A Stochastic Dynamic Game of Carbon Emissions Trading - CiteSeerX

NCCR-WP4 Working Paper 15

A Stochastic Dynamic Game of Carbon Emissions Trading A. Haurie and L. Viguier December, 2002

Swiss National Centre of Competence (NCCR) “Climate” Work Package 4: “Climate Risk Assessment” University of Geneva & Paul Scherrer Institute Contact: Prof. Alain B. Haurie University of Geneva 40, Bld du Pont d’Arve CH-1211 Geneva, Switzerland. Phone +41-22-705- 8132 Webpage: http://ecolu-info.unige.ch/~nccrwp4/ Copyright © *date* NCCR-WP4. All rights reserved. No portion of this paper may be reproduced without permission of the authors

A STOCHASTIC DYNAMIC GAME OF CARBON EMISSIONS TRADING ALAIN HAURIE & LAURENT VIGUIER Abstract. This paper proposes a computable stochastic equilibrium model to represent the possible competition between Russia and China on the international market of carbon emissions permits. The model includes a representation of the uncertainty concerning the date of entry of developing countries (e.g. China) on this market in the form of an event tree. Assuming that this date of entry is an uncontrolled event, we model the competition as a dynamic game played on an event tree and we look for a solution called S-adapted equilibrium. We compare the solution obtained from realistic data describing the demand curves for permits and the marginal abatement cost curves in different countries, under different market and information structures: (i) Russia’s monopoly, (ii) Russia-China competition in a deterministic framework, (iii) Russia-China competition in a stochastic framework. The results show the possible impact of this competition on the pricing of emissions permits and on the effectiveness of Kyoto and post-Kyoto agreements, without a US participation.

1. Introduction The economic response to global climate change has already been addressed in a variety of dynamic game models[3][11][18][22]. In general these models concern the respective greenhouse gas abatement policies of different countries that are diversely exposed to the damages caused by the concentrations increase. Most of the time these are very aggregated and theoretical models, in the sense that they provide “synthetic paradigm” that do not correspond immediately to the decisions that have to be taken by the concerned governments. In this paper we propose a stochastic game model that is directly linked with the Kyoto or post-Kyoto agreement mechanisms. More precisely we formulate, solve and interpret a dynamic stochastic game formulation of the competition between major (dominant) actors on the international market of greenhouse gases emissions permits. In our formulation two dominant players are represented by Russia and a representative developing country (RDC), corresponding to China, respectively. The Annex-B countries are supposed to behave as a competitive fringe that trades emissions permits in a marginal cost equalization manner. Russia and China have strategic power because of the important zero-cost abatement allowance obtained by Russia in the Kyoto-Marrakech negotiations and the very low potential abatement costs in China, respectively. In [7] the dominant player situation of Russia has been analyzed as a two level dynamic optimization problem. In [8] a computable game model has been proposed to study the strategic interactions between Russia, and a RDC (China) in international markets for carbon emissions permits created by the Kyoto protocol. In the present paper we extend this formulation to the case where uncertainty prevails on the timing of the possible entry of DCs on the international emissions trading market. We also assess the impact on the permits market of DC’s participation in the next commitment periods. The model we propose uses transaction costs to represent the main uncertainty affecting the game. RCD’s entry is thus represented by a sensible lowering of the transaction costs1. In the current Kyoto/Marrakech agreement, developing countries may supply Certified Emissions Date: December 08 2002. Key words and phrases. Kyoto Protocol, Emissions trading, stochastic game. This work has been undertaken with the support of the Swiss NSF through the NCCR Climate research program. Helpful comments and suggestions have been provided by Ferenc Toth and participants of the NCCR/WP4 seminar organized in Geneva on November 21. 1 The impact of transaction costs in oligopolistic markets for tradable emissions permits is studied in [36]. 1

2

ALAIN HAURIE & LAURENT VIGUIER

Reductions (CERs) from CDM projects that would enter into competition with the emissions permits supplied by Russia. However one may expect relatively large transaction costs for the marketing of CDM projects. A much more effective move would be for DCs to set their own abatement targets and to join the international emissions trading market. This would result in much lower transaction costs for the supply of permits. The dynamic game model that we propose involves only one state variable for each player, namely the stock of emissions permits banked. The time horizon on which Russia and the RDC compete to sell emissions rights to Annex B countries is 2030. Each player has three control variables that are the rate of permits banking, the amount of permits supplied, and the emissions abatement levels, respectively. The equilibrium decisions by the two players are driven by the functions describing the demand for permits from Annex B countries and by their respective marginal abatement cost functions (also called MAC curves). In this study, we compute a so-called S-adapted Cournot-Nash equilibrium for the dynamic game [25][27]2. We compare the solution with the monopoly equilibrium where only Russia is strategically supplying the market to assess the benefits obtained from allowing DCs to compete on the emissions market. We also compare it with the duopoly situation without uncertainty where we compute the open-loop Cournot-Nash equilibrium. In our scenarios, the emissions permits game takes place between Russia and China, knowing that China is likely to be the main exporter of emissions permits in a full global trading regime [13][19][31]. An event tree represents the time at which China enters the international market of emissions permits. This corresponds to the lowering of the transactions costs for that country. We assume that the time of entry is not a decision variable but the consequence of an uncontrolled random process. The paper is organized as follows. In Section 2 we recall the economic elements of the Kyoto protocol, and we describe the uncertainty about post-Kyoto, that motivate the proposed model. In Section 3, the dynamic game is formulated and the conditions characterizing an S-adapted Nash equilibrium are given in the form of a nonlinear complementarity problem [20]. In Section 4 we present the simulation results. The S-adapted Nash equilibrium strategy is compared with a case where Russia acts as a monopoly in the emissions market. The sensitivity of results to the probability of the scenarios is assessed. In section 5, we evaluate the impact on emissions markets of China’s participation in abatement policies. In section 6, we draw some conclusion from our findings. In appendix A, we give the AMPL code that has been used to solve the stochastic game. 2. Uncertainty in Kyoto and Post-Kyoto At the Third Conference of the Parties (COP-3) to the United Nations Framework Convention on Climate Change (UNFCCC), Annex B Parties3 committed to reducing, either individually or jointly, their total emissions of six greenhouse gases (GHGs) by at least 5 percent within the period 2008 to 2012, relative to these gases’ 1990 emissions levels4. However, the U.S. withdrawal from the Kyoto Protocol changed dramatically the character of the agreement. In particular, it may put the international market for GHG emissions permits at risk. Using the MIT-EPPA model, Babiker et al. [2] estimate that Annex B GHG emissions may increase by around 9% 2

Differential game models have already been used successfully in environmental economics. The approach has been more recently applied to analyze the acid rain game [32]. In the Kyoto protocol context, A. Loschel and Z. Zhang [31] have analyzed the interactions between Eastern Europe and Russia as a static Cournot model of duopoly, where the two regions simultaneously set their quantity supplied to the permits market by 2010. 3Annex B refers to the group of developed countries comprised of OECD (as defined in 1990), Russia, and Eastern Europe. 4The Protocol is subject to ratification by Parties to the Convention. It shall enter into force on the ninetieth day after the date on which not less than 55 Parties to the Convention, incorporating Annex I Parties which accounted in total for at least 55% of the total carbon dioxide emissions for 1990 from that group, have deposited their instruments of ratification, acceptance, approval or accession. By mid 2002, the Protocol had been ratified by 77 countries representing 36% of the total CO2 emissions of Annex B parties in 1990.

3

under Marrakech and that the international carbon price might fall below $5 per ton of carbon if all Russian and Ukrainian hot air were freely traded, and if Annex B countries made full use of the additional Article 3.4 sinks. Since Russia is a major potential supplier of emissions permits in the context of an international emissions trading regime limited to Annex B countries, and since banking is possible, strategic behavior can be envisioned. Bernard and Vielle [6] and Bernard et al. [7] have considered a monopolistic behavior by Russia in a dynamic optimization framework. Permit sales are restricted considerably, in particular in the early time periods, compared to the competitive case. The economic incentives to act strategically are thus much larger than when the U.S. is in the Protocol. In the competitive case, carbon prices in 2010 are 13 dollars par ton of carbon ($/tC) in EPPA and 9 $/tC in GEMINI-E3. When Russia is assumed to adopt a strategic inter-temporal behavior, prices rise to 60 $/tC in EPPA and 80 $/tC in GEMINI-E3. In Bernard et al. [8], a deterministic dynamic game model has been used to show that Russia should take into account the possible entry of developing countries in the emissions market. We found that the Nash-Cournot equilibrium price is much lower than the monopoly price. In this previous study, we assumed that the RDC enters the emissions trading markets in the next commitment period and that its emissions target would correspond to its emissions baseline. However, the deadlock in recent international negotiations shows that the timing and level of DCs participation is highly uncertain. A broad political statement meant to signify the meeting’s success, the “Delhi declaration”, was adopted at the eighth Conference of the Parties (COP8) that took place in New Delhi at the end of 2002. The draft is silent on the question of steps beyond Kyoto’s first commitment period (2008-2012), prompting strong objections from the European Union and developed countries. The G-77, representing developing countries, called for a stronger emphasis on financial assistance and on the adverse economic effects on developing countries of measures taken to reduce greenhouse gas emissions. However, the US administration has repeatedly cited the lack of developing country commitments as a primary basis for its rejection of the Kyoto Protocol. In response to the Delhi declaration, the EU asks for “a forward-looking process” that should be conducted with a view to “a more inclusive and long-term global cooperation based on broader and balanced participation”. This large uncertainty on DCs’ participation should therefore be taken into account in the analysis of strategic behavior of Russia and China on the international carbon emissions trading market. In order to introduce uncertainty in this trading game, while keeping a framework of computable equilibrium, we adopted the paradigm of S-adapted market equilibrium initially proposed in [43] and [26] and recently revisited in [24], [25] and [27]. We refer the reader to these references for a complete discussion of the properties of this type of stochastic equilibrium.

3. The Model The model has the structure of a Cournot duopoly model with renewable resource stocks representing the banked emissions permits. These stocks can be replenished via an abatement activity. Due to the standard structure à la Cournot and the linearity of the state equations we can easily check that the conditions for existence and uniqueness of a Nash equilibrium will be met under mild conditions on the cost and demand structures[38]. The stochastic structure of the game is represented by an event tree, with uncontrolled probability measure. The concept of Sadapted equilibrium is used to represent the possibility for the players to use Nash-equilibrium strategies that are dynamically adapted to the scenarios represented in the event tree. The equilibrium solution can then be computed as an enlarged variational inequality as shown in [24][25][26][27], or equivalently by solving an enlarged nonlinear complementarity problem [20].

4


3.1. The Equations. We use a discrete time model with periods t = 0, 1, . . . , T . An event tree represents the (uncontrolled) uncertainty affecting the market. The topology of the event tree is described as follows: N N (t) ⊂ N a[n]∈ N (t − 1) S[n]⊂ N (t + 1) π[n]

: : : : :

is the is the is the is the is the i.e. it

set of nodes set of nodes at period t; N [0] = {n0 }, i.e. the tree has a single root node unique predecessor of n for t = 1, ..., T and each n ∈ N (t) set of direct successors of n for t = 0, ..., T − 1 and each n ∈ N (t) probability of a scenario to include node n, is the sum of probabilities of all scenarios that include n.

Each player (j=1,2) controls a dynamical system described with the use of the following variables and parameters: βj xj (n) x0j xTj uj (n) ∈ Uj [n] hj (n) qj (n) cj (qj )

: : : : : : : :

discount factor for player j stock of permits that are banked by player j at node n initial stock of permits (usually 0) terminal stock of permits (usually 0) permits that are supplied by player j at node n “hot air” input for player j at node n emissions abatement for player j at node n cost function for emissions abatement

In the above list of parameters and variables, the function h(n) is exogenously given. It represents the amount of credited permits from the “hot air” at each node n. For China (j = 2) we shall set h(n) ≡ 0 We assume hj (n) ≥ 0 if t < T and h(T ) = 0. The dynamical system representing Player j is defined as follows: (3.1)

T −1 X

max

t=0

(3.2) (3.3) (3.4) (3.5) (3.6)

xj (n) xj (n0 ) uj (n) xj (n) xj (n)

s.t. = = ∈ ≥ =

βjt

X

π[n][p(n)uj (n) − cj (qj (n))]

n∈N [t]

xj (a[n]) − uj (a[n]) + h(a[n]) + qj (a[n]) ∀n ∈ N [t], t = 1, . . . , T 0 Uj [n] ∀n ∈ N [t], t = 0, . . . , T − 1 0 ∀n ∈ N [t], t = 0, . . . , T − 1 0 ∀n ∈ N [T ].

The market clearing price of the permits is represented as an inverse demand law for permits in Annex B countries (3.7)

p(n) = D[n] (uj (n) + u2 (n)).

This demand function is derived from the competitive equilibrium conditions for the Annex B countries in each node.

3.2. The Optimality Conditions. In this section we formulate the first order Nash equilibrium conditions as a nonlinear complementarity problem for which efficient algorithms exists. In this application we have used the PATH solver. For more details on these conditions, the

5

reader is referred to [21][26][27]. For each Player j we introduce the Hamiltonian Hj (λj (S[n]), xj (n), uj (n), qj (n)) = βjt [p(n)uj (n) − cj (qj (n))] +   X π[n0 ]  λj (n0 ) (xj (n) − uj (n) + hj (n) + qj (n)) + µj (n)xj (n) π[n] 0 n ∈S[n]

(3.8)

t = 0, . . . , T − 1, n ∈ N [t],

where λj (n) is the costate variable associated with the state equation and µj (n) is the KuhnTucker multiplier associated with the non-negativity constraint on xj (n). Then the following must hold at equilibrium: X π[n0 ] ∂ − Hj [n] = βjt [D(U (n)) + D0 (U (n))uj (n)] + (3.9) λj (n0 ) ∂uj π[n] 0 n ∈S[n]

(3.10)

(3.11)

t = 0, . . . , T − 1, n ∈ N [t] ∂ ∂ Hj [n]uj (t) = 0, uj (t) ≥ 0, − Hj [n] ≥ 0 − ∂uj ∂uj t = 0, . . . , T − 1, n ∈ N [t] X π[n0 ] ∂ − Hj [n] = βjt [c0j (qj (t))] + λj (n0 ) ∂qj π[n] 0 n ∈S[n]

(3.12)

t = 0, . . . , T − 1, n ∈ N [t] ∂ ∂ Hj [n]qj (t) = 0, qj (t) ≥ 0, − Hj [n] ≥ 0 − ∂qj ∂qj t = 0, . . . , T − 1, n ∈ N [t]

with λj (n) = (3.13)

=

∂ Hj (λj (S[n]), µj (t), xj (t), uj (t), qj (t)) ∂xj X π[n0 ] λj (n0 ) + µj (n) π[n] 0

n ∈S[n]

(3.14)

t = 0, . . . , T − 1, n ∈ N [t] µj (n)xj (n) = 0, xj (n) ≥ 0, µj (n) ≥ 0 t = 0, . . . , T − 1 n ∈ N [T ].

These equations are completed by the state equations (3.3) describing the accumulation of tradable permits, with the end point conditions (3.5) and (3.6). In appendix A, we give the AMPL code that has been used to submit this problem to the PATH solver.

4. Numerical Results In this section, the model presented above is solved numerically for realistic data representing MAC curves and demand laws. The methodology we implement is to estimate parameters set out above from simulation results of a computable general equilibrium (CGE) model, GEMINIE3 [5][6], and a partial equilibrium model of the world energy system, POLES [12][13][15]. As explained in more details in Bernard et al. [7] and [8], the demand for emissions permits from Annex B regions and marginal abatement costs curves for Russia are taken from GEMINI-E3. The demand for emissions permits computed with GEMINI-E3 assumes that the US are not in the Kyoto Protocol. For the next commitment periods, we assume the “Kyoto forever” case where the Kyoto targets for 2008-2012 are retained through the whole simulation period. We consider only abatement of fossil CO2 emissions, excluding forest and agricultural sinks and non

6


CO2 emissions. Marginal abatement costs (MAC) curves for China are based on the POLES model. MAC curves from economic models give the maximum potential of emissions reductions in the economy. However, several authors have commented on the potential importance of transaction costs in tradable permits markets[23][39]. Analysts do not expect that the full potential will be realized if emissions reduction in China come from CDM projects [29][40]. Six types of transaction costs are likely to confront project-based instruments [17]: • Search costs will be incurred as investors and hosts seek out partners for mutually advantageous projects • Negotiation costs will arise as interested partners work out the details of project design, obligations on each participant, assignment of benefits (such cash or technology payments and GHG abatement credits), the schedule over which benefits will be paid for multiyear projects and the legal drafting to spell out contractual terms, and to provide for contingencies • Certification costs will be incurred at least when the GHG abatement credits are presented to national or international authorities for recordation. • Reporting and verification costs will be necessary to ensure that participants are fulfilling their obligations • Enforcement costs will arise if monitoring reveals departures from the agreed transaction • Insurance costs will likely be incurred to guard against project failure. In our model, a distinction is made between certified emission credits (CER) from CDM projects and emissions permits sold in the international emissions trading market. With the rules yet still incomplete, estimates of CDM supply are fairly speculative. If strict conditions of eligibility exist, and as expected, case-by-case evaluation is required to certify them, high transaction costs are likely. We parameterize supply from CDM in order to take into account the fact that only some technologies will be feasible as projects and that transaction costs with be associated with the transactions. As in [29], the estimated abatement at 10 $/tC is scaled back to one tenth of the economy-wide POLES estimates for China. Transaction costs used CERs from CDM in China are 5 $/tC. Finally, the amount of Russian hot air is far from being certainly established as it depends, among other things, on how rapidly Russia’s GDP recovers. According to model-based analysis, the amount of hot air ranges from 150 to 500 MtC in 2010[37]. based on the estimates from the EPPA-MIT model[7], the hot air is projected to decline from 186 MtC in 2010 to 105 MC in 2020, and to 41 MtC in 2030. 4.1. Scenarios and Results. In these simulations, we suppose that each Annex B country or region implements the necessary policies to meet its Kyoto commitment, except the US. We assume that emissions permits can be freely traded across the Annex B countries. In accordance with the Kyoto Protocol, we also assume that emissions permits can freely be banked5. Finally, we suppose no reduction targets for the developing world during the simulation period. Three basic cases are computed: 5To address the risk of Parties overselling, the Marrakech agreement states that Parties must set aside a part

of their 2008-2012 assigned amount in a reserve: ”Each Party included in Annex I shall maintain, in its national registry, a commitment period reserve which should not drop below 90 per cent of the Party’s assigned amount calculated pursuant to Article 3, paragraphs 7 and 8, of the Kyoto Protocol, or 100 per cent of five times its most recently reviewed inventory, whichever is lowest”. To avoid Parties from “pumping out” all low cost abatement projects in DCs, the agreement limits banking of permits generated under CDM: “[...] the Party may carry over to the subsequent commitment period [...] any CERs held in its national registry, which have not been retired for that commitment period or cancelled, to a maximum of 2.5 per cent of the assigned amount pursuant to Article 3, paragraphs 7 and 8, of that Party”. The rules for emissions trading and banking of permits under CDM do not hold in our simulations since we assume that Annex I Parties do not bank emissions permits, except Russia. Being far below its assigned amount, the rule for permits supply is not constraining for Russia in the first commitment period. We have supposed that this rule will not apply in the next commitment periods

7

• Monopoly case: it assumes that Russia is the only supplier of permits. Since a forward looking behavior is assumed, Russia will maximize its revenues from permits sales by banking a share of the available hot air. • Duopoly case: the RDC is supposed to sell CERs from CDM projects by 2010 and to enter the emissions permits market in 2015. Since RDC’s participation through emissions targets is highly uncertain, we assume that it will enter the emissions market on the basis of its baseline emissions trend. • Stochastic case: four scenarios are considered to take into account the uncertainty on DC’s entry in the permits market. As described in figure 1, the stochastic process is represented by an event tree. In the initial period (t = 0) , corresponding to 2010, Russia is the only supplier in the emissions market but China may supply CERs from CDM projects. In the first scenario S1 , the RDC is assumed to enter the emissions trading market in t = 1 (2015). The RCD enters in the market in t = 2 (2020) and in t = 3 (2030) in the second scenario S2 and third scenario S3 , respectively. We suppose that the RCD does not enter the permits market at all in scenario S4 . In our example, the RDC has the opportunity to sell CERs from CDM projects when it is not in a position to sell emissions permits6. At the terminal period (t = 4), the stock of emissions permits is supposed to be zero (xTj = 0). Finally, we assume that the probability of each scenario is 1/4. 11

21

31

41

S1

12

22

32

42

S2

23

33

43

S3

34

44

S4

t=3

t=4

0

t=0

t=1

t=2

Figure 1. The event tree As in [8], figure 2 shows that the competition between Russia and China in the deterministic Duopoly case would increase the size of the international markets for carbon emissions permits, and lower significantly the permit prices in the long run, compared to the Monopoly case. Uncertainty on the timing of the RDC’s participation affects Russia’s behavior in the market. Since Russia does not know when the RDC will enter the emissions markets, it is rational to limit permits banking and to supply more in the Stochastic case by 2010 (figure 3). In the short run (2010), the permits price is then lower in the stochastic case than in the duopoly case (figure 4). In the long run, Russia tends to sell less permits in the stochastic case than in the deterministic cases. Carbon prices are then higher in S1 , S2 and S3 in 2030 than in the duopoly scenario, and higher in S4 than in the monopoly scenario. The RDC has the same behavior as Russia its entry in the market is uncertain: it tends to sell more permits in the short run than in the deterministic Duopoly case but less in the long run. Since MAC curves for the RDC are very close at this level of emissions reduction and knowing that a 5 per cent discount rate is 6China is supposed to sell CERs from CDM in nodes 0, 12, 23, and 34 (see figure 1).

8


assumed, this country has no incentive to bank permits. Appendix B summarizes simulations results of our stochastic dynamic game.

180

250

160

200

140 120 MtC

MtC

150

100

100 80 60 40

50

20

0

0

2010

2015 Monopoly

2020

Duopoly

S1

S2

2030 S3

2010

S4

2015 Monopoly

Duopoly

2020 S1

S2

2030 S3

S4

Figure 2. Supply of permits from Russia (left) & the RDC (right)

250

200

MtC

150

100

50

0 2010

2015 Monopoly

Duopoly

2020 S1

S2

2030 S3

S4

Figure 3. Banking of permits from Russia 4.2. Sensitivity Analysis. The sensitivity of the results to the probability of each scenario has been assessed. First, we assume that the probability of the RCD’s entry in 2015 (S1) may range from 0 to 100%, the other three scenarios sharing equally the complementarity probability. Second, we assume that the probability no entry in 2030 (S4) may range from 0 to 100%, the other scenarios being equiprobable. Figures 5 and 6 show the sensitivity of supply from Russia and the RDC in 2010 to the probability of the RDC’s entry in the emissions trading market. As expected, Russia sells more permits in 2010 when it is almost sure that the RDC will not enter the market (figure 5). In contrast, the RDC tends to supply less CERs from CDM project when there is a high probability that it will not enter the market (figure 6). The DCs supply of credits from CDM is particularly low in 2010 when it is almost sure that it will never participate in emissions trading. As abatement costs associated with CDM projects are higher than with emissions permits, the

9

250

Carbon price (in $/tC)

200

150

100

50

0 2010

2015 Monopoly

Duopoly

2020 S1

S2

2030 S3

S4

Figure 4. Carbon prices

RDC does not bank CERs when the probability to enter is high. The RDC has an incentive to bank some CERs in 2010, and use them in the next periods, only when it is almost sure that it will never enter the market. The resulting effect of the probability of the RDC’s entry on carbon prices is depicted in figure 7. As shown in the graph, carbon prices tend to go up when the RDC’s entry is highly improbable. The price increase is particularly significant when the RDC’s entry is unexpected even in 2030. Indeed, in that case the RDC banks credits from CDM and the total supply is reduced. 95 94 93 92

MtC

91 90 89 88 87 86 85 0

0.2

0.4

0.6

0.8

1

Probability of China's entry (in %) Entry in 2015

No entry

Figure 5. Sensitivity of Russia’s supply in 2010 to the probability of the RDC’s entry

10


64 62

MtC

60 58 56 54 52 50 0

0.2

0.4

0.6

0.8

1


No entry

Figure 6. Sensitivity of China’s supply of CDM in 2010 to the probability of the RDC’s entry 105 104

Carbon price (in $/tC)

103 102 101 100 99 98 97 96 95 0

0.2

0.4

0.6

0.8

1


No entry

Figure 7. Sensitivity of carbon prices in 2010 to the probability of the RDC’s entry 5. The Impact of China’s Participation As said before, the differentiation of national commitments to limit GHG emissions in the next commitment period is a very controversial issue in climate change negotiations. Several comprehensive studies have been launched to address the issue of post-Kyoto differentiation of global mitigation commitments, including both Annex I and non-Annex I countries[10] [1][35]. In this section, we compare the “no target” scenario described above with three worldwide scenarios of differentiated commitments as in [9]: • The Per Capita Convergence Scenario. According to this approach, the global emission budget has to be equally allocated among all the people of the world. The Per Capita

11

Convergence scenario sets the emission convergence year at 2050, meaning that by then, per capita emissions allowances will be 0.95 tons of carbon equivalent (tC) per year for every country in the world. The transition period is divided into three subperiods and reflects the most common curve identified by the IPCC for emission trajectories in concentration stabilization scenarios. From 2010 to 2030, global emissions are supposed to grow in a linear fashion from 7.8 to 9.4 GtC. They stabilize for the next 10 years and finally decrease by 1 percent per year from 2040 to 2050. Thereafter, these yearly carbon budgets are then allocated to countries on the basis of population. • The Relative Responsibility Scenario. This scenario defines responsibility on the basis of cumulative CO2 emissions, rather than in terms of contribution to global warming, as in the original version of the Brazilian Proposal. In Blanchard[9], cumulative emissions since 1900 are used as a proxy to assess historical responsibility for global warming, partly because the CO2 emissions estimates exist (from fossil fuel use only) and may be used with reasonable confidence. This scenario is applied to all countries of the world, not just industrialized countries. It is based on emission reductions relative to the “business-as-usual” (BAU) case to reach the 2030 environmental target of 9.4 GtC. The yearly global CO2 emission reductions are the difference between the global BAU yearly emissions and these yearly global budgets. The yearly global reductions are distributed to each country in proportion to their relative responsibility for CO2 emissions since 1900. Relative responsibility is measured as the ratio of the cumulative emissions of a country to the world cumulative emissions. • The Emissions-Intensity Target Scenario. The scenario is built on country-level targets expressed as relative changes with respect to BAU emissions intensities, defined as the ratio of CO2 emissions to gross domestic product (GDP), rather than absolute changes. A simulation that meets this participation criterion is one in which Annex I countries improve their emissions intensity by approximately 2 percent annually from their BAU activities, while non-Annex I countries improve their emissions intensities by 0.5 percent. This would amount to a 34 percent improvement in emissions intensities from BAU levels for Annex I countries, and almost 10 percent for non-Annex I countries by 2030. It would imply an approximate 3 percent annual reduction in carbon intensity for most Annex I countries. Intensity changes required to meet the targets in non-Annex I countries would vary more widely, ranging from a 0.5 percent annual intensity increase to a 2 percent decrease. Still, on average, most countries would have to reduce their emissions intensity by around 1 percent annually. According to the POLES model, China’s emissions of CO2 are likely to be 2.4 MtC in 2030 in the BAU scenario. The per capita convergence scenario is by far the harder to implement in China. China would have to reduce CO2 emissions by 618 MtC under this scenario whereas emissions reduction are 294 MtC in the relative responsibility scenario and 228 MtC in the emissions-intensity targets scenario. The different scenarios have been implemented in the stochastic game model. As shown in figures 8, the supply emissions rights from the RDC and Russia is rather different in the four scenarios. In particular, the RDC has a very limited capacity to supply CERs from CDM projects under the per capita scenario7. As shown in figure 9, it is also the case in the next periods when the RDCs does not enter the emissions trading market in 2030 (S4). Transaction costs associated with CDM projects are the main reason for that. Thus, sooner is better than later. China’s supply of permits is not very affected by a domestic commitment when it enters the emissions trading market soon (S1 or S2), except in the per capita scenario. Finally, figure 10 shows the impact of China’s emissions targets on the carbon price when China enters the permits market in the next commitment period (S1). It appears that the carbon prices may increase significantly in 2010 but would not be impacted in the longer term. 7This surprising result is consistent with the findings of [30] and [14].

12


Table 1. China’s Emissions Allowances Under Different Scenarios in 2030 (in MtC) No target scenario Emissions allowances 2395 Reduction from the baseline 0

Per capita Relative CO2 -intensity convergence responsibility targets scenario scenario scenario 1777 2101 2167 618 294 228

120 100

MtC

80 60 40 20 0 Supply Russia

Supply China

No target scenario Responsability scenario

Intensity targets scenario Per capita scenario

Figure 8. Supply of permits under the different scenarios, in 2010

160 140 120

MtC

100 80 60 40 20

No target scenario

Intensity targets scenario

Responsability scenario

2030-S4

2020-S4

2015-S4

2010-S4

2030-S3

2020-S3

2015-S3

2010-S3

2030-S2

2020-S2

2015-S2

2010-S2

2030-S1

2020-S1

2015-S1

2010-S1

0

Per capita scenario

Figure 9. Supply of permits from China under the different scenarios

13

200 180 Carbon price (in $/tC)

160 140 120 100 80 60 40 20 0 2010

2015

2020

2030

No target scenario

Intensity targets scenario

Responsability scenario

Per capita scenario

Figure 10. Price of permits under the different scenarios

6. Conclusion In this paper we have used a stochastic game model to study the possible impact of the entry of a major developing country actor on the international market of carbon emissions permits. Representing the time of DCs entry as the main uncertainty, we have obtained the optimal contingent strategy of Russia concerning the use of its “hot air”. We have compared this strategy with the one that would result from the absence of competition from DCs and when immediate entry of DCs is assumed. The paper has shown that the uncertainty on the timing of DCs participation in the emissions trading market affects the behaviors of the players. In our example, Russia banks less permits in the short run, and more in the long run, when the RDC’s entry in the market is uncertain. We also show that the supply of permits from Russia tends to increase when it becomes highly probable that China will not enter. In that case, the RDC tends to supply less CERs from CDM in the short run and bank them for the next periods. The trading position of DCs may changes significantly if we assume that they will accept emissions targets in the next commitment periods. In particular, we show that China will not be in a position to sell CERs from CDM projects under the per capita scenario. It means that DCs participation through clmiate chnage mitigation should be linked with the entry in an international emissions trading scheme. References [1] Aldy J. E., Orszag P. R., Stiglitz J. E., “Climate Change: An Agenda for Global Collective Action”, Prepared for the conference on “The Timing of Climate Change Policies”, Pew Center on Global Climate Change, October 2001. [2] Babiker M., Jacoby H., Reilly J., and Reiner D., “The Evolution of a Climate Regime: Kyoto to Marrakech”, Report no 82, MIT Joint Program on the Science and Policy of Global Change, Cambridge, MA, February 2002. [3] Barrett S., “Self-Enforcing International Environmental Agreements”, Oxford Economic Papers, 46, 1994, 878-894. [4] Bas¸ar T. and Olsder G.J., Dynamic Noncooperative Game Theory, Academic Press, London, 1989. [5] Bernard A., Vielle M., “Toward a Future for the Kyoto Protocol: Some Simulations with GEMINI-E3”, unpublished paper, 2001.

14


[6] Bernard A., Vielle M., “Does Non Ratification of the Kyoto Protocol by the US Increase the Likelihood of Monopolistic Behavior by Russia in the Market of Tradable Permits?”, paper presented at the 5th Annual Conference on Global Economic Analysis, GTAP, Taipei 2002. [7] Bernard A., Reilly J., Vielle M., and Viguier L., “ Russia’s role in the Kyoto Protocol”, paper presented at the Annual Meeting of the International Energy Workshop jointly organized by EMF/IEA/IIASA, Stanford University, USA, 18-20 June 2002. [8] Bernard A., haurie A., Vielle M., and Viguier L., “A Two-level Dynamic Game of Carbon Emissions Trading Between Russia, China, and Annec B Countries”, NCCR-WP4 Working paper #11, Geneva, September 2002. [9] Blanchard O., “Scenarios for Differentiating Commitments: A Quantitative Analysis”, in K. A. Baumert (Ed.), Building on the Kyoto Protocol: Options for Protecting the Climate, World Resources Institute, October 2002. [10] Blanchard O., Criqui P. and Kitous A., “Après La Haye, Bonn et Marrakech : le futur marché international des permis de droits d’émissions et la question de l’air chaud, IEPE, working Paper, Janvier 2002. [11] Carraro C., Siniscalco D., “Strategies for the International Protection of the Environment”, Journal of Public Economics, 52, 1993, 309-328. [12] Criqui P., POLES 2.2., JOULE II Programme, European Commission DG XVII - Science Research Development, Bruxelles, Belgium, 1996. [13] Criqui P., Mima S., Viguier L., “Marginal abatement costs of CO2 emission reductions, geographical flexibility and concrete ceilings: an assessment using the POLES model”, Energy Policy, 27, 1999, 585-601. [14] Criqui P., Vielle M., Viguier L., “Les coˆ uts des politiques climatiques” in R. Guesnerie (Ed.), Les enjeux économiques de l’effet de serre, Rapport au Conseil d’analyse économique, La Documentation Fran¸caise, in press. [15] Criqui P., Viguier L., “Kyoto and Technology at World Level: Costs of CO2 Reduction under Flexibility Mechanisms and Technical Progress”, International Journal of Global Energy Issues, 14, 2000, 155-168. [16] Dockner E.J., Jorgensen S., Long N.V., and Sorger G., Differential Games in Economics and Management Sciences, Cambridge University Press, Cambridge, UK. [17] Dudek D.J., Wiener J.B., Joint Implementation, Transaction Costs, and Climate Change, OCDE, OCDE/GD(96)173, Paris, 1996. [18] Eyckmans J., Tulkens H., “ Simulating coalitionally stable burden sharing agreements for the climate change problem”, CORE Discussion Paper 9926, Louvain, Belgium, July 2002. [19] Ellerman A.D., and Decaux A., “Analysis of Post-Kyoto CO2 Emissions Trading Using Marginal Abatement Curves”, MIT Joint Program on the Science and Policy of Global Change, Report no 40, Cambridge, MA, 1998. [20] Ferris M.C., Pang J.S., Complementarity and Variational Problems: State of the Art, SIAM Publications, Philadelphia, Pennsylvania, 1997. [21] Ferris M.C., Munson T.S., “Complementarity problems in GAMS and the PATH solver”, Journal of Economic Dynamics and Control, 24, 2000, 165-188. [22] Germain M., Van Ypersele J.-P., “Financial Transfers to Sustain International Cooperation in the Climate Change Framework”, CORE Discussion Paper n 9936, Louvain, Belgium, 1999. [23] Hahn, R.W., Hester, G.L., 1989. Marketable Permits: Lessons for Theory and Practice. Ecology Law Quarterly 16, 361-406. [24] Haurie A. and Moresino F., “Computation of S-adapted equilibria in piecewise deterministic games”, in E. Altman and O. Pourtallier eds. Advances in Dynamic Games Annals of International Society of Dynamic Games, 6, 225-252, 2001. [25] Haurie A. and Moresino F., “S-Adapted Oligopoly equilibria and Approximations in Stochastic Variational Inequalities”, Annals of Operations Research, to appear. [26] Haurie A., Smeers Y., and Zaccour G., “Stochastic Equilibrium Programming for Dynamic Oligopolistic Markets”, Journal of Optimization Theory and applications, 66, 2, August 1990. [27] Haurie A. and Zaccour G., “S-Adapted Equilibria in Games Played over Event Trees: an Overview”, to appear in Annals of International Society of Dynamic Games, 7. [28] Joskow P.L., Schmalensee R., Bailey E.M., “The Market for Sulfur Dioxide Emissions”, The American Economic Review, 88, 4, 1998, 669-685. [29] Jotzo F., Michaelowa A., “Estimating the CDM market under the Marrakech Accords”, Energy Policy, article in press. [30] Leimbach, Toth F., “Economic Development and Emission Control Over the Long Term: The ECLIPS Aggregated Economic Model”, Climatic Change, 56, 1, 2003, 139-165. [31] L¨ oschel, A., and Zhang, Z.X., “The Economic and Environmental Implications of the US Repudiation of the Kyoto Protocol and the Subsequent Deals in Bonn and Marrakech”, Nota Di Lavoro 23.2002, Fondazione Enie Enrico Mattei, 2002.

15

¨ ler K.-G., and de Zeeuw A.J., “The Acid Rain Differential Game”, Environmental and Resource [32] Ma Economics, 12, 1998, 167-184. [33] Michaelowa, A., Stronzik, M., Transaction Costs of the Kyoto Mechanisms, HWWA Discussion Paper 175, Hamburg, 2002. [34] de Moor, A.P.G., Berk M.M., den Elzen M.G.J., and van Vuuren D.P., “Evaluating the Bush Climate Change Initiative”, RIVM Report 728001019/2002, 2002. [35] Mueller B., “Varieties of Distributive Justice in Climate Change”, Climatic Change, Vol. 48, No. 2-3, February 2001. [36] Nagurney A. and Kanwalroop K.D. “Marketable pollution permits in oligopolistic markets with transaction costs”, Operations Research, Vol. 48, No. 3, pp. 424-435, 2000. [37] Paltsev, S. V., The Kyoto Protocol: “Hot air” for Russia?, Department of Economics, University of Colorado, Working Paper No. 00-9, October 2000. [38] Rosen J. B., Existence and uniqueness of equilibrium points for concave N -person games, Econometrica, 33 (1965), pp. 520-534. [39] Stavins R.N., “Transaction Costs and Tradeable Permits”, Journal of Environmental Economics and Management, 29, 1995, 133-148. [40] van Vuuren D., Yun L., de Vries B., Kejun J., Graveland C., Fengxi Z., “Energy and emission scenarios for China in the 21st century exploration of baseline development and mitigation options”, Energy Policy, in press. [41] de Zeeuw A.J., van der Ploeg F., “Differential Games and Policy Evaluation: A Conceptual Framework”, Oxford Economic Papers, 43, 1991, 612-636. [42] Zhang, Z.X., “Estimating the Size of the Potential Market for the Kyoto Flexibility Mechanisms”, Weltwirtschaftliches Archiv - Review of World Economics, 136(3), 491-521. [43] Zaccour G., Théorie des jeux et marchés énergétiques: marché européen de gaz naturel et échanges d’électricité, PhD thesis, HEC, Montréal, 1987.

16


Appendix A. The AMPL code for solving the stochastic dynamic game model set J;

# Players

set J2; # constrained players set T; # set of periods set T0; # initial period set T1; # terminal period set TT0 := T union T0; # planning period set TT1 := T union T1; # non root period set scen; # scenarios set N; # set of nodes set N2{TT0}; # set of nodes at time t set N0; # set of initial nodes set NT; # set of terminal nodes set NN := N union NT union N0; # set of all nodes set NI := N union N0; # set of decision nodes set NF := N union NT; # set of non-root nodes set succ{n in NI}; # successors of n set Sc{NN}; # set of scenarios including node n param prob{scen} >= 0, = 0; # lower bound on variable x param f_max{n in NN} >= f_min[n]; # upper bound on variable x var u{j in J,n in NI} >= 0

; # supply indexed on scenarios

var q{j in J,n in NI} >= 0 ; # abatement level indexed on scenarios var nux{J,n in NI} >= 0; # x positive multiplier indexed on scenarios var p{NI}; # permit price indexed on scenarios var x{J,n in NN} >= 0; # permits banking indexed on scenarios var lambda{J,NN}; # costate variable indexed on scenarios subject to posix {j in J, n in NI}: x[j,n] >= 0 complements nux[j,n] >= 0 ; subject to supply {j in J, n in NI}: sum {m in succ[n]}((pi[m]/pi[n])*lambda[j,m]) -((rho[j,n])*(p[n]+u[j,n]/delta[n])) >= 0 complements u[j,n] >= 0 ; subject to abatement {j in J, n in NI}: (rho[j,n])*(c[j,n]*q[j,n]**3+beta[j,n]*q[j,n]**2+d[j,n]*q[j,n]+tc[j,n] +tc2[j,n]*q[j,n]**2) - (sum {m in succ[n]}((pi[m]/pi[n])*lambda[j,m])) >= 0 complements q[j,n] >= 0;

18


subject to demandsupply {n in NI}: sum {j in J} u[j,n] = delta[n]*p[n]+a[n]; subject to state {j in J, n in NF}: ha[j,pred[n]]+x[j,pred[n]]-u[j,pred[n]] +q[j,pred[n]]-tar[j,pred[n]] = x[j,n]; subject to costate {j in J, n in NI}: lambda[j,n] = sum {m in succ[n]}((pi[m]/pi[n])*lambda[j,m])+nux[j,n]; subject to initial {j in J}: x[j,0]=xinit[j]; subject to terminal {j in J, n in NT}: x[j,n] = xterm[j];

19

Appendix B. The Event Tree

node 21

node 11 j1 node 0

j2

x:

141.9

0.0

u:

96.2

103.1

j1

j2

q:

41.0

103.1

x:

0.0

0.0

p:

104.1

104.1

u:

89.5

60.2

q:

45.5

60.2

p:

99.0

99.0

node 12 j1

j2

x:

141.9

0.0

u:

111.1

70.6

q:

51.1

70.6

p:

121.2

121.2

node 31

j1

j2

x:

191.7

0.0

x:

160.0

0.0

u:

112.9

119.9

u:

128.1

134.6

q:

40.2

119.9

q:

46.1

134.6

p:

126.7

126.7

p:

171.7

171.7

node 22

j1

j2

node 32

j1

j2

x:

186.9

0.0

x:

157.5

0.0

u:

112.5

120.1

u:

127.8

134.8

q:

42.1

120.1

q:

48.3

134.8

p:

126.9

126.9

p:

171.9

171.9

node 23

j1

j2

node 33

j1

j2

x:

186.9

0.0

x:

j1 151.7

j2 0.0

u:

130.5

80.6

u:

127.1

135.1

q:

54.3

80.6

q:

53.4

135.1

p:

148.8

148.8

p:

172.3

172.3

node 34 j1

j2

x:

151.7

0.0

u:

146.4

92.9

q:

72.6

92.9

p:

201.0

201.0

Figure 11 LOGILAB-HEC, Faculty of Economics and Social Sciences, University of Geneva, 40 Blvd. du Pont d’Arve, CH-1211, Geneva 4, Switzerland. E-mail address: [email protected], [email protected]

Working Papers of the WP Climate Risks Assessment WP4-1

Thalmann P. (2001). The public acceptance of green taxes: 2 million voters express their opinion, November.

WP4-2

Haurie A. (2001). Integrated assessment modeling for climate change: an infinite horizon optimization viewpoint (Draft), December.

WP4-3

Barrieu P., Chesney M. (2001), Optimal timing for an environmental policy in a strategic framework, October 16.

WP4-4

Haurie A., Siverguina I., Zachary D. S. (2002), A reduced-Order PhotoChemical Air Quality Model, January 23.

WP4-5

Carlson D.A., Haurie A., Vial J.-P., Zachary D. S. (2002). An Oracle Method for Coupling an E3 Model With a Photo-Chemical Air Quality Model, January 30.

WP4-6

Viguier L. (2002). The U.S. Climate Change Policy: A Preliminary Evaluation, February 28.

WP4-7

Chiera B., Filar J., Zachary D.S.(2002). Comparative Forecasting Analysis of the ENSO, June 19.

WP4-8

Greppin H., Priceputu A. (2002). Dialectique du bioespace et de l'écoespace : émergence de la territorialité, de la biocénose aux sociétés, July.

WP4-9

Bahn O., Kypreos S. ( 2002). MERGE-ETL: An optimisation equilibrium model with two different endogenous technological learning formulations, July.

WP4-10

Haurie A. (2002). Turnpikes in multi-discount rate environments and GCC policy evaluation, August.

WP4-11

Bernard A., Haurie A., Vielle M., Viguier L. (2002). A Two-Level Dynamic Game of Carbon Emissions Trading Between Russia, China, and Annex B Countries, September.

WP4-12

Greppin H., Degli Agosti R., Priceputu A. M. (2002). From Viability Envelopes to Sustainable Societies, October.

WP4-13

Greppin H., Degli Agosti R., Priceputu A. M. (2002). The Concept of Viability Envelopes, November.

WP4-14

Babiker M., Reilly J., Viguier L. (2002). Is Emissions Trading Always Beneficial?, November.