Time horizon, uncertainty Time horizon, uncertainty and cost benefit analysis.and cost benefit analysis.

Long run discount rate for Long run discount rate for environmental goods.environmental goods.

Cost benefit analysisCost benefit analysis

The cost of Kyoto : The cost of Kyoto : the verdict of models.the verdict of models.

Why models ?Why models ?• Sectoral effects (électricityé).Sectoral effects (électricityé).• effect on final demande: econometrics of price effects.…effect on final demande: econometrics of price effects.…• General interactions. General interactions.

Which models ?Which models ?• sectoral.aggregate.sectoral.aggregate.• Computable general equilibrium.macroéconomics.Computable general equilibrium.macroéconomics.

The double dividend controversy.The double dividend controversy.

0

50

100

150

200

250

300

350

400

0% 10% 20% 30% 40%

Carbon emissions reductions (in%)

CarbonvalueinUS$95/tC

DEU

UK

ESP

ROEFRITA

NLD

FIN

DNK

SWE

The benefits of climate policiesThe benefits of climate policies

The difficultiesThe difficulties• Many chaptersMany chapters

Agriculture, extreme weather eventsAgriculture, extreme weather events Bio-diversity, health, quality of climate.Bio-diversity, health, quality of climate. Flooding, large scale migrations..Flooding, large scale migrations..

• Difference across regionsDifference across regions Northern areas and vulnerable, (southern) places.Northern areas and vulnerable, (southern) places.

• Differences according to the range of Differences according to the range of temperaturetemperature

1 to 3 degrees : agriculture in northern areas.1 to 3 degrees : agriculture in northern areas. Above high reductions of general fertility.Above high reductions of general fertility.

Uncertainty has to be faced.Uncertainty has to be faced.

The benefits of climate policiesThe benefits of climate policies

The solutions of the Stern review.The solutions of the Stern review. A comprehensive qualitative coverage of the A comprehensive qualitative coverage of the

phenomena.phenomena. A long run probabilistic assessmentA long run probabilistic assessment A synthetical money assessmentA synthetical money assessment

• Damages = (T/2,5) power g, g=1,5 to 3Damages = (T/2,5) power g, g=1,5 to 3• Probabilistic assesment : high climate scenario, Probabilistic assesment : high climate scenario,

markets and non market impacts, 95markets and non market impacts, 95thth percentile 35per percentile 35per cent of global GDP in 2200.cent of global GDP in 2200.

The presentation of numbers.The presentation of numbers. Equivalent GDP loss.Equivalent GDP loss. Skips partly the discount rate issue.Skips partly the discount rate issue.

The discount rate in the Stern The discount rate in the Stern Review.Review.

The issue :The issue :• How should one unit of consumption for the present generation How should one unit of consumption for the present generation

be valued in comparison of the same unit for the present be valued in comparison of the same unit for the present generation.generation.

• If perfect altruism the answer depends upon the elasticity of If perfect altruism the answer depends upon the elasticity of marginal utility (xU``/U`) or relative risk aversion.marginal utility (xU``/U`) or relative risk aversion.

• Pure rate of time preference.Pure rate of time preference. Example :Example :

• Isoelastic utility functionIsoelastic utility function• U= [1/(1- U= [1/(1-  ’] ’]t=0t=0

infiniinfini{(exp(- {(exp(- t))[U(x t))[U(xtt)])](1 - (1 - ’)’)}} The solution of the Stern reviewThe solution of the Stern review

• Elasticity close to one (Log utility…)Elasticity close to one (Log utility…)• Does not kill the future.Does not kill the future.• Underestimate risk aversion….Underestimate risk aversion….

Questions on long run discount Questions on long run discount rates for environmental goods. rates for environmental goods.

Discounting « kills » the distant future.Discounting « kills » the distant future. 10 per cent discount rate :120 in 50 years, 10 per cent discount rate :120 in 50 years, 14000 in 10014000 in 100 years years 7 per cent, discount rate : < 30 in 50 years, 7 per cent, discount rate : < 30 in 50 years, 860 in 100860 in 100 years, years, 5 per cent discount rate : 5 per cent discount rate : 130 in 100130 in 100 years, 17 000 in 200 years, years, 17 000 in 200 years, 2 per cent discount rate : 2,7 in 50 years, 2 per cent discount rate : 2,7 in 50 years, 7,37,3, in 100 years, 52 in , in 100 years, 52 in

200 years.200 years. Is standard discounting appropriate fIs standard discounting appropriate for long run decisions ?or long run decisions ? Argument 1Argument 1 : « ecological intuition » : « ecological intuition »

• Discounting=selfishness of existing generations, eDiscounting=selfishness of existing generations, ethically thically unacceptableunacceptable

• Destroys our common natural patrimony, for Destroys our common natural patrimony, for second rate second rate interests.interests.

Argument 2 :Argument 2 : « economic reason » « economic reason »• Cost benefit analysis provides the weights for decisions about Cost benefit analysis provides the weights for decisions about

public versus private goods.public versus private goods.• Cost benefit analysis rightly stresses that it is useless Cost benefit analysis rightly stresses that it is useless to to

sacrifice present generations to future and much wealthier sacrifice present generations to future and much wealthier generations.generations.

How to reconcile economic and How to reconcile economic and ecological intuition ? ecological intuition ?

Ingredient 1 Ingredient 1 Environmental goods and the long run. Environmental goods and the long run. • They They differ fromdiffer from

private goodsprivate goods : out put cannot be continually expanded. : out put cannot be continually expanded. non renewable resources non renewable resources : not destroyed by cautious use.: not destroyed by cautious use.

• in the in the long run, their long run, their relative scarcityrelative scarcity (/ private goods) (/ private goods) increases.increases.

Ingredient 2Ingredient 2 Uncert. lowers long run discount rate.Uncert. lowers long run discount rate. Argument Argument : valuation by generation 0 of 1 euro given to generation : valuation by generation 0 of 1 euro given to generation

T : exp(-Rt)T : exp(-Rt) If uncertainty : R or r, R>rIf uncertainty : R or r, R>r

• (1/2) exp(-Rt) + (1/2)exp(-rT) =(1/2) exp(-Rt) + (1/2)exp(-rT) =• exp(-rT) [(1/2)+(1/2)exp((-R+r)T)]=exp(-rT) [(1/2)+(1/2)exp((-R+r)T)]=• exp(-r ’(T)T), exp(-r ’(T)T), • r ’(T) tends to r when T tends to infinityr ’(T) tends to r when T tends to infinity

Weitzman (2000), AERWeitzman (2000), AER

How to reconcile CB analysis and How to reconcile CB analysis and economic intuition. economic intuition.

Ingredient 3Ingredient 3 : Substitutability : : Substitutability : • If private and environmental goods were perfectly If private and environmental goods were perfectly

substitutablesubstitutable, then, no reason to treat them differently in Cost , then, no reason to treat them differently in Cost Benefit analysis.: Benefit analysis.:

• If they are If they are strict complémentsstrict compléments Min{x,y}Min{x,y} Private output increases, the environmental good level Private output increases, the environmental good level

does not.does not. After a while, increasing the welfare of a wealthier future After a while, increasing the welfare of a wealthier future

generation relies on improving environmental quality.generation relies on improving environmental quality. Discount rate for private good : + Discount rate for private good : + Discount rate for environmental good : almost zero. Discount rate for environmental good : almost zero.

Ingredient 4Ingredient 4 : : « ethical » considerations. « ethical » considerations. • Pure rate of time preference close to zeroPure rate of time preference close to zero • > probability of the planet’s survival ? > probability of the planet’s survival ?

A formal modelA formal modelRG « Calcul économique et Développement durable », Revue Economique, RG « Calcul économique et Développement durable », Revue Economique,

2004, 2004,

2 goods 2 goods : : aggregate consumption good : quantityaggregate consumption good : quantity.. « environnemental quality »« environnemental quality »

Utility function Utility function ::• Formulation.Formulation.

v(xv(xtt ,y ,ytt) ={[x) ={[xtt((((- 1)/ - 1)/ ) ) + + yytt

(((( -1)/ -1)/ ) ) ] ] (( / /(( -1)) -1))}} V(xV(xtt ,y ,ytt) =[1/(1- ) =[1/(1-  ’)][v(x  ’)][v(xtt ,y ,ytt)])](1 - (1 - ’) ’)

• Comment.Comment. y/x decreases of 1/100, the willingness to pay increases of y/x decreases of 1/100, the willingness to pay increases of

((1/1/))     pour 100pour 100 Iso-élastic cardinal utilty for generation t, Iso-élastic cardinal utilty for generation t, Constant relative risk aversion Constant relative risk aversion ’.’.

Uncertainty :Uncertainty : On the long run elasticity of substitution between private and On the long run elasticity of substitution between private and

environnemental good, environnemental good,

A formal modelA formal modelRG « Calcul économique et Développement durable », Revue Economique, RG « Calcul économique et Développement durable », Revue Economique,

2004, 2004,

2 goods 2 goods : : aggregate consumption good : quantityaggregate consumption good : quantity.. « environnemental quality »« environnemental quality » NoteNote : :

only parameter, summary statistics of much information only parameter, summary statistics of much information  ’  ’ different possible interprétations.different possible interprétations.

Social welfareSocial welfare• U= [1/(1- U= [1/(1-  ’] ’]t=0t=0

infiniinfini{(exp(- {(exp(- t))[v(x t))[v(xtt ,y ,ytt)])](1 - (1 - ’)’)}}• RemarksRemarks• Index t associated to generationIndex t associated to generation• Utilitarian.Utilitarian. • When When __0, « ethical » viewpoint.__0, « ethical » viewpoint.

Cost Benfit analysis at the margin Cost Benfit analysis at the margin • A « reform » viewpoint.A « reform » viewpoint.• Combines the four previous ingredients.Combines the four previous ingredients.

ResultsResults « « Canonical » Ecological Cost benefit AnalysisCanonical » Ecological Cost benefit Analysis

• Generation 0 evaluates an investment (at 0), generating an Generation 0 evaluates an investment (at 0), generating an improvement of the environmental quality for generation timprovement of the environmental quality for generation t

• The value of the improvement is measured with The value of the improvement is measured with the marginal the marginal willingness to pay of generation 0willingness to pay of generation 0 : : « canonical procedure »« canonical procedure »

Proposition A :Proposition A :• If the If the probability probability of « ecological strangling » in the long of « ecological strangling » in the long

run is run is null.null. • Standard discount rate : Min (gStandard discount rate : Min (g’)+’)+ • ethical « canonical » ecological long run discount rate : ethical « canonical » ecological long run discount rate : • lim lim TT (T) = (T) = g[g[  ’-(1/  ’-(1/ )] )]• Min{g}[Min{Min{g}[Min{’}-1/{Min ’}-1/{Min } : } : • (1) (1,4 - 0.9) = 0,5 pour cent !(1) (1,4 - 0.9) = 0,5 pour cent !

ResultsResults « « Canonical » Ecological Cost benefit AnalysisCanonical » Ecological Cost benefit Analysis

• Generation 0 evaluates an investment (at 0), generating an Generation 0 evaluates an investment (at 0), generating an improvement of the environmental quality for generation timprovement of the environmental quality for generation t

• The value of the improvement is measured with The value of the improvement is measured with the marginal the marginal willingness to pay of generation 0willingness to pay of generation 0 : : « canonical procedure ».« canonical procedure ».

Proposition B :Proposition B :• If the If the probability probability of « ecological strangling » in the long run is of « ecological strangling » in the long run is

non zeronon zero.. • The ethical long run discount rate for private goods : MinThe ethical long run discount rate for private goods : Min{{g/ g/

}} • The ethical « canonical » ecological long run discount The ethical « canonical » ecological long run discount

rate is zerorate is zero.. Lessons : Lessons :

• Substitutability is essential … Substitutability is essential … • and uncertain..and uncertain..

Irreversibility and option value.Irreversibility and option value. Irreversibility of the greenhous effect.Irreversibility of the greenhous effect.

• Irreversibility of concentrationsIrreversibility of concentrations• Climate irreversibility. Climate irreversibility.

Cost benefit analysis : the value of preserving options.Cost benefit analysis : the value of preserving options.• A stylised argument. :A stylised argument. :• To morow cost, value C, prob. (½), 0, prob. (1/2)To morow cost, value C, prob. (½), 0, prob. (1/2)• action allow to avoid it cost a, action allow to avoid it cost a, • Information will arrive : C or 0Information will arrive : C or 0• Willingness to pay to keep the option ? : (1/2)(C-a)>0Willingness to pay to keep the option ? : (1/2)(C-a)>0• Possibly (1/2)C-a<0,Possibly (1/2)C-a<0,• More generally….More generally….

Some references.Some references. Aldy, J.E., P. R. Orszag and J. E. Stiglitz, ''(2001) ''Climate Change: Aldy, J.E., P. R. Orszag and J. E. Stiglitz, ''(2001) ''Climate Change:

An Agenda for Global Collective Action'', Prepared for the An Agenda for Global Collective Action'', Prepared for the conference on ``The Timing of Climate Change Policies'', Pew conference on ``The Timing of Climate Change Policies'', Pew Center on Global Climate Change, October. Center on Global Climate Change, October.

Bradford, D.F. (2001), « Improving on Kyoto: A No Cap but Trade Bradford, D.F. (2001), « Improving on Kyoto: A No Cap but Trade Approach to Greenhouse Gas control » Princeton University.Approach to Greenhouse Gas control » Princeton University.

Chakrovorty U, Magné B. and Moreaux M, (2003) « Energy Chakrovorty U, Magné B. and Moreaux M, (2003) « Energy resource substitution and carbon concentration targets with non resource substitution and carbon concentration targets with non stationary needs'', Leerna 31, Université de Toulouse.stationary needs'', Leerna 31, Université de Toulouse.

Cooper, R., (1998), ''Toward a real global warming treaty'', Foreign Cooper, R., (1998), ''Toward a real global warming treaty'', Foreign Affairs, vol. 77 no 2, March-AprilAffairs, vol. 77 no 2, March-April CC

Carraro C.(1999) ''The Structure of International Agreements on Carraro C.(1999) ''The Structure of International Agreements on Climate Change''in C. Carraro C. (ed), International Environmental Climate Change''in C. Carraro C. (ed), International Environmental Agreements on Climate Change, Kluwer Academic Publishers, Agreements on Climate Change, Kluwer Academic Publishers, Dordrecht, NLDordrecht, NL

Chandler L and Tulkens H. (2005) « Stability issues and climate Chandler L and Tulkens H. (2005) « Stability issues and climate related dynamic externalities »38p related dynamic externalities »38p

Some references.Some references. Freixas X, Guesnerie R, et Tirole J. (1985) « Planning under Freixas X, Guesnerie R, et Tirole J. (1985) « Planning under

incomplete information and the ratchet effect », Review of incomplete information and the ratchet effect », Review of Economic Studies, LII, 173-191..Economic Studies, LII, 173-191..

Guesnerie R. (2003) « Les enjeux économiques de l'effet de Guesnerie R. (2003) « Les enjeux économiques de l'effet de serre » in «Kyoto et l‘économie de l'effet de serre », sous la serre » in «Kyoto et l‘économie de l'effet de serre », sous la direction de R. Guesnerie, La Documentation Française, Paris.direction de R. Guesnerie, La Documentation Française, Paris.

Guesnerie R. ( 2004) « Calcul Economique et Développement Guesnerie R. ( 2004) « Calcul Economique et Développement Durable », Revue Economique, p.363-382.Durable », Revue Economique, p.363-382.

Guesnerie R. (2005) ''Assessing Rational Expectations :2- Guesnerie R. (2005) ''Assessing Rational Expectations :2- ''Eductive'' stability in economics », MIT Press, 453 P.''Eductive'' stability in economics », MIT Press, 453 P.

Guesnerie R. (2006) The design post Kyoto climate schemes : an Guesnerie R. (2006) The design post Kyoto climate schemes : an introductory analytical assesment ». introductory analytical assesment ». 

Ha-Duong M, Grubb M et. Hourcade J.C, (1997) ''Influence of Ha-Duong M, Grubb M et. Hourcade J.C, (1997) ''Influence of socio--economic inertia and uncertainty on optimal CO2-emissions socio--economic inertia and uncertainty on optimal CO2-emissions abatment'', Nature, Vol. 390.abatment'', Nature, Vol. 390.

Newell, R.G. and W.A. Pizer, (2000), « Regulating Stock Newell, R.G. and W.A. Pizer, (2000), « Regulating Stock Externalities Under Uncertainty », Discussion Paper 99-10, Externalities Under Uncertainty », Discussion Paper 99-10, Resources for the Future, Washington DC, February. Resources for the Future, Washington DC, February.

Some references.Some references. Nordhaus, W.D, (2002), ''After Kyoto: Alternative Mechanisms to Nordhaus, W.D, (2002), ''After Kyoto: Alternative Mechanisms to

Control Global Warming'', Paper prepared for the meetings of the Control Global Warming'', Paper prepared for the meetings of the American Economic Association and the Association American Economic Association and the Association of.IEA/SLT(2002)28of.IEA/SLT(2002)28

Philibert, C. (2000). ``How could emissions trading benefit Philibert, C. (2000). ``How could emissions trading benefit developing countries.'' Energy Policy , volume 28, no 13.developing countries.'' Energy Policy , volume 28, no 13.

Philibert, C., and J. Pershing. (2001). ``Des objectifs climatiques Philibert, C., and J. Pershing. (2001). ``Des objectifs climatiques pour tous les pays : les options.'' Revue de l‘Energie 524.pour tous les pays : les options.'' Revue de l‘Energie 524.

Pizer, W.A., (2001), ''Combining Price and Quantity Control to Pizer, W.A., (2001), ''Combining Price and Quantity Control to Mitigate Global Climate Change'', Journal of Public Economics, 85,Mitigate Global Climate Change'', Journal of Public Economics, 85,(3), 409-434.(3), 409-434.

Rieu J.(2002) ''Politiques nationales de lutte contre le changement Rieu J.(2002) ''Politiques nationales de lutte contre le changement climatique et réglementation de la concurrence : le cas de la climatique et réglementation de la concurrence : le cas de la fiscalité », mimeo.fiscalité », mimeo.

Weitzman, M. L., (1974) ''Prices vs. Quantities'', Review of Weitzman, M. L., (1974) ''Prices vs. Quantities'', Review of Economic Studies, vol.41, October.Economic Studies, vol.41, October.

Weitzman, M. L., (2000),AERWeitzman, M. L., (2000),AER