Estimation of Spatial Regression Models with Autoregressive Errors by Two-Stage Least Squares Procedures: A Serious Problem

Time series regression models that have autoregressive errors are often estimated by two-stage procedures which are based on the Cochrane-Orcutt (1949) transformation. It seems natural to also attempt the estimation of spatial regression models whose error terms are autoregressive in terms of an analogous transformation. Various two-stage least squares procedures suggest themselves in this context, including an analog to Durbin's (1960) procedure. Indeed, these procedures are so suggestive and computationally convenient that they are quite "tempting." Unfortunately, however, as shown in this paper, these two-stage least squares procedures are generally, in a typical cross-sectional spatial context, not consistent and therefore should not be used.