Bayesian Quantile Modeling with Climate-Adaptive Spatial Smoothing for Crop Insurance Pricing

Abstract

Agricultural production is often affected by spatially correlated weather shocks, which increase systematic yield risk across regions. Hence, robust spatially coherent risk modelling strategies are essential for accurate risk-sensitive modelling. The paper develops a Bayesian spatial quantile regression model for crop insurance rating, which explicitly considers spatial smoothing and heterogeneous tail risk in agricultural production. Our methodology incorporates spatial priors, including both distance-based and adjacency-based covariance structures, to capture spatial information sharing across regions. Moreover, remote sensing indicator and climate variables are also included as covariates that measure time-varying and spatially heterogeneous production risk. In comparison to existing models, the proposed framework models multiple conditional yield distribution across quantiles, providing a more inclusive representation of downside risk. Spatial smoothing allows the model to share strength with neighboring areas, minimizing local noise and oversensitive volatility in premiums by maintaining substantial spatial variation. These lead to better fitting and coherent spatial risk surfaces and actuarial fairness. Empirical comparisons done through out of sample retain-cede rating game show that quantile based spatial pricing produces actuarially fair premium structures compared to traditional empirical rates. Overall, the proposed methodology provides a flexible and policy-relevant framework for designing sustainable, risk-sensitive and spatially coherent crop insurance pricing.