The use of copulas in explaining crop yield dependence structures for use in geographic diversification

Purpose – What copulas are, their estimation, and use is illustrated using a geographical diversification example. To accomplish this, dependencies between county-level yields are calculated for non-irrigated wheat, upland cotton, and sorghum using Pearson linear correlation and Kendall's tau. The use of Kendall's tau allows the implementation of copulas to estimate the dependency between county-level yields. The paper aims to discuss these issues. Design/methodology/approach – Four parametric copulas, Gaussian, Frank, Clayton, and Gumbel, are used to estimate Kendall's tau. These four estimates of Kendall's tau are compared to Pearson's linear correlation, a more typical measure of dependence. Using this information, functions are estimated to determine the relationships between dependencies and changes in geographic and climate data. Findings – The effect on county-level crop yields based on changes of geographical and climate variables differed among the different dependency measures among the three different crops. Implementing alternative dependency measures changed the statistical significance and the signs of the coefficients in the sorghum and cotton dependence functions. Copula-based elasticities are consistently less than the linear correlation elasticities for wheat and cotton. For sorghum, however, the copula-based elasticities are generally larger. The results indicate that one should not take the issue of measuring dependence as a trivial matter. Originality/value – This research not only extends the current literature on geographical diversification by taking a more detailed examination of factors impacting yield dependence, but also extends the copula literature by comparing estimation results using linear correlation and copula-based rank correlation.