Ambiguity and Climate Policy. Antony Millner (UC Berkeley) Simon Dietz (LSE) Geoffrey Heal (Columbia)

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1 Ambiguity and Climate Policy Antony Millner (UC Berkeley) Simon Dietz (LSE) Geoffrey Heal (Columbia) 1

2 Reasoning about climate change Science inputs Economics inputs RaIonal choice EvaluaIon framework Ethics, Preferences Policy RecommendaIons 2

3 What do we know about the effect of CO 2 on global climate?!#$,#!!!#$+#!!!"#$%$&'&()*+,-.&()*!#$*#!!!#$)#!!!#$(#!!!#$'#!! S = Equilibrium temperature change from a doubling of CO 2 concentraion!#$&#!!!#$%#!!!"!!!!!"!!!!!%$##!!!&$##!!!'$##!!!($##!!!)$##!!!*$##!!!+$##!!!,$##!!!-$##!!!%#$##!! /'&0%(,*1,-.&23&()*415* 3

4 Road Map Risk vs. Ambiguity Formal framework for decision making under ambiguity. When will concern about ambiguity cause us to make more/less ambiious policy choices? ApplicaIon to Climate Change: How does scienific ambiguity affect the azraciveness of miigaion? 4

5 Risk vs. Ambiguity: MoIvaIon 1. Objec(vity: We would like policy to be based on objecive knowledge about the world. 2. Ambiguity: We o]en don t know enough to be able to discern between compeing models of the world. 3. Expected U(lity: Arbitrary subjecive weights on models are compounded with objecive model probabiliies. The Rub: Our standard decision tools cannot disinguish objecive knowledge and arbitrary judgments. 5

6 BeZer the devil you know? Your Coin Stranger s Coin Front Back Front Back Fair Coin 1/3? P(Heads) = 0.5 P(Heads) = 0.5 Heads Cheat 1/3 Arbitrary subjecive weights Tails Cheat 1/3 P(Heads) = (1/3)*0.5 + (1/3)*1 + (1/3)*0 = 0.5 6

7 Risk vs. Ambiguity: Does this disincion mazer for policy?!#$,#!!!#$+#!!!"#$%$&'&()*+,-.&()*!#$*#!!!#$)#!!!#$(#!!!#$'#!! S = Equilibrium temperature change from a doubling of CO 2 concentraion!#$&#!! Weighted average of PDFs!#$%#!!!"!!!!!"!!!!!%$##!!!&$##!!!'$##!!!($##!!!)$##!!!*$##!!!+$##!!!,$##!!!-$##!!!%#$##!! 7 /'&0%(,*1,-.&23&()*415*

8 Ambiguity Aversion We d like to maintain a disincion between: CondiIonally objecive knowledge: Model predicions assuming the model is correct Arbitrary subjecive choices: Weights on models. All else equal, we d prefer to choose policies whose consequences are less ambiguous. This cannot be achieved in the standard Expected UIlity framework: Ellsberg 1961: ViolaIon of the Sure Thing Principle 8

9 Related Literature Macroeconomics: Hansen & Sargent (AER, 2001) Finance: Dow & da Costa Werlang (Econometrica, 1992) Gollier (ReStud, 2011) Robust Decision Lempert (PNAS, 2002) Decision Theory Savage, 1954 Arrow & Hurwicz, 1972 Gilboa & Schmeidler (Econometrica, 1989) Klibanoff, Marinacci, Mukerji (Econometrica, 2005) Climate Lange & Treich (ClimaIc Change, 2008) Lemoine & Traeger,

10 Modeling Ambiguity Aversion Klibanoff et. al. (Econometrica 05) V 0 (a) = X p m E m U(a) V (a) = X Models m Models m p m (E m U(a)) =E subj obju(a) =E subj (E obj U(a)) φ (E subj obju(a)) φ(e 2 U) Ambiguity Premium φ(e 1 U) E subj (E obj U(a)) E 1 U E 2 U 10

11 Some comparaive staics V (a) = p m (EU m (a)), EU m (a) := U(c) m (c, a)dc m V (a ) = 0 ˆp m (a) := ProposiIon 1: m ˆp m (a ) deu m da p m (EU m (a)) n p n (EU n (a)) a=a =0 Increasing A.A. places more weight (in the sense of the monotone likelihood ra?o order) on models with low expected u?lity at the level of the first order condi?ons. Proof Straight forward (Gollier & Gierlinger 08) 11

12 When will ambiguity aversion make us abate more? EU 1 (a) π 1 (S) S EU p 1 EU 1 (a) + p 2 EU 2 (a) p 1 φ(eu 1 (a)) + p 2 φ(eu 2 (a)) EU 2 (a) π 2 (S) S a * 0 a * φ a 12

13 MathemaIcal Version ProposiIon: V 0 (a) := m p m EU m (a), V (a) := Proof See paper. Relies on proving concavity, and log- supermodularity of the expectaions in the FOC. m p m V 0(a 0 ) := 0 V (a ) := 0 i) V 0 (a) < 0 ii) a, {EU m } and {EU m} are comonotonic. (EU m (a)) iii) a, {EU m } and {EU m} are anti-comonotonic. a a 0 13

14 Dynamics: The DICE model Capital Invest CO 2 SensiIvity (S) Temp Damage f n Output ConsumpIon Emissions Abatement 14

15 Dynamics & Ambiguity Klibanoff et. al. (2009) obtain a consequenialist, dynamically consistent representaion of preferences over Ime- dependent plans, which accounts for ambiguity aversion: V st (f) = u(f(s t )) + 1 SubjecIve weights V (st,x t+1 )(f)d (x t+1 ; s t ) dp( s t ) X t+1 Current payoff Ambiguity preferences ConInuaIon value under model θ 15

16 Resolving ambiguity: Two polar cases 1. Ambiguity over S resolves a]er one 30 year Ime period Risk + ambiguity in first period, only risk in all other periods We learn which model is correct 2. Ambiguity over S persists for all Ime unaltered Both risk and ambiguity in every period We never learn which model is correct 16

17 Preferences & Welfare Symbol Name Interpreta(on Reasonable Values η ElasIcity of Marginal UIlity i) Risk aversion ii) IncenIve to smooth consumpion ξ Coefficient of RelaIve Ambiguity Aversion Ambiguity aversion β = (1+δ) - 1 Discount factor Pure Ime preference ? 0.1% (Stern) 1.5% (Nordhaus) Measuring Welfare: Stationary Equivalent: TX z } { U( c(v Policy ))N t t=0 SE t := V Policy Fractional change in SE: := c(v ABAT E) c(v BAU ) c(v BAU ) 17

18 Exogenous abatement policies 0.8" 0.7" 0.6" Emissions'control'rate' 0.5" 0.4" 0.3" BAU" 2"CO2" 0.2" 0.1" 0" 2005" 2015" 2025" 2035" 2045" 2055" 2065" 2075" 2085" 2095" 2105" Year' 18

19 RepresentaIon of ScienIfic Ambiguity!#$,#!!!#$+#!!!#$*#!!!"#$%$&'&()*+,-.&()*!#$)#!!!#$(#!!!#$'#!! S = Equilibrium temperature change from a doubling of CO 2 concentraion!#$&#!!!#$%#!!!"!!!!!"!!!!!%$##!!!&$##!!!'$##!!!($##!!!)$##!!!*$##!!!+$##!!!,$##!!!-$##!!!%#$##!! /'&0%(,*1,-.&23&()*415* Assume equal second order weight on each PDF. 19

20 Two views on damages Damage funcions (muliply producion f n ): DICE(t) = WEITZ(t) = T (t)+ 2 T (t) ( 1 T (t)) 2 +( 2 T (t)) Nordhaus (2008) Weitzman (2010) 1- Ω T = 2.5 C T = 3.5 C T = 4 C T=5 C DICE 1.7% 3.3% 4.3% 6.5% WEITZ 1.7% 5.1% 9% 25% For comparison: Global average surface temps during Last Glacial Maximum approx. 5 C lower than today 20

21 Effect of ambiguity aversion on welfare benefits of miigaion (Discount rate = 1.5%, ElasIcity of Marginal UIlity = 2) % change in Stationary Equivalent ( ) CO 2 stabilization, DICE damages Persistent Ambiguity 30 year Ambiguity % change in Stationary Equivalent ( ) CO 2 stabilization, Weitzman damages Ambiguity Aversion ( ) Ambiguity Aversion ( ) StaIonary Equivalent = RelaIve Welfare benefit of ABATE vs. BAU 21

22 Ambiguity Aversion and Risk Aversion: DICE Damages 2 CO 2 stabilization, Discount Rate = 0.1% 2 CO 2 stabilization, Discount Rate = 1.5% Ambiguity neutral ( = 0) Persistent ambiguity ( = 10) 30 year ambiguity ( = 10) 1.6 % change in Stationary Equivalent ( ) % change in Stationary Equivalent ( ) Elasticity of Marginal Utility ( ) Elasticity of Marginal Utility ( ) StaIonary Equivalent = RelaIve Welfare benefit of ABATE vs. BAU 22

23 Ambiguity Aversion and Risk Aversion: Weitzman Damages 2 CO 2 stabilization, Discount Rate = 0.1% 2 CO 2 stabilization, Discount Rate = 1.5% Ambiguity neutral ( = 0) Persistent ambiguity ( = 10) 30 year ambiguity ( = 10) % change in Stationary Equivalent ( ) % change in Stationary Equivalent ( ) Elasticity of Marginal Utility ( ) Elasticity of Marginal Utility ( ) StaIonary Equivalent = RelaIve Welfare benefit of ABATE vs. BAU 23

24 Parameter μ σ 2 σ 0 2 δ η ξ HeurisIc explanaion risk ambiguity PTP ITS 2 Social discount rate: = + µ 2 ( 2 + 0) Gollier & Gierlinger (2008), Traeger (2009) Empirically, we find: Interpreta(on Average consumpion growth Within model variance in consumpion growth Between model variance in average consumpion growth Pure Ime preference ElasIcity of marginal uility Ambiguity Aversion µ >> 2 > 2 0 However going from DICE to WEITZ damages increases σ 02 /μ by about 2 orders of magnitude. 24

25 Conclusions I Policy choices should disinguish between different kinds of knowledge Policies whose consequences are objecively agreed on are more desirable than polices whose consequences are dependent on arbitrary subjecive judgments. Our standard decision tools don t make this disincion 25

26 Conclusions II In general, accouning for ambiguity may push policy choices in either direcion. Our limited empirical analysis suggests that accouning for scienific ambiguity makes climate change abatement more azracive. This is a small effect for flat damages, and a large effect for steep damages. More research is needed on: Costs Learning Ambiguity Preferences Surprises 26

27 Other recent research highlights AdaptaIon to climate change and economic growth in developing countries (submized, J. Dev. Econ, 2011) Climate predicion for adaptaion: Who needs what? (ClimaIc Change, 2012) Welfare frameworks and climate catastrophes (submized, RESTAT, 2011) Do climate scienists have probabilisic knowledge about climate change? (R&R, Nature Climate Change, 2011) PoliIcal economy of domesic climate policy (in progress) What should economists know about climate modeling? (in progress) 27

Scientific Ambiguity and Climate Policy

Environ Resource Econ (2013) 55:21 46 DOI 10.1007/s10640-012-9612-0 Scientific Ambiguity and Climate Policy Antony Millner Simon Dietz Geoffrey Heal Accepted: 4 October 2012 / Published online: 20 October