Linear partially time-varying coefficient spatial panel data model with fixed effects

In this paper, we propose a semiparametric spatial panel data model with fixed effects and partially time-varying coefficients. The proposed model serves as an intermediate class of models with good robustness by nonparametric treatment on certain explanatory variables and relatively more precise estimation on the parametric effects of other explanatory variables. To estimate the model parameters, we develop an estimation procedure based on local linear regression and profile likelihood. Moreover, a generalized likelihood ratio testing procedure is developed to identify explanatory variables with constant coefficients, in which a bootstrap procedure is suggested to approximate the null distribution of the resulting statistic. Simulation studies show that our estimation and testing procedures perform quite well in finite samples. In particular, our simulation studies demonstrate that efficiency gain can be achieved when information about the partially time-varying coefficient structure is appropriately utilized. We finally apply the proposed model and its estimation and testing procedures to study spatial spillover effects and time-varying feature of province-level house price in China.