Semiparametrically highly efficient estimation of spatial autoregressive models

Spatial autoregressive (SAR) models cannot generally be estimated using ordinary least squares given the simultaneity that results from interactions among individuals. Instead, two-stage least squares (Kelejian and Prucha, 1998; Bramoullé et al., 2009), generalized method of moments (Liu et al., 2010), or (quasi-)maximum likelihood (Lee, 2004) approaches are used. In this article, we propose a semiparametrically highly efficient estimator, based on the Local Asymptotic Normality theory of Le Cam (1960) and the rank-and-sign semiparametric approach developed by Hallin et al. (2006, 2008). Monte Carlo simulations show that the suggested estimator outperforms existing estimators as soon as one deviates from a normal distribution of the error term. A trade regression from Behrens et al. (2012) (used differently from the original paper) is mobilized to illustrate how empirical findings might be affected when the Gaussian distribution is not imposed.