Robust Optimal Taxation and Environmental Externalities

Transcription

1 Robust Optimal Taxation and Environmental Externalities Xin Li Borghan Narajabad Ted Loch-Temzelides Department of Economics Rice University

2 Outline Outline 1 Introduction 2 One-Energy-Sector Model 3 Complete Model 4 Numerical Results

3 Introduction Research Question Environmental Externality: CO 2 Emission Global Temperature output. Model Uncertainty: Our knowledge is limited regarding how CO 2 emission affects future global mean temperature and output. Robust Control: The fear of catastrophic events alters the optimal path of energy extraction and thereby production and consumption. We want to find out: Robust vesion of optimal energy extraction How to achieve it in a decentralized economy

4 Introduction Literature Review Golosov, Hassler, Krusell, and Tsyvinski (GHKT, 2012): 1. Assume that the mapping from carbon concentration to output damages is subject to a risk γ: y = e γs ỹ (the true distribution of γ is known). 2. Obtain analytical expressions for carbon externality. 3. Assess optimal use of energy based on average performance (w.r.t. the know distribution) 4. Optimal taxation: A Pigouvian tax on carbon emission with a rate equal to the marginal externality of carbon.

5 Introduction Literature Review Hansen and Sargent (2002, 2008) Robust Control: 1. Decision maker does not know the true distribution of γ, but has an approximating one in his mind. 2. Only concerns about social (individual) walfare in the worst case scenario. 3. Chooses the worst case distribution of γ around a neighborhood centered at the approximating one. 4. Uses entropy as a measure of the deviation from the approximating model. 5. Linear-Quadratic-Gaussian world.

6 Introduction Our Contribution To the Literature of Environmental Externality: 1. Incorporate model uncertainty into GHKT (2012) and characterize optimal allocation and tax as functions of the size of model uncertainty. 2. The concern of robustness matters both qualitatively and qnantatively. To the Literature of Robust Control: 1. Study a dynamic model outside the LQG world. 2. Develop a simple method which divide the model into two parts and solve them separately.

7 Complete Model Complete Model In this section, we extend the analytical one-sector model as follows: Three Energy Sectors: 1. The oil sector produces oil (E 1 ) at zero cost but is subject to a resource feasibility constraint, R 0 > The coal and the green energy sector use linear technologies E i = A i N i ; i = 2, 3. The stock of coal is assumed to be infinity. 3. A 2 N 2 and A 3 N 3 grow at a rate of two percent per year.

8 Complete Model Complete Model The composite energy is produced by E = (κ 1 E ρ 1 + κ 2E ρ 2 + κ 3E ρ 3 )1/ρ. As in GHTK, suppose S = P + T where P and T are the permanent and temporary components of S, respectively. P = P + φ L (E 1 + E 2 ) and T = (1 φ)t + (1 φ L )φ 0 (E 1 + E 2 ).

9 Numerical Results Calibration Table: Calibration Summary Parameter φ φ L φ 0 θ Value Parameter ν β ρ 1 + g Value Parameter P 0 T 0 R 0 κ 1 Value Parameter κ 2 A 2,0 A 3,0 λ 1 Value ,693 1,

10 Numerical Results Optimal Energy Path when R 0 = 253.8GtC (The same as in GHKT) Figure: Optimal Use of Energy when R 0 = 253.8

11 Numerical Results Optimal Energy Path when R 0 = 8000GtC (Including Methane) Figure: Optimal Use of Energy when R 0 = 8000