Optimal Control of a Global Model of Climate Change with Adaptation and Mitigation

IMF Working Papers, December 10, 2018

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Extends the Integrated Assessment Model (IAM) to include optimal policies for mitigation, adaptation and infrastructure investment, studying the dynamics of the transition to a low fossil-fuel economy.
Focuses on the adverse effects of increase in atmospheric CO2 concentration on households.
The model gives rise to an optimal control problem of finite horizon consisting of a dynamic system with a five-dimensional state vector consisting of stocks of private capital, green capital, public capital, stock of brown energy in the ground, and emissions.
The control vector is five-dimensional.
Solutions are characterized by turnpike property.
The optimal policy that accomplishes the objective of keeping the CO2 levels within bound is characterized by a significant proportion of investment in public capital going to mitigation in the initial periods.
When initial levels of CO2 are high, adaptation efforts also start immediately, but during the initial period, they account for a smaller proportion of government's public investment.

State vector (five-dimensional): stocks of private capital; green capital; public capital; stock of brown energy in the ground; emissions.
Control vector (five-dimensional).
Formal characterization: optimal control problem of finite horizon.
Solution properties: turnpike property; involvement of adjoint variable and control-state equality constraint (keywords indicate use of adjoint methods).

Optimal transition to a low fossil-fuel economy requires significant initial public capital investment directed toward mitigation.
If initial CO2 levels are high:
- Adaptation efforts commence immediately.
- Adaptation receives a smaller proportion of government's public investment during the initial period compared with mitigation.
Investment in infrastructure is an explicit policy instrument alongside mitigation and adaptation.

Early public capital allocation should prioritize mitigation to keep CO2 levels within bound.
Adaptation should be deployed immediately when initial CO2 levels are high, but policymakers should expect adaptation to constitute a smaller share of public investment in initial periods compared with mitigation.
Infrastructure investment is a third pillar of optimal policy alongside mitigation and adaptation and should be integrated into transition planning.

Authors: Manoj Atolia, Prakash Loungani, Helmut Maurer, Willi Semmler
Date: December 10, 2018
Series: Working Paper No. 2018/270
Issue: 270
Volume: 2018
Pages: 20
DOI: https://doi.org/10.5089/9781484387795.001
Stock No: WPIEA2018270
ISBN: 9781484387795
ISSN: 1018-5941
Subjects: Climate change, Consumption, Greenhouse gas emissions, Infrastructure, Stocks
Keywords: adjoint variable, control-state equality constraint, infrastructure investment effort, mitigation policy, policy variable, WP

IMF Working Paper: "Optimal Control of a Global Model of Climate Change with Adaptation and Mitigation", December 10, 2018.