Testing Day's Conjecture that More Nitrogen Decreases Crop Yield Skewness

While controversy surrounds skewness attributes of typical yield distributions, a better understanding is important for agricultural policy assessment and for crop insurance rate setting. Day (1965) conjectured that crop yield skewness declines with an increase in low levels of nitrogen use, but higher levels have no effect. In a theoretical model based on the law of the minimum (von Liebig) technology, we find conditions under which Day's conjecture applies. Employing four experimental plot datasets, we investigate the conjecture by introducing (a) a flexible Bayesian extension of the Just-Pope technology to incorporate skewness, and (b) a quantile-based measure of skewness shift. For corn yields, the Bayesian estimation provides strong evidence in favor of negative skewness at commercial nitrogen rates and for Day's conjecture. There was weaker evidence in favor of positively skewed cotton yield and little evidence in favor of the conjecture. The results are also confirmed by the quantile-based measure.