Shrinkage estimation of spatial panel data models with multiple structural breaks and a multifactor error structure

This study investigates spatial panel data models with a multifactor error structure and multiple structural breaks occurring in the coefficients of both spatial lagged and explanatory variables. While extensive research has addressed cross-sectional dependence in panel data, including approaches that integrate spatial and factor structures within a single framework, few studies account for time-varying model parameters and achieving consistent estimation remains a significant challenge. To address the dual challenges of endogeneity and time heterogeneity, we propose a novel penalized generalized method of moments estimation with common correlated effects (PGMM-CCEX). Specifically, this method addresses the endogeneity issue by utilizing the cross-sectional averages of regressors as factor proxies when constructing the internal instrumental variables, while employing adaptive group fused Lasso to detect multiple structural breaks. The PGMM-CCEX method consistently estimates both the number of breaks and their locations. Furthermore, the post-PGMM-CCEX regime-specific coefficient estimates are consistent and asymptotically follow a normal distribution. Notably, the method remains valid even when factor loadings vary over time, whether synchronously or asynchronously with the parameters of interest. Monte Carlo simulations confirm the satisfactory finite-sample performance of the proposed PGMM-CCEX method. Finally, we apply our method to analyze cross-country economic growth across 106 countries from 1970 to 2019, revealing the time-varying influence of key economic factors on growth dynamics.