Using a Farmer's Beta for Improved Estimation of Actual Production History (APH) Yields

The effect of sampling error in estimation of farmers' mean yields for crop insurance purposes is explored using farm-level corn yield data in Iowa from 1990 to 2000 and Monte Carlo simulations. We find that sampling error combined with nonlinearities in the insurance indemnity function will result in empirically estimated crop insurance rates that exceed actuarially fair values by between 2 and 16 percent, depending on the coverage level and the number of observations used to estimate mean yields. Accounting for the adverse selection caused by sampling error results in crop insurance rates that will exceed fair values by between 42 and 127 percent. We propose a new estimator for mean yields based on a common decomposition of farm yields into systemic and idiosyncratic components. The proposed estimator reduces sampling variance by approximately 45 percent relative to the current estimator.