This article considers a semiparametric spatial autoregressive (SAR) panel data model with fixed effects and time-varying coefficients. The time-varying coefficients are allowed to follow unknown functions of time, while the other parameters are assumed to be unknown constants. We propose a local linear quasi-maximum likelihood estimation method to obtain consistent estimators for the SAR coefficient, the variance of the error term, and the nonparametric time-varying coefficients. The asymptotic properties of the proposed estimators are also established. Monte Carlo simulations are conducted to evaluate the finite sample performance of our proposed method. We apply the proposed model to study labor compensation in Chinese cities. The results show significant spatial dependence among cities and the impacts of capital, investment, and the economy’s structure on labor compensation change over time.