Time horizon, uncertainty and cost benefit analysis.

1
Time horizon, uncertainty and cost benefit
analysis.

• Long run discount rate for environmental goods.

2
Cost benefit analysis
3
The cost of Kyoto the verdict of models.

• Why models ?
• Sectoral effects (électricityé).
• effect on final demande econometrics of price
  effects.
• General interactions.
• Which models ?
• sectoral.aggregate.
• Computable general equilibrium.macroéconomics.
• The double dividend controversy.

4
The benefits of climate policies

• The difficulties
• Many chapters
• Agriculture, extreme weather events
• Bio-diversity, health, quality of climate.
• Flooding, large scale migrations..
• Difference across regions
• Northern areas and vulnerable, (southern) places.
• Differences according to the range of temperature
• 1 to 3 degrees agriculture in northern areas.
• Above high reductions of general fertility.
• Uncertainty has to be faced.

5
The benefits of climate policies

• The solutions of the Stern review.
• A comprehensive qualitative coverage of the
  phenomena.
• A long run probabilistic assessment
• A synthetical money assessment
• Damages (T/2,5) power g, g1,5 to 3
• Probabilistic assesment high climate scenario,
  markets and non market impacts, 95th percentile
  35per cent of global GDP in 2200.
• The presentation of numbers.
• Equivalent GDP loss.
• Skips partly the discount rate issue.

6
The discount rate in the Stern Review.

• The issue
• How should one unit of consumption for the
  present generation be valued in comparison of the
  same unit for the present generation.
• If perfect altruism the answer depends upon the
  elasticity of marginal utility (xU/U) or
  relative risk aversion.
• Pure rate of time preference.
• Example
• Isoelastic utility function
• U 1/(1- ? ?t0infini(exp(- ? t))U(xt)(1 -
  ?)
• The solution of the Stern review
• Elasticity close to one (Log utility)
• Does not kill the future.
• Underestimate risk aversion.

7
Questions on long run discount rates for
environmental goods.

• Discounting  kills  the distant future.
• 10 per cent discount rate 120 in 50 years, 14000
  in 100 years
• 7 per cent, discount rate lt 30 in 50 years,
  860 in 100 years,
• 5 per cent discount rate 130 in 100 years, 17
  000 in 200 years,
• 2 per cent discount rate 2,7 in 50 years, 7,3,
  in 100 years, 52 in 200 years.
• Is standard discounting appropriate for long run
  decisions ?
• Argument 1  ecological intuition 
• Discountingselfishness of existing generations,
  ethically unacceptable
• Destroys our common natural patrimony, for second
  rate interests.
• Argument 2  economic reason 
• Cost benefit analysis provides the weights for
  decisions about public versus private goods.
• Cost benefit analysis rightly stresses that it is
  useless to sacrifice present generations to
  future and much wealthier generations.

8
How to reconcile economic and ecological
intuition ?

• Ingredient 1 Environmental goods and the long
  run.
• They differ from
• private goods out put cannot be continually
  expanded.
• non renewable resources not destroyed by
  cautious use.
• in the long run, their relative scarcity (/
  private goods) increases.
• Ingredient 2 Uncert. lowers long run discount
  rate.
• Argument valuation by generation 0 of 1 euro
  given to generation T exp(-Rt)
• If uncertainty R or r, Rgtr
• (1/2) exp(-Rt) (1/2)exp(-rT)
• exp(-rT) (1/2)(1/2)exp((-Rr)T)
• exp(-r (T)T),
• r (T) tends to r when T tends to infinity
• Weitzman (2000), AER

9
How to reconcile CB analysis and economic
intuition.

• Ingredient 3 Substitutability
• If private and environmental goods were perfectly
  substitutable, then, no reason to treat them
  differently in Cost Benefit analysis.
• If they are strict compléments
• Minx,y
• Private output increases, the environmental good
  level does not.
• After a while, increasing the welfare of a
  wealthier future generation relies on improving
  environmental quality.
• Discount rate for private good ?
• Discount rate for environmental good almost
  zero.
• Ingredient 4  ethical  considerations.
• Pure rate of time preference close to zero
• gt probability of the planets survival ?

10
A formal modelRG  Calcul économique et
Développement durable , Revue Economique, 2004,

• 2 goods
• aggregate consumption good quantity.
•  environnemental quality 
• Utility function
• Formulation.
• v(xt ,yt) xt((?- 1)/ ? ) yt((? -1)/ ? ) (?
  /(? -1))
• V(xt ,yt) 1/(1- ?  )v(xt ,yt)(1 - ?)
• Comment.
• y/x decreases of 1/100, the willingness to pay
  increases of (1/?)
•   pour 100
• Iso-élastic cardinal utilty for generation t,
• Constant relative risk aversion ?.
• Uncertainty
• On the long run elasticity of substitution
  between private and environnemental good, ?

11
A formal modelRG  Calcul économique et
Développement durable , Revue Economique, 2004,

• 2 goods
• aggregate consumption good quantity.
•  environnemental quality 
• Note
• ? only parameter, summary statistics of much
  information
• ?   different possible interprétations.
• Social welfare
• U 1/(1- ? ?t0infini(exp(- ? t))v(xt
  ,yt)(1 - ?)
• Remarks
• Index t associated to generation
• Utilitarian.
• When ?__0,  ethical  viewpoint.
• Cost Benfit analysis at the margin
• A  reform  viewpoint.
• Combines the four previous ingredients.

12
Results

•  Canonical  Ecological Cost benefit Analysis
• Generation 0 evaluates an investment (at 0),
  generating an improvement of the environmental
  quality for generation t
• The value of the improvement is measured with
  the marginal willingness to pay of generation 0
   canonical procedure 
• Proposition A
• If the probability of  ecological strangling 
  in the long run is null.
• Standard discount rate Min (g?) ?
• ethical  canonical  ecological long run
  discount rate
• lim T?? ? (T) g?  -(1/ ? )
• MingMin?-1/Min ?
• (1) (1,4 - 0.9) 0,5 pour cent !

13
Results

•  Canonical  Ecological Cost benefit Analysis
• Generation 0 evaluates an investment (at 0),
  generating an improvement of the environmental
  quality for generation t
• The value of the improvement is measured with
  the marginal willingness to pay of generation 0
   canonical procedure .
• Proposition B
• If the probability of  ecological strangling 
  in the long run is non zero.
• The ethical long run discount rate for private
  goods Ming/ ?
• The ethical  canonical  ecological long run
  discount rate is zero.
• Lessons
• Substitutability is essential
• and uncertain..

14
Irreversibility and option value.

• Irreversibility of the greenhous effect.
• Irreversibility of concentrations
• Climate irreversibility.
• Cost benefit analysis the value of preserving
  options.
• A stylised argument.
• To morow cost, value C, prob. (½), 0, prob. (1/2)
• action allow to avoid it cost a,
• Information will arrive C or 0
• Willingness to pay to keep the option ?
  (1/2)(C-a)gt0
• Possibly (1/2)C-alt0,
• More generally.

15
Some references.

• Aldy, J.E., P. R. Orszag and J. E. Stiglitz,
  ''(2001) ''Climate Change An Agenda for Global
  Collective Action'', Prepared for the conference
  on The Timing of Climate Change Policies'', Pew
  Center on Global Climate Change, October.
• Bradford, D.F. (2001),  Improving on Kyoto A No
  Cap but Trade Approach to Greenhouse Gas
  control  Princeton University.
• Chakrovorty U, Magné B. and Moreaux M, (2003)
   Energy resource substitution and carbon
  concentration targets with non stationary
  needs'', Leerna 31, Université de Toulouse.
• Cooper, R., (1998), ''Toward a real global
  warming treaty'', Foreign Affairs, vol. 77 no 2,
  March-April C
• Carraro C.(1999) ''The Structure of International
  Agreements on Climate Change''in C. Carraro C.
  (ed), International Environmental Agreements on
  Climate Change, Kluwer Academic Publishers,
  Dordrecht, NL
• Chandler L and Tulkens H. (2005)  Stability
  issues and climate related dynamic
  externalities 38p

16
Some references.

• Freixas X, Guesnerie R, et Tirole J. (1985)
   Planning under incomplete information and the
  ratchet effect , Review of Economic Studies,
  LII, 173-191..
• Guesnerie R. (2003)  Les enjeux économiques de
  l'effet de serre  in Kyoto et léconomie de
  l'effet de serre , sous la direction de R.
  Guesnerie, La Documentation Française, Paris.
• Guesnerie R. ( 2004)  Calcul Economique et
  Développement Durable , Revue Economique,
  p.363-382.
• Guesnerie R. (2005) ''Assessing Rational
  Expectations 2- ''Eductive'' stability in
  economics , MIT Press, 453 P.
• Guesnerie R. (2006) The design post Kyoto climate
  schemes an introductory analytical
  assesment . 
• Ha-Duong M, Grubb M et. Hourcade J.C, (1997)
  ''Influence of socio--economic inertia and
  uncertainty on optimal CO2-emissions abatment'',
  Nature, Vol. 390.
• Newell, R.G. and W.A. Pizer, (2000),  Regulating
  Stock Externalities Under Uncertainty ,
  Discussion Paper 99-10, Resources for the Future,
  Washington DC, February.

17
Some references.

• Nordhaus, W.D, (2002), ''After Kyoto Alternative
  Mechanisms to Control Global Warming'', Paper
  prepared for the meetings of the American
  Economic Association and the Association
  of.IEA/SLT(2002)28
• Philibert, C. (2000). How could emissions
  trading benefit developing countries.'' Energy
  Policy , volume 28, no 13.
• Philibert, C., and J. Pershing. (2001). Des
  objectifs climatiques pour tous les pays les
  options.'' Revue de lEnergie 524.
• Pizer, W.A., (2001), ''Combining Price and
  Quantity Control to Mitigate Global Climate
  Change'', Journal of Public Economics, 85,(3),
  409-434.
• Rieu J.(2002) ''Politiques nationales de lutte
  contre le changement climatique et réglementation
  de la concurrence le cas de la fiscalité ,
  mimeo.
• Weitzman, M. L., (1974) ''Prices vs.
  Quantities'', Review of Economic Studies, vol.41,
  October.
• Weitzman, M. L., (2000),AER