Bayesian Hierarchical Analysis of US Homeowners’ Insurance Markets: Integrating Socioeconomic Indicators with Actuarial Risk Metrics

Abstract

This study presents a comprehensive Bayesian hierarchical analysis of the U.S. homeowners’ insurance market from 2018 to 2022. By integrating federal insurance metrics with American Community Survey (ACS) income data, we model the drivers of premiums across more than 25,000 ZIP codes. Our findings reveal that policy cancellations and temporal trends are the dominant drivers of premium variation, while geographic and socioeconomic factors play secondary roles. Comparative regularization analysis shows that the Bayesian model with Lasso priors exhibits strong shrinkage, effectively reducing variables such as ZIP Code and Income to near-zero coefficients, whereas the Ridge model retains all predictors with moderate shrinkage to offer a more balanced view of the feature space. The Ridge and Pitman-Yor models achieved the highest predictive accuracy, explaining approximately 7% of variance, compared with 4.8% for the Dirichlet Process Mixture model. The Bayesian model with Lasso priors was used primarily for variable selection rather than predictive accuracy, and its R² is therefore not directly compared here. Notably, both the Dirichlet Process Mixture (DPM) and Pitman-Yor models identified only a single unified cluster, indicating that insurance risk exists on a continuous spectrum rather than in distinct, isolated risk pools. This finding was further confirmed by the Normal Random Intercepts Model (NREM), which showed minimal variance explained by decile groupings. Across all models, cancellation rates, particularly non-payment and other cancellations, and year consistently emerge as the most influential predictors of homeowners’ insurance premiums, though the magnitude of these effects varies according to the specific regularization approach employed. These results suggest that market stability and policy retention are more critical to understanding premium behavior than traditional geographic or income-based risk segmentation.