Estimation of Spatial Autoregressions with Stochastic Weight Matrices

We examine a higher-order spatial autoregressive model with stochastic, but exogenous, spatial weight matrices. Allowing a general spatial linear process form for the disturbances that permits many common types of error specifications as well as potential 'long memory', we provide sufficient conditions for consistency and asymptotic normality of instrumental variables and ordinary least squares estimates. The implications of popular weight matrix normalizations and structures for our theoretical conditions are discussed. A set of Monte Carlo simulations examines the behaviour of the estimates in a variety of situations and suggests, like the theory, that spatial weights generated from distributions with ?smaller? moments yield better estimates. Our results are especially pertinent in situations where spatial weights are functions of stochastic economic variables.