Testing for Spatial Error Autocorrelation in the Presence of Endogenous Regressors
This paper examines the properties of Moran's I test for spatial error autocorrelation when endogenous variables are included in the regression specification and estimation is carried out by means of instrumental variables procedures (such as two stage least squares). We formally derive the asymptotic distribution of the statistic in a general model that encompasses endogeneity due to system feedbacks as well as spatial interaction (in the form of spatially lagged dependent variables). We assess the small sam-ple performance of the test in a series of Monte Carlo simulation experiments and compare it to a number of ad hoc approaches that have been suggested in the literature. While some of these ad hoc procedures perform surprisingly well, the new test is the only acceptable one in the presence of spatially lagged dependent variables. The test is straightforward to compute and should become part of routine specifica-tion testing of models with endogeneity that are estimated for cross-sectional data.