Spatial Econometric STAR models: Lagrange Multiplier Tests, Monte Carlo Simulations and an Empricial Application

This paper investigates nonlinearity in parametric spatial process models that incorporate regime-switching by means of a smooth transition autoregressive process. We derive a Lagrange Multiplier (LM) test for nonlinearity as well as several joint LM tests for nonlinearity and the traditional spatial processes of autoregressive errors and an erroneously omitted spatially lagged dependent variable. Monte Carlo simulations demonstrate the size and power of the tests in finite samples. In an empirical application, we demonstrate that the suggested approach can be used to test for spatial heterogeneity in the form of spatial regimes or for the appropriateness of the spatial cross-regressive model containing spatially lagged exogenous variables.