Best Spatial Two‐Stage Least Squares Estimators for a Spatial Autoregressive Model with Autoregressive Disturbances

Estimation of a cross‐sectional spatial model containing both a spatial lag of the dependent variable and spatially autoregressive disturbances are considered. [Kelejian and Prucha (1998)] Kelejian, H. H. and Prucha, I. R. 1998. A generalized spatial two‐stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances. J. Real Estate Financ. and Economics, 17: 99–121. [Crossref], [Web of Science ®] , [Google Scholar]described a generalized two‐stage least squares procedure for estimating such a spatial model. Their estimator is, however, not asymptotically optimal. We propose best spatial 2SLS estimators that are asymptotically optimal instrumental variable (IV) estimators. An associated goodness‐of‐fit (or over identification) test is available. We suggest computationally simple and tractable numerical procedures for constructing the optimal instruments.