Pseudo Maximum Likelihood Estimation of Spatial Autoregressive Models with Increasing Dimension

Pseudo maximum likelihood estimates are developed for higher-order spatial autoregres- sive models with increasingly many parameters, including models with spatial lags in the dependent variables and regression models with spatial autoregressive disturbances. We consider models with and without a linear or nonlinear regression component. Sufficient conditions for consistency and asymptotic normality are provided, the results varying ac- cording to whether the number of neighbours of a particular unit diverges or is bounded. Monte Carlo experiments examine nite-sample behaviour