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The Benefits of Cooperation Under Uncertainty: the Case of Climate Change

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Abstract

This article presents an analysis of the behaviour of countries defining their climate policies in an uncertain context. The analysis is made using the S-CWS model, a stochastic version of an integrated assessment growth model. The model includes a stochastic definition of the climate sensitivity parameter. We show that the impact of uncertainty on policy design critically depends on the shape of the damage function. We also examine the benefits of cooperation in the context of uncertainty: We highlight the existence of an additional benefit of cooperation, namely risk reduction.

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Notes

  1. Here we do not raise the issue of countries’ incentive for cooperation. For such an analysis, see, e.g. [13].

  2. The objective function is linear if the agent is risk neutral, but the constraints are always linear in the decision variables.

  3. The parameter value is discretized in three values.

  4. Recently, the expected utility model has been challenged in the context of uncertainty, and several alternatives have been proposed to represent ambiguity aversion and probabilities misperceptions. For the role of these models in the case of climate change, see for instance [5, 16, 32]. However, the expected utility model is a useful benchmark which has hardly been studied in IAMs. It is natural to take this approach as a starting point.

  5. In contrast, not taking the transform u −1 would yield the objective function \(W_i=u\left(\sum_{t=1}^T\frac{Z_{i,t,s}}{(1+\rho)^{t-1}}\right)\) in the deterministic case, which looks quite unusual.

  6. For a modelling of climate change policies with update of beliefs, see [11, 12], or [14] for decision patterns using ‘model predictive control’.

  7. Many other pdf are available in the literature review carried out by the IPCC report [27], for instance [18, 22, 24]. We have performed some sensitivity analysis, which showed that our numerical results are robust to the choice of the pdf.

  8. Specifically, the simulation horizon is 2330.

  9. For short, we use the term country to denote the regions/countries of the S-CWS model.

  10. For the list of variables and the complete description of the model, see the “Appendix”.

  11. Values for those polynomials have been updated from the DICE-2010 model.

  12. In the terminology of dynamic noncooperative games, this is an open loop Nash equilibrium. Closed loop or feedback Nash equilibria have also been introduced in dynamic core-stability analysis in [37], albeit with a simpler model.

  13. A third kind of scenario can also be computed, namely the partial agreement Nash equilibria with respect to a coalition scenarios (PANEs). Each PANE is the outcome of a subset of countries maximizing jointly their welfare, while the others act individually (there are as many such scenarios considered as there are coalitions). See [15, 36] for applications with PANEs.

  14. The CWS model has been initially developed for coalition analyses that need a huge number of model runs. The limited size of the generated problem was then a main constraint. In that sense, CWS is different from other growth models such as WITCH or DICE that are more detailed, but also less manageable.

  15. This phase could also be used to contrast several approaches, for instance models with different values of S.

  16. In a multistage context, the computation set should be aggregated in a tree to be exploited by the model.

  17. There is no optimization, only computation using the optimal policy found.

  18. Empirically, it is well-known that the result of stochastic programming optimization, or prediction value, is very optimistic and, in a sense, not realistic and that the policy found is very sensitive, not robust.

  19. θ 3 = 2.0 is the benchmark value in the CWS model as well as in many IAMs.

  20. Indeed, if the relationship between global emissions and damages is convex, we know by Jensen’s inequality that damages from expected emissions are lower than expected damages from emissions. Therefore, there are additional incentives to reduce emissions when risk is explicitly taken into account. The opposite is true when the relation is concave.

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Acknowledgements

The authors are grateful to Johan Eyckmans, Alain Haurie and Henry Tulkens for fruitful comments on preliminary versions of the paper. The CWS model has been developed under the CLIMNEG research project supported by the Belgian Science Policy (contract CP/05A).

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Authors and Affiliations

  1. CORE, Chair Lhoist Berghmans in Environmental Economics and Management, Université catholique de Louvain, 34 voie du Roman pays, 1348, Louvain-la-Neuve, Belgium

    Thierry Bréchet, Julien Thénié, Thibaut Zeimes & Stéphane Zuber

  2. ORDECSYS Company, Chêne-Bougeries, Switzerland

    Julien Thénié

Authors
  1. Thierry Bréchet
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  2. Julien Thénié
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  4. Stéphane Zuber
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Correspondence to Thierry Bréchet.

Appendix

Appendix

1.1 Regions of the CWS Model

Table 4 Regions of the CWS model
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1.2 Statement of the CWS Model

1.2.1 Variables and Parameters Definitions

Table 5 Names and units of variables
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Table 6 Names and units of parameters
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1.2.2 Constraints

The index i = 1,...N stands for region/country.

$$ Y_{i,t}=A_{i,t}K_{i,t}^{\alpha}L_{i,t}^{1-\alpha}$$
(5)
$$ Y_{i,t}=Z_{i,t,s}+I_{i,t}+C_{i}(\mu_{i,t})+D_i \big(T_{t,s}^{E}\big)$$
(6)
$$ K_{i,t+1}=(1-\delta_K)^{10} K_{i,t} + 10 I_{i,t} \ \mbox{, with } K_{i,0} \mbox{ given} $$
(7)
$$ E_{i,t}=\sigma_{i,t}(1-\mu_{i,t})Y_{i,t}, with \mu \in (0,1) $$
(8)
$$ C_{i}(\mu_{i,t})=-Y_{i,t} \mbox{ }c_i\left[(1-\mu_{i,t})log(1-\mu_{i,t})+\mu_{i,t}\right] $$
(9)
$$ M^{\rm AT}_{t+1}=M^{\rm AT}_{t}+10\left(M^{\rm AT}_{t}b_{11}+\sum\limits_{j=1}^{n}E_{j,t}+M^{\rm UO}_{t}b_{21}\right) $$
(10)
$$ M^{\rm UO}_{t+1}=M^{\rm UO}_{t}+10\left(M^{\rm AT}_{t}b_{12}+M^{\rm UO}_{t}b_{22}+M^{\rm LO}_{t}b_{32}\right) $$
(11)
$$ M^{\rm LO}_{t+1}=M^{\rm LO}_{t}+10\left(M^{\rm LO}_{t}b_{33}+M^{\rm UO}_{t}b_{23}\right) $$
(12)
$$ F_t =F2X\left(\frac{ \log{(M_t/M_0)}}{\log(2)}\right)+RFOgas_{t} $$
(13)
$$\begin{array}{rll} T_{t+1,s}^{E} &= & \frac{T_{t,s}^{E}}{1+c_{1} (F2X/T2X_{s})+c_{1}c_{3}}\\ &&+\, c_{1}\big(F_{t+1}+c_{3}T_{t,s}^{\rm L}\big)\mbox{, with } T_{0}^{E} \mbox{ given}\end{array}$$
(14)
$$ T_{t+1,s}^{\rm L}=T_{t,s}^{\rm L}+c_{4}\big(T_{t,s}^{E}-T_{t,s}^{\rm L}\big)\mbox{, with } T_{0}^{\rm L} \mbox{ given} $$
(15)
$$ D_i \big(T_{t,s}^{E}\big)=Y_{i,t}\left[ \theta_{i,1} T_{t,s}^{E}+ \theta_{i,2} \left(T_{t,s}^{E}\right)^{ \theta_{3}}\right] $$
(16)

1.2.3 Parameters Values

Table 7 General scalars
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Table 8 Asymptotic values
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Table 9 Parameters for abatement cost and damage functions
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Table 10 Parameters for abatement cost and damage functions
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Table 11 Parameter values carbon cycle
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Table 12 Parameter values temperature cycle
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1.3 Probability Distribution

Table 13 Validation set: probability of elements
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Bréchet, T., Thénié, J., Zeimes, T. et al. The Benefits of Cooperation Under Uncertainty: the Case of Climate Change. Environ Model Assess 17, 149–162 (2012). https://doi.org/10.1007/s10666-011-9281-3

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