The Green Paradox The Green Paradox Reyer Gerlagh Tilburg - - PowerPoint PPT Presentation

The Green Paradox The Green Paradox

Reyer Gerlagh

Tilburg University

Introduction

Policy questions Policy questions

What is optimal climate change policy?

• Should we tax carbon dioxide emissions?
• Now / in the future / ramping up carbon taxes?
• Now / in the future / ramping up carbon taxes?
• Should we develop clean energy alternatives for oil / coal / gas?

Main insight:

• Fossil fuels markets are dynamically integrated
• Fossil fuels markets are dynamically integrated
• Expected policies at future time t affect current market (!)
• Future carbon taxes can backfire if they increase current emissions
• If we cannot set optimal pollution constraints, we must worry about effect of

policy on abundant polluting resource extraction: coal and unconventional oil

04 July 2011 2 Reyer Gerlagh

1992-1997

Discovery of Climate Change Oil connection Discovery of Climate Change – Oil connection

Oil crisis: Maedows et al 1972; Solow/Stiglitz/Dasgupta/Heal 1974 Climate change: Earth Summit Rio de Janeiro 1992 High does nothing and rising is worse: carbon taxes should keep d li i t t h f l i i (Si l i 1992) declining to cut harmful emissions (Sinclair 1992) On the optimum trend of fossil fuel taxation (Sinclair 1994) Th i l i h f b (Ul h d Ul h 1994) The optimal time path of a carbon tax (Ulph and Ulph 1994) Depletion of fossil fuels and the impact of global warming (Hoel d K d kk 1996) and Kverndokk 1996) Fossil fuels, stock externalities, and backstop technology (Tahvonen 1997) (Tahvonen 1997)

04 July 2011 3 Reyer Gerlagh

1997-2008

Silence? (‘more important’ questions) Silence? ( more important questions)

Shift in attention, from optimal climate change policy connected to exhaustible resources considerations, to distributional question: who pays who gains: (1) timing of optimal policy (discounting) & who pays, who gains: (1) timing of optimal policy (discounting) & (2) international cooperation Act or delay climate change policy? Should we discount future Act or delay climate change policy? Should we discount future damages? They will only happen after 2100, so why worry?

• Nordhaus WD (1993), Rolling the DICE: an optimal transition path for

controlling greenhouse gases, Resource and Energy Economics 15: 27-50.

We will not be able to cooperate internationally!

• Barret, S. (1994), Self-enforcing international environmental agreements,

Oxford Economic Papers 46: 878-894.

04 July 2011 4 Reyer Gerlagh

2008

The oil market matters: The Green Paradox The oil market matters: The Green Paradox

Public policies against global warming: a supply side approach (Sinn 2008) T h l t ti d f il f l t ti (St d 2008) Technology treaties and fossil-fuels extraction (Strand 2008) Bush meets Hotelling: effects of improved renewable energy technology on greenhouse gas emissions (Hoel 2008) technology on greenhouse gas emissions (Hoel 2008) Strategic Resource Dependence (Gerlagh and Liski 2011)

04 July 2011 5 Reyer Gerlagh

2010-now

The Green Paradox revised The Green Paradox, revised

Too much oil (Gerlagh 2009/2011) Biofuel subsidies and the green paradox (Grafton, Kompas, van L 2010) Long 2010) Is there really a green paradox? (van der Ploeg and Withagen 2010) 2010) Climate change and carbon tax expectations (Hoel 2010) Climate change and carbon tax expectations (Hoel 2010) The Supply Side of CO2 with Country Heterogeneity (Hoel 2011) C tti t f t hi b (H l d J 2010) Cutting costs of catching carbon … (Hoel and Jensen 2010) Can Brown Backstops undo the GP (Michielsen 2011)

04 July 2011 6 Reyer Gerlagh

Introduction

Overview Overview

Aim: connect climate policy questions to resource economics models G d ll b ild d l ( dd l t ) Gradually build model (add elements) Open research questions

04 July 2011 7 Reyer Gerlagh

Model I: Sinclair (1992,1994)

Fossil fuels & climate change Fossil fuels & climate change

High does nothing and rising is worse: carbon taxes should keep declining to cut harmful emissions (Manchester School 60:41-52) “Th k d i i f th l k h t il ll i t “The key decision of those lucky enough to own oil-wells is not so much how much to produce as when to extract it.” (1992) “Fossil fields are a stock Coal or oil burnt at one date means that

• Fossil fields are a stock. Coal or oil burnt at one date means that

there is less to burn later” (1994) Rising carbon taxes mean lower future profits for fossil fuel Rising carbon taxes, mean lower future profits for fossil fuel

• wners, and dynamic arbitrage implies they accept lower present

prices (at higher supply) p ( g pp y)

04 July 2011 8 Reyer Gerlagh

Model I: Sinclair (1992,1994)

Reduced Model Set Up Reduced Model Set Up

Sinclair has fully closed model (Cobb-Doublas production with utility max) with endogenous interest rate

• I think that’s insubstantial Main intuition is simple / partial
• I think that s insubstantial. Main intuition is simple / partial

Demand: ( )

( ) ( ( )) ( )

at c c

Q t A t D P t e P t

σ −

= =

Supply: R i i l i t

= − ( ) ( ) S t E t ( ) ( ) ( ) P t P t Z t

∞

= ∫0 (0) ( ) S E t dt

Resource price inclusive tax: Dynamic Fossil Fuel Policy:

( ) ( ) ( )

c

P t P t Z t = ≡ ( ) ( ) / ( ) z t Z t Z t

y y Hotelling rule (dynamic arbitrage):

( ) ( ) ( ) ( ) / ( )

c c

P t P t r z = +

• 04 July 2011

9 Reyer Gerlagh

Model I: Sinclair (1992,1994)

Iso elastic demand Iso-elastic demand

( ) ( )

Substitution: Total stock:

σ σ ∞ − + −

∫

( )

(0) (0)

at z r t

S E e e dt

( ) ( )

( ) (0) ( ) (0)

z r t at z r t c c

P t P e E t e E e σ

+ − +

= ⇔ =

Total stock:

σ ∞ − +

= ∫ = = ∫

( ) { ( )}

(0) (0) (0) (0)

a r z t

S E e e dt E E e dt σ = = ∫ + − (0) ( ) E e dt r z a

Present emissions increase with increasing taxes:

σ = + − (0) { ( ) } (0) E z r a S

Can we do ‘better’ = more general?

( ) { ( ) } ( )

04 July 2011 10 Reyer Gerlagh

Model I: Sinclair (1992,1994)

General demand General demand

Assume competitive market = Hotelling rule: Stock = cumulative supply = cumulative demand

( )

( ) ( )

r z t ∞ +

∫

Ch i f t t ( ) t b ff t b h i i iti l i

( ) 0 0

( , , ) ( )

r z t

S P Z z D e Z P dt Δ

∞ +

= = ∫ 0; 0;

P Z z

Δ Δ Δ < < <

Change in future tax (z), must be offset by change in initial price

P P z

dP dS d dP dz d Δ Δ Δ Δ Δ − = = = + ⇒ = <

Future higher carbon tax (dz>0) implies lower current price (dP0<0) implies higher current emissions (dE 0)

P z z

dz Δ

implies higher current emissions (dE0>0).

04 July 2011 11 Reyer Gerlagh

Model I: Sinclair (1992,1994)

Policy implications Policy implications

Sinclair emphasizes that to study climate change requires closed economy, as climate change causes major damages.

• Otherwise his analysis would resemble too much Dasgupta & Heal (1979)
• Otherwise, his analysis would resemble too much Dasgupta & Heal (1979)
• but his analysis is unclear (who understands 1992, eq (2)+(7)?)

Moreover I wonder whether closed economy + strong unrealistic Moreover, I wonder whether closed economy + strong unrealistic assumption on damages is better then partial economy Main climate change damages after 2100, main fossil fuel use a c a e c a ge da ages a e 00, a

• ss

ue use before 2100 → separation? Conclusion stands: “High does nothing and rising is worse: carbon g g g taxes should keep declining to cut harmful emissions”

• [discuss] Declining refers to ad valorem tax as price factor, per volume tax

i can increase

04 July 2011 12 Reyer Gerlagh

Model II: Ulph and Ulph (1994)

Efficient carbon tax = NPV marginal damage Efficient carbon tax = NPV marginal damage

Fundamental principle: Optimal carbon tax = Pigouvian tax = NPV marginal damage A CO2 l l i d d i l As CO2 levels increase, and damages are convex, marginal damages are increasing in CO2 → marginal damages increasing

• ver time
• ver time

Sinclair (1992) cannot be correct. Sinclair assumes (Z0,z) policy,

• ptimal policy must be more complicated
• p

a po cy us be

• e co

p ca ed Use partial analysis (utility of resource use), no closed economy Use linear demand and marginal damages to solve explicitly Use linear demand and marginal damages to solve explicitly

04 July 2011 13 Reyer Gerlagh

Model II: Ulph and Ulph (1994)

Increasing tax = decreasing tax? Increasing tax = decreasing tax?

Is there a fundamental difference in result? Optimal carbon tax = NPV marginal damage = increasing per l volume To delay fossil fuel extraction, carbon tax must be decreasing as percentage of rent value percentage of rent value As rent prices increase with interest rate, both can be satisfied Numerical illustration U&U suggest optimal carbon tax that is Numerical illustration U&U suggest optimal carbon tax that is hump-shaped (increasing-decreasing) as percentage of value

• Intuition: optimal carbon tax tries to smooth damages shave off large
• Intuition: optimal carbon tax tries to smooth damages, shave off large

concentration levels (convex damages), more early emissions (2010), more late emissions (>2100), less peak emissions (2050).

04 July 2011 14 Reyer Gerlagh

Model II: Ulph and Ulph (1994)

Model set up Model set up

f f ( ) ( f ) f Benefits of resource use U(E) (net of extraction costs), damages of pollution stock D(M) M { ( ( )) ( ( ))}

rt

W U E t M t dt Ω

∞ −

∫ Max λ: ( ) ( ) S t E t = −

• { ( ( ))

( ( ))}

rt

W e U E t M t dt Ω

∞

= − ∫ τ: H il i ( ) ( ) ( ) M t E t M t δ = −

• Hamiltonian:

( ( )) ( ( )) ( ) ( ) ( )( ( ) ( )) H U E t M t t E t t E t M t Ω λ τ δ = − − − −

• FOC: 0

; ;

E S M

H r H r H λ λ τ τ = = + = +

04 July 2011 15 Reyer Gerlagh

Model II: Ulph and Ulph (1994)

Main results Main results

• ( )

FOC: r λ λ = ( ) '( ) r M τ τ δ Ω − = +

• '( )

U E λ τ = + Marginal productive value of FF = Hotelling rent + Pigouvian tax Hotelling rent increases with interest rate Pigouvian tax:

• (i) Pollution depreciation → present emissions maximally exploits nature’s

capacity to neutralize! Favour high current use → High future taxes capacity to neutralize! Favour high current use → High future taxes

• (ii) Increasing marginal damages of stock → present pollution increases

future marginal damages → smooth emissions → high present taxes

• At initial low concentrations (2010), (i) dominates, at peak concentrations

(2050), (ii) dominates → optimal carbon taxes will first increase fast, then curve back curve back

04 July 2011 16 Reyer Gerlagh

Model II: Ulph and Ulph (1994)

Graphical representation Graphical representation

E i i (E) BAU vs Optimal Policy C i (M) 2200 Emissions (E) 2010 2200 2100 2010 2100 Concentrations (M) Optimal policy ‘tries’ to avoid peak concentration with peak i l d 2200 2010 2200 2100 2010 2100 marginal damages Total cumulative emissions not affected

04 July 2011 17 Reyer Gerlagh

Model II: Ulph and Ulph (1994)

Linear demand and damages Linear demand and damages

(1) (2) U uE λ τ − = +

• T

S Edt = ∫

(3) (4)

r λ λ =

• M

E M δ = −

• (5)

Given M(0), choose λ(0) and τ(0) such that (2) is met, where d d h ld b t fi l d t d Pi i t ti fi ( ) r M τ δ τ ω = + −

• demand should be zero at final date T, and Pigouvian tax satisfies

(6) ( ) ( ) T T U λ τ + =

( ) ( )

( )

t T t

M T

δ

ω

∞ ∞ +

(7)

( ) ( )

( ) ( ) ( ) ( )

r t T r t T

M T T e M t dt M T e dt r

δ

ω τ ω ω δ

∞ ∞ − − − +

= = = ∫ ∫ +

04 July 2011 18 Reyer Gerlagh

Model II: Ulph and Ulph (1994)

Conclusions Conclusions

Even linear model is too difficult to say much about path, analytically. N i l ill t ti t i i d l t i iti ll Numerical illustrations suggest increasing ad valorem tax, initially, curving back, later.

04 July 2011 19 Reyer Gerlagh

Model III: Hoel and Kverndokk (1996) & Tahvonen (1997)

Economic exhaustion of fossil fuels Economic exhaustion of fossil fuels

(1) Extraction costs depend on cumulative extraction: we go into deep-water oil wells (Gulf of Mexico) as we run out of ‘cheap oil’. Oil h ti i i t h i l l ti i i Oil exhaustion is economic, not physical → cumulative emissions depend on economy & policy + (2) future energy supply when running out of oil depends on + (2) future energy supply when running out of oil depends on substitute = backstop Use similar partial equilibrium framework as Ulph & Ulph Use similar partial equilibrium framework as Ulph & Ulph Main result: carbon taxes should delay part of fossil fuel use to long-term, overlap fossil fuels and clean energy (backstop) era long term, overlap fossil fuels and clean energy (backstop) era

04 July 2011 20 Reyer Gerlagh

Model III: Hoel and Kverndokk (1996) & Tahvonen (1997)

Model set up Model set up

f f ( ) ( ) ( ) Benefits of energy use U(E+B) (with backstop), extraction costs c(S), (c'<0 as stocks decrease), damages of pollution stock D(M) M ( ) ( ( )) ( { ( ( ) ) ( ( ) ) ) )} (

rt

B t S t E t W U E t M B t dt t Ω

∞ −

∫ Max Hamiltonian: ( ( ( ) ( ) ) ) B S E B H U E M E E M Ω λ δ ( ) ( ( )) ( { ( ( ) ) ( ( ) ) ) )} (

rt

B t c S t E t W e U E t M B t dt t Ω ψ

∞

+ = − ∫ − − FOC ( ( ( ) ( ) ) ) B c S E B H U E M E E M Ω λ τ ψ δ = − − − − + − −

( ) ( )

FOC:

'( ) ( ) c S U E B E λ τ + ≤ + ⊥ ≥ − '( ) U E B B ψ + ≤ ⊥ ≥ '( ) c r S E λ λ + =

• (

) '( ) r M τ δ τ Ω = + −

• (

) ψ

04 July 2011 21 Reyer Gerlagh

( ) ( )

Model III: Hoel and Kverndokk (1996) & Tahvonen (1997)

Long term steady state Long-term steady state

( ) ( ) ( ) Economically viable resources are used: E(∞)=0; S(∞)=S∞; λ(∞)=0 All pollution has decayed: M(∞)=0 No Pigouvian tax needed: τ(∞)=0 Marginal value of energy = marginal costs for substitute: U'(∞)=ψ marginal extraction costs = marginal value: U'(∞)=c(S(∞)) Cumulative fossil fuel use independent of climate change problem!

• But what is economic counterpart of mathematical convergence?

04 July 2011 22 Reyer Gerlagh

Model III: Hoel and Kverndokk (1996) & Tahvonen (1997)

Transition to long term steady state Transition to long-term steady state

Available backstop sets limit to fossil fuel extraction costs c(S) ≤ U'(E+B) – λ – τ and U'(E+B) ≤ ψ => c(S) ≤ ψ – τ When backstop is in use, and pollution decays (τ decreases), fossil fuels will slowly be further depleted BAU vs Optimal Policy BAU vs Optimal Policy Emissions (E) Emissions (E) 2200 2100 2010

04 July 2011 23 Reyer Gerlagh

2200 2100 2010

Sinclair, Ulph&Ulph, Hoel & Kverndokk, Tahvonen: 1970-2000

Summary Summary

Dasgupta-Heal (1979): constant ad-valorem taxes don’t change resource extraction Si l i (1992 1994) t d li t h t d l Sinclair (1992,1994): to reduce climate change, we must delay fossil fuel extraction → high upfront taxes, decreasing over time Ulph & Ulph (1994): we must reduce peak climate change smooth Ulph & Ulph (1994): we must reduce peak climate change, smooth fossil fuel use through high taxes at peak Hoel and Kverndokk (1996) & Tahvonen (1997): use all fossil fuel Hoel and Kverndokk (1996) & Tahvonen (1997): use all fossil fuel reserves but extend fossil fuel era to overlap with backstop era

04 July 2011 24 Reyer Gerlagh

Model IV: Sinn (2008)

The Green Paradox The Green Paradox

Climate change policy has looked at demand side only: reducing demand for fossil fuels. But demand-side policy doesn’t carry far if supply is inelastic supply is inelastic. Result 1: 100% carbon leakage: “environmental sinners to consume what the Kyoto countries have economized on” consume what the Kyoto countries have economized on Result 2: Green paradox: gradual greening of Kyoto policies will advance fossil fuel extraction ad a ce oss ue e ac o Fossil fuels about 4,000 GtC → 1200 ppmv → very hot

04 July 2011 25 Reyer Gerlagh

Model IV: Sinn (2008)

Dynamics: extraction vs stock Dynamics: extraction vs. stock

Nice math: consider Nice math: consider movement in (E,S)-space: dE/dS Notice that E=–dS/dt, y-value is speed to left If E=f(S) is continuously differentiable, then curves t cannot cross If all scenarios go through (0 0) and Scenario I has (0,0) and Scenario I has higher dE/dS, then resource is exhausted earlier exhausted earlier

04 July 2011 26 Reyer Gerlagh

Model IV: Sinn (2008)

The economy The economy

f ( ( ) ( )) f f Welfare with non-constant interest rate (r(t)=R'(t)), fossil fuel extraction, and climate damages with no depreciation:

( ) R t

( )

( )

{ ( ) ( ) ( )}

R t

W e U E c S E S S dt Ω

∞ −

= − − − ∫ S E = −

• ( '

0; ' 0) c Ω < > FOC E: P(t)≡U'(E(t))=c(S(t))+λ(t) FOC ( ) ( )

• FOC

Substitution: '( ) '( ) r c S E S S λ λ Ω = + − − ' ( ) ' P E P λ Ω

• '

( ) ' P c E r P c λ Ω = − = − − ' ˆ (1 ) c P r P P Ω = − −

04 July 2011 27 Reyer Gerlagh

P P

Model IV: Sinn (2008)

Demand side Demand side

C f f f ( ) ( ) Competitive energy demand market for fossil fuels: U'(E) = P(E) From demand: '' U E P =

• '

ˆ ˆ ( ) '' dE E P U E E P dS S EU P σ − = = − = =

• Pareto optimal path:

' ( ){ (1 ) } dE c E r Ω σ = − − ‘Efficient Market’ equilibrium: ( ){ (1 ) } E r dS P P σ ( ) (1 ) dE c E r dS P σ = −

04 July 2011 28 Reyer Gerlagh

Model IV: Sinn (2008)

Supply side with insecure property rights Supply side with insecure property rights

Insecure property rights: hazard rate of loosing

• wnership π:
• wnership π:

Substitution in rents:

( ) '( ) r c S E λ π λ = + +

• Substitution in rents:

Substitution in demand side

( )( ( )) P r P c S π = + −

• Substitution in demand-side

dynamics

( ) ( )( )( ) dE c S

Extraction goes up with π

( ) ( )( )(1 ) ( ) dE c S E r dS P E σ π = + −

Extraction goes up with π.

04 July 2011 29 Reyer Gerlagh

Model IV: Sinn (2008)

Green policies Green policies

f f f Assume government taxes fossil fuel rents at factor Z, growing at constant rate Z

( )

( ) ( )

R t πt P E E

c S E Λ e dt Z

∞ − −

− = ∫

( ) ( )

1 { ( ) ( ) } (0)

R t π z t

e P E E c S E dt Z

∞ − − +

= − ∫ The tax just works as extra time discounting: ( )( ( )) P r π z P c S = + + −

• 04 July 2011

30 Reyer Gerlagh

Model IV: Sinn (2008)

Green Paradox Green Paradox

Benchmark: Market with full Benchmark: Market with full property rights Insecure property rights Insecure property rights speed up extraction Green policies with p increasing taxes further speed up extraction! While PE policy would be to delay

04 July 2011 31 Reyer Gerlagh

Model IV: Sinn (2008)

Robust policies? A gloomy picture Robust policies? A gloomy picture

High upfront carbon taxes

• Politically impropable

S f t i ht Safer property rights

• Practically difficult in many countries

Binding supply quantity constraints Binding supply quantity constraints

• Needs rigid global agreement
• Would kill fossil fuel rents!
• Would kill fossil fuel rents!

Technical means to decouple the accumulation of carbon dioxide from carbon consumption p

• Afforestation insufficient
• CCS dangerous to trust on

04 July 2011 32 Reyer Gerlagh

Model V: Strand (2008)

Can technology cooperation save us? Can technology cooperation save us?

International negotiators search for ‘acceptable’ solutions to combat climate change P liti i d ’t lik b t d i i t Th d Politicians don’t like carbon taxes, and emission quota. They do like technology fixes If we jointly search for competitive clean energy = marginal costs < If we jointly search for competitive clean energy = marginal costs < extraction costs for fossil fuels, and find one, we ‘solve’ the climate change problem. Or do we? c a ge p ob e O do e The perspective of future cheap clean energy, will drive extraction up. p

04 July 2011 33 Reyer Gerlagh

Model V: Strand (2008)

Model set up Model set up

( ) Demand without substitute: D(P) Demand after technology breakthrough: 0 Break through hazard rate π Supply:

( )

{ ( ) ( ) }

r π t

Λ e P E E c S E dt

∞ − +

= − ∫ Dynamics very much the same as in Sinn (2008) (not known to Strand) ( ) ( )( )(1 ) dE c S σ E π r = + − Implication: Technology agreement will speed up fossil fuel use, d if f l d l ti ( )( )(1 ) ( ) σ E π r dS P E + and if successful, reduce cumulative use

04 July 2011 34 Reyer Gerlagh

Model V: Strand (2008)

Result Result

Emissions go up BAU T h l t Emissions go up If lucky, we may solve the problem BAU vs Technology agreement problem If unlucky, we may have added to climate change E i i (E) added to climate change Emissions (E) 2200 2100 2010 2200 2100 2010

04 July 2011 35 Reyer Gerlagh

Model VI: Hoel (2008)

Bush meets Hotelling: cheap clean energy Bush meets Hotelling: cheap clean energy

Cheap clean energy has the advantage that it doesn’t cost jobs (or votes, as taxes do) If d l titi l i l t < If we develop a competitive clean energy = marginal costs < extraction costs for fossil fuels, and find one, we ‘solve’ the climate change problem Or do we? change problem. Or do we? The perspective of future cheap clean energy, will drive extraction up, increasing climate damages. up, c eas g c a e da ages Cheaper clean energy may reduce welfare! Model specifics: continuum of countries ordered with respect to Model specifics: continuum of countries ordered with respect to willingness to pay for reducing emissions

04 July 2011 36 Reyer Gerlagh

Model VI: Hoel (2008)

Model set up case I Model set up, case I

As in Sinclair (1992) define cumulative demand up to time T: As in Sinclair (1992), define cumulative demand up to time T: But realize that termination date T is determined by substitute

( )

( , ) ( )

T r z t

P T D e P dt Δ

+

= ∫

But realize that termination date T is determined by substitute (choke) price: P(T)=ψ → Δ(P0,ψ) with ΔP<0, Δψ>0 Change in substitute price (ψ) must be offset by change in initial Change in substitute price (ψ), must be offset by change in initial price

P P ψ

Δ dP dS dΔ Δ dP Δ dψ dψ Δ − = = = + ⇒ = >

Cheaper substitute (dψ<0) implies lower price at every period!

ψ ψ

dψ Δ

Cheaper substitute (dψ 0) implies lower price at every period! (dPt<0) implies higher cumulative emissions at every T (dET>0).

04 July 2011 37 Reyer Gerlagh

Model VI: Hoel (2008)

Model set up case II Model set up, case II

Assume some countries have willingness to pay not to use fossil Assume some countries have willingness to pay not to use fossil fuels above ψ. Alternative, assume that substitute has supply curve and ψ is inverse measure of technology: D(P,ψ) with DP<0, Dψ>0 ψ gy ( ψ)

P ψ

Cheaper substitute (dψ<0) still implies lower fossil fuel price at p ( ψ ) p p every period (dPt<0). But as cheaper substitute reduces demand as well, the effect on emissions at every t is ambiguous (dEt>?0). Current emissions decrease if energy substitute is immediately

• used. Current emissions increase if energy substitute is mostly a

future option.

04 July 2011 38 Reyer Gerlagh

Sinn, Strand & Hoel: 2008

Summary: Green Paradox everywhere Summary: Green Paradox everywhere

Sinn (2008): market is distorted towards advanced extraction. Carbon tax plans worsen the problem St d (2008) I t ti l t f l b k Strand (2008): International agreement for clean energy break- through will increase emissions, and if unsuccessful, worsen climate change climate change Hoel (2008): cheap clean energy causes a green paradox as much as carbon tax plans, especially if clean energy is a future option as ca bo a p a s, espec a y c ea e e gy s a u u e op o and not immediately available

04 July 2011 39 Reyer Gerlagh

Model VII: Gerlagh (2011)

Too Much Oil (Fossil Fuels) Too Much Oil (Fossil Fuels)

We cannot tolerate all fossil fuels to be used Hence, we must either implement strong climate policy

• r we must develop competitive clean energy = marginal costs <

future extraction costs for fossil fuels If d b t f th i i h ill If we do so, carbon tax or further improving cheap energy will reduce cumulative fossil fuel use Analysis focuses on developing cheap clean energy (no tax) Analysis focuses on developing cheap clean energy (no tax) Models: simple linear demand & supply M t ll f t k t i t ti j tifi d Message: urgent call for strong market intervention; justified as there is no Green Paradox

04 July 2011 40 Reyer Gerlagh

Model VII: Gerlagh (2011)

Model features Model features

From Ulph and Ulph (1996): Linear demand & supply functions, so that path is linear combination of ‘eigenvectors’. E t ti t li i S(t) Extraction costs linear in S(t):

• Argument: the amount of fossil fuels is too much to accept full depletion (Sinn

2008, Allen et al. 2009). 008, e et a 009)

• Consequence: cumulative emissions are endogenous

Linear clean energy supply gy y

• Argument: clean energy has decreasing returns to scale (Pacala & Sokolow

2004). Consequence: cheaper clean energy reduces current fossil fuel demand

• Consequence: cheaper clean energy reduces current fossil fuel demand

(Hoel 2008)

04 July 2011 41 Reyer Gerlagh

Model VII: Gerlagh (2011)

Redefining Green Paradoxes Redefining Green Paradoxes

Weak Green Paradox: current emissions go up Strong Green Paradox: NPV total damages go up If cumulative emissions are constant, then Weak = Strong If cumulative emissions decrease, but current emissions increase? Total damages: Where ( ( )) ( ) ( )

rt rt

Γ e Ω M t dt e τ t E t dt Γ

∞ ∞ − −

= = + ∫ ∫

( )

( ) '( ( ))

r δ τ t

τ t e Ω M τ dt

∞ − +

= ∫ Assume damages increase not too fast. E.g. M(t) increases not too fast, Ω(t) not too convex → ˆ' Ω r < → Marginal damages increase not too fast: Necessary condition for Strong Green Paradox: i (L 1) ˆ r τ < ( )

rt

e E t dt

∞ −

∫ increases (Lemma 1)

04 July 2011 42 Reyer Gerlagh

Model VII: Gerlagh (2011)

Intermezzo: Lemma 1 Intermezzo: Lemma 1

rt rt ∞ ∞

ˆ Lemma 1. Given then implies

1

( ) ( )

rt rt

e E t dt e E t dt

∞ ∞ − −

> ∫ ∫

1

( ) ( ) ( ) ( )

rt rt

e τ t E t dt e τ t E t dt

∞ ∞ − −

> ∫ ∫ ˆ r τ < Proof:

04 July 2011 43 Reyer Gerlagh

Model VII: Gerlagh (2011)

Base model Base model

Linear energy demand: Constant extraction costs: ( ) ( ( )) ' ( ) E t D P t E D P t = = + ( ) ( ( ) ) P t r P t c = −

• Extraction dynamics: S

E = −

• '

( ) ' c E D P r E E D = = − +

• When clean energy becomes cheaper (dψ<0), then dE/dS

d th h t i i i f b th D − decreases throughout → emissions increase for every t → both Weak and Strong Green Paradox

04 July 2011 44 Reyer Gerlagh

Model VII: Gerlagh (2011)

Phase Diagram: replicating Sinn/Strand/Hoel Phase Diagram: replicating Sinn/Strand/Hoel

E Phase diagram: E S E = −

• stop

c E E E +

• '

( ) ' c E D P r E E D = − = − + −

• E =

g backs Condition: ' E E E D = ⇔ = + − mproving

• S(0)=S0
• E(T) =D(ψ) (maximal rent)

Ch l S S =

• Imp

Cheaper clean energy moves path up iff D(ψ)>0 D(ψ)>0

04 July 2011 45 Reyer Gerlagh

Model VII: Gerlagh (2011)

New: Linear extraction costs New: Linear extraction costs

f f Linear fossil fuel demand: Linear extraction costs: P(t) = c(S0–S(t))+λ(t) ( ) ( ( )) ' ( ) E t D P t E D P t = = + Gerlagh (2011) inverts S from remaining stock to cumulative extraction, we don’t C titi l ( ) ( ( ) ( ( )))

• Competitive supply:

Extraction dynamics: ( ) ) ' (S c E D P r E E S − +

• ( )

( ( ) ( ( ))) P t r P t c S S t = − − S E = −

• Locus

( ) ' ) ' ( E D P r E E D = = − + − ' ) ( c E E S E S D = ⇔ + − = −

• D

04 July 2011 46 Reyer Gerlagh

Model VII: Gerlagh (2011)

Graphics Phase Diagram Graphics, Phase Diagram

Phase diagram: E S E = −

• (

) E =

• E

c ( ) ' ( ) ' c S S E D P r E E D − = − = − +

• E

( ) ' c E E E S S D = ⇔ = + −

• '

ED Sinn (2008): S ' ED S c < S =

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47 Reyer Gerlagh

Model VII: Gerlagh (2011)

Stable and Unstable balanced paths Stable and Unstable balanced paths

E E =

• E

E S S =

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48 Reyer Gerlagh

Model VII: Gerlagh (2011)

Equilibrium path (Sinn (2008) assumption) Equilibrium path (Sinn (2008) assumption)

Equilibrium path = linear combination of stable and unstable balanced E E =

• and unstable balanced

growth Condition: E E Condition:

• S(0)=S0
• E(T) =0 (maximal rent at

final period, no backstop)

S S =

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49 Reyer Gerlagh

Model VII: Gerlagh (2011)

Equilibrium path (a backstop) Equilibrium path (a backstop)

Equilibrium path = linear combination of stable and unstable balanced E E =

• and unstable balanced

growth Condition: E E Condition:

• S(0)=S0
• E(T) =D(ψ) (maximal rent

at final period)

When backstop is h f il f l i S S =

• cheap, fossil fuel is

abundant:

• λ(T)=0
• λ(T)=0

04 July 2011 50 Reyer Gerlagh

Model VII: Gerlagh (2011)

Equilibrium path (Too much fossil fuels) Equilibrium path (Too much fossil fuels)

Equilibrium path = stable balanced growth Ab t t f b k t E E =

• Abstract from backstop

Condition:

S(0) S (large)

E E

• S(0)=S0(large)
• E(∞) =0 (no rent at infinite

horizon)

S S =

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51 Reyer Gerlagh

Model VII: Gerlagh (2011)

Equilibrium path (with backstop) Equilibrium path (with backstop)

Equilibrium path = stable balanced growth C diti E E =

• Condition:
• S(0)=S0(large)
• λ(T)=0 → P(T) =cS (no rent

E E

• λ(T)=0 → P(T) =cS (no rent

at final period)

Improving backstop = g moving T along the red curve S S =

• E increases, cumulative

E decreases

04 July 2011 52 Reyer Gerlagh

Model VII: Gerlagh (2011)

Linear clean energy supply cnsnt extrn costs Linear clean energy supply, cnsnt extrn costs

Linear energy demand: Linear clean energy supply (renewables with DRS): N(t) = AP(t) ( ) ( ( )) ' ( ) E t D P t E D P t = = + ( ) ( ) ( ) ( ) ( ) Fossil fuel demand: Constant extraction costs: ( ) ( ( ) ) P t r P t c = −

• ( )

( ) ( ) ( ') ( ) E t E t N t E A D P t = − = − − Extraction dynamics: S E = −

• (

') ( ) c E A D P r E E = − − = − +

• When clean energy becomes more productive (dA>0), then dE/dS

( ) ( ) ' A D − decreases throughout → emissions decrease for every t → no Weak nor Strong Green Paradox

04 July 2011 53 Reyer Gerlagh

Model VII: Gerlagh (2011)

Phase Diagram: no backstop Phase Diagram: no backstop

Phase diagram: E S E = −

• c

( ') ( ) ' c E A D P r E E A D = − + = − + +

• E =
• Condition:

' c E E E A D = ⇔ = + +

• S(0)=S0
• E(T) =0 (maximal rent)

Ch l S S =

• Cheaper clean energy

changes path iff c>0

04 July 2011 54 Reyer Gerlagh

Model VII: Gerlagh (2011)

Graphics Phase Diagram Graphics, Phase Diagram

Recall Sinn (2008): E ( ) (1 ) dE c E r dS P σ = − Cheaper clean energy d t h ( ) ( ) dS P E =

• need not change

elasticity of demand for fossil fuels but just fossil fuels, but just lowers demand → lower price, hence, lowers S S =

• p

slope.

04 July 2011 55 Reyer Gerlagh

Model VII: Gerlagh (2011)

Conclusions Conclusions

Cheaper current clean energy replace fossil fuels and don’t lead to Cheaper current clean energy replace fossil fuels and don t lead to Green Paradox. Cheaper future clean energy imply that fossil fuel price decreases Cheaper future clean energy imply that fossil fuel price decreases → current emissions increase + fossil fuels are earlier replaced → NPV damages decrease As there is much-too-much coal + nonconventional oil, we must develop clean energy that is competitive In this context, no need to worry for Green Paradox

04 July 2011 56 Reyer Gerlagh

Model V: Grafton, Kompas, van Long (2010)

Biofuels Biofuels

Can biofuel subsidies help reduce cumulative emissions? Supply curve for biofuel, as opposed to backstop First result (Prop 1) equals Gerlagh (2011): no extraction costs & linear demand → no effect. Positive constant extraction costs & linear demand → Green Orthodox linear demand → Green Orthodox Then consider non-linear demand. Sinn (2008): Question is: does biofuel subsidy increase or decrease elasticity of ( ) (1 ) dE c E r dS P σ = − Question is: does biofuel subsidy increase or decrease elasticity of fossil fuel demand? If energy demand and biofuel supply are linear then fossil fuel If energy demand and biofuel supply are linear, then fossil fuel demand elasticity, σ(E), remains unaffected. But if energy demand is iso-elastic …

04 July 2011 57 Reyer Gerlagh

Model V: Grafton, Kompas, van Long (2010)

Iso elastic energy dem + linear biofuel supply Iso-elastic energy dem + linear biofuel supply

ε

Energy demand: Biofuel supply (with subsidy z): = N zP

ε

β

−

= En P Fossil fuel demand: Elasticity of demand:

ε

ε ε

−

− − + (1 ) ( ) dE P P zP zP E

ε

β

−

= − E P zP Increasing with z: σ ε − = = = − − ( ) ( ) E dP E E E ( ) ( )

E cnst E E E

d d d d d E zP P E P P dz dz dz dz dz

− − =

= − = − > ∼ ∼

ε ε

σ

04 July 2011 58 Reyer Gerlagh

Model V: Grafton, Kompas, van Long (2010)

Illustration Illustration

biofuel subsidy moves you up, as in Sinn (2008) d ( ) (1 ) dE c E r dS P σ = − but for different reason S l h ld if Same results holds if one country out of two subsidizes A d if f il f l l i And if fossil fuel supply is monopolistic

04 July 2011 59 Reyer Gerlagh

Model V: Grafton, Kompas, van Long (2010)

Increasing extraction costs Increasing extraction costs

f f ( ) Assumed that fossil fuels remain scarce, λ(T)>0, which means that the last drop of oil is cheaper to extract than marginal value of energy then same results continue to hold (no change of energy, then same results continue to hold (no change of cumulative emissions)

• Similar to Sinn (2008), contrasts Gerlagh who poses that we can’t afford to

( ), g p exhaust fossil fuels (must ensure λ(∞)=0)

04 July 2011 60 Reyer Gerlagh

Model V: Grafton, Kompas, van Long (2010)

Linear extraction costs + biofuels Linear extraction costs + biofuels

Condition:

• S(0)=S0
• E(T) 0 (maximal rent at

E

• E(T) =0 (maximal rent at

final period)

Cheaper biofuels E E = p reduce fossil fuel demand and delay exhaustion S S =

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61 Reyer Gerlagh

Van der Ploeg and Withagen (2009)

Add welfare to the analysis Add welfare to the analysis

Green Paradox occurs if the backstop is relatively expensive and full exhaustion of fossil fuels is optimal Add lf l i Add welfare analysis: Without a carbon tax, taxing the backstop might enhance social welfare if fossil fuel reserves are fully exhausted welfare if fossil fuel reserves are fully exhausted. Without a carbon tax, subsidizing the backstop might enhance social welfare if fossil fuel reserves are not fully exhausted social welfare if fossil fuel reserves are not fully exhausted. If backstops are already used, a lower cost of the backstop will postpone fossil fuel exhaustion or leave more fossil fuel in situ, postpone fossil fuel exhaustion or leave more fossil fuel in situ, thus boosting green welfare Add monopolistic supply p pp y

04 July 2011 62 Reyer Gerlagh

Model IX: van der Ploeg and Withagen (2009)

Equilibrium path (a backstop) Equilibrium path (a backstop)

Green Paradox occurs if the backstop is relatively expensive and E E =

• Green Orthodox

relatively expensive and full exhaustion of fossil fuels is optimal E E Green Paradox p What matters is whether λ(T)=0 Green Paradox: carbon tax & backstop subsidy S S =

• decreases welfare

Green Orthodox: might i lf increase welfare

04 July 2011 63 Reyer Gerlagh

Model IX: van der Ploeg and Withagen (2009)

‘Backstops’ in use Backstops in use

Recall Sinn (2008): E ( ) (1 ) dE c E r dS P σ = − Recall Gerlagh (2011): Ch l ( ) ( ) dS P E =

• Cheaper clean energy

need not change elasticity of demand for elasticity of demand for fossil fuels, but just lowers demand → lower S S =

• price, hence, lowers

slope.

04 July 2011 64 Reyer Gerlagh

Gerlagh; Grafton, Kompas & van Long; vd Ploeg & Withagen

Summary: Green Paradox not everywhere Summary: Green Paradox not everywhere

Gerlagh (2011): cannot afford to use all fossil fuels → fossil fuel rent must be zero at end → no full exhaustion Ch l f ll f il f l h ti Cheap clean energy = no full fossil fuel exhaustion → no green paradox → carbon tax & clean energy subsidy might increase welfare (vdP&W) welfare (vdP&W) Clean energy in use → green orthodox if linear demand (G) / green paradox if iso-elastic demand (GKvL) → carbon tax & clean energy pa ado so e as c de a d (G ) ca bo a & c ea e e gy subsidy might increase welfare (vdP&W)

04 July 2011 65 Reyer Gerlagh

What’s in it for you?

Past future research Past future research

Country Heterogeneity What if countries differ wrt resource endowments / substitute d t / b t li (H l) endowments / carbon tax policy (Hoel) Carbon Capture and Sequestration Wh t if th it lf ff l ti (H&J )? What if the resource itself offers a clean option (H&Jensen)? Resource heterogeneity Wh if i (Mi hi l )? What if various resources compete (Michielsen)?

• Integrate coal, oil, gas & unconventional oil as exh. resources

04 July 2011 66 Reyer Gerlagh

Learn from the best

Intuition Intuition

From Hoel (2011) 2 countries: Country A has hi h b t C t high carbon tax. Country B has low carbon tax, but increases its tax to the increases its tax to the level in Country A Result: Green Paradox esu G ee a ado

04 July 2011 67 Reyer Gerlagh

What’s in it for you?

Suggestions for future research Suggestions for future research

Broadening Consider jointly interspatial & intertemporal market integration Deepening Exploration: resources versus reserves

• Future policies may affect current expected reserves?

Endogenous substitute development

h t if t ff t R&D i t b tit t ?

• what if taxes affect R&D into substitute?

Alternatives Alt ti f th i l h tibl d l Alternatives for the simple exhaustible resource model

• any sign for oil price increase with interest rate 1980-2000?

04 July 2011 68 Reyer Gerlagh