testing isotropy in spatial econometric models

Stationarity in space presents two aspects: homogeneity and isotropy. They correspond\r\nrespectively to stationarity under translations and stationarity under rotations. Testing the hypothesis of\r\nisotropy is a common practice in many fields of application of spatial statistics where directional biases\r\nare of paramount importance like, for instance, in meteorology, geology or medicine to name only a few.\r\n10 In spatial econometrics, however, isotropy has been systematically neglected and just assumed away\r\nwith no formal testing. This lack is somehow surprising, because anisotropies are more the rule rather\r\nthan the exception when observing most economic phenomena. In this paper we introduce a testing\r\nprocedure for spatial econometric models based on regional data that derives from Besag’s idea of the\r\nunilateral approximations (Besag, 1974). The power of the test is assessed by means of a Monte Carlo\r\n15 experiment. Finally, we perform an empirical data analysis to test isotropy when analysing the regional\r\nconvergence in Italy in the years 2000–2008