Climate Mitigation. and the. Importance of Networks and Centrality. Global Public Goods Provision

Transcription

1 Climate Mitigation and the Importance of Networks and Centrality in Global Public Goods Provision Draft paper To be presented on EPSA Conference Milan 2017 **Please do not circulate or cite** Authors: Rutger Hagen Christophe Crombez

2 Introduction In 2015 the Climate Summit in Paris (UNCCC 2015) introduced a period of enthusiasm concerning the capabilities of the international community in tackling global problems. At that conference nearly all countries on the world agreed on the need for policy measures to battle climate change. National measures in every participant were deemed necessary in making sufficient progress. But on the first of June 2017 the United States, historically the largest polluter, announced that it would withdraw from the accords since the USA can put no other consideration before the wellbeing of American citizens 1. This paper will look into the dynamics of such a refusal, why does a country such as the USA decide to stay on the side line of such an important issue? And why do other countries do still commit to take costly mitigation measures even in view of non-compliers? Countries differ in their need and wishes to curb climate change. This can be due to a favorable geographical location or the presence of polluting industrial activities. Paradoxically the developed countries in North-America and Europe exhibit a low risk when temperatures and sea levels rise 2, while they are the main contributors to global warming. Since developing countries are the main victims of climate change the standard Coasion solution for negative externalities cannot work. The countries that have the largest incentive to halt climate change are also the ones who are the least responsible for the problem and have the least financial leeway in paying the industrialized countries and emerging economies to stop their polluting ways (Bernauer, 2013). The ability of the countries of the world to combat climate change is thus hampered due to their differentiating needs. Geography and the local interests of polluting industries influence the motivational vigor of countries to engage in climate mitigation. How the linkages between countries can influence the willingness of countries to increase their expenditures on climate mitigation is a subject we will attempt to shed more light upon. In this paper we will try to explain why countries are willing to spend their resources on something that, at first sight, does not benefit them directly, using a public good framework. Samuelson (1954) was one of the first economists that was theoretically interested in the provision of public goods. In his seminal article The pure theory of public expenditure he devised a distinction between certain types of goods based on two characteristics: Excludability and Rivalry. A public good distinguishes itself because it is non-excludable; meaning that it is impossible or at least very difficult and costly to exclude actors from consuming it, while at the same time being non-rivalrous; which in turn means that the good does not diminish when it is consumed (meaning that excluding actors from the resource is also unnecessary). Classical examples of these type of goods are street lights or lighthouses. Public good theory suggests that a public good is ever in danger of being underprovided, especially when the benefits of the provision are hard to measure and when interests of 1 President Donald J. Trump; Statement on the Paris Climate Accord, 1 st of June

3 contributing partners are diverse (Ostrom and Ostrom, 1977). In addition to this, agreements on climate change are made on a strict voluntary basis without any specified penalty when rules are broken. Climate mitigation is oft coined as a Global Public Good (GPG). This came into popular use after the publication of the book Global Public Goods by Inge Kaul and her associates (1999). In this book not only the potential of GPG provision is discussed but also the problems and pit falls that can occur when these goods are provided. Just as with local public goods provision the main problem in an international sphere remains the danger of under provision that is mainly caused by free (or cheap)riding. Since public goods are nonexcludable it is difficult to let consumers pay for their usage, since its benefits cannot be targeted to special groups (Lizzeri and Persico, 2001). Since consumers know this, they tend to express a lower personal demand than their social optimum really is to avoid higher general taxes (see for instance Hirshleifer, 1983). In the international realm, though individuals remain the real end-consumers, the states express the collective need for GPGs. GPG theory usually assumes that states act as unitary rational actors on the international stage. When we zoom in on climate change mitigation we clearly see that although there is a general consensus in the scientific community that reducing CO² levels will help counter global warming and its devastating effects countries have, as of yet not acted accordingly and their efforts in provision remain below the theorized social optimum. In the next section we will give a short overview of the literature concerning the provision of climate mitigation measures, where we will focus on the interstate relations and the reasons why some countries have achieved a higher provision level than others. After that section we will look more closely at the possible influence of networks on provision levels zooming into Bonachich (1987) centrality. We will then introduce our modified theoretical model, which, we believe, gives a new insight in why and how countries can work together without the benefit of direct penalties for rule breakers or an international system that can force countries to comply and why some other countries can afford it to remain unresponsive. That the behavior of countries on the world stage is affected by their peers is an oft made observation. But observing and measuring these effects is more difficult. Many studies operationalize them as average group externalities that effect all members equally or fail to set group boundaries for these effects that are arbitrary. In this paper we pres ent a model where we relate Nash equilibrium behavior to network location using Katz-Bonachich centrality. We assume that climate mitigation output is separable into an idiosyncratic output and also has a peer-effect. These peer-effects aggregate at the group level, and helps explain why we observe certain group dynamics on the international stage. This paper contributes by introducing a network model of climate mitigation in a GPG-game for a research area that although it has made large empirical breakthroughs has of yet disregarded to a large extend the influence of networks. This paper is an attempt to close this theoretical gap, and could be a potential guide for future empirical research.

4 Kyoto and Paris Barrett (1998) distinguishes 5 distinct phases in international negotiations on climate change: Pre-negotiation; which can be seen as a form of cheap talk by signaling to other parties what you would be willing to accept. Negotiation; such a negotiation not only takes place on account for measurable outcomes but also on treaty design, voting rules and deadlines. All of which will be influencing the main outcomes. Ratification; which can be viewed as the second stage of the game, now being played out on the national level (Putnam, 1988). Implementation; or the passing of domestic legislation and finally Re-negotiation. Although all aspects are important, this paper will focus on the implementation part. This is, in our view, the most telling since true actions of countries are fueled by more than cheap talk alone. Bernauer (1995) stresses the importance of institutions in determining the behavior and output of states. Although one could also argue that the design of institutions simply reflect the existing distribution of power such as the proponents of realism do. When following that logic institutions simply cease to exist when they no longer are beneficial to the participants Evidence for such a relation remains inconclusive. For our coming discussion it is relevant to review the two largest climate agreements ever conducted. Kyoto was a large breakthrough in The basics of the treaty obliged the industrialized countries (or annex B countries) to cut their greenhouse emissions by on average 5% on 1990 levels by The goals of these countries all differed somewhat based on their individual situation at that time. The other signatories consisted mostly of nonindustrialized countries in the global south, including China and India. These countries faced no such obligations but agreed to encourage green growth. The rationale behind this divide was that developing countries only had a small role in the current climate problems and that cutting back on emissions would hurt their emerging economies disproportionally. This argumentation was, in the end, not backed by the USA, and although the Clinton administration did sign the treaty, Congress eventually blocked ratification after which the USA withdrew in Thus leaving the 2 largest polluters: China and the USA without any legal restrictions to cut their emissions. In 2005, however, Russia decided to join the treaty. When Russia joined the number of signatories grew to account for 55% of emissions, enough to activate the treaty. Although all the signatories cannot really be held accountable due to the characteristics of international law the largest polluters (USA and China) faced no restrictions at all. Still the other industrialized signatories upheld the treaty and even managed to cut back their emissions, with not just 5% but with a staggering 22.6% (UNFFCC, 2015). Still this was not enough to lower CO² levels overall and Kyoto was seen by many as a failure. It is, however, extraordinary that not only was the treaty signed by most countries, in full knowledge that the largest polluters abstained from taking any measures. It was also uphold and the GPG was even oversupplied in some cases, whereas public good theory would suggest an under provision. Researchers were puzzled by this outcome and found that many countries were already busy implementing carbon restriction measures before the Kyoto treaty took effect (Bernauer, 2013).. This shows an interesting dynamic that this paper will try to explain.

5 The Paris 2015 UNFCCC has been a breakthrough in many ways and is a depart of the kind of agreement Kyoto was. First of all it is a truly global accord; applying to all signatories and not just the developed nations. Second it is a flexible instrument, thereby learning from the outcomes of Kyoto where some signatories strongly outperformed others. Paris adopted a flexible approach, accounting for different and changing circumstances in the participating countries with new negotiations every 5 years. To ensure transparency a justification network will be set up, allowing countries to monitor developments elsewhere. Although Paris will still fall short in solving the climate problems, it, if indeed implemented, will lead to a staggering decrease of emissions, even now the USA will no longer ratify the treaty (Bodansky, 2016). The logic of Paris follows in the academic footsteps of Urpelainen (2013) who advocated a similar approach of making small gains now, that are politically feasible, to realize large gains later on possible. This can be done since technological innovation can facilitate ambitious mitigation activities in the future. While political transformation can create green constituencies that will support more ambitious efforts. Bernauer (2013) also stresses that a focus on regime design solutions can give valuable insights but is not enough to truly understand its mechanics. Special attention must be given to the variation between the contributions of different political entities on the GPG. The ability to view the results and learn from others is key in the Paris accord. Paris has in effect created a network where actors can influence each other. Adaptation or Mitigation Roughly countries can either decide to lower its own emissions to make overall CO² levels drop, or invest in adaptation, such as the raising of dikes. Adaptation measures can thus be seen as private goods since they benefit only one country. Bernauer (2013) found that rich states are more likely to invest in climate adaptation measures than in climate mitigation to avoid becoming the victim of free riders ( Bernauer,2013). When investing in adaptation a country can directly reap the benefits from it without being dependent of others. The same results have been found by Polk and Schmutzler (2015). They explored the strategies polluting industries use in lobbying for new environmental policies. Industries can either work together and lobby for laxer overall policies, or try and achieve a loophole that benefits only their own businesses. The authors conclude that vying for loopholes often results in higher social optimums than when industries lobby for general lobbying. This is the case since it eliminates free rider incentives and leads to a higher effectiveness. Their results can be extrapolated to the international level, where high polluting countries were also able to lobby for laxer policies at the Paris Climate Conference, and in the case for the USA, finding the ultimate loop hole of non-compliance. Bailer and Weiler (2015) also found evidence that private benefits and costs of individual countries are detrimental in explaining their negotiation positions. Countries that are more vulnerable to the effects of climate change would be more willing to cooperate and finding compromises than countries who, do and shall, not feel extra burdens when global

6 temperatures rise. All these results illustrate that although GPGs require collective action, it are often private motives that initiate them. Climate mitigation as a GPG or Joint Product Public good theory suggests that a public good is in danger of being underprovided, es pecially when the benefits of the provision are hard to measure and when interests of contributing partners are diverse. In addition to this, most international agreements, including those on climate change are made on a strict voluntary basis without any specified penalty when rules are broken. But then why is climate mitigation provided anyway? We argue that, through country linkage and polycentric governance, provision levels can be much higher than public good theory alone suggests. This paper builds on the state-of-the-art literature on coalition building by using game theoretical insights. Providing climate mitigation yields public but also country-specific benefits. Next to lowering global temperatures climate mitigation can also be beneficial for the own economy. When cleaner technologies are developed it can give a huge boost to a country s knowledge sector. Or can prove to be harmful, so that country specific costs are incurred, for instance when a state has a huge oil or gas industry. This makes climate mitigation an impure public good, or in other words a joint product (Sandler, 1992). The benefits or costs a country incurs are not solely dependent on its own contributions. They also spill in from other countries. A higher demand for solar energy in country A can lead to a rise of solar panel exports in country B. While it is evident that global contributions remain too low to counter the effects of climate change it is unexpected to see that there is a large heterogeneity when viewing it from a crossnational perspective (Bättig and Stern, 2009). Several small states and even subnational political units, such as cities, have adopted ambitious climate mitigation targets. This is surprising because, according to the exploitation hypothesis that sprouts from public good theory, rich actors make larger contributions to the public good than poor ones. Resulting in their exploitation in the strategic context of a contribution game (Sandler, 1992). These results show that solely looking at compliance by countries to the injunctions set by an institution (Bernauer, 1995) might not be giving us a complete picture. Since some states will even over comply and may overvalue the importance of institutions themselves. We argue that not so much formal institutions shape state behavior, but that linkages with other countries are important, whether they are visualized in treaties or remain more obscure in direct contact. Governments acting on the world stage can be seen as chess players that have to win two different games, a domestic and international one, but are only permitted the same moves on both boards. Interest groups and voters together with international pressures determine the stance of governments in climate mitigation. Considering this it is not surprising that the type

7 of government is seen as important by many scholars on this subject. Bättig and Stern (2009) focus in their study on the role of democracy. They empirically show that democracies tend to have a higher climate mitigation policy output than their less liberal counter parts. However, the same effect is less evident when they measured emissions. Their higher compliance level can be explained by the higher internal pressures to democratic countries to act more cooperative on the international stage. Several authors stress the importance of reciprocity as a way to defeat the prisoners dilemma that is often used to describe climate policies. States would be more inclined to halt climate change if they would be able to instate strict reciprocity measures and monitoring and enforcement procedures would be present (Ostrom, 1990: 90). Such is only possible when countries are closely linked on multiple issues and arena s since it is not possible to enforce a climate agreement directly. But the fact that there are no concrete enforcement mechanisms present because of international unwillingness does not mean that negative actions taken by states on climate mitigation are without repercussions. Canada received much backlash after it withdrew from the Kyoto protocol (Bernauer, 2013) and also the USA now faces a more and more adverse international stage after it denounced the Paris accord. But achieving reciprocity is difficult when it is hard to know the exact contributions of others but also how much contributions are really needed. One of the difficulties, identified by Barrett and Dannenberg (2012), in achieving successful collective action in climate governance is the high level of uncertainty. It has of yet, been impossible to identify a threshold for when catastrophic climate change will occur. The proposed maximum of a 2 C rise which is mentioned in the Paris treaty is still a very broad estimate, and most likely not enough to curb devastating effects. This high level of uncertainty makes it difficult to propose and maintain a collective action target. Which leads to outcomes that lie well below the social optimum. We argue that countries that have a high level of interconnectedness will have a shared understanding of the threshold and will mimic each other in their climate mitigation measures. Ínterconnectedness While true network analysis is mostly absent in main stream literature in this area, its subject matter is discussed widely. We have seen that high reciprocity and low uncertainty seem key in the provision of GPGs. An interesting way to achieve this is by linking actors and issues closer together. Axelrod (1984) already argued that increased interactions can help countries in achieving successful collective action since its extends the future horizon. An extended horizon means that small immediate gains that can be achieved by deviating from collective action no longer outweigh higher long term benefits achieved by cooperation. Following this line of reasoning Axelrod and Keohane (1985) argue that IO membership fosters cooperation and reciprocity while at the same time delegitimizes defection of agreed measures. Increased interconnectedness should thus foster policies that reflect a higher public goods provision level concerning climate change (Bernauer et al., 2010). Higher interconnectedness can also facilitate vote trading from one policy area to the other (Tollison and Willett, 1979) resulting in higher cooperation between states. A loss of reputation when rules are broken in a policy

8 arena can also be of importance. It can namely lead to ostracization by other members of the group, effectively punishing the rule breaker. Reputational damage can thus counter opportunistic behavior. For such a mechanism to work efficiently a society needs good information networks and credible punishment strategies. Bernauer and Koubi (2009) did find evidence that extensive IO membership leads to a higher provision public goods provision level. This is also in accordance with Neumayer (2002) who finds that democratic countries are not only more likely to join international climate initiatives, they are also performing better with respect to the set requirements of these agreements. Bailer and Weiler (2015) did not find evidence of any of such relations, however. They instead conclude that a country s vulnerability to climate change in combination with its power and democratic status is important in determining negotiation positions while IO membership is not. The authors usage of IO membership as a proxy for international interconnectedness. This is, however, by default a very crude and limited instrument which is unable to catch all the finesses surrounding international contacts. While understanding linkages in explaining virtually all public goods provisions, it is paramount in climate mitigation since the GPG itself is very interlinked. It has implications on the entire development spectrum ranging from every climate sensitive to emission sensitive sector in finance and governance (Tanner and Allouche, 2011). Bernauer et al. (2010) do discuss the importance of linkage relative to domestic factors that can influence global governance efforts. But they and most authors do not acknowledge possible spillins from states with whom they are linked. They focus more on the interdependence states have in the international system. And by this assume that more linkage will always result in more cooperative behavior. When this indeed would be true it fails to explain the non-compliance of the USA, while virtually all other countries do support the outcomes of the Paris UNCCCC. Our approach modifies this and will take into account that not all entanglement of states is equally important or works in the same way. Networks Ostrom, Tiebout and Warren coined the term polycentric governance in an article on the organization of government in metropolitan areas (1961). Since that time the concept of polycentricity has been used to address many collective action problems in the sphere of public goods. Vincent Ostrom (1999: 57) defined polycentricity as one where many elements are capable of making mutual adjustments for ordering their relationships with one another within a general system of rules where each element acts with independence of other elements. Whereas Ostrom mostly focused on local governance polycentric governance is also very well applicable on a global scale where issues that are multi-sectoral and multi-level in nature. The interests of citizens no longer lie on just local, regional or even national levels. Globalization has made is paramount that resources must be managed on a global level as well. In this paper we will focus on how polycentric governance can help explain on how global

9 governance effectively works and how global initiatives that require the active participation of a variety of actors can work. The insights on the influence of networks on public goods provision are relatively new. Bramoullé and Kranton (2007) were the first to use it in that field. Their analysis consisted of a distinction between specialized and hybrid contribution equilibria under complete information, whereby in some instances individuals would contribute, while others freeride as an extreme. And in others specialization would take place when contributors are linked, collectively to new agents. Several studies have shown that network analysis can help explain various economic interactions (Goyal, 2012; Jackson, 2010) such as development and labor economics. That linkage not necessarily lead to higher public good provision is contested by Buchholz et. al. (2014). In their game-theoretical model the show that country coalitions not necessarily achieve higher provision level when there is only partial cooperation. The opposite can be true when a coalition withholds GPGs and let the non-participants pay for them. In our paper we are interested in how individual network positions affect individual actions. The most used centrality measures are degree centrality, betweenness centrality, closeness centrality and eigenvector or Bonachich centrality (Jackson, 2010). They are so popular since they are able to give us a micro-perspective on the links a specific node has in a network while a macro perspective cannot give us the same in depth view. In our paper we will use Katz-Bonacich centrality (Bonachich, 1987) also known as Eigenvector centrality. The basic premise of this type of network is that an actor is more central when there are more connections in their local network. The power of an actor is derived from the connections it has with the powerless. When there are few connections in a local network this means that within that network the actor is more powerful. Bonacich thus departed from the idea that actors with more connections are more likely to be powerful also known as Freeman s centrality (Freeman, 1978). That, at first sight seems logical, since someone with more connections is more likely to be powerful since he can influence other actors more. But having the same degree of connections does not make actors have the same importance. As an example we can look at the world stage. Suppose the USA and Russia both have the same direct ties with other countries. But the closest allies of the USA also have a lot of connections since they are open democracies while the allies of Russia are much more isolated and have fewer outside connections. While one could argue that the USA is more influential in its network since its friends have more friends than the ones of Russia. But it is also possible that demands of the USA are more likely to be ignored by its allies because they have more connections to fall back on. Bonachich s argument is that having more connections makes you central, but not powerful per se. You achieve power by being connected to actors that themselves are not well connected.

10 When a country is more powerful in an international context some authors hypothesize that they are also less willing to cooperate with others because they can influence negotiations to fit their interests (Grundig, 2006). And since the economic power of a country is closely related to the size of their emissions it is hypothesided by Bailer and Weiler (2015) that these countries are less willing to assume cooperative bargaining positions. Bernauer et al. find evidence that powerful states are less likely to ratify a treaty. Rich (GDP wise) countries thus seem to be able to get away with less co-operative behavior. This is in accordance with Katz- Bonachich centrality whereby powerful nodes can influence less powerful ones they are in contact with, but are prone to react less to outside stimuli. The Katz-Bonacich centrality counts the full number of direct and indirect paths of any length for each node in a network. By using a geometrically decaying factor the paths are weighted. Its results thus depend on the typology of the network, as well as on the value of the decaying factor. Our theoretical result establishes that our peer-effects game has a unique Nash equilibrium where each agent s strategy is proportional to its Katz-Bonachich centrality measure. The nuance of Bonachich centrality is lost when authors of empirical papers solely look at the number of international organization memberships a country has assuming that it accounts for more compliance to international standards. The opposite could well be true, better connected states can disregard international climate accords more, because they are less dependent on keeping a high reputation on just one policy area. Theoretical Framework Our model is an example of a network game (for more uses of such games please refer to: Jackson, 2010; Gallop, 2016; Larson, 2016) In such a game the actions of country I are linked and in response to the actions of country j. The best response in climate mitigation in equilibrium is given by the direct and indirect ties with other countries. Country s i private benefits go up when country j increseases his spending. When a country has more of those ties its Bonacich centrality score (Bonachich, 1987) goes up. Our model argues that countries with a high Bonacich score have a higher chance of increased climate mitigation spending since these countries are subjected to more positive spillin effects than those with few ties (Ballester et al., 2006: 104). When objectives and goals are shared within a group of countries it provides them with private benefits and thus incentives to spend more on climate mitigation. These effects are not only present in direct links between country i and j, but also indirectly, for instance when j and k are working together in combating climate change it benefits country i indirectly. A network emerges when these policies are complimentary such as in the case of climate mitigation. Private benefits emerge in various ways. Not unimportantly public support for climate expenditures may lower when citizens observe that other countries are not carrying their load.

11 However, when it is observed that climate change is taken seriously by other countries it may lead to support for these policies and the politicians advocating them. A joint effort also leads to higher chances of success. If climate change is indeed halted or slowed it leads to lower private expenditures for climate adaptation. When dikes no longer have to be raised and farmland does not have to sacrificed to higher sea levels it yields immediate positive private benefits. The improved rate of success clearly depends on uniform policy preferences of countries involved. When policies fail, it is costly. Not only do countries that did participate in Kyoto have high expenditures, relatively to non-participants, they are even more at a disadvantage. Network analysis finds its origin in sociology, dealing with social relations and interactions between individuals. Jackson (2010) argues that all relationships can be seen as a network, no matter the actors. Network analysis has been used in international relations studies to explain why certain international networks exist and how they are maintained, for instance in trade (Hafner-Burton et al., 2009). Dorussen and Ward (2008) argue that the success of several of these networks are successful because they are able to harmonize the preferences of the participating countries. In our model we analyze how international networks are created and what the role of complementary preferences is when establishing them (Maoz & Joyce, 2016).Our model is an adaptation of Ward and Dorussen (2016) who in turn were inspired by the work of Ballester, Calvó-Armengol & Zenou s (2006) and Calvó-Armengol, Patacchini & Zenou (2009). Whereby we focus on the spillins, or spillouts of potential private benefits of country i when country j increases its contribution. Such a decrease is in theory possible when the preferences of these countries are misaligned and another state would actually benefit from climate change and so would incur private costs when confronted with climate mitigation efforts by others. The Model Consider there are n countries. The financial contribution of country i in climate mitigation is noted as: x i 0 The utility of country i is a function of the contributions of all other countries in the system: j i u i (x 1, x 2,, x i,, x n ) = α (x i + x j j i (1) ) + πx i σ iix i 2 + σ ij x j x i j i

12 The first term of the model represents the total gains of country i of the total production of the public good which are linear with i s own contributions. Or in other words, the full sum of the contributions of all countries when: α 0 The second term deals with private benefits that solely depend on the contributions of i, for instance the difference for a developed country compensating developing countries or investing in clean technologies that benefit local companies. Bernauer (2013) considers this perhaps the most effective option since, although new technologies require massive investments, new technologies that come into use are quite cheap due to economies of scale and network effects. In our model we assume that these private benefits exist: π > 0 Our third term represents the costs of country i for climate mitigation, where for all country s i: σ ii A = σ > 0 When we take these first three terms together the payoffs of i are strictly concave in its effort. The fourth term is the representation of the complementary production of private goods. When it is positive: σ ij > 0 The policies complement each other and the private benefits of country i increases with the efforts done by country j. But would the term be negative: σ ij < 0 The private benefits of country i are reduced when others supply the public good. This is in this case perhaps counterintuitive but some countries will not benefit from cleaner economies. When the demand for oil goes down because renewable energy sources become more popular, several states in the Middle East will incur private costs. If we rearrange (1) we can group the costs for climate mitigation together with the effect of negative complementarities. We can do this by adding the following notations: σ min = min {σ ij i j} σ max = max {σ ij i j} We assume that the payoff of i is concave with its own effort:

13 σ ii < 0 σ ii < min {σ min,0} And the marginal returns of i in accordance with its own efforts decrease at the same rate as the private returns component complimentary to j, when: If we set: And assume that: σ min < 0 γ = min { σ min,0} 0 λ = σ max + γ λ > 0 So that at least in some instances private benefits increase together with the efforts of these countries. ʎ represents the attenuation factor, a term that originates from physics. It is the gradual loss of intensity of any flux when travelling through a medium, in this case a network. When countries are less well connected the influence of Country j on Country i diminishes and vice versa. When we then norm the term g ij to σ ij on an interval of [0,1] we set: For: g ij = (σ ij γ) λ j i And: g ii = 0 We can represent the strength of the complimentary efforts of other countries that are an incentive to i to increase climate mitigation expenditures. When we adapt the model of Ballester et. al (2006) accordingly we can rearrange (1) in: u i (x 1,x 2,, x i,, x n ) = α (x i + j i xj) + πx i 1 2 (β γ)x i 2 γ x i x j (2) n j=1 n + λ g ij x i x j j=1 Equilbrium The terms g ij can be understood as the entries in an (nxn) adjacency matrix that represents a network. This network gives the relative complementary policies in producing private goods while executing climate mitigation together with other countries. When g ij =g ij the network

14 is symmetric, but this is not a necessment.it is possible for a game to have a unique pure strategy equilibrium under the assumptions we have set. Since the strict concavity of i s payoffs in its own efforts, the first order condition defines i s best response,setting α + π equal to the constant so contributions are scaled into benefits dependent on the actions of i. This holds since we assume that the benefits of the public good of i are linear with the contributions of j. Such an assumption is reasonable if the contributions of i to the public good are not extremely large (Ballester et. al, 2006). The relative contributions of the involved countries lead to the same outcome that is proportional to their Bonachich centrality since the equilibria of games with the best reply functions must be identical. Using the model we can thus explain the heterogeneity of contributions. When: σ max > 0 The joint production of private benefits gives a higher pay off then if a country would free ride. This model can only reach an equilibrium if the ʎ is not too high. This is the case since if the attenuation factor is high and not restrained by the costs for contributing more to the public good (second term) is too high, a country would want to contribute more and more to climate mitigation. The feedback effects must thus remain small relative to the costs. In our model the Bonachich centrality represents the degree to which country i is motivated to contribute to the public good in response to contributions by others when they increase its private benefits. Our model allows first order effects by direct links in the network, but also second and higher order effects as well, represented by longer paths in that same network. The value of the attenuation factor ʎ is of crucial importance since it represents the measure of response by a country to this feedback. The equilibrium of a country contribution thus increases with the direct and indirect effects of the contributions of others on its own private goods from climate mitigation. Thus when a country (j) increases its mitigation efforts due to an outside shock, and it has the same foreign-policy preferences as country i it will encourage country i to do more. Because of the attenuation factor the influence of countru i s extra contribution will slowly diminish as it moves through the several paths of the network. Understanding a country s position in a network is thus key in understanding how policies of other countries will effect it. Having the same policy preferences is thus not enough for spillins to take place. Some limitiations we like to mention is the fact that although this paper establishes the importance of the attenuation factor, it is very difficult to achieve a solid estimate of it. Also the costs and benefits in environmental politics are difficult to measure because they are often nonmonetary (Bernauer, 1995).

15 Conclusion Network analysis is a relative newcomer in the debate on the provsion of public goods. Academic literature has identified several factors that have an influence on the height of climate mitigation in a country such as its wealth, industrialization level and its level of democracy. But there is still a large empirical gap on how countries influence each other through their networks. This paper presened a theoretical model that by combining public and private benefits that reach a country through its network can explain the heterogeneity in GPG provision in climate mitigation by the participating countries. Katz-Bonacich network centrality counts for every node in a network the total number of direct and indirect paths of any length stemming from that node. Through the usage of Bonachich centrality we explained why and how complementary policy preferences can increase GPG provision levels especially when a more central position in a networkis occupied. Moderate policy preferences are thus not enough to receive beneficial spillins, network centrality matters.

16 Appendix A Important used annotations: n x i u i country contribution of country i to the GPG utility of country i α(x i + j i x j ) gains of i by total GPG production πx i private benefits of country i s own GPG production 1 σ 2 ii x i 2 costs of GPG production for i j i σ ij x j x i complementaries in the joint production of private goods ʎ g ij attenuation factor network

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