A Pairwise Difference Estimator for Partially Linear Spatial Autoregressive Models

Su and Jin (2010) develop for partially linear spatial autoregressive (PL-SAR) model a profile quasimaximum likelihood based estimation procedure. More recently, Su (2011) proposes for this model a semiparametric GMM estimator. However, both of them can be computationally challenging for applied researchers and are not easy to implement in practice. In this article, we propose a computationally simple estimator for the PL-SAR model in the presence of either heteroscedastic or spatially correlated error terms. This estimator blends the essential features of both the GMM estimator for linear SAR model and the pairwise difference estimator for conventional partially linear model. Limiting distribution of the proposed estimator is established and consistent estimator for its asymptotic CV matrix is provided. Monte Carlo studies indicate that our estimator is attractive particularly when one is interested in estimating the finite-dimensional parameters in the model.