Abstract :
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 Kr¨amer (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.
