Introduction Model Results Discussion Conclusions Climate Policy and Growth Uncertainty: Dicing with DICE Svenn Jensen ∗ Christian Traeger ∗ ∗ ARE, UC Berkeley London, 13 December 2012 1 / 27
Introduction Model Results Discussion Conclusions Research questions 1. How does uncertainty about economic growth affect optimal climate policies? 2. How do risk preferences govern the effect? 2 / 27
Introduction Model Results Discussion Conclusions Integrated Assessment Models & Growth Economic growth shapes climate policy in IAMs 700 80% Social Cost of Carbon Abatement rate 70% 600 DICE growth +1% 60% 500 DICE growth +1% DICE growth 50% DICE growth 400 DICE growth - 1% $/C % 40% DICE growth - 1% 300 30% 200 20% 100 10% 0% 0 Year Year 3 / 27
Introduction Model Results Discussion Conclusions Integrated Assessment Models & Growth Uncertainty 1. Present IAMs ignore uncertainty about economic growth Time path technology 0.05 mean 95% bounds iid 95% bounds AR(1) 0.04 0.03 0.02 0.01 0 2000 2020 2040 2060 2080 2100 years 4 / 27
Introduction Model Results Discussion Conclusions Integrated Assessment Models & Growth Uncertainty 2. Present IAMs using the standard Discounted Expected Utility Model cannot calibrate discount rate and risk premium correctly Several key aspects of asset market data pose a serious challenge to economic models. It is difficult to justify the 6% equity premium and the low risk-free rate (Bansal and Yaron, 2004). ⇒ More comprehensive, rational framework from finance literature: Epstein-Zin-Weil preferences 5 / 27
Introduction Model Results Discussion Conclusions Related Literature Recursive IAMs & uncertainty Kelly and Kolstad (1999); Leach (2007) Crost and Traeger (2010); Lemoine and Traeger (2010) Golosov et al. (2011); Cai et al. (2012) Epstein-Zin-Weil preferences (Finance literature) Bansal et al. (2010); Bansal and Yaron (2004); Vissing-Jørgensen and Attanasio (2003) Growth uncertainty & climate change Fischer and Springborn (2011); Heutel (2011) Gollier (2002); Ha-Duong and Treich (2004); Traeger (2011) 6 / 27
Introduction Model Results Discussion Conclusions Preview of results 1 Standard expected utility model Growth uncertainty irrelevant for investments and emission reductions 2 Epstein-Zin-Weil preferences Risk aversion determines magnitude of effects Intertemporal consumption smoothing influences direction of effect on climate policy Persistence in shock amplifies effects 7 / 27
Introduction Model Results Discussion Conclusions Outline Introduction Model DICE model and modifications Bellman equations, for standard model and Epstein-Zin-Weil preferences Numerical Results Standard vs disentangled preferences iid vs persistent shock Analytical Discussion Concluding remarks 8 / 27
Introduction Model Results Discussion Conclusions Model 9 / 27
Introduction Model Results Discussion Conclusions DICE-model - carbon cycle + recursive structure CO2 Technology Capital Temperature T Temp Prod Production ion Consumption Investment Emissions E ns Abatement 10 / 27
Introduction Model Results Discussion Conclusions DICE-model - carbon cycle + recursive structure CO2 Technology Capital Temperature T Temp Prod Production ion Consumption Investment Emissions E ns Abatement Changes to DICE : Replace the carbon cycle by a fitted CO 2 decay function Simplify equation of motion for temperatures Calibrate model to fit baseline policies in DICE Match 11 / 27
Introduction Model Results Discussion Conclusions Introducing Uncertainty CO2 Technology Capital T Temp Temperature Production Prod ion E Emissions ns Abatement Consumption Investment Y G = ( A t L t ) 1 − κ K κ Production: t t ˜ Exogenous technology: A t +1 = A t exp [˜ g A,t ] Technological growth: ˜ g A,t = g A, 0 ∗ exp [ − δ A t ] + ˜ z t Shock: x t ∼ iid N ( µ A , σ 2 1. iid ˜ z t = ˜ A ) ′ 2. persistent ˜ z t = ˜ x t + ˜ y t 2 , σ 2 ′ ǫ t ∼ iid N ( µ A ˜ y t = ζy t − 1 + ˜ ǫ t ˜ x t , ˜ 2 ) A 12 / 27
Introduction Model Results Discussion Conclusions Bellman equation, standard preferences c t ) 1 − ˆ η L t (¯ V ( K t , M t , A t , t, d t ) = max 1 − ˆ η c t ,µ t ¯ � � V ( K t +1 , M t +1 , ˜ A t +1 , t + 1 , ˜ + exp[ − δ u ]I E d t +1 ) Controls : per capita consumption ¯ c and abatement µ States : Capital K , carbon stock M , time t , uncertain technology A , persistent shock d 13 / 27
Introduction Model Results Discussion Conclusions Bellman equation, standard preferences V ( K t , M t , A t , t, d t ) = max L t u (¯ c t ) ¯ c t ,µ t � � V ( K t +1 , M t +1 , ˜ A t +1 , t + 1 , ˜ + exp[ − δ u ]I E d t +1 ) Controls : per capita consumption ¯ c and abatement µ States : Capital K , carbon stock M , time t , uncertain technology A , persistent shock d c 1 − ˆ η c t ) = ¯ u (¯ t 1 − ˆ η 13 / 27
Introduction Model Results Discussion Conclusions Time and risk preferences Default: Expected Utility Model Same parameter (ˆ η ) for consumption smoothing & risk preference 14 / 27
Introduction Model Results Discussion Conclusions Time and risk preferences Default: Expected Utility Model Same parameter (ˆ η ) for consumption smoothing & risk preference Better: Epstein-Zin-Weil preferences Disentangle risk & consumption smoothing Normatively: Why should they be the same? Empirically: They are not (finance literature) Note: Standard rationality assumptions satisfied (von Neumann-Morgenstern, time consistency) 14 / 27
Introduction Model Results Discussion Conclusions Bellman equation, Epstein-Zin-Weil preferences c t ) 1 − η L t (¯ V ( K t , M t , A t , t, d t ) = max + 1 − η ¯ c t ,µ t 1 − η � � � 1 − RRA exp[ − δ u ] � 1 − RRA (1 − η ) V ( K t +1 , M t +1 , ˜ A t +1 , t + 1 , ˜ 1 − η I E d t +1 ) 1 − η RRA: Relative risk aversion η : Aversion to intertemporal substitution 15 / 27
Introduction Model Results Discussion Conclusions Bellman equation, Epstein-Zin-Weil preferences V ( K t , M t , A t , t, d t ) = max L t u (¯ c t ) + c t ,µ t ¯ exp[ − δ u ] f − 1 � � � ��� V ( K t +1 , M t +1 , ˜ A t +1 , t + 1 , ˜ I E f d t +1 ) 1 − RRA Intertemporal risk aversion: f ( z ) = ((1 − η ) z ) 1 − η IRA Numerics 15 / 27
Introduction Model Results Discussion Conclusions Numerical Results 16 / 27
Introduction Model Results Discussion Conclusions Research question revisited 1. How does uncertainty about economic growth affect the optimal levels of abatement (and the SCC) and investment? 2. How does the effect depend on specifications of preferences (Expected Utility vs Epstein-Zin-Weil)? 17 / 27
Introduction Model Results Discussion Conclusions Standard EUT model, RRA = η = 2 iid shock; standard deviation 2x initial growth rate Abatement rate Social cost of carbon 50 220 iid iid 200 certainty certainty 40 180 % of potential emissions 160 30 140 US$/tC 120 20 100 80 10 60 40 0 20 2000 2020 2040 2060 2080 2100 2000 2020 2040 2060 2080 2100 year year Miniscule increase in abatement/SCC & investment Zoom Intuition: Intertemporal risk neutrality 18 / 27
Introduction Model Results Discussion Conclusions Disentanglement I, RRA = 10 & η = 2 Empirical evidence suggests: RRA ↑ , shock persistent Abatement rate Investment rate 34 certainty certainty 50 iid, RRA=10 iid, RRA=10 32 % of potential emissions 40 30 28 30 % 26 20 24 10 22 0 20 2000 2020 2040 2060 2080 2100 2000 2020 2040 2060 2080 2100 year year Uncertainty increases abatement & investment Intuition: Intertemporal risk aversion Persistence (50%): magnifies effect More 19 / 27
Introduction Model Results Discussion Conclusions Disentanglement I, RRA = 10 & η = 2 Empirical evidence suggests: RRA ↑ , shock persistent Abatement rate Investment rate 34 certainty certainty 50 iid, RRA=10 iid, RRA=10 32 AR(1), RRA=10 AR(1), RRA=10 % of potential emissions 40 30 28 30 % 26 20 24 10 22 0 20 2000 2020 2040 2060 2080 2100 2000 2020 2040 2060 2080 2100 year year Uncertainty increases abatement & investment Intuition: Intertemporal risk aversion Persistence (50%): magnifies effect More 19 / 27
Introduction Model Results Discussion Conclusions Disentanglement II, RRA = 10 & η = 2 / 3 Empirical evidence also suggests: η ↓ Abatement rate Investment rate 70 34 certainty, η =2 certainty, η =2 certainty, η =2/3 certainty, η =2/3 60 32 % of potential emissions 50 30 40 28 % 30 26 20 24 10 22 0 20 2000 2020 2040 2060 2080 2100 2000 2020 2040 2060 2080 2100 year year Lower η increases abatement & investment Uncertainty decreases abatement & increases investment 20 / 27
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