A Bayesian Updating Approach to Crop Insurance Ratemaking

A Bayesian Updating Approach to Crop Insurance Ratemaking by Stephen Milton Stohs Doctor of Philosophy in Agricultural and Resource Economics University of California, Berkeley Professor Peter Berck, Chair The U.S. government operates the multiple peril crop insurance (MPCI) program to provide farmers with comprehensive protection against yield risk due to weather-related causes of loss and certain other unavoidable perils. Coverage is available on over 75 crops in primary production areas of the U.S. Producers may elect a coverage level on the range from 50 to 75 percent of the actual production history (APH) mean yield, where APH mean yield is defined as the farm-level average of a minimum of four, and a maximum of up to ten, consecutive years of yield. A widely recognized feature of crop yield data are the high levels of spatial and temporal dependence. The MPCI ratemaking procedure currently in force makes little use of this dependency in the data, thereby failing to utilize information which could be used to more accurately price the insurance. I propose and implement a methodology for estimating farm-level yield distributions that incorporates the spatial and temporal dependencies in yield data. The U.S. federal crop insurance program has long been plagued with low participation rates, and taxpayer-funded subsidies are routinely employed to increase participation levels. Current provisions of the insurance contract allow for premium subsidies on the range from 64 percent at the 75 percent coverage level up to 100 percent at the 50 percent coverage level. Besides covering over 50 percent of the premiums, additional subsidies are employed to provide incentives for private insurers to market the coverage, in the form of delivery expenses (marketing and service 1 cost reimbursements), and reinsurance protection. Unlike private insurance, where the insurance company must charge a premium to cover the cost of claims payments and administrative expenses, government-provided MPCI relies on the taxpayer to cover well over half the cost of the program. According to insurance theory, with actuarially fair insurance a risk-averse producer would prefer participating to foregoing coverage, risk-neutral producers would be indifferent between participating and not participating, and risk-loving individuals would prefer exposure to the full range of possible yield outcomes to the smoothing effect of insurance on income. Hence with unsubsidized but actuarially fair premiums, theory predicts full participation among risk-averse producers whose expected utility would increase with insurance, while risk-loving producers would maximize expected utility by foregoing coverage. Low participation rates with subsidized premiums suggest either that many farmers are risk-lovers, or the premium rates are not perceived to be actuarially fair. 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