QML and Efficient GMM Estimation of Spatial Autoregressive Models with Dominant (Popular) Units

This article investigates QML and GMM estimation of spatial autoregressive (SAR) models in which the column sums of the spatial weights matrix might not be uniformly bounded. We develop a central limit theorem in which the number of columns with unbounded sums can be finite or infinite and the magnitude of their column sums can be O(nδ) if δ<1. Asymptotic distributions of QML and GMM estimators are derived under this setting, including the GMM estimators with the best linear and quadratic moments when the disturbances are not normally distributed. The Monte Carlo experiments show that these QML and GMM estimators have satisfactory finite sample performances, while cases with a column sums magnitude of O(n) might not have satisfactory performance. An empirical application with growth convergence in which the trade flow network has the feature of dominant units is provided. Supplementary materials for this article are available online.