Michael Price
Department of Statistics
Iowa State University

An Investigation of Actuarial Fair Crop Insurance Rates Using Partial Derivatives of Penalized Bivariate Tensor Product B-splines

Crop insurance is a risky business. Central to  program implementation in the United States is the rate-setting procedure, as implemented by the US Department of Agriculture's Risk Management Agency.  We investigate if the premium rates of yield insurance are actuarially fair by comparing the conditional yield density inferred from premium data with the conditional yield density inferred from yield data.

A procedure is developed to estimate the conditional yield density using premium data through partial derivatives of the premium rate function based on the penalized bivariate tensor product B-splines (BTPB).  We extend Xiao et al. (2012) to study the asymptotic properties of partial derivatives of a penalized BTPB estimator and provide variance estimation.  The conditional yield density inferred from premium data and its variance estimator are evaluated through simulation studies.

The procedure is also applied to a crop insurance data set from Iowa to examine the actuarial fairness of the premium rates. On average, premium rates are close to our estimates and this is true for each coverage level. However, premiums for low productivity land are generally too low while those for high productivity land are generally too high. Even after subsidies, premiums for the more productive land are generally substantially higher than what they should be.

Xiao, L., Li, Y., Apanasovich, T. V., and Ruppert, D. (2012). Local Asymptotics of P-splines. ArXiv e-prints.