BATH ECONOMICS RESEARCH PAPERS

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1 Endogenous Learning to Reduce Uncertainty in Climate Change: The Role of Knowledge Spillovers and the Degree of Cooperation in International Environmental Agreements Francisco J. André Michael Finus Leyla Sayin No. 66 /17 BATH ECONOMICS RESEARCH PAPERS Department of Economics

2 Endogenous Learning to Reduce Uncertainty in Climate Change: The Role of Knowledge Spillovers and the Degree of Cooperation in International Environmental Agreements Francisco J. André (1) Michael Finus () Leyla Sayin () (1) Department of Economic Analysis, Universidad Complutense de Madrid, Spain () Department of Economics, University of Bath, UK Abstract: One important obstacle to address climate change effectively is the global public bad nature of greenhouse gases. Another important difficulty is the existence of large uncertainties surrounding the relation between greenhouse gas emissions, temperature increase and the climate system. The international community tries to mitigate these uncertainties by means of research, both at the country and international level. Some recent studies have addressed the effects of uncertainty and learning on the formation of climate change agreements. However, they assume either an exogenous learning process or learning-by-doing. In contrast, we consider an endogenous process of learning-by-investment. In a three stage game, countries decide on membership in an agreement in the first stage, the level of investment in research in order to reduce the systematic ris of the damages of emissions in the second stage and the level of abatement in the third stage. We consider different cooperative scenarios in stage and (two versions of partial and one version of full cooperation) and different degrees of nowledge spillovers in terms of stable agreements and global welfare. We show that even though modesty in the form of partial cooperation may generate larger stable agreements, full cooperation tends to generate higher global welfare in equilibrium. Moreover, surprisingly, if countries cooperate on abatement, nowledge spillovers lead not to smaller but larger stable agreements with higher global welfare, suggesting that research output should be publicly available and not exclusive. Acnowledgement: The authors have greatly benefitted from discussions with Alistair Ulph. This paper was written, in part, while F. J. André was visiting the Department of Economics at the University of Bath. Financial as well as logistic support from the Department is indly acnowledged. F. J. André also acnowledges support from the Spanish Ministry of Economy, Industry and Competitiveness and Development Fund, ERDF (grants ECO C04-01, ECO P) as well as the Complutense University of Madrid and Banco Santander (grant PR6/16-15B-4).

3 1. INTRODUCTION Climate change is one of the most severe environmental threats human mind-ind is currently facing, but also one of the most difficult issues to solve. The global public bad nature of climate change, the long time lag between emissions today and future environmental damages, and the large uncertainties surrounding the relation between greenhouse gas emissions, temperature increase and the climate system pose severe difficulties to tacle the climate change problem cooperatively and effectively. This pessimistic view is mainly shared by the game theoretic literature on the formation of international environmental agreements (IEAs), going bac to Barrett (1994) and Carraro and Siniscalco (199), but also by more recent articles, of which the most important contributions have been collected in a volume edited by Finus and Caparrós (015), who also provide a survey of this literature. Barrett (1994) called this the paradox of cooperation, which may be summarized as follows: only small agreements are stable if the gains from cooperation would be large, though large stable coalitions may emerge but only if the gains from cooperation are small. 1 In reality, considering the entire array of IEAs (Kellenberg and Levinson 014), there has also been some success in overcoming the paradox of cooperation, which necessitates to extend the basic model in order to capture this grey area of reality. Also from a normative point of view it is important to consider the impact of alternative agreement designs and their contribution to at least mitigate the free-rider problem. For instance, several papers consider the possibility to cooperate on R&D to discover new innovative abatement technologies instead of cooperating on abatement itself (Barrett 006, El-Sayed and Rubio 014, Hoel de Zeeuw 010 and Rubio 017). Countries invest in R&D that can generate a breathrough technology with zero emissions. Depending on the particular assumptions about nowledge spillovers and whether members of an IEA jointly conduct and share their research, more successful IEAs may emerge. Another extension considers the possibility of a consensus treaty with modest emission reduction targets in contrast to a focal treaty with ambitious targets (Barrett 00 and Finus and Maus 008). Despite a departure from optimality implies a welfare loss for a given agreement, this allows to stabilize larger agreements, which, overall, lead to more positive 1 Karp and Simon (01) have shown that this pessimistic view rests on the payoff functions which have been typically considered in the literature on IEAs. 1

4 results. So modesty reduces the free-rider incentives, though the first-best outcome (grand coalition with ambitious targets) cannot be achieved. Another issue mentioned above which influences agreement formation is uncertainty. Na and Shin (1998) consider uncertainty about the distribution of benefits of emission reduction in the form of reduced damages. They show that the veil of uncertainty can pay: with uncertainty all players are ex-ante symmetric whereas with no uncertainty they now that the gains from cooperation will be asymmetrically distributed, leading to smaller stable coalitions. Kolstad (007) and Kolstad and Ulph (008) consider uncertainty about the level of the benefits from emission reduction which they call systematic uncertainty. Apart from the scenario of uncertainty, which they call no learning and the scenario of no uncertainty, which they call full learning, they consider the intermediate scenario of partial learning : in a two-stage IEA-game, countries decide on membership without information, using a priori expectations, in the first stage, but learn the parameters of the model once they choose their abatement strategies in the second stage. Again, they come to the conclusion that in a strategic context learning may be bad for the success of IEAs. This negative conclusion about the role of learning has been later qualified by Dellin and Finus (01) and Finus and Pintassilgo (01, 01) who show that the pessimistic conclusions rest on special assumptions which do not generalize, but also suggest a way to fix the problem should it occur. In particular, Finus and Pintassilgo (01, 01) point out that the assumption of a linear payoff function in Kolstad (007) and Kolstad and Ulph (008, 011), also frequently used in the experimental literature on public good provision, leads to inconsistent results in the context of uncertainty and learning. This line of literature lends support to at least three possible extensions. The first extension considers the role of ris aversion. Based on the linear payoff specification and systematic uncertainty as considered in Kolstad (007) and Kolstad and Ulph (008), Bramoullé and Treich (009) include ris aversion in a non-cooperative model which Boucher and Bramoullé (010) modify to include IEA-formation and Hong and Karp (01) generalize based on Hong and Karp (01). Hong and Karp (01) call uncertainty about the parameters of the payoff function exogenous uncertainty and uncertainty about membership endogenous The assumption of a linear payoff function is less problematic in the context of ris aversion because the expected utility approach transforms the linear payoff function into a concave objective function such that abatement levels are not necessarily a binary choice with corner solutions (i.e. abate and not abate).

5 uncertainty. Depending on the type of ris, they show that exogenous ris can lead either to lower emissions but also lower membership or higher emissions but higher membership. Ulph et al. (017) add the aspect of partial learning to this setting and conclude that with sufficiently high ris aversion full and partial learning performs better than no learning. The second extension considers uncertainty in a dynamic IEA-game. Ulph (004) as well as Nuiya et al. (014) consider a simple two period IEA-model with exogenous uncertainty but no learning process. Karp and Zhang (006) and Masoudi et al. (016) consider a fully fledge dynamic climate model with learning-by-doing as a Bayesian learning process. Due to the complexity of these type of models, Karp and Zhang (006) do not test for stability of an IEA but assume some form of partial cooperation, whereas Masoudi (016) consider only a Nash equilibrium without coalition formation. General conclusions are difficult for this type of models, and most results are based on simulations. The third extension considers learning-by-investment, which we pursue in this paper. That is, unless all of the literature of which we are aware of, we do not assume a costless exogenous learning process with partial or full learning, but instead consider an endogenous investment decision of countries whether and how much they want to invest in research in order to reduce exogenous ris, i.e. the uncertainty about the parameters of the payoff function. We consider systematic uncertainty about the benefits from emission reduction lie in Kolstad (007) and Kolstad and Ulph (008), but unlie them and based on the insights in Finus and Pintassilgo (01 and 01) we assume a strictly concave payoff function. The structure of our game is similar to R&D and output or price cartels (Amir 000, Cabral 000, D Aspremont and Jacquemin 1998 and Kamien et al. 199) and R&D and IEA-games (El-Sayed and Rubio 014 and Rubio 017). In the first stage, players decide whether to join a coalition or remain an outsider. In the second stage, players decide on their R&D investments. Outsiders R&D investment is conducted non-cooperatively, members R&D investment may be conducted cooperatively or non-cooperatively. In output and price cartels, R&D reduces production cost, in IEA-games it reduces abatement cost. That is, R&D can lead to an improved production/abatement technology. In the third stage, players choose their output/price (abatement). In output or price cartels, it is typically assumed that firms cannot collude in stage (see D Aspremont and Jacquemin 1998 for a different assumption), and hence all firms choose their strategies non-cooperatively. In IEA-games, in principle, members may choose their abatement levels either cooperatively or non-cooperatively, whereas non-members always

6 choose their abatement levels non-cooperatively. In our setting, research in the second stage is about acquiring better information about an uncertain parameter. Thus, if investment is successful in stage, abatement choices in stage are better informed. Similar to the R&D technology games (e.g. Amir 000, Cabral 000, Endres and Rundshagen 01 and Endres et al. 015), in our research information game, nowledge is shared among coalition members, but nowledge between coalition members and outsiders and among outsiders may disseminate to different degrees (also called nowledge spillovers or leaage). In line with the assumptions in D Aspremont and Jacquemin (1998), we consider three scenarios of cooperation. Coalition members cooperate in stage and (full cooperation), cooperate in stage but not in stage and finally, do not cooperate in stage but only in stage (two scenarios of partial cooperation). For tractability, we focus on two extreme research spillover cases: the public good case with perfect spillovers and the club good case with no spillovers. This gives rise to six combinations of assumptions for which we determine equilibrium strategies for each stage and finally evaluate the overall outcome in terms of global welfare. The following interesting results may be highlighted. Cooperation on abatement in the last stage encourages investment in research. Signatories will invest more in research than non-signatories, irrespective of the scenario of cooperation. Provided that signatories cooperate on abatement, the existence of endogenous research, whether conducted cooperatively or not, will lead to larger stable coalitions as compared to a pure abatement model if nowledge travels freely (public good case) but not in the absence of spillovers (club good case) If signatories do not cooperate on abatement in the last stage, this may lead to larger stable coalitions, which may even include the grand coalition. Thus, cooperation on research is easier to sustain than cooperation on abatement under partial cooperation. Even though partial cooperation may lead to larger stable coalitions, overall, in equilibrium, full cooperation tends to generate larger global welfare than partial cooperation. That is, modesty does not pay. In El-Sayed and Rubio (014) and Rubio (017) all countries chose their abatement levels noncooperatively. However, given that R&D generates a breathrough technology with zero emissions, cooperation in the last stage game is not really important in their setting. 4

7 Surprisingly, exclusive nowledge tends to lead to inferior outcomes than public nowledge, which is particular true if there is cooperation on abatement in stage. This is because, different from abatement, research generates not only direct benefits to those conducting research but also indirect benefits because also other countries tae better informed decisions. This is in line with Goeschl and Perino (017) who find that intellectual property rights of R&D technology create a hold-up problem with smaller stable IEAs and lower global welfare. In the remainder of this paper, we proceed as follows. In Section, we introduce the model. In sections (abatement), 4 (research) and 5 (membership) we solve the model for each stage, proceeding in the sequence of bacwards induction. In section 6, we pull results together and evaluate the overall outcome and section 7 concludes. All proofs are collected in the Appendix.. THE MODEL Let there be n symmetric countries 4 (i.e. they have the same payoff function) which can either choose non-cooperatively (individually) or cooperatively (jointly) their research and abatement activities. If countries cooperate regarding at least one of these activities, they are part of coalition S N with m members, 1 m n. Countries are called signatories or nonsignatories depending on whether they are in the coalition or not. The gross payoff function of country i (excluding research costs) is given by qi i Q (1) and the net payoff (including research costs) is given by qi i Q zi. () where the gross (net) payoff of a coalition is defined as the sum of the gross (net) payoffs of all the signatories, i.e., S i ( S i ). The abatement activity of country i is q i, n is is Q qi is total abatement and z i is the investment in research of country i. That is, i1 4 In the context of agreement formation, it maes sense to assume n. For expositional simplicity of our results in later sections, we disregard n and assume n. 5

8 benefits from abatement depend on total abatement, abatement costs depend on individual abatement and research costs depend on individual investment. Thus, abatement is a pure public good; the nature of research will be discussed below. The marginal benefit parameter from abatement is and the unit cost parameter of investment is, both parameters being strictly positive. A priori, the value of is assumed to be unnown. That is, is a random variable; the distribution is assumed to be public nowledge, with expected value 0 and standard deviation 0. That is, we consider what Kolstad (007) called systematic uncertainty, i.e. ex-ante all players have symmetric expectations and information about the distribution of the random variable and the ex-post realization of the random variable is the same for all countries. Following Finus and Pintassilgo (01, 01), this can be interpreted as uncertainty about the level (in contrast to the distribution) of benefits from abatement, which are the benefits from reduced climate change damages. 5 We assume that countries can decrease their uncertainty by investing in research. For simplicity, following Dahm et al. (009, 016), we assume that, with a certain probability, p, research is successful for player, with denoting either an individual country or a coalition. This means that, with probability p, player finds out the true value of with certainty and, with probability 1 p, the research is unsuccessful and player ends up with exactly the same information as before, i.e., the true value of is not revealed and only the distribution is nown. 6 Denote by z the investment conducted by player, with z zi if conducted by an individual non-signatory i and by z zs z is i if conducted by signatories in coalition S. A player does not only benefit from its own research, but may also benefit from the research of others, due to the existence of nowledge spillovers. In order to capture this idea, we define the concept of effective research of player, denoted by Z, which includes all the research 5 Systematic uncertainty about the benefits from global abatement appears to be the most frequent assumption in the literature. See for instance Boucher and Bramoullé (010), Bramoullé and Treich (009), Kolstad (007), Kolstad and Ulph (008). Alternative assumptions are considered for instance in Dellin and Finus (01), Finus and Pintassilgo (01, 01), Kolstad and Ulph (011) and Na and Shin (1998). 6 In a more realistic framewor, countries could reduce their uncertainty only to a certain extent but not fully. Our approach allows us to have manageable analytical expressions and captures the central idea that research is a risy investment in the sense that success is not guaranteed. 6

9 that is relevant for a player, including own research L z. z, and spillovers from others, Z : z +L z () That is, for simplicity, we assume that there are always perfect spillovers among signatories, which implies that they all have the same effective research, i.e., ZS Z is, and thus have the same probability to find out the true value of the uncertain parameter. However, for spillovers between signatories and non-signatories as well as among non-signatories, the general formulation of () allows for the possibility that research is a pure public, impure public or club good, depending on the specification of on spillovers. L z. In section, we will further elaborate We assume that the probability of player s research being successful is given by p Z Z (4) 1 Z so that p 0 0 and lim p Z 1 Z. The objective of each player (either a country or a coalition) is to maximize its expected net payoff. The timing of the game is as follows: - Stage 1, Coalition formation: Each country decides whether to join coalition S. Countries which do not join coalition S act as singletons. - Stage, Research: Each player (either a country or the coalition) choses the level of investment z. Research can be successful or not according to the probability given in (4). As a result of this stage, there will be informed and uninformed players. The former now the true value of, the latter only now its prior distribution. Players in coalition S share information and hence have the same probability. - State, Abatement: Each player (either a country or the coalition) choses the level of abatement q i, conditional on its information after stage. 7

10 In stages and, non-signatories always decide non-cooperatively, i.e., they individually maximize their expected payoff. Regarding signatories, we consider the possibility that they cooperate, i.e., they jointly maximize their aggregate payoff in terms of research (stage ), in terms of abatement (stage ) or in terms of both strategies. In order to differentiate among these three different cases, it is convenient to define the following variables: h 1 0 if signatories cooperate in stage h h,. otherwise According to this notation, in the full cooperative scenario, denoted by CC, in which signatories cooperate both on research and abatement, we have 1. If signatories cooperate on research but not on abatement, denoted by CN, we have 1, 0 and, finally, if the signatories cooperate only on abatement but not on research, denoted by NC, we have 0, 1. We treat these three scenarios as alternative assumptions. In order to determine the subgame-perfect Nash equilibrium of the overall game, we solve the model bacwards. Hence, we start in Section by solving the third stage, and then, chronologically, proceed to the second and first stage in Section 4 and 5, respectively.. THIRD STAGE: ABATEMENT GAME In stage, generally, countries can face four different situations according to two dimensions. The first dimension relates to whether they cooperate ( C ) or do not cooperate ( N ) in terms of abatement. Non-signatories always act non-cooperatively. In the case of signatories, they can also act non-cooperatively (as if they were singletons) in the case that the coalition does not cooperate on abatement, i.e., the CN scenario. However, signatories can also cooperate on abatement, i.e., the NC and CC scenarios. In these two last scenarios, all members of the coalition will act as a single player, choosing the abatement level of each member with the objective of maximizing the total payoff of the entire coalition. The second dimension refers to whether a player is informed ( I ) or uninformed (U ), i.e., whether a player nows the true value of parameter or just its a-priori distribution. This depends on whether the research conducted in stage was successful. An informed player (whether a single country or a coalition) acts with the objective of maximizing the realized value of its payoff whereas an uninformed player can only maximize its expected payoff. 8

11 Throughout the paper, we assume that the information status of all coalition members is common, i.e., either all the signatories are informed or all are uninformed. This seems to be the most obvious assumption and implies that, regardless of whether coalition members cooperate on research, they will ultimately share the results of their research when choosing their abatement in stage, i.e. they will mae a joint assessment of. Proposition 1 determines the optimal level of abatement in all four situations. PROPOSITION 1. Equilibrium Abatement. The equilibrium abatement of country i, depending on whether it is informed (I) or uninformed (U), is given by I q is ; U q ; I q i S m ; U q i S m. i S From Proposition 1 we can conclude that, as it is usually the case in the literature on IEAs, countries which cooperate on abatement choose higher abatement levels than those which do not cooperate, as the former internalize the external effect of their actions on other cooperative countries. This is true irrespective of their information status. Thus, in the CC and NC scenario, signatories choose m if informed and m if uninformed but will choose I q j I U qi or qi in the CN scenario. The two latter expressions also apply to non-signatories. Due to the linearity of the benefit function from abatement, being informed or uninformed does not affect expected abatement levels from an ex-ante perspective. U q j COROLLARY 1. Expected aggregate abatement. For a given coalition S of size m, and regardless of the number of countries that are informed, the expected aggregate abatement in equilibrium is given by 1 E Q m n m which increases in the coalition size m if there is cooperation on abatement. Corollary 1 reveals that the size of the coalition matters for expected total abatement only if there is cooperation on abatement (CC or NC scenarios). Then, we have E Q m n m which increases in m. In contrast, if there is no cooperation on abatement (CN scenario), expected abatement only depends on the total number of countries: E Q n. 9

12 4. SECOND STAGE: RESEARCH Corollary 1 showed that in our model the number of countries being informed or uninformed does not matter for expected abatement. However, it matters for expected payoffs. If a player is informed, she can choose optimal abatement, depending on the realized value of the uncertain parameter. In contrast, if a player is uninformed, abatement is only optimal on average. To illustrate this, notice that the total expected benefit from abatement of a country i, E B i, can be expressed in the following way: where E Con j E B E Q E q q E Con j1 j1 j1 n n n i j j j q j is the expected contribution of each country j to country i s benefit. The contribution of a country j which does not cooperate on abatement is E Con j E if it is uninformed and E Con j E if it is informed. The contribution of a country j which cooperates on abatement is E Con j E m m if uninformed and E Con j E m m if informed. Therefore, due to the public good nature of abatement, other things being equal, each country s payoff is increasing in the number of informed countries. This is an important piece of information in order to understand some of the later results. It implies for instance that countries cooperating on research benefit if their research spreads to non-cooperating countries. That is, countries do not only directly benefit from joint research but also indirectly through higher expected contributions to their benefits from abatement through other countries. As in stage, in stage there are two types of countries. Countries that do not cooperate on research, which are non-signatories, or signatories in scenario NC, and countries that do cooperate on research, which are signatories in scenario CN and CC. We assume that each player decides its investment in research, z, in order to maximize its expected payoff, taing as given the amount of research and the information status ( I or U ) of other players. As pointed out above, signatories understand that there are perfect spillovers within the coalition and, therefore, the effective research and the information status of the coalition will ultimately be the same for all signatories. The investment decision in research is taen by considering the unit cost of research and the expected benefits. The benefits emerge from the fact that learning increases the 10

13 probability of being informed. We define the value of information (VI ) as the difference between the expected gross payoff in the event of being informed and the expected gross payoff in the event of being uninformed, i.e., VI E / I E / U. Using the definition of gross payoffs given in (1) and the optimal values of abatement established in Proposition 1, we can compute the value of information as follows. PROPOSITION. Value of Information. The value of information of a non-signatory, a signatory and the coalition are given, respectively, by VI 1 m is, V I is m, m VIS mvi is m. 1 From Proposition it is straightforward to conclude that firstly the value of information of all players depends positively on the variance of the uncertain parameter. In the extreme case, if there was no uncertainty ( 0 ), research would be meaningless while if, on the contrary, uncertainty was high, the fact of being informed would mae an important difference when it comes to mae abatement decisions. Secondly, the value of information of a signatory, and hence that of the coalition, is increasing in the coalition size and is always higher than that of a non-signatory. Moreover, the value of information of a signatory is higher if there is cooperation on abatement: VIi S 1 VIi S 0 VIi S, noting that VIi S 1 the value of information of a signatory in the NC and CC scenario and VI i S is is the value of information in the CN scenario. As a general conclusion, cooperation on abatement maes information more relevant and hence strengthens the incentives to invest in research. 0 Given this preliminary discussion about the value of information, we can now turn to derive equilibrium investment in research. To this end, each player solves the following problem: z 0 1 max E p E / I p E / U E / U p VI z (5) where the probability of being informed, p, is given in (4) and the relation between investment in research and effective research, including spillovers, is given by (). The objective function in (5) can be split in two parts. The first part, E / U, is the expected payoff in the absence of learning (i.e., z 0 ). This component can be viewed as the baseline payoff, as it corresponds to the (expected) payoff which player would receive in a standard 11

14 pure abatement model without research. The second component, p VI z, can be viewed as the informational payoff, and is the expected additional gain, net of research cost, that a player can obtain due to the possibility to conduct research. Note that in (5), VI is the coalitional value of information of signatories who cooperate on research ( VI VI S ; CN and CC scenario), is the individual value of information of a signatory who does not cooperate on research (NC scenario; VI VIi S ) and is the individual value of information of a nonsignatory ( VI VIi S ) with reference to Proposition. The solution of problem (5) gives raise to the best reply function of each player as stated in the following result. PROPOSITION. Best replies in terms of research. The best reply of player (whether a country or a coalition) in terms of research effort is given by where is the target value of effective research of player. ˆ z z max Z L z, 0 (6) Ẑ : VI 1 (7) According to Proposition, the best reply of player is the difference between the target value of effective research, Ẑ, which could also be called the autary value, and the spillovers it receives, which are treated as given. In other words, player will cover the research that is not already done by others in order to reach its target level of effective research, where the latter is increasing in the value of information and decreasing in the unit cost of research. To avoid uninteresting solutions, we introduce the following assumption: ASSUMPTION 1:. Assumption 1 states that the unit cost of research is not too high or the value of information is sufficiently high. This ensures that the target value of effective research Ẑ is positive for all players. Nevertheless, as we discuss below, depending on the degree of spillovers, individual research, z, can be zero for some countries. For the sae of convenience, in the CN and CC scenarios in which signatories jointly choose their research effort, we define the target value of effective research of a signatory as that of the entire coalition, i.e. 1

15 VIS Z ˆ ˆ is : ZS 1 if 1. (8) Using the value of information displayed in Proposition, we can derive the target value of effective research for each type of player as displayed in the following table: Scenarios NC Ẑi s VIi S m 1 Ẑ is VI m 1 1 S CN m VIi S 1 CC VIS m 1 1 TABLE 1. Target value of effective research of signatories and nonsignatories. A direct comparison of the target values of effective research implies the following. COROLLARY. Cooperation scenarios and the target value of effective research. The target value of effective research of a signatory is higher than that of a non-signatory. Moreover, the target value of effective research of non-signatories is constant across cooperation scenarios and the target value of effective research of signatories depends on the cooperation scenario in the following way: Z ˆ CC Z ˆ CN Z ˆ NC Z ˆ CC Z ˆ CN Z ˆ NC. is is is is is is Hence, the target value of effective research of coalition members is highest if countries cooperate on research and abatement, followed by cooperation on research only. But even cooperation only on abatement implies a higher target value than for non-signatories: the value of information is higher if there is cooperation on abatement and hence the target level of effective research. Up to now, we have wored with a general formulation of spillovers, L z. For the sae of concreteness, we introduce the following assumption that considers a linear specification. 1

16 ASSUMPTION. The effective research of non-signatories is given by Z z + z + z (9) i S i j l js ls,l i and the effective research of signatories is equal to the effective research of each coalition member and given by: Z Z z z (10) with, [ 0, 1]. S is j l js ls According to Assumption, represents the proportion of signatories research that spills over to non-signatories and determines the proportion of a non-signatory s research that spills over to other countries (including signatories and other non-signatories). Note that this specification is quite general and covers some important cases such as the club good case (which corresponds to 0 ) and the public good case (that corresponds to 1). We explore those important cases below. Given symmetric payoff functions of countries, it is natural to focus on symmetric equilibria. 7 Moreover, due to the linearity of research cost, only optimal total research is uniquely determined for a coalition that cooperates on research. In order to preserve symmetry, we mae the following standard assumption henceforth. ASSUMPTION. When the coalition cooperates on research ( 1 ), the total research effort is split evenly among all the coalition members, i.e., z z / m i S. i S PROPOSITION 4. Equilibrium levels of research. Let spillovers be given by (9) and (10), then equilibrium research in stage is given by z is Zˆ ˆ is n m Z m n m Ẑi S 0 m is 0 if if 7 With symmetric equilibrium we mean that players that belong to the same group of countries choose the same equilibrium research investment. Thus, all signatories choose the same and all non-signatories choose the same investment. However, this does not mean that signatories chose the same equilibrium investment as non-signatories. 14

17 Zˆ ˆ is Zi S zi S n m 0 if if where : 1 n m 1, Ẑ Ẑ is is, Ẑi S is the target effective research of a non-signatory and Ẑi S is the target effective research of a signatory as defined above. According to Proposition 4, signatories always invest a positive amount of research, whereas non-signatories may invest nothing at all. In technical terms, we can find both interior and corner solutions in terms of investment in research. The ey parameter which determines this is, which measures the spillovers that non-signatories receive from signatories. Nonsignatories will invest in research if and only if the spillovers which they receive from signatories are small enough. Otherwise, if signatories were to generate enough spillovers to satisfy non-signatories information requirements, then their equilibrium choice would be to abstain from research. In the latter case, non-signatories would enjoy an effective research in equilibrium that is equal or larger than their target value at no cost. Note that the threshold value that separates both cases,, is the ratio of the target effective research of a non-signatory and signatory. Given Corollary, we have: NC CN CC 1 0. This implies that there are some values of such that, in equilibrium, non-signatories research is positive if the coalition cooperates only on research but may be zero if the coalition cooperates on all aspects. There also some values of for which non-signatories conduct some research if the coalition cooperates only on abatement but not in any of the other scenarios. So, the fact that the coalition cooperates in research maes it more liely that non-signatories will not invest at all, as the coalition generates sufficient spillovers for non-signatories to mae it optimal to fully free-ride. In order to avoid getting distracted by too many subcases, we focus in the following on two important cases that correspond to the two situations identified above (interior and corner solutions): the public good case and the club good case. 15

18 Assume firstly that research is a public good, represented by the parameter combination 1. In this case, the research conducted by any player spills over to all other players. As a consequence, all countries (whether signatories or not) will share the same effective research. As we now from Corollary, the target value of effective research of a signatory is always higher than that of a non-signatory. This implies that non-signatories can obtain their target effective research (and actually, even more) at no cost by free-riding on signatories research efforts without bearing any research cost, while signatories assume all the cost. Consider now that research is a club good, which corresponds to the parameter combination 0. In this case, the research effort by a signatory spills over to all other signatories, but not to non-signatories. That is, every signatory learns thans to the effort made by the entire coalition, while each non-signatory only learns from its own research. Thus, information does not spread and the only way to benefit from shared information is to join the coalition. The implication is that, in equilibrium, all countries, whether signatories or not, must conduct a positive amount of research in order to learn with a positive probability. Moreover, for non-signatories, effective research is equal to individual research because they do not receive any spillovers. For signatories, effective research is equal to the aggregation of the individual research conducted by all signatories, i.e., individual research times the coalition size. The discussion is summarized in the following corollary. COROLLARY. Individual and effective research in the public and club good case. Both in the public good case ( 1) and in the club good case ( 0 ), the equilibrium effective research, Z i, and the equilibrium individual research, z i, of signatories is given by Z is 1 1 m m m Zˆ is 1 0, Ẑi S z is m. Equilibrium effective research and equilibrium individual research of non-signatories is given by ˆ zi S Zi S Zi S 1 in the club good case and z 0, Z Z Zˆ Zˆ in the public good case. i S is is is is 16

19 From Corollary we can extract some interesting conclusions regarding the comparison between signatories and non-signatories, between the public good case and the club good case and also across cooperation scenarios. Firstly, given a coalition size, m, both in the public good and the club good case, in equilibrium, individual research of signatories is larger than that of non-signatories, i.e., z z for all three cooperative scenarios, CC, CN and NC ( z i S being equal to zero in the is is public good case and larger than zero in the club good case). Moreover, individual research of non-signatories is independent of the cooperative scenario, whereas individual research of signatories follows the same ordering as effective research (see Corollary ) and thus, it is highest in the full cooperation scenario (CC) and lowest when there is cooperation only on abatement (NC), i.e., z CC z CN z NC z CC z CN z NC. is is is is is is Secondly, in the club good case, the equilibrium effective research of non-signatories is constant across cooperation scenarios (CC, CN and CN) because they do not receive any spillovers. However, in the public good case, although individual research of non-signatories is always zero, effective research does depend on the cooperative scenario due to the spillovers that they receive from the coalition. In fact, effective research of non-signatories is exactly the same as that of signatories by construction and, thus, it follows the same ordering, i.e., Z CC Z CN Z NC i N. i i i Thirdly, both in the club good case and the public good case, effective research of signatories is always equal to the entire research of the coalition in equilibrium, as they do not receive any spillovers from non-signatories, although this is true for different reasons: in the club good case it is true by construction, and in the public good case because non-signatories do not conduct research in equilibrium. As for non-signatories, in the club good case they conduct more research but enjoy a lower effective research than in the public good case. 5. FIRST STAGE: MEMBERSHIP Regarding the first stage, we employ the stability concept of internal and external stability, frequently applied in the literature on IEAs (e.g. Barrett 1994, Carraro and Siniscalco 199 and Rubio and Ulph 006). Given a coalition with m signatories, internal stability 17

20 requires that no signatory has an incentive to leave the coalition, E is m E is m 1 and external stability that no non-signatory has an incentive to join the coalition, is is 1 E m E m (so we assume that in case of indifference a non-signatory joins the coalition to avoid nife edge cases) which together, for symmetry, can be compactly summarized in the stability function m : E is m E is m 1. (11) A coalition of size m is said to be internally stable if m 0 and externally stable if m 1 0. It is stable if it is both internally and externally stable. In what follows, we analyze equilibrium coalition sizes under the three cooperative scenarios outlined above (CC, NC and CN) and distinguish between the club good and public good case. We start with the scenarios where there is cooperation on abatement (NC and CC) as these are the scenarios that can be directly compared to the standard abatement coalition model without research. PROPOSITION 5. Equilibrium coalition size in the NC and the CC scenario. If there is cooperation on abatement, the equilibrium coalition size given by: a) Club good case: m. b) Public good case: m. Specifically, a coalition of size m is only stable if n is large enough. The grand coalition ( m n ) is never stable for n. As it is well nown in the literature (see the collections of articles and the survey in Finus, and Caparrós 015), the standard result in the pure abatement model with linear benefits and quadratic costs and no uncertainty is that the equilibrium coalition size is m. The same is true for exogenous learning and systematic uncertainty about parameter as derived for this payoff function by Finus and Pintassilgo (01), regardless whether there is no learning, partial learning or full learning as explained in the Introduction. We can now as what changes when we allow for endogenous learning through the investment in research, with the purpose of reducing uncertainty. Proposition 5 reveals that if research is a club good the standard result persists, regardless whether signatories choose their research levels cooperatively or non-cooperatively. This is different if research is a public good. In this case, two results should be highlighted. 18

21 Firstly, the coalition size is potentially higher than in the club good case. Hence, surprisingly, nowledge spillovers from signatories to non-signatories do not aggravate but may mitigate the free-rider problem. Secondly, unlie the club good case, the size of the coalition depends on the total number of countries n. In fact, unlie what is found for other payoff functions in the standard literature on environmental agreements, m does not decrease (because the externality effect is aggravated and free-riding encouraged with the number of players) but increases with the number of countries n. 8 To understand these apparently surprising results note that in our public good case, we have de facto two public goods: abatement and research. By definition of public goods, any effort made by a player generates benefits to all other players while the cost is borne solely by one player. Signatories abate and research more than non-signatories and hence generate a positive externality to non-signatories. This maes free-riding attractive. In the case of abatement this is the only effect. In the case of research, there is also an indirect effect, with means that signatories harvest some of the positive externalities. Signatories research increases the probability of learning, their own but also of non-signatories, which increases the contribution of non-signatories to signatories benefits of abatement as explained at the beginning of Section 4. In other words, via the contribution of non-signatories to abatement, signatories indirectly capture part of the positive externalities they generate to non-signatories due to the dissemination of information. This harvesting effect increases with the number of players. This alleviates the free-riding problem. However, even in the public good case, the grand coalition is never stable. We now turn to the scenario in which signatories cooperate on research but not on abatement, the CN scenario. Hence, this scenario is not directly comparable with the pure abatement coalition game, though it can be compared with our two scenarios discussed above. PROPOSITION 6. Equilibrium coalition size in the CN scenario. If there is cooperation on research only but not on abatement, the equilibrium coalition size is as follows: a) Club good case: m 5 (provided n 5). Specifically, a coalition of size m 5 is always internally stable. A coalition of size m 5 is internally stable if the ratio is small enough. If 0. 17, the grand coalition is always stable for any n. 8 See the survey and the collection of papers in Finus and Caparrós (015). 19

22 b) Public good case: m. Specifically, a coalition of size m is internally stable for any n. A coalition of size m is internally stable if and only if n is large enough. The grand coalition ( m n ) is never stable for n. One conclusion which is similar to Proposition 5 is that in the public good case, the equilibrium coalition size increases with the number of countries, n. However, there are also two interesting differences. Firstly, unlie the two previous scenarios, in the CN scenario, the possibility of conducting research improves the prospects of coalition formation in the club good case. Whereas in the previous two scenarios we had m, we now have m 5. In fact, in our simulations, which covers a wide range of parameter values, and on which we report in the Appendix, we find substantially larger coalitions than 5 if we allow n to be large enough. Moreover, as Proposition 6 states, the grand coalition is always stable if the unit cost of research is small enough compared to the variance of the uncertain benefit parameter. Secondly, it appears that the public good case may not necessarily lead to larger stable coalitions than the club case as this was true in the NC and CC scenarios above. In our simulations, we find that m is only larger in the public than in the club good case in 5.6% of all simulations runs, but in 6.1% this is reversed and in 1.% both have the same membership. Hence, informational spillovers reduce free-riding if there is cooperation on abatement, but they are less useful if countries choose their abatement levels non-cooperatively. Taing Proposition 5 and 6 together, and looing across the three scenarios of cooperation, we can conclude: COROLLARY 4. Comparing coalition sizes across the three scenarios of cooperation: In the three scenarios of cooperation, the equilibrium coalition sizes can be raned as follows: a) Club good case: m CN m NC m CC. b) Public good case: m NC m CC. Whereas in the club good case the raning follows directly from the previous two propositions, in the public good case m NC m CC the public good case, the relation between m CN and m NC as well as m is established in the Appendix. In CC does not follow a general pattern as in the club good case, even though our simulations show that in 98.5% of the simulations, m CN m NC m CC with strict inequality between m NC and m equality in 94% of the simulations). is true lie in the club good case, CC in only 6% of the simulations (and 0

23 Taing together, cooperation only on research generates the largest stable coalitions, including the grand coalition. Cooperation on abatement suffers from stronger free-rider incentives, with only small coalitions being stable. Cooperation on all issues leads to the smallest stable coalitions. Research, cooperatively or non-cooperatively, can mitigate the freerider incentives associated with abatement, but only if information does freely travel. 6. OVERALL RESULTS: WELFARE ANALYSIS 6.1 Preliminaries In this section, we pull results from the three stages together, in order to draw overall conclusions. In preparation of this, we have a first a loo at some fundamental features of our model in this subsection, which will be useful in deriving and understanding some later results. In particular, we derive some results which relate to expected payoffs when combining stage and for a generic coalition of size m. That is, we tae an ex-ante perspective once some coalition of size m has formed. Note that the equilibrium decisions about research and abatement have direct implications on countries payoffs. Therefore, it is useful to write expected net payoffs of an arbitrary country i in the following way: E qi E i E Q zi E q E m p q 1 p q n m p q 1 p q z I U I U i S js S js js js js js i I U 1 p 1 1 i qi pi q i m n m m ps n m pi S z i. (1) The expression in the last line in (1) comprises four terms. The first two relate to expected benefits and the last two relate to expected costs. The first term of expected benefits (from total abatement) is deterministic and depends only on the parameters of the model (the number of countries n and the expectation of the marginal benefit ) as well as the coalition size m. The second term is probabilistic because, apart from parameter values (the variance of the random variable,, and the number of countries, n ) and the coalition size, m, it also depends on the probabilities that signatories and non-signatories are informed. This second term captures the potential additional benefits due to the possibility of learning. The first term 1