On the Treatment of Heteroscedasticity in Crop Yield Data

In empirical applications with crop yield data, conditioning for heteroscedasticity is both important and challenging. It is important because the scale of the distribution can markedly influence the results, and challenging because statistical tests for the common heteroscedasticity assumptions (constant or proportional variance) often lead to ambiguous conclusions. Alternatively, Harri et al. (2011) proposed a methodology that estimates the degree of heteroscedasticity, removing the need to make a specific assumption. Such approaches assume that volatility changes are symmetric (identical) across tails of the yield distribution. We propose a generalization to the Harri et al. (2011) methodology, which allows asymmetry between the tails, akin to the generalization of GARCH to AGARCH. Using U.S. county level yield data from 1951–2017, we find evidence of asymmetry in corn and soybean, but not wheat. Moreover, the asymmetry takes a particular form—increasing volatility in the lower tail. To investigate economic significance, we consider the effect of imposing symmetric heteroscedasticity in rating crop insurance contracts, as currently done by the USDA’s Risk Management Agency in rating their Area Risk Protection products. We find that relaxing the symmetry assumption leads to economically and statistically significant rents. Our results suggest that the Risk Management Agency and others should consider the possibly asymmetric nature of heteroscedasticity in crop yield data.