Ratemaking Of Hubei Province County Level Rice Yield Insurance Contract

Crop area yield insurance that is as an innovation of agricultural insurance contract can not only reduce or eliminate, moral hazard, but also partly mitigate the inverse selection. Meanwhile, compared to individual yield insurance, crop area yield insurance is more convenient for loss determination and claims settlement, and easier to collect yield data. A fundamental parameter of any insurance contract is the premium rate, this article rates Hubei's county-level rice yield insurance contract based on the yield data from 1991 to 2007, which provides some useful information for the application of crop area yield insurance in China.This article builds 23 Hierarchical Bayesian spatial-temporal models with consideration of the temporal trend, spatial heterogeneity, spatial effect and spatial-temporal effect. And it selects the best one from 23 Models according to the DIC standard by Gibbs Sampling with WinBUGS, then predicts rice yield of each county from 1992 to 2009. Based on the predicted yields in 2008 and the posterior distributions, it calculates the county-level pure premium rate of rice yield insurance, the average premium rate is 2.99%, and the standard error is 0.62. The main conclusions are: the predicted yields of 1992-2007 are close to the actual yields, and the standard errors are small, which show that the selected model has a good capacity of prediction in short term; The premiums among neighboring counties are similar; The Pearson correlation coefficient between the pure premium rates and Monte Carlo errors is 0.6793, and the MC error contains the yields' uncertainty from time, space, and spatial-temporal effect.This article estimates each county's parameters under the assumption of Normal, LogNormal, Logistic, Beta, Weibull distribution by Maximum Likelihood method, based on the yields detrended by Spatial-temporal model. It's concluded that: the average premium rate is 3.92%, and the standard error is 1.90; 74 counties have the smallest AD statistics under the Logistic distribution having larger skewness or Weibull distribution the kurtosis of which is non-equated to 0, which shows that the yields of most of counties are better fitted by these two distributions; the pure premiums under non-symmetrical distribution are generally higher than under the symmetric. Therefore, different assumptions of yield distribution generally have significant impact on pure premium rates. The Pearson correlation coefficient between standard errors of the samples and the pure premium rates under the best fitted distribution is 0.7298, and the error contains the yields' variation in the whole term.It's found that there is a significant difference between the pure premium rates calculated from the posterior and the best fitted distribution, and the pure premium rate under the latter distribution is averagely 1% higher than the former one. In the view of utilization of experiential information, the pure premium rates under the best fitted distribution are selectable, because they can reflect the yields' variation in the whole term, whereas the rates under posterior reflect the yields' variation in recent term. But the rates under posterior may be selected when in the view of credibility theory, in that the recent data is endowed with a larger weight.