Tests for spatial dependence and temporal heterogeneity in time-varying coefficient spatial autoregressive panel data model

Time-varying coefficient spatial autoregressive panel data model is a powerful tool to simultaneously deal with spatial dependence and temporal heterogeneity in spatial panel data analysis. However, little work has been devoted to related statistical inference issues, which largely limits the application scope of the model. In this paper, we develop two generalized-likelihood-ratio-statistic-based bootstrap tests to detect spatial dependence of the response variable and temporal heterogeneity of the regression relationship, respectively. The simulation studies show that both tests are of accurate size and satisfactory power, and are quite robust to non-normality of error distribution. A house price data set is finally analyzed to demonstrate the application of the proposed tests in detecting spatial dependence and temporal heterogeneity.