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An Extended Integrated Assessment Model for Mitigation and Adaptation Policies on Climate Change

Willi Semmler 1, Helmut Maurer2 and Antony Bonen 1

1New School for Social Research, New York, USA. 2Institute 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 : K : private capital per capita, g : public capital per capita, b : country’s level of debt, R : non-renewable resource , M : GHG (Green House Gas) concentration in the atmosphere. Control variables: C : per capita consumption, eP : government’s net tax revenue, u : extraction rate from the non-renewable resource, The stock of public capital g is allocated among three uses: ν1 : standard infrastructure, ν2 : climate change adaptation, ν3 : climate change mitigation (IAM; µ), ν1, ν2, ν3 ≥ 0, ν1 + ν2 + ν3 = 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(AKK + Auu)α · (ν1g)β Dynamical system ˙ K = Y − C − eP − (δK + n)K − u ψR−τ, K(0) = K0, ˙ g = α1eP + iF − (δg + n)g, g(0) = g0, ˙ b = (¯ r − n)b − (1 − α1 − α2 − α3) · eP, b(0) = b0 ˙ R = −u, R(0) = R0 ˙ M = γ u − µ(M − κ M) − θ(ν3 · g)φ, M(0) = M0. State variable : X = (K, g, b, R, M) ∈ R5 Control variable : U = (C, ep, u) ∈ R3 Control System : ˙ X = f (X, U), X(0) = X0 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 W (T, X, U) = T

0 e−(ρ−n)·t ·

• C(α2eP)η(M−

M)

−ǫ(ν2g)ω1−σ

−1 1−σ

dt such that for all t ∈ [0, T] : ˙ X(t) = f (X(t), U(t)), X(0) = X0 , 0 ≤ u(t) ≤ umax , K(t) ≥ 0, R(t) ≥ 0 . Further constraints: terminal constraint : K(T) = KT ≥ 0 state constraint : M(t) ≤ Mmax ∀ 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 CO2-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 AK 1 Efficiency index of private capital Au ∈ [50, 500] Efficiency index of the non-renewable resource α 0.5 Output elasticity of privately-owned inputs, Ak k + Auu β 0.5 Output elasticity of public infrastructure, ν1g ψ 1 Scaling factor in marginal cost of resource extraction τ 2 Exponential factor in marginal cost of resource extraction δK 0.075 Depreciation rate of private capital δg 0.05 Depreciation rate of public capital iF 0.05 Official development assistance earmarked for public infrascture α1 0.1 Proportion of tax revenue allocated to new public capital α2 0.7 Proportion of tax revenue allocated to transfers and public consumption α3 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 κ 2 Atmospheric concentration stabilization ratio (relative to M) θ 0.01 Effectiveness of mitigation measures φ ∈ [ 0.2, 1 ] exponent in mitigation term (ν3 g)φ 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 ν1, ν2, ν3
• 3. Numerics: Efficiency Index Au,Au = 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 ν1, ν2, ν3

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) = KT = 3. Strategy 1 : Choose fixed values ν1 = 0.6, ν2 = 0.2, ν3 = 0.2. Strategy 2 : Consider ν1, ν2, ν3 as additional optimization variables satisfying the constraints ν1 + ν2 + ν3 = 1. Strategy 3 : Consider ν1 = ν1(t), ν2 = ν2(t), ν3 = ν3(t), t ∈ [0, T], as control functions satisfying the constraints ν1(t) + ν2(t) + ν3(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 ν1, ν2, ν3

Exponent φ = 1 and efficiency index Au = 50 :

0.5 1 1.5 2 2.5 3 3.5 4 5 10 15 20 25 time t Consumption C ν=optimal ν=constant 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 5 10 15 20 25 time t Net tax revenue eP ν=optimal ν=constant 1 2 3 4 5 6 7 8 9 5 10 15 20 25 time t Private capital K ν=optimal ν=constant 1.5 1.6 1.7 1.8 1.9 2 2.1 5 10 15 20 25 time t GHG concentration M ν=optimal ν=constant

• ptimal values ν1 = 0.9534, ν2 = 0.04662, ν3 = 0 :

W (T) = 5.1086 fixed values ν1 = 0.6, ν2 = 0.2, ν3 = 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 ν1, ν2, ν3

Exponent φ = 1 and efficiency index Au = 50 :

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 5 10 15 20 25 time t Public capital g ν=optimal ν=constant 1 1.5 2 2.5 5 10 15 20 25 time t Level of debt b ν=optimal ν=constant 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 5 10 15 20 25 time t Non-renewable resource R ν=optimal ν=constant

• 0.02

0.02 0.04 0.06 0.08 0.1 0.12 0.14 5 10 15 20 25 time t Extraction rate u ν=optimal ν=constant

• ptimal values ν1 = 0.9534, ν2 = 0.04662, ν3 = 0 :

W (T) = 5.1086 fixed values ν1 = 0.6, ν2 = 0.2, ν3 = 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

Au ∈ [50, 500]

5 10 15 20 25 30 50 200 350 500 efficiency index Au Welfare W(T) 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 50 200 350 500 efficiency index Au Terminal value M(T) 0.92 0.93 0.94 0.95 0.96 50 200 350 500 efficiency index Au

• ptimal ν1

0.05 0.06 0.07 0.08 50 200 350 500 efficiency index Au

• ptimal ν2

Terminal values W (T) and M(T) and optimal parameters ν1, ν2.

Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation

• 3. Numerics: Efficiency Index, for homotopy Au ∈ [50, 500]

0.2 0.4 0.6 0.8 1 1.2 50 200 350 500 efficiency index Au Terminal resource R(T) 0.4 0.8 1.2 1.6 2 50 200 350 500 efficiency index Au Terminal debt b(T)

Terminal values R(T) and b(T) for Au ∈ [50, 500]

Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation

• 3. Numerics: Efficiency Index, Solutions for

Au = 100, Au = 200, Au = 500

, φ = 1

2 4 6 8 10 5 10 15 20 25 time t Private capital K Au=100 Au=200 Au=500 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 5 10 15 20 25 time t GHG concentration M Au=100 Au=200 Au=500 1 2 3 4 5 6 7 8 9 10 5 10 15 20 25 time t Consumption C Au=100 Au=200 Au=500 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 5 10 15 20 25 time t Extraction rate u Au=100 Au=200 Au=500

φ = 1 : comparing solutions for Au = 100, Au = 200, Au = 500.

Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation

• 3. Numerics: Efficiency Index, Solutions for

Au = 100, Au = 200, Au = 500

, φ = 1

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 5 10 15 20 25 time t Non-renewable resource R Au=100 Au=200 Au=500 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 5 10 15 20 25 time t Public capital g Au=100 Au=200 Au=500 0.2 0.4 0.6 0.8 1 1.2 5 10 15 20 25 time t Net tax revenue eP Au=100 Au=200 Au=500 0.2 0.4 0.6 0.8 1 5 10 15 20 25 time t Level of debt b Au=100 Au=200 Au=500

φ = 1 : comparing solutions for Au = 100, Au = 200, Au = 500.

Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation

• 4. Numerics: Mitigation Exponent,0.2 ≤ φ ≤ 1

Consider the mitigation exponent 0.2 ≤ φ ≤ 1 in

˙ M = γu − µ(M − κ M) − θ(ν3 · g)φ.

For φ = 1 we always obtain ν3 = 0. However, for φ ≤ φ0 ≈ 0.88 we obtain ν3 > 0. These findings can be confirmed by computing

• ptimal solutions via a homotopy with respect to φ ∈ [0.2, 1].

Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation

• 4. Numerics: Mitigation Exponent, Homotopy for

φ ∈ [0.2, 1] with Au = 150

0.928 0.93 0.932 0.934 0.936 0.938 0.94 0.2 0.4 0.6 0.8 1 Exponent φ

• ptimal ν1

0.0594 0.0596 0.0598 0.06 0.0602 0.0604 0.2 0.4 0.6 0.8 1 Exponent φ

• ptimal ν2

0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.2 0.4 0.6 0.8 1 Exponent φ

• ptimal ν3

11.9 12 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 0.2 0.4 0.6 0.8 1 Exponent φ Welfare W(T)

φ ∈ [ 0.2, 1 ] : optimal values ν1, ν2, ν3 and welfare W (T) .

Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation

• 4. Numerics: Mitigation Exponent, Homotopy for

φ ∈ [0.2, 1] with Au = 150

2.52 2.54 2.56 2.58 2.6 2.62 2.64 0.2 0.4 0.6 0.8 1 Exponent φ Terminal concentration M(T) 0.268 0.27 0.272 0.274 0.276 0.278 0.28 0.282 0.2 0.4 0.6 0.8 1 Exponent φ Terminal resource R(T)

φ ∈ [ 0.2, 1 ] : terminal values M(T) and R(T) .

Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation

• 4. Numerics: Mitigation Exponent, φ = 0.2 : terminal

values for homotopy Au ∈ [50, 500]

φ = 0.2 : homotopy parameter 50 ≤ Au ≤ 500

6 10 14 18 22 26 50 200 350 500 efficiency index Au Welfare W(T) 0.9 0.91 0.92 0.93 0.94 0.95 50 200 350 500 efficiency index Au

• ptimal ν1

0.04 0.05 0.06 0.07 0.08 50 200 350 500 efficiency index Au

• ptimal ν2

0.01 0.012 0.014 0.016 0.018 50 200 350 500 efficiency index Au

• ptimal ν3

Welfare W (T) and optimal parameters ν1, ν2, ν3.

Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation

• 4. Numerics: Mitigation Exponent, φ = 0.2 : terminal

values for homotopy Au ∈ [50, 500]

1.6 2 2.4 2.8 50 200 350 500 efficiency index Au Terminal concentration M(T) 0.5 1 1.5 2 50 200 350 500 efficiency index Au Terminal debt b(T) 0.2 0.4 0.6 0.8 1 1.2 1.4 50 200 350 500 efficiency index Au Terminal resource R(T) 1 1.1 1.2 1.3 1.4 1.5 50 200 350 500 efficiency index Au terminal public capital g(T)

Terminal values M(T), R(T), b(T), g(T) depending on Au

Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation

• 4. Numerics: Mitigation Exponent, φ = 0.2 : Solutions for

Au = 100, Au = 200, Au = 500

2 4 6 8 10 5 10 15 20 25 time t Capital K Au=100 Au=200 Au=500 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 5 10 15 20 25 time t CO2 concentration M Au=100 Au=200 Au=500 1 2 3 4 5 6 7 8 9 10 5 10 15 20 25 time t Consumption C Au=100 Au=200 Au=500 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 5 10 15 20 25 time t Extraction rate u Au=100 Au=200 Au=500

φ = 0.2 : comparing solutions for Au = 100, Au = 200, Au = 500.

Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation

• 4. Numerics: Mitigation Exponent, φ = 0.2 : Solutions for

Au = 100, Au = 200, Au = 500

0.5 1 1.5 2 2.5 5 10 15 20 25 time t Resource R Au=100 Au=200 Au=500 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 5 10 15 20 25 time t public infrastructure g Au=100 Au=200 Au=500 0.2 0.4 0.6 0.8 1 1.2 5 10 15 20 25 time t Control eP Au=100 Au=200 Au=500

• 0.2

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 5 10 15 20 25 time t Level of debt b Au=100 Au=200 Au=500

φ = 0.2 : comparing solutions for Au = 100, Au = 200, Au = 500.

Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation

• 5. Numerics: Discount Rate, φ = 0.2 : terminal values for

homotopy ρ ∈ [0.02, 0.1]

φ = 0.2 : homotopy for dicount rate 0.02 ≤ ρ ≤ 0.1

6 7 8 9 10 11 12 13 14 15 0.02 0.04 0.06 0.08 0.1 discount rate ρ Welfare W(T) 0.921 0.923 0.925 0.927 0.929 0.931 0.02 0.04 0.06 0.08 0.1 discount rate ρ

• ptimal ν1

0.055 0.0575 0.06 0.0625 0.065 0.0675 0.07 0.02 0.04 0.06 0.08 0.1 discount rate ρ

• ptimal ν2

0.0085 0.01 0.0115 0.013 0.02 0.04 0.06 0.08 0.1 discount rate ρ

• ptimal ν3

Welfare W (T) and optimal parameters ν1, ν2, ν3.

Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation

• 5. Numerics: Discount Rate, φ = 0.2 : terminal values for

homotopy ρ ∈ [0.02, 0.1]

2.49 2.5 2.51 2.52 2.53 2.54 2.55 2.56 0.02 0.04 0.06 0.08 0.1 discount rate ρ Terminal value M(T) 1.26 1.28 1.3 1.32 1.34 1.36 1.38 1.4 1.42 1.44 0.02 0.04 0.06 0.08 0.1 discount rate ρ Terminal public capital g(T) 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.02 0.04 0.06 0.08 0.1 discount rate ρ Terminal resource R(T)

Terminal values M(T), R(T), g(T)

Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation

Simplified Model–Financing of Climate Policies through Burden Sharing

Sachs (2014), Gevorkyan et al. (2016), Solved with NMPC, see Gruene et al (2015) Phase 1: Business As Usual (BAU, no carbon tax or climate bonds) MaxC N

t=0

e−ρtln(C)dt ˙ K = D · Y − C − (δ + n)K ˙ M = βE − µM E = (aK A0 )γ D(·) = (a1 · M2 + 1)−ψ

Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation

Simplified Model–Financing of Climate Policies through Burden Sharing

Phase 2: Carbon tax, and green bonds MaxC N

t=0

e−ρtln(C)dt ˙ K = D · Y − C − χ.Y − (δ + n)K ˙ M = βE − µM ˙ b = r · b + A E = ( aK 5(A + χ.Y ) + A0 )γ χ = b1 2 πatan(b2M2 − 0.01)

Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation

Simplified Model–Financing of Climate Policies through Burden Sharing

Phase 3: Debt repayment after elimination of carbon emission ˙ K = Y (1 − τ) − C − χ.Y − (δ + n)K ˙ b = r · b − τY

Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation

Numerical Results for the 3 Phases

Left: BAU, right: Phase 2 (tax and no tax) and phase 3 (debt repayment) Issue: Integrating all three phases into one model, Welfare computation with optimal switches

Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation

Conclusion

Developing a Macro Framework for Climate Policies (Extended IAM) Control Model with 5 State Variables, up 6 Controls Variables, Finite Time Exploration of Parameter Uncertainty using AMPL Simplified Model: Financing of Climate Policies through Intertemporal Burden Sharing

Implementation of cap and trade, carbon tax, and climate bonds Phasing in of climate bonds under current macroeconomic/financial conditions

Calibration for North-South Countries?

Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation

Thank you for your attention

Willi Semmler , Helmut Maurer and Antony Bonen An Extended Integrated Assessment Model for Mitigation and Adaptation