DSICE - Dynamic Stochastic General Equilibrium Analysis of Climate

Introduction DICE DSICE Uncertain Climate Change & Discounting Conclusion

DSICE - Dynamic Stochastic General EquilibriumAnalysis of Climate Change Policies and

Discounting

Yongyang Cai(Hoover Institution)

Kenneth L. Judd(Hoover Institution)

Thomas S. Lontzek(University of Zurich)

July 29, 2011Yongyang Cai (Hoover Institution) Kenneth L. Judd (Hoover Institution) Thomas S. Lontzek (University of Zurich)

DSICE - Dynamic Stochastic General Equilibrium Analysis of Climate Change Policies and Discounting


I All IAMs (Integrated Assessment Models) are deterministic

I Most are myopic, not forward-looking

I This combination makes it impossible for IAMs to consider decisions ina dynamic, evolving and uncertain world

I We formulate dynamic stochastic general equilibrium extensions ofDICE (Nordhaus)

I Conventional wisdom: ”Integration of DSGE models with long runintertemporal models like IGEM is beyond the scientific frontier at themoment” (Peer Review of ADAGE and IGEM, June 2010)

I Fact: We use multidimensional dynamic programming methods,developed over the past 20 years in Economics, to study dynamicallyoptimal policy responses

Yongyang Cai (Hoover Institution) Kenneth L. Judd (Hoover Institution) Thomas S. Lontzek (University of Zurich)



Today’s Presentation

I Fix DICE

I Introduce DSICE

I Apply DSICE to ask what is optimal policy when faced with potentialtipping points?




I DICE: maximize social utility subject to economic and climateconstraints

max ct ,lt ,µt

∞∑t=0

βtu(ct , lt)

s.t. kt+1 = (1 − δ)kt +Ωt(1 −Λt)Yt − ct ,

Mt+1 = ΦMMt + (Et , 0, 0)>,

Tt+1 = ΦTTt + (ξ1Ft , 0)>,

I output: Yt ≡ f (kt , lt , t) = Atkαt l1−αt

I damages: Ωt ≡ 11+π1TAT

t +π2(TATt )2

I emission control effort: Λt ≡ ψ1−θ2t θ1,tµ

θ2t




I Mass of carbon concentration: Mt = (MATt ,MLO

t ,MUPt )>

I Temperature: Tt = (TATt ,T LO

t )>

I Total carbon emission: Et = EInd,t + ELand,t , where

EInd,t = σt(1 − µt)(f1(kt , lt , θt , t))

I Total radiative forcing (watts per square meter from 1900):

Ft = η log2(MATt /MAT

0 ) + FEXt




I DICE analysis

I 10 year time periods

I First, we compare the deterministic case to Nordhaus DICE model

I Strange finite-difference scheme for dynamics, incompatible with anymethod in the numerical literature

I We build a 10-year and 1-year period length model, and find Nordhaus’approach is unreliable:




0 100 200 300 400 500 6000

2

4

6

8

10

12x 104

Year

Capital Stock

N10CJL10CJL4CJL2CJL1




0 100 200 300 400 500 6000.5

1

1.5

2

2.5

3

3.5

4

4.5

Year

Temparature of Atmosphere





0 100 200 300 400 500 600800

900

1000

1100

1200

1300

1400

1500

1600

1700

Year

Carbon in Atmosphere





0 50 100 1500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Year

Emission Control Rate





0 50 100 1500

50

100

150

200

250

300

350

400

Year

Carbon Tax





Cai-Judd-Lontzek DSICE Model:Dynamic Stochastic Integrated Model of Climate and Economy

DSICE = DICE 2007

− constraint on savings rate , i .e. : s = .22

− ad hoc finite difference method

+ stochastic production function

+ stochastic damage function

+ 1-year period length

stochastic means: intrinsic random events within the specific model, notuncertain parameters




I DSICE: solve stochastic optimization problem

max ct ,lt ,µt E

∞∑t=0

βtu(ct , lt)

s.t. kt+1 = (1 − δ)kt +Ωt(1 −Λt)Yt − ct ,

Mt+1 = ΦMMt + (Et , 0, 0)>,

Tt+1 = ΦTTt + (ξ1Ft , 0)>,

ζt+1 = gζ(ζt ,ωζt ),

Jt+1 = g J(Jt ,ωJt )

I Yt ≡ f (kt , lt , ζt , t) =

ζt Atkαt l1−αt

I Ωt ≡

Jt1+π1TAT

t +π2(TATt )2

, Λt ≡ ψ1−θ2t θ1,tµ

θ2t

I ζt : productivity shock, Jt : damage function shock




I DP model for DSICE :

Vt(k , ζ, J,M,T ) = maxc,l,µ

u(c , l) + βE[Vt+1(k+, ζ+, J+,M+,T+)]

s.t. k+ = (1 − δ)k +Ωt(1 −Λt)f (k , l , ζ, t) − c ,

M+ = ΦMM + (Et , 0, 0)>,

T+ = ΦTT + (ξ1Ft , 0)>,

ζ+ = gζ(ζ,ωζ),

J+ = g J(J,ωJ)




Application: Uncertain climate change & discounting

I Standard assumption in DICE: damages are a function ofcontemporaneous temperature

I However, many scientists are worried about triggering abrupt andirreversible climate change

I Consequence: permanent and significant damage over a large timehorizon

I Abrupt climate change must be modeled stochastically

I How does optimal emission control policy respond to the threat ofabrupt and irreversible climate change?

I What is the appropriate discount rate?




hazard rate

I Lenton et al. (PNAS, 2008) characterize some major tipping elementsin the earth’s climate system:

Tipping Element key Impacts

Thermohaline circulation reg. sea level rise (1m)collapse cool North Atl, warm south. ocean

West Antarctic ice sheet sea level (up to 5 m)changes in El Nino Drought (e.g: SE Asia)

Southern Oscillation + El Nino frequency and persistence

Permafrost melting enhanced global warming due toCH4 and CO2release




Zickfeld et al. (2007, Climatic Change): Expert’s subjective probability (%)that a collapse of THC will occur or be irreversibly triggered by 2100

Effect of un




I Kriegler et al. (PNAS, 2009) conduct an extensive expert elicitation on

some major tipping elements and their likelihood of abrupt change.

I THC collapse

I Greenland ice sheet melting

I WestAntarctic ice sheet melting

I Amazon rainforest dieback

I ElNino/Southern Oscillation

I They compute conservative lower bounds for the probability of

triggering at least 1 of those events

I 0.16 for medium (2 − 4C) global mean temperature change

I 0.56 for high (above 4C) global mean temperature change




We calculate (reverse engineer) the annual hazard rate of THC collapse as a

function of global mean temperature rise based on Zickfeld et al. (2007, Climatic

Change)

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 60

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

∆ T − from preindustrial level

annu

al h

azar

d ra

te

average optimistic expert

average pessimistic expert




I The time of tipping is a poisson process

I Once the tipping point is reached the shock to the damage function

persists

I We assume a tipping point causes a permanent 10 % reduction in

output.

I Probability of a tipping point occurring at time t is equal to the hazard

rate as a function of temperature at t

I ht = 0.01 · Tt − T2000

I We simulate 1000 optimal paths

I We report mean, median and quartiles




I the Nordhaus (DICE) specification of

externality implies a rising emission control

rate

I intuition

I temperature is rising

I damage at time t is rising

I present value of damages is rising

I marginal benefit of emissions control is

rising




In RICE (Nordhaus, 2010 PNAS) seal level rise is a linear function of

current temperature and hence persistent. However, it is reversible and

deterministic.

DSICE has stochastic irreversible damages.




50 100 150 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Stage


50 100 150 200

0.15

0.1

0.05

0

0.05

0.1

0.15

Stage

Deviation of Emission Control Rate

I red: 0 % and

100% quartiles

represent outer

envelopes of the

paths

I blue: 25% and

75% quartiles

I cyan: median

I black: expectation

of (average) at t




50 100 150 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Stage


50 100 150 200

0.15

0.1

0.05

0

0.05

0.1

0.15

Stage

Deviation of Emission Control RateI µ is higher if the

tipping has not yet

occurred

I the drop in µ after

the tipping

represents the

effort to delay

tipping

I the anti-tipping

effort is constant

over time even

though the danger

and costs are rising




50 100 150 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Stage


50 100 150 200

0.15

0.1

0.05

0

0.05

0.1

0.15

Stage

Deviation of Emission Control Rate

I constant

anti-tipping effort

in the face of a

rising tipping

hazard implies a

low effective

discount rate, as is

the case with

insurance

expenditures.




0 20 40 60 80 100 120 140 160 1800

0.05

0.1

0.15

0.2

0.25

Year

Difference of Emission Control Rate

10% Damage2% Damage1% Damage I sensitivity of

results to damage

factor

I optimal policy

towards tipping

applies a very

small discount rate

to future damage

from tipping

(insurance

analogy)




Summary of Application

I DSICE is the first example of a stochastic IAM

I DSICE models tipping points where current temperature can have a

permanent damage effect on output

I DICE model damage function does not incorporate this kind of

externality which is in the nature of tipping points.

I DICE implies steeply rising emission control rates

I DSICE implies a constant effort to delay a catastrophe despite the

rising prob. of crossing a tipping point and higher expected damage as

percentage of GDP

I Policies towards catastrophes resemble insurance expenditures which

always have a negative return




Conclusion

I Stochastic IAM analysis with short time periods is tractable

I DSICE implies a constant effort to delay a catastrophe, not a ”ramp”

I Including stochastic elements in climate and economics can

substantially effect policy results



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