Time-Varying Coefficient Spatial Autoregressive Panel Data Model with Fixed Effects

This paper develops a time-varying coefficient spatial autoregressive panel data model with the individual fixed effects to capture the nonlinear effects of the regressors, which vary over the time. To effectively estimate the model, we propose a method that incorporates the nonparametric local linear method and the concentrated quasi-maximum likelihood estimation method to obtain consistent estimators for the spatial coefficient and the time-varying coefficient function. The asymptotic properties of these estimators are derived as well, showing the regular sqrt(NT)-rate of convergence for the parametric parameters and the common sqrt(NTh)-rate of convergence for the nonparametric component, respectively. Monte Carlo simulations are conducted to illustrate the finite sample performance of our proposed method. Meanwhile, we apply our method to study the Chinese labor productivity to identify the spatial influences and the time-varying spillover effects among 185 Chinese cities with comparison to the results on a subregion East China.