Big assumptions for small samples in crop insurance

Abstract

Purpose – The purpose of this paper is to investigate the effects of crop insurance premiums being determined by small samples of yields that are spatially correlated. If spatial autocorrelation and small sample size are not properly accounted for in premium ratings, the premium rates may inaccurately reflect the risk of a loss. Design/methodology/approach – The paper first examines the spatial autocorrelation among county-level yields of corn and soybeans in the Corn Belt by calculating Moran's I and the effective spatial degrees of freedom. After establishing the existence of spatial autocorrelation, copula models are used to estimate the joint distribution of corn yields and the joint distribution of soybean yields for a group of nine counties in Illinois. Bootstrap samples of the corn and soybean yields are generated to estimate copula models with the purpose of creating sampling distributions. Findings – The estimated bootstrap confidence intervals demonstrate that the copula parameter estimates and the premium rates derived from the parameter estimates can vary greatly. There is also evidence of bias in the parameter estimates. Originality/value – Although small samples will always be an issue in crop insurance ratings and assumptions must be made for the federal crop insurance program to operate at its current scale, this analysis sheds light on some of the issues caused by using small samples and will hopefully lead to the mitigation of these small sample issues.