Ecological discountingChristian GollierToulouse School of Economics (LERNA and EIF)1July 14, 20081The financial support of the Chair ”Sustainable Finance and Responsible In-v estment” at IDEI/TSE is acknowledged.AbstractWhic h rates should we use to discount costs and benefits of different natureat different time horizons? We answer to this question by considering arepresentative agent consuming two goods whose availability evolves overtime in a stochastic way. We extend the Ramsey rule by taking into accoun tof the degree of substitutability between the two goods and of the uncertaintysurrounding the economic and environmental growths. The rate at whichenvironmental impacts should be discounted is in general different from theone at which monetary benefits should be discounted. We provide argumentsin fa vor of an ecological discount rate smaller than the economic discountrate. In particular, we show that, under certainty, the difference between theeconomic and the ecological discount rates equals the difference between theeconomic and the ecological growth rates. We also justify a decreasing termstructure of the ecological discount rate on the basis of the large parametricuncertainty affecting the evolution of the environmental quality.Keywords: Discounting, Ramsey rule, bivariate utility function, precau-tionary premium, sustainable development.JEL Classification: G12, E43, Q511IntroductionHo w much effort should we exert to improve the environmental quality thatwe will leave to future generations? This is a central question for a wideset of environmental contexts, as global warming, nuclear wastes, or biodi-versit y. Its answer d epends upon our expectations about the quality of theenvironment and about the level of economic development that these futuregenerations will face. For example, it is intuitive that our optimal effortshould be relatively large if we believe that the environment will be muchdeteriorated in the future or/and if the economy will be ruined. The problemis made complex because of the considerable uncertainties that we face withrespect to both the ecological and the economic evolutions of our societies.There are two possible methods to evaluate the present monetary valueof a sure future environmental impact. The classical one consists in first mea-suring the future monetary value of the impact, and second discounting thismonetary equivalent impact to the present. This involve s a pricing formulato value future changes in environmental quality, and an economic discountrate to discount these monetarized impacts. The second approach wouldconsist in first discoun ting the future environmental impact to transform itinto an immediate equivalent environmental impact, and then measuring themonetary value of this immediate impact. This involves an ecological dis-count rate, to discount environmental impacts. Of course, these two methodsare strictly equivalent. As shown by Hoel and Sterner (2007) in the case ofcertainty, the two discount rates differ if the monetary value of environmentalassets evolves over time.The classical method is not well adapted to the case of uncertainty. In-deed, the value of environmental assets in the future depends upon theirrelativ e scarcity, which is unknown. This is a problem because the economicdiscount rate is useful to discount sure future monetary benefits. Because themonetary value of environmental impacts is uncertain, one needs to computeits certainty equivalent. This requires the use of a stochastic discount fac-tor, which determines at the same time the risk premium and the economicdiscount rate. Standard pricing formulas exist that can be borrowed fromthe theory of finance, but there are seldom used in cost-benefitanalysesofenvironmental projects because of their complexity. In this paper, w e followthe alternative methods based on the ecological discount rate. The ecologi-cal discount factor associated to date t is the immediate sure en vironmental1impact that has the same impact on in tergenerational welfare than a unitenvironmental impact at date t. The (shadow) price of an immediate envi-ronmental impact can then be used to value environmental projects. Thisalternative method is simpler because one does not need to compute certaintyequivalent future values.The aim of this paper is to characterize the determinants of the economicand the ecological discount rates. The efficient economic (resp. ecological)discount rate equals the marginal rate of substitution between future andpresent consumption (resp. environmental qualities). Since Ramsey (1928),we know that the socially efficient economic discount rate is driven by aneconomic growth effect: if aggregate consumption is gro wing over time, andif the marginal utility of consumption is decreasing, the marginal utility ofconsumption is decreasing with time, yielding a positive economic discountrate. A symmetric argument exists for the ecological discount rate: if thequality of the en vironment improves with time, and if the marginal utility ofthe quality of the environment is decreasing, this environmental growth effectjustifies a positive ecological discount rate. On the contrary, if one believ esthat the quality of the environment will deteriorate over time, a negativeecological discount rate may be socially efficient. However, assuming thatconsumption is a substitute to the quality of the environment, the economicgrowth has a positive impact on the ecological discount rate, thereby poten-tially counterbalacing the effect of the deterioration of the environment. Asobserved for example by Traeger (2007), the possibility to substitute the de-teriorating environment quality by othergoodsisatthecoreofthenotionofsustainable development. If the substitutability is limited, the environmentaldeterioration effect dominates the economic growth effect, and the ecologicaldiscount rate should be small or negative, thereby inducing us to preserveenvironmental assets.Following Weitzman (2007) and Gollier (2002, 2007), we consider a consumption-based theory of discount rates under uncertainty. Uncertainty adds three ele-ments into the picture. Besides the gro w th effects and the substitution effect,there is a precautionary effect. The uncertainty associated to the future qual-ity of the environment reduces the ecological rate if the marginal utility of theenvironment is convex in it. This assumption is very intuitive, as show n bythe following thought experimen t.