Combining Adaptation and Mitigation: A Game Theoretic Approach

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ISSN:

0711–2440

Combining Adaptation and Mitigation: A Game Theoretic Approach O. Bahn G–2010–26 April 2010 Revised: October 2010

Les textes publi´ es dans la s´ erie des rapports de recherche HEC n’engagent que la responsabilit´ e de leurs auteurs. La publication de ces rapports de recherche b´ en´ eficie d’une subvention du Fonds qu´ eb´ ecois de la recherche sur la nature et les technologies.

Combining Adaptation and Mitigation: A Game Theoretic Approach Olivier Bahn GERAD & MQG HEC Montr´eal 3000, chemin de la Cˆ ote-Sainte-Catherine Montr´eal (Qu´ebec) Canada, H3T 2A7 [email protected]

April 2010 Revised: October 2010

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Abstract This paper deals with an application of dynamic games for the design of efficient climate policies involving both adaptation and mitigation elements. More precisely, this paper extends the integrated assessment model Ada-BaHaMa to a game theoretic framework where several world regions define noncooperatively their energy and climate policies all the while being affected by climate change damages induced by their total greenhouse gas emissions. The paper provides also a numerical illustration for a setting with two players.

R´ esum´ e Ce papier propose une application des jeux stochastiques pour la conception de politiques climatiques efficaces impliquant ` a la fois des mesures d’adaptation et de r´eduction. Plus pr´ecis´ement, ce papier ´etend le mod`ele Ada-BaHaMa ` a un formalisme de jeu, o` u plusieurs groupes de pays d´efinissent de fa¸con non-coop´erative leurs politiques ´energ´etiques et climatiques tout en ´etant affect´es par des dommages dus aux changements climatiques induits par leurs ´emissions. Le papier fournit ´egalement une illustration num´erique pour une configuration ` a deux joueurs.

Acknowledgments: The author acknowledges financial support by HEC Montr´eal (Research Office) and the Natural Sciences and Engineering Research Council of Canada.

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1

Introduction

The aim of this paper is to use a game formalism for the design of efficient energy and climate policies. The paper is a continuation of Bahn et al. (2010a) where the Ada-BaHaMa model has been proposed to assess the interplay of climate change adaptation and mitigation measures. In the present paper, one extends Ada-BaHaMa to a game theoretic framework and gives a numerical illustration for a two-region version of the model. To address climate changes, policy makers rely mostly on mitigation measures, designing (energy, in particular) policies to curb greenhouse gas (GHG) emissions. The Kyoto Protocol to the United Nations Framework Convention on Climate Change is such an example, as it imposes emission reduction targets to the so-called Annex-B countries of the Protocol to be reached by 2012. Besides, post-Kyoto negotiations are under way to provide a new international framework for emission reductions after 2012. But these negotiations are currently (2010) facing many difficulties and global GHG emissions are still increasing. In this context, and since future climate changes appear now unavoidable to some extent, adaptation options have gained a new political momentum in the design of efficient climate policies. Contrary to mitigation measures, adaptation options do not curb GHG emissions, but provide strategies to deal effectively with their effects by reducing climate change damages (Tol, 2005; Adger et al., 2007; Klein et al., 2007). Adaptation measures can be reactive or preventive and applied in many sectors, for instance agriculture (crops for new climate conditions), health (e.g., medical preventions against spreading tropical diseases) or urban planning (e.g., dykes to protect against sea level rise). To address the interplay of adaptation and mitigation options for climate changes, one may use an integrated assessment, which is an interdisciplinary approach that uses information from different fields of knowledge, in particular climatology and economy. Integrated assessment models (IAMs) are tools for conducting an integrated assessment. Well known examples of IAMs are DICE (Nordhaus, 1994, 2007), MERGE (Manne et al., 1995; Manne and Richels, 2005) and RICE (Nordhaus and Yang, 1996). Research incorporating adaptation measures into IAMs has been rare until recently, despite the importance of these models for policy making. Hope et al. (1993) (updated in Hope, 2006) were the first to consider adaptation as a policy variable in an IAM, the PAGE model. But since 2008, several models have been proposed, based either on DICE or RICE. Bosello (2008) developed a FEEM-RICE model with mitigation, adaptation and R&D development in a strategic setting. de Bruin et al. (2009b) proposed to include adaptation as an explicit strategy in DICE (AD-DICE model). In follow-up studies, de Bruin et al. (2009a) expanded this methodology to RICE (AD-RICE model), Felgenhauer and de Bruin (2009) introduced uncertainty in the climate outcome and finally Hof et al. (2009) tested for the effectiveness of adaptation funds in a combined AD-RICE/FAIR model. One uses in this paper the Ada-BaHaMa model, the deterministic version of a simple integrated assessment model (Bahn et al., 2008, 2010b) enriched to consider explicit adaptation measures. Ada-BaHaMa is in the spirit of the DICE model but distinguishes between two types of economy: the “carbon economy” (our present economy) where a high level of fossil fuels is necessary to produce the economic good and a so-called “carbonfree” or “clean economy” (for instance an hydrogen1 economy) that relies much less on fossil fuels to obtain output. Besides, compared to the other IAMs modeling adaptation, Ada-BaHaMa considers adaptation efforts as investments (“stock ”) instead of costs (“flow ”) and as such emphasizes its proactive aspect instead of its reactive one (see Lecocq and Shalizi, 2007). Ada-BaHaMa can therefore assess the timing of adoption of clean technologies in the presence of adaptation strategies. In doing so, the model can contribute to the current debate about the required incentives to foster adequate “green” R&D investments. In Bahn et al. (2010a), a single decision maker has been considered. In the present paper, one extends Ada-BaHaMa to a non-cooperative game setting (Nash, 1950) where world regions define non-cooperatively their energy and climate policies (which consist of both mitigation and adaptation measures) all the while being affected by climate change related damages induced by their total GHG emissions. 1 One refers here to hydrogen production using carbon-free processes, such as biomass gasification or water electrolysis using carbon-free electricity; see for example IEA (2005).

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The paper is organized as follows. In Section 2, one proposes a multi-region version of Ada-BaHaMa. Section 3 characterizes the solutions of the game regions play to design their energy and climate policies under different optimality concepts. In Section 4, one presents a numerical illustration for a two-player version of the model. Finally Section 5 concludes.

2

A n-player version of Ada-BaHaMa

This section extends the one-region Ada-BaHaMa model to a version where the world is comprised of n independent regions. It relies on the n-player version of the BaHaMa model proposed in Bahn and Haurie (2008).

2.1

Variables

The model uses the following variables, where j = 1, . . . , n is the index of each of the n regions and t the model running time: AD(j, t): reduction of damages due to adaptation measures in region j at time t, in %; C(j, t) ≥ 0: total consumption in region j at time t, in trillions (1012 ) of dollars; c(j, t) ≥ 0 : per capita consumption in region j at time t, c(j, t) =

C(j,t) L(j,t) ;

E1 (j, t) ≥ 0: yearly emissions of GHG (in Gt–109 tons–carbon equivalent) in the carbon economy of region j at time t; E2 (j, t) ≥ 0: yearly emissions of GHG in the clean economy of region j at time t, in GtC; ELF(j, t): economic loss factor in region j due to climate changes at time t, in %; Ii (j, t) ≥ 0: investment in capital Ki (i = 1, 2, 3) in region j at time t, in trillions of dollars; K1 (j, t) ≥ 0: physical stock of productive capital in the carbon economy of region j at time t, in trillions of dollars; K2 (j, t) ≥ 0: physical stock of productive capital in the clean economy of region j at time t, in trillions of dollars; K3 (j, t) ≥ 0: physical stock of adaptation capital in region j at time t, in trillions of dollars; K3max (j, t) ≥ 0: maximal stock of adaptation capital in region j at time t, in trillions of dollars; L1 (j, t) ≥ 0: part of the (exogenously defined) labor force L(j, t) of region j allocated at time t to the carbon economy, in millions (106 ) of persons; L2 (j, t) ≥ 0: part of the labor force of region j allocated at time t to the clean economy, in millions of persons; M (t) ≥ 0: atmospheric concentration of GHG at time t, in GtC equivalent; WRG(j): discounted welfare of region j; Y (j, t) ≥ 0: economic output of region j at time t, in trillions of dollars.

2.2

Economic modeling

In each region j = 1, . . . , n, a social planner is assumed to maximize social welfare (WRG), given by the sum over T 10-year periods of a discounted utility from per capita consumption (c) with the discount rate dr(j, t): WRG(j) =

T −1 X

10 dr(j, t) L(j, t) log[c(j, t)].

(1)

t=0

Total labor (L) is divided between labor allocated to the carbon economy (L1 ) and labor allocated to the clean economy (L2 ): L(j, t) = L1 (j, t) + L2 (j, t). (2) Consumption comes from an optimized share of production (Y ), the remaining being used to invest in the production capitals (dirty—K1 —and/or clean—K2 ), in the adaptation capital (K3 ) and to pay for energy

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costs (energy being measured through emission levels Ei ). The presence of damages (defined by the ELF factor) reduces the available production such that: C(j, t) = ELF(j, t) Y (j, t) − I1 (j, t) − I2 (j, t) − I3 (j, t) − pE1 (j, t) φ1 (j, t) E1 (j, t) − pE2 (j, t) φ2 (j, t) E2 (j, t), (3) where pEi are energy prices and φi energy conversion factors for emissions Ei . Capital stock evolves according to the choice of investment (Ii ) and a depreciation rate δKi through a standard relationship: Ki (j, t + 1) = 10Ii (j, t) + (1 − δKi )10 Ki (j, t)

i = 1, 2, 3.

(4)

Economic output (Y ) occurs in the two economies according to an extended Cobb-Douglas production function in three inputs, capital (K), labor (L) and energy (measured through emission levels E): Y (j, t) = A1 (j, t) K1 (j, t)α1 (j) (φ1 (j, t) E1 (j, t))θ1 (j,t) L1 (j, t)1−α1 (j)−θ1 (j,t) + A2 (j, t) K2 (j, t)α2 (j) (φ2 (j, t) E2 (j, t))θ2 (j,t) L2 (j, t)1−α2 (j)−θ2 (j,t) , (5) where Ai is the total factor productivity in the carbon (resp. clean) economy (when i = 1, resp. i = 2), αi the elasticity of output with respect to capital Ki and θi the elasticity of output with respect to emissions Ei .

2.3

Damages and adaptation

Accumulation M of GHG in the atmosphere evolves according to the following equation: M (t + 1) = 10 β

n X

(E1 (j, t) + E2 (j, t)) + (1 − δM ) M (t) + δM Mp ,

(6)

j=1

where β is the marginal atmospheric retention rate, δM the natural atmospheric elimination rate and Mp the preindustrial level of atmospheric concentration. Eq. (6) constitutes a rather crude representation of GHG concentration dynamics. But it is however consistent with the archetypal DICE model. Increasing atmospheric GHG concentrations trigger climate changes that yield economic losses affecting regional production (see Eq. (3)). These (net) regional damages take into account the effects of adaptation (AD): ELF(j, t) = 1 − AD(j, t)



M (t) − Md (j) catM (j) − Md (j)

2

,

(7)

where Md (j) is the concentration level at which damages start to occur in region j = 1, . . . , n and catM (j) the climate sensitivity dependent “catastrophic” concentration level at which the entire production of region 2  M(t)−Md (j) . j would be wiped out. Notice that regional damages correspond then to AD(j, t)Y (j, t) cat M (j)−Md (j) Adaptation levels in each region j correspond to: AD(j, t) = 1 − αAD (j)

K3 (j, t) , K3max (j, t)

(8)

where αAD is the maximal adaptation effectiveness and K3max the maximal amount of adaptation capital that would ensure the optimal effectiveness of the adaptation measures. To capture the fact that adaptation costs should increase whenever atmospheric GHG concentration (and therefore damages) increases, K3max is modeled as an increasing function of the current GHG concentration: K3max (j, t) = βAD (j) where βAD and γAD are calibration parameters.



M (t) Md (j)

γAD (j)

,

(9)

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Solution concepts

This section presents two solution concepts for Ada-BaHaMa: a collaborative (or Pareto equilibrium) solution and a non-collaborative (or Nash equilibrium) solution.

3.1

Collaborative solutions

Pn Suppose that one allocates to each region j = 1, . . . , n a weight rg(j) > 0, such that j=1 rg(j) = 1. A collaborative (or Pareto equilibrium) solution associated with this weighting is obtained when one optimizes the criterion: n X rg(j)WRG(j), (10) j=1

under constraints (1)–(9).

3.2

Nash equilibrium solutions

A Nash equilibrium is obtained when each region has chosen an emission path and an investment path that correspond to its best reply to the choices made by the other regions. The game has the open-loop information structure. A strategy sj for region j consists of: • a sequence of emissions {E1 (j, t), E2 (j, t) : t = 0, 1, . . . , T − 1}; • a sequence of investments {I1 (j, t), I2 (j, t), I3 (j, t) : t = 0, 1, . . . , T − 1} in capital K1 , K2 and K3 respectively; • a sequence of labor allocations {L1 (j, t), L2 (j, t) : t = 0, 1, . . . , T − 1} in the carbon and clean economy respectively. Because accumulation of GHG in the atmosphere depends on emissions of all players (see Eq. (6)), accumulation that translates into damages affecting each player (see Eq. (7)), payoff (WRG) to each region j will depend on the strategy choices of the other regions. One shall denote it ψj (sj , s−j ), where s−j represents the strategies chosen by regions other than j. One shall also denote s = (sj : j = 1, . . . , n) the strategy vector of all regions. Let S denotes the set of all admissible strategy vectors. Consider the so-called reply function defined as follows over the product set S × S: θ(r : s′ , s) =

n X

r(j)ψj (s′j , s−j ), ∀ s′ ∈ S, s ∈ S,

(11)

j=1

where r(j) is any positive weight allocated to player j. A Nash equilibrium for this game is a fixed point of the optimal reply mapping: Θ(r : s) = {s∗ ∈ argmaxs′ ∈S θ(r : s′ , s)} . (12) A cobweb approach is implemented to compute this fixed-point solution. Although it is not guaranteed to converge, it does in practice, see next Section 4. Doing so, it defines a Nash equilibrium.2

4

Numerical results

As numerical illustration, one considers for simplicity the case where the world would be divided into two coalitions of countries: the first one (region j = 1) regroups all Annex I countries of the Kyoto Protocol (the developed countries), the second region (j = 2) regroups all other non-Annex I countries (developing countries and emerging economies). One considers thus the simplified case of two players (n = 2) and one selects rg(1) = rg(2) = 0.5. 2 Indeed, the approach implemented here is akin to asking each player sequentially to choose its strategy given the choices made by the other players. Once the approach has converged, no player is willing to modify its strategy, which corresponds then to a Nash equilibrium.

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One considers three basic scenarios: a counterfactual baseline without any climate change related damages, a mitigation-only scenario where adaptation is not possible and finally a combined scenario with both mitigation and adaptation efforts allowed. For each of the last two scenarios, one computes both a collaborative (Pareto equilibrium) solution and a non-collaborative (Nash equilibrium) solution.

4.1

Model calibration

The calibration of the 2-player Ada-BaHaMa model follows the approach detailed in Bahn et al. (2010a). It is done for the combined scenario (with both adaptation and mitigation strategies implemented) under the collaborative (Pareto) approach. In short, the different economic and climate parameters (Eq. (1) to (6)) are mostly from the DICE model (version 2007,3 thereafter referred to as DICE2007). Note however that, compared to the dirty economy, production in the clean economy has higher energy costs but a better energy efficiency. In addition, some regional parameter values have been adapted in the spirit of the RICE model as follows. The two regions have different population levels and energy prices, and region 2 is assumed to have a higher elasticity of output with respect to capital as well as a lower initial value for energy efficiency: L(j, 0): initial value for population level of region j, in millions of persons; L(1, 0) = 2204.5; L(2, 0) = 4204.5; πi (j, 0) : initial energy price in the carbon economy (i = 1), resp. clean economy (i = 2) in region j; π1 (1, 0) = 0.35; π1 (2, 0) = 0.3; π2 (1, 0) = 0.41; π2 (2, 0) = 0.46; αi (j): elasticity of output with respect to productive capital Ki (i = 1, 2) in region j; αi (1) = 0.3; αi (2) = 0.35; φi (j, 0): initial value for energy conversion factor in the carbon economy (i = 1), resp. clean economy (i = 2) in region j; φ1 (1, 0) = 1.1; φ1 (2, 0) = 1.0; φ2 (1, 0) = 10.0; φ2 (2, 0) = 9.0. Note that as a result, the overall production of the 2-player Ada-BaHaMa reproduces the economic output of DICE2007. Damages and adaptation parameters (Eq. (7) to (9)) are from the AD-DICE model and the World Bank (Margulis and Narain, 2009). Note that region 2 is assumed to bear higher damages for a given GHG atmospheric concentration level but also to have a higher capacity for adaptation: Md (j): concentration level at which damages start to occur in region j, in GtC; Md (1) = 686.0; Md (2) = 635.0; αAD (j) : maximal adaptation effectiveness in region j; αAD (1) = 0.33; αAD (2) = 0.43. As a result, Ada-BaHaMa reproduces the overall magnitude of climate change damages estimated by DICE2007 and AD-DICE. The next sections detail the numerical results. First, one gives the evolution of GHG emissions and atmospheric concentrations. Next, one reports on the accumulation of production and adaptation capitals and on the evolution of net climate change related damages. Finally one gives the gross domestic product.

4.2

GHG emissions and concentrations

Table 1 reports first on atmospheric GHG concentration levels. In the BaU scenario, concentration reaches around 720 ppmv by 2100. This corresponds approximately to the SRES A1B scenario of the IPCC(2000). When taking into account climate damages, and assuming that the two regions are collaborating to reach a Pareto equilibrium by optimizing Eq. (10) with rg(1) = rg(2) = 0.5, GHG concentration is much lower by 2100: 566 ppmv in the mitigation-only scenario, and 578 ppmv in the combined scenario as the availability of adaptation options enable players to rely more on fossil energy while suffering from less (net) damages (see below). In the Nash equilibrium setting, as each player optimizes its own welfare without consideration of the other player’s welfare, the environmental situation deteriorates 3 See:

http://www.econ.yale.edu/ nordhaus/DICE2007.htm.

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Table 1: GHG atmospheric concentrations in ppmv for the baseline (denoted BAU), the mitigation-only (denoted MI) and the combined (denoted CO) scenarios. Cases P- and N- denote the collaborative (Pareto) and non-collaborative (Nash) settings respectively. BAU P-MI P-CO N-MI N-CO 2015 385 385 385 385 385 2025 402 402 402 402 402 2035 423 421 421 422 422 2045 448 443 443 445 445 2055 479 461 465 472 473 2065 517 481 486 504 506 2075 562 502 509 540 544 2085 617 526 534 581 588 2095 682 552 562 612 623 2105 758 580 593 640 658 2115 845 582 627 656 693 with GHG concentration levels sightly higher than the Pareto solution: 626 ppmv in the mitigation-only scenario and 641 ppmv in the combined scenario. Table 2 reports next on GHG emission levels for the two regions. Table 2: GHG emissions in GtC for the two regions (1,2) in the baseline (denoted BAU), the mitigation-only (denoted MI) and the combined (denoted CO) scenarios. Cases P- and N- denote the collaborative (Pareto) and non-collaborative (Nash) settings respectively. BAU P-MI P-CO N-MI N-CO 1 2 1 2 1 2 1 2 1 2 2015 3.1 5.4 2.7 5.0 2.7 5.0 3.0 5.0 3.0 5.1 2025 3.5 6.5 3.0 5.8 3.1 5.8 3.4 5.9 3.4 6.0 2035 4.2 7.9 1.2 6.9 2.4 6.9 3.9 7.0 3.9 7.1 2045 5.0 9.7 0.5 8.0 0.9 8.2 4.5 8.1 4.5 8.5 2055 6.0 11.8 0.2 9.2 0.4 9.5 5.2 9.3 5.3 10.0 2065 7.1 14.2 0.1 10.3 0.2 10.8 6.0 10.4 6.0 11.7 2075 8.3 17.0 0.1 11.4 0.1 12.1 2.0 11.5 2.1 13.1 2085 9.7 20.0 0.1 12.5 0.1 13.3 0.7 12.6 0.7 14.5 2095 11.0 23.2 0.1 4.1 0.1 14.6 0.3 9.1 0.3 15.9 2105 12.3 26.2 0.0 1.4 0.0 4.9 0.1 3.1 0.1 17.3 2115 13.0 28.2 0.0 0.5 0.0 1.7 0.1 1.1 0.1 6.7 In the Pareto solution, the reduction effort is mostly borne by the developed countries (region 1), whereas the developing countries and emerging economies (region 2) are still allowed to emit a significant amount of GHGs almost until the end of the 21st century. By contrast, in the Nash equilibrium where each region acts selfishly, they all emit more than in the Pareto case, but especially region 1. One notes again that in the combined scenario the availability of adaptation options enables players to rely more on GHGs for their economic production.

4.3

Productive capital accumulations

Clean capital accumulation levels are given in Table 3. The accumulation of clean capital K2 and thus the transition towards clean energy sources are directly related to the emission reduction efforts carried out by the players. Notice first that clean capital does not accumulate in the baseline, where in the absence of climate change related damages there is no need to curb GHG emissions. In the Pareto cases, region 1 starts accumulating clean capital by 2035, whereas region 2 does so only by 2095 in the mitigation-only scenario (by 2105 in the combined scenario) at a time when it

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Table 3: “Clean” capital K2 accumulations in trillion USD for the two regions (1,2) in the baseline (denoted BAU), the mitigation-only (denoted MI) and the combined (denoted CO) scenarios. Cases P- and N- denote the collaborative (Pareto) and non-collaborative (Nash) settings respectively. BAU P-MI P-CO N-MI N-CO 1 2 1 2 1 2 1 2 1 2 2015 0 0 0 0 0 0 0 0 0 0 2025 0 0 0 0 0 0 0 0 0 0 2035 0 0 41 0 19 0 0 0 0 0 2045 0 0 63 0 55 0 0 0 0 0 2055 0 0 79 0 77 0 0 0 0 0 2065 0 0 96 0 95 0 0 0 0 0 2075 0 0 113 0 112 0 81 0 80 0 2085 0 0 133 0 133 0 121 0 122 0 2095 0 0 154 201 155 0 148 97 150 0 2105 0 0 175 296 178 236 171 257 175 0 2115 0 0 199 361 201 347 194 339 199 248 significantly curbs its GHG emissions. Note that the higher overall accumulation in region 2 is due to an economy (as measured by total economic output) larger than the one of region 1. In the non-collaborative cases, following the postponement of GHG abatement, investments in the clean clean capital are delayed by 40 years in region 1 and by at most 10 years in region 2. Table 4 gives next accumulation levels of dirty capital K1 . Table 4: “Dirty” capital K1 accumulations in trillion USD for the two regions (1,2) in the baseline (denoted BAU), the mitigation-only (denoted MI) and the combined (denoted CO) scenarios. Cases P- and N- denote the collaborative (Pareto) and non-collaborative (Nash) settings respectively. BAU P-MI P-CO N-MI N-CO 1 2 1 2 1 2 1 2 1 2 2015 54 71 54 71 54 71 54 71 54 71 2025 55 81 55 80 55 80 55 80 55 81 2035 60 96 19 95 41 95 60 95 60 96 2045 70 117 7 115 14 115 69 115 69 115 2055 83 142 2 139 5 138 82 140 82 140 2065 98 172 1 167 2 168 97 168 98 170 2075 116 208 0 200 1 201 34 201 34 203 2085 136 248 0 238 0 240 12 236 12 241 2095 159 294 0 83 0 283 4 180 4 282 2105 184 344 0 29 0 99 1 63 1 328 2115 211 400 0 10 0 34 1 22 1 134 In the baseline scenario, stock of dirty capital keeps increasing following the “laissez-faire” policy characteristic of this setting. Whereas in the other cases, dirty capital accumulates only until one starts to invest in clean capital. Afterwards, dirty capital is progressively phased out.

4.4

Adaptation capital accumulation and net damages

Table 5 reports next on the accumulation of adaptation capital K3 in the combined scenarios. Note that neither in the baseline, where it is not needed, nor in the mitigation-only scenarios, where it is not available, does capital K3 accumulate. Region 1, under both Pareto and Nash settings, starts accumulating adaptation capital by 2075, where K3 reaches immediately its maximal level (K3max ) and stays at this level afterwards. The 60 years delay in implementing adaptation measures comes from the relatively low effectiveness of adaptation (αAD (1) = 0.33)

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Table 5: Adaptation capital K3 accumulations and maximal amount of adaptation capital K3max in trillion USD for the two regions (1,2) in the combined (denoted CO) scenarios. Cases P- and N- denote the collaborative (Pareto) and non-collaborative (Nash) setting respectively. P-CO N-CO K3 K3max K3 K3max 1 2 1 2 1 2 1 2 2015 0.0 0.0 0.8 1.1 0.0 0.0 0.8 1.1 2025 0.0 0.0 0.9 1.3 0.0 0.0 0.9 1.3 2035 0.0 0.0 1.2 1.7 0.0 0.0 1.2 1.7 2045 0.0 0.0 1.5 2.1 0.0 2.2 1.6 2.2 2055 0.0 2.5 1.8 2.5 0.0 3.0 2.1 3.0 2065 0.0 3.1 2.2 3.1 0.0 4.1 2.9 4.1 2075 2.7 3.8 2.7 3.8 4.1 5.8 4.1 5.8 2085 3.4 4.8 3.4 4.8 5.4 7.5 5.4 7.5 2095 4.3 6.0 4.3 6.0 6.8 9.6 6.8 9.6 2105 5.5 7.7 5.5 7.7 8.6 12.1 8.6 12.1 2115 5.6 7.9 5.6 7.9 10.9 15.4 10.9 15.4 and the corresponding trade-off between costs of adaptation and reduction of at most 33% of damages. One can thus note that for region 1 adaptation acts as a complement to the mitigation efforts started either by 2035 in the P-CO case or by 2075 in the N-CO case (see again Table 3). For region 2, the main difference is that accumulation of adaptation capital starts much earlier: by 2045 in the Nash setting and by 2055 in the Pareto setting. This results from the assumed higher effectiveness of adaptation (αAD (2) = 0.43) but also from the assumed higher climate change related damages compared to region 1 (see again Section 4.1). For region 2, there is thus during some initial periods a clear substitution between adaptation and mitigation efforts (that start only in the 22nd century). Note also that for both regions the maximal level of adaptation capital (K3max ) depends on GHG concentration; see again Eq. (9). As concentration reaches higher levels in the non-collaborative setting (see again Table 1), the required amount of adaptation capital for a maximal effectiveness is much higher compared to the collaborative setting. Evolution of net damages, as computed by the ELF variable (see Eq. (7)), is given in Table 6. In the absence of adaptation (mitigation-only scenarios), damages follow directly atmospheric GHG concentrations (see again Table 1). They reach higher values in region 2, assumed to be more sensitive to climate changes, and in the non-collaborative cases, where the transition toward the clean economy is delayed. When adaptation strategies are implemented (in the combined scenarios), net damages are reduced accordingly (compared to the corresponding mitigation-only scenarios). Note that in these combined scenarios, net damages are initially reduced when adaptation capital starts accumulating (by 2075 in region 1 and by 2045 or 2055 in region 2). But as adaptation measures reach immediately their full potential (gross damages avoided: at most 33% in region 1 and 43% in region 2) they cannot compensate during the following years for the continuous increase in GHG concentrations and thus in damages.

4.5

Gross domestic product

Compared to the counterfactual baseline, GDP losses occur in all other scenarios. These losses are given in Table 7. They are due on the one hand to the costly (mitigation) efforts of abating GHG emissions (switching from a dirty to a more costly clean production system), and on the other hand to climate change related (net) damages. As expected, preventing adaptation (in the mitigation-only scenarios) yields higher GDP losses (compared to the corresponding combined scenarios), as this reduces the choice of options to address climate changes. When comparing the collaborative and non-collaborative cases, the latter ones (that imply lower mitigation efforts) have lower GDP losses during some initial periods. Afterwards, as net damages reach higher and higher levels (see again Table 6), non-collaborative cases yield higher GDP losses. Besides, the overall welfare (computed with rg(1) = rg(2) = 0.5) indicates that the non-collaborative cases yield as expected a worse

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Table 6: Evolution of net damages (% of production lost) for the two regions (1,2) in the mitigation-only (denoted MI) and the combined (denoted CO) scenarios. Cases P- and N- denote the collaborative (Pareto) and non-collaborative (Nash) settings respectively. P-MI P-CO N-MI N-CO 1 2 1 2 1 2 1 2 2015 0.3 0.5 0.3 0.5 0.3 0.5 0.3 0.5 2025 0.5 0.8 0.5 0.8 0.5 0.8 0.5 0.8 2035 0.8 1.1 0.8 1.1 0.8 1.1 0.8 1.1 2045 1.0 1.4 1.1 1.4 1.2 1.6 1.2 0.9 2055 1.3 1.7 1.4 1.0 1.8 2.2 1.8 1.3 2065 1.7 2.1 1.9 1.3 2.5 3.0 2.6 1.8 2075 2.2 2.7 1.6 1.6 3.6 4.2 2.6 2.5 2085 2.8 3.3 2.1 2.1 4.5 5.1 3.3 3.2 2095 3.6 4.2 2.7 2.6 5.5 6.1 4.1 3.9 2105 3.6 4.2 3.4 3.2 6.0 6.7 5.0 4.7 2115 3.5 4.0 3.4 3.3 5.9 6.6 6.1 5.7 Table 7: GDP losses, in % from the baseline, and overall welfare (denoted WRG), for the two regions (1,2) in the mitigation-only (denoted MI) and the combined (denoted CO) scenarios. Cases P- and N- denote the collaborative (Pareto) and non-collaborative (Nash) settings respectively. P-MI P-CO N-MI N-CO 1 2 1 2 1 2 1 2 2015 -0.5 -0.7 -0.5 -0.7 -0.4 -0.7 -0.4 -0.6 2025 -0.7 -1.1 -0.7 -1.0 -0.6 -1.0 -0.6 -1.0 2035 -1.4 -1.6 -1.2 -1.5 -0.9 -1.5 -0.9 -1.3 2045 -2.1 -2.1 -2.0 -2.0 -1.4 -2.2 -1.4 -1.5 2055 -2.6 -2.8 -2.6 -2.2 -2.1 -3.1 -2.1 -1.9 2065 -3.2 -3.5 -3.2 -2.6 -3.1 -4.3 -2.9 -2.6 2075 -3.9 -4.5 -3.4 -3.1 -4.8 -5.9 -3.9 -3.6 2085 -4.7 -5.4 -3.9 -3.8 -6.4 -7.5 -4.9 -4.7 2095 -5.7 -7.5 -4.5 -4.5 -7.9 -9.6 -6.1 -5.8 2105 -6.2 -8.7 -5.5 -6.3 -9.1 -11.6 -7.3 -7.0 2115 -6.2 -9.2 -5.8 -7.3 -9.5 -12.5 -8.9 -9.3 WRG 9’961’585 9’961’592 9’961’576 9’961’585 outcome than the collaborative cases. When comparing the two regions, region 2 experiences more losses (as it bears more climate change related damages), except when adaptation is fully used (with again an assumed higher efficiency). Note however that at the end of the model horizon, GDP losses are again higher in region 2 in the combined scenario when this region starts investing massively in clean capital K2 (see again Table 3) to curb its GHG emissions.

5

Conclusion

In this paper, one has extended the Ada-BaHaMa model, a simple IAM enriched to consider explicit adaptation strategies, to a game setting where several world regions define non-cooperatively their energy and climate policies. This new model embodies some fundamental economy/environment trade-offs faced by the different world economies. More precisely, two main policy decisions are integrated in the model: adaptation and mitigation. The latter consists for the regional economies in choosing the speed with which they will switch for a carbon-intensive economy (relying on fossil fuels) to a much cleaner but more expensive “clean” economy (relying e.g. on nuclear and renewable energy). The former climate policy decision consists for the regional economy in choosing a level of adaptation that will shield them from (a fraction of) climate change damages.

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The numerical illustration provided for two players delivers several insights. The non-collaborative setting is as expected detrimental to the environment: compared to the collaborative setting, players delay their transition to the clean economy, so atmospheric GHG concentrations reach higher values by the end of the 21st century. When it is available, adaptation is only used as a complement to mitigation in region 1. But in region 2, assumed to be more sensitive to climate changes and where adaptation is assumed to be more efficient, adaptation substitutes for mitigation during some initial periods. In all cases however, adaptation does not prevent an (almost complete) phase-out of the dirty economy by the end of the model horizon. Note that the insights the paper provides are basically consistent with the ones obtained by the AD-RICE model (Felgenhauer and de Bruin, 2009). Such insights would be of course more meaningful with a multi-regional model describing the main world regions involved in the current (2010) climate negotiations (e.g., BRIC–Brazil, Russia, India and China–, European Union, USA, ...). This development would require a precise calibration of economic, damage and adaptation parameters for the regions considered. This will be carried out in a future research. Besides, an important element that has been neglected in the present modeling concerns economic and environmental uncertainty, in particular on the magnitude of climate damages and on the effectiveness of adaptation. A stochastic control approach has been proposed by Bahn et al. (2010b) for a model similar to the one developed here but without adaptation. A natural extension of this present paper would thus be to consider explicitly uncertainty along with the strategic decision of each player. This will allow in particular to test the sensitivity of the results to the uncertain (adaptation and climate) parameters.

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