A semiparametric spatio‐temporal model of crop yield trend and its implication to insurance rating

We demonstrate the benefit of spatial smoothing for crop trend estimation with a deterministic spatio‐temporal trend model. The proposed model is semiparametric, where the parametric temporal trend is modeled with a two‐knot spline function for forecasting robustness, and the nonparametric spatially‐varying coefficients are modeled by the radial basis function method for flexibility. To select the smoothing parameter of our trend model, we propose a forward validation criterion tailored to meet the forecasting nature of rating crop insurance. This criterion is based on a rolling regression approach that adds one year of data at a time for validation. We also propose a new criterion for model comparison using relative mean squared error in forecasting insurance payouts. Our empirical results show that the proposed trend model is more efficient and capable of identifying profitable insurance policies than two competing models in most state‐crop combinations.