Munich Personal RePEc Archive Uncertainty in optimal pollution levels: Modeling the benefit area Halkos, George Department of Economics, University of Thessaly June 2013 Online at https://mpra.ub.uni-muenchen.de/47768/ MPRA Paper No. 47768, posted 22 Jun 2013 20:03 UTC 1 Uncertainty in optimal pollution levels: Modeling the benefit area By George E. Halkos and Dimitra C. Kitsou Laboratory of Operations Research Department of Economics, University of Thessaly, Volos Greece Abstract This paper identifies the optimal pollution level under the assumptions of linear, quadratic and exponential damage and abatement cost functions and investigates analytically the certain restrictions that the existence of this optimal level requires. The evaluation of the benefit area is discussed and the mathematical formulation provides the appropriate methods, so that to be calculated. The positive, at least from a theoretical point of view, is that both the quadratic and the exponential case obey to the same form of evaluating the benefit area. These benefit area estimations can be used as indexes between different rival policies and depending on the environmental problem the policy that produces the maximum area will be the beneficial policy. Keywords: Benefit area; damage cost; abatement cost; pollution. JEL Classifications: C02; C62; Q51; Q52. This research has been co.financed by the E ropean Union /E ropean 0ocial 1 nd 2 E013 and Gree4 national f nds thro gh the Operational 5rogram 6Ed cation and Lifelong Learning6 of the National 0trategic Reference 1ramewor4 /N0R13 . Research 1 nding 5rogram: 8eracleit s II. Investing in 4nowledge society thro gh the E ropean 0ocial 1 nd. 2 1. Introduction Rationality in the form lation and applicability of environmental policies depends on caref l consideration of their conseq ences on the nat re and on the society. 1or this reason it is important to q antify the costs and benefits in the most acc rate way. B t the validity of any cost benefit analysis /hereafter CBA3 is ambig o s as the res lts may have large ncertainties. Uncertainty is present in all environmental problems and this ma4es clear the need for tho ghtf l policy design and eval ation. We may have ncertainty over the nderlying physical or ecological processes, as well as over the economic conseq ences of the change in environmental q ality. These so rces of ncertainty and their impact on policy form lation may be represented by the non.linear nat re of the damage and abatement cost f nctions. Damage or external costs can be estimated by an analysis of the chain of poll tion emissions, their dispersion and “transportation” /in cases of transbo ndary poll tion li4e the acid rain problem3, their effect meas red among others with a dose.response f nction and their final /if feasible3 monetary val ation. A similar pict re is realized when referring to abatement costs, which may be less ncertain, compared to damage costs, b t they are q ite severe. The main problem in this case is related to technological change which may be essentially diffic lt to predict or sometimes even to characterize. Uncertainty is obvio s not only in the parameters’ estimation, b t also in the choice of the appropriate model that “fits” the problem. To ma4e parameters’ ncertainty clearer, we may thing in terms of the fitted model ass med for the damage and abatement c rves in a regression analysis that “lies” between the pper and the lower bo nd of a 3 A5B confidence interval. That is there are two c rves creating an interval of val es for the fitted model and in this way ncertainty d e to variation of the estimated coefficients. As ncertainty may be d e to the lac4 of appropriate abatement and damage cost data, we apply here a method of calibrating non.existing damage cost estimates relying on individ al co ntry abatement cost f nctions. In this way a “calibrated” Benefit Area /BAc3 is estimated. 0pecifically, we try to identify the optimal poll tion level nder the ass mptions of linear, q adratic and exponential abatement and damage cost f nctions. As far as the parameters are concerned the first two are linear while the third is a non. linear f nction. That is we improve the wor4 of 8al4os and Citsos /20053 extending the n mber of different model approximations of abatement and damage cost f nctions and th s the ass med correct model eliminates ncertainty abo t c rve fitting. The target of this paper is to develop the appropriate theory whatever the model choice is. The str ct re of the paper is the following. 0ection 2 disc sses the bac4gro nd of the problem and reviews the relative existing literat re. 0ection 3 identifies analytically the intersection of the marginal abatement cost c rve /hereafter DAC3 with the marginal damage cost c rve /hereafter DD3, in order to examine when and if an optimal poll tion level exists. The existence of the intersection, despite the general belief, is not always tr e and the conditions are analytically examined here. In section E an empirical application for a sample of E ropean co ntries, with different ind strial str ct re, is presented. 1or these co ntries, the “calibrated” Benefit Area /BAc3 is eval ated explicitly, provided there is an intersection of the DD and DAC f nctions. The last section concl des the paper and comments on the policy implications related to this analysis providing evidence sef l to researchers and policy ma4ers. E 2. Background to the problem Abatement and damage cost f nctions are highly non.linear and the precise shapes of the f nctions are n4nown. At the same time, environmental policies are related with significant irreversibilities, which s ally interact in a very complex way with ncertainty. This complexity becomes worse, if we thin4 of the very long time periods that characterize environmental problems /5indyc4, 20073. The damage cost f nction relates poll tion and emissions of a specific poll tant. Damages are meas red as the effect of these emissions on health, mon ments, recreational activities, la4es, b ildings etc. Efforts to meas re the existence or other indirect se val es are made with the help of contingent val ation and other methods /8al4os and Gones, 2012; 8al4os and Datsiori, 2012; BHornstad and Cahn, 1AA6; 1reeman, 1AA33. As expected, the acc rate meas rement of damage is significant b t also diffic lt d e to many practical problems as presented in 1armer et al. /20013, Georgio et al. /1AA73 and Barbier /1AAI3. Uncertainties in the f nctions of damage and control costs infl ence the policy design in a n mber of ways /8al4os, 1AA63. The first effect is in terms of the choice of the appropriate policy instr ment. Weitzman /1A7E3, in his seminal paper, showed that in the presence of ncertainty in cost f nctions, the instr ment choice depends on the slopes of the c rves. In certainty conditions either instr ment will be eq ally effective b t in ncertainty the choice is important and depends on the slopes of the marginal damage and abatement cost c rves. In the case of steep marginal damage and flat marginal control cost c rves, q antity.based instr ments are more adeq ate; while in the case of steep marginal abatement cost and flat marginal damage c rves, a price.based instr ment is to be chosen /8al4os, 20003. 5 A n mber of st dies have extended the Weitzman’s thesis and showed that in the case of ncertainty “hybrid” policies of combining both instr ments will dominate to the single instr ment /Roberts and 0pence, 1A76; Weitzman, 1A7I; 5izer 2002; Gacoby and Ellerman, 200E3. It is worth mentioning that ncertainty may also affect the optimal timing of policy implementation if there are s n4 costs in the implementation of that policy or the environmental damage from the lac4 of any policy is at least partly irreversible. The conseq ences of irreversibility have been st died extensively in the literat re /5indyc4 2000, 2002; 1isher and 8anemann 1AA0; Gollier et al., 2000; Ulph and Ulph, 1AA7; Colstad, 1AA63. As mentioned, damage and abatement cost f nctions seem to have a large c rvat re and in many cases to be non.linear f nctions. A n mber of st dies have tried to assess the ca se and extent the ncertainty over the benefits from emissions red ction1. Rabl et al. /20053 compare damage and abatement costs for a n mber of air poll tants. They disting ish between discrete and contin o s policy choices. 0etting a limit for s lph r dioxide emissions from power plants is an example of a contin o s choice while the decision to demand a specific abatement method associated with a constant rate of emissions may be considered as a case of a discrete choice. They have also foc sed on ncertainties not only in damage costs b t also in abatement costs claiming that the extent 1 The cost f nctions may not behave well or may not satisfy the conditions of convexity or concavity. In the case of the damage cost f nction this may ta4e place by threshold effects as well as by any irreversibility where poll tion reaches a critical point at which the receptor /rivers, la4es, etc3 is damaged completely and cannot s stain any life. If one or both of the cost f nctions are not well behaved then o r res lts will be different.