Spatial fixed effects and spatial dependence in a single cross-section

We investigate the common conjecture in applied econometric work that the inclusion of spatial fixed effects in a regression specification for a single cross-sectional data set removes spatial dependence. We demonstrate analytically and by means of a series of simulation experiments how evidence of the removal of spatial autocorrelation by spatial fixed effects may be spurious when the true data generating processes (DGP) takes the form of a spatial lag or spatial error dependence. In addition, we also show that spatial fixed effects correctly remove spatial correlation only in the special case where the dependence is group-wise, with all observations in the same group as neighbours of each other.