An anisotropic model for spatial processes

One of the key assumptions in spatial econometric modelling is that the spatial process is isotropic, which means that direction is irrelevant in the specification of the spatial structure. On one hand, this assumption largely reduces the complexity of the spatial models and facilitates estimation and interpretation; on the other hand, it appears rather restrictive and hard to justify in many empirical applications. In this paper a very general anisotropic spatial model, which allows for a high level of flexibility in the spatial structure, is proposed. This new model can be estimated using maximum likelihood and its asymptotic properties are well understood. When the model is applied to the well-known 1970 Boston housing prices data, it significantly outperforms the isotropic spatial lag model. It also provides interesting additional insights into the price determination process in the properties market.