A Bayesian updating approach to crop insurance ratemaking

The current ratemaking procedure employed by the Federal Crop Insurance Corporation multiplies a pooled rate times the ten year farm-level average yield to determine farm-level premiums. Pooling results in adverse selection, as low-risk producers will pay too much, and high-risk producers will pay too little. Further, the ten year average yield is a noisy measure of the farm-level mean yield; setting premiums proportional to the ten-year average thus results in a high level of intertemporal variance in premiums.;To address these problems with the current premium calculations, I propose a fundamentally different approach to computing premiums. I possess two data sets on Kansas winter wheat yield: farm-level sample moments, based on ten years of APH yield data, and county-level yields, covering the period from 1947 through 2000. My objective is to combine the information from the two data sources in order to increase the credibility of farm-level premium calculations. I first use regression analysis to estimate the moments of the county-level yield distribution. I apply a Bayesian updating technique to combine these moment estimates with farm-level residual moment data in order to obtain estimates of the farm-level yield distributions. Maximum entropy is used to estimate farm-level yield densities from these moments. Actuarially fair premiums are computed by using numerical quadrature to integrate the claim function over the farm-level yield distribution.;The spatial and temporal dependence in crop yield data represent information which should be reflected in premium calculations. My approach is designed to set rates which explicitly reflect the dependency structure of the data. I anticipate premiums which are more temporally stable and which better reflect farm-level risk. (Abstract shortened by UMI.).