The Law of the Minimum and Sources of Nonzero Skewness for Crop Yield Distributions

Crop yields are not commonly found to be normally distributed, but the cause of the non-normal distribution is unclear. The non-normality might be due to weather variables and/or an underlying von Liebig law of the minimum (LoM) production function. Our objective is to determine the degree to which an underlying linear response stochastic plateau production function can explain the skewness of Oklahoma wheat yields at varied nitrogen rates. We use farm-level wheat data from a long-term experiment in Oklahoma, which is a unique data set to the literature. The Tembo et al. (2008) production function provides negative skewness at all levels of nitrogen with skewness near zero for both very high and very low levels of nitrogen. Observed skewness for wheat yields, however, is positive. The variation in the plateau by year shows positive skewness. Skewness in yield potential related to weather should be considered as a possible explanation of skewness.