Evaluating three proposals for testing independence in non linear spatial processes

Resumen

Spatial econometric studies have usually employed linear regression frameworks when modelling relationships between geo-referenced units. Nevertheless, as Kovach (1960) stated, life can be (and used to be) non linear. This fact explains the growing interest of the profession in developing new models for dealing with non linearities. As a natural complement, new families of tests have also become necessary, particularly those better suited to a non linear world. This paper evaluates the behaviour of the main type of tests employed when checking for spatial independence assumptions in the presence of non linearities: parametric, nonparametric and semiparametric. To reach this goal we select three representative proposals from each family of tests. First, we study one of the most well known parametric tests, the I-Moran test. Secondly, we select the nonparametric proposal of Brett and Pinkse (1997), the BP test. Finally, we analyse the behaviour of a semiparametric test which has been applied to epidemiology studies but still not generalised to spatial econometrics literature, namely the Kulldorff test or Ku test (Kulldorff et al., 2009). In order to establish a comparison among these proposals, we generate different nonlinear spatial structures throughout Monte Carlo simulations and conduct an empirical exercise on the matter. Results of both sections indicate that, under nonlinear spatial structures, the classical IMoran test usually fails, but semiparametric and nonparametric proposals perform much better, showing greater power in all cases. Results recommend updating spatial testing proposals in the presence of non linearities, allowing for corresponding robustness gains in the estimation procedure.