Royal Economic Society

Royal Economic Society

Endogenous growth, convexity of

damages and climate risk: how

Nordhaus’ framework supports deep

cuts in carbon emissions

Simon Dietz and Nicholas Stern

London School of Economics

RES Manchester 2015

Gross underestimation of risk

• “There are very strong grounds for arguing

that [IAMs] grossly underestimate the risks of

climate change”

1a. Underlying exogenous drivers of growth (in one-

good models)

1b. Damage functions that only work on annual

output

2. Quantitatively weak damage functions

3. Very limited distributions of risk

An illustration from Nordhaus’ DICE

• Production, without climate change

�� , ��

�

• Production with climate change

�� 1 � ��

�

• The damage multiplier

�� 1/�1 � ��

where π1 = 0 and π2 ≈ 0.003

• Temperature is a complex function of emissions, climate sensitivity = 3degC

Examining the proposition

• In this paper we build on DICE by including

1a. Endogenous growth

1b. Climate damages to drivers of growth, i.e. capital

stocks or TFP

2. Strong convexity in the damage function

3. Large climate risk via climate sensitivity

parameter

Endogenous growth (i)

• A model of capital damages and learning by investing (Arrow-Romer)

– Production

�� 1 � ��

��

– Capital accumulation

�� 1 � �� 1 � ��

– Partitioning of damages

��

�� 1 ��1 � ��

�1 � ��

Endogenous growth (ii)

• A model of endogenous TFP and damages to TFP

– Production

�� 1 � ��

��

– Capital and TFP dynamics

�� 1 � �� 1 � ��

1 � �� !��

"#

– Partitioning of damages

��

�� 1 ��1 � ��

�1 � ��

Convexity of damages

• Damage function suggested by Weitzman

(JPET, 2012)

�� 1 � 1/�1 � �� $��

%.'()�

• Three scenarios:

1. Set π3 = 0, i.e. standard DICE (‘Quadratic’)

2. Set π3 so that D = 0.5 at T = 6 (‘Weitzman’)

3. Set π3 so that D = 0.5 at T = 4 (‘High’)

Climate sensitivity distribution-1 0 1 2 3 4 5 6 7 8

Source: own fit

of IPCC AR5

WG1, SPM

Results: baseline growth

Results: optimal emissions cuts

2015 2055 2105

Standard 16% 27% 45%

Quadratic damage 26% 59% 100%

Weitzman damage 31% 74% 100%

High damage 48% 100% 100%

n.b. TFP model, random S

Results: optimal carbon prices

2015 2055 2105

Standard 44$/tC 106 237

Quadratic damage 110 435 1012

Weitzman damage 147 657 1012

High damage 329 1121 1012

n.b. TFP model, random S

Results: optimal atmospheric CO2

Conclusions

• Main aim was to explore assumptions

necessary and sufficient to sustain deep

emissions cuts at the optimum

• Examine proposition that standard DICE

grossly underestimates climate risks to

economy

• Shows deep cuts are optimal even if discount

rate is high

Supplementary slides

Results: baseline atmospheric CO2

Results: baseline temperature


R O Y A L E C O N O M I C S O C I E T Y

M A N C H E S T E R , 2 0 1 5

R I C K V A N D E R P L O E G

O X F O R D U N I V E R S I T Y

( W I T H A A R T D E Z E E U W )

CLIMATE TIPPING AND ECONOMIC GROWTH

How to model catastrophes?

Real possibility that a discontinuous change in damages or in carbon cycle will take place. This change can be abrupt as with shifts in monsoonal systems, but loss of ice sheets resulting in higher sea levels have slow onsets and can take millennium or more to have its full effect (Greenland 7m and Western Antarctica 3m, say) and may already be occurring.

9 big catastrophes are waiting to happen, not all at same time.

Collapse of the Atlantic thermohaline circulation is fairly imminent and might occur at relatively low levels of global warming. This affects regions differently, but we capture this with a negative TFP shock.

We look at TFP calamity and also at K, P and climate sensitivity calamities. Expected time of calamity falls with global warming.

Possible Tipping Points Duration before

effect is fully realized (in years)

Additional Warming by 2100

0.5-1.5 C 1.5-3.0C 3-5 C

Reorganization of Atlantic MeridionalOverturning Circulation about 100 0-18% 6-39%

18-67%

Greenland Ice Sheet collapse at least 300 8-39% 33-73%

67-96%

West Antarctic Ice Sheet collapse at least 300 5-41% 10-63%

33-88%

Dieback of Amazon rainforest about 50 2-46% 14-84%

41-94%

Strengthening of El Niño-Southern Oscillation about 100 1-13% 6-32% 19-49%

Dieback of boreal forests about 50 13-43% 20-81%

34-91%

Shift in Indian Summer Monsoon about 1 Not formally assessed

Release of methane from melting permafrost Less than 100 Not formally assessed.

Probabilities of Various Tipping Points from Expert Elicitation

Previous work

Gollier (2012): Markov 2-regime switching model & exogenous risk of big drop in GDP growth much higher SCC.

Threat of doomsday scenario: Bommier et al. (2013).

Regime shifts with uncertain arrival of catastrophe: Partial equilibrium: Tsur & Zemel (1996), Karp & Tsur (2011),

Naevdal (2006), Polasky, de Zeeuw & Wagener (2011).

General equilibrium: Lemoine and Traeger (2014) use Ramsey model to understand effect of release of permafrost as instantaneous doubling of ECS and of learning and multiple catastrophes. Cai, Judd and Lontzeck (2015) similar and focus on shock to damage function and numerical challenge.

Messages

Chance of catastrophe can lead to much higher SCCwithout an extremely low discount rate provided hazard rises sharply with temperature. The motive is to avert risk.

There is also a social benefit of capital (SBC) which gives a rationale for precautionary capital accumulation and being better prepared.

Calibrate a global IAM with Ramsey growth with both catastrophic and marginal climate damages.

Show role of convexity of the hazard function.

Show effect of more intergenerational inequality aversion and thus more risk aversion on SCC and SBC: i.e., on carbon tax and capital subsidy.

Climate disaster and Ramsey growth

Concave time-separable utility function.

Concave and CRTS production function.

Factors of production: capital K, labour, fossil fuel and renewables. All factors are imperfect substitutes.

Fossil fuel E is abundant at cost d .

Supply of renewable R is infinitely elastic at cost c.

Extremely simple carbon cycle: nothing stays up permanently in the atmosphere, constant decay rate.

Hazard of catastrophic drop in TFP is H(P) and is modelled with Poisson process with H 0

Climate disaster and Ramsey growth

0, ,

0

0

max E ( ( )) subject to

( ) ( ( ), ( ), ( )) ( ) ( ) ( ) ( ),

0, (0) ,

( ) ( ) ( ), 0, (0)

t

C E Re U C t dt

K t AF K t E t R t dE t cR t C t K t

t K K

P t E t P t t P

0

0

,

( ) , 0 , ( ) (1 ) , , 0 1,

Pr[ ] 1 exp ( ( )) , 0.

t

P

A t A t T A t A t T

T t H P s ds t

Backward induction

For time being, damages only result from calamities.

Solve post-catastrophe problem as standard Ramsey problem to give post-calamity value function:

Solve before-catastrophe problem from the HJB:

( , ).AV K

, ,

'( ) ( , ),

( , ) Max ( )

( , ) ( , , ) ( , )( )

with optimality conditions

( , , ) , ( , ) / ( , ) 0,

(

( ,

) ( , ) ( , )

, ) .

B B

K

B

C E R

B BK P

B BE

R

A B

P KU C V K P

V K P U C

V K P AF K E R dE cR C K V K P E P

AF K E R d V K P V

H P V K V K

K P

AF K E

P

R c

Precautionary saving and curbing risk of calamity

The Euler equation has a precautionary return or social benefit of capital (SBC):

The SCC is:

1/

( , , , ) with

( , )( ) 1 ( ) 1 0.

'( )

BK

A BK

A

C Y K d c A C

V K CH P H P

U C C

' ( ) ( ') ( ') ( ') '' ( )

( ') '

( ) ( )( ) exp

' ( ) ( ) ( ) exp / ' ( ) .

B As

B t

s

t

t

B A B

t

V VH P s r s s H P s ds

U C s

H P s ds

s st ds

H P s V s V s ds U C t

Interpretation

‘Doomsday’ scenario has VA = 0, so the discount rate is increased frantic consumption and less investment. Mr. Bean!

But if world goes on after disaster, precaution is needed. Since consumption will fall after disaster, SBC > 0 and the discount rate is reduced. This calls for precautionary capital accumulation (if necessary internalized via a capital subsidy)

The SBC is bigger if the hazard and size of the disaster are bigger. And if intergenerational inequality aversion (CRIIA) is bigger.

Illustrative calibration of hazard function

Use H(826) = 0.025 and H(1252) = 0.067

So doubling carbon stock (rise in temperature with 3 degrees) brings forward expected time of calamity from 40 to 15 years.

After-disaster, naïve and before-disaster steady states

After disaster

Naive solution

Constant hazard h = 0.25

Linear hazard

Quadratic hazard

EIS = 0.8

Capital stock (T $) 276 392 472 530 486 436

Consumption (T $) 41.3 58.6 59.4 59.6 59.2 58.9

Fossil fuel use (GtC/year) 7.3 10.4 11.0 9.7 7.7 7.7

Renewable use (million GBTU/year) 8.2 11.7 12.4 12.7 12.2

11.8

Carbon stock (GtC) 1218 1731 1838 1623 1281 1279

Precautionary return (%/year) 0 0 0.76 1.24 0.990.57

SCC ($/tCO2) 0 0 0 22.4 56.9 51.0

Precautionary capital can be negative if hazard function is very convex

Steady-state pre-disaster K is bigger than naive K iff:

This is always so if hazard constant and SCC zero. With convex enough hazard function effects of SCC can

outweigh effect of SBC, so inequality need not hold. With quartic SCC is very high and SBC very low. The high

carbon tax averts disaster so much that there is less need for precautionary capital accumulation. Put differently, precautionary capital is bad as it induces more fossil fuel use, more global warming and a relatively big increase in hazard of climate disaster. So avoid Green Paradox.

1 *

*.

B

B

d

d

Role of intergenerational inequality aversion

Much debate is about discount rate but CRIIA = 1/is at least as important.

Higher or lower CRRA and CRIIA has two effects: Lower CRRA, so lower SBC, less precautionary saving and thus

less fossil fuel demand and emissions. Need lower carbon tax

Lower CRIIA so more prepared to sacrifice consumption and have a higher carbon tax.

With = 0.8 and linear hazard first effect dominates: lower SCB and lower SCC so less capital before disaster and less sacrificing of consumption.

Gradual damages A(Temp) and the SCC

Before-disaster SCC has in general 3 components:

( ( ')

conventional Pigouvian social cost of carbon

( ( ')

'raising the stakes' effec

( ) ' ( ) ( ) ' ( )' ( )

( ) ( ) , , ( )' ( )

s

t

s

t

H P s ds

t

H P s dsAP

t

t A P s F s U C s e dsU C t

H P s V K s P s e dsU C t

t

( ( ')

'risk averting' effect

, 0 .' ( ) ( ) ( )' ( )

s

tB AH P s ds

tV V t TH P s s s e ds

U C t

Catastrophic and marginal climate damages

Naïvesolution

20% shock in TFP 10% shock in TFP

after shock linear quadratic

after shock linear quadratic

Capital stock (T $)378 271 492 465 323 431 421

Consumption (T $)57.1 40.8 58.3 58.2 48.7 57.8 57.8

Carbon stock (GtC)1502 1107 1287 1161 1303 1425 1320

Temperature (degrees

Celsius)4.00 2.68 3.33 2.88 3.38 3.77 3.44

Precautionary return (%/year)

0 0 1.10 0.90 0 0.57 0.49

SCC ($/GtCO2) 15.4 11.0 54.8 71.2 13.2 29.8 41.5

marginal 15.4 11.0 4.3 5.7 13.2 3.8 4.7

risk averting 0 0 35.0 51.9 0 12.4 24.2

raising stakes 0 0 15.4 13.7 0 13.7 12.5

Effect of climate sensitivity on damages

Carbon and capital catastrophes

Naïve solution

CS jumps from 3 to 4

20% drop in P

20% drop in K

Aftercalamity

Before calamity

Capital stock (T $) 379 372382

381 433

Consumption (T $) 57.1 56.3 57.3 57.1 57.6

Carbon stock (GtC) 1503 13741400

1490 1534

Temperature (degrees Celsius) 4.00 4.823.69

3.96 4.09

Precautionary return (%/year) 0 0

0.05

0.03 0.57

SCC ($/GtCO2) 15.5 26.726.5

16.9 18.5

Marginal 15.5 26.74.1

3.8 3.8

risk averting 0 02.2

1.4 2.5

raising stakes 0 020.2

11.7 12.2

Conclusions

Small risks of climate disasters may lead to a much bigger SCC even with usual discount rates. Rationale is to avoid risk.

Also need for precautionary capital accumulation.

Need estimates of current risks of catastrophe and how these increase with temperature.

Recoverable shocks such as P or K calamities are less problematic.

Catastrophic changes in system dynamics unleashing positive feedback may be much more dangerous than TFP calamities.

Extension: North-South perspective

Carbon taxes and capital stocks

Non-coop bias in carbon tax, not in precautionary return on capital

Regime shifts

Other extensions

Adaptation capital (sea walls, storm surge barriers) increases with global warming: trade-off with productive capital.

Positive feedback in the carbon cycle changes carbon cycle dynamocs(e.g., Greenland or West Antarctica ice sheet collapse).

Multiple tipping points with different hazard functions and lags (Cai, Judd, Lontzek). ‘Strange’ cost-benefit analysis (Pindyck).

Learning about probabilities of tipping points, but also about whether they exist all (cf. ‘email-problem’). How to respond to a tipping point which may never materialize?

Second-best issues: Green Paradox can lead to ‘runaway’ global warming if the system is tipped due to more rapid depletion of oil, gas and coal in face of a future tightening of climate policy (Ralph Winter, JEEM, 2014).

Pure rate of time preference, 0.014

Elasticity of intertemporal substitution, 0.5 (and 0.8)

Share of capital in value added, 0.3

Share of fossil fuel (oil, gas, coal) in value added, 0.0626

Share of fossil fuel in total energy, 0.9614

Share of energy in value added, 0.0651

Share of labour in value added, 1 0.6349

Depreciation rate of manmade capital, 0.05

Initial level of GDP, Y0 63 trillion US $

Initial capital stock, K0 200 trillion US $

Initial fossil fuel use, E0 468.3 million G BTU = 8.3 GtC

Initial renewable use, R0 9.4 million G BTU

Total factor productivity, A 11.9762

Cost of fossil fuel, d 9 US $/million BTU = 504 US $/tC

Cost of renewable, c 18 US $/million BTU

Initial stock of carbon, P0 826 GtC = 388 ppm by vol. CO2

Pre-industrial carbon stock 596.4 GtC = 280 ppm by vol. CO2

Fraction of carbon that stays up in atmosphere, 0.5

Eventual climate shock, 0.2 (and 0.1)

Equilibrium climate sensitivity 3 (and 4)


Why finance ministers favor carbon taxes, even ifthey do not take climate change into account

Ottmar Edenhofer, Max Franks, Kai Lessmann

01.04.2015

MOTIVATION

MODEL SETUP

RESULTS

,Ottmar Edenhofer, Max Franks, Kai Lessmann */18

The climate problem at a glance

Resources and reserves to remainunderground:

• 80 % coal

• 40 % gas

• 40 % oil

Source: Bauer et al. (2014), Jakob, Hilaire (2015),

Ottmar Edenhofer, Max Franks, Kai Lessmann 1/18

The Globalisation Paradox: A Trilemma

,Ottmar Edenhofer, Max Franks, Kai Lessmann 2/18




Source: Benassy-Quere et al. (2010)


Resource rents as solution

Source: Jakob et al. (2015),


Research questions

• Most economists agree on carbon pricing to address theclimate externalty, many prefer taxes.

• What is the role of a carbon tax under the assumption that noclimate externality exists?

• Can carbon taxes finance infrastructure more efficiently thancapital taxes when input factors are mobile?

• What are the supply side dynamics when resource importingcountries tax carbon?


Research questions






Research questions






Research questions






Results

1. In Nash equilibrium, carbon tax more efficient than capital tax.

Both taxes subject to race to the bottom.

Carbon tax captures part of the Hotelling rent.

2. No green paradox:

Demand side fully determines extraction.

Carbon taxes postpone extraction,

and reduce cumulative emissions.

3. Both results are robust under different strategic settings:(Non-)cooperative importers, (non-)strategic exporter.


Results










Results










Results










Results










Results










Results










Results










MOTIVATION

MODEL SETUP

RESULTS




Government:

maxτζ

W =T∑

t=0

LtU(C/L)

(1 + ρ)t, ζ ∈ {K ,R,C , L}

IG + Tax transfer = rτKK + τRR + τCC + wτLL

Gt+1 = Gt(1− δ) + IGt

Firm:

maxK ,R,L

ΠF = F (K ,G ,R, L)− r(1 + τK )K − (p + τR )R − w(1 + τL)L

=⇒ FK = r(1 + τK ), FR = p + τR , FL = w(1 + τL)

Household:

maxC/L

W =T∑

t=0

U(Ct/Lt)

(1 + ρ)t,

Ct(1 + τC ,t) = wtLt + rtKt − It + ΠFt + Tax transfer

t


Government:

maxτζ

W =T∑

t=0

LtU(C/L)

(1 + ρ)t, ζ ∈ {K ,R,C , L}


Gt+1 = Gt(1− δ) + IGt

Firm:

maxK ,R,L



Household:

maxC/L

W =T∑

t=0

U(Ct/Lt)

(1 + ρ)t,


t


Government:

maxτζ

W =T∑

t=0

LtU(C/L)

(1 + ρ)t, ζ ∈ {K ,R,C , L}


Gt+1 = Gt(1− δ) + IGt

Firm:

maxK ,R,L



Household:

maxC/L

W =T∑

t=0

U(Ct/Lt)

(1 + ρ)t,


t


Government:

maxτζ

W =T∑

t=0

LtU(C/L)

(1 + ρ)t, ζ ∈ {K ,R,C , L}


Gt+1 = Gt(1− δ) + IGt

Firm:

maxK ,R,L



Household:

maxC/L

W =T∑

t=0

U(Ct/Lt)

(1 + ρ)t,


t





Resource exporter: Resource market:

Capital market:

maxRt

T∑t=0

ptRt − ct∏ts=0(1 + rs )

R supply =∑

j

Rdemandj

p = pj ∀j

∑j

K supplyj =

∑j

K demandj

r = rj ∀j


Resource exporter: Resource market: Capital market:

maxRt

T∑t=0

ptRt − ct∏ts=0(1 + rs )

R supply =∑

j

Rdemandj

p = pj ∀j

∑j

K supplyj =

∑j

K demandj

r = rj ∀j,


Nash equilibrium, two sub-games,

solved for

non-cooperative behavior

maxτ i

K,τ i

R

Wi , given τ jK , τ

jR , i 6= j

or cooperative behavior of governments

max{τ i

K,τ i

R}i=1,2

W1 + W2



solved for


maxτ i

K,τ i

R


jR , i 6= j


max{τ i

K,τ i

R}i=1,2

W1 + W2



solved for


maxτ i

K,τ i

R


jR , i 6= j


max{τ i

K,τ i

R}i=1,2

W1 + W2



solved for


maxτ i

K,τ i

R


jR , i 6= j


max{τ i

K,τ i

R}i=1,2

W1 + W2


Nash equilibrium, two sub-games, solved for


maxτ i

K,τ i

R


jR , i 6= j

or

cooperative behavior of governments

max{τ i

K,τ i

R}i=1,2

W1 + W2


Nash equilibrium, two sub-games, solved for


maxτ i

K,τ i

R


jR , i 6= j


max{τ i

K,τ i

R}i=1,2

W1 + W2


MOTIVATION

MODEL SETUP

RESULTS

• Numerical solution due to high complexity (dual game structure,intertemporal optimization, two international markets, etc.)

• Calibration: Two symmetric countries to avoid that results are driven byasymmetries.

• Flexibility of modelling framework also allows for calibration to setupswith specific regions (e.g. USA, EU, Australia, and OPEC).


MOTIVATION

MODEL SETUP

RESULTS

• Numerical solution due to high complexity (dual game structure,intertemporal optimization, two international markets, etc.)

• Calibration: Two symmetric countries to avoid that results are driven byasymmetries.

• Flexibility of modelling framework also allows for calibration to setupswith specific regions (e.g. USA, EU, Australia, and OPEC).


Single instrument portfolio


Single instrument portfolio


Mixed portfolio


Timing and volume effects


Timing and volume effects


No green paradox: Demand for infrastructure fullydetermines supply side dynamics

The optimal financing of infrastructure with a carbon tax from an importing

government’s perspective impliesτR,t+1−τR,t

τR,t< rt − δ. Thus, extraction is

postponed (see, e.g., Edenhofer and Kalkuhl, 2011).


Assumptions about strategic behavior of exporter

• Portfolios, which include the carbon tax τR yield higher NPVof consumption in importing countries.

• This finding is independent of whether the exporter mayinteract strategically or not.


Summary of results

1. Carbon tax more efficient than capital tax.

asymmetry between capital and carbon as tax base,

only the resource stock gives rise to rent.

2. Carbon tax delays extraction, reduces cumulative emissions.Timing of infrastructure demand fully determines supply sidedynamics.

3. Results are robust under different sorts of strategic behavior:Cooperating importers, strategic exporter.


Summary of results







Summary of results







Summary of results







Summary of results







Policy conclusions

• Carbon pricing can help to mitigate the race to the bottom.

• The supply side dynamics of carbon pricing matter, but poseno environmental problem.

• Rethink role of environmental policy:Not only environmental ministers should favor carbon pricing,but also finance ministers.


Policy conclusions





Policy conclusions





Backup slides


There is far more carbon in the ground than emittedin any basline scenario

Source: Edenhofer, Hilaire, Bauer


The scarcity rent of CO2 emissions

• Fossil fuel rents decrease with theambition of climate policy.

• If the optimal CO2 price isimplemented globally, this loss isovercompensated by the carbonrent.

• The revenues of the carbon tax orauctioning of emission permits canbe used to finance tax reductions,infrastructure investments, ordebt reduction.

Source: Bauer et al. (2013),














Volume effects under behavioral assumptions


The resource rent


Welfare evaluation


Welfare evaluation


No problem with time inconsistency


No problem with time inconsistency


If taxing carbon is so good, why do we not see moreof it in reality?

1. In the past: ignorance on the part of policy-makers. Today not trueanymore in many places.

2. Practical problems, caused e.g. by spacially differentiated taxes, complextrading rules for non-uniformly mixes pollutants, etc...

3. Institutional problems:

Cost-effectiveness ranked lower in regulators list of multiple policyobjectives.Ethical implications: Tax debases notion of environmental quality(Kelman, 1981); emission permits as ’right to pollute’.

4. Resistance from those with vested interest in preservation of existingsystem.

’... all of the main parties involved [have] reasons to favor[command-and-control policies]: firms, environmental advocacy groups,organized labor legislators and bureaucrats’ (Stavins, 1998, p.72).

Source: Hanley et al. (2007)


Why might public spending be too low?How can additional revenues from climate policyenhance welfare?

1. Weak institutions (non-OECD).

2. Existing allocation of public funds inefficient. New revenuesfrom climate policy free to allocate.

3. Myopia towards projects with long term benefits. Climatepolicy might supply both funds and political momentum toimplement such projects.

4. If in contrast projects with long term benefits were realized,there might be a lack of fiscal tools to finance high up-frontcosts, e.g. political debt-limit.

Source: Siegmeier et al. (2015)


Model setup - solution algorithm

• Households, firms and the resource owner are Stackelbergfollowers of governments.

• Governments engage in Nash game using policy instruments:

• Repeat...for each player j

I unfix avaliable policy instrument for jI maximize objective for jI fix newly found policies

• ...until policy instruments converge.




















I unfix avaliable policy instrument for j

I maximize objective for jI fix newly found policies







I unfix avaliable policy instrument for jI maximize objective for j

I fix newly found policies

















Numerical Model: Details

CES production function


CES production function

F (K ,G ,R, L) = (α1Rs1 + (1 − α1)Z s1)

1s1

Z (K ,G , L) = (α2Xs2 + (1 − α2)Ls2)

1s2

X (K ,G ) = (α3Ks3 + (1 − α3)G s3)

1s3

CiES social welfare function

W =∑

t

Lt(Ct/Lt)1−η

1 − η

1

(1 + ρ)t

Parameter values

σ1 α1 σ2 α2 σ3 α3 η ρ

0.5 0.1 0.7 0.42 1.1 0.65 1.1 0.03, si = σi−1

σi

Source: Empirical literature, details in appendix


Intertemporal optimization: Household

maxC/L

W =T∑

t=0

U(C/L)

(1 + ρ)t,

s.t. C(1 + τC ) = wL + rK s + ΠF + Tax transfer − I

It = K st+1 − (1− δ)K s

t

taking ΠFt and Tax trans

t as given.

Use discrete Maximum Principle with Hamiltonian:

HHHt = U(Ct/Lt) + λt

[(1 + (rt − δ))K s

t + wtLt + ...

...+ ΠFt + Tax trans − Ct(1 + τC ,t)

]FOCs and TC: Lη−1

t /Cηt = λt(1 + τC ,t),

λt−1(1 + ρ) = λt (1 + rt(1 + τC ,t)− δ) ,

0 = (IT − (1− δ)K sT )λT .


Intertemporal optimization: Resource exporter

maxRt

T∑t=0

(pt − ct − τRO,t)Rt + Ψt∏ts=0(1 + rs )

, ct(St) = rt

(1 +

χ2

χ1((S0 − St)/S0)χ3

)subject to∑

t

Rt ≤ S0

where Rt = St − St+1, S0 is given, and Ψt = τRO,tRt is taken as given.

Hamiltonian:

HROt = (pt − ct − τRO,t)Rt + λR (St − Rt) + Ψt ,

FOCs and TC:

λRt = pt(1− τRO,t)− ct ,

λRt = λR

t−1(1 + rt − δ)− rtRtχ2χ3

χ1S0

(S0 − St

S0

)χ3−1

,

λRT−1ST = 0.


Intertemporal optimization: Government

maxτ

W =T∑

t=0

LtU(Ct/Lt)

(1 + ρ)t

subject to


Gt+1 = Gt + IGt − δGt

and

• the international market clearing conditions,

• the maximization problems of households, firms, and theresource exporter,

• their respective FOCs and TCs


Some parameter values

Description symbol value range sources

Intertemporal elasticity of substitution η 1.1Pure rate of time preference ρ 0.03Annual depreciation rate of capital δ 0.025Share parameter of fossil resource α1 0.11 Edenhofer et. al. (2005)Elasticity of substitution btw. Z and R σ1 0.5 0.25 – 0.92 Hogan and Manne (1979)

Kemfert and Welsch (2000)Burniaux et. al. (1992)Markandya et. al. (2007)

Share parameter of private capital α2 0.7Elasticity of substitution btw. K and G σ2 1.1 0.5 – 4 Baier and Glomm (2001)

Coenen et. al. (2012)Otto and Voss (1998)

Total factor productivity A 0.8Initial world capital [tril. US$] K0 165Initial world infrastructure [tril. US$] G0 50Initial world resource stock [GtC] S0 4000Fixed VAT rate [%] τC 16 OECD (2014)Fixed labor tax rate [%] τL 16 World Bank (2014)Time horizon [years] T 75


References (general)Benassy-Quere, Agnes , Economic Policy: Theory and Practice, 2010, Oxford University Press

Edenhofer, Ottmar and Kalkuhl, Matthias, When do increasing carbon taxes accelerate global warming? A note onthe green paradox, 2011, Energy Policy

Eichner, Thomas and Runkel, Marco, Interjurisdictional Spillovers, Decentralized Policymaking, and the Elasticityof Capital Supply, 2012, American Economic Review

Hanley, N., Shogren, J. F., White, B., Environmental Economics in Theory and Practive, 2nd edition, 2007,Palgrave Macmillan

Kelman, S. Economists and the environmental policy muddle, 1981, Public interest

van der Meijden, Gerard et. al., International Capital markets, Oil Producers and the Green Paradox, 2014,OxCarre Research Paper 130

OECD Tax data base, 2014, accessed: 2014-08-27, www.oecd.org/tax/tax-policy/tax-database.htm#vat

Siegmeier, J., Mattauch, L., Franks, M., Klenert, D., Schultes, A., A public finance perspective on climate policy:Six interactions that may enhance welfare, 2015, mimeo

Sinn, Hans-Werner, Public policies against global warming: a supply side approach, 2008, International Tax andPublic Finance

Stavins, R., What can we learn from the grand policy experiment? Lessons from SO2 allowance trading, 1998,Journal of Economic Perspectives

Tahvonen, Olli, International CO2 Taxation and the Dynamics of Fossil Fuel Markets, 1995, International Tax andPublic Finance

Withagen, Cees and Halsema, Alex, Tax competition leading to strict environmental policy, 2013, International Taxand Public Finance

World Bank, World Development Indicators, Labor tax and contributions, Accessed: 2014-08-27,data.worldbank.org/indicator/IC.TAX.LABR.CP.ZS



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