Quantifying and pricing crop yield risk under climate change: a hierarchical model forecasting perspective

Abstract Accurate and internally coherent crop-yield forecasts are important for agricultural risk management, crop-insurance ratemaking, and regional risk assessment under climate variability. However, crop yields are influenced by high-dimensional and strongly correlated weather conditions, while forecasts produced at different spatial levels often violate aggregation constraints. Existing studies focus on yield prediction within individual regions and pay limited attention to weather-informed forecasting, hierarchical coherence, and insurance-oriented risk measurement. This paper develops an integrated framework for hierarchical crop-yield forecasting and risk assessment by combining dimensionality reduction for high-dimensional weather variables, probabilistic forecasting, and forecast reconciliation. Using county- and state-level spring and winter wheat yields in Montana from 1982 to 2022, we compare alternative base forecasting models and reconciliation methods under scenarios with and without weather information. Forecast performance is evaluated using point and probabilistic scoring rules, and the reconciled predictive distributions are used to construct scenario-based measures of downside yield risk. The results show that incorporating weather information and hierarchical reconciliation improves the quality and coherence of hierarchical yield forecasts. The resulting probabilistic forecasts provide a basis for loss-rate estimation, cross-county risk comparison, and spatial risk mapping and also support crop-insurance ratemaking under a retain–cede game between private insurers and the government.