Multi-Dimensional Models for Spatial Panels

Spatial econometric models are widely used to formalize interactions in geographical space or along networks. When applied to panel data, the methodologies and specifications developed are mainly related 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 can be non-hierarchical or hierarchical. The multi-dimensional models that are not necessarily connected to a hierarchical structure are described in Chapters 12 and 14. Therefore, this chapter mostly considers the case of hierarchical multidimensional spatial panels. Focusing on static panel data models, we organize all this recent literature, provide an encompassing specification, 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 Moments (GM) approaches, determination and inference of direct and indirect (or spillover) effects. The last section considers a range of possible extensions.