Spatial panel data models with structural change

Spatial panel data models have gained widespread application in social sciences, particularly in economics, due to their ability to capture spatial dependencies. However, existing studies on spatial models typically rely on the assumption of parameter stability, which may be overly restrictive given the well-documented prevalence of structural changes in economic relationships. This paper addresses this limitation by proposing and analyzing spatial panel data models that explicitly incorporate structural change. The primary focus of this paper is on a static spatial autoregressive (SAR) panel data model, which we estimate using the quasi-maximum likelihood (QML) method. We establish a comprehensive asymptotic theory for the QML estimators, including proofs of consistency, convergence rates, and limiting distributions, under a large-N and large-T framework. Furthermore, we extend our theoretical framework in two important directions: dynamic spatial panel data models and settings with large-N and fixed-T. Additionally, we develop hypothesis testing procedures for detecting structural change, proposing three sup-type test statistics for this purpose. To validate our theoretical results, we conduct extensive Monte Carlo simulations, which demonstrate that the QML estimators perform well in finite samples. These findings underscore the practical relevance and robustness of our proposed methodology.