The focus here is on the log-normal version of the spatial interaction model. In this context, we consider spatial econometric specifications that can be used to accommodate two types of dependence scenarios, one involving endogenous interaction and the other exogenous interaction. These model specifications replace the conventional assumption of independence between origin-destination-flows with formal approaches that allow for two different types of spatial dependence in flow magnitudes. Endogenous interaction reflects situations where there is reaction to feedback regarding flow magnitudes from regions neighboring origin and destination regions. This type of interaction can be modeled using specifications proposed by LeSage and Pace (2008) who use spatial lags of the dependent variable to quantify the magnitude and extent of feedback effects, hence the term endogenous interaction. Exogenous interaction represents a situation where spillover arise from nearby (or perhaps even distant) regions, and these need to be taken into account when modeling observed variation in flows across the network of regions. In contrast to endogenous interaction, these contextual effects do not generate reaction to the spillovers, leading to a model specification that can be interpreted without considering changes in the long-run equilibrium state of the system of flows. We discuss issues pertaining to interpretation of estimates from these two types of model specification, and provide an empirical illustration. (authors' abstract)

This study suggests a two-step approach to identifying and interpreting regional convergence clubs in Europe. The first step involves identifying the number and composition of clubs using a space-time panel data model for annual income growth rates in conjunction with Bayesian model comparison methods. A second step uses a Bayesian space-time panel data model to assess how changes in the initial endowments of variables (that explain growth) impact regional income levels over time. These dynamic trajectories of changes in regional income levels over time allow us to draw inferences regarding the timing and magnitude of regional income responses to changes in the initial conditions for the clubs that have been identified in the first step. This is in contrast to conventional practice that involves setting the number of clubs ex ante, selecting the composition of the potential convergence clubs according to some a priori criterion (such as initial per capita income thresholds for example), and using cross-sectional growth regressions for estimation and interpretation purposes. (authors' abstract)