Rating Area-yield Crop Insurance Contracts Using Bayesian Model Averaging and Mixture Models

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 light of the sizable resources directed toward these programs, accurate rating of insurance contracts is of utmost importance to producers, private insurance companies, and the federal government. Unlike most forms of insurance -- where 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 interpretation of Bayesian Model Averaging 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. Simulations indicate finite sample performance -- in particular small sample performance -- is quite promising. The proposed approach does not require knowledge of the form or extent of any possible similarities, is relatively easy to implement, admits correlated data, and can be used with either parametric or nonparametric estimators. We use the proposed approach to estimate U.S. crop insurance premium rates for area-type programs and develop a test to evaluate its efficacy. An out-of-sample game between private insurance companies and the federal government highlights the policy implications for a variety of crop-state combinations. We repeat the empirical analyses under reduced sample sizes given: (i) new programs will dramatically expand area-type insurance to crops and states that have significantly less historical data; and (ii) changes in technology could render some historical loss data no longer representative. Consistent with the simulation results, the performance of the proposed approach with respect to rating area-type insurance -- in particular small sample performance -- remains quite promising.