Political Influence on Non-Cooperative International Climate Policy

We analyze non-cooperative international climate policy in a setting of political competition by national interest groups. In the first stage, countries decide whether to link their domestic emission permit markets to an international market, which only forms if it is supported by all countries. In the second stage, countries non-cooperatively decide on the number of tradable emission allowances. In both stages, special interest groups try to sway the government in their favor. We find that both the choice of regime and the levels of domestic and global emissions only depend on the aggregate levels of organized stakes in all countries and not on their distribution among individual interest groups, and an increase in lobbying influence by a particular lobby group may backfire by inducing a change towards the lobby group's less preferred regime.


Introduction
When analyzing international (environmental) policy, we often consider individual countries to be represented by a single benevolent decision maker, e.g. a government, acting in the best interest of the country as a whole. In this paper, we depart from this idealized abstraction by assuming that each country's decision maker is vulnerable to the influence of national political competition. As a consequence, international policy is governed by two forces: (i) the influence of political competition on a national level and (ii) the interplay of national governments on the international policy arena.
By political competition we mean that incumbent politicians not only maximize the welfare of the general electorate (national social welfare) but are also susceptible to the influence of lobby groups which try to sway them in their favor by providing campaign contributions, information or simply bribes. This may give them an advantage over their challengers at the next election and hence increases their likelihood of reelection. Deviating from the socially optimal policy, however, leads to an alienation of voters and decreases this likelihood. Policy-makers thus face a trade-off between securing political support by interest groups and maximizing national social welfare.
On the international level, the particular environmental policy we consider is the noncooperative formation of an international emission permit market (Helm 2003). Our choice for non-cooperative climate policies is twofold. On the one hand, the international negotiations for a successor of the Kyoto Protocol in Durban in 2012 have shown how difficult it is to achieve international cooperation. As a consequence, alternatives such as linking already established regional emissions trading systems have been discussed (Flachsland et al. 2009). 1 On the other hand, Carbone et al. (2009) have recently shown that even non-cooperative climate policies exhibit substantial potential for greenhouse gas reductions.
We analyze the political economy of international climate policy in a two-country setup with legislative lobbying in each country. In a first stage governments decide whether to link domestic emission permit markets to an international market. An international permit market is formed if and only if both countries agree to it. In the second stage governments decide about the amounts of emission permits which are issued to the domestic firms.
In both stages governments are lobbied by domestic pressure groups which try to sway the government policy in their favor. Governments are susceptible to the interests of lobby groups, as they maximize a weighted sum of national social welfare and lobby contributions.
Trading of permits -within or between countries depending on the regime choice of the first stage -takes place in the third stage.
We find that, as long as all lobby groups exhibit strictly positive contribution schedules in the second stage, both the choice of regime in the first stage and the amounts of emission permits issued in the second stage only depend on the aggregate levels of organized stakes in both countries. In particular, they are independent of the number of interest groups and the distribution of stakes among them.
In addition, we find that an increase in the influence of a particular interest group may result in a policy change which is counter to the interests of the respective lobby. The intuition behind this result is that a change in the political environment has two effects. The direct effect induces the home government to be more in favor of this lobby group's preferred regime. In addition, there is an indirect effect, as a change in the political environment changes the equilibrium emission allowance choices in both regimes and in both countries.
Although the change in equilibrium allowances is in both regimes and both countries in the direction which is preferred by the lobby group whose influence rises, it may induce a change towards the lobby group's less preferred regime. If the increasing influence of the lobby group induces a change to this group's less preferred regime, the lobby group may be worse off than before. In this respect, our analysis suggests that national political influence by lobby groups has important ramifications for the political feasibility of linking national permit markets.
Our paper contributes to several strands of literature. It builds on the literature on noncooperative international permit markets, developed by Helm (2003), Carbone, Helm and Rutherford (2009) and Helm and Pichler (2011). While these papers assume benevolent national governments, we introduce a political economy framework. Therefore, we draw on the literature on special interest groups, the "common agency" approach, originally developed by Bernheim and Whinston (1986) and extended by Grossman and Helpman in various seminal contributions Helpman 1994, 1995a,b). In particular, we combine a binary regime choice and a continuous emission allowance choice, both of which are prone to lobbying by special interest groups.
Another closely related strand of literature examines the political economy of tradable emission permits and, in particular, the question whether permits should be auctioned or grandfathered in the presence of lobbying (Lai 2007(Lai , 2008. While Lai's analysis is confined to the national level, we analyze how political competition on the national level influences international policies. In our analysis we do not consider lobbying influences on permit issuance, but rather assume an exogenously given redistribution regime of emission permit revenues. Our paper is also closely related to the so called "strategic delegation" literature, which offers a complementary view on national political competition. In these models the principal, i.e. the median voter, elects a politician who then bargains with a foreign politician over an issue at stake. Taking these negotiations into account, the median voter may actually vote for a politician with different preferences than her own in order to manipulate the threat point in the international negotiations in her favor. 2 Strategic delegation in the context of environmental policy has been analyzed by Siqueira (2003) and Buchholz et al. (2005) who both find a bias towards politicians who are less green than the median voter. By electing a more conservative politician, the home country commits itself to a lower tax on pollution, shifting the burden of a cleaner environment to the foreign country. Taking into account emissions leakage through shifts in production, Roelfsema (2007) finds that median voters may delegate to politicians who put more weight on environmental damage than themselves, whenever their preferences for the environment are sufficiently strong compared to firms' profits. In a more general set-up, Harstad (2010) studies the incentives to delegate to more conservative or more progressive politicians. While delegation to the former increases the bargaining position, the latter are more likely to be included in majority coalitions and hence increase the political power of their jurisdiction. The direction of delegation then depends on the design of the political system.

The model
We consider two countries, indexed by i = 1, 2 and −i = {1, 2} \ i. 3 In each country i, emissions e i imply country-specific benefits B i (e i ) from the productive activities of a representative firm with B i (0) = 0, B ′ i > 0 and B ′′ i < 0 for all i = 1, 2. Global emissions, E = e 1 + e 2 , cause strictly increasing and convex country-specific damages D i (E) with D i (0) = 0 and D ′ i > 0, D ′′ i ≥ 0 for all E > 0 and i = 1, 2.

Non-cooperative international climate policy
Countries set up perfectly competitive domestic emission permit markets in which each country i non-cooperatively decides on the amount of emission permits ω i issued to its 2 There are fundamental differences between the common agency approach and the strategic delegation literature. Whereas the common agency set-up assumes an incumbent government which is swayed by interest groups to implement policies in their favor, the strategic delegation literature models the election of a politician, where the median voter takes into account that she might be better off by electing a politician who does not represent her own preferences because of strategic interactions of the elected politicians with other policy-makers. Thus, the common agency and the strategic delegation model represent complementary perspectives on the political process of modern democracies. In addition, although both approaches analyze principal-agent relationships, the common agency approach differs from strategic delegation in that it includes competition by the principals with their rivals for political influence. A median voter, however, never faces any competition by other voters and hence is not required to engage in rent-seeking. 3 All our results can be generalized to n countries in a straightforward manner.
representative domestic firm. As firms in all countries i need (at least) emission permits amounting to emissions e i , global emissions are given by the sum of emission permits issued, E = ω 1 + ω 2 . Countries may agree upon linking the domestic permit markets to an international permit market, which we will refer to as the "choice of regime". Then permits issued from both countries are traded on a perfectly competitive international permit market at price p.
Environmental policy imposes an additional cost to the representative firms reducing the gross (of transfers) profits, but it generates revenues which can be redistributed in different ways. Denoting the type of regime by R = {I, D} (International if an international emission permit market is formed and Domestic otherwise), gross profits π R i of the representative firm and emission permit revenues T R i are given by: We give special attention to two prominent redistribution schemes: (i) the emission permit revenues are redistributed to the representative firms, and (ii) revenues benefit the general public via a lump-sum transfer. 4 Social welfare in country i is given by the gross profits of the representative firm, the environmental damage and the permit market revenues: (2)

Political actors
Each country i is represented by a government deciding on its environmental policy. Governments face two consecutive decisions, which we model as a sequential game: (i) a binary decision whether the respective country wants to participate in an international emission permit market and (ii) the choice of the level of issued permits contingent on whether an international permit market is formed. Governments in each country care about national social welfare but are also vulnerable to lobbying contributions of special interest groups.
There are M i interest groups in country i, which exhibit different stakes in the elements of the social welfare function W i . The degree to which interest group j is a stakeholder of the representative domestic firm is defined as 0 ≤ β ij ≤ 1. The share 0 ≤ δ ij ≤ 1 characterizes the extent to which lobby group j in country i suffers from damages caused by emissions.
The interest groups' stakes in the revenues from permit issuance are denoted by 0 ≤ ρ ij ≤ 1.
Thus, the gross utility of lobby group j in country i reads: Redistributing the emission permit revenues to the representative domestic firm implies ρ ij = β ij for all j = 1, . . . , M i . For simplicity, we assume that transferring permit revenues to the general public corresponds to ρ ij = δ ij for all j = 1, . . . , M i . 5 The national aggregates Organized interest groups in country i offer contributions to the local government in order to sway chosen policies in their favor. As we model the two policy decisions the governments face as a sequential game, they may offer contributions for each of the policy decisions separately. Lobby groups are assumed to maximize the total payoff of their members, which is the organized stakes in national social welfare U R ij that the lobby group j in country i represents minus lobbying contributions in the first and second stage: where C 1,R ij and C 2,R ij are the lobbying contributions of lobby group j in country i in the first and second stage, respectively, contingent on the implemented regime and, in case of stage-two lobbying contributions, depending on the governments' policy choices.
Governments in both countries are assumed to care about the weighted sum of national social welfare and lobbying contributions: where θ i is the relative weight the government in country i attaches to lobbying contributions compared to domestic social welfare W R i . As pointed out by Grossman and Helpman (1994), there is a close connection between the common agency approach employed here and the political support approach pioneered by Stigler (1971). In the latter framework an incumbent government seeks to maximize its chances of reelection by maximizing its political support of the different interest groups among the electorate. As a consequence, the government's utility function has as arguments the welfare that different interest groups derive depending on the chosen policy plus the deadweight loss these policies impose on the society as a whole, while contributions of interest groups do not directly enter the government's welfare. As we shall see, the common agency approach bridges the gap between interest groups' welfare and contributions, as in equilibrium -and at least in case of truthful contribution schedules -the marginal contributions offered to the government by all interest groups represent the change in the interest groups' welfare due to a marginal change in the governments' chosen policy. 7 Who are the special interest groups that are strongly affected by national and international climate policies, and therefore have an interest to offer contributions? The enaction process of the EU Emission Trading Scheme (EU-ETS) has shown that in particular the electricity producers and large energy intensive industries -such as refining, iron, steel, aluminium, pulp and paper, and cement -are represented by influential interest groups and had a significant impact on the final design of the EU-ETS (Markussen and Svendsen 2005). Obviously, these interest groups oppose stringent caps for greenhouse gas emissions or, if they cannot avert them, lobby for free issuance of permits. In favor of stricter emission caps are national and international environmental NGOs. In addition, these interest groups often would like to see the revenues for emission permits being earmarked for environmental projects such as fostering renewable energies, etc. On the consumers' side, automobile associations have established a reputation to fiercely oppose any policies that increase the costs of driving, for example, environmental taxes on driving fuels.

Structure of the game
We model the consecutive decisions on the choice of regime and the issuance of emission permits as a non-cooperative sequential game. In the first stage, governments of both countries simultaneously decide whether to link the domestic emission permit markets to an international emission permit market. An international permit market is set up if and only if both countries consent to it. In the second stage, the governments simultaneously decide 7 Besides trading money for influence in the form of campaign contributions or direct compensations like in our model, the dissemination of information is the second important channel of influence for interest groups in pursuing their political goals. In the public choice literature, these different channels have either been modeled through contests for policy rents (such as rent-seeking contests, menu and other auctions and bargaining), through the transmission of strategic information (such as persuasion, signaling, screening and search) or a combination of both. An excellent survey on modeling rent-seeking contests is Nitzan (1994), while Grossman and Helpman (2001) and Winden (2003) survey the literature on special interest groups.
on the amount of emission permits issued to the domestic firms. In the third stage, emission permits are traded.
In our model setup, two separate non-cooperative games take place in the first two stages: On the one hand, organized interest groups act non-cooperatively in choosing their contribution schedules to influence the respective government's policy. On the other hand, countries decide non-cooperatively on international environmental policy. As a consequence, each of the two model stages comprises a lobbying game in each country Helpman 1994, 1995a), which gives rise to several consecutive sub-stages: c) Third, lobby groups pay contributions contingent on policy choice.

Permit trade:
Depending on the regime established in the first stage, emission permits are traded on national or international permit markets.
Finally, we impose the following assumptions on the benefit functions B i and the lobbying parameters θ i , r i and b i :

Assumption 1 (Sufficient conditions for SOCs to hold)
For the remainder of the paper, we assume 1. The benefit functions of both countries are almost quadratic: B ′′′ i (e i ) ≈ 0, i = 1, 2.

The following condition holds for the lobbying parameters in both countries:
These assumptions are sufficient (but not necessary) conditions for all second-order conditions throughout the paper to hold. By almost quadratic, we mean that B ′′′ i (e i ) is so small that it is irrelevant for determining the sign of all expressions in which it appears. The second condition states that the aggregate organized stakes r i in the permit revenues must not be too small compared to the aggregate organized stakes in the profits of the organized firm. Obviously, the condition is always satisfied if r i = b i , i.e. if the permit market revenues are redistributed to the stakeholders of the representative firm.

The third stage: Permit market equilibrium
We solve the game by backward induction, starting with the third stage. In case of national emission permit markets, the market clearing condition implies that ω i = e i for both countries i = 1, 2. Profit maximization of the representative firm implies that the equilibrium permit price equals marginal benefits: In case of an international permit market, there is only one permit market price implying that in equilibrium the marginal benefits of all participating countries are equal: In addition, the market clearing condition implicitly determines the permit price p(E) in the market equilibrium as a function of the total number of issued emission allowances E. Existence and uniqueness follow directly from the assumed properties of the benefit functions B i . From equation (7) and , it follows directly that:

The second stage: Permit choices
In the second stage, the regime choice of the first stage is known to all lobby groups and governments. Also the contributions C 1,R ij paid in the first stage are sunk and do not influence the governments' and the lobby groups' decisions. In the second stage, governments in both countries set non-cooperatively the levels of emission permits, while organized interest groups in each country sway the local government to choose policies in their favor by offering contribution schedules.
As outlined in Section 2.3, the second stage splits into several sub-stages. First, all lobby groups in all countries simultaneously offer contribution schedules C 2,R ij (ω 1 , ω 2 ) to their governments, which specify the lobby contributions contingent on the policy choices ω i and ω −i of the domestic and the foreign government. Then, the governments in both countries simultaneously set the levels of emission permits ω 1 and ω 2 they issue to the representative domestic firm. Finally, lobby groups in both countries pay contributions according to the choice of emission permits to their governments.
We seek the subgame perfect Nash equilibrium of this non-cooperative game in the second stage for truthful contribution schedules of all interest groups (Bernheim and Whinston 1986). A truthful contribution schedule offers for any change of the government's policy the corresponding change in the respective lobby group's welfare, except when the contribution would be negative. 9 In this case, we require a zero contribution instead: This implies that the net of contributions utilityŪ R ij of all lobby groups is independent of the chosen policy of the government. In fact, the restriction to truthful contribution schedules boils the first sub-stage of the non-cooperative lobbying game in all countries down to the simultaneous non-cooperative choice of the base utility levelsŪ R ij . For the case of strictly positive contribution schedules, marginal contributions do not depend onŪ R ij and are given by ∂C 2,R ij (ω 1 , ω 2 )/∂ω i = ∂U R ij (ω 1 , ω 2 )/∂ω i , which de facto solves the first sub-stage in the second stage of the game. 10 In the following, we restrict our attention to strictly positive contribution schedules. 9 This definition implies that a truthful contribution schedule follows the lobby group's payoff function minus a constant except for the non-negativity constraint. 10 Focusing on truthful contribution schedules may seem restrictive. However, Bernheim and Whinston (1986) showed that lobby groups suffer no loss from playing truthful contribution schedules, since each lobby group's set of best-response strategies for any given contribution schedules of all other lobby groups contains a truthful contribution schedule. Furthermore, in a game setting of complete information truthful payment schedules constitute a simple device to achieve efficiency without any player conceding his right to grab as much as she can for herself. For a detailed discussion of truthful contribution schedules, see Bernheim and Whinston (1986) and Dixit et al. (1997).

Domestic permit markets under lobby group pressure
We first assume that no international permit market has been formed in the first stage of the game. Then, the government of country i sets the level of emission permits ω i to maximize subject to (6), (10) and given the permit choice ω −i of the other country.
Assuming strictly positive contribution schedules for all lobby groups j in both countries, and recalling that ω i = e i and p i (ω i ) = B ′ i (e i ), the reaction function of government i is implicitly given by and there exists a unique Nash equilibrium of this second stage of the game.

Proposition 1 (Unique Nash equilibrium on domestic permit markets)
For truthful and strictly positive contribution schedules of all lobby groups, there exists a unique Nash equilibrium of the game in which all countries i = 1, 2 simultaneously set emission permit levels ω i to maximize (11) subject to equation (6) and a given permit level ω −i of the other country.
The proof of Proposition 1 is given in the Appendix.
Equation (12) implies that both domestic emission levels e i and total emissions E only depend on the aggregate levels of organized stakes b i , d i and r i in the three components of social welfare in both countries and neither on the number nor the composition of lobby groups, as long as all lobby groups exhibit strictly positive equilibrium contribution schedules.
For the two redistribution schemes r i = b i and r i = d i , the following corollary states how domestic and global emissions in the Nash equilibrium react to a change of the political environment:

Corollary 1 (Comparative statics of domestic permit markets)
For r i = b i and r i = d i , the following conditions hold for the levels of national emissions e i , e −i and global emissions E in the Nash equilibrium: The proof of Corollary 1 is given in the Appendix.

International permit markets under lobby group pressure
If an international permit market is formed in the first stage, the government in country i chooses ω i to maximize subject to equations (7), (8), (10) and given ω −i .
Again, considering only strictly positive truthful contribution schedules and taking into account that p(E) = B ′ i e i (E) , the reaction function of country i is given by implying the existence of a unique Nash equilibrium.

Proposition 2 (Unique Nash equilibrium on international permit markets)
For truthful and strictly positive contribution schedules of all lobby groups, there exists a unique Nash equilibrium of the game in which both countries simultaneously set the level of emission permits ω i to maximize (14) subject to equations (7), (8) and given permit levels ω −i of the other country.
The proof of Proposition 2 is given in the Appendix.
Again, we observe from equation (15)  For the effects of a change in the political environment on the issuance of emission permits, we find similar results as in the case of non-linked domestic permit markets. On international permit markets, however, the permit choices of the two countries are not necessarily strategic

Corollary 2 (Comparative statics of international permit markets)
For r i = b i and r i = d i , the following conditions hold for the levels of emission allowances ω i , ω −i and global emissions E in the Nash equilibrium: The proof of Corollary 2 is given in the Appendix.
Defining politically adjusted marginal damages we can interpret the influence of lobbying in the second stage as leading to a distorted perception of environmental damages by the government, depending on the redistribution scheme. Summing up the reaction functions (15) for both countries, we find that the equilibrium permit price equals the average politically adjusted marginal damage: Inserting this equation for the permit price back into the reaction function (15) yields the straightforward generalization of Proposition 1 of Helm (2003): implying that the country with above average politically adjusted marginal damages buys permits from the country with below average politically adjusted marginal damages. Thus, our analysis provides a new rationale for international permit trade: Even economically identical countries can gain by trading on international permit markets if politically adjusted marginal damages in both countries differ due to different political environments.

Global emissions under domestic and international permit markets
Similar to Proposition 2 of Helm (2003), we find that global emissions on an international permit market can be higher or lower compared to global emissions in case of two non-linked domestic permit markets. We denote the Nash equilibrium in case of domestic permit markets by ω D i = e D i , E D , and by ω I i , E I in case of an international permit market. Introducing the abbreviations , and summing up the reaction functions (12) and (15) over both countries, we obtain Then, the following relationship between global emissions in the international and domestic permit market regime follows directly fromD ′′ i ≥ 0:

Equilibrium lobby contributions
Finally, we determine the equilibrium lobbying contributions in the second stage. In the equilibrium of each regime R, the government must be indifferent with respect to the participation of any individual lobby group in the lobbying game, as lobbies want to contribute as little as possible and the government can never be worse off with lobbying than without (Grossman and Helpman 1995a): where ω −k i indicate equilibrium permit levels that did arise if lobby group k would not offer any contributions. Then, the following proposition holds for the equilibrium contributions of all lobbying groups.

Proposition 3 (Equilibrium contributions in the second stage)
For truthful and strictly positive contribution schedules of all lobby groups, the equilibrium contribution in regime R of lobby group k in country i yields: The proof of Proposition 3 is given in the Appendix.
A particular lobby group k has to compensate the government twofold: First, it has to recompense proportionally for the loss (gain) in domestic welfare attributable to the change in issued permit levels due to the lobby's influence. The proportionality factor equals 1/θ i since lobby contributions enter the government's objective function with a weight of θ i .

The first stage: To link or not to link
Having characterized the level of emission permits on domestic and international permit markets depending on the political situation, we now move on to analyze the governments' decision in the first stage. The decision process in the first stage is also prone to be affected by lobbies, as interest groups either gain or lose depending on whether an international permit market is formed. As a consequence, also the first stage splits into several consecutive substages: First, lobby groups in all countries simultaneously offer contributions contingent on the established regime. As regime choice is binary, lobbies offer a non-negative payment for their preferred regime (and zero for the other regime). Second, governments simultaneously decide whether to form an international permit market which only comes into existence if both countries consent to it. Finally, lobby groups pay contributions.

Unilateral stances
The preferred regime of the government in country i is independent of the preferred regime in country −i. Thus, regime choices of governments (unilateral stances in the terminology of Grossman and Helpman 1995a) are dominant strategies and the lobbying games in both countries can be analyzed separately.
Governments choose the regime R to maximize their total payoff G R i , which is given by the social welfare of country i and the weighted lobbying contributions in the first and second stage. For establishing regime R, a lobby is willing to pay to the government at most as much as it gains in the second stage by a change of regime from the alternative regimeR to R, which is given by the difference in the lobby's utilities between both regimes net of lobbying contributions in the second stage: Thus, lobby group j in country i supports regime R if and only if ∆U R,R ij > 0 which also implies that ∆UR ,R ij < 0. As contributions must be non-negative, the contribution of lobby j supporting regime R is given by: First, we examine under which conditions no contributions of all lobby groups in the first stage is a unilateral stance. Therefore, suppose that without lobbying in the first stage the government in country i supports regime R. Then, G R i0 > GR i0 , where G R i0 denotes the government's payoff without the lobbying contributions in the first stage under regime R.
Given that all other lobby groups in country i do not contribute, not contributing itself is a best response for lobby group j if and only if If inequality (27) holds, then no single lobby group can profitably contribute enough in the first stage to unilaterally sway the government to change its support from regime R to regimeR. Thus, no contributions from all lobby groups in the first stage is a unilateral stance if and only if condition (27) holds simultaneously for all organized lobby groups in country i. Grossman and Helpman (1995a) call this equilibrium an unpressured unilateral stance.
Second, we examine the conditions under which there exists a unilateral stance with positive lobbying contributions in the first stage, which Grossman and Helpman (1995a) call a pressured unilateral stance. For a pressured stance the government must be indifferent with respect to the choice of regime, i.e., This condition states that the potential payoff the government is able to collect under regime R must be higher than the potential payoff under the alternative regime. The sum of actual contributions is determined by equation (28).
Note that condition (29) is necessary but not sufficient for a pressured stance in favor of regime R to exist. In addition we need that otherwise, the supporters of regime R could refrain from positive lobbying contributions and still have their preferred regime adopted, and we would be back to an unpressured stance.
For a pressured unilateral stance only the sum of lobbying contributions of all winning lobby groups is determined but not its distribution among individual lobby groups. Thus, there exist, in general, a continuum of pressured unilateral stances, which differ in individual contributions but coincide in the sum of contributions and the adopted regime choice.

The choice of regime
Both an unpressured and a pressured unilateral stance may exist simultaneously. This holds if condition (27) holds for one regime R = {D, I} and at the same time conditions (29) and (30) hold for the same or the other regime. If, in addition, then both stances select the same regime R. Otherwise, there exists a pressured stance in favor of regime R and an unpressured stance supporting regimeR. As Grossman and Helpman (1995a) pointed out, in the case of coexistence unpressured stances are not coalition-proof, a notion introduced by Bernheim et al. (1987). Thus, allowing for a minimum level of communication between the lobby groups eliminates unpressured stances whenever there are also pressured stances. As a consequence, we assume that the pressured stance prevails unless there exists only an unpressured stance. Then, the following proposition holds: The proof is given in the Appendix.

Proposition 4 (Regime choice and distribution of organized stakes)
The intuition for this result is that the necessary condition (29) for the existence of a pressured stance does not depend on the distribution of stakes as long as the national aggregates are constant. This implies that whenever there exists a pressured stance, the selected regime R only depends on the national aggregates of organized stakes. However, for a pressured stance in favor of R to exist, also the necessary condition (30) has to hold. In fact, this condition does, in general, depend on the distribution of organized stakes β ij , δ ij and ρ ij . But if condition (29) holds for regime R while condition (30) is violated, then there exists an unpressured stance in favor of R. Of course, there may be a pressured stance in favor of regime R and an unpressured stance in favor of regimeR. But assuming that pressured stances beat unpressured stances, as discussed above, again regime R would be selected.
In summary, condition (29), which only depends on the aggregate organized stakes, always holds for one of the two regimes and this regime is also the regime choice of the government (or the government is indifferent between both regimes). However, the distribution of organized stakes β ij , δ ij and ρ ij among individual lobby groups determines whether the selected regime is a pressured or unpressured stance. It also influences the contributions in the first stage and, thus, the government payoffs and the lobby groups' net utilities.

International permit markets
Having established each country's choice of regime, it is now straightforward to characterize the conditions under which an international permit market is established. By definition, an international permit market only forms if both countries consent to it, i.e. if regime R = I is a unilateral stance in both countries. By virtue of equation (29) and Proposition 4, a permit market is thus established if and only if the following condition holds for both countries simultaneously: As already pointed out by Proposition 4 in Helm (2003), there are three possible cases: (i) The international permit market regime may lead to lower total emissions and higher payoffs for the governments of both countries. (ii) Even if total emissions were lower, an international permit market may not be established because the government's payoff in one of the countries is lower compared to domestic permit markets. (iii) Although total emissions were lower under domestic permit markets, both governments may consent to an international permit market because their payoffs are higher.
In the following, we analyze how the likelihood of establishing an international permit market depends on the political parameters by differentiating equation (32) with respect to θ i , b i , d i and r i . This likelihood is not only determined by the reaction of the home country where the political change takes place but also by the reaction of the other country to a change in its neighbor's political environment, as the following corollary states.

Corollary 3 (Comparative statics of regime choice)
For the condition for a unilateral stance in favor of an international permit market in country i, it holds: 11 where x ∈ {θ, b, d, r} denotes one of the political parameters and

losses of the respective stakes from international trade.
A marginal change in one of the political parameters in country i has a direct effect on the condition for a unilateral stance in favor of an international permit market by changing the weight which the payoff functions of the respective stakes receive (first three terms in equation (33a)) which is confined to the home country. In addition, indirect effects in both countries arise that change the equilibrium allowance choices under both regimes. These effects may be of opposite sign compared to the direct effect, and they can have the same or different signs in the two countries. As a consequence, although the direct effect may go in favor of the regime with lower (higher) global emissions, the marginal change in ∆G i and/or ∆G −i may go towards the regime with higher (lower) global emissions. If the indirect effects oppose the direct effect and are sufficiently strong, we get the counterintuitive result of the following proposition.

Proposition 5 (Lobbying may backfire) An increase in the influence of organized interest groups favoring higher (lower) global emissions may actually result in a decrease (increase) of global emissions through a change in their home country's and/or the foreign country's unilateral stance.
The proof of Proposition 5 is given in the Appendix.
The intuition is as follows. Suppose the current regime is the regime with higher global emissions. Suppose further that in country i organized interest groups in favor of higher emissions gain influence in government i's decision. This influence on government i causes a direct effect in favor of the regime with higher global emissions. In addition, global emissions in both regimes increase (but, in general, to different degrees), leading to indirect effects in both countries. These may go in the opposite direction of the direct effect, i.e. it may influence the governments in any of the two countries in favor of the regime with lower global 11 Note that d∆Gi/dω R i = 0 due to the first-order conditions of the second stage.
emissions, and may even outweigh the direct effect. If the indirect effect is strong enough to change the regime choice in at least one country, this may lead to a regime change to the regime with lower global emissions. In this case, global emissions may be lower compared to the initial regime.

Discussion
Within our framework of legislative lobbying, we found that both the choice of regime in the first stage and the amount of emission allowances issued in the second stage only hinge on the aggregate organized stakes b i , d i and r i of the different components of social welfare within a country and not on their distribution among different interest groups. However, our formal results hinge on several assumptions.
First, we considered Assumption 1 to hold. Interpreting the benefits from emissions as the negative of the corresponding abatement costs, the empirical literature finds that, at least with respect to climate change, abatement cost curves can be well approximated by quadratic functions (e.g., Klepper and Peterson 2006). When emission permit revenues are redistributed to the firms -for example by grandfathering emission allowances, which is the most common practice so far -the second condition of Assumption 1 is always satisfied.
Second, we assumed strictly positive lobbying contributions in the second stage of all lobby groups. What would happen if we relaxed this assumption? Consider a lobby group k in country i refraining from offering contributions in equilibrium. Then the amount of emission allowances issued in equilibrium is determined byb Thus, the influence of legislative lobbying can be interpreted as adjusting the incumbent governments' perception of the three different components of social welfare. 12 This has an important consequence: All our results -in particular that the increase in influence of a special interest group may result in a policy change which is counter to the interests of this group -are not only restricted to the influence of legislative lobbying, but extend to all influences that alter governments' perceptions of firm profits, environmental damages and transfers. For example, damage perception may change because of increasing (or decreasing) environmental awareness of the voters and/or the government, or new scientific intelligence on the harmfulness of emissions.
In particular, this challenges the conventional wisdom that higher environmental awareness leads to lower global emissions and acts as a partial remedy to failures in the international coordination of public goods problems (e.g. Franzen 2003). Indeed, an increase in environmental awareness in one country (which corresponds to an increase inD i in our model framework) reduces global emissions in both regimes but may, at the same time, induce a switch from the regime with lower to the regime with higher global emissions. If the indirect outweighs the direct effect, then global emissions increase with environmental awareness.
In this regard, our model extends the literature on counterintuitive effects of rising environmentalism. In a coalition formation game, Endres (1997) and Endres and Finus (1998) find that increasing environmental awareness has a positive effect on the reduction targets that are bargained within an international environmental agreement but may also increase free-riding incentives and hence lead to higher stability requirements. Within a framework of international trade and environmental policy, Conconi (2003) concludes that lobbies may reduce their efforts for a higher domestic pollution tax if they are aware of the corresponding emissions leakage. In a similar setting, Aidt (2005) shows that rising environmentalism is not able to prevent an increase in total pollution, even if pollution is immobile, when green lobbies are sufficiently concerned about pollution abroad.

Conclusion
We have analyzed the non-cooperative formation of an international emission permit market in a setting of political competition by national interest groups. We find that for both the continuous choice of emission allowances in the second stage and the binary choice whether an international permit market is formed only the aggregate levels of organized stakes in each country matter and not their distribution among individual lobby groups. In addition, an increase in lobbying influence by a particular lobby group may weaken the support for the interest group's preferred regime in both countries, thwarting the lobby group's efforts.
How the preferences of the elected governments and the median voters differ, depends on the particular model set-up.
Although we found that for given national levels of organized stakes the equilibrium outcome is independent of the number and composition of individual special interest groups, this does not hold for equilibrium contributions and payoffs. In fact, we presume that lobbies with the same interests exert a positive externality on each other. Then, a higher fragmentation of such lobbies would effectively reduce equilibrium contributions which the government is able to collect. However, the investigation of this issue is left to future research.
Our analysis has focused on international climate policy by non-cooperative countries. There are, however, some notable exceptions to the extreme case of non-cooperation, one of them being the European Union which introduced a permit trading system in 2005. Thus, another promising agenda for future research is the investigation of cooperative international climate policies under political pressure from special interest groups.

Proof of Proposition 1
(i) Existence: By virtue of Assumption 1, the maximization problem of country i is strictly concave: Thus, for all countries i = 1, 2, the reaction function yields a unique best response for any given choice ω −i of the other country. This guarantees the existence of a Nash equilibrium.
(ii) Uniqueness: Solving the best response functions (12) for e i and summing up over both countries yields the following equation for the aggregate emissions E: 13 As the left-hand side is strictly increasing and the right-hand side is strictly decreasing in E, there exists a unique level of total emissions E D in the Nash equilibrium. Substituting back into the reaction functions yields the unique Nash equilibrium (ω D 1 , ω D 2 ).

Proof of Corollary 1
Introducing the abbreviation by virtue of Assumption 1, and applying the implicit function theorem to the first-order conditions FOC i , equation (12), for both countries, we derive: where x ∈ {θ, b, d} denotes one of the political parameters and the derivatives of the firstorder conditions, dFOC i /d i , in the two cases r i = b i and r i = d i are as follows: For the signs of equations (A.5), we used the first-order conditions to find: To determine the sign of dFOC r i =d i i /dd i , we re-wrote the first-order condition to yield: Inserting equations (A.5) into equations (A.4) yields Corollary 1.

Proof of Proposition 2
(i) Existence: By virtue of Assumption 1 and as e ′ i (E) ∈ [0, 1], the maximization problem of country i is strictly concave: Thus, for all countries i = 1, 2, the reaction function yields a unique best response for any given choice ω −i of the other countries, which guarantees the existence of a Nash equilibrium.
(ii) Uniqueness: Summing up the reaction function (15) over both countries yields the following condition, which holds in the Nash equilibrium: The left-hand side is strictly decreasing in E, while the right-hand side is strictly increasing in E as p ′′ (E) ≈ 0 by virtue of Assumption 1. Thus, there exists a unique level of total emission allowances E I in the Nash equilibrium. Inserting E I back into the reaction function (15) yields the unique equilibrium allowance choices (ω I i , ω I −i ).

Proof of Corollary 2
Introducing the abbreviation (A.11) and applying the implicit function theorem to the first-order conditions FOC i , equation (15), for both countries, we derive: where x ∈ {θ, b, d} denotes one of the political parameters and as indicated by equation (16).
The derivatives of the first-order conditions, dFOC i /d i , in the two cases r i = b i and r i = d i are as follows: For r i = b i , the signs of equations (A.14a) and (A.14b) can be found by re-writing the first-order condition as follows: Re-writing the first-order condition again yields: For r i = d i , the signs of equations (A.14a) and (A.14c) can be found by re-writing the first-order condition as follows: ( Re-writing the first-order condition again yields: Inserting equations (A.14) into equations (A.12) yields Corollary 2.

Proof of Proposition 3
Assuming that C 2,R ij > 0 for all j = 1, . . . , M i and both R, we can re-write equation (23) by virtue of condition (10) to yield: Solving forŪ R ik and inserting into condition (10), we obtain: Inserting the lobby's utility function (3) yields equation (24).

Proof of Proposition 4
Condition (29) is a necessary condition for a pressured stance. We can re-write this condition to yield Obviously, this condition does not depend on the distribution of organized stakes, as welfare and the sum of the lobby groups' (gross) utilities are determined by the aggregate level of organized stakes b i , d i and r i . This implies that whenever there exists a pressured stance -no matter what the distribution of organized stakes among the individual lobby groups -the pressured stance supports regime R. However, whether a pressured stance exists or not may well depend on the distribution, as condition (30), which also has to hold for the existence of a pressured stance, is not immune to change in the distribution of organized stakes.

Proof of Proposition 5
To prove the proposition, we focus on r i = b i and introduce the special case of quadratic benefit functions and linear environmental damages: where φ i > 0 denotes a country-specific benefit parameter, and ǫ i > 0 is country-specific but constant marginal damage. We define the following shortcuts for politically adjusted marginal damages, average politically adjusted marginal damages and the average benefit parameter: Then, the national allowance choices and the global emissions in the two regimes are: Global emissions are lower in case of linking the domestic permit market to an international permit market if the country with the higher φ i exhibits the lower politically adjusted marginal damages ψ i : Equation (32) can be written as: where the last term cancels out for r i = b i . Factoring out (1 + θ i b i ) before differentiating equation (A.28) and defining γ i ≡ (1 + θ i d i )/(1 + θ i b i ), we derive: where x ∈ {θ, b, d, r} and Consider the situation of an established international permit market with E D > E I . Now, assume, for example, that the green lobby in country i gains momentum (i.e. d i increases).
Then, the first term in equation (A.29a) drops out. The direct effect goes into the direction of the regime with lower emissions, which is the international trade regime. However, the indirect effect of country i goes in favor of the domestic regime and may even outweigh the direct effect. As a consequence, the government in country i is less in favor of the international regime than before. Also the indirect effect in country −i may induce the government of country −i to support the international permit trading regime less than before. Thus, the gain in influence of the green lobby in country i may cause the support for this regime to cease in one or both of the countries. As a consequence, the regime changes to the other regime. As (by assumption) the domestic trading regime exhibits higher global emissions than the international trading regime, global emissions rise which is counter to the interests of the green lobby group.