An Extended Integrated Assessment Model for Mitigation and Adaptation Policies on Climate Change Willi Semmler 1 , Helmut Maurer 2 and Antony Bonen 1 1 New School for Social Research, New York, USA. 2 Institute for Computational and and Applied Mathematics, University of Muenster, Germany BoE, November 14-15, 2016 Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation
Overview: Mitigation and Adaption Builds on previous Models with Alfred Greiner, Lars Gruene and Helmut Maurer Builds on Bonen, Loungani and Semmler, IMF paper (2016) Extended IAM: 5 State Variables; up to 6 Control Variables; Finite Time; Parameter Uncertainty Explores numerically Proper balance of spending for mitigation, adaptation and productive infrastructure Decreasing efficiency of fossil fuel energy use Decreasing returns from mitigation efforts Variation in discount rate Simplified Model: Financing of Climate Change Policies with intertemporal Burden Sharing (Jeff Sachs 2014, Gevorkyan et al., 2016) Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation
Model of Mitigation and Adaptation to Climate Change State variables, IAM only K , T , M : : private capital per capita, K g : public capital per capita, : country’s level of debt, b R : non-renewable resource , : GHG (Green House Gas) concentration in the atmosphere. M Control variables: C : per capita consumption, e P : government’s net tax revenue, : extraction rate from the non-renewable resource, u The stock of public capital g is allocated among three uses: ν 1 : standard infrastructure, : climate change adaptation, ν 2 ν 3 : climate change mitigation (IAM; µ ), ν 1 , ν 2 , ν 3 ≥ 0 , ν 1 + ν 2 + ν 3 = 1 . Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation
Dynamic Model of Adaptation and Mitigation Production function Y = A ( A K K + A u u ) α · ( ν 1 g ) β Dynamical system ˙ Y − C − e P − ( δ K + n ) K − u ψ R − τ , = K (0) = K 0 , K ˙ = α 1 e P + i F − ( δ g + n ) g , g (0) = g 0 , g ˙ = (¯ r − n ) b − (1 − α 1 − α 2 − α 3 ) · e P , b (0) = b 0 b ˙ R = − u , R (0) = R 0 ˙ γ u − µ ( M − κ � M ) − θ ( ν 3 · g ) φ , = M (0) = M 0 . M X = ( K , g , b , R , M ) ∈ R 5 State variable : U = ( C , e p , u ) ∈ R 3 Control variable : ˙ Control System : X = f ( X , U ) , X (0) = X 0 Planning Horizon : [0 , T ], terminal time T > 0 Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation
Welfare Functional and Optimal Control Problem Optimal Control Problem Maximize the welfare functional � − ǫ ( ν 2 g ) ω � 1 − σ � T C ( α 2 e P ) η ( M − � M ) − 1 0 e − ( ρ − n ) · t · W ( T , X , U ) = dt 1 − σ such that for all t ∈ [0 , T ] : ˙ X ( t ) = f ( X ( t ) , U ( t )) , X (0) = X 0 , 0 ≤ u ( t ) ≤ u max , K ( t ) ≥ 0 , R ( t ) ≥ 0 . Further constraints: terminal constraint : K ( T ) = K T ≥ 0 state constraint : M ( t ) ≤ M max ∀ t ∈ [0 , T ] . Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation
Model Parameters Parameter Value Definition ρ 0.03 Pure discount rate n 0.015 Population Growth Rate η 0.1 Elasticity of transfers and public spending in utility ǫ 1 . 1 Elasticity of CO 2 -eq concentration in (dis)utility ω 0.05 Elasticity of public capital used for adaptation in utility σ 1.1 Intertemporal elasticity of instantaneous utility A ∈ [1 , 10] Total factor productivity A K 1 Efficiency index of private capital A u ∈ [50 , 500] Efficiency index of the non-renewable resource α 0.5 Output elasticity of privately-owned inputs, A k k + A u u β 0.5 Output elasticity of public infrastructure, ν 1 g ψ 1 Scaling factor in marginal cost of resource extraction τ 2 Exponential factor in marginal cost of resource extraction δ K 0.075 Depreciation rate of private capital δ g 0.05 Depreciation rate of public capital i F 0.05 Official development assistance earmarked for public infrascture α 1 0.1 Proportion of tax revenue allocated to new public capital α 2 0.7 Proportion of tax revenue allocated to transfers and public consumption α 3 0.1 Proportion of tax revenue allocated to administrative costs ¯ r 0.07 World interest rate (paid on public debt) � M 1 Pre-industrial atmospheric concentration of greenhouse gases γ 0.9 Fraction of greenhouse gas emissions not absorbed by the ocean µ 0.01 Decay rate of greenhouse gases in atmosphere Atmospheric concentration stabilization ratio (relative to � 2 M ) κ 0.01 Effectiveness of mitigation measures θ exponent in mitigation term ( ν 3 g ) φ φ ∈ [ 0 . 2 , 1 ] Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation
Dynamic Model for Mitigation and Adaptation to Climate Change: Parameter Uncertainty, Homotopic Solutions 1. Initial Conditions and Constraints, Controls 2. Comparison: Fixed and optimal values of ν 1 , ν 2 , ν 3 3. Numerics: Efficiency Index A u , A u = 100 , 200 , 500, φ = 1 4. Numerics: Mitigation Efficiency, φ = 1, or 0 . 2 ≤ φ ≤ 1 5. Numerics: Discount Rate, 0 . 02 ≤ ρ ≤ 0 . 1 Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation
1. Initial conditions, constraints, choice of ν 1 , ν 2 , ν 3 Initial conditions K (0) = 1 . 5 , g (0) = 0 . 5 , b (0) = 0 . 8 , R (0) = 1 . 5 , M (0) = 1 . 5 . Control constraint : 0 ≤ u ( t ) ≤ 0 . 1 ∀ t ∈ [0 , T ] . Terminal constraint : K ( T ) = K T = 3 . Strategy 1 : Choose fixed values ν 1 = 0 . 6 , ν 2 = 0 . 2 , ν 3 = 0 . 2. Strategy 2 : Consider ν 1 , ν 2 , ν 3 as additional optimization variables satisfying the constraints ν 1 + ν 2 + ν 3 = 1. Strategy 3 : Consider ν 1 = ν 1 ( t ) , ν 2 = ν 2 ( t ) , ν 3 = ν 3 ( t ) , t ∈ [0 , T ] , as control functions satisfying the constraints ν 1 ( t ) + ν 2 ( t ) + ν 3 ( t ) = 1 ∀ t . Strategy 3 improves only slightly on Strategy 2 and will be discarded in the numerical results. Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation
2. Comparison : fixed and optimal values of ν 1 , ν 2 , ν 3 Exponent φ = 1 and efficiency index A u = 50 : Net tax revenue e P Consumption C 4 0.55 ν =optimal ν =optimal 0.5 3.5 0.45 ν =constant ν =constant 3 0.4 2.5 0.35 2 0.3 0.25 1.5 0.2 1 0.15 0.5 0.1 0 0.05 0 5 10 15 20 25 0 5 10 15 20 25 time t time t Private capital K GHG concentration M 2.1 9 ν =optimal ν =optimal 8 2 ν =constant ν =constant 7 1.9 6 1.8 5 4 1.7 3 1.6 2 1 1.5 0 0 5 10 15 20 25 0 5 10 15 20 25 time t time t optimal values ν 1 = 0 . 9534, ν 2 = 0 . 04662, ν 3 = 0 : W ( T ) = 5 . 1086 fixed values ν 1 = 0 . 6 , ν 2 = 0 . 2, ν 3 = 0 . 2 : W ( T ) = − 2 . 1006 Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation
2. Comparison: fixed and optimal values of ν 1 , ν 2 , ν 3 Exponent φ = 1 and efficiency index A u = 50 : Public capital g Level of debt b 1.4 ν =optimal ν =optimal 1.3 2.5 1.2 ν =constant ν =constant 1.1 2 1 0.9 0.8 1.5 0.7 0.6 1 0.5 0 5 10 15 20 25 0 5 10 15 20 25 time t time t Non-renewable resource R Extraction rate u 1.8 0.14 ν =optimal ν =optimal 1.7 0.12 ν =constant ν =constant 1.6 0.1 1.5 0.08 1.4 0.06 1.3 0.04 1.2 0.02 1.1 0 1 -0.02 0 5 10 15 20 25 0 5 10 15 20 25 time t time t optimal values ν 1 = 0 . 9534, ν 2 = 0 . 04662, ν 3 = 0 : W ( T ) = 5 . 1086 fixed values ν 1 = 0 . 6 , ν 2 = 0 . 2, ν 3 = 0 . 2 : W ( T ) = − 2 . 1006 Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation
3. Numerics: Efficiency Index, fossil energy, for homotopy A u ∈ [50 , 500] Welfare W(T) Terminal value M(T) 30 2.7 2.6 25 2.5 2.4 20 2.3 2.2 15 2.1 2 10 1.9 5 1.8 50 200 350 500 50 200 350 500 efficiency index A u efficiency index A u optimal ν 1 optimal ν 2 0.96 0.08 0.95 0.07 0.94 0.06 0.93 0.05 0.92 50 200 350 500 50 200 350 500 efficiency index A u efficiency index A u Terminal values W ( T ) and M ( T ) and optimal parameters ν 1 , ν 2 . Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation
3. Numerics: Efficiency Index, for homotopy A u ∈ [50 , 500] Terminal resource R(T) Terminal debt b(T) 2 1.2 1.6 1 1.2 0.8 0.8 0.6 0.4 0.4 0.2 0 50 200 350 500 50 200 350 500 efficiency index A u efficiency index A u Terminal values R ( T ) and b ( T ) for A u ∈ [50 , 500] Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation
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