The Impact of Spatial Interpolation Techniques on Spatial Basis Risk for Weather Insurance: An Application to Forage Crops

Abstract

Weather index insurance for crops is at the developmental stage, however, this type of insurance is particularly susceptible to the problem of spatial basis risk. Spatial basis risk occurs when the weather observed at weather stations does not match the weather experienced on the farmer’s property, causing improper indemnities to be paid to the farmer. However, spatial basis risk may be reduced through the use of averaging and spatial interpolation techniques, such as inverse distance weighting and kriging. These techniques make it possible to incorporate multiple weather stations in the estimation process rather than using only the single closest station, potentially resulting in more accurate estimations and thereby reducing spatial basis risk. Therefore, the objective of this study is to examine the extent to which the choice of spatial interpolation techniques can influence the amount of spatial basis risk in a weather-based insurance model. Using forage crops from the province of Ontario, Canada, as an example, a weather insurance index is developed based on cooling degree days. The weather index represents the heat stress that the crops receive over the growing season. This insurance index is used to determine to what extent spatial basis risk can be reduced by the insurer’s choice of spatial interpolation technique. Seven different interpolation methods are applied to temperature data from Ontario, and theoretical indemnities are calculated for forage producers across the province. By analyzing the correlation between the estimated indemnities and reported forage yields, the amount of spatial basis risk in each model is quantified. The results of this study highlight the importance of choosing an appropriate method based on the characteristics of the target region (and data). Operationally this is important because insurers typically apply the same interpolation methods across an entire region. While one finding of this research may suggest that governments and/or insurance companies may wish to invest in additional weather stations to improve the accuracy of the interpolation method and index, this may not be feasible in practice. Given this, future research may consider utilizing satellite-based remote sensing weather estimates to augment the weather station data and reduce basis risk.

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Additional information

Funding

The authors gratefully acknowledge funding for this research by the Society of Actuaries Center for Actuarial Excellence Research Grant, and the Natural Sciences and Engineering Research Council of Canada Collaborative Research and Development Grant.