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 nitrogen use at low levels but not at higher levels. Employing four corn yield 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. 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 confirmed by the quantile-based measure. We also find evidence that skewness becomes more negative upon moving from corn-after-corn to corn-after-soybean.