Crop Yield Skewness under the Law of Minimum Technology

David A. Hennessy
July 2007  [07-WP 451]

A large empirical literature exists seeking to identify crop yield distributions. Consensus has not yet formed. This is in part because of data aggregation problems but also in part because no satisfactory motivation has been forwarded in favor of any distribution, including the normal. This article explores the foundations of crop yield distributions for the Law of the Minimum, or weakest-link, resource constraint technology. It is shown that heterogeneity in resource availabilities can increase expected yield. The role of stochastic dependence is studied for the technology. With independent, identical, uniform resource availability distributions the yield skew is positive, whereas it is negative whenever the distributions are normal. Simulations show how asymmetries in resource availabilities determine skewness. Extreme value theory is used to suggest a negative yield skew whenever production is in a tightly controlled environment so that the left tails of resource availability distributions are thin.

Keywords: beta-normal distribution, crop insurance, extreme value theory, Liebig technology, limiting factors, order statistics, reliability, weakest link.

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