The Return of von Liebig's “Law of the Minimum”

The development of optimal fertilizer recommendations requires a renewed collaborative effort between agronomists and agricultural economists. The purpose of this study is to emphasize the direction of this interdisciplinary effort in the area of crop response analysis. Using information from two separate experiments [corn (Zea mays L.) response to N and P fertilization and cotton lint (Gossypium hirsutum) response to N and irrigation water], it is shown that the best response model is a von Liebig specification, more commonly known as the law of the minimum. When the selection of a statistical specification is made among models that do not share the parameter space, hypothesis testing cannot be done by means of the familiar F-test and likelihood ratio. The selection of the von Liebig specification (chosen against square-root polynomial and Mitscherlich-Baule models) is, thus, made on the basis of a rigorous statistical analysis using a nonnested hypothesis approach. Giannini Foundation Research Paper no. 1021.