Spatial Methods

This paper is concerned with methods for analysing spatial data. After initial discussion on the nature of spatial data, including the concept of randomness, we focus most of our attention on linear regression models that involve interactions between agents across space. The introduction of spatial variables in to standard linear regression provides a flexible way of characterising these interactions, but complicates both interpretation and estimation of parameters of interest. The estimation of these models leads to three fundamental challenges: the reflection problem, the presence of omitted variables and problems caused by sorting. We consider possible solutions to these problems, with a particular focus on restrictions on the nature of interactions. We show that similar assumptions are implicit in the empirical strategies - fixed effects or spatial differencing - used to address these problems in reduced form estimation. These general lessons carry over to the policy evaluation literature.