Indirect inference in spatial autoregression

Abstract

Ordinary least-squares (OLS) is well known to produce an inconsistent estimator of the spatial parameter in pure spatial autoregression (SAR). In this paper, we explore the potential of indirect inference to correct the inconsistency of OLS. Under broad conditions, it is shown that indirect inference (II) based on OLS produces consistent and asymptotically normal estimates in pure SAR regression. The II estimator used here is robust to departures from normal disturbances and is computationally straightforward compared with quasi-maximum likelihood (QML). Monte Carlo experiments based on various specifications of the weight matrix show that: (a) the II estimator displays little bias even in very small samples and gives overall performance that is comparable to the QML while raising variance in some cases; (b) II applied to QML also enjoys good finite sample properties; and (c) II shows robust performance in the presence of heavy-tailed error distributions.