Estimation and testing of time-varying coefficients spatial autoregressive panel data model

This paper investigates a spatial autoregressive (SAR) panel data model featuring fixed effects and time-varying coefficients in both the covariates and spatial dependence. We propose a two-stage least squares estimation based on local linear dummy variables (2SLS-LLDV). This method effectively captures individual heterogeneity via dummy variable construction while maintaining computational tractability. Under mild regularity conditions, we establish the asymptotic normality of the proposed estimators. Furthermore, we devise a residual-based bootstrap procedure to test the temporal stability of time-varying spatial dependence parameter, providing a robust mechanism for p-value calculation in finite-sample scenarios. Monte Carlo simulations are conducted to evaluate the finite sample performance of our proposed methods. Finally, we employ our proposed estimation and testing methods to analyze carbon emissions in China and cigarette demand in the United States, demonstrating their practical applicability.