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Newton-step approximations to pseudo maximum likelihood estimates of spatialautoregressive models with a large number of parameters are examined, in thesense that the parameter space grows slowly as a function of sample size. Thesehave the same asymptotic efficiency properties as maximum likelihood underGaussianity but are of closed form. Hence they are computationally simple andfree from compactness assumptions, thereby avoiding two notorious pitfalls ofimplicitly defined estimates of large spatial autoregressions. For an initialleast squares estimate, the Newton step can also lead to weaker regularityconditions for a central limit theorem than those extant in the literature. Asimulation study demonstrates excellent finite sample gains from Newtoniterations, especially in large multiparameter models for which grid search iscostly. A small empirical illustration shows improvements in estimationprecision with real data.

Efficient closed-form estimation of large spatial autoregressions