Maps of Continuous Spatial Dependence

Heterogeneity is one of the distinguishing features in spatial econometric models. It is a frequent problem in applied work and can be very damaging for statistical inference. In this paper, we focus on the problems implied by the existence of instabilities in the mechanism of spatial dependence in a spatial lag model, assuming that the other terms of the specification remain stable. We begin the discussion with the role played by the algorithms of local estimation in detecting the instabilities. Problems appear when one must decide what to do once the existence of heterogeneity has been confirmed. The logical reaction is trying to parameterize this lack of stability. However, the solution is not obvious. Assuming that a set of indicators related to the problem has been identified, we propose a simple technique to deal with the unknown functional form. In the final part of the paper, we present some Monte Carlo evidence and an application to evaluate the instability in the mechanisms of spatial dependence in the convergence process of the European Regions.