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International Environmental Agreements with reference points
Journal of Behavioral and Experimental Economics 59 (2015) 68–73
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Journal of Behavioral and Experimental Economics journal homepage: www.elsevier.com/locate/socec
International Environmental Agreements with reference pointsR Fuhai Hong∗ Division of Economics, Nanyang Technological University, Singapore
a r t i c l e
i n f o
Article history: Received 19 November 2014 Revised 11 March 2015 Accepted 1 October 2015
JEL Classification: D03 Q5
a b s t r a c t Whether or not the current climate talks achieve a meaningful treaty, the current negotiation forms important reference points for future negotiations. In this paper, we introduce reference points to a canonical model of International Environmental Agreements (IEAs). Countries have reference points on IEA membership. An IEA member that abates is aggrieved if there is a material loss relative to the case with the referenced membership. We find that reference points weakly reduce the abatement level for an IEA with given membership, while interestingly, reference points weakly increase the equilibrium membership and thus the equilibrium abatement level of the IEA. These results imply that effective management of reference points could be conducive to the resolution of the climate problem.
Keywords: International Environmental Agreements Reference points
1. Introduction In order to control climate change, concerted efforts in abating Greenhouse Gas (GHG) emissions should be made. However, GHG abatement is a global public good and the provision of this global public good suffers from the usual free riding problem, in the absence of a world government. An International Environmental Agreement (IEA) is a coalition mechanism that aims to resolve the free riding problem from transboundary pollutions. However, the literature on IEAs is generally pessimistic regarding the equilibrium participation level in an IEA (see, e.g., Barrett, 2005 for a survey). With insufficient participation, the IEA mechanism has little chance to resolve the climate problem. Much of the IEA theory relies on a particular type of participation games in which countries decide on whether to participate in an IEA and the resulting IEA makes abatement decisions for its members. In the equilibrium, some countries choose to join the IEA and contribute to the public good while the others stay out. The asymmetry of the equilibrium raises an important but debatable concern revolving around the climate problem: equity (see, e.g. Cazorla and Toman, 2001). Countries exhibit a preference for equity in international environmental negotiations (Lange and Vogt, 2003). However, lacking a consensus on what is equity, countries’ perception of an equitable
R
I thank Teh Tat How for research assistance, Larry Karp, Akihisa Mori, an anonymous referee and participants at the 2014 EAAERE Inter-congress Conference for helpful comments or discussions, and a start-up grant of Nanyang Technological University (Grant no. HSS-SUG) for financial support. ∗ Tel. +65 67904496. E-mail address: [email protected] http://dx.doi.org/10.1016/j.socec.2015.10.004 2214-8043/© 2015 Elsevier Inc. All rights reserved.
© 2015 Elsevier Inc. All rights reserved.
way to address the climate problem critically depends on their reference points in viewing the climate issue. The literature has shown that reference points play a crucial role in human decisions and interactions. Kahneman (1992) reviews the role of reference points in individual choices and interpersonal negotiations. Reference points are characterized by the abrupt changes in the valuation of gains and losses and of acceptable or reprehensible behavior. More recently, Brandts and Solà (2001) and Abeler et al. (2011) provide evidence on how reference points affect reciprocal behavior and effort provision. Hart and Moore (2008) and Fehr, Hart, and Zehnder (2011) introduce reference points to the negotiation between contracting parties: if a party does not get what he feels entitled to, he is aggrieved and provides perfunctory rather than consummate performance, causing deadweight losses. Kristensen and Gärling (1997) provide empirical evidence showing that reference points influence negotiation process and outcome. Reference points not only affect behavior at the individual and interpersonal level, but could also make a difference at the international arena. Nations’ behavior is not purely driven by materialistic interests.1 In a country, if voters have certain preference with reference points, the government should take this into account and respond to the voters’ reference points. In a recent study,
1 For instance, equity is an important issue in international negotiation of climate treaties. The principle of equity is articulated in Article 3 of the Convention on Climate Change and the decision approved by the COP 6 in Bonn. For another example, Kennan (1985) provides anecdotes and a critique on the moralistic judgments of American statesmen on foreign policies. Many papers, e.g. Lange and Vogt (2003), Eyckmans and Kverndokk (2010) and Kolstad (2014), consider countries’ non-materialistic preferences in decision-makings regarding IEAs.
F. Hong / Journal of Behavioral and Experimental Economics 59 (2015) 68–73
Charite, Fisman, and Kuziemko (2015) show that social planners do respect people’s reference points in decision-makings. Moreover, in international negotiations, the decisions of diplomats or national delegates may be influenced by their own reference points. Starkey, Boyer, and Wilkenfeld (2010) point out that “Diplomacy is not just about bargaining. There is a human dimension to the negotiation game that should not be ignored.” Zartman (2007) discusses the role of reference points in international negotiations on the European Development Fund. Reference points can also be important in international negotiations on climate treaties. Countries are dissatisfied if other countries’ participation level in climate treaties is below their referenced level and may thus be unwilling to make consummate efforts to address the transboundary pollutions. For instance, many members of the Kyoto Protocol, including Australia, Canada, Japan and New Zealand, harbored discontent towards the United States for not ratifying the Kyoto Protocol (see, e.g., Hara, 2005), although the U.S. was not pivotal for the enforcement of the Protocol. These countries were also aggrieved by the fact that developing countries were out of regulation under the Kyoto Protocol, and some expressed unwillingness to take part in the second phase of the Protocol.2 In this paper, we introduce reference points to a canonical IEA model. Countries have reference points regarding the membership of the IEA. If the actual membership falls short of the reference points, the IEA members may feel aggrieved by being free ridden, which results in perfunctory performance of the IEA. Interestingly, anticipating such responses of IEA members, in the equilibrium, more countries would participate in the IEA with high reference points. Therefore, if there is a way to “manage” countries’ reference points, reference points could be used as an instrument to increase the membership and abatement level of the IEA. Our result thus provides a less pessimistic insight than the standard IEA literature. Gerber, Neitzel, and Wichardt (2013) consider minimum participation rules for coalitions providing public goods. These rules increase the level of participation above which the coalition is successfully implemented and could thus increase the equilibrium level of participation. In their model, the minimum participation rules are exogenous. Carraro, Marchiori, and Oreffice (2009) consider endogenous determination of minimum participation constraints by a prior stage of unanimity. In both models, the size of the minimally successful coalition increases because of the participation rules which were legally imposed. In our paper, we show that a sort of psychological trait with reference points is able to increase the size of the minimally successful IEA and thus the equilibrium membership, in the absence of explicitly imposed participation constraints on the agreement. A few studies have investigated the role of social preferences in IEA negotiation and institution formation in public good games. Eyckmans and Kverndokk (2010) and Kolstad (2014) consider moral concerns and (impure) altruism in IEAs. Lange and Vogt (2003) and Kosfeld, Okada, and Riedl (2009) incorporate equity preference and inequality aversion into models of coalition formation. In particular, Kosfeld, Okada, and Riedl (2009) show that inequality aversion in the sense of Fehr and Schmidt (1999) can increase the size of a sanctioning organization. Although equity is undoubtedly important in climate negotiations, what is equitable allocation is controversial, and people “appear to desire equality relative to some reference point” (Alesina and Angeletos, 2005).3 In this paper, we follow the tradition of Kahneman (1992) and Hart and Moore (2008) by incorporating reference points to an IEA model. While the inequality-averse
2 See, e.g. the entry of “Canada and the Kyoto Protocol” in the Wikipedia, “Australia rejects Kyoto pact,” in BBC News, June 5, 2002, and “NZ ‘ahead of the curve’ in quitting Kyoto Protocol”, in 3 News, 3 December 2012. 3 Cazorla and Toman (2001) review the alternative equity criteria for climate change policy. Depending on different reference points, the equity arguments include equal burden shares, equal percentage reduction of pollutants, and reducing differences between developed and developing countries (see e.g. Lange and Vogt, 2003).
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Fig. 1. The game.
preference is exogenous in Kosfeld, Okada, and Riedl (2009), reference points are endogenous and can be affected by pre-play communication in our extended model in Section 2.3. With this model, we show that effective management of countries’ reference points, and more broadly their perception towards the climate problem, could increase the chance of achieving a successful IEA. The rest of this paper is organized as follows. Sections 2.1 and 2.2 present the IEA model, with and without reference points, respectively, while Section 2.3 considers an extended model with preplay communication and endogenous reference points. Section 3 concludes with a discussion on the implications of our results. 2. Model The first subsection below presents the canonical IEA model as a benchmark case, the second subsection introduces reference points to the model, while the last subsection discusses the choice of reference points by including a prior stage of communication in which countries announce the intention of participation in the IEA. 2.1. The canonical IEA model Barrett (1999) firstly proposed the following “canonical” IEA model. This model is also used in, e.g., Barrett (2003, Chap. 7) and Kolstad (2011, Chap. 19). There are N identical countries. Each country has two binary decisions: participation in an IEA and abatement. If we assume linear costs and benefits of abatement, then a country will either abate at capacity or does not abate at all. So there is no additional loss of generality in assuming binary abatement. Abatement is a global public good. We normalize the benefit of one unit of abatement, to each country, to one. The country that abates incurs an abatement cost, c. We assume that 1 < c < N, where the first inequality implies that it is a dominant strategy for a country acting alone to choose not to abate, while the second inequality means that the world is better off from any country’s abatement. The game consists of two stages: in stage 1, each country decides on whether to participate in the IEA; in stage 2, members of the IEA let the IEA decide on abatement, while the outsiders make their own abatement decisions. Fig. 1 summarizes the game. The IEA is assumed to maximize the total welfare of its members. The game can be solved backward. In stage 2, outsiders choose not to abate, following their individually rational decisions. Let the membership of the IEA be m. The IEA will instruct its members to abate if and only if m ≥ c, where m is the coalition’s benefit from one unit of abatement and c is the cost. Let f(x) be the smallest integer no less than x, for any x. Then f(c) is the membership of the “minimally successful IEA” given the IEA’s decision rule. We say that a country is pivotal if exactly f (c) − 1 other countries join the IEA, because the country’s participation will affect the IEA’s decision. A pivotal country has an incentive to join the IEA because by doing so, the country obtains a payoff of f − c ≥ 0. A country’s additional membership is superfluous from its own viewpoint if at least f(c) other countries
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F. Hong / Journal of Behavioral and Experimental Economics 59 (2015) 68–73
join the IEA, because by joining, it does not affect any other country’ abatement decision, but incurs a cost of c − 1 > 0. We then assume a tie breaking condition in stage 1 that a country that is indifferent between participation and not will choose to participate.4 Then in this participation game, there is a unique Nash equilibrium membership where f(c) countries join the IEA. f(c) is internally stable since no member has an incentive to leave the IEA (because of the benefit of being pivotal f − c), and is also externally stable because no outsider has an incentive to join (as an additional member would be superfluous from its own viewpoint). An IEA with f (c) − 1 members is not externally stable because an additional membership is pivotal and an outsider thus has an incentive to join. An IEA with less than f (c) − 1 members is not externally stable because of the tie-breaking assumption on participation. An IEA with more than f(c) members is not internally stable because the IEA does not cease abating even if a member leaves and the cost of being superfluous is c − 1 > 0. This IEA model has the advantage of providing an analytical solution. With abatement cost c, the IEA contains f(c) members, and the abatement level is f(c). In the first best case with full cooperation, every country abates and the abatement level is N. In the Nash equilibrium without the IEA, no country abates. The IEA mechanism is useful f c in the sense that it achieves a fraction, (N ) , of total gains of cooperation. However, the equilibrium abatement of the IEA still falls short of efficiency, especially when the abatement cost, c, is much lower than N. 2.2. A model with reference points In the model by Hart and Moore (2008), a reference point means the feeling of entitlement. They suppose that a party is happy to provide consummate performance if he feels that he is getting what he is entitled to, but will withhold some part of consummate performance if he is shortchanged, which they refer to as “shading”. This idea has implications on international environmental and climate negotiations. In the above IEA model, ex ante countries are identical; in the equilibrium, however, some countries join the IEA and provide public goods, while the other countries free ride. If the IEA membership is low, the IEA members may feel being shortchanged by providing the public good, as many of the countries free ride on them. Therefore, the IEA members may be unwilling to provide the public good, even if it is materialistically beneficial to do so, i.e., m ≥ c. An IEA member may feel happy to abate, only when a sufficient number of other countries also join the IEA and abate (or, in other words, not many countries free ride). To operationalize this idea, we assume that a country has a reference point on IEA participation, mR , an integer.5,6 We make the following assumptions about member countries’ preference. First, we assume that an IEA member feels aggrieved only if it abates. This is because a non-abating IEA member does not contribute more than non-members, and will not feel being shortchanged. Second, we assume that member countries have rational expectation about their material payoffs in an IEA with mR members. An IEA with mR members instructs its members to abate if and only if mR ≥ c. So the 4
This assumption is also adopted in studies such as Karp and Simon (2013) and Hong and Karp (2012, 2014), to rule out the “trivial” equilibria in which less than f (c) − 1 countries join and thus there is no a meaningful IEA to be formed. Alternatively, one may consider a dynamic game, where countries take their participation decisions sequentially according to some pre-determined order. This will give us the same result. We thank an anonymous referee for pointing this out. 5 Starkey, Boyer, and Wilkenfeld (2010) write, “Although nation’s culture is different from one another, the main reference points are the same across most lands.” For simplicity, we keep the assumption of identical countries such that each country has the same reference point. The next subsection will discuss the choice of reference points. 6 For a country that has a preference for “perfect equity” which requires all countries to join the IEA, the reference point equals N.
material payoff of a member in such an IEA is mR − c when mR ≥ c and 0 otherwise. Third, we assume that an abating member country feels aggrieved if its material payoff is lower than that under the referenced case. Note that if mR ≥ c and m < mR , there is a material payoff loss relative to the referenced case for the abating member, which equals (mR − c) − (m − c) = mR − m; when mR < c and m < c, there is a material payoff loss for the abating member, equal to 0 − (m − c) = c − m. With the above assumptions, the preference of a member/signatory country is given by
us =
πs − θ max[mR − m, 0]I if mR ≥ c , πs − θ max[c − m, 0]I if mR < c
(1)
where π s is the material payoff, I is an indicator function which equals one if the country abates and zero otherwise, and θ indicates how aggrieved the country is about the material payoff loss relative to the referenced case.7 With the above preference, in stage 2, the following lemma shows the IEA’s decision rule. Lemma 1. If the reference point mR ≤ f(c), the IEA abates if and only if θ mR ). m ≥ f(c); if mR > f(c), the IEA abates if and only if m ≥ f ( c+1+ θ Proofs are relegated to the appendix. Lemma 1 implies that reference points weakly increase the size of the minimally successful IEA. In the benchmark case without reference points, the minimally successful IEA is f(c). In the model with reference points, the minimally θ mR ) (which is weakly successful IEA is f(c) if f(c) ≥ mR , and is f ( c+1+ θ
greater than f(c) when mR > f(c)) if mR > f(c). Since the IEA’s decision rule on abatement is a step function with a jump at the minimally successful IEA in both models (with and without reference points), the increase in the size of the minimally successful IEA leads to the following remark. Remark 1. For a given level of membership, reference points weakly reduce the abatement level of the IEA.
θ m ), In particular, Lemma 1 implies that when f (c) ≤ m < f ( c+1+ θ the IEA may not instruct its members to abate even if abatement is materialistically beneficial to all. These results echo the observation in Hart and Moore (2008) that parties with high reference points may provide perfunctory rather than consummate performance, causing deadweight losses. We then move backward to stage 1, the participation game. The following proposition shows the equilibrium membership with reference points. Interestingly, consideration of the participation equilibrium overturns the pessimistic result in Remark 1. R
Proposition 1. With reference point mR , if mR ≤ f(c), in equilibrium f(c) θ mR ) countries countries join the IEA; if mR > f(c), in equilibrium f ( c+1+ θ join the IEA. The proposition is straightforward, with the IEA decision rule given by Lemma 1, so its proof is relegated to an online appendix. Note that when mR > f(c), Lemma 1 and Proposition 1 together imθ mR ), which is weakly ply that the global level of abatement is f ( c+1+ θ θ m ) ≥ f (c), for mR > f(c). We thus increasing in mR . Meanwhile, f ( c+1+ θ have the following remark. R
Remark 2. When mR > f(c), the equilibrium abatement level is (weakly) higher than that in the benchmark case without reference points, and is weakly increasing in the reference point mR . When mR ≤ f(c), the equilibrium abatement level is not different from the benchmark case without reference points. Overall, consideration of reference points in IEA games provides a less pessimistic 7 The max function and the indicator function I in the utility function are consistent with Kahneman (1992) characterization of reference points by the abrupt changes in the valuation of gains and losses and of acceptable or reprehensible behavior.
F. Hong / Journal of Behavioral and Experimental Economics 59 (2015) 68–73
view on the equilibrium IEA participation and abatement level than the standard model, when the reference points are sufficiently high. 2.3. Discussion In this subsection, we discuss a determinant of the reference point, mR . We introduce a prior stage, stage 0, of pre-play communication to the above model. In this prior stage, each country chooses whether to announce intention of participating in the IEA. The announcement is costless, non-binding and non-verifiable. In this sense, the communication stage is close to the cheap-talk stage in Palfrey and Rosenthal (1991) public good game. However, the number of announcements made on the intention of participation is supposed to increase countries’ expectation on the participation level in the IEA. Moreover, Abeler et al. (2011) show that expectation determines reference points. Therefore, we assume that the reference point in later stages is a weakly increasing function of the number of countries that make announcements: mR (K), where K is the number of countries that announce intention of participation in the prior stage.8 To focus on the more interesting case, in this subsection we assume that mR (0) ≥ c.9 Taking into account the asymmetry of the equilibrium in the participation game where some countries join the IEA while the others stay out, as in Barrett (2006), Rubio and Ulph (2007) and Hong and Karp (2012), we further assume that in this prior stage, each country faces the same probability of becoming an IEA member in the next stage.10 In stage 0, a country’s expected welfare, denoted by w(K), can be written as
w(K ) = f
c + θ m (K ) 1+θ R
⎡ ⎣1 −
c + θ mR (K ) − f
c+θ mR (K ) 1+θ
N
⎤
⎦. (2)
The appendix shows the derivation of Eq. (2). Let g(K ) ≡ Eq. (2) can be rewritten as
w(K ) = g(K ) 1 −
mR (K ) f ( c+θ1+ θ ).
c + θ mR (K ) − g(K ) N
.
Note that mR is an integer. When mR increases by 1, θ
c+θ mR 1+θ
in-
< 1, so the resulting increase in g(K) cannot be 1+θ
greater than 1. Thus, the grievance θ mR − g(K ) weakly increases
creases by
as mR increases. Meanwhile, the equilibrium membership g(K) is weakly increasing in mR . Therefore, the expected welfare w(K) is nonmonotonic in reference point mR , as an increase in mR may increase the equilibrium membership, but may also increase the grievance. This result implies that, given K countries announcing intention of participation, an additional country has an incentive to make an announcement only if
g(K + 1) > g(K ), i.e., only if an additional announcement increases mR to the extent that the equilibrium membership is also increased. The nonmonotonicity of w(K) makes multiplicity of equilibria possible. We have the following remark.
Remark 3. (i) If g(1) = g(0), then no country making announcement is an equilibrium. (ii) For 0 < K < N, a sufficient condition for K countries making announcements to be an equilibrium is g(K + 1) = g(K ) and mR (K ) = mR (K − 1); (iii) moreover, if g(K + 1) = g(K ) and g(K ) > g(K − 1), K countries making announcements is an equilibrium for sufficiently large N. (iv) If mR (N) = mR (N − 1), or if g(N) > g(N − 1) and N is sufficiently large, then all countries announcing intention of participation is an equilibrium. Parts (ii) and (iii) of Remark 3 show that there may be interior equilibria in which some of the countries make announcements.11 This is in line with the observation that during the ongoing climate negotiations, a number of countries/regions, including the U.S., the E.U., China and India, claimed that they were going to make substantial endeavors in cutting GHG emissions.12 3. Conclusion This paper incorporates reference points into a model of International Environmental Agreements. We show that a sufficiently high reference point on the IEA membership has positive effects on the equilibrium IEA membership and abatement level. This result thus provides a less pessimistic insight than the canonical IEA model. Our result implies that effective management of reference points is helpful to resolve the climate problem. The current climate talks have reached an impasse, postponing the specification of binding commitments to a future negotiation (Beccherle & Tirole, 2011). However, this does not mean that the ongoing climate negotiations are unimportant, as these negotiations will form the basis of expectations, or reference points, of countries in the future negotiations. Although an effective and binding climate treaty has yet to emerge, many countries have promised mitigation of GHG emissions through the current climate talks. Many criticized that these promises are just non-binding cheap talks. However, our model shows that these promises could be beneficial, as they may raise the reference points of countries. Overall, a central message of this paper is that even if the current climate negotiations have not been very fruitful, it is still worthwhile maintaining a high expectation (reference point), as this would affect the chance of success in the next climate negotiations. Appendix A.1. Derivation of Eq. (2) Since mR is an integer, we have mR (K) ≥ mR (0) ≥ f(c). By Proposition 1 and Eq. (1), in equilibrium, the feeling of grievance arises only if mR > m ≥ c. In stage 0, a country’s expected welfare, denoted by w(K), equals the equilibrium level of abatement minus the expected cost of abatement and the expected grievance from the gap between mR and actual membership:
w(K ) = f
c + θ m (K ) 1+θ R
f −
c+θ mR (K ) 1+θ
N
× c + θ max m (K ) − f R
8
Relatedly, Kristensen and Gärling (1997) and Zartman (2007) show that initial offers influence reference points in negotiations. 9 In the equilibrium of the participation game without reference points, the IEA membership is f(c), which could be much lower than N, the most efficient and equitable membership. It is thus reasonable to assume that the referenced membership, mR , is not lower than c, no matter how many countries announce participation. 10 The cheap talk communication in the pre-play stage imposes no obligation of joining the IEA for the countries that announced. Meanwhile, those countries that did not announce intention of participation can also participate. Many current climate negotiations are conducted under the United Nations Framework Convention on Climate Change (UNFCCC) where every country can participate.
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c + θ mR (K ) ,0 1+θ
.
2 if K ≤ 2 . K if K > 2 Then we have a corner equilibrium in which no country announces participation and multiple interior equilibria in which one, two or five countries make announcements. 12 See, e.g. “EU Promises 20% Reduction in Carbon Emission by 2020,” The Guardian, 21 February, 2007, and “U.S. Commits to Greenhouse Gas Cuts under Copenhagen Climate Accord,” Scientific American, January 29, 2010. 11
For a numerical example, let N = 10, c = 1.5, θ = 0.2, and mR (K ) = {
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F. Hong / Journal of Behavioral and Experimental Economics 59 (2015) 68–73
Since mR (K) ≥ f(c) ≥ c, we have c+θ mR (K )
c+θ mR (K ) 1+θ
≤ mR (K ), which implies
f ( 1+θ ) ≤ mR (K ) as mR (K) is an integer. Therefore, w(K) can be rewritten as
w(K ) = f
c + θ mR (K ) 1+θ
f −
× c + θ m (K ) − f R
= f
c + θ mR (K ) 1+θ
c+θ mR (K ) 1+θ
N c + θ mR (K ) 1+θ
Proof (Remark 3). (i) If g(1) = g(0), then mR (0) − g(0) ≤ mR (1) − g(1) since mR (0) ≤ mR (1), yielding
w(0) = g(0) 1 −
N
A.2. Proofs
πs − θ max mR − m, 0 I if mR ≥ c us = . πs if mR < c
m − c − θ mR − m ≥ 0 ⇒m≥
c + θ mR . 1+θ
Note that
c+θ mR 1+θ
∈ (c, mR ) for case (ii). Combining cases (i) and (ii), we
see that when mR ≥ c, the IEA instructs its members to abate if and θ mR . only if m ≥ c+1+ θ We have considered all the possible cases. To summarize, the IEA will instruct its members to abate if and only if one of the following two (mutually exclusive) conditions is satisfied: (1) m ≥ f(c), mR < c; (2) m ≥ f(c), mR ≥ c and m ≥
c+θ mR . 1+θ
For condition (2), note that when the integer mR equals c, then = c = f (c). So the above summary can be rewritten as the following claim. Claim : The IEA will instruct its members to abate if and only if one of the following two (mutually exclusive) conditions is satisfied: c+θ mR 1+θ
(1 ) m ≥ f(c), mR ≤ f(c); (2 ) m ≥ f(c), mR > f(c) and m ≥ mR > f(c) and m ≥
c+θ mR 1+θ
c + θ mR (K ) − g(K ) N
≥ g(K + 1) 1 −
c + θ mR (K + 1) − g(K + 1) N
= w(K + 1),
(A.1)
w(K ) = g(K ) 1 −
c + θ mR (K ) − g(K )
≥ g(K − 1) 1 − = w(K − 1).
N
c + θ mR (K − 1) − g(K − 1) N
(A.2)
Like in Part (i), g(K + 1) = g(K ) and mR (K ) ≤ mR (K + 1) (by the monotonicity of mR (K)) ensure that Inequality (A.1) is satisfied. mR (K ) = mR (K − 1) implies that g(K ) = g(K − 1), and therefore w(K ) = w(K − 1) so Inequality (A.2) is also satisfied. So, if g(K + 1) = g(K ) and mR (K ) = mR (K − 1), K countries making announcement is an equilibrium. (iii) As shown in the paragraph immediately above Remark 3, θ (mR (K ) − g(K )) is weakly increasing in mR (K). g(K ) > g(K − 1) implies mR (K ) > mR (K − 1). Therefore, if g(K ) > g(K − 1), then θ (mR (K ) − g(K )) ≥ θ (mR (K − 1) − g(K − 1)). However, note that θ (mR (K ) − g(K )) is independent of N. Therefore, for sufficiently large N, the term in the square brackets in the left side of “≥” in Inequality (A.2) is sufficiently close to the term in the square brackets in the right side of “≥”, such that Inequality (A.2) is satisfied given g(K ) > g(K − 1). Also, as shown in the proof of Part (ii), g(K + 1) = g(K ) implies Inequality (A.1). (iv) For K = N countries making announcement to be an equilibrium, Inequality (A.1) (external stability) is irrelevant. The proof is similar to that for Inequality (A.2) in Parts (ii) and (iii). Supplementary Materials
c+θ mR . 1+θ
Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.socec.2015.10.004.
imply m > c, and thus imply m ≥ f(c) as m
is an integer. Also note that m ≥
= w(1).
N
w(K ) = g(K ) 1 −
and
If mR < c, by Eq. (1), us = πs ; given m ≥ f(c), the IEA will then instruct its members to abate. If mR ≥ c, there are two cases (i) c ≤ mR ≤ m and (ii) c ≤ m < mR . In case (i), by Eq. (1), us = πs ; given m ≥ f(c), the IEA will instruct its members to abate. In case (ii), an IEA member’s payoff from not abating is 0, and the payoff from abatement is m − c − θ (mR − m). So the IEA will instruct its members to abate if and only if
c + θ mR (1) − g(1)
Therefore, given that no other country announces, no country has an incentive to announce intention of participation. As a result, no country making announcement is an equilibrium. (ii) For K ∈ (0, N) countries making announcement to be an equilibrium, the following two conditions (external stability and internal stability, respectively) should be satisfied:
Proof (Lemma 1). In the abatement game, the material payoff of an IEA member, π s , equals m − c if it abates, and 0 otherwise. Given this, by Eq. (1), obviously, the IEA will not instruct its members to abate if m < c. We will next focus on the case when m ≥ c. Suppose m ≥ c, implying m ≥ f(c) as m is an integer. Eq. (1) can be rewritten as
N
≥ g(1) 1 −
⎤ ⎡ c+θ mR (K ) c + θ mR (K ) − f 1+θ ⎦. ⎣1 −
c + θ mR (0) − g(0)
c+θ mR 1+θ
θm ) is equivalent to m ≥ f ( c+1+ θ R
as m is an integer. So condition (2’) can be simplified as: mR > f(c) and θ mR ). The claim with the simplified condition (2’) thus gives m ≥ f ( c+1+ θ us the lemma.
References Abeler, J., A. Falk, L. Goette, and D. Huffman, 2011. “Reference points and effort provision.” American Economic Review 101, 470–492. Alesina, A. and G. Angeletos, 2005. “Fairness and redistribution.” American Economic Review 95, 960–980.
F. Hong / Journal of Behavioral and Experimental Economics 59 (2015) 68–73 Barrett, S., 1999. “A theory of full international cooperation.” Journal of Theoretical Politics 11, 519–541. Barrett, S., 2003. Environment and Statecraft: Oxford University Press. Barrett, S., 2005. “The theory of international environmental agreements.” In Maler, K.G. and J. Vincent (Eds.), The Handbook of Environmental Economics. 1457–1516 Amsterdam North Holland. Barrett, S., 2006. “Climate treaties and ‘breakthrough’ technologies.” American Economic Review 96(2), 22–25. Beccherle, J. and J. Tirole, 2011. “Regional initiatives and the cost of delaying binding climate change agreements.” Journal of Public Economics 95(11–12), 1339–1348. Brandts, J. and C. Solà, 2001. “Reference points and negative reciprocity in simple sequential games.” Games and Economic Behavior 36(2), 138–157. Carraro, C., C. Marchiori, and S. Oreffice, 2009. “Endogenous minimum participation in international environmental treaties.” Environmental and Resource Economics 42, 411–425. Cazorla, M. and M. Toman, 2001. “International equity and climate change policy.” In Toman, M. (Ed.). Climate Change Economics and Policy: An RFF Anthology. Washington, DC: Resource for the Future. Charite, J., R. Fisman, I. Kuziemko, 2015. Reference points and redistributive preferences: Experimental evidence. NBER Working Paper #21009. Eyckmans, J. and S. Kverndokk, 2010. “Moral concerns on tradable pollution permits in international environmental agreements.” Ecological Economics 69(9), 1814–1823. Fehr, E., O. Hart, and C. Zehnder, 2011. “Contracts as reference points – Experimental evidence.” American Economic Review 101(2), 493–525. Fehr, E. and K. Schmidt, 1999. “A theory of fairness, competition and cooperation.” Quarterly Journal of Economics 114(3), 817–868. Gerber, A., J. Neitzel, and P. Wichardt, 2013. “Minimum participation rules for the provision of public goods.” European Economic Review 64, 209–222. Hara, T., 2005. The future of the kyoto protocol: Mimeo. Hart, O. and J. Moore, 2008. “Contracts as reference points.” Quarterly Journal of Economics 123(1), 1–48.
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Hong, F. and L. Karp, 2012. “International environmental agreements with mixed strategies and investment.” Journal of Public Economics 96, 685–697. Hong, F. and L. Karp, 2014. “International environmental agreements with endogenous or exogenous risk.” Journal of the Association of Environmental and Resource Economists 1(3), 365–394. Kahneman, D., 1992. “Reference points, anchors, norms, and mixed feelings.” Organizational Behavior and Human Decision Processes 51(2), 296–312. Karp, L. and L. Simon, 2013. “Participation games and international environmental agreements: A non-parametric model.” Journal of Environmental Economics and Management 65(2), 326–344. Kennan, G., 1985. “Morality and foreign policy .” Foreign Affairs 64(2), 205–218. Kolstad, C., 2011. Environmental Economics, 2nd edition. New York: Oxford University Press. Kolstad, C., 2014. International environmental agreements among heterogenous countries with social preferences. NBER Working Paper 20204. Kosfeld, M., A. Okada, and A. Riedl, 2009. “Institution formation in public goods games.” American Economic Review 99(4), 1335–1355. Kristensen, H. and T. Gärling, 1997. “The effects of anchor points and reference points on negotiation process and outcome.” Organizational Behavior and Human Decision Processes 71(1), 85–94. Lange, A. and C. Vogt, 2003. “Cooperation in international environmental negotiations due to a preference for equity.” Journal of Public Economics 87(9–10), 2049–2067. Palfrey, T. and H. Rosenthal, 1991. “Testing for effects of cheap talk in a public goods game with private information.” Games and Economic Behavior 3(2), 183–220. Rubio, S. and A. Ulph, 2007. “An infinite-horizon model of dynamic membership of international environmental agreements.” Journal of Environmental Economics and Management 54(3), 296–310. Starkey, B., M. Boyer, and J. Wilkenfeld, 2010. International Negotiation in a Complex World: Rowman & Littlefield Publishers. Zartman, I.W., 2007. Negotiation and Conflict Management: Essays on Theory and Practice: Taylor & Francis.
Contents lists available at ScienceDirect
Journal of Behavioral and Experimental Economics journal homepage: www.elsevier.com/locate/socec
International Environmental Agreements with reference pointsR Fuhai Hong∗ Division of Economics, Nanyang Technological University, Singapore
a r t i c l e
i n f o
Article history: Received 19 November 2014 Revised 11 March 2015 Accepted 1 October 2015
JEL Classification: D03 Q5
a b s t r a c t Whether or not the current climate talks achieve a meaningful treaty, the current negotiation forms important reference points for future negotiations. In this paper, we introduce reference points to a canonical model of International Environmental Agreements (IEAs). Countries have reference points on IEA membership. An IEA member that abates is aggrieved if there is a material loss relative to the case with the referenced membership. We find that reference points weakly reduce the abatement level for an IEA with given membership, while interestingly, reference points weakly increase the equilibrium membership and thus the equilibrium abatement level of the IEA. These results imply that effective management of reference points could be conducive to the resolution of the climate problem.
Keywords: International Environmental Agreements Reference points
1. Introduction In order to control climate change, concerted efforts in abating Greenhouse Gas (GHG) emissions should be made. However, GHG abatement is a global public good and the provision of this global public good suffers from the usual free riding problem, in the absence of a world government. An International Environmental Agreement (IEA) is a coalition mechanism that aims to resolve the free riding problem from transboundary pollutions. However, the literature on IEAs is generally pessimistic regarding the equilibrium participation level in an IEA (see, e.g., Barrett, 2005 for a survey). With insufficient participation, the IEA mechanism has little chance to resolve the climate problem. Much of the IEA theory relies on a particular type of participation games in which countries decide on whether to participate in an IEA and the resulting IEA makes abatement decisions for its members. In the equilibrium, some countries choose to join the IEA and contribute to the public good while the others stay out. The asymmetry of the equilibrium raises an important but debatable concern revolving around the climate problem: equity (see, e.g. Cazorla and Toman, 2001). Countries exhibit a preference for equity in international environmental negotiations (Lange and Vogt, 2003). However, lacking a consensus on what is equity, countries’ perception of an equitable
R
I thank Teh Tat How for research assistance, Larry Karp, Akihisa Mori, an anonymous referee and participants at the 2014 EAAERE Inter-congress Conference for helpful comments or discussions, and a start-up grant of Nanyang Technological University (Grant no. HSS-SUG) for financial support. ∗ Tel. +65 67904496. E-mail address: [email protected] http://dx.doi.org/10.1016/j.socec.2015.10.004 2214-8043/© 2015 Elsevier Inc. All rights reserved.
© 2015 Elsevier Inc. All rights reserved.
way to address the climate problem critically depends on their reference points in viewing the climate issue. The literature has shown that reference points play a crucial role in human decisions and interactions. Kahneman (1992) reviews the role of reference points in individual choices and interpersonal negotiations. Reference points are characterized by the abrupt changes in the valuation of gains and losses and of acceptable or reprehensible behavior. More recently, Brandts and Solà (2001) and Abeler et al. (2011) provide evidence on how reference points affect reciprocal behavior and effort provision. Hart and Moore (2008) and Fehr, Hart, and Zehnder (2011) introduce reference points to the negotiation between contracting parties: if a party does not get what he feels entitled to, he is aggrieved and provides perfunctory rather than consummate performance, causing deadweight losses. Kristensen and Gärling (1997) provide empirical evidence showing that reference points influence negotiation process and outcome. Reference points not only affect behavior at the individual and interpersonal level, but could also make a difference at the international arena. Nations’ behavior is not purely driven by materialistic interests.1 In a country, if voters have certain preference with reference points, the government should take this into account and respond to the voters’ reference points. In a recent study,
1 For instance, equity is an important issue in international negotiation of climate treaties. The principle of equity is articulated in Article 3 of the Convention on Climate Change and the decision approved by the COP 6 in Bonn. For another example, Kennan (1985) provides anecdotes and a critique on the moralistic judgments of American statesmen on foreign policies. Many papers, e.g. Lange and Vogt (2003), Eyckmans and Kverndokk (2010) and Kolstad (2014), consider countries’ non-materialistic preferences in decision-makings regarding IEAs.
F. Hong / Journal of Behavioral and Experimental Economics 59 (2015) 68–73
Charite, Fisman, and Kuziemko (2015) show that social planners do respect people’s reference points in decision-makings. Moreover, in international negotiations, the decisions of diplomats or national delegates may be influenced by their own reference points. Starkey, Boyer, and Wilkenfeld (2010) point out that “Diplomacy is not just about bargaining. There is a human dimension to the negotiation game that should not be ignored.” Zartman (2007) discusses the role of reference points in international negotiations on the European Development Fund. Reference points can also be important in international negotiations on climate treaties. Countries are dissatisfied if other countries’ participation level in climate treaties is below their referenced level and may thus be unwilling to make consummate efforts to address the transboundary pollutions. For instance, many members of the Kyoto Protocol, including Australia, Canada, Japan and New Zealand, harbored discontent towards the United States for not ratifying the Kyoto Protocol (see, e.g., Hara, 2005), although the U.S. was not pivotal for the enforcement of the Protocol. These countries were also aggrieved by the fact that developing countries were out of regulation under the Kyoto Protocol, and some expressed unwillingness to take part in the second phase of the Protocol.2 In this paper, we introduce reference points to a canonical IEA model. Countries have reference points regarding the membership of the IEA. If the actual membership falls short of the reference points, the IEA members may feel aggrieved by being free ridden, which results in perfunctory performance of the IEA. Interestingly, anticipating such responses of IEA members, in the equilibrium, more countries would participate in the IEA with high reference points. Therefore, if there is a way to “manage” countries’ reference points, reference points could be used as an instrument to increase the membership and abatement level of the IEA. Our result thus provides a less pessimistic insight than the standard IEA literature. Gerber, Neitzel, and Wichardt (2013) consider minimum participation rules for coalitions providing public goods. These rules increase the level of participation above which the coalition is successfully implemented and could thus increase the equilibrium level of participation. In their model, the minimum participation rules are exogenous. Carraro, Marchiori, and Oreffice (2009) consider endogenous determination of minimum participation constraints by a prior stage of unanimity. In both models, the size of the minimally successful coalition increases because of the participation rules which were legally imposed. In our paper, we show that a sort of psychological trait with reference points is able to increase the size of the minimally successful IEA and thus the equilibrium membership, in the absence of explicitly imposed participation constraints on the agreement. A few studies have investigated the role of social preferences in IEA negotiation and institution formation in public good games. Eyckmans and Kverndokk (2010) and Kolstad (2014) consider moral concerns and (impure) altruism in IEAs. Lange and Vogt (2003) and Kosfeld, Okada, and Riedl (2009) incorporate equity preference and inequality aversion into models of coalition formation. In particular, Kosfeld, Okada, and Riedl (2009) show that inequality aversion in the sense of Fehr and Schmidt (1999) can increase the size of a sanctioning organization. Although equity is undoubtedly important in climate negotiations, what is equitable allocation is controversial, and people “appear to desire equality relative to some reference point” (Alesina and Angeletos, 2005).3 In this paper, we follow the tradition of Kahneman (1992) and Hart and Moore (2008) by incorporating reference points to an IEA model. While the inequality-averse
2 See, e.g. the entry of “Canada and the Kyoto Protocol” in the Wikipedia, “Australia rejects Kyoto pact,” in BBC News, June 5, 2002, and “NZ ‘ahead of the curve’ in quitting Kyoto Protocol”, in 3 News, 3 December 2012. 3 Cazorla and Toman (2001) review the alternative equity criteria for climate change policy. Depending on different reference points, the equity arguments include equal burden shares, equal percentage reduction of pollutants, and reducing differences between developed and developing countries (see e.g. Lange and Vogt, 2003).
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Fig. 1. The game.
preference is exogenous in Kosfeld, Okada, and Riedl (2009), reference points are endogenous and can be affected by pre-play communication in our extended model in Section 2.3. With this model, we show that effective management of countries’ reference points, and more broadly their perception towards the climate problem, could increase the chance of achieving a successful IEA. The rest of this paper is organized as follows. Sections 2.1 and 2.2 present the IEA model, with and without reference points, respectively, while Section 2.3 considers an extended model with preplay communication and endogenous reference points. Section 3 concludes with a discussion on the implications of our results. 2. Model The first subsection below presents the canonical IEA model as a benchmark case, the second subsection introduces reference points to the model, while the last subsection discusses the choice of reference points by including a prior stage of communication in which countries announce the intention of participation in the IEA. 2.1. The canonical IEA model Barrett (1999) firstly proposed the following “canonical” IEA model. This model is also used in, e.g., Barrett (2003, Chap. 7) and Kolstad (2011, Chap. 19). There are N identical countries. Each country has two binary decisions: participation in an IEA and abatement. If we assume linear costs and benefits of abatement, then a country will either abate at capacity or does not abate at all. So there is no additional loss of generality in assuming binary abatement. Abatement is a global public good. We normalize the benefit of one unit of abatement, to each country, to one. The country that abates incurs an abatement cost, c. We assume that 1 < c < N, where the first inequality implies that it is a dominant strategy for a country acting alone to choose not to abate, while the second inequality means that the world is better off from any country’s abatement. The game consists of two stages: in stage 1, each country decides on whether to participate in the IEA; in stage 2, members of the IEA let the IEA decide on abatement, while the outsiders make their own abatement decisions. Fig. 1 summarizes the game. The IEA is assumed to maximize the total welfare of its members. The game can be solved backward. In stage 2, outsiders choose not to abate, following their individually rational decisions. Let the membership of the IEA be m. The IEA will instruct its members to abate if and only if m ≥ c, where m is the coalition’s benefit from one unit of abatement and c is the cost. Let f(x) be the smallest integer no less than x, for any x. Then f(c) is the membership of the “minimally successful IEA” given the IEA’s decision rule. We say that a country is pivotal if exactly f (c) − 1 other countries join the IEA, because the country’s participation will affect the IEA’s decision. A pivotal country has an incentive to join the IEA because by doing so, the country obtains a payoff of f − c ≥ 0. A country’s additional membership is superfluous from its own viewpoint if at least f(c) other countries
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F. Hong / Journal of Behavioral and Experimental Economics 59 (2015) 68–73
join the IEA, because by joining, it does not affect any other country’ abatement decision, but incurs a cost of c − 1 > 0. We then assume a tie breaking condition in stage 1 that a country that is indifferent between participation and not will choose to participate.4 Then in this participation game, there is a unique Nash equilibrium membership where f(c) countries join the IEA. f(c) is internally stable since no member has an incentive to leave the IEA (because of the benefit of being pivotal f − c), and is also externally stable because no outsider has an incentive to join (as an additional member would be superfluous from its own viewpoint). An IEA with f (c) − 1 members is not externally stable because an additional membership is pivotal and an outsider thus has an incentive to join. An IEA with less than f (c) − 1 members is not externally stable because of the tie-breaking assumption on participation. An IEA with more than f(c) members is not internally stable because the IEA does not cease abating even if a member leaves and the cost of being superfluous is c − 1 > 0. This IEA model has the advantage of providing an analytical solution. With abatement cost c, the IEA contains f(c) members, and the abatement level is f(c). In the first best case with full cooperation, every country abates and the abatement level is N. In the Nash equilibrium without the IEA, no country abates. The IEA mechanism is useful f c in the sense that it achieves a fraction, (N ) , of total gains of cooperation. However, the equilibrium abatement of the IEA still falls short of efficiency, especially when the abatement cost, c, is much lower than N. 2.2. A model with reference points In the model by Hart and Moore (2008), a reference point means the feeling of entitlement. They suppose that a party is happy to provide consummate performance if he feels that he is getting what he is entitled to, but will withhold some part of consummate performance if he is shortchanged, which they refer to as “shading”. This idea has implications on international environmental and climate negotiations. In the above IEA model, ex ante countries are identical; in the equilibrium, however, some countries join the IEA and provide public goods, while the other countries free ride. If the IEA membership is low, the IEA members may feel being shortchanged by providing the public good, as many of the countries free ride on them. Therefore, the IEA members may be unwilling to provide the public good, even if it is materialistically beneficial to do so, i.e., m ≥ c. An IEA member may feel happy to abate, only when a sufficient number of other countries also join the IEA and abate (or, in other words, not many countries free ride). To operationalize this idea, we assume that a country has a reference point on IEA participation, mR , an integer.5,6 We make the following assumptions about member countries’ preference. First, we assume that an IEA member feels aggrieved only if it abates. This is because a non-abating IEA member does not contribute more than non-members, and will not feel being shortchanged. Second, we assume that member countries have rational expectation about their material payoffs in an IEA with mR members. An IEA with mR members instructs its members to abate if and only if mR ≥ c. So the 4
This assumption is also adopted in studies such as Karp and Simon (2013) and Hong and Karp (2012, 2014), to rule out the “trivial” equilibria in which less than f (c) − 1 countries join and thus there is no a meaningful IEA to be formed. Alternatively, one may consider a dynamic game, where countries take their participation decisions sequentially according to some pre-determined order. This will give us the same result. We thank an anonymous referee for pointing this out. 5 Starkey, Boyer, and Wilkenfeld (2010) write, “Although nation’s culture is different from one another, the main reference points are the same across most lands.” For simplicity, we keep the assumption of identical countries such that each country has the same reference point. The next subsection will discuss the choice of reference points. 6 For a country that has a preference for “perfect equity” which requires all countries to join the IEA, the reference point equals N.
material payoff of a member in such an IEA is mR − c when mR ≥ c and 0 otherwise. Third, we assume that an abating member country feels aggrieved if its material payoff is lower than that under the referenced case. Note that if mR ≥ c and m < mR , there is a material payoff loss relative to the referenced case for the abating member, which equals (mR − c) − (m − c) = mR − m; when mR < c and m < c, there is a material payoff loss for the abating member, equal to 0 − (m − c) = c − m. With the above assumptions, the preference of a member/signatory country is given by
us =
πs − θ max[mR − m, 0]I if mR ≥ c , πs − θ max[c − m, 0]I if mR < c
(1)
where π s is the material payoff, I is an indicator function which equals one if the country abates and zero otherwise, and θ indicates how aggrieved the country is about the material payoff loss relative to the referenced case.7 With the above preference, in stage 2, the following lemma shows the IEA’s decision rule. Lemma 1. If the reference point mR ≤ f(c), the IEA abates if and only if θ mR ). m ≥ f(c); if mR > f(c), the IEA abates if and only if m ≥ f ( c+1+ θ Proofs are relegated to the appendix. Lemma 1 implies that reference points weakly increase the size of the minimally successful IEA. In the benchmark case without reference points, the minimally successful IEA is f(c). In the model with reference points, the minimally θ mR ) (which is weakly successful IEA is f(c) if f(c) ≥ mR , and is f ( c+1+ θ
greater than f(c) when mR > f(c)) if mR > f(c). Since the IEA’s decision rule on abatement is a step function with a jump at the minimally successful IEA in both models (with and without reference points), the increase in the size of the minimally successful IEA leads to the following remark. Remark 1. For a given level of membership, reference points weakly reduce the abatement level of the IEA.
θ m ), In particular, Lemma 1 implies that when f (c) ≤ m < f ( c+1+ θ the IEA may not instruct its members to abate even if abatement is materialistically beneficial to all. These results echo the observation in Hart and Moore (2008) that parties with high reference points may provide perfunctory rather than consummate performance, causing deadweight losses. We then move backward to stage 1, the participation game. The following proposition shows the equilibrium membership with reference points. Interestingly, consideration of the participation equilibrium overturns the pessimistic result in Remark 1. R
Proposition 1. With reference point mR , if mR ≤ f(c), in equilibrium f(c) θ mR ) countries countries join the IEA; if mR > f(c), in equilibrium f ( c+1+ θ join the IEA. The proposition is straightforward, with the IEA decision rule given by Lemma 1, so its proof is relegated to an online appendix. Note that when mR > f(c), Lemma 1 and Proposition 1 together imθ mR ), which is weakly ply that the global level of abatement is f ( c+1+ θ θ m ) ≥ f (c), for mR > f(c). We thus increasing in mR . Meanwhile, f ( c+1+ θ have the following remark. R
Remark 2. When mR > f(c), the equilibrium abatement level is (weakly) higher than that in the benchmark case without reference points, and is weakly increasing in the reference point mR . When mR ≤ f(c), the equilibrium abatement level is not different from the benchmark case without reference points. Overall, consideration of reference points in IEA games provides a less pessimistic 7 The max function and the indicator function I in the utility function are consistent with Kahneman (1992) characterization of reference points by the abrupt changes in the valuation of gains and losses and of acceptable or reprehensible behavior.
F. Hong / Journal of Behavioral and Experimental Economics 59 (2015) 68–73
view on the equilibrium IEA participation and abatement level than the standard model, when the reference points are sufficiently high. 2.3. Discussion In this subsection, we discuss a determinant of the reference point, mR . We introduce a prior stage, stage 0, of pre-play communication to the above model. In this prior stage, each country chooses whether to announce intention of participating in the IEA. The announcement is costless, non-binding and non-verifiable. In this sense, the communication stage is close to the cheap-talk stage in Palfrey and Rosenthal (1991) public good game. However, the number of announcements made on the intention of participation is supposed to increase countries’ expectation on the participation level in the IEA. Moreover, Abeler et al. (2011) show that expectation determines reference points. Therefore, we assume that the reference point in later stages is a weakly increasing function of the number of countries that make announcements: mR (K), where K is the number of countries that announce intention of participation in the prior stage.8 To focus on the more interesting case, in this subsection we assume that mR (0) ≥ c.9 Taking into account the asymmetry of the equilibrium in the participation game where some countries join the IEA while the others stay out, as in Barrett (2006), Rubio and Ulph (2007) and Hong and Karp (2012), we further assume that in this prior stage, each country faces the same probability of becoming an IEA member in the next stage.10 In stage 0, a country’s expected welfare, denoted by w(K), can be written as
w(K ) = f
c + θ m (K ) 1+θ R
⎡ ⎣1 −
c + θ mR (K ) − f
c+θ mR (K ) 1+θ
N
⎤
⎦. (2)
The appendix shows the derivation of Eq. (2). Let g(K ) ≡ Eq. (2) can be rewritten as
w(K ) = g(K ) 1 −
mR (K ) f ( c+θ1+ θ ).
c + θ mR (K ) − g(K ) N
.
Note that mR is an integer. When mR increases by 1, θ
c+θ mR 1+θ
in-
< 1, so the resulting increase in g(K) cannot be 1+θ
greater than 1. Thus, the grievance θ mR − g(K ) weakly increases
creases by
as mR increases. Meanwhile, the equilibrium membership g(K) is weakly increasing in mR . Therefore, the expected welfare w(K) is nonmonotonic in reference point mR , as an increase in mR may increase the equilibrium membership, but may also increase the grievance. This result implies that, given K countries announcing intention of participation, an additional country has an incentive to make an announcement only if
g(K + 1) > g(K ), i.e., only if an additional announcement increases mR to the extent that the equilibrium membership is also increased. The nonmonotonicity of w(K) makes multiplicity of equilibria possible. We have the following remark.
Remark 3. (i) If g(1) = g(0), then no country making announcement is an equilibrium. (ii) For 0 < K < N, a sufficient condition for K countries making announcements to be an equilibrium is g(K + 1) = g(K ) and mR (K ) = mR (K − 1); (iii) moreover, if g(K + 1) = g(K ) and g(K ) > g(K − 1), K countries making announcements is an equilibrium for sufficiently large N. (iv) If mR (N) = mR (N − 1), or if g(N) > g(N − 1) and N is sufficiently large, then all countries announcing intention of participation is an equilibrium. Parts (ii) and (iii) of Remark 3 show that there may be interior equilibria in which some of the countries make announcements.11 This is in line with the observation that during the ongoing climate negotiations, a number of countries/regions, including the U.S., the E.U., China and India, claimed that they were going to make substantial endeavors in cutting GHG emissions.12 3. Conclusion This paper incorporates reference points into a model of International Environmental Agreements. We show that a sufficiently high reference point on the IEA membership has positive effects on the equilibrium IEA membership and abatement level. This result thus provides a less pessimistic insight than the canonical IEA model. Our result implies that effective management of reference points is helpful to resolve the climate problem. The current climate talks have reached an impasse, postponing the specification of binding commitments to a future negotiation (Beccherle & Tirole, 2011). However, this does not mean that the ongoing climate negotiations are unimportant, as these negotiations will form the basis of expectations, or reference points, of countries in the future negotiations. Although an effective and binding climate treaty has yet to emerge, many countries have promised mitigation of GHG emissions through the current climate talks. Many criticized that these promises are just non-binding cheap talks. However, our model shows that these promises could be beneficial, as they may raise the reference points of countries. Overall, a central message of this paper is that even if the current climate negotiations have not been very fruitful, it is still worthwhile maintaining a high expectation (reference point), as this would affect the chance of success in the next climate negotiations. Appendix A.1. Derivation of Eq. (2) Since mR is an integer, we have mR (K) ≥ mR (0) ≥ f(c). By Proposition 1 and Eq. (1), in equilibrium, the feeling of grievance arises only if mR > m ≥ c. In stage 0, a country’s expected welfare, denoted by w(K), equals the equilibrium level of abatement minus the expected cost of abatement and the expected grievance from the gap between mR and actual membership:
w(K ) = f
c + θ m (K ) 1+θ R
f −
c+θ mR (K ) 1+θ
N
× c + θ max m (K ) − f R
8
Relatedly, Kristensen and Gärling (1997) and Zartman (2007) show that initial offers influence reference points in negotiations. 9 In the equilibrium of the participation game without reference points, the IEA membership is f(c), which could be much lower than N, the most efficient and equitable membership. It is thus reasonable to assume that the referenced membership, mR , is not lower than c, no matter how many countries announce participation. 10 The cheap talk communication in the pre-play stage imposes no obligation of joining the IEA for the countries that announced. Meanwhile, those countries that did not announce intention of participation can also participate. Many current climate negotiations are conducted under the United Nations Framework Convention on Climate Change (UNFCCC) where every country can participate.
71
c + θ mR (K ) ,0 1+θ
.
2 if K ≤ 2 . K if K > 2 Then we have a corner equilibrium in which no country announces participation and multiple interior equilibria in which one, two or five countries make announcements. 12 See, e.g. “EU Promises 20% Reduction in Carbon Emission by 2020,” The Guardian, 21 February, 2007, and “U.S. Commits to Greenhouse Gas Cuts under Copenhagen Climate Accord,” Scientific American, January 29, 2010. 11
For a numerical example, let N = 10, c = 1.5, θ = 0.2, and mR (K ) = {
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F. Hong / Journal of Behavioral and Experimental Economics 59 (2015) 68–73
Since mR (K) ≥ f(c) ≥ c, we have c+θ mR (K )
c+θ mR (K ) 1+θ
≤ mR (K ), which implies
f ( 1+θ ) ≤ mR (K ) as mR (K) is an integer. Therefore, w(K) can be rewritten as
w(K ) = f
c + θ mR (K ) 1+θ
f −
× c + θ m (K ) − f R
= f
c + θ mR (K ) 1+θ
c+θ mR (K ) 1+θ
N c + θ mR (K ) 1+θ
Proof (Remark 3). (i) If g(1) = g(0), then mR (0) − g(0) ≤ mR (1) − g(1) since mR (0) ≤ mR (1), yielding
w(0) = g(0) 1 −
N
A.2. Proofs
πs − θ max mR − m, 0 I if mR ≥ c us = . πs if mR < c
m − c − θ mR − m ≥ 0 ⇒m≥
c + θ mR . 1+θ
Note that
c+θ mR 1+θ
∈ (c, mR ) for case (ii). Combining cases (i) and (ii), we
see that when mR ≥ c, the IEA instructs its members to abate if and θ mR . only if m ≥ c+1+ θ We have considered all the possible cases. To summarize, the IEA will instruct its members to abate if and only if one of the following two (mutually exclusive) conditions is satisfied: (1) m ≥ f(c), mR < c; (2) m ≥ f(c), mR ≥ c and m ≥
c+θ mR . 1+θ
For condition (2), note that when the integer mR equals c, then = c = f (c). So the above summary can be rewritten as the following claim. Claim : The IEA will instruct its members to abate if and only if one of the following two (mutually exclusive) conditions is satisfied: c+θ mR 1+θ
(1 ) m ≥ f(c), mR ≤ f(c); (2 ) m ≥ f(c), mR > f(c) and m ≥ mR > f(c) and m ≥
c+θ mR 1+θ
c + θ mR (K ) − g(K ) N
≥ g(K + 1) 1 −
c + θ mR (K + 1) − g(K + 1) N
= w(K + 1),
(A.1)
w(K ) = g(K ) 1 −
c + θ mR (K ) − g(K )
≥ g(K − 1) 1 − = w(K − 1).
N
c + θ mR (K − 1) − g(K − 1) N
(A.2)
Like in Part (i), g(K + 1) = g(K ) and mR (K ) ≤ mR (K + 1) (by the monotonicity of mR (K)) ensure that Inequality (A.1) is satisfied. mR (K ) = mR (K − 1) implies that g(K ) = g(K − 1), and therefore w(K ) = w(K − 1) so Inequality (A.2) is also satisfied. So, if g(K + 1) = g(K ) and mR (K ) = mR (K − 1), K countries making announcement is an equilibrium. (iii) As shown in the paragraph immediately above Remark 3, θ (mR (K ) − g(K )) is weakly increasing in mR (K). g(K ) > g(K − 1) implies mR (K ) > mR (K − 1). Therefore, if g(K ) > g(K − 1), then θ (mR (K ) − g(K )) ≥ θ (mR (K − 1) − g(K − 1)). However, note that θ (mR (K ) − g(K )) is independent of N. Therefore, for sufficiently large N, the term in the square brackets in the left side of “≥” in Inequality (A.2) is sufficiently close to the term in the square brackets in the right side of “≥”, such that Inequality (A.2) is satisfied given g(K ) > g(K − 1). Also, as shown in the proof of Part (ii), g(K + 1) = g(K ) implies Inequality (A.1). (iv) For K = N countries making announcement to be an equilibrium, Inequality (A.1) (external stability) is irrelevant. The proof is similar to that for Inequality (A.2) in Parts (ii) and (iii). Supplementary Materials
c+θ mR . 1+θ
Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.socec.2015.10.004.
imply m > c, and thus imply m ≥ f(c) as m
is an integer. Also note that m ≥
= w(1).
N
w(K ) = g(K ) 1 −
and
If mR < c, by Eq. (1), us = πs ; given m ≥ f(c), the IEA will then instruct its members to abate. If mR ≥ c, there are two cases (i) c ≤ mR ≤ m and (ii) c ≤ m < mR . In case (i), by Eq. (1), us = πs ; given m ≥ f(c), the IEA will instruct its members to abate. In case (ii), an IEA member’s payoff from not abating is 0, and the payoff from abatement is m − c − θ (mR − m). So the IEA will instruct its members to abate if and only if
c + θ mR (1) − g(1)
Therefore, given that no other country announces, no country has an incentive to announce intention of participation. As a result, no country making announcement is an equilibrium. (ii) For K ∈ (0, N) countries making announcement to be an equilibrium, the following two conditions (external stability and internal stability, respectively) should be satisfied:
Proof (Lemma 1). In the abatement game, the material payoff of an IEA member, π s , equals m − c if it abates, and 0 otherwise. Given this, by Eq. (1), obviously, the IEA will not instruct its members to abate if m < c. We will next focus on the case when m ≥ c. Suppose m ≥ c, implying m ≥ f(c) as m is an integer. Eq. (1) can be rewritten as
N
≥ g(1) 1 −
⎤ ⎡ c+θ mR (K ) c + θ mR (K ) − f 1+θ ⎦. ⎣1 −
c + θ mR (0) − g(0)
c+θ mR 1+θ
θm ) is equivalent to m ≥ f ( c+1+ θ R
as m is an integer. So condition (2’) can be simplified as: mR > f(c) and θ mR ). The claim with the simplified condition (2’) thus gives m ≥ f ( c+1+ θ us the lemma.
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