Modeling Non-Linear Spatial Dynamics: A Family of Spatial STAR Models and an Application to U.S. Economic Growth

This paper investigates non-linearity in spatial processes models and allows for a gradual regime-switching structure in the form of a smooth transition autoregressive process. Until now, applications of the smooth transition autoregressive (STAR) model have been largely confined to the time series context. The paper focuses on extending the non-linear smooth transition perspective to spatial processes models, in which spatial correlation is taken into account through the use of a so-called weights matrix identifying the topology of the spatial system. We start by deriving a non-linearity test for a simple spatial model, in which spatial correlation is only included in the transition function. Next, we propose a non-linearity test for a model that includes a spatially lagged dependent variable or spatially autocorrelated innovations as well. Monte Carlo simulations of the various test statistics are performed to examine their power and size. The proposed modeling framework is then used to identify convergence clubs in the context of U.S. county-level economic growth over the period 1963–2003