Modeling Spatial Regimes With Smooth Transitions

In this paper, we introduce a new way of modeling spatial regimes using smooth transitions. We propose an autoregressive spatial lag model where a logistic function captures structural variation in the spatial lag parameter. In the regime-switching spatial lag model with smooth transitions, the effect of the spatial neighbors depends on the transition variable that governs the regime switch. An LM test for detecting nonlinearity is derived, and a simulation study, where the properties of the test are investigated, is conducted. The test shows good power in relatively small samples with moderate deviation from linearity. An empirical application is included, where data on median house prices from the Boston area is used to explore the spatial dependence between census tracts. A smooth shift between regimes governed by the variable property tax rate is found. The smooth spatial lag model performs slightly better than the regular spatial lag model in terms of model fit and capturing spatial dependence.