The W Matrix in Network and Spatial Econometrics : Issues Relating to Specification and Estimation

Network and spatial econometric models commonly embody a so-called W matrix which defines the connectivity between nodes of a network. The reason for the existence of W is that it facilitates parsimonious parametrization of inter-nodal interaction which would otherwise be very difficult to achieve from a practical modelling perspective. The problem considered in this paper is the effect of misspecifying W. The paper demonstrates the effect in the context of two types of model, the dynamic spatial autoregressive panel model and the multilevel spatial autoregressive panel model, both of which include W as part of the model specification and use W in estimation. Monte Carlo results are presented showing the impact on bias and RMSE of misspecification of W. The paper highlights the need for careful attention to the correct structure of W in spatial econometric and network modelling