Growth and Climate Change Modeling, Solution Methods and Policy Issues Willi Semmler New School for Social Research, New York

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1 Growth and Climate Change Modeling, Solution Methods and Policy Issues Willi Semmler New School for Social Research, New York I. Introduction: Climate Research II. Basic models Growth and Fossil Energy The Canonical Model (Nordhaus) Model with Tipping Points III. Climate Policies Phasing in Renewable Energy Optimal Mitigation and Adaptation Policy Climate Policy with Burden Sharing Climate Policy and Employment Effects

2 Literature: I. Introduction Nordhaus, The Question of Balance (2007), Climate Casino (2013) Greiner and Semmler: Gobal Environment, Natural Resources and Growth, OUP (2008) Bernard and Semmler (eds): OUP Handbook, The Macroeconomics of Global Warming (2015) Gruene, Greiner and Semmler, Economic Growth and the Transition from Non-renewable to Renewable Energy (2013) Maurer and Semmler, Mitigation and Adapatation Policy (2015) Flaherty et al (2016): Climate Financing through Climate Bonds Kato, Mittnik et al (2014): Employment Effects of Climate Policies Papers on the web-site: SSRN

3 I. Introduction: Temperature trend Tung and Zhou (2013), wavelets

4 I. Introduction: Impacts (IPCC) Impacts will vary by extent of adaptation, rate of temperature change, and socio-economic pathway

5 I. Introduction: Causes CO2 concentration has increased arising from the use of a nonrenewable resource: fossil energy (coal, gas, petroleum) CO2 grew from 280 ppm in 1750 to 379 ppm in

6 II. Basic Models 2. Growth and Nonrenewable Resource Hotelling (1931), Chichilnisky and Heal (1982), Greiner and Semmler (2008), 2 decision variables, 2 state variables The Model:

7 II. Basic Models: 2. Growth and Nonrenewable Resources Solution Methods Dynamic programming (DP), Gruene and Semmler, JEDC (2004) Software: in Linux (infinite time horizon): Advantages: Global solution, steep value function, multiple equilibria Disadvantage: Computation of value function and control variables over the entire grid space, curse of dimension (limit: 3-4 state and 3-4 control variables) Nonlinear Model Predictive Control (NMPC), see Gruene, Semmler and Stieler, JEDC, 2015 Software: Matlab, C++ (finite time horizon) Advantage: Global solution, computes one trajectory at a time, allows for multiple equilibria, regime switching, no need of terminal constraints (steady states), limited information agents (Sims: Rational Inattention), high-dim models

8 2. Growth and Nonrenewable Resources Energy, Solution with NMPC 2 state variables x_1=k (capital), x_2=s (resource), 2 controls C= consumption), R= extraction rate (no terminal constraints) NMPC solution Paths for: Blue (resource): x_2(0)=10 Green (capital): x_1(0)=1

9 3. Canonical Model: Nordhaus (2008) reduced large scale model The Canonical Model

10 3. Canonical Model: Nordhaus (2008) Objective Function: Temperature: Concentration of CO2: Capital stock:

11 3. Canonical Model: With Tipping Point; Gruene et al. (2013 ) Temperature: Concentration of CO_2: Capital stock:

12 3. The Canonical Model: Tipping point literature Hansen et al. (2008): Slow Feedbacks Brock et al. (2009):Tipping points

13 3. The Canonical Model: Tipping point, with slow feedbacks (Hansen et al. 2008), Gruene et al. (2013), with tipping point => Temperature feedback: albedo effect => Tipping points: Collapse of large scale ice sheets Large scale change of ocean circulation Release of locked-in carbon Warming triggers warming

14 3. The Canonical Model: With Tipping Point Solution Method: DP Hamiltonian, solving for steady state: Objective function Hamiltonian

15 3. The Canonical Model: Numerical Results of our Threshold Model Abatement: A=0.0012, with low abatement effort there are multiple equilibria and a tipping point (temperature measured in Kelvin)

16 3. The Canonical Model: Numerical Results of our Threshold Model End results depending on initial conditions (Skiba plane) Damages would accelerate after the tipping point, Nordhaus, chs 9-10

17 4. Phasing in Renewable Energy Motivation- Fossil energy, finite supply

18 4. Phasing in Renewable Energy Motivation, Gruene et al. (2014) Infinite supply of renewable (green) energy -- Wind, solar, hydro, biomass, geothermal - Abundantly available (free harvesting, but storage and grid problem), more certain cost and price paths - Large set up cost, but low operating cost => Mark Jacobson (Stanford): 100% renewable energy could be achieved by 2050, see Jacobson et al (2013) Falling cost curves for renewable (Jacobson ) If energy storing is solved

19 4. Phasing in Renewable Energy-- Motivation Long run cost trends of fossil energy (without and with including externalities) and renewable energy (see Jacobson et al. 2013)

20 III. Climate Policies 4. Phasing in Renewable Energy: Model Our model with externalities and damages in preferences: The externalities are created through the use of a fossil energy, but this creates damages for households Distinction between a socially optimal solution (planner`s solution) and a laissez- faire solution (market solution) We study the transition dynamics to renewable energy (as back stop technology) Role of policies for faster transition is considered in Maurer and Semmler (2014) Similar studies: Van der Ploeg et al. 2011, 2012) Heinzel et al (2011), Models with new technology, for example Aghion, Acemoglu, Greiner et al, and Edenhofer et al (2010)

21 4. Phasing in Renewable Energy Model Externalities from fossil energy, transition to renewable energy:

22 4. Phasing in Renewable Energy--Model Hamiltonian: Optimality conditions:

23 4. Phasing in Renewable Energy--Model Transition to renewable energy (market solutions)

24 4. Phasing in Rewable Energy-- Results The results of phasing out fossil energy and phasing in renewable energy depends on initial conditions Yet in contrast to the Hotelling strategy to exhaust the available resource optimally until it is depleted is not a reasonable policy if the resource has externality effects (CO2 emission) Some resources should be left in the ground Initial conditions:.

25 5. Optimal Mitigation and Adaptation Policy (Larger Scale Model) Motivation: Importance of both -- Mitigation and Adaptation -- IPCC reports -- Climate policies (Obama, Fund raising) -- Climate research, Brechet et al (2013) Maurer and Semmler (2015) Results from Maurer/Semmler; Trade-off between mitigation and adaptation - fixed Results from Maurer/Semmler; Trade-off between mitigation and adaptation - optimal

26 5. Optimal Mitigation and Adaptation Policy (Larger Scale Model)

27 5. Optimal Mitigation and Adaptation Policy Gruene/Semmler/Stieler (2014); varying time horizon, NMPC, b<2.0, fixed policies, welfare loss

28 5. Optimal Mitigation and Adaptation Policy (solution method: AMPL) Maurer and Semmler, 2015, optimal policies Using:

29 6. Climate Policy with Burden Sharing Three stage model, finite time, Sachs model, climate bonds see Flaherty et al (2016), solved by NMPC Stage 1: BAU

30 6. Climate Policy with Burden Sharing Climate bonds issued Stage 2:

31 6. Climate Policy with Burden Sharing Climate bonds repaid Stage 3: Next step: Model with green bonds (future generations) and carbon tax (current generation)

32 6. Climate Policy with Burden Sharing Extension: Climate bonds and carbon tax Introduce in stage 2 a carbon tax for the current generation, so that there is a burden sharing between current and future generations: Remark: Carbon tax and income from climate bonds used for 1) transition cost (subsidies, adjustment cost, compenstation, recycling revenues), 2) use of revenues to further reduce emission through green energy 3) adaptation; provide green climate funds for developing economies (see also IMFstudy on ca rbon tax)

33 7. Climate Policy and Employment Effects Kato, Mittnik, Semmler and Samaan (2014), work for ILO Three sector model: H=high carbon intensity, L=low carbon intensity, K=capital goods Tt

34 7. Climate Policy and Employment Effects, Kato, Mittnik, Semmler and Samaan (2014), work for ILO Estimating effect on employment: 1) carbon tax, 2) tax and subsidy 3) tax and wage subsidy, for 9 countries Using Input-output system and double sided VAR Tt

35 IV. Conclusions => Models so far are still rather small scale: - model with nonrenewable resource in growth - including externalities - CO2 emission and temperature rise - damage functions, and tipping points - policies (renewable energy, mitigation, adaptation policy) - funding and burden sharing - employment effects from transition Those models cannot be solved analytically, but need to be solved through numerical methods (DP and NMPC), for finite horizon, and policy decions should be included Next Step: Calibration of some of the model variants for regions (advanced countries, developing economies), DFG project Further important dimensions on climate policies discussed at SCEPA:

36 SCEPA Public Lectures, on YouTupe video

37 Appendix: DP Solution Method, see Grüne and Semmler, JEDC 2004) Dyn Program Discrete approximation Discrete dynamic state equations Value function (Bellman equation)

38 Appendix: DP Solution Methods Using the operator Approximation on a grid with iteration Error estimation and grid refinement Applicable to: steep value function non differentiable value function multiple equilibria domains of attraction (Skiba points, lines or surfaces)

39 Appendix. What Mitigation Policy to Follow? Nordhaus Scenarios on Fossil Fuel Price Nordhaus: Carbon prices for the different scenarios:

I. Introduction: Country Difference. C0_2 Emission 2005, country differences

I. Introduction: Country Difference. C0_2 Emission 2005, country differences Growth, Climate Change and Mitigation Policies: The Case for A Carbon Tax Alfred Greiner (Bielefeld University), Lars Grüne (Bayreuth University), Willi Semmler (New School for Social Research), Helmut