Spatial econometric modeling of regional convergence in continuous time

Abstract

In this article, the authors use a continuous-time framework to model the potential convergence dynamics in a group of regions. They propose a model based on the classical Lotka-Volterra predator-prey system of two equations-a model originally proposed by Samuelson in 1971 to perform dynamic economic analysis-and extend the model to the case of more than two regions by introducing dependence on neighboring regions. The authors state the conditions under which the system of regions moves toward a mathematically stable point of convergence and show that the model can be seen as more general than the popular β-convergence model. Finally, they also consider statistical inference and introduce a discrete approximate solution based on simultaneous dynamic least squares to estimate the parameters of the model.