendix A ... 77
A.1. Proof of Proposition 2.1 ... 77
A.2. Proof of Proposition 2.2 ... 77
A.3. Proof of Proposition 2.3 ... 79
A.4. Proof of Proposition 2.4 ... 79
Appendix B ... 81
B.1. Proof of Proposition 3.1 ... 81
B.2. Proof of Proposition 3.2 ... 83
Appendix C ... 85
C.1. Proof of Proposition 4.3 ... 85
C.2. Proof of Proposition 4.4 ... 85
References ... 88
Chapter 1 Introduction
1.1. Research Background
Environmental issues always relate to the negative, widespread, and long-lasting impacts on human activities. With the development of economics and technologies, environment has deteriorated in the past centuries.
Environmental degradations are undoubtfully harmful to people’s daily life and even lives. An old example includes London Smog in 1960s which is caused by severe atmospheric pollution and has led thousands of people to die. To solve it, the Clean Air Act of 1956 introduced smokeless zones, requiring householders to convert open coal fires to closed stoves burning smokeless fuels or gas. This policy marks the start of the UK’s modern pollution-control legislation. A latest example is the 2019 Amazon rainforest wildfires due to lack of rainfall. The wildfire has burned across the southern swath of the Amazon within Brazil, Bolivia, Paraguay, and Peru; has blanketed people who live downwind with thick, dirty air; has hurted wildlife in their path and has destroyed part of one of the most important carbon storehouses left on the planet. Even though international leaders at the G7 summit have committed to provide financial support to help fight fires, the losses are uncountable and whether such wildfire will happen again is unwarrantable.
The distinctive difference between the above-mentioned two examples of environmental deterioration is the international dimension. Different from former domestic environmental problem that the government can force to solve, transboundary
environmental issue as shown in the second example can only resort to sovereign nations’ voluntary actions.
Forming International Environmental Agreements (hereafter IEAs), which requires countries’ voluntary participations and stipulates these participants’ abatement responsibilities, is a promising way to combat for global environmental degradation.
Based on the rules of IEAs, member countries coordinate their actions so as to reach a common goal. Specifically, such actions may include: decrease or avoid emission activities; develop and share abatement-related technology; financially support other countries to abate pollutants and so on.
The best-known successful IEA is the Montreal Protocol on chlorofluorocarbon (CFC) production, which is adopted in September 1986. When released to the atmosphere, CFCs damage the stratospheric ozone layer, which is the Earth’s protective shield that protects human beings and the environment from harmful levels of ultraviolet radiation from the sun. With the signatory countries offering side-payments to India, China and other developing nations so as to induce them to sign, the Montreal Protocol has been ratified by 156 countries in March 1996. By that time, it has totally implemented the phase-out of CFC production.
Nevertheless, IEAs regarding climate change are not so effective, at least in terms of completion of the abatement target. Effects that scientists had predicted in the past would result from global climate change are now occurring: loss of sea ice, accelerated sea level rise and longer, more intense heat waves. The major cause of climate change should be attributed to the enormous emissions of greenhouse gases (GHG) coming from combustions of fossil fuels. The Kyoto Protocol, agreed in 1997, ever aimed to reduce the GHG emissions in aggregate by 5% from a 1990 baseline for the period
2008–2012. Besides, this protocol set minimum participation rule that the agreement would enter into force only if it had been ratified by at least 55 Parties, including the Annex I Parties1 accounting for 55 percent of the group’s 1990 carbon dioxide emissions. Since the only binding emissions reduction targets were set for industrialized countries, and since the largest emitter, the U.S., stayed outside the agreement, the lifespan of the protocol came to an end in 2012 without making any differences to global GHG reductions. Recent years, international negotiations focus on a successor — The Paris Agreement.
The Paris Agreement’s central aim is to strengthen the global response to the threat of climate change by keeping a global temperature rise this century well below 2 degrees Celsius above pre-industrial levels and to pursue efforts to limit the temperature increase even further to 1.5 degrees Celsius. Instead of setting a specific abatement level for each signatory, The Paris Agreement requires all Parties to put forward their best efforts through nationally determined contributions (NDCs) and to strengthen these efforts in the years ahead. It has entered into force on November 4, 2016, after at least 55 parties accounting in total for over 55% of the global GHG emissions have signed.
Up to now, 194 states and the European Union have become members of the agreement.
Nevertheless, the efficiency of The Paris Agreement is still open to doubt. Some parties
1 Annex 1 parties refer to industrialized and transition parties, including Australia, Austria, Belarus, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, European Union, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Japan, Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, Monaco, Netherlands, New Zealand, Norway, Poland, Portugal, Romania, Russian Federation, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey, Ukraine, United Kingdom of Great Britain and Northern Ireland and United States of America.
have proposed low NDCs and some crucial countries, i.e. the U.S. under the presidency of Donald Trump, have withdrawn after signing the agreement out of political reasons.
However, the commendable performance of the Montreal Protocol provides a convincing evidence for the potential efficiency of “additional rules”, i.e. transfers, in the design of successful IEAs. These additional rules trigger us to ask: whether specific rules can be employed to design well-functioned IEAs so as to deal with transboundary environmental problems? The failure of the Kyoto Protocol and the possible failure of the Paris Agreement also leads us to consider: why this kind of IEAs usually fail; can some rules help to improve the performance of these agreements?
Game theory is always employed as a theoretical instrument to model the formation of IEAs. As we all know, the outcomes of IEAs depend on the behaviors of the countries. That is, whether one country sign or not sign the agreement and which abatement level it chooses. In game theoretical model, these can be interpreted as that the payoffs of players depend on how they responded to the incentives structured by the rules of the game. By designing different game theoretical models, we consider IEAs with different rules. By assuming different payoff functions for players, we characterize countries’ situations facing different environmental problems.
Theoretically, the largest obstacle for the success of IEAs is that high incentives to free ride cause low cooperation level. Cooperation level here refers to number of participants and aggregate abatement levels as well. In the context of global environmental issues, given that pollutants abatement generated by one country is a global public good, any other countries can enjoy the benefits without reducing emissions by themselves. Therefore, some countries may lack incentives to spontaneously take part in the agreement since being a member means higher abatement
burden comparing with being a non-member. Higher burden corresponds to higher abatement costs. In addition, no supranational organization with enough power exists to coerce sovereign nations’ actions. Henceforth, without additional rules, the multilateral IEAs cannot comprise of a large number of member countries.
Another kind of free-riding relates to the domestic politics within a country. In most cases, citizens vote for the government and such government then enacts environmental policies. By electing less green government that prefers loose environmental regulatory policies, the citizens can shift abatement burden to other countries and at the meanwhile enjoy the benefits from pollutants abatement. These incentives will become stronger when IEAs are allowed and thus the aggregate abatement level may be lower than optimal.
Under this background, more studies should be conducted to analyze the above- mentioned free riding incentives in IEAs and to find suitable measures to alleviate such incentives. In the next section, we make a review about the development of theoretical research on IEAs, in order to show the importance of our research.
1.2. Literature Review
1.2.1 International Environmental Agreements
As mentioned before, forcing countries to make decisions violates international laws and thus countries spontaneously take actions to solve environmental problems.
Henceforth, a large body of literature applies non-cooperative game theory (rather than
cooperative game theory) to analyze the formation of IEAs. We review some of the basic theory at work as follows.
Since no global police organization exists to enforce an IEA, a climate treaty must be self-enforcing. This concept is developed by D'Aspremont et al. (1983) in cartel theory. It shows that all countries that enter into the agreement have no incentives to defect and no outside country should have an incentive to interfere with the agreement.
However, self-enforcing IEAs without additional rules prove to be far away from effective. Its formation is often modelled as a two-stage game. In the first stage, countries decide whether to become members of IEA. In the second stage, all countries choose their abatement level under the assumption that members maximize joint payoff while non-members maximize individual payoffs. Barrett (1994) considers homogeneous countries and several forms for payoff functions2 in such game. It is suggested that a self-enforcing IEA with many signatories does not exist, when the difference in the global net benefit under the full cooperative and non-cooperative outcomes is large. Nevertheless, when an IEA can sustain a large number of signatories, the global net benefit is only marginally improved compared with the non-cooperative outcome. Hoel (1992a) analyzes the similar game model where signatories choose the median value of their most preferred emission level3 in the second stage. In his study, countries are identical with respect to marginal abatement costs but differ in marginal
2 In the first case, countries are supposed to have linear marginal abatement benefits and costs. In the second and third cases, countries are supposed to have constant marginal benefits but linear and logarithmic marginal costs, respectively. In the last case, countries have linear marginal benefits and constant marginal costs.
3 The most preferred emission level for a country is that maximizes its individual payoff.
abatement benefits. The numerical example shows that only 2 out of 100 countries cooperate in the equilibrium outcome. Moreover, these two countries abate emissions of pollutions trivially.
In the later decades, related works dedicate in exploring ways to design a more effective IEA. On one hand, they relax conventional assumptions to make the model more reasonable. On the other hand, they change the structure of the standard game and design rules to encourage participants and abatement actions in IEAs. In what follows, we focus on “Asymmetric Countries”, “Transfers”, “Minimum Participation Rule” and
“Strategic Delegation”.
Asymmetric Countries
When analyzing IEAs as coalition formation game, sovereign states are players and their choices are strategies. The assumption of symmetric players regards countries as identical, in terms of the parameters in the payoff function. The purpose of such assumption is to keep the model simple so as to get some analytical results. Most real world evidences, however, would favor that countries are not identical and consequently the conclusion may be different from that of symmetric model. For example, developed countries usually have stronger preferences for environmental quality and advanced abatement technology than less developed ones, which lead to higher benefit and cost for the same abatement level. Therefore, Barrett (1997) considers two cases assuming asymmetric countries. In the first case, countries have fully different parameters in the linear-quadratic benefit-cost function for pollutants abatement. He finds that self- enforcing IEAs can include at most three countries. In the second case, assuming two
types of countries with quadratic-quadratic benefit-cost function, an agreement can encompass lots of signatories for some parameter values. McGinty (2007) allows for fully asymmetry across countries with quadratic-quadratic benefit-cost payoff function, and overturns the conventional wisdom in IEAs with symmetric nations. The simulation results of his model suggest that self-enforcing IEA with both large size and high effectiveness4 exist. Bakalova and Eyckmans (2019) also use simulation method but consider alternative coalition making procedures. They testify the efficiency of uniform emission tax that maximizes coalition welfare and that forms by voting in both linear- quadratic and quadratic-quadratic functional forms. The outcomes confirm that without transfers, the share of self-enforcing IEAs is low. Finus and McGinty (2019) analytically examine the stability of IEAs assuming that each country has a linear- quadratic benefit-cost payoff function with individual parameters. The results show that when there is a positive covariance between the individual benefit and cost parameters of coalition members, the size of IEA can never be larger than three; however, if there is a negative covariance, even grand coalition can be self-enforcing.
In summary, when asymmetry in the benefit or cost parameters is introduced, the conclusions regarding the size of stable5 coalition are mixed. Therefore, the assumption of symmetry is deficient in analyzing the formation of self-enforcing IEAs and should be considered carefully in relevant theoretical studies.
4 Abatement effectiveness of an IEA is ( )( ) (∅)(∅)× ( )
(∅) , payoff effectiveness of an IEA is ( )( ) (∅)(∅)×
( )
(∅), where Q is total abatement and 𝜋 is total payoff. 𝜙, N, k represent the situation of non-cooperation, full-cooperation and IEA, respectively.
5 Despite the fact that “self-enforcing” and “stable” are slightly different, we use these two terms in turns to express the same meaning.
Transfers
Few participants in IEAs is an obstacle to initiate efficient actions in emissions abatement. Some scholars favor that countries that gain much from IEAs can compensate others that gain less or even lose so as to incentivize participants in IEAs.
Such compensation is formally called transfers or side-payments. Transfers have two major roles in IEAs. First, by compensating member countries’ abatement costs, transfers incentivize countries to participate and thus induce higher cooperation level.
Second, via reallocating welfare, transfers improve equality especially among asymmetric countries. Whereas, there are also some crucial problems to solve when applying this approach. To begin with, it is necessary to figure out which countries should pay the transfers voluntarily, as none of them can be forced to give up their welfare. Moreover, it is important to know how much should these countries pay and how to allocate these transfers among the receivers.
Barrett (2001) gives some instructive answers. He assumes that there are two types of country with strong asymmetry and each of them has a binary choice about either abate (A) or pollute (P). The payoff of type 𝑖 country, where 𝑖 ∈ {1,2}, when it chooses P is 𝜋 and when it chooses A is 𝜋 . It can be written as
𝜋 = 𝛼 (𝑏 𝑚 + 𝑏 𝑚 ), 𝜋 = −𝑐 + 𝛼 (𝑏 𝑚 + 𝑏 𝑚 ). (1.1)
Here, 𝑚 is the number of type 𝑖 member countries. Strong asymmetry refers to that rich countries6 have much higher 𝛼 and 𝑏 than poor ones. That is, 𝑏 is large enough relative to 𝑏 and 𝛼 is large enough relative to 𝛼 . The coalition formation is modeled as a four-stage game. In the first stage, every type 2 country moves first to choose whether or not to be a signatory. In the second stage, type 2 signatories collectively choose (i) whether to play Abate or Pollute and (ii) a monetary transfer 𝑡 to every type 1 country that agrees to become signatory and play abate. In the third stage, every type 1 country chooses to be a signatory or a non-signatory. In the fourth stage, all non- signatories of whatever type choose to play Abate or Pollute. In equilibrium, the transfer 𝑡 to each type 1 signatory satisfies,
𝑡 = 𝜋 (𝑚 , 𝑚 ) − 𝜋 (𝑚 + 1, 𝑚 ) = 𝑐 − 𝛼 𝑏 . (1.2) In other words, the transfer should quell each receiver’s incentive to free ride. After solving the game backwards, the author concludes that if the number of type 2 countries is large enough, part of type 2 countries can pay transfers to induce all type 1 countries to accede into the agreement and to play abate.
Simply assuming that countries either abate or pollute is less than reasonable, as each of them may have different abatement level even if choosing to abate. Fuentes- Albero and Rubio (2010) make advancement by defining country’s net benefit as the difference between its benefit and cost in terms of emission abatement, which is a
6 The background of Barrett (2001)’s model is the Montreal Protocol, which aims to protect ozone layer.
Since rich countries use more ozone-depleting substances, their abatement can improve the environment much more than abatement by poor ones (𝑏 > 𝑏 ). Moreover, poor countries benefit less from abatement than rich ones, because depletion is higher away from the equator, and because people with darker skin are less likely to get skin cancer (𝛼 > 𝛼 ).
continuous choice. In their model, 𝑁 is the set of type 𝑖 countries. Type 1 countries have both higher abatement benefit and cost parameters than type 2 countries, that is 𝛽 > 𝛽 and 𝛾 > 𝛾 . They analyze two cases where countries differ only in abatement benefit and where countries differ only in abatement cost.
A country 𝑗 of type 𝑖’s payoff function is
𝜋 = 𝛽 𝑄 −1
2𝛾 (𝑞 ) , 𝑗 ∈ 𝑁 , (1.3)
where 𝑞 is the abatement of this country while 𝑄 = ∑ ∑ 𝑞 is the aggregate abatement level of all countries. In the first stage, an agreement 𝑀 = 𝑀 ⋃𝑀 is formed and 𝑚 ≡ |𝑀 | denotes the number of type i member countries. Since a country’s payoff and the total abatement will depend on the composition of the agreement, we write them as 𝜋 (𝑀) and 𝑄(𝑀) , respectively. In the second stage, member countries choose abatement levels and transfers so as to maximize aggregate welfare. When transfer is added, (1.3) becomes
𝜋 (𝑀) + 𝑡 = 𝛽 𝑄 −1
2𝛾 (𝑞 ) + 𝑡 , 𝑗 ∈ 𝑀 , (1.4) where
∑ ∑ ∈ 𝑡 = 0. (1.5)
To make it clear, total transfer within the agreement is equal to zero. If 𝑡 > 0, the country receives a transfer. If, however, 𝑡 < 0, it pays a transfer. The analysis does not precisely specify how to allocate transfers in the second stage but gives the following sufficient condition for an agreement to be self-enforcing:
[𝜋 (𝑀) +
∈
𝑡 ] ≥ 𝜋 (𝑀 ∖ {𝑗}),
∈
(1.6)
[𝜋 (𝑀 ∪ {𝑘}) + 𝑡 ]
∈ ∪{ }
≤ 𝜋 (𝑀 ∪ {𝑘} ∖ {𝑗})
∈ ∪{ }
. (1.7) The underlying interpretation is that if (1.6) is satisfied, at least one transfer scheme exists to compensate each member country for its free-rider payoff and thus 𝑀 is potentially internal stable. Moreover, if (1.7) is satisfied, no self-financed transfer exists to quell each member country’s free-rider incentive which suggests that 𝑀 is potentially external stable.
The stable coalition without transfers is proved to be (𝑚 , 𝑚 ) = (0,3) and (𝑚 , 𝑚 ) = (3,0), regardless of the heterogeneity in abatement benefit and abatement cost. When transfers between countries are taken into account, the largest coalition includes all type 2 countries and at most two type 1 countries when they have different abatement benefit parameters.
A later work by Pavlova and de Zeeuw (2013) uses a similar function form as that of Fuentes-Albero and Rubio (2010). In the case of one-sided asymmetry but 𝑛 asymmetric countries, that is, 𝛽 = 1 or 𝛾 = 1, for 𝑖 = 1,2, … , 𝑛, the size of the stable coalition cannot be larger than 3. In the case of two-sided asymmetry and two types of countries, that is, 𝛽 ≡ > 1 , 𝛾 ≡ < 1, the maximal size of the stable coalition without transfers consists of two countries of type 1 and all countries of type 2, provided that 𝛽 is large enough and 𝛾 is small enough. Coalition including three type 1 countries is also stable and can induce higher total abatements. With the option of transfers, the size of largest stable coalition does not change while it is possible to relax the demands on 𝛽 and 𝛾.
The aforementioned literature focuses exclusively on internal transfers and asymmetric countries, which requires some members transfer welfare to the other
members. A seminal work by Ansink et al. (2019) analyzes the effectiveness of external transfers considering both linear-quadratic and quadratic-quadratic benefit-cost function forms. External transfers originate from Carraro and Siniscalco (1993) and mean that some free-riders, which are called “supporters”, transfer welfare to members so as to incentivize their accedence. If moderate condition about the number of supporters is satisfied, a coalition including all the remaining countries can form and all countries’
social welfare is improved.
In a word, transfers, either internal or external, are effective to induce more participants and higher abatement level in both the IEAs with symmetric and asymmetric countries. Besides transfers, some other rules have also been examined to improve the effectiveness of IEAs. A representative is the minimum participation rule.
Minimum Participation Rule
Lots of real world examples, i.e. the Kyoto Protocol and the Paris Agreement as we mentioned in Section 1.1, show that many IEAs come into force only after the Minimum Participation Rules (hereafter MPRs) are satisfied. The “MPRs” may be the number of member countries or the aggregate benchmark abatement level7 of member countries. The earlier study to analyze MPRs is Black et al. (1993), which assumes homogeneous countries and exogenous decision about the minimum number of member countries that are required for IEAs to go into effect. It is shown that inclusion of a socially maximizing MPR is able to distinctly improve the efficiency of IEAs, even
7 The benchmark abatement level is country’s abatement level when there is no cooperation..
though the resulting coalition falls well short of universal participation. This conclusion is further proved in Rutz (2001) which incorporates MPRs into a common two-stage game. He also lists 122 treaties in practice, out of which 120 require various types of participation rules. Carraro (2009) endogenizes the choice of MPRs via a three-stage game model. In the first stage, an arbitrary country proposes the minimum number of participants and the decision is made via unanimity voting by all countries. Only if the constraint is satisfied, the common two-stage game as mentioned before will be initiated.
Consistent with the conventional MPR studies, an endogenous decision can also achieve the goal of increasing the equilibrium number of member countries. As long as the participant’s payoff function increases sufficiently rapidly with the number of participants, even the grand coalition can be induced. Allowing for full asymmetry, Weikard et al. (2015) suggest that a stricter MPR stabilizing a larger coalition and full participation can be established when a country with small benchmark abatement level proposes the participation constraint.
In summary, requiring a minimum participation constraint for the agreement to enter into force is an effective tool to stimulate participation in IEAs. Even though member countries have to burden higher abatement cost, the higher benefit comes from more abatement of a larger coalition offsets their incentives to free-ride.
Strategic delegation
In all the studies we have reviewed, a negotiator of the environmental issues is regarded as a single player, i.e. the government. However, in most countries, policies in modern democracies are typically hierarchical: a principal (for example, a median voter) first
decides upon the rough orientation of the policy and then appoints an agent (for example, the elected government) to elaborate on the details of this policy; the households elect a government via pairwise majority voting to represent them for enacting environmental policies; the parliament delegates an executive to negotiate with executives from other countries about the terms of IEAs. Buchholz et al. (2005) analyze the second relationship in a two-player bargaining game and find that principals always strategically appoint agents who care less for environmental damage than themselves, and these agents always choose abatement levels lower than optimal. These incentives become stronger when cooperation is allowed, which suggests the inefficiency of IEAs.
Siqueira (2003) explores how strategic delegation impacts the consumption tax on the emissions generating goods. Similar to the last-mentioned literature, the policy maker is voted by households and thus decision of the median voter is crucial. When there are reciprocal externalities between two countries, the tax rate will be lower than that preferred by the median voter in the absence of delegation. However, when there is just unidirectional externality, delegation is largely irrelevant since voters will choose governments sincerely. In contrast to Buchholz et al. (2005), this study shows that cooperation between policy makers will bring about better result than no cooperation is allowed. In other words, whether bilateral environmental agreements are necessary and effective depends on the characteristics of environmental issues.
Segendorff (1998) compares different delegation relationships in a bilateral environmental agreement. Weak delegation means that if there is a breakdown, the agents return to the principals while in strong delegation, each principal delegates the whole decision making and commits herself not to intervene at a later stage. The case that principals make all decisions by themselves is called autarchy. It is concluded that
principals prefer weak delegation to autarchy, and autarchy to strong delegation.
Harstad (2008) investigates the efficiency of transfers when 𝑛 asymmetric parties negotiate a collective project. Those who gain much from the project will transfer welfare to those who lose. Since principals tend to delegate less green agents so as to get higher bargaining power, the project is too seldom implemented given that agents do not value the project much. Habla and Winkler (2018) shed light on the puzzle why there is no international permit market using a two-player bargaining model. After both principals determine whether to link their domestic permit markets to international market, delegated agents decide on the levels of emission permits. Finally, these permits are traded on domestic or international permit markets. The equilibrium results suggest that each principal has incentives to select less green agent and such incentives become stronger under the international market, rendering at least one country less beneficial.
Therefore, permit market fails to link despite the seemingly favorable characteristics.
These researches warn that outcome of cooperative efforts depends on how cooperative process is designed.
An interesting study conducted by Roelfsema (2007) explains why in some rich area there is no evident environmental degradation even though cooperation does not exist. The theoretical analysis proves that when median voter cares sufficiently for the environment, he will choose policy maker that cares more for the environment than himself. By doing so, there is a “race to top” in environmental taxes. However, in the poor regions, incentives to delegate less green government still exist and consequently there will be “race to bottom” in environmental taxes.
In a nutshell, most strategic delegation literature tell us that bilateral environmental agreements are useless and unnecessary in solving transboundary environmental issues.
Some explain why cooperation does not happen and some show that noncooperation will not induce bad outcomes.
1.2.2 Emission tax
In the above literature regarding IEAs, after determining the membership of an agreement, each country has to adopt appropriate instrument to control its emission level. At least since Pigou, economists favor emission tax to be an efficient instrument in regulations of pollutants. Henceforth, some studies explore the effectiveness of uniform carbon tax in the framework of IEAs. In what follows, we review some representative works.
Prices versus quotas
Charging for pollutant emissions can partially internalize the externality of environmental damage, since polluters will pay for their emissions. In a seminal paper, Weitzman (1974) considers uncertainty in marginal abatement cost and marginal abatement benefit from abatement of carbon emissions and shows that if the curve of the former is steeper than that of the latter, emission tax causes less deadweight loss than quantity control and thus is more effective. Nordhaus (2006) gives same conclusion and points out the less room for corruption from price approach in international negotiation. What’s more, negotiating an uniform price is more convenient than negotiating lots of different abatement levels. Hoel and Karp (2002) examine this
intuition for a stock pollutant in a dynamic model. It concludes that taking discount rate and stock decay rate into account, tax continues to be preferred than quotas.
Charging for global carbon emissions
For the above reasons, Cooper (2010) proposes to levy a common charge on all emissions of GHG worldwide. In principle, all countries should be covered, but his proposal could even be implemented with a small number of countries that take up most of the emissions. This study also supports to adjust the charge from time to time, and to let each country collect and keep the revenue it generated. The main merits are: 1) global charge is fair to both developed and developing countries; 2) global charge can directly change the consumption model of fossil fuels. Begin by assuming cooperative action, Weitzman (2014, 2017) postulates that an internationally harmonized, nationally collected carbon tax voted by “World Climate Assembly (WCA)” and decided via the principle of one-person one-vote majority rule, can maximize social welfare. In his blueprint, each sovereign state should designate a WCA-agent to vote for its preferred uniform global carbon tax. The key part of the uniform tax mechanism is that a countervailing force exists to internalize the externalities of global carbon emissions, since each country will burden at least part of their damage to environment.
IEAs and carbon tax
Given the priority of emission tax, but considering the irrational assumption of full cooperation, Nordhaus (2015) proposes an IEA, of which member countries need to
impose an uniform tax domestically on each unit of carbon emission. What’s more, these member countries have the rights to levy tariff for imports from non-member countries. The empirical analyses show that this approach contributes to more participants and consequently higher emission reductions.
Taking transfers among heterogeneous countries into account, Cramton et al.
(2015) propose an international carbon-price agreement to promote cooperation. First, countries pledge their highest acceptable uniform carbon tax and the result is decided via a specific rule8. Only countries that pledge the tax higher than that price would sign the global carbon tax agreement. Second, considering the heterogeneity among countries, a “green fund” exists to coordinate the transfers. If a country’s emission exceeds world-average per-capital emissions, it pays into the green fund in proportion to their excess emissions and receives payments from the green fund in proportion to their negative excess emissions.
In the conventional two-stage IEA formation model, McEvoy and McGinty (2018) replace the choice of abatement level in the second stage with uniform tax rate. After deciding their membership in the first stage, every signatory proposes its preferred carbon tax which all signatories vote to accept or reject. The final decision is determined via pairwise majority voting and upon decision, all signatories have to levy this tax domestically for each unit of carbon emission. By assuming identical country with quadratic-quadratic benefit-cost function for abatement, the result shows that a self-enforcing agreement may include at most two countries. Even though tax rate can
8 This study doesn’t provide a definite decision rule but give a possible one. For example, the highest price target acceptable to 70% of the countries (emissions-weighted) determines the global price commitment.
induce firms and individuals to burden at least part of their damage to environment, and such tax revenues will retain in the country, lack of incentives to voluntarily take actions discourages countries to participate into the uniform tax agreement. This conclusion is further testified in Bakalova and Eyckmans (2019)’s numerical simulations.
The above literature show that though scholars propose uniform emission tax as a way to combat for global warming, the result of employing it in IEAs is pessimistic given the low participation rate. Therefore, research about how to encourage participants in such coalition needs to be conducted.
1.3. Objectives
In recent years, over-emission of greenhouse gases have become the largest global environmental issue that human beings are facing. Nevertheless, both the performance of the Kyoto Protocol and the Paris Agreement are far away from satisfactory. On one hand, the number of signatories that reduce carbon emissions as required is small. On the other hand, negotiating about abatement levels has long been criticized as a less effective tool in the implementation of IEAs.
When it comes to bilateral IEAs that deal with pollutants generated within small range, whether we need cooperation or how to realize effective cooperation remains unknown. Domestic politics hugely affect the design of bilateral IEAs.
In the case of multilateral IEAs on climate change, theoretical researches have proposed some novel ways to improve the efficiency (i.e. Ansink et al. 2019). In
addition, some seminal work have tried to consider alternative regulatory policies (i.e.
McEvoy and McGinty, 2018).
However, in studies about either bilateral or multilateral IEAs, heterogeneity among countries has seldom been considered. As reviewed at the beginning of Subsection 1.2.1, assumption of asymmetric countries may overturn the major conclusions in some studies considering only symmetric countries. Inspired by these, this doctoral thesis focuses on extending recent theoretical studies in multilateral IEAs toward two directions.
First, we extend external transfers put forward by Ansink et al. (2019) to asymmetric case, in order to testify this transfer scheme in a more reasonable model.
The failure of the Kyoto Protocol can be attributed to the withdrawl of some developed countries9. Our consideration is that allowing such developed countries with high abatement benefits and costs be free-riders and financially support IEA members should be a practical way to induce higher participation.
Second, we compare the efficiency of uniform regulatory policies in IEAs under heterogeneity. Both uniform abatement level and uniform emission tax are considered.
The reason for this extension is that when countries are asymmetric, uniform environmental policy is more effective in terms of negotiation costs. Moreover, even
9 Even though signed by the Clinton administration on November 12, 1998, the US senate didn’t ratify the Kyoto Protocol which makes the US be the non-signatory. The first round signatories, Canada, Japan and Russia in 2011 stated that they would not take on further Kyoto targets. On June 1, 2017, United States President Donald Trump announced that the U.S. would cease all participation in the 2015 Paris Agreement on climate change mitigation.
though previous studies propose uniform emission tax, it hasn’t been analyzed in IEAs under heterogeneity and it hasn’t been compared with uniform abatement level, neither.
In the case of bilateral IEAs, this doctoral thesis explores how strategic delegation affects the implementation of environmental polices when countries in question are asymmetric. We find that all the previous studies regard countries as identical and studies about asymmetric nations are rare.
The main contents of this thesis are about IEAs under heterogeneity. In what follows, we explain the thesis structure which is into five chapters.
1.4. Thesis structure
In this chapter, we have briefly introduced the research background and review some important former literature.
In the second chapter, we analyze the effectiveness of external transfers in multilateral IEAs with two types of countries and two-sided strong asymmetry. To make it clear, developed countries have sufficiently larger abatement benefit and abatement cost parameters than developing ones. The game modelling IEAs with external transfers goes as follows. The developed countries move first to decide whether or not to become supporters and pay transfers proposed by the international climate agency. Then remaining developed countries and all developing countries decide whether or not to become IEA members and choose their abatement level, based on the assumption that members maximize joint payoff while free-riders and supporters maximize individual payoffs. When it comes to IEAs with internal transfers, countries
decide whether to enter into the agreement in the first stage and then member countries decide both the abatement levels and transfers among them in the second stage. We conclude that both types of transfers are effective to enlarge the size of self-enforcing IEAs, to increase the aggregate abatement level, to improve total social welfare.
Moreover, external transfers are always preferred.
The third chapter explores the efficiency of uniform abatement level and uniform emission tax in multilateral IEAs with unlimited types of asymmetric countries.
Specifically, each country has linear-quadratic benefit-cost function for pollutant abatement, and has its own benefit and cost parameters. The final result of uniform abatement level and uniform emission tax is decided via pairwise majority voting by all countries. We show that self-enforcing IEAs under neither uniform abatement level nor uniform emission tax can include more than two countries. Therefore, internal transfers may be necessary to encourage participants in IEAs.
In the fourth chapter, we investigate the effectiveness of bilateral IEAs formed by two asymmetric countries in the context of domestic politics, which is also the so-called strategic delegation. One country is developed country and another is developing country. Asymmetries exist not only in their cost parameters but also in their households’ environmental awareness. We assume that developed country has a larger cost parameter than developing counterpart. Moreover, the households in developed country value environment more than those in developing country. Our result shows that in the cooperative case, even though governments being elected are less green than the median voters, all households’ aggregate payoff and total abatement levels are increased, comparing with the case when no cooperation is allowed.
In other words, cooperation is always effective. In addition, developing country always burden higher abatement responsibility than the developed country when they cooperate.
In the last chapter, we conclude this doctoral thesis.
Chapter 2 Transfers in International Environmental Agreements under Heterogeneity *
2.1. Introduction
As mentioned in Chapter 1, theoretical researches regarding IEAs often use a non- cooperative two-stage game which originates from d’Aspremont et al. (1983) to model the formation of environmental coalitions. In the first stage, countries decide whether or not to enter into the agreement. After that, member countries jointly while free-riders individually decide their abatement levels to maximize payoffs. The resulting coalition is said to be self-enforcing if no country has the incentive to change its membership status. However, self-enforcing IEAs typically have few members when large coalition is desirable, due to the high incentives of free-riding (Barrett, 1994). Transfers, which mean that some countries give welfare to the others, have shown to be effective to quell free-riding in IEAs. In this chapter, we investigate and compare the efficiency of internal and external transfers in IEAs, assuming two types of countries that differ simultaneously in abatement related benefits and costs.
Some studies (Barrett, 2001; Fuentes-Albero & Rubio, 2010; Pavlova & de Zeeuw, 2013) have proposed internal transfers, which means that transfers are conducted within the coalition, as effective way to encourage participants in IEAs. Such studies divide countries into two types. One type is assumed to have higher abatement benefit or abatement cost parameters than another type. The result suggests a larger stable
*This study is partially based on Li and Fujita (2020).
coalition with higher aggregate abatement levels. The efficiency of internal transfers is also verified in more general model with unlimited types of countries and any degree of asymmetry using simulation (McGinty, 2007) as well as analytical method (Finus &
McGinty, 2019).
The role that external transfers plays in enlarging IEAs has also been recognized.
As Carraro and Siniscalco (1993) noted, if some free-riders commit to transfer welfare to bribe other free-riders to participate, the resulting coalition can be larger. For simplicity, we call the free-riders that provide transfers as supporters. Ansink et al.
(2019) revise this approach by introducing an international climate agency that offers transfer proposal to supporters before IEA is formed. If supporters accept such proposal, they will transfer welfare to countries who later become IEA members. It is concluded that even the coalition without free-riders (that is, only members and supporters) can be achieved if the transfer proposal is well designed. Nevertheless, countries are assumed to be identical in these literature so that more analytical results in this area are still needed.
The purpose of this chapter is to compare the effectiveness of internal and external transfers in enlarging IEAs. This idea originates from Carraro et al. (2006), which estimates the self-enforcing coalitions as well as the aggregate abatement level in a simulation model. Our study extends their work by analytically investigating the efficiency of the above-mentioned transfers separately under the assumption of two types of countries, namely, developed and developing countries. In the context of internal transfers, we contribute by clarifying the self-enforcing coalition for the model with linear benefits and quadratic costs in terms of abatement, when strong asymmetry exists. We notice that strong asymmetry is a frequently mentioned while seldomly
analyzed point in related literature (Fuentes-Albero & Rubio, 2010; Pavlova & de Zeeuw, 2013). It means that the parameters in the payoff function of countries of different types are quite different, which is reasonable for developed and developing nations. In the context of external transfers, this study reinforces Ansink et al. (2019)’s analysis by allowing for asymmetric players. That is, only developed countries that gain much from and pay much for abatement have the options to become supporters.
This chapter shows that, only a coalition consisting of three developed countries is self-enforcing under the above model setting, when no transfers are allowed. However, the largest stable coalition with internal transfers includes all developing countries and one developed country. We also show that if external transfers are implemented, all developing countries and at least four developed countries will become IEA members.
Moreover, the total abatement level and aggregate payoff is higher than that with internal transfers. In other words, both types of transfers can increase the efficiency of IEAs. Specifically, external transfers are preferred.
2.2. International environmental agreements without transfers
2.2.1 The model
Players of the game are the governments of developing (type 1) countries, 𝑛 , and of developed (type 2) countries, 𝑛 . Countries of the same type are identical and the set of type 𝑖 countries is denoted as 𝑁 . Every country 𝑗 of type 𝑖 selects a continuous abatement level 𝑞 of carbon emissions and consequently suffers loss from its own
abatement action. The aggregate abatement taken by all countries becomes 𝑄=∑ ∑ ∈ 𝑞 and will benefit each country, since it is a public good. Thus, following the literature (Barrett, 1994; Finus & McGinty, 2019), we retain a representative country’s social welfare as follows,
𝜋 = 𝛽 𝑄 −1
2𝛾 ∙ 𝑞 . (2.1)
It may be overly simple to reflect the countries’ real welfares. However, we apply it for the following reasons. First, it allows us to obtain analytical solutions and avoid heavy calculation burden as well. Second, we can compare our results clearly with those of previous studies (Barrett, 1994; Finus & McGinty, 2019).
Although exception exists, following Chou and Sylla (2008), we assume that developed countries have both higher abatement benefits and steeper abatement cost curve than developing ones. That is, 0 < 𝛽 < 𝛽 and 0 < 𝛾 < 𝛾 . This assumption is convincing for the following reasons. Developed countries have higher environmental awareness and thus, value environment more than developing countries. Henceforth, the same abatement level will benefit them more. Meanwhile, developed countries already have exploited advanced abatement technology, so that achieving an extra unit of abatement will cost them more. Moreover, in Nagashima et al. (2009) which employs a simulation model to investigate the stability of climate coalitions, Japan and European countries are also assumed to have larger abatement benefit parameter and larger abatement cost parameters than the less developed ones, i.e. former Soviet union and India, which suggests the validity of our assumption. Recall that Pavlova and de Zeeuw (2013) apply a similar model but allow for negative covariance between benefit and cost parameters without clarifying developed or developing nations. As we will show in
later part, our result about the self-enforcing coalitions is also different from that of Pavlova and de Zeeuw (2013).
We use a two-stage game to model the formation of IEAs without transfers. In the first stage, each country decides simultaneously whether to become a signatory of an agreement or a non-signatory. Then an agreement 𝑀 = 𝑀 ⋃𝑀 is formed and let 𝑚 ≡
|𝑀 | (correspondingly 𝑚 ≡ |𝑀 | ) denote the number of developing countries (correspondingly developed countries ) being part of an agreement. In the second stage, the signatories collectively choose abatements to maximize their total payoffs while each non-signatory chooses that to maximize individual payoff.
In what follows, we will derive the subgame perfect Nash equilibrium (SPNE) of the two-stage game by backward inductions.
2.2.2 Choice of abatement
Solution of the second stage is each country’s abatement level, given that a coalition M is formed in the first stage. The first-order condition for a signatory 𝑗 ∈ 𝑀 is
𝜕 ∑ ∑ ∈ 𝜋
𝜕𝑞 = 0, (2.2)
which yields 𝑞 = . Let us denote it as 𝑞 (𝑚 , 𝑚 ). Correspondingly, the first-order condition for the non-signatory 𝑗 ∉ 𝑀 is
𝜕𝜋
𝜕𝑞 = 0, (2.3)
which yields 𝑞 = . Let us denote it as 𝑞 . Thus, the aggregate abatement becomes
𝑄(𝑚 , 𝑚 ) = 𝑚 (𝑚 𝛽 + 𝑚 𝛽 ) + (𝑛 − 𝑚 )𝛽
𝛾 +𝑚 (𝑚 𝛽 + 𝑚 𝛽 ) + (𝑛 − 𝑚 )𝛽
𝛾 .
(2.4) From the above equations, one can easily conclude that a free-rider’s payoff is always higher than that of a member country of the same type. Taking partial derivatives of eq.(2.4), we find that ( , )> 0 and ( , )> 0, which suggests that total abatement level will become higher if more countries, no matter which type, enter into the agreement. In addition, a free-rider always gains from the enlargement of coalition since its benefit becomes higher while the cost remains identical.
2.2.3 Self-enforcing agreements
In the first stage, countries simultaneously choose whether to sign and the agreement is formed by countries who have signed. An IEA including 𝑚 developing countries and 𝑚 developed countries is self-enforcing if it satisfies the following internal and external stability conditions. Let 𝜋 and 𝜋 denote social welfare of a type 𝑖 signatory and non-signatory, respectively. They depend on the agreement size.
Internal stability
A developing country that is a signatory does not increase the payoff if it becomes a non-signatory,
𝜋 (𝑚 , 𝑚 ) ≥ 𝜋 (𝑚 − 1, 𝑚 ). (2.5)
A developed country that is a signatory does not increase payoff if it becomes a non- signatory,
𝜋 (𝑚 , 𝑚 ) ≥ 𝜋 (𝑚 , 𝑚 − 1). (2.6)
External stability
A developing country that is a non-signatory suffers loss if it becomes a signatory, 𝜋 (𝑚 , 𝑚 ) > 𝜋 (𝑚 + 1, 𝑚 ). (2.7) A developed country that is a non-signatory suffers loss if it becomes a signatory,
𝜋 (𝑚 , 𝑚 ) > 𝜋 (𝑚 , 𝑚 + 1). (2.8)
Using payoff function (2.1) and conducting some manipulations, we rewrite the above inequalities as follows.
Internal stability for a developing country:
𝛽 𝛾
−(𝑚 𝛽 + 𝑚 ) + (4𝑚 𝛽 + 2𝑚 − 3𝛽)𝛽
2 + 𝑚 𝛾𝛽 ≥ 0. (2.5 )
Internal stability for a developed country:
𝛽 𝛾
−(𝑚 𝛽 + 𝑚 ) 𝛾 + (4𝑚 + 2𝑚 𝛽 − 3)𝛾
2 + 𝑚 ≥ 0 . (2.6 )
External stability for a developing country:
𝛽 𝛾
(𝑚 𝛽 + 𝑚 ) − 2𝑚 𝛽
2 − 𝑚 𝛾𝛽 > 0 . (2.7 )
External stability for a developed country:
𝛽 𝛾
(𝑚 𝛽 + 𝑚 ) 𝛾 − 2𝑚 𝛾
2 − 𝑚 > 0 . (2.8 )
Here, 𝛽 ≡ and 𝛾 ≡ (𝛽, 𝛾 ∈ (0,1)). Note that, since 𝛽 and 𝛾 measure the difference of abatement benefits and costs between developed and developing countries, we say strong asymmetry exists if both of them are close enough to 0. By making such an assumption, we recognize the fact that the gap between developed and developing countries is very large, as suggested in some empirical studies (Nagashima et al. 2009).
The result after checking (2.5’) to (2.8’) is summarized in the following proposition.
Proposition 2.1. Under strong asymmetry, the unique self-enforcing international environmental agreement without transfers includes three developed (type 2) countries.
Proof: See Appendix A.1. ∎
Consistent with most former literature (Finus & McGinty, 2019; Fuentes-Albero &
Rubio, 2010), an intuitive result in Proposition 1 is that asymmetry, at least of this type, does not work automatically. That is, it does not increase the size of IEAs. The crucial part in our analysis, however, is that we verify the identities of IEA members when the difference between countries is large. In Pavlova and de Zeeuw (2013), which assumes a negative covariance between the benefit and cost parameters of the two types of countries, the largest size of a self-enforcing IEA can include two countries of one type and all countries of another type. Therefore, our result strongly depends on the assumption about the type of asymmetry between developed and developing countries.
Given that few countries sign IEAs, in what follows, we resort to transfers to encourage participants.
2.3. International environmental agreements with internal transfers
The option of internal transfers is a common and useful way to enlarge coalition since it allows member countries who gain from cooperation to compensate those who gain less or even lose. Thus, a larger number of countries have no incentives to leave the coalition.
In most previous studies (Carraro et al., 2006; Weikard, 2009), internal transfers are decided through optimal transfer scheme, which means that aggregate welfare will be reallocated within the coalition such that each member gets at least its free-rider payoff. In what follows, if we talk about internal transfers, we mean the optimal transfer scheme. For an agreement 𝑀 = (𝑚 , 𝑚 ) to be internally stable with internal transfers, the following condition, which is also the so-called potential internal stability, should hold.
𝑚 𝜋 (𝑚 , 𝑚 ) + 𝑚 𝜋 (𝑚 , 𝑚 )
≥ 𝑚 𝜋 (𝑚 − 1, 𝑚 ) + 𝑚 𝜋 (𝑚 , 𝑚 − 1)
(2.9)
The left-hand side of the inequality (2.9) is member countries’ total welfare when coalition 𝑀 is formed while the right-hand side shows the sum of member countries’
free-rider payoffs. Given the above inequality, it is clear that internal stability conditions ((2.5) and (2.6)) will always hold under optimal transfer scheme, since the aggregate welfare is enough to cover each member country’s free-rider payoff. Note that if neither 𝑀 = (𝑚 + 1, 𝑚 ) nor 𝑀 = (𝑚 , 𝑚 + 1) satisfies potential internal
stability, 𝑀 = (𝑚 , 𝑚 ) is externally stable. Rewriting (2.9) leads to the following inequality:
𝛾𝑚 [(𝑚 − 2)𝑚 𝛽 + 2(𝑚 − 1)𝑚 + (𝑚 − 1)(𝑚 − 3)]
+𝑚 [𝛽 (𝑚 − 1)(𝑚 − 3) + 2𝑚 𝛽(𝑚 − 1) + 𝑚 (𝑚 − 2)] ≤ 0.
(2.10)
The classical result in this type of model is that all countries of one type are willing to enter into the agreement when in the agreement there is only one or two countries of another type (Pavlova & de Zeeuw (2013) for two-sided asymmetry, Fuentes-Albero &
Rubio (2010) for one-sided asymmetry). In the context of two-sided strong asymmetry, however, a coalition with just one developed country is more likely to be stable because in the other case, (2.10) can only be satisfied if 𝛽 is much smaller than 𝛾. In other words, strong asymmetry will increase developed country’s free-rider incentive when internal transfers are allowed. This is summarized as follows.
Proposition 2.2. With the option of internal transfers, the largest self-enforcing coalition consists of one developed country and all developing countries if strong asymmetry exists.
Proof: See Appendix A.2. ∎
Comparing with Proposition 1, the implication of Proposition 2 is straightforward:
more countries are willing to sign the agreement if they are compensated by other member countries. The difference from the result in Fuentes-Albero and Rubio (2010)
also shows that strong asymmetry will increase a developed country’s incentive to free ride when internal transfers are allowed.
To gain insights on how the internal transfers affect total abatement, we compare the result with that when no transfers is allowed. According to eq.(2.4), the aggregate abatement level under the self-enforcing coalition with internal transfers is 𝑄(𝑛 , 1) =
( )
+( ) ( ) . A simple manipulation shows that
𝑄(𝑛 , 1) − 𝑄(0,3) = [𝑛 𝛽𝛾 + (𝑛 − 1)𝑛 𝛽 + 𝑛 − 6𝛾]. (2.11)
Since the sign of eq.(2.11) is always positive, it is clear that both the size of coalition and the abatement of emissions will increase, owing to the internal transfers. Let us further denote the total social welfare as 𝜋(𝑚 , 𝑚 ), which can be written as
𝜋(𝑚 , 𝑚 ) = 𝑚 𝜋 (𝑚 , 𝑚 ) + (𝑛 − 𝑚 )𝜋 (𝑚 , 𝑚 )
+𝑚 𝜋 (𝑚 , 𝑚 ) + (𝑛 − 𝑚 )𝜋 (𝑚 , 𝑚 ).
Given that 𝜋(𝑛 , 1) − 𝜋(0,3) > 0, if 𝑛 > 12 and 𝑛 > 7, total social welfare is also increased.
2.4. International environmental agreements with external transfers
In this section, we turn our attention to external transfers which may be promising to encourage participations in IEAs. This transfer scheme requires free-riders, namely supporters, that do not abate by themselves to provide financial transfers to countries who later enter into the IEAs. The concept of external transfers originates from Carraro
