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

Abstract

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. AbstractWhile controversy surrounds skewness attributes of typical yield distributions, a

Modeling skewness with the linear stochastic plateau model to determine optimal nitrogen rates

“…Despite several researchers finding evidence of nonzero skewness in crop distributions, no consensus has been reached regarding the underlying cause of the observed nonzero skewness in crop distributions (Harri et al., ; Hennessy, ). Researchers have sought to provide a rationale for the observed nonzero skewness in crop yield distributions and have developed several theories to explain nonzero skewness such as weather, cropping practices, geographic region, and resource availability (Du et al., ; Harri et al., ; Hennessy, ). Of these hypotheses, the hypothesis about resource availability is perhaps the best developed.…”

“…Day showed that skewness decreased as the quantity of nitrogen applied to the crops increased. Recently, Hennessy () and Du et al () have extended Day's work to try to explain how fertilizer inputs impact crop yield distributions. Hennessy () argued that nonzero skewness found in yield distributions is associated with minimum quantities of a limiting resource such as fertilizer.…”

“…Du et al () further investigated resource availability causing yield skewness by testing Day's () findings. Du et al () calculated skewness at various nitrogen rates for corn and cotton.…”

“…Du et al () further investigated resource availability causing yield skewness by testing Day's () findings. Du et al () calculated skewness at various nitrogen rates for corn and cotton. They offered empirical support for yield skewness decreasing with increasing amounts of nitrogen applied to corn, and presented some evidence that no further effect on skewness should be expected when nitrogen is no longer a limiting resource of corn production.…”

Are Actuarial Crop Insurance Rates Fair?: An Analysis Using a Penalized BivariateB-Spline Method

“…The covariates z i (land quality) are IID from a truncated normal distribution N (200,15 2 ) on the interval [100,300]. The beta distribution for error and the non‐constant scaling factor are included to introduce left skewness in corn yield distributions (Ker and Goodwin, ; Du et al ., ) and increasing yield variation as the historical yield increases (Tannura et al ., ). Based on this yield model, observed premiums are generated from y i = μ ( x i , z i )+ ζ i , where ζ i ∼ N (0,0.1 2 ) are measurement errors, the covariates x i (coverage rates) are IID from a uniform distribution on the discrete numbers (0.55,0.60,…,0.90,0.95) and the true premium price is by equation .…”