A Dynamic Stochastic Integrated Climate–Economic Spatiotemporal Model for Agricultural Insurance Products

We propose a new methodology for area yield distribution modeling. We explore a variety of new hybrid data emulators for spatialtemporal statistical modeling of agricultural crop yields. The regression models explored leverage from a combination of model-generated and observed features incorporating climate/weather variables relating to temperature and precipitation over space and time and agricultural variables for farms such as crop allocations, crop types, land use, and crop rotation. This provides the modeling framework to achieve a hierarchical decomposition of the yield distribution at multiple spatial scales over time, allowing us to study both county- and individual farm-level information with suitably selected weighting functions that take into account farm size and crop type. A core component of our model framework is the climate model component that involves a spatialtemporal local approximate seasonal autoregressive integrated moving average Gaussian process (La-SARIMA-GP) model that is suitable for accurately studying local monthly temperatures and rainfalls. Upon construction of the crop yield model, we demonstrate that for practitioners, there is a clear incentive to consider such a model because it accommodates apportioning of the county yield information to the farms level. This is of significance for both individual and index-based agricultural crop insurance product design and for farm risk management. We demonstrate an application of our model in the insurance context of crop insurance risk pooling and insurance policy rating where we investigate the impact of different temporal and spatial interpolation methods on insurance loss ratios using a rating game.