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). The asymptotic distribution of the statistic is formally derived in a general model that encompasses endogeneity due to system feedbacks as well as spatial interaction (in the form of spatially lagged dependent variables). The small sample performance of the test is assessed in a series of Monte Carlo simulation experiments, and the test is compared 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 specification testing of models with endogeneity that are estimated for cross-sectional data.