The Social Cost of Stochastic & Irreversible Climate Change

Transcription

1 The Social Cost of Stochastic & Irreversible Climate Change Thomas S. Lontzek (University of Zurich and RDCEP) joint work with Yongyang Cai and Kenneth L. Judd (both at Hoover Institution, RDCEP and NBER)

2 Introduction Climate Change Economics becoming increasingly important Carbon Tax: highly debated instrument for climate policy The US Government IWG on Social Cost of Carbon (IWG, 2010): Range of carbon tax: US$5 - US$65 Central price: US$21. Integrated Assessment Models (IAM) used by IWG (2010): DICE2007 (Nordhaus, 2008) FUND (Anthoff et al., 2009) PAGE (Hope, 2006)

3 All those IAMs assume perfect certainty for climate and economics Individual economic actors face risk and uncertainty about the actual structure of the economic and climate systems Policy makers must consider how economic actors respond to risk and uncertainty. The next generation of IAMs should attempt to incorporate risk Preferences over risk needs to be modelled in a manner that is compatible with empirical evidence on RA and the IES. Some climate change might be discontinuous (stochastic and irreversible)

4 Nat. Science Part Abrupt and Irreversible Climate Change IAM lit.: damages are a function of contemporaneous temperature Possible climate change externalities are more complex. Some elements of the climate system which might exhibit a tipping point (see, e.g., Kriegler et al. 2009) Lenton et al. (2008): tipping points in the climate system: Weakening or shut down of the North Atlantic thermohaline circulation. Melting of the Greenland ice sheet Melting of the West Antarctic ice sheet. Die-back of the Amazon rainforest. Increasing frequency and amplitude of El Niño-Southern Oscillation.

5 modelling abrupt climate change Past Approaches More convex damage function (e.g. Mastrandrea & Schneider, Climate Policy 2001) Probabilistic assessment studies (e.g. Mastrandrea & Schneider, Science 2004; Yohe et. al, The Integrated Assessment Journal, 2006) Known thresholds (e.g. Keller et. al. 2004, JEEM) Unknown thresholds (e.g. Lemoine and Traeger, AEJ Policy, in press.)

6 modelling abrupt climate change The policy response to the threat of tipping points is very different from the policy response to standard damage representations Carbon tax "ramp" in DICE

7 irreversibility Our Approach to Stochastic Climate Change and Irreversibility: damage from tipping damage at final stage abrupt tipping process 0 stage 1 stage 2 stage 3 absorbing (final) stage stage of the tipping process

8 hazard Kriegler et al. (PNAS, 2009) conduct an extensive expert elicitation on some major tipping elements and their likelihood of abrupt change. THC collapse Greenland ice sheet melting WestAntarctic ice sheet melting Amazon rainforest dieback ElNiño/Southern Oscillation They compute conservative lower bounds for the probability of triggering at least 1 of those events 0.16 for medium (2 4 C) global mean temperature change 0.56 for high (above 4 C) global mean temperature change

9 Central question: How is optimal climate policy affected by preferences over risk and stochastic and irreversible climate change? Our Approach: Use DSICE, a DSGE extension of the DICE2007 model (Nordhaus, 2008) Use the DICE2007 box model for the climate system Use long time horizon of 600 years. Use 1-year time steps Productivity shocks to the economy Empirically acceptable preferences (Epstein-Zin) Critical elements of riskiness in the climate system: Abrupt and irreversible climate change Uncertain impact on productivity

10 The Climate-Economy Dynamic Integrated Model of Climate and Economy Mitigation Emissions Atmosphere Economy Upper Ocean Deep Ocean Temp. Atmosphere Temp. Ocean Utility Damage State Variable Control Variable

11 The Climate-Economy Dynamic Stochastic Integration Model of Climate and Economy Mitigation Business Cycle Emissions Atmosphere Economy Upper Ocean Deep Ocean Temp. Atmosphere Temp. Ocean Utility Damage Abrupt Climate Change State Variable Control Variable Markov Process

12 The Carbon System The Carbon System: M t = (M AT t, M UP t M t+1 = Φ M M t + (E t, 0, 0), M LO ) : Carbon concentrations, with: t E t : anthropogenic sources of carbon Φ M = 1 φ 12 φ 12 ϕ 1 0 φ 12 1 φ 12 ϕ 1 φ 23 φ 23 ϕ 2 0 φ 23 1 φ 23 ϕ 2, ϕ 1 = M AT /M UP and ϕ 2 = M UP /M LO M AT, M UP, M LO : preindustrial equilibrium states of the carbon cycle

13 The Climate System The Climate System: T t = (T AT t, Tt LO ) : temperatures in the atmosphere and ocean T t+1 = Φ T T t + ( ( ) ) ξ 1 F t M AT t, 0 Φ T = [ 1 ξ 1 η/ξ 2 ξ 1 ξ 3 ξ 1 ξ 3 ξ 4 1 ξ 4 ξ 2 : climate sensitivity parameter (we choose ξ 2 = 3) ], ( Radiative forcing: F ) ( ) t M AT = η log 2 M AT /M0 AT + F EX t External forcing, F EX t

14 The Stochastic Climate (Case: Abrupt Damage Path) The Stochastic Climate (Case: Abrupt Damage Path): The climate shock occurs at a random time. The stochastic damage function: Ω ( Tt AT ) 1 J t, J t = 1 + π 1 T AT + π 2 (T AT t t ) 2 J t : discrete Markov chain with probability transition matrix: [ 1 p t p t 0 1 p t = 1 exp { ν max { 0, (T AT t 1) }} Conditional probability of the tipping point to occur at time t State 2: absorbing state (irreversibility) ν: Hazard rate parameter ]

15 The Stochastic Economy The Stochastic Economy: Stochastic production function Y t(k t, T AT t, µ t, ζ t, J t) = (1 ψ 1 θ 2 t θ 1,tµ θ 2 t ) }{{} mitigation costs economic shock {}}{ ζ t A tkt α lt 1 α climate shock {}}{ J t 1 + π 1Tt AT + π 2(Tt AT ) 2 }{{} damage from global warming k t+1 = (1 δ)k t + Y t (k t, T AT t, µ t, ζ t, J t ) c t, ζ t : mean-reverting productivity shock representing economic fluctuations. Stochastic Emissions: E t (k t, µ t, ζ t ) = σ t (1 µ t )ζ t A t kt α lt 1 α σ: carbon intensity of output µt fraction of mitigated emission + E Land t

16 Epstein-Zin Preferences: A recursive formulation of the maximand is: U t (k, M, T, ζ, J) = max c,µ { (1 β) (c t/l t ) 1 ψ 1 ψ l t [ { (Ut+1 ( + β E k +, M +, T +, ζ +, J +)) }] } 1 1 ψ 1 ψ 1 γ 1 γ ψ: Inverse of the inter-temporal elasticity of substitution γ: Risk Aversion

17 The DP Formulation The Dynamic Programming Problem: V t (k, M, T, ζ, J) = max c,µ u(c t, l t ) + β 1 ψ [ E { ((1 ψ) Vt+1 ( k +, M +, T +, ζ +, J +)) }] 1 ψ 1 γ 1 γ 1 ψ s.t. k + = (1 δ)k t + Y t (k, T AT, µ, ζ, J) c t, M + = Φ M M + (E t (k, µ, ζ), 0, 0), T + = Φ T T + ( ( ξ 1 F t M AT ), 0 ), ζ + = g ζ (ζ, ω ζ ), J + = g J (J, T, ω J )

18 The DP Formulation We apply numerical dynamic programming for finite horizon problems with value function iteration Terminal value function: V 600 (k +, M +, T +, ζ +, J + ) Solve recursively ( t = 599, 598,..., 0) for: Value function V (k, M, T, ζ, J) Consumption c Emission control rate µ

19 Results: We report statistics for 1000 simulated runs of the optimal carbon tax path Benchmark Case: ν = , J t = 0.025, ψ = 2, γ = 10 Sensitivity to RA, hazard rate and post-tipping impact Uncertain damage level Disaster case Multi-stage, gradual tipping impact path Multiple tipping points Economic shocks

20 Benchmark Case Benchmark Case: ν = , J t = 0.025, ψ = 2, γ = 10 Carbon Tax when ψ= Range of all sample paths 5% quantile 10% quantile 20% quantile path with no tipping Year Pre-tipping tax in 2005 is 55$ additional preventive carbon tax is almost constant (20 US$) Risky cash flows are generally not discounted at the same rate as deterministic cash flows

21 Damage Level Effect Hazard and Damage effect in 2005: ψ = 2, γ = ν = ν = ν = 0.01 carbon tax Higher post-tipping damage and higher hazard rate increase the carbon tax damage level

22 Disaster Case Disaster Case: ν = , J = 0.2, ψ = 2, γ = Range of all sample paths 3% quantile 7% quantile 10% quantile path with no tipping Carbon Tax Prob. of tipping after 2100 is 97% Carbon tax in 2005 triples Year

23 Uncertain Damage Level Uncertain damage level with σ, with probability 50%, J t = 0.05 σ, with probability 50%, where 0 σ < is called as the volatility of the uncertain damage level. J t is a three-state Markov chain with the probability transition matrix 1 p t 0.5p t 0.5p t ,

24 Uncertain Damage Level Carbon tax in 2005 carbon tax γ =2 γ =10 γ =20 low RA tax driven by mean Here: CAPM story: Price of risk related to its covariance with aggregate output Here: damage proportional AND: only stoch. element Covariance is unity variance of uncertain damage level x 10 4 Carbon tax has a price of risk component linear in the variance

25 Advanced Formulations of Tipping Points 3 iid tipping points multi-stage processes Tipping Point and the Business Cycle

26 3 iid Tipping Points 3 iid Tipping Points: ν i = , J t,i = , ψ = 2, γ = % quantile the earliest tipping sample path 25% quantile median 75% quantile 100% quantile pre tipping path No tipping existed path 25% chance of Carbon Tax out 3 by out 3 by out 3 by Year

27 4-Stage Tipping Process 4-Stage Tipping Process: J i t = (i 1)/3 ν i = , ψ = 2, γ = % quantile the earliest tipping sample path 25% quantile median 75% quantile 100% quantile pre tipping path No tipping existed path Carbon Tax Facing one stage at a time Year

28 Gradual Post-tipping Impact Path Gradual Post-tipping Impact Path only stage 1 is associated with an endogenous tipping point probability subsequent stage :exogenous J t : discrete Markov chain with 11 possible values of 0, 0.01, 0.02,..., 0.1, probability transition matrix 1 p t p t 1 q t q t 1 q t qt 1 q t q t 1, q t = 1 e χ, calibrate χ to be in line with the expected duration of the entire tipping Example χ = 0.2, expected duration: 50 years.

29 Gradual Post-tipping Impact Path maximal damage level = 2.5% maximal damage level = 5% maximal damage level = 10% 80 carbon tax Expected duration of tipping process (years)

30 Rel. Diff of Carbon Tax Relative Difference of Carbon Tax Expectation 0% or 100% quantile 25% or 75% quantile Median 0 Productivity Shock No Tipping Point Rel. Diff. of Tax Year

31 Productivity Shock & Tipping Point Productivity Shock + Tipping: ν i = , J t,i = 0.95, ψ = 2, γ = 10 Carbon Tax % quantile 25% quantile median 65% quantile 100% quantile No shocks existed path Combined effect of Productivity Shock and tipping point 25% chance of tipping by end of this century Year

32 Dynamic stochastic IAM analysis is necessary for a coherent and reliable evaluation of policy alternatives to deal with abrupt climate change Much greater urgency to immediately enacting in significant GHG reductions policies than implied by DICE2007 and similar models that ignore uncertainty. Dynamic stochastic IAM analysis with DSGE-style models is tractable DSICE is solved with stable and fast dynamic programming When we apply dynamic programming to the deterministic cases, results agree withe constrained optimisation approach The benchmark case solves in 18 minutes (7D, 600 periods - single core)