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Weather is a pivotal factor for crop production as it is highly volatile and can hardly be controlled by farm management practices. Since there is a tendency towards increased weather extremes in the future, understanding weather-related yield factors becomes increasingly important not only for yield prediction, but also for the design of insurance products. Although insurance products mitigate financial losses for farmers, they suffer from considerable basis risk, i.e., a discrepancy between losses and the indemnity payment. The objective of this paper was to explore the potential of machine learning for estimating the relationship between crop yield and weather conditions at the farm level and to use it as a tool for reducing basis risk in index insurance applications. An artificial neural network was set up and calibrated to a rich set of farm-level yield data in Germany, covering the period from 2003 to 2018. A nonlinear regression model, which uses rainfall, temperature, and soil moisture as explanatory variables for yield deviations, served as a benchmark. The empirical application revealed that compared with traditional estimation approaches, the gain in forecasting precision by using machine learning techniques was substantial. Moreover, the use of regionalized models and disaggregated high-resolution weather data improved the performance of artificial neural networks. A considerable part of yield variability at the farm level, however, could not be captured by statistical methods which solely use "big weather data". Our findings have important implications for the design of weather-index based insurance because they document that a rather high level of basis risk remains if insurance products are based on an estimation of the weather-yield relationship. [Display omitted] • Due to increasing weather extremes in the future, understanding weather-related yield factors becomes more important. • This paper explores the potential of machine learning for estimating farm-level yield losses and basis risk reduction. • Use of high-resolution weather data improves the performance of artificial neural networks for estimating yield losses. • More homogenous insurance zones can reduce the basis risk and improve estimation precision. • The findings have implications for the design of weather-index based insurances because a rather high level of basis risk remains. [ABSTRACT FROM AUTHOR]