china, the united states, bargaining, and climate change

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ORIGINAL PAPER China, the United States, bargaining, and climate change Robert Y. Shum Accepted: 23 October 2013 / Published online: 10 November 2013 Ó Springer Science+Business Media Dordrecht 2013 Abstract Knowing what is at stake in terms of likely damages from accumulating greenhouse gases, how can major emitters fail to reach agreement on limits? Bargaining analysis suggests that an uneven distribution of abatement costs over time may play a significant part. Using a stylized, complete-information model of the strategic space facing the two largest emitters of greenhouse gases, China and the United States, a simple numerical example reaches a strong and surprising conclusion: To be feasible under cur- rent technological and economic conditions, any international agreement on climate change will have to allocate a level of future emissions for carbon dioxide in China that is at least twice as large as the level for the United States, in order to account for the effects on Chinese interests from continued economic growth. Keywords Bargaining Á Climate change Á Energy Á Rising powers Á China Á United States 1 Introduction Among the vivid descriptions we have of the events leading up to the Copenhagen Con- ference (COP-15), several remind us of the surprise expressed by witnesses at the time concerning the assertiveness of China’s negotiating position (Christoff 2010; Grubb 2010; Roberts 2011; Cf. Bodansky 2010; Dimitrov 2010; Parker et al. 2012). Some observers additionally described the logic behind this position: simply in order to preserve its future ‘‘emissions space,’’ China’s negotiators felt compelled to reject any declared targets that Electronic supplementary material The online version of this article (doi:10.1007/s10784-013-9231-4) contains supplementary material, which is available to authorized users. R. Y. Shum (&) Department of Political Science and International Studies, The College at Brockport, State University of New York (SUNY), 350 New Campus Drive, Brockport, NY 14420, USA e-mail: [email protected] 123 Int Environ Agreements (2014) 14:83–100 DOI 10.1007/s10784-013-9231-4

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ORI GIN AL PA PER

China, the United States, bargaining, and climate change

Robert Y. Shum

Accepted: 23 October 2013 / Published online: 10 November 2013� Springer Science+Business Media Dordrecht 2013

Abstract Knowing what is at stake in terms of likely damages from accumulating

greenhouse gases, how can major emitters fail to reach agreement on limits? Bargaining

analysis suggests that an uneven distribution of abatement costs over time may play a

significant part. Using a stylized, complete-information model of the strategic space facing

the two largest emitters of greenhouse gases, China and the United States, a simple

numerical example reaches a strong and surprising conclusion: To be feasible under cur-

rent technological and economic conditions, any international agreement on climate

change will have to allocate a level of future emissions for carbon dioxide in China that is

at least twice as large as the level for the United States, in order to account for the effects

on Chinese interests from continued economic growth.

Keywords Bargaining � Climate change � Energy � Rising powers � China �United States

1 Introduction

Among the vivid descriptions we have of the events leading up to the Copenhagen Con-

ference (COP-15), several remind us of the surprise expressed by witnesses at the time

concerning the assertiveness of China’s negotiating position (Christoff 2010; Grubb 2010;

Roberts 2011; Cf. Bodansky 2010; Dimitrov 2010; Parker et al. 2012). Some observers

additionally described the logic behind this position: simply in order to preserve its future

‘‘emissions space,’’ China’s negotiators felt compelled to reject any declared targets that

Electronic supplementary material The online version of this article (doi:10.1007/s10784-013-9231-4)contains supplementary material, which is available to authorized users.

R. Y. Shum (&)Department of Political Science and International Studies, The College at Brockport, State Universityof New York (SUNY), 350 New Campus Drive, Brockport, NY 14420, USAe-mail: [email protected]

123

Int Environ Agreements (2014) 14:83–100DOI 10.1007/s10784-013-9231-4

would place an upper bound on emissions and begin a process of imposing a downward

trajectory on global emissions that would be evident by 2050 (Christoff 2010: 648).

Conversely, the negotiating position of the United States reflected above all the admin-

istration’s need to be domestically perceived as being in active defence of the US’ eco-

nomic interests, especially in the midst of a prolonged recession.1 In sum, it appears that

China and the United States ‘‘had a determinant influence on the creation of an Accord that

appears to suit their separate needs despite, or because of, its weaknesses’’ (Christoff 2010:

644). The result was yet another failure to limit greenhouse gases produced by the world’s

two largest emitters, comprised now of the United States and China.2

This article presents a theory to explain how such a convergence of avoidance strate-

gies occurred despite acknowledgement by all sides that a problem exists. The starting

point for this theory is to recognize the importance of ongoing changes in energy use and

emissions paths in shaping the content of international negotiations on climate change.3

These changing paths create uncertainty for states about the potential gains and exposures

to risk that could result from regulation by a comprehensive international regime. Under

such conditions, negotiating outcomes are dominated by practical concerns in the United

States and China over the distribution of abatement and opportunity costs relating to

foregone fossil fuel-driven growth, as well as over the capacity of their economies to

maintain growth and competitiveness—either with or without negotiated constraints on

energy policy.4

To understand the effects of changing expectations about future emissions, the present

article applies bargaining theory, a powerful analytical tool for understanding political

negotiations as an incremental process—over the long run, instead of as a series of dis-

continuous events alternating between cooperation and discord. Remarkably, formal

models of bargaining developed within the international relations tradition have rarely

been applied to international environmental negotiations, or the issue of climate change

and the international effort to regulate emissions of greenhouse gases specifically.5 In the

economics literature, a number of approaches employing a bargaining framework have

1 For evidence of the pivotal importance of economic recession in determining public attitudes about theseriousness of the climate change problem, see Shum (2012).2 Together, in 2008, the United States and China produced 60.5 % of the world’s coal, and 43.5 % of globalcarbon dioxide emissions (British Petroleum Company 2009; International Energy Agency 2009). See alsoZhang (2011), Walsh et al. (2011), Massetti (2011).3 See, e.g., Paterson (2009: 152).4 As in most economic analyses of climate policy, we intend to incorporate such concerns directly, in ameasure of the marginal cost of emissions reduction, that is, ‘‘the costs that the economy undertakes toreduce a unit of greenhouse gas emissions (or the equivalent in other policies that would slow greenhousewarming)’’ (Nordhaus 1993: 18).5 There have been few game-theoretic analyses in the applicable issue area that extend beyond the usualPrisoners’ Dilemma analogies or enumerations of coalitional participation possibilities, despite the strikingresults yielded from exceptions like Ward’s (1993) and Pittel and Rubbelke’s (2012) efforts to incorporatechicken game frameworks into analyses of the climate change problem, or Ward et al.’s (2001) veto playeranalysis, which tended to predict that a successful cooperative outcome would be more difficult thancommonly believed. Barrett (2003) also provides numerous useful examples centered on settings where itmay be difficult to find any self-enforcing agreements (in contrast to the classical bargaining problem ofreconciling alternative preferences among multiple available agreements). Fearon (1998) applies a dynamic‘‘war-of-attrition’’ stopping game framework to international cooperation generally, and the insights derivedfrom this work apply equally to international environmental cooperation (see also note 28 below). Stone(2009) also draws interesting insights from modeling ‘‘long-term policy,’’ but takes a different approach byusing a median-voter tax-policy framework to analyze negotiating relationships within the subset of dem-ocratic states.

84 R. Y. Shum

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been applied to the climate change problem. Chen (1997) uses a two-player bargaining

approach, as does the present article; Chen, however, focuses on the nature of side pay-

ments in a potential climate change agreement, rather than on the substantive quantitative

concessions that are required to reach an agreement. Similarly, Pinto and Harrison (2003)

develop a computable general equilibrium (CGE) model to analyze bargaining in a mul-

tiplayer context of multilateral bargaining within a multidimensional issue space and

accordingly concentrate their attention on the generalized give-and-take that can occur

across different issues among different groupings of actors.6 Caparros et al. (2004) also

develop a sequential game in a multilateral framework and explicitly attempt to model

negotiations between developed and developing countries, while adding the feature of

asymmetric information in order to find separating and pooling equilibria for actors with

varying informational characteristics, in terms of general functional forms. Finally, Okada

(2007) presents a multilateral bargaining model with random proposers and focused on

reduction commitments with emissions trading, with the result that bargaining power

increases with the probability of being a proposer in such a model.7

This article intends to fill a gap in the literature by applying a bargaining-inspired

approach to the problem of setting quantitative limits on greenhouse gas emissions within a

numerical example that specifically includes the two largest emitters globally, China and

the United States. Since this problem is in the end an exercise in controlling and restricting

a quantity of output among producers, it is particularly amenable to an approach that draws

upon oligopoly theory as a source, as the bargaining approach indeed does.8 By accounting

for the domestic calculus of the costs and benefits from cooperation, bargaining models can

also focus our attention on a more sophisticated characterization of the strategic situations

confronting states than can be achieved by a priori suppositions about the exogenous

propensity of states to cooperate (or not) within the international system (Powell 1994:

337). In the international relations literature, bargaining theory has been used especially to

explain the breakdown of negotiations that lead to war. For example, James D. Fearon

concluded that war among rational actors can arise as a result of failures either to com-

municate or to commit, and possibly also in the case that an object of desire is impossible

to divide (Fearon 1995). Robert Powell then showed that a commitment problem lies at the

heart of all three scenarios and how this can arise from a rapid change in the distribution of

power (Powell 2006). The present article asserts that it is similarly crucial to understand

the role of shifts in the distribution of natural and technological resources relating to energy

use. In short, for the purposes of this analysis, energy is power. By highlighting the role of

shifts in the balance of resource consumption, it is argued that complete-information

bargaining analysis adds as much predictive and analytical power to the analysis of

international environmental negotiations as it has done in the area of international

security.9

6 This approach generates interesting insights about interdependence among the issues of timing and levelsof participation for abatement obligations. However, the results are both highly variable and specification-sensitive, and this CGE model developed in 2003 does not include China as a player in climate negotiations.7 This model is then applied to a numerical example of negotiations that also does not include China as aplayer—only the European Union, the former Soviet Union, Japan, and the United States.8 On oligopoly theory, see, e.g., Cournot (1838), Friedman (1971, 1986), Kreps and Wilson (1982), Tirole(1988).9 For examples of the latter, see Wittman (1979), Powell (1996a, 2002), Wagner (2000), Reiter (2003),Slantchev (2003), Tarar (2006).

China, the United States, bargaining, and climate change 85

123

This article therefore considers how the balance of bargaining power among states can

determine the scope for coordination in the issue area of carbon emissions from fossil fuel

consumption and offers predictions concerning the necessary conditions for rising powers

such as China to participate in a global climate change agreement. The next sub-section

describes how a bargaining approach can be applied in combination with stylized models

of the economic costs of atmospheric emissions, beginning with an introductory applica-

tion to the case of ozone-depleting substances (ODS). Sections 2 and 3 then turn to the

central case of climate change, before concluding with some final observations.10 Most

importantly, the results here suggest that to be feasible under current technological and

economic conditions, any international agreement on climate change will have to allocate a

level of future emissions for carbon dioxide in China that is at least twice as large as the

level for the United States. If such a settlement is politically indigestible, then the model

predicts that no agreement at all will be reached.

1.1 Bargaining in international relations theory: an initial application to stratospheric

ozone depletion

International anarchy—that is, an international system composed of states pursuing their

own self-interest under conditions of formal sovereign equality—creates its own challenges

for coordinated action in response to problems of transboundary pollution (Young 1994).

The incentives to free ride on the efforts of others—and the difficulties involved in moni-

toring and enforcement—can be enormous; this is especially so when the timeframe and

geographic scale of a pollution problem are large (Shum 2009). The relative lack of an

effective global response to climate change presents a prime example: annual average

increases continue to be observed in the instrumental record of global surface temperature,

along a linear trend of 0.74 �C for the past 100 years; this trend also appears to be accel-

erating, so that a decadal warming trend of 0.13 �C per decade has been observed for the

50-year period between 1956 and 2005 (Intergovernmental Panel on Climate Change 2008).

Yet, progress on reaching an international agreement on climate change remains as elusive

as ever, despite continuing diplomatic and scholarly activity intended to advance imple-

mentation of existing Kyoto Protocol obligations as well as to develop a successor agree-

ment (or alternatively, a new ‘‘framework’’ or ‘‘governance architecture,’’ possibly taking a

‘‘bottom-up’’ orientation) for the future.11

In a context of dynamic change, international anarchy also creates conditions where

states find it impossible to make credible commitments. If, for example, a government

knows that it will have greater bargaining power vis-a-vis another government in a future

time period, it cannot credibly pledge in the present period that it will refrain from

exploiting its improved power position in the future (Fearon 1995: 405). A bargaining

model can analyze such a situation, beginning with two states, A and B, who can choose

between an agreement to implement a bargained outcome on the one hand, or else a refusal

to coordinate on the other. Rubinstein provides the framework for analyzing a situation in

which two actors are trying to divide the gains from cooperating by making a series of

alternating offers, and Powell develops applications for an international relations context of

explicitly analyzing the effects of a changing balance of power (Rubinstein 1982; Powell

10 For the approach adopted here to model the damage from greenhouse gas emissions, see the Appen-dix available as Supplementary Material in the online version of this article, and Fankhauser and Kverndokk(1996), cf. Nordhaus (1991a).11 See, e.g., Aldy and Stavins (2009); Dubash and Rajamani (2010); Falkner et al. (2010); Grubb (2011).

86 R. Y. Shum

123

1999: 118–133, 272–277).12 In the Rubinstein game, one actor begins by proposing a

division of gains to the other who can either accept the offer or reject it and make a

counteroffer, with both parties alternating offers until one party accepts the other’s offer,

and they both in effect agree on a division (Rubinstein 1982; Powell 1999: 87). The key

advantage of the modeling approach embodied in these models—from both Rubinstein

(1982) and Powell (1996b, 1999)—is to allow the players to make decisions about the size

of the offers made during a negotiating process, so that the model can represent the risk-

return trade-off that a state faces in offering and agreeing to cooperate (Powell 1999: 86).

This feature can be complicated for multiple players, but clear predictions can be found in

a two-player context. By allowing us to analyze the potential distribution of gains from an

agreement, this framework can help us understand the effects of changing conditions.

Specifically, we can apply this framework to international negotiations to address climate

change and reduce greenhouse gas emissions. This will be the task in Sects. 2 and 3.

The rest of this section discusses the case of ozone-depleting substance (ODS) emis-

sions and describes how cooperation easily emerges in this case, given the favorable payoff

structure. Indeed, no formal model is needed at all to understand how the benefits of

restricting ODS emissions far outweigh the costs. It is, however, worthwhile to introduce a

complete-information cost-benefit analysis in this simplified setting.

First, let us therefore suppose that there is a status quo level of ODS production for a

two-country world and that p represents country B’s proportional share of the benefits from

this production, while 1 - p represents country A’s proportional share.13 Thus, if p is close

to one, B produces most of the world’s ODS and has a controlling share of this market. If

p is closer to zero, A is the larger producer instead.

Next, let b represent B’s costs from the damages caused by its business-as-usual

emissions, and let a similarly represent A’s damage costs. B’s business-as-usual payoff is

therefore p - b, and A must offer concessions equivalent in value to in order to secure

B’s participation and willing compliance with a proposed agreement to limit emissions.

12 Powell provides additional solutions by backward programming for his games (Powell 1999: 274). Toarrive at these solutions, we begin by labeling a player as ‘‘dissatisfied’’ if it prefers an imposed settlement towhat it would obtain in the bargaining game were the option of reaching a settlement not present; because itis costly to impose a settlement, at most only one bargainer can be dissatisfied. Most importantly, inequilibrium, the satisfied bargainer makes what is effectively an optimal take-it-or-leave-it offer, and thedissatisfied bargainer either accepts this offer or imposes a costly conflictual resolution (since in the eventthat a plausible counteroffer were available, the party would make it and by definition would no longer bedissatisfied). If both bargainers are satisfied, the options of imposing conflict have no effect, and the game isequivalent to one without outside options (Powell 1996b: 258ff.). In the present setting, we can assume setroles for our players in accordance with the international relations application where one state is in relativedecline and always satisfied with the status quo, while the other ‘‘rising’’ state is either satisfied or dis-satisfied with the status quo distribution (relative to what it can obtain in the future—in other words, time ison the rising power’s side), so that in either case counteroffers by this rising state are effectively off theequilibrium path. Then solving by backward programming, Powell establishes the result that the decliningstate prefers to a make an offer sufficient to appease the rising state throughout the shift in power if its initialstake in the status quo is at least as large as the costs of fighting, and if the total per-period cost of fighting isat least as large as the per-period change in the balance of power. For details and proofs, see Powell (1999:272, 274–277).13 It should be stressed that p represents the benefits from production of relevant private goods—i.e., in thevalue of the actual CFCs used as refrigerants in the ODS case, or in the climate case, in the steel oraluminium produced in the course of burning fossil fuels, for example. Such benefits from production arenot to be confused with the damages avoided by regulation and pollution control; the latter constitutebenefits of abatement, which are obviously non-excludable public goods that are externalized and distrib-uted globally irrespective of where production capacity is located. It is, of course, the tension between thesedifferentially distributed costs and benefits that creates a collective action problem.

China, the United States, bargaining, and climate change 87

123

For example, in the most extreme case of disagreement, we can suppose that A prefers to

eliminate all ODS production, and B prefers to continue to produce as usual. In that case,

A has to compromise enough, so that B obtains concessions equivalent in value to the

payoff it would get without cooperating and without having to reduce business-as-usual

emissions.

In the ozone-depletion case, the balance of costs and benefits strongly favors tight

restrictions on production and emissions. For example, the United States Environmental

Protection Agency (EPA) estimated the net cost of continuing to produce its unilateral

share of ODS production to be USD$21 billion for the value of unabated ODS pro-

duction, minus USD$1,373 billion of damage costs from this additional production,

mostly from excess skin cancer mortality (Barrett 2003: 228). In other words, the United

States estimated the costs of its own continued business-as-usual production to be sixty-

five times greater than the benefits. It is this relationship between costs and benefits in the

ozone case that made cooperation inevitable. The above calculation was applied to the

United States alone; the costs of worldwide production were correspondingly greater, for

both the United States and the world. For other countries, even dramatically smaller

estimates of costs and vulnerabilities to ozone depletion are unlikely to be outweighed by

the limited benefits from production. Under such circumstances, b is greater than p, and

p - b is negative, so that no offer is necessary to induce a country such as B to

cooperate.

The ODS case therefore shows how, depending on the nature of the specific problem,

cooperation can be a reflection of cost and benefit calculations. This case provides an

illuminating contrast with the additional complexities of the climate change problem. Most

importantly, in the climate case, we will see how a shifting balance in the use of resources

relevant to an emissions problem can create a commitment problem that hinders cooper-

ative outcomes.

2 Climate change as a commitment problem: a model

In the ozone case, the distribution of production resources remained relatively constant

during and leading up to the period of negotiations for the Montreal Protocol. For example,

the United States’ share of world production in 1986 was the same as it had been 10 years

earlier (Benedick 1998: 27). Things are not so simple today, when climate negotiations are

taking place at the same time as major shifts are occurring in the composition of the ranks

of world’s largest economies, especially in the case of the rapid economic growth of China.

The model presented in this section can capture this change, along with the longer time

lags and smaller differentials between the costs and benefits of abatement, in order to

explain why cooperation on this issue is so elusive. In addition, the next section will

employ this model so as to offer concrete predictions of the kind of offer that is necessary

to secure the cooperation of rapidly growing states. As before, we begin by analyzing the

implications of a distributional shift over time in the parameter p,14 which continues to be

used here to represent a country’s proportional share in the benefits to be derived from

business-as-usual consumption of resources and the emissions that such consumption

entails.

In the case of climate change, let us suppose that the likely distribution of the benefits

from continued business-as-usual carbon dioxide (CO2) emissions is distributed between

14 Powell (1999: chapter 4) provides the precedent for this analysis.

88 R. Y. Shum

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the two states as a proportion p [ [0, 1].15 Specifically, p now represents B’s proportional

share of carbon emissions, while 1 - p represents A’s share. To make this stylization more

concrete, further suppose that states A and B correspond to two distinct types of states, with

A representing a slower-growing ‘‘advanced’’ (or ‘‘satisfied’’) economy, and B representing

a country that is ‘‘backward’’ in the sense employed by Alexander Gerschenkron (1962),

where one can capitalize on underutilized resources and use established strategies and

technologies in order to achieve faster growth. Thus, at the outset of the emissions case

being analyzed, B’s level of emissions is small compared to A’s. However, projected

growth rates for the two countries diverge, so that B’s emissions will overtake those of A in

the future, and p is increasing over time. Finally, let us assume that the shift in resource use

is occurring due to exogenous drivers of uneven economic growth.

To capture this change over time and its effects on bargaining, we require additional

parameters. Hence, for periods t = 1, 2,…, state A can attempt an agreement for both states

to act jointly in departing from the business-as-usual emissions scenario and propose an

agreement to limit emissions according to a proportional distribution xt. On seeing the

proposed agreement xt, state B can either agree or not. If B accepts the proposal, it will

receive xt in future periods, as specified in the agreement. If B rejects the offer, B is

assumed to receive a probable allocation of business-as-usual energy resources pt, and

A would receive 1 - pt.16 Figure 1 presents the situation at time t graphically. In words,

A and B are bargaining about the distribution of benefits and costs associated with the

existing international energy system. A begins the game by either consuming energy and

emitting greenhouse gases on a business-as-usual basis or else making a cooperative

proposal x0 [ [0, 1], where the interval [0, 1] represents B’s agreed share of benefits from

world energy consumption. If A does not try to cooperate and chooses to proceed with

business-as-usual, the game ends. If A makes a proposal, B can either accept it or else reject

it and proceed on a business-as-usual basis. If B accepts the proposal, the distribution of

benefits changes permanently to x0 starting in the next period, and the game ends. If

B rejects the proposal, the first round ends with the distribution of benefits remaining at the

initial level of p0 for the first round and increasing to p1 for the next round. This sequence

of moves is then repeated in the second and all subsequent rounds until the game ends. The

game continues as long as A makes offers, and B rejects them.

15 However, since it is impossible to separate out and precisely measure the benefits derived from the CO2

emitted during the process of consuming energy, we will assume that the proportion of benefits correspondswith the proportion of emissions. This is necessarily an approximation, and there is certainly reason tobelieve that the actual relationship is nonlinear, with the marginal benefit of added emissions diminishing athigher levels of income and energy consumption (see, e.g., Holtz-Eakin and Selden 1995; Schmalensee et al.1998); nonetheless, it is beyond the scope of this article to estimate where this point will be reached, forexample, in China. Therefore, for simplicity’s sake, we will use projected levels of emissions as a proxy forthe benefit derived from emissions. In this respect, we face difficulties that are similar to (and likely lessacute than) those facing scholars of bargaining and war in operationalizing the distribution of benefits from agiven geopolitical setting for the balance of power—i.e., to measure the spoils of war and peace, distinctfrom measures of power capabilities at a given moment in time. This difficulty is rarely discussed in thebargaining-and-war literature, but two notable exceptions are Werner (1999) and Reed et al. (2008).16 As presently described, the present game appears to be exclusively of a take-it-or-leave-it nature; a betterinterpretation of this game, however, is to consider it to be a specific application of Powell’s (1999) infinite-horizon game (see Powell 1999: Chapter 4 and Appendix 4 for formal details), with the choices simplified sothat the outside options of outright war and non-binding agreements are no longer relevant, and where stateB, the ‘‘backward’’ or ‘‘rising’’ state, would be content with the indefinite continuation of a business-as-usualtrajectory that allows B’s energy use to grow indefinitely and for B to fully enjoy the benefits from thatgrowth—i.e., that B’s counteroffer at any stage of the game is in effect assumed always to be continuation of‘‘business-as-usual.’’ See also note 11 supra.

China, the United States, bargaining, and climate change 89

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To specify the states’ payoffs, we first have to suppose the states never agree: Thus, let

p0, p1, p2,… be the distribution of benefits in each period.17 We note that beginning in the

present day, at time t = 0, p0 = p, and p is closer to zero than to one, since state A is

producing more emissions than state B. For B, the total expected payoff in the absence of

cooperation is p - b, where b denotes B’s costs from the damages caused by B’s business-

as-usual emissions in excess of what these emissions would be under cooperation. Simi-

larly, A’s expected noncooperative payoff is 1 - p - a, where a is state A’s additional

business-as-usual damage costs.

Next, consider what happens if state B has a growing economy. A simple case could

involve B having a probable business-as-usual share of world energy consumption that

begins at p and increases to p1 [ p in period one, then increases to p2 [ p1 in the next

period, and further increases to p3 [ p2 in the period after that. For the purposes of the

present analysis, let us assume that such a process of change in the rates and balance of

economic growth between A and B continues over time until a certain stable point of

convergence is reached far into the future. We can model this process of a shift in power

that occurs over T periods. After the T-period shift, the distribution of bargaining power

remains constant; more formally, assume that the distribution of power starts at p in the

first round, rises by D in each of the next T periods, and then remains constant, so that

pk = p ? kD for 0 B k B T and pk = p = p ? TD for k [ T. Thus, the overall change

in the distribution of power is the difference p - p, and the rate at which this shift

occurs is D = (p - p)/T. In terms of the overall payoff, if the states fail to reach an

agreement in period t, and p does not change after t, expected payoffs from period t on

are (1 - pt - a)/(1 - d) for state A and (pt - b)/(1 - d) for state B. From this baseline,

we can now see what happens when changes in the distribution of power, p, occur over

time.

We are specifically interested here in the substantive problem of how states cope with

shifts in the distribution of resources between them during the shift in power (Powell 1999:

122). For this reason, we focus on how the game changes during the power transition up to

and until T. T represents, in other words, an upper bound in the shifting balance of power,

over a finite course in the rise and fall of two specific powers that is perceptible to each.

From time T forward, the solution of the game is intuitively straightforward and formally

Fig. 1 A round in the climate bargaining game

17 Additional simplifying assumptions are that the utility functions are increasing and concave, and that thestates are risk neutral.

90 R. Y. Shum

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established by Powell (1999): the satisfied state’s optimal offer at T and in all future

periods is to give the rising state just enough to ensure that it will prefer cooperation over

conflict (that is, the business-as-usual state).18 Working backward from time T, Powell

(1999) also shows that the satisfied state prefers offering xt* over conflict at time t \ T if

its initial stake in the distribution of benefits is at least b ? a and if the total per-period cost

of conflict is at least as large as D.19 Finally, Powell’s (1999: 276–277) solution shows that

throughout the period of the rise in B’s power, and under conditions of complete infor-

mation (as we are assuming in the present application), A will prefer offering xt* to the

alternative of costly conflict. The crucial question, then, concerns the conditions under

which B will prefer a negotiated agreement to the business-as-usual outcome.

A can avoid business-as-usual emissions in future periods by offering B enough to make

the payoff to accepting the offer as large as the payoff to business-as-usual emissions. We

define this condition by stating, in other words, that the rising state prefers accepting a

proposal to business-as-usual emissions if the advanced state offers at least xt*.20 To

specify this condition, let us first suppose that A offers xt at time t. If B rejects this proposal

and continues emitting at business-as-usual levels, its expected future payoff is

(d ? D)(pt - b) ? (d ? D)2(pt - b) ? (d ? D)3(pt - b) ? …. The first term in this sum

is the rising state’s per-period expected payoff to business-as-usual emissions in the next

period, at time t ? 1; the second term is the discounted value of receiving this per-period

payoff at time t ? 2; the third term represents the discounted per-period payoff at time

t ? 3; and so on. This sum simplifies to (pt - b)/(1 - (d ? D)), as long as (d ? D) is a

positive number less than one, as it is for any reasonable scenario within our application.

The expected business-as-usual payoff therefore incorporates D into the discounted value

of future payoffs starting from pt?1. In other words, the discounting of future payoffs for

B is mitigated by the expected growth and change in bargaining power represented by D.

If, by contrast, B were to accept xt, its expected payoff would then be

d(xt) ? d2(xt) ? d3(xt) ?…. The first term in this sum is the rising state’s discounted

expected per-period payoff to emitting according to the negotiated allocation in the next

period, t ? 1, when the negotiated treaty first comes into effect. The second term is the

rising state’s discounted expected per-period payoff to cooperating at time t ? 2, and the

third and subsequent terms are discounted values of future per-period payoffs to having

agreed at time t when the distribution of power was pt. This sum and expected payoff can

then be simplified to xt/(1 - d) since d is a positive number less than one. Country A can

therefore secure cooperation by offering B enough to make the payoff from participating in

an agreement covering future periods as large as the payoff from noncompliance and

continuing business-as-usual emissions over the same periods of time. By comparing the

two payoffs, we arrive at the condition that xt/(1 - d) = (pt - b)/(1 - (d ? D)), or

xt = (pt - b) 9 (1 - d) / (1 - d - D).

This condition can be more conveniently represented in terms of the discount rate r,

instead of the discount factor ,, so that we arrive at the following conclusion: B prefers to

participate in a cooperative agreement as long as it receives an offer at least as large as xt*

where xt* = (pt - b) 9 r / (r - D).

18 See Powell (1999: 274) and Appendix 3 for detailed proofs. Briefly, B’s payoff to conflict at any t C T is(p - b)/(1 - d), so the satisfied state’s optimal offer at all t C T is = UB

-1(p - b), where the utilityfunction UB is given by the stream of benefits from energy use extending into the future and is assumed to beincreasing and concave.19 See Powell (1999: 274–277) for formal proofs.20 This summary is based on the explanation in Powell (1999: 124–125).

China, the United States, bargaining, and climate change 91

123

3 A shift in the balance of carbon: a numerical example

Table 1 lists the projected estimates of the International Energy Agency (IEA) and its

World Energy Outlook (International Energy Agency: 2009, 2010) for carbon emissions

from the United States and China until 2035, from which p and D are then derived and

presented, in the two columns at furthest right.

In the present application, p is China’s proportion of the total carbon dioxide emitted by

both itself and the United States. Column 4 of Table 1 shows the extent of the shift in this

proportion since 1990, when it was less than a third of the total, to the recently recorded

level of 54 % in 2008; this growth is projected to continue through to a level of over 70 %

in 2035.

In addition, the last column shows the annual rate of change in China’s proportion of the

two countries’ emissions. The cell on the bottom right gives the estimate of D that will be

used to calculate the minimum share of emissions necessary for an offer that can satisfy

China: 0.48 %. In other words, China’s proportion of emissions between 2015 (i.e., t0, or

the potential year for the entry into effect of an agreement) and 2035 is projected to grow

on the average by 0.48 % each year. This projected rate of growth, while substantial, is

actually considerably smaller than the 0.87 % annual rate of proportional growth that was

actually observed from 1990 to 2008.

Next, Table 2 shows estimated values for the other variables needed to calculate the

minimum value of an offer to China.

Rows (3–4) and (6–7) of Table 2 relate to two different assumptions for the present

discounted value of future payoffs. Discounting has generated a great deal of debate, but

that discussion is beyond the scope of this article. Instead, two alternative rates of discount

are provided: 1.4 and 4 %, corresponding to those employed in the widely known analyses

of Stern (2007) and Nordhaus (1991b), respectively. The implications of these two con-

trasting assumptions are displayed in Column 3 of Table 2, where the cumulative effects of

the discount rates in conjunction with D, the estimated change in the balance of carbon

emissions, are listed.

The first two columns of Table 2 show estimates of the additional damage caused by

business-as-usual growth in emissions above the projected first-period level in 2015 for the

United States and China, respectively. The second row contains values for the variables

a and b, or the average annual post-2015 damages from each country’s respective emis-

sions, stated as a share of total economic activity. These estimates are based on the

methodology of Fankhauser and Kverndokk, and are provided for illustrative purposes

rather than as a realistic accounting of the highly complex consequences likely to result

from additional climate change.21 Nevertheless, the intuition for these estimates can be

readily understood. If, for example, the Stern Review (2007: 161ff.) estimates the cost of a

[2 �C rise in temperature from business-as-usual emissions to be at least 5 % of global

GDP, it is reasonable to estimate that damages from the growth in emissions in a single

year would be a fraction of the estimated 5 %, in as much as the total volume of emissions

that was necessary to produce the 2 �C rise has accumulated over more than a century,

since the beginnings of economic industrialization.

The bottom three rows of Table 2 provide a robustness check for these estimates by

presenting an alternative calculation of the benefits of abatement (in terms of damages

21 The estimates do not, for example, account for the impacts of sea level change (Fankhauser andKverndokk 1996). Additional details on the methodology for calculating a and b are also provided in thesupplementary online appendix.

92 R. Y. Shum

123

avoided) based on higher values that are derived from the global estimates presented in

Nordhaus (1991a: 146). Finally, the final two columns of Table 2 present the values for

x2015, the minimum emissions-sharing offer acceptable to China in 2015. Column 4 states

this offer in terms of China’s business-as-usual proportion of carbon emissions in 2015,

while Column 5 states it in terms of the United States’ proportion. The final figures

presented in Column 5 show the remarkable result that the minimum offer acceptable to

China is a present-day formula for the sharing of global emissions that amounts to an

emissions quota that is at least twice as large as that for the United States.

Thus, as in the stratospheric ozone case, the likely damages from climate change are

significant and accumulate globally, leading to a coordination problem of the first order.

The climate change problem, however, differs from the ozone case and is most importantly

exacerbated by a critical feature: the uneven distribution of the costs of abatement. In terms

of one particular component of these costs—that is, the opportunity costs of forgone

energy-intensive growth—the burden for these costs falls hardest on precisely those states

whose emissions are growing fastest; hence, these states are also the least inclined to agree

to binding limits or reductions in emissions, despite the absolute necessity for securing

their participation in order to achieve an effective agreement. The result is, in other words,

an extremely high degree of bargaining power that is vested in a growing, rising power.

This result has two further implications deserving further discussion. First, it once again

demonstrates the importance of discounting assumptions, but does so in a new light.22 The

existing literature on the economics of climate change focuses on the implications of a

lower discount rate in terms of a higher valuation of future damages, thereby increasing the

urgency of the need to make immediate global policy changes.23 The analysis here,

however, shows the potentially drastic effects of a lower discount rate on the distribution of

the policy burden on climate change through the resulting change in valuation of future

abatement costs across countries. In effect, our analysis shows a different aspect of how a

Table 1 IEA projected estimates of carbon emissions

CO2 emissions,USA (Mt)

CO2 emissions,China (Mt)

PUSA (%) PChina (%) D (%)

1990 4,850 2,244 68.37 31.63 –

2008 5,571 6,550 45.96 54.04 1.87

2015 5,494 8,610 38.95 61.05 1.00

2020 5,466 9,583 36.32 63.68 0.53

2025 5,494 10,657 34.02 65.98 0.46

2030 5,310 11,711 31.20 68.80 0.56

2035 5,202 12,561 29.29 70.71 0.38

1990–2035 average 5,341 8,845 37.65 62.35 0.87

2015–2035 average 5,393 10,624 33.67 66.33 0.48

22 Although the setting is different, the underlying dynamic here is similar to that in Fearon (1998: 294,296), and its finding that ‘‘costly standoffs are more likely to occur in cases where state leaderships discountfuture payoffs relatively little’’.23 See, e.g., Stern (2007), and the analysis of climate-model discount rate choices in Dasgupta (2008). Thepeculiar relevance of discounting for climate policy is summarized concisely by Weitzman (2009: 1) whenhe notes that part of the ‘‘economic uniqueness of the climate change problem’’ is the fact that ‘‘today’sdecisions have difficult-to-reverse impacts that will be felt very far out into the future, thereby straining theconcept of time discounting and placing a heavy burden on the choice of an interest rate’’.

China, the United States, bargaining, and climate change 93

123

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94 R. Y. Shum

123

lower discount rate values the welfare of future generations more highly: It not only values

future damages more highly, but also places a premium on the increases in welfare that

would be forgone in rapidly growing regions in the event of severe and uniform restrictions

on carbon emissions.

Second, this analysis provides a framework for understanding a critical challenge for

any cooperative burden-sharing agreement on climate change. While the opportunities for

mutual gain from a coordinated response exist, they are also constrained by the incentives

to gain from the increased use of energy within a growing economy. A realistic approach to

climate policy must therefore address the true costs and benefits of proposed policy options

for all countries, including those that constitute rapidly growing emerging markets, in

addition to those of mature and demographically contracting advanced economies whose

levels of nonrenewable energy use are in any event likely to stabilize or even diminish.

Recognition of the crucial role of change in the balance of resource use and carbon

emissions is in this way a necessary element of policy analysis—an element particularly

highlighted by the use of dynamic models.

The primary limitation of this analysis lies in its use of projected estimates for future

energy use and emissions. Actual patterns of energy demand and consumption will clearly

vary a great deal from even the most careful projections. In the past, some analysts have

argued that the International Energy Agency’s models and projections understate the

tendency for energy use and emissions to level off and decline in higher-income economies

(Schmalensee et al. 1998), while other observers insist that the potential exists for rapid

gains from technological innovation to achieve substantial emissions reductions at a lower

cost than currently expected (Porter 1991; Esty and Andrew 2009). Regulation can in some

cases encourage innovation that shifts static calculations of costs and benefits in a favor-

able direction (Porter and van der Linde 1995); on the other hand, it is also important to

recognize the costs and inefficiencies that could result from premature deployment of

technologies that are unsuitable, or merely underdeveloped and therefore better positioned

to reap cost savings accruing from more gradual accumulation of experience in installation

and transmission.24 In any event, the analysis here shows that the impact of China’s recent

economic growth is on such a scale that even a drastic shortfall in projections for growth or

energy use is unlikely to change the trajectory of a global energy shift that is not only

ongoing, but also heavy with consequence for the dynamics of international climate change

negotiations.

Despite these reservations, promising areas for further research exist. One would be to

adjust the settings for the relative bargaining power of the two parties, including different

and more realistic possibilities for counteroffers to be made, or outside options to be

taken.25 Another would be to analyze the implications of negotiations that involve multiple

actors. Finally, another possible extension would venture further into the future, so as to

factor in costs and benefits of abatement that are more distant in time. Such an analysis

could incorporate additional scenarios such as the design of international agreements to last

more than 20 years and reveal more about prospective negotiating dynamics over the

longer duration.

24 See Grubb (1997: 161). Numerous episodes in the history of energy policy—for example, the drives tocommercialize synthetic fuels or generate nuclear power—point to real hazards in large-scale diversions ofresources in pursuit of illusory technological solutions.25 This valuable suggestion is due to the comments of an anonymous reviewer.

China, the United States, bargaining, and climate change 95

123

4 Conclusion and theoretic implications

This article has shown how recent changes in the emissions paths of the world’s two largest

carbon dioxide emitters, the United States and China, affect the bargaining dynamics of

international climate negotiations. The analysis draws attention to the counterintuitive role

played by parameters such as the discount rate: although a lower discount rate is con-

ventionally held to strengthen the aggregate global case for aggressive abatement in the

near term, this is not true for the specific case of an individual state that is enjoying rapid

economic growth while on an accelerating emissions path. This finding, in turn, highlights

the sensitivity of policy conclusions to parameters such as discount rates and future

expectations of growth and technological innovation, all of which must be assumed in the

present, but are nevertheless subject to great uncertainty for the future. By using conser-

vative estimates and assumptions found elsewhere in the literature, the numerical example

in this study arrives at a pessimistic conclusion about the ‘‘bottom line’’ of an international

climate change agreement: limits on carbon emissions negotiated on a country-by-country

basis must allocate a limit for China that is twice as large as a limit for the United States in

order for a bargained outcome to be feasible. Such a result is unlikely to be politically

palatable in the immediate future. Even so, this relative amount is still considerably lower

than the proportion that would be allocated to China under a strictly per capita-based

formula. Viewed in this way, the two-to-one China-to-US ratio is plausibly a negotiating

focal point that will provide a way out of the impasse between arguments in favor of per

capita-based formulas and those based on past consumption.

In terms of theory and methodology, this study applied a bargaining model to climate

change negotiations, one that was adapted from approaches that are prominent in the recent

international relations literature. A key advantage of the bargaining approach to interna-

tional relations is found in the parsimonious manner in which it incorporates domestic

considerations and their consequences on international strategy, by modeling them as the

internalized costs that a society incurs from undertaking a given course of action. In this

respect, the bargaining approach recognizes two components that are crucial for under-

standing global environmental politics in general and efforts to regulate climate change

specifically: the distribution of conflicting interests, and uncertainty about future devel-

opments.26 Whenever such factors are overlooked, or even merely underspecified, it

becomes impossible to explain when or why a change in global governance practices

occurs (as in the ozone-depletion case), or does not occur (as in the climate change case).

As this article has demonstrated, bargaining theory provides a useful means for filling this

gap in our understanding of outcomes in global environmental governance.

Bargaining theory has consequently provided a tool for confronting the central question

of how to ‘‘divide the pie’’ of global greenhouse gas emissions among the countries of the

world in a politically feasible manner—either with or without the customary a priori

assumption that the prospect of future damages will necessitate policies to shrink the pie at

any cost. At present, despite decades of international conferences and declarations, there is

consensus on neither the principles that are necessary to organize an agreement on global

climate change, nor the specific formulae that states could reasonably accept for the use of

allocating binding numerical limits on emissions. It has been observed that given this lack

of agreement on substantive obligations, much recent negotiating activity has instead

concerned itself with the scope of provisions for flexibility in implementation (Von Stein

2008; Biermann et al. 2009; Thompson 2010)—a trend observed not only in the present-

26 See Biermann (2007), Hovi et al. (2009), Stone (2009) and Keohane and Victor (2011).

96 R. Y. Shum

123

day climate change ‘‘regime complex’’ specifically (Keohane and Victor 2011), but also in

other international and multilateral environmental agreements generally.27 In this article,

we have directly addressed how the substantive content of cooperation in the issue area of

carbon emissions is constrained by the balance of bargaining power that has accrued to

states as a reflection of their relative economic strength and overall share of world fossil

fuel consumption.

While bargaining theory has in the past been used most extensively in the international

relations literature to explain why states engage in costly wars instead of reaching nego-

tiated agreements that avoid such costs, there is in fact no reason for this approach to be

limited to cases of violent interstate conflict.28 This article has extended the bargaining

approach to the case of global environmental politics. As a final observation, we note that it

is curious that additional applications of this kind have not been carried out in the field of

international relations generally, given that fruitful applications of related dynamic com-

plete-information game-theoretic approaches have been made outside of political science

in areas far removed from war and the use of force,29 in areas such as evolutionary biology

(Maynard Smith 1982), labor markets (Shapiro and Stiglitz 1984; Fernandez and Glazer

1991), and macroeconomic policy reform (Barro and Gordon 1983; Bulow and Rogoff

1989; Alesina and Drazen 1991; Chang 1995; Barta 2009). Relevant insights are promised

by the use of such an approach to analyze global policy problems such as climate change.

Acknowledgments Financial support enabling this research, as well as a warm intellectual home duringthe article’s writing, were provided during my residence at the Bologna Institute for Policy Research (BIPR)and the Johns Hopkins University SAIS-Bologna Center under the direction of Erik Jones and KennethKeller. The original inspiration for this article was imparted by Zsofi Barta, who also provided valuablecomments and suggestions to earlier drafts along with two anonymous reviewers. All errors and unfoundedopinions remain my own.

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