Models for Spatial Panels

Economic interactions in space and other forms of peer effects now receive considerable attention both from a theoretical as well as from an applied perspective, especially on panel data. Until recently, the methodologies and specifications developed are related mainly to two-dimensional approaches that refer to observations on a cross-section of households, firms, countries, etc. over several time periods. However, lots of data exhibit more complex multi-dimensional structures that could be non-hierarchical or hierarchical. The multi-dimensional models that are not necessarily connected to a hierarchical structure are described in Chaps. 11, 13 and 14. Therefore, this chapter considers the case of hierarchical multi-dimensional spatial panels. We organize all the recent literature and emphasize a range of issues pertaining to the specification, estimation, testing procedures and prediction for these models. These issues include a mixture of usual topics on panel data, i.e., the form taken by individual and temporal heterogeneity, or topics more specific to spatial econometrics, i.e., dependence among observations across space, structures of the spatial matrix, Maximum Likelihood (ML) and Generalized Method of Moments (GMM) approaches, the determination and inference of direct and indirect (or spillover) effects. Only static panel data models will be considered.