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Probabilistic programming are typically used to model economic-environmental trade-when environmental outcomes are stochastic. Application of available probabilistic programming techniques such as the upper partial moment (UPM) is problematic due to the conservativeness of the estimated the compliance probability. Conservatively estimated trade-offs may result in overregulation of agricultural production practices. Although the conservativeness of the UPM is usually acknowledged by researchers, none of the researchers investigated the size of conservativeness of the UPM. An alternative non-linear trade-off model specification is developed to investigate the conservativeness of the UPM. Meta data from the validated Soil Water Balance (SWB) crop growth simulation model for irrigated maize in South Africa is used to show that the UPM is very conservative in the estimation of the trade-offs comparing to the new method. However, the size of the conservativeness is very situation-specific and varies due to differences in fixed resources, fertilizer application methods and conservativeness measures.


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