A Simple Spatial Dependence Test Robust to Local and Distributional Misspecifications

It is well known that the standard Lagrange multiplier (LM) test loses its local optimality when the true non-null model is not correctly specified. In this paper, we derive a score test robust to local and distributional misspecifications for spatial error autocorrelation and spatial lag dependence. The proposed test is general enough to include several popular tests for the spatial dependence as special cases. In our framework, we find that Burridge (1980) and Anselin, Bera, Florax and Yoon (1996)’s tests are automatically robust to distributional misspecification in some special cases. The size and power performances of our proposed score tests are investigated by a Monte-Carlo simulation.