Higher-order least squares inference for spatial autoregressions

We develop refined inference for spatial regression models with predetermined regressors. The ordinary least squares estimate of the spatial parameter is neither consistent nor asymptotically normal, unless the elements of the spatial weight matrix uniformly vanish as sample size diverges. We develop refined testing of the hypothesis of no spatial dependence, without requiring such negligibility of spatial weights, by formal Edgeworth expansions. We also develop such higher-order expansions for both an unstudentized and a studentized transformed estimate, where the studentized one can be used to provide refined interval estimates. A Monte Carlo study of finite sample performance is included.