Testing for spatial group-wise heteroskedasticity in spatial autocorrelation regression models: Lagrange multiplier scan tests

The aim of this paper is to develop a spatial group-wise heteroskedasticity test based on the scan approach, specifically developed for spatial autocorrelation regression models (spatial lag and spatial error models): the "scan-LM test." Based on the Lagrange multiplier (LM) principle, its main advantage lies in its comparative ease of implementation as it is not necessary to obtain the maximum likelihood estimations for the alternative hypothesis. Moreover, when rejecting the null hypothesis, this test identifies the shape and size of the spatial clusters with different residual variance, a feature which proves very useful for specification search of the regression model. Another important benefit of the scan-LM test is that it does not require the specification of a spatial weights matrix. An extensive Monte Carlo simulation confirms the good properties of the scan-LM test in terms of size and power. This test is also robust in the presence of non-normality and other forms of a spatial heteroskedasticity. We finally propose an application on housing prices in the agglomeration of Madrid for a specific submarket: the attics.