Efficient estimation of large spatially-clustered spatial autoregressive models for the analysis of spillovers in the voting concentration of Italian municipalities

This paper examines spatial spillovers in voting concentration across Italian municipalities, a key aspect for understanding electoral competition and political representation. To estimate heterogeneous spatial dependencies at the cluster level, while accounting for a broad set of socio-economic and institutional covariates, we adopt the recently introduced spatially-clustered spatial autoregressive (SCSAR) model. The standard SCSAR requires the evaluation of logdeterminants of matrices whose dimension grows with the number of spatial units. Due to the large number of Italian municipalities, we address the computational burden of maximizing the log-likelihood function in SCSAR by means of matrix factorization methods. A computational benchmarking experiment shows that sparse factorization substantially improves scalability relative to the eigenvalue-based implementation, making SCSAR feasible for large municipal systems. This approach therefore enables a fast identification of clusters of Italian municipalities characterized by similar structural relationships. We find that global SAR models provide limited explanatory power of voting concentration compared to clustered specifications. Moreover, spatial spillovers are positive in the main specifications but vary substantially across clusters and electoral chambers, confirming that a single global spatial autoregressive coefficient masks important territorial heterogeneity. Economic and demographic variables are the most robust predictors of voting concentration, while several covariates display heterogeneous or even opposite effects across local contexts.