Specification Tests for Temporal Heterogeneity in Spatial Panel Data Models with Fixed Effects

We propose adjusted quasi score (AQS) tests for testing the existence of temporal heterogeneity in slope and spatial parameters in spatial panel data (SPD) models, allowing for the presence of individual-specific and/or time-specific fixed effects (or in general intercept heterogeneity). The SPD model with spatial lag is treated in detail by first considering the model with individual fixed effects only, and then extending it to the model with both individual and time fixed effects. Two types of AQS tests (naive and robust) are proposed, and their asymptotic properties are presented. These tests are then fully extended to SPD models with both spatial lag and spatial error. Monte Carlo results show that the robust tests have much superior finite and large sample properties than the naive tests. Thus, the proposed robust tests provide reliable tools for identifying possible existence of temporal heterogeneity in regression and spatial coefficients. Empirical applications of the proposed tests are given.