Climate Policy in a Dynamic Stochastic Economy 1 Yongyang Cai The Ohio State University June 4, 2019 1 Presentation for Blue Waters project (PI: Yongyang Cai (OSU); Team members: Kenneth Judd (Hoover), William Brock (UW), Thomas Hertel (Purdue). The presentation is mainly based on the following two working papers: Cai, Brock, Xepapadeas and Judd (2019), “Climate policy under spatial heat transport: cooperative and noncooperative regional outcomes”; Cai and Judd (2019), “Climate policy with carbon capture and storage in the face of economic risks and climate target constraints”.
Polar Amplification Polar Amplification (PA): high latitude regions have higher/faster temperature increases (almost twice that of low latitude regions) ◮ accelerate the loss of Arctic sea ice ◮ meltdown of Greenland and West Antarctica ice sheets ◮ global sea level rise ◮ thawing of permafrost ◮ change in ecosystems ◮ infrastructure damage ◮ release of greenhouse gases stored in permafrost ◮ increase frequency of extreme weather events ◮ tipping points
Contributions ◮ We develop a Dynamic Integration of Regional Economy and Spatial Climate under Uncertainty (DIRESCU), incorporating ◮ an endogenous SLR module ◮ an endogenous permafrost melt module ◮ the more realistic geophysics of spatial heat and moisture transport from low latitudes to high latitudes ◮ use recursive preferences ◮ allow for adaptation to regional damage from SLR and temperature increase. ◮ Calibrate our parameter values to match history as well as to fit the representative concentration pathway (RCP) scenarios ◮ Solve a dynamic stochastic feedback Nash equilibrium of DIRSCUE ◮ Climate policy: ◮ ignoring PA, SLR, or adapation leads to serious bias ◮ non-cooperation leads to much smaller carbon tax than cooperation ◮ the North has higher carbon taxes than the Tropic-South
DIRESCU Model Dynamic Integration of Regional Economy and Spatial Climate under Uncertainty (DIRESCU)
Climate Tipping Point ◮ Uncertain tipping time with tipping probability � � �� 0 , T AT p t = 1 − exp − ̺ max t , 1 − 1 , ◮ Transition matrix � � 1 − p t p t 0 1 ◮ Duration: D years ◮ transition law of tipping state J t : J t + 1 = min( J , J t + ∆) χ t (1) ◮ χ t : indicator for tipping’s occurrence ◮ J : final damage level ◮ ∆ = J / D : annual increment of damage level after tipping ◮ We use Atlantic Meridional Overturning Circulation (AMOC) as a representative tipping element ( D = 50 years, J = 0 . 15, λ = 0 . 00063)
Social Planner’s Deterministic Problem ◮ Social planner’s problem in the cooperative determistic case � ∞ � 2 β t max u ( c t , i ) L t , i (2) I t , i , c t , i ,µ t , i , P t , i t = 0 i = 1 ◮ utility u ( c ) = c 1 − 1 ψ , (3) 1 − 1 ψ ◮ Market clearing condition � 2 � 2 � ( I t , i + c t , i L t , i + Γ t , i ) = (4) Y t , i i = 1 i = 1
Social Planner’s Stochastic Problem ◮ Epstein-Zin preference: ◮ γ : risk aversion ◮ ψ : intertemporal elasticity of substitution ◮ Bellman equation: � 2 � Θ �� 1 /Θ � � �� � u ( c t , i ) L t , i + β � V Social ψ V Social ( x t ) = max ( x t + 1 ) , E t t t + 1 � ψ a t i = 1 where � ψ and Θ ≡ ( 1 − γ ) / � ψ ≡ 1 − 1 ψ ◮ State variables x t : x t = ( K t , 1 , K t , 2 , M AT , M UO , M DO , T AT t , 1 , T AT t , 2 , T OC , S t , J t , χ t ) t t t t ◮ Decision variables a t = ( I t , 1 , I t , 2 , c t , 1 , c t , 2 , µ t , 1 , µ t , 2 , P t , 1 , P t , 2 )
Computational Method for Social Planner’s Problems ◮ Parallel Value Function Iteration for Social Planner’s Problems ◮ Terminal condition: estimate V Social ( x ) for time T T ◮ Backward iteration over time t : V Social = F t V Social t t + 1 ◮ Step 1. Maximization step (in parallel). Compute v t , j = ( F t � V Social )( x t , j ) t + 1 for each approximation node x t , j (#node: 5 10 × 2 = 19 . 5 million) ◮ Step 2. Fitting step. Using an appropriate approximation (complete � 10 + 4 � Chebyshev polynomial #term: × 2 = 2002 ) method 4 V Social � ( x t , j ; b t ) ≈ v t , j t
Feedback Nash Equilibrium ◮ Feedback Nash Equilirbium (FBNE), also known as Markov Perfect Equilirbium ◮ nocooperation = ⇒ no transfer of capital between the regions, so the market clearing condition is � I t , i + c t , i L t , i = Y t , i (5) ◮ Bellman equations: V FBNE ( x t ) = c t , i , P t , i ,µ t , i { u ( c t , i ) L t , i + β G t , i ( x t + 1 ) } , max (6) t , i for i = 1 , 2, where � �� � Θ �� 1 /Θ G t , i ( x t + 1 ) ≡ 1 � ψ V FBNE t + 1 , i ( x t + 1 ) E t � ψ
Feedback Nash Equilibrium ◮ First-order conditions (FOCs) over c t , i , P t , i , µ t , i : u ′ ( c t , i ) − β ∂ G t , i ( x t + 1 ) 0 = , (7) ∂ K t + 1 , i ∂ � Y t , i 0 = (8) ∂ P t , i ∂ � ∂ E Ind ∂ G t , i ( x t + 1 ) Y t , i + ∂ G t , i ( x t + 1 ) t , i 0 = (9) ∂ M AT ∂ K t + 1 , i ∂µ t , i ∂µ t , i t + 1 ◮ Use the solution of the FOCs and the transition laws to compute V FBNE ( x t ) = u ( c t , i ) L t , i + β G t , i ( x t + 1 ) t , i
Computational Method for Feedback Nash Equilibrium ◮ Parallel Value Function Iteration for Feedback Nash Equilirbium ◮ Terminal condition: estimate V FBNE ( x ) for the terminal time T and T , i i = 1 , 2 ◮ Backward iteration over time t : V FBNE = F t , i V FBNE , i = 1 , 2 t , i t + 1 ◮ Step 1 (in parallel). For each approximation node x t , j (#node: m = 5 10 × 2 = 19 . 5 million), compute the feasible action ( a t , 1 , j , a t , 2 , j ) for both regions that satisfies the FOCs and the transition laws, and then comptute v t , i , j = u ( c t , i , j ) L t , i + β G t , i ( x t + 1 , j ) for i = 1 , 2 and j = 1 , ..., m . ◮ Step 2. Fitting step. Using an appropriate approximation (complete � 10 + 4 � Chebyshev polynomial #term: × 2 = 2002 ) method 4 such that � V FBNE ( x t , j ; b t , i ) ≈ v t , i , j , for i = 1 , 2 and j = 1 , ..., m . t , i
Parallelization Example # of Optimization #Cores Wall Clock Total CPU problems Time Time 1 2 billion 3K 3.4 hours 1.2 years 2 372 billion 84K 8 hours 77 years
Results of the Benchmark Case
Bias from Ignoring PA
Bias from Ignoring PA
Bias from Ignoring SLR, Adaptation, and Transfer of Capital Table: Initial carbon tax from ignoring elements Ignored Element Model Deterministic Stochastic North Tropic-South North Tropic-South SLR Coop. 84 58 294 207 FBNE 32 33 116 109 Adaptation Coop. 553 384 855 601 FBNE 355 214 400 299 Capital Transfer Coop. 236 118 540 275
Sensitivity on the IES and Risk Aversion Table: Initial carbon tax under various IESs ( ψ ) and risk aversion ( γ ) IES Model Deterministic Stochastic ( ψ ) North Tropic North Tropic-South -South γ = 3 . 066 γ = 10 γ = 3 . 066 γ = 10 0.69 Coop. 58 35 114 132 69 80 FBNE 29 17 55 63 32 38 1.5 Coop. 198 137 454 519 318 363 FBNE 90 67 185 208 152 174
Summary ◮ The North has higher carbon taxes than the Tropic-South in a cooperative or noncooperative world ◮ Noncooperation leads to much lower carbon taxes than the social planner’s model with economic interactions between the regions ◮ Closed economy has higher carbon taxes than (semi-)open economy ◮ Ignoring PA leads to many biases in carbon tax, adaptation, & temperature ◮ Ignoring SLR underestimates carbon taxes significantly ◮ Ignoring adaptation overestimates carbon taxes significantly ◮ For climate tipping risks, larger IES values imply larger carbon taxes in a cooperative or non-cooperative world
Carbon Capture and Storage ◮ Capital transition law K t + 1 = ( 1 − δ ) K t + � Y t − C t − p t R t − Γ t ( R t − 1 , R t ) ◮ p t : cost in directly removing a unit of carbon from the atmosphere ◮ R t : removed carbon amount ◮ Γ t ( R t − 1 , R t ) : adjustment cost ◮ The carbon cycle is M t + 1 = Φ M M t + ( E t − R t , 0 , 0 ) ⊤ , (10)
Economic Risk ◮ stochastic productivity, � A t ≡ ζ t A t ◮ A t : deterministic trend ◮ ζ t : productivity shock with long-run risk log ( ζ t + 1 ) = log ( ζ t ) + χ t + ̺ω ζ, t χ t + 1 = r χ t + ςω χ, t
Results with/without CCS or 2°C target
Results with/without CCS or 2°C target
Publications Using Blue Waters ◮ Cai, Y., and T.S. Lontzek (2018). The social cost of carbon with economic and climate risks. Journal of Political Economy , forthcoming. ◮ Cai, Y., K.L. Judd, and J. Steinbuks (2017). A nonlinear certainty equivalent approximation method for stochastic dynamic problems. Quantitative Economics , 8(1), 117–147. ◮ Yeltekin, S., Y. Cai, and K.L. Judd (2017). Computing equilibria of dynamic games. Operations Research , 65(2): 337–356 ◮ Cai, Y., T.M. Lenton, and T.S. Lontzek (2016). Risk of multiple climate tipping points should trigger a rapid reduction in CO2 emissions. Nature Climate Change 6, 520–525. ◮ Lontzek, T.S., Y. Cai, K.L. Judd, and T.M. Lenton (2015). Stochastic integrated assessment of climate tipping points calls for strict climate policy. Nature Climate Change 5, 441–444. ◮ Cai, Y., K.L. Judd, T.M. Lenton, T.S. Lontzek, and D. Narita (2015). Risk to ecosystem services could significantly affect the cost-benefit assessments of climate change policies. Proceedings of the National Academy of Sciences , 112(15), 4606–4611.
Recommend
More recommend
