Bayesian Model Averaging, Mixture Models, and Rating Crop Insurance Contracts

The Agricultural Act of 2014 solidified insurance as the cornerstone of U.S. agricultural policy. The Congressional Budget Office (2014) estimates this Act will increase spending on agricultural insurance programs by $5.7 billion to a total of $89.8 billion over the next decade. In 2014, total government liabilities associated with the crop insurance program exceeded $108.5 billion. In light of the sizable resources directed toward these programs, accurate pricing or rating of insurance contracts is of utmost importance to farmers, private insurance companies, and the federal government. Unlike most forms of insurance in which sufficient information exists to accurately estimate the probability and magnitude of losses (i.e. the underlying density), agricultural insurance is plagued by a paucity of spatially correlated data. A novel application of Bayesian Model Averaging and mixture models is used to estimate a set of possibly similar densities that offers greater efficiency if the set of densities are similar while seemingly not losing any if the set of densities are dissimilar. Standard simulations indicate that finite sample performance -in particular small sample performance -is quite promising. The BMA methodology is relatively easy to implement, does not require knowledge of the form or extent of any possible similarities, admits correlated data, and can be used with either parametric or nonparametric estimators. The proposed methodology is used to estimate U.S. crop insurance premium rates for area-type programs. A simulated out-of-sample game between private insurance companies and the federal government highlights the policy implications for a number of crop-state combinations. Two tests are developed to evaluate the efficacy of the proposed methodology. Also of policy relevance is the expansion of area-type programs, via the Supplemental Coverage Option, to crops and states with significantly less historical data. To this end, the empirical analysis is also undertaken for a variety of reduced sample sizes. As with the standard finite sample simulations, the performance of the proposed methodology for rating area-type crop insurance contracts -in particular small sample performance -appears quite promising. Contact info: Alan P. Ker, Professor and Director (Institute for the Advanced Study of Food and Agricultural Policy), Department of Food, Agricultural and Resource Economics, University of Guelph, [email protected]. Yong Lui is a Ph.D. student, Department of Food, Agricultural and Resource Economics. Tor Tolhurst is a research associate, Department of Food, Agricultural and Resource Economics.