Testing Isotropy in Spatial Econometric Models

Stationarity in space presents two aspects: homogeneity and isotropy. They correspond respectively to stationarity under translations and stationarity under rotations. Testing the hypothesis of isotropy is a common practice in many fields of application of spatial statistics where directional biases are of paramount importance like, for instance, in meteorology, geology or medicine to name only a few. In spatial econometrics, however, isotropy has been systematically neglected and just assumed away with no formal testing. This lack is somehow surprising, because anisotropies are more the rule rather than the exception when observing most economic phenomena. In this paper we introduce a testing procedure for spatial econometric models based on regional data that derives from Besag's idea of the unilateral approximations (Besag, 1974). The power of the test is assessed by means of a Monte Carlo experiment. Finally, we perform an empirical data analysis to test isotropy when analysing the regional convergence in Italy in the years 2000–2008.