Crop Yield Skewness under the Law of Minimum Technology
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The Center for Agricultural and Rural Development (CARD) conducts innovative public policy and economic research on agricultural, environmental, and food issues. CARD uniquely combines academic excellence with engagement and anticipatory thinking to inform and benefit society.
CARD researchers develop and apply economic theory, quantitative methods, and interdisciplinary approaches to create relevant knowledge. Communication efforts target state and federal policymakers; the research community; agricultural, food, and environmental groups; individual decision-makers; and international audiences.
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Abstract
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.