Global warming as an asymmetric public bad

Louis-Gaëtan Giraudet (Ecole des Ponts ParisTech, CIRED)

Céline Guivarch (Ecole des Ponts ParisTech, CIRED)

A Toxa – June 27, 2016

Global warming has asymmetric impacts

2

Identical damages ( d = - b )

Symmetric impacts ( d = b )

3

Vu

lner

abili

ty In

dex

(z-

sco

re)

Sou

rce:

Sam

son

et

al. (

20

11

)

Abatement Cost Parameter Source: Nordhaus (2015)

%: share of 2010 global GHG emissions Source: WRI (2014)

Adaptation and mitigation little correlate

Adaptation may exacerbate warming

Isaac & van Vuuren (2009)

• Growing concerns about the warming potential of air conditioning (Barrecca et al., 2016; Davis and Gertler, 2015; Auffhammer and Mansur, 2014).

• At least conceptually, agriculture could also be a concern (fertilizers, irrigation). 4

We extend the canonical dynamic game of global warming to capture three stylized facts 1. Asymmetric impacts (gainers & losers) 2. Correlations between adaptation and mitigation capabilities 3. Warming potential of adaptation (“free-driving”)

We examine the policy implications of those asymmetries for

• “Bottom-up” approaches: e.g., US-China Agreement, NDCs • Optimal solutions: GHG emission pricing

We contribute to opening up the public good model, besides • Kotchen’s “impure public goods” (2005) • Nordhaus’ “climate clubs” (2015)

5

Dynamic Games of Global Warming: Background

• Mitigation – Prevailing structure: Linear-quadratic in state, identical players. – Discussion of open-loop vs. feedback non-cooperative strategies (van der

Ploeg & de Zeeuw, 1992; Hoel, 1993) – With small enough discount rate, non-linear feedback can induce too

little warming (Dockner and Long, 1993). Restrictions subsequently placed on the result (Rubio and Casino, 2002; Wirl, 2007)

– Partial account of heterogeneity (Martin et al., 1993; Zagonari, 1998)

• Adaptation – Mitigation in period 1, adaptation in period 2 (Buob and Stephan, 2011;

Ingham et al., 2013) – Discussion of the private/public aspects of adaptation (Mendelsohn,

2000), but not of its implications for warming

Missing:

Full characterization of asymmetry of impacts Full integration of mitigation and (potentially emitting) adaptation

6

A 2-player Model of Space Heating and Cooling

7

cold region

warm region

Energy for heating (ec)

CO2 concentration

Atmospheric temperature ( T ) Climate

sensitivity Carbon intensity

Energy for cooling (ew)

Mitigation in the cold region (qc)

Carbon sink

Mitigation in the warm region (qw)

“Perfect adaptation”

“Perfect adaptation”

-

-

-

+

“Adaptive Mitigation”

,ce q T q bT

8

,we q T q dT

Controlled mitigation (energy/carbon efficiency)

“Perfect” adaptation to asymmetric, linear impacts

Energy use

Warming , ,c c w wT e q T e q T sT

2, 2i ii c w m q q

Natural sink

Technology

Retroaction

Taxonomy of Public Goods

9

damages (d)

benefits (b)

d = b

d = -b

Public bad

Public good

Asymmetric public bad

Heterogeneous public bad

0 Heterogeneous public good

Asymmetric public good

Focus on the Public Bad Corner ( d > | b | )

10

Usually studied: homogeneous & heterogeneous public bad

Our study: More general public bad (incl. asymmetric)

Optimization Problems

,,0

Minimize , e d

subject to , ,

c w

i i i rt

iq q

i c w

i i i i

e q T m q t

T e q T e q T sT

Energy expenditure

Mitigation cost

11

, , ,i i i i i i i i ie q T m q e q T e q T sT

, , ,i i i i i i i

i

e q T m q e q T e q T sT Cooperative

Non-coop., fwd-looking

,i i i ie q T m q Non-coop.,

myopic

Optimality Conditions

12

r b d s b d

Optimal mitigation

Co-state Dynamics

c c

w w

r b d s b

r b d s d

Cooperative (social optimum)

Forward-looking (Nash equilibrium)

Stable steady state d d 0 T

T T s d b

T is absent Open-loop and feedback coincide, ensuring subgame perfectness

d d 0 1i i i i iq q

d dir T

Co-state Variables at Steady State

13

d b

r s b d

0

0

c

w

b

r s b d

d

r s b d

Global public bad

(small) local public good

(large) local public bad

Social optimum (S)

Nash (N)

0 Myopic (M)

0

d b

Not shown here: Co-state variables (hence mitigation efforts) are STATIONARY

Heterogeneous Public Bad (canonical – both lose)

14

M

S

N

qw

Free-riding

Free-riding

Assumptions

0

c w

d b

qc

1:1

Asymmetric Public Bad ( = gainer & loser)

15

S

qw

qc

N

Free-riding

Free-driving

Assumptions

0

c w

d b

M

1:1

Five Regimes of Asymmetric Public Bad (d>b>0)

16

Global public good

Unstable steady state

v

i

ii

iii

iv

Mitigation ratio

Imp

act

rati

o d

/ b

w c

1

N S

d b

T T

21 1

N M

d b

1 s b

N M

d b

T T

Efficiency-Warming Tradeoffs

17

Glo

bal

War

min

g

Economic Efficiency

M

S

Incr

easi

ng

da

ma

ges

i

ii

iii

iv

v

Ni

Nii Niii

Niv

Nv

cheaper mitigation in WARM

cheaper mitigation

in COLD

Interpretation: Bilateral Agreements

18

Glo

bal

War

min

g

Economic Efficiency

M

S

Heterogeneous bads, e.g., China vs. USA

e.g., India vs. USA

e.g., India vs. Russia

1

2

3

4

1

2

3

4

1

2

3

4

1

2

3

4

1

2

3

4

1

2

3

4

0.5 1 2

0.5 1 2 0.5 1 2 0.5 1 2

0.5 1 2 0.5 1 2

Nash Social optimum Myopia Social optimum Myopia Nash

Hicks-Kaldor: c gains, w loses

Pareto: c and w gain

Hicks-Kaldor: w gains, c loses

c gains, w loses

w gains, c loses

c and w lose

Het

ero

gen

. bad

(d

/-b

vs.

μ)

Asy

mm

etri

c b

ad (

d/b

vs.

μ)

Welfare Improvements

Homogeneous bad (canonical)

Optimal Pigouvian Prices (pki)

20

1

ii kk i

k

p

(Positive) externality

Negative externality

=>

Two externalities necessitate two prices

UNLESS

the players are myopic (λMi =0) or identical (λM

c = λMw)

Conditions under which a dynamic public bad can be under-supplied

Restrictions on Pareto improvements (esp. )

A case for differentiated emission prices, which can include (small) subsidies for GHG-intensive adaptation

21

Taking into account asymmetries in adaptation and mitigation, we find

M N

Discussion

• Climate change restricted to smooth warming – No sea level rise, ocean acidification, etc. – No stochastic events, catastrophes, etc.

• Linear-state structure

– Pertinent at the global scale, less at the local one (e.g., Dell et al., 2014) – Flexibility of open loop & strength of feedback (subgame perfectness)

• Specific technology

– Emissions induced by adaptation: what potential? – No accumulation of mitigation capital

Our model is therefore most relevant to Large countries (China + USA ~ 40% of global emissions) Sectors such as buildings, agriculture (resp. 6% and 24% of emissions) Short-term, moderate impacts

22

23

Extension: Non-linear Adaptation

24

2

i ia T T T

ia T wa T ca T

cTwT

Ad

apta

tio

n C

ost

Temperature

cw

Asym. PG Asym. PB Heterogeneous Public Good Heterogeneous Public Bad

2

with

i i

i i

i i

T Ta T T T

T T

(Burke et al., 2015) 13 CT

Quadratic-State Model

,i ie q T q a T

25

Energy use

Warming , ,c c w wT e q T e q T sT

2, / 2i ii c w m q q Technology

Adaptation 2

i ia T T T

Non-linear payoff function Open-loop and feedback no longer coincide Non-linear transition equation Numerical resolution (Kossioris et al., 2008)

I’ll emphasize a graphical exposition 26

27