Crop Yield Skewness and the Normal Distribution

Empirical studies point to negative crop yield skewness, but the literature provides few clear insights as to why. This paper formalizes three points on the matter. Statistical laws on aggregates do not imply a normal distribution. Whenever the weather-conditioned mean yield has diminishing marginal product with respect to a weather-conditioning index, then there is a disposition toward negative yield skewness. This is because high marginal product in bad weather stretches out the yield distribution’s left tail relative to that for weather. For disaggregated yields, unconditional skewness is decomposed into weather-conditioned skewness plus two other terms and each is studied in turn.