Testing for spatial error dependence in probit models

In this note, we compare three test statistics that have been suggested to assess the presence of spatial error autocorrelation in probit models. We highlight the differences between the tests proposed by Pinkse and Slade (J Econom 85(1):125–254, <CitationRef CitationID="CR13">1998</CitationRef>), Pinkse (Asymptotics of the Moran test and a test for spatial correlation in Probit models, <CitationRef CitationID="CR11">1999</CitationRef>; Advances in Spatial Econometrics, <CitationRef CitationID="CR12">2004</CitationRef>) and Kelejian and Prucha (J Econom 104(2):219–257, <CitationRef CitationID="CR8">2001</CitationRef>), and compare their properties in a extensive set of Monte Carlo simulation experiments both under the null and under the alternative. We also assess the conjecture by Pinkse (Asymptotics of the Moran test and a test for spatial correlation in Probit models, <CitationRef CitationID="CR11">1999</CitationRef>) that the usefulness of these test statistics is limited when the explanatory variables are spatially correlated. The Kelejian and Prucha (J Econom 104(2):219–257, <CitationRef CitationID="CR8">2001</CitationRef>) generalized Moran’s I statistic turns out to perform best, even in medium sized samples of several hundreds of observations. The other two tests are acceptable in very large samples. Copyright Springer-Verlag Berlin Heidelberg 2013