Economic-environmental trade-offs and the conservativeness of the upper partial moment

Accounting for the stochastic nature of environmental outcomes when quantifying economic environmental trade-offs with mathematical programming models requires the use of probabilistic programming approaches like the upper partial moment (UPM) method. Application of the UPM model may result in overregulation and losses in farm profit because the probabilistic constraint is satisfied at a higher level than the specified compliance probability, resulting in conservative responses from polluters. The main objective of this article was to present the upper frequency method as an alternative to enforce a probabilistic constraint with a close bound to the actual compliance probability. The UFM uses binary variables in a linear programming framework to enforce the probability bound on an empirically distributed outcome variable. Results showed that the UPM model was very conservative in the estimation of the upper probability bound, which resulted in an overestimation of abatement costs and an underestimation of the average amount of pollution above the environmental goal. Inconsistencies also exist between the ranking of alternatives when comparing the UPM and UFM methods. The UFM is general enough to ensure that the technique can be applied to any problem where the researcher is concerned with the risk of exceeding a specified target level.