An Application of Kernel Density Estimation via Diffusion to Group Yield Insurance

The recent priority given to Federal Crop Insurance as an agricultural policy instrument has increased the importance of rate making procedures. Actuarial soundness requires rates that are actuarially fair: the premium is set equal to expected loss. Formation of this expectation depends, in the case of group or area yield insurance, on precise estimation of the probability density of the crop yield in question. This paper applies kernel density estimation via diffusion to the estimation of crop yield probability densities and determines ensuing premium rates. The diffusion estimator improves on existing methods by providing a cogent answer to some of the issues that plague both parametric and nonparametric techniques. Application shows that premium rates can vary significantly depending on underlying distributional assumptions; from a practical point of view there is value to be had in proper specification.