Efficient closed-form estimation of large spatial autoregressions

TL;DR

This paper introduces a computationally simple closed-form method for estimating large spatial autoregressive models that maintains efficiency and improves finite sample performance, especially in multiparameter settings.

Contribution

It develops Newton-step approximations for large spatial autoregressions that are both computationally efficient and theoretically sound, avoiding common pitfalls of traditional methods.

Findings

Newton-step estimates are asymptotically efficient under Gaussianity.

Simulation shows significant finite sample improvements with Newton iterations.

Empirical data demonstrates enhanced estimation precision.

Abstract

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