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, g=1,5 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-  ’]t=0infini{(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 : < 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 » • Discounting=selfishness 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 2Uncert. lowers long run discount rate. • Argument : valuation by generation 0 of 1 euro given to generation T : exp(-Rt) • If uncertainty : R or r, R>r • (1/2) exp(-Rt) + (1/2)exp(-rT) = • exp(-rT) [(1/2)+(1/2)exp((-R+r)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 • Min{x,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 • > probability of the planet’s 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-  ’]t=0infini{(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/ )] • Min{g}[Min{’}-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 : Min{g/ } • 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)>0 • Possibly (1/2)C-a<0, • 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 l‘économie 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 l‘Energie 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