Efficient closed-form estimation of large spatial autoregressions

Newton-step approximations to pseudo maximum likelihood estimates of spatial autoregressive models with a large number parameters are examined, in the sense that parameter space grows slowly as function sample size. These have same asymptotic efficiency properties under Gaussianity but closed form. Hence they computationally simple and free from compactness assumptions, thereby avoiding two notorious pitfalls implicitly defined autoregressions. When commencing an initial least squares estimate, Newton step can also lead weaker regularity conditions for central limit theorem than some extant literature. A simulation study demonstrates excellent finite gains iterations, especially multiparameter which grid search is costly. small empirical illustration shows improvements estimation precision real data.