Stochastic dominance analysis of on‐farm‐trial data: The riskiness of alternative phosphate sources in Burkina Faso

Stochastic dominance was used to determine the risk characteristics of phosphate fertilization of millet, sorghum and maize with commercial NPK fertilizer, rock phosphate and partially acidulated rock phosphate in Burkina Faso. On‐farm‐trial data from 1989, 1990 and 1991 in three rainfall zones was used. The analysis shows that among the four treatments tested, commercial NPK fertilizer has the most desirable risk characteristics. It is acceptable to risk averse decision makers for all three crops in all rainfall zones. The no‐fertilizer control is dominated by the fertilizer treatments. The rock phosphate treatments have higher yields and in certain cases higher returns than the no fertilizer control, but those benefits are less sure than for the soluble commercial fertilizer. The distributions of cash returns to rock phosphate treatments are rarely significantly different from those of the control. Rock phosphate treatments never dominate the commercial fertilizer treatment. If farmers have a choice between commercial fertilizer, rock phosphate and partially acidulated rock phosphate, at current prices most of those who use fertilizer would choose the soluble commercial product. If the availability of commercial fertilizer were limited (e.g. by lack of hard currency), some farmers would use rock phosphate—especially the partially acidulated product. Stochastic dominance permitted a timely and detailed analysis of risk inherent in phosphate fertilizer alternatives. Because on‐farm‐trails involve a modest number of alternatives, pairwise stochastic dominance comparisons are feasible. The stochastic dominance analysis permits researchers to communicate to extension staff and policymakers not only the degree of risk, but also something about the characteristics of the crop response that contribute to risk. The key to effective use of stochastic dominance is careful study of the distributions and understanding why a technology is dominated or is potentially acceptable to risk averse decisionmakers.