Estimation of the spatial weights matrix under structural constraints

•Incorrect specification of the spatial weights matrix has important consequences.•We show that the spatial weights matrix is only partially identified by the data.•It is fully identified under the structural constraint of symmetric spatial weights.•We propose an estimator for the spatial weights under the assumption of symmetry.•The estimated matrix enhances understanding of spatial diffusion and its drivers.

While estimates of models with spatial interaction are very sensitive to the choice of spatial weights, considerable uncertainty surrounds the definition of spatial weights in most studies with cross-section dependence. We show that, in the spatial error model, the spatial weights matrix is only partially identified, and is fully identified under the structural constraint of symmetry. For the spatial error model, we propose a new methodology for estimation of spatial weights under the assumption of symmetric spatial weights, with extensions to other important spatial models. The methodology is applied to regional housing markets in the UK, providing an estimated spatial weights matrix that generates several new hypotheses about the economic and socio-cultural drivers of spatial diffusion in housing demand.