Tests for time-varying coefficient spatial autoregressive panel data model with fixed effects

As an extension of the spatial autoregressive panel data model and the time-varying coefficient panel data model, the time-varying coefficient spatial autoregressive panel data model is useful in analysis of spatial panel data. While research has addressed the estimation problem of this model, less attention has been given to hypotheses tests. This paper studies two tests for this semiparametric spatial panel data model. One considers the existence of the spatial lag term, and the other determines whether some time-varying coefficients are constants. We employ the profile generalized likelihood ratio test procedure to construct the corresponding test statistic, and the residual-based bootstrap procedure is used to derive the p-value of the tests. Some simulations are conducted to evaluate the performance of the proposed test method, the results show that the proposed methods have good finite sample properties. Finally, we apply the proposed test methods to the provincial carbon emission data of China. Our findings suggest that the partially linear time-varying coefficients spatial autoregressive panel data model provides a better fit for the carbon emission data.