Stochastic dominance analysis in the selection of risk-efficient cropping strategies

Stochastic dominance analysis is a method of partial ordering of risky choices for decision-makers with similar risk-aversion attitude. The procedure involves comparison of cumulative probability distributions of random variables representing outcomes of risky actions, using only limited assumptions on the risk-taking behavior of the decision-maker instead of an exact utility function. A procedure that linked stochastic dominance analysis with crop simulation modeling was developed to determine risk-efficient cropping strategies defined by cropping sequence, planting date and other management practices. The simulation model estimated crop yields, which were translated to probability distributions of net returns and used as inputs to stochastic dominance analysis. To identify stochastically dominant or risk-efficient strategies, three criteria were used, namely: 1) first-degree stochastic dominance (FSD); 2) second-degree stochastic dominance (SSD); and 3) stochastic dominance with respect to a function (SDWRF). The mean-variance criterion, a special form of SSD, was also applied but only on strategies that passed the test for normality, which eliminated the required assumption of a quadratic utility function. The procedure also included step-by-step application of the FSD Rule on dominated strategies to identify the `most risky' strategies, and the application of SDWRF at the highest level of risk aversion to determine the `least risky' strategies. The procedure was applied to a typical farm in Maasin, Southern Leyte, Philippines, where crop yields were stimulated using the crop model POLYCROP, with crop-specific characteristics, soil characteristics like organic matter content, daily weather data, and date of planting as model inputs. Several possible cropping strategies defined by combination of crop sequence, planting date and level of nitrogen fertilizer, were evaluated for risk efficiency, using the Stochastic Dominance with Respect to a Function (SDRF) model. Risk-efficient strategies for each crop sequence group and for all groups, as well as the "most risky" and "least risky" strategies were identified following the proposed procedure. Moreover, a discriminant function, which was capable of identifying preliminary the risk-efficient strategies, was derived using variables based on rainfall (e.g. accumulated rainfall at flowering), crop characteristics (e.g. number of days to flowering), net returns and ratios of gross returns to production costs. Application of the developed technology has demonstrated that a large number of possible choices of cropping strategies can be narrowed down to only a few risk-efficient strategies, which may be identified further, in addition to those strategies that are preferable with respect to other criteria. The study has also shown that a discriminant function could be used to classify new strategies into risk-efficient and dominant sets in a preliminary screening process prior to stochastic dominance analysis