a1 University of Reading
This paper derives some exact power properties of tests for spatial autocorrelation in the context of a linear regression model. In particular, we characterize the circumstances in which the power vanishes as the autocorrelation increases, thus extending the work of Krämer (2005). More generally, the analysis in the paper sheds new light on how the power of tests for spatial autocorrelation is affected by the matrix of regressors and by the spatial structure. We mainly focus on the problem of residual spatial autocorrelation, in which case it is appropriate to restrict attention to the class of invariant tests, but we also consider the case when the autocorrelation is due to the presence of a spatially lagged dependent variable among the regressors. A numerical study aimed at assessing the practical relevance of the theoretical results is included.
I am grateful to the co-editor and two anonymous referees for suggestions that have led to substantial improvements in the paper. I thank Giovanni Forchini, Grant Hillier, Pierre Perron, Benedikt Pötscher, Tony Smith, and Kees Jan van Garderen for helpful comments, and Anurag Banerjee for providing GAUSS routines for the Imhof's procedure. This paper is based on a chapter from my Ph.D. dissertation at the University of Southampton.