Semiparametric Spatial Autoregressive Panel Data Model with Fixed Effects and Time-Varying Coefficients

This paper considers a semiparametric spatial autoregressive panel data model with fixed effects with time-varying coefficients. The time-varying coefficients are allowed to follow an unknown function of time while the other parameters are assumed to be constants. We propose a "local linear concentrated quasi-maximum likelihood estimation" method to obtain consistent estimators for the spatial autoregressive coefficient, the variance of the error term and the nonparametric time-varying coefficients. We show that the estimators of the parametric components converge at the rate of sqrt(NT), and those of the nonparametric time-varying coefficients converge at the rate of sqrt(NTh). Monte Carlo simulations are conducted to illustrate the finite sample performance of our proposed method. We apply our method to study the spatial influences and the time-varying spillover effects in the wage level among 159 Chinese cities.