While the preponderance of empirical studies point to negative crop yield skewness in a wide variety of contexts, the literature provides few clear insights on why this is so. The purpose of this paper is to make three points on the matter. We show formally that statistical laws on aggregates do not suggest a normal yield distribution. We explain that whenever the weather-conditioned mean yield has diminishing marginal product, then there is a disposition toward negative skewness in aggregate yields. This is because a high marginal product in bad weather states stretches out the left tail of the yield distribution relative to that of the weather distribution. Turning to disaggregated yields, we decompose unconditional skewness into weather-conditioned skewness plus two other terms and study each in turn.
Hennessy, David A., "Toward a Normative Theory of Crop Yield Skewness" (2008). CARD Working Papers. 504.