Efficient estimation of clustered SDPD models with exogenous components

This paper studies a class of Spatial Dynamic Panel Data (SDPD) models in which spatial units are grouped into clusters that have the same parameters within clusters but different across clusters. This specific formulation of the model is called the Clustered SDPD model. When exogenous components are included, efficient estimation of their associated parameters becomes crucial for accurate cluster identification. To address this, we propose a two-step estimation procedure that enhances the efficiency of parameter estimation in a Heterogeneous SDPD framework, where each location has its own parameters, and provides a direct method for estimating fixed effects. This leads to increased precision in cluster detection. Theoretical results establish the consistency and asymptotic properties of the proposed estimators. Monte Carlo simulations and a real data application demonstrate substantial efficiency gains and superior clustering performance compared to standard methods.