Beyond Average Hive Performance: Tail Risk Measurement in Italian Apiculture With Honey-at-Risk

This paper provides a framework for measuring honey-production risk that complements standard mean-based analyses by explicitly targeting downside tail risk. Using hive-weight data from a large sample of Italian hives over the period 2021–2024, downside tail risk is quantified through the Honey-at-Risk (HaR) metric, defined as the quantile of aggregate daily production shocks for groups of hives exposed to homogeneous climatic conditions. The aggregate shock distribution is modeled based on a flexible meta-distributional framework that combines hive-specific marginal distributions with a copula for the cluster dependence structure, allowing for improved accuracy in representing heterogeneous marginal behavior and cross-hive dependence. The implementation of HaR documents substantial spatial heterogeneity, with mountain clusters facing not only higher downside tail risk but also higher variability in the magnitude of the risk measure, compared to plains and hills. Moreover, logistic regressions suggest that the probability of realizing extreme losses, that is, losses smaller than HaR, is negatively associated with the average atmospheric temperature but positively associated with the occurrence of abnormal temperature maxima. Taken together, these results position HaR as an operational complement to elasticity-based assessments, enabling the identification of high-risk areas and supporting targeted adaptation measures as well as the design of weather-indexed insurance and compensation schemes.

Duke Scholars

Author Alessio Brini Engineering Graduate and Professional Programs