On the Distribution of Crop Yields: Does the Central Limit Theorem Apply?

In this paper we take issue with the applicability of the central limit theorem (CLT) on aggregate crop yields. We argue that even after correcting for the effects of spatial dependence, systemic heterogeneities and risk factors, aggregation does not necessarily lead to normality. We show that aggregation is also likely to lead to nonnormal distributions, which exhibit both skewness and excess kurtosis. In particular, we consider the case in which the number of summands is not constant but varies with time, which corresponds to the empirically relevant situation where the number of acres used for cultivation of a particular crop exhibits substantial variation over time. In this case, the CLT is not applicable while the limit theorems for random sums of random variables, which apply, predict that the limiting distribution of the sum is not normal and depends on the postulated distribution of the number of summands. Using data from aggregate US states crop yields, we provide empirical support regarding the deviation of aggregate crops yields from normality.