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Summary In this paper, we investigate whether the yield insurance premium rates given by the US Department of Agriculture's Risk Management Agency 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 by using premium data through partial derivatives of the premium rate function, as fitted by penalized bivariate tensor product B-splines. We study the asymptotic properties of partial derivatives of a penalized bivariate tensor product B-spline estimator and provide variance estimates. 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 the state of 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 whereas those for high productivity land are generally too high. Even after subsidies, premiums for the more productive land are generally substantially higher than are our estimates of the corresponding actuarially fair rates.
Price et al. (Tue,) studied this question.