Estimation of higher†order spatial autoregressive cross†section models with heteroscedastic disturbances

This paper generalizes the two†step approach to estimating a first†order spatial autoregressive model with spatial autoregressive disturbances (SARAR(1,1)) in a cross†section with heteroscedastic innovations by Kelejian and Prucha to the case of spatial autoregressive models with spatial autoregressive disturbances of arbitrary (finite) order (SARAR(R,S)). We derive a generalized moments (GM) estimation procedure of the spatial regressive parameters of the disturbance process and a generalized two†stage least squares estimator for the regression parameters of the model, prove consistency of proposed estimators thereof, and establish their (joint) asymptotic distribution. Monte Carlo evidence suggests that the estimation procedure performs reasonably well in small samples and that – apart from being of interest in itself – a proper specification of the spatial regressive disturbance process is also crucial for obtaining consistent estimates of the variance†covariance matrix used in the generalized least squares estimation.