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Testing Isotropy in Spatial Econometric Models

2013; Routledge; Volume: 8; Issue: 3 Linguagem: Inglês

10.1080/17421772.2013.804629

1742-1780

Giuseppe Arbia, Marco Bee, Giuseppe Espa,

Housing Market and Economics

Abstract 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. RÉSUMÉ la stationnarité dans l'espace implique à la fois l'homogénéité et l'isotropie. Les tests d'isotropie sont une pratique courante dans un grand nombre de domaines d'application, mais, dans celui de l'économétrie spatiale, ils ont été tout simplement présumés sans procéder au moindre essai officiel. Dans la présente communication, nous présentons une procédure pour tester l'isotropie dans des modèles d'économétrie spatiale, basés sur des données régionales dérivés du concept des approximations unilatérales. Nous évaluons la puissance de ce test à l'aide d'une expérience de Monte Carlo. Enfin, nous effectuons une analyse de données empiriques pour tester l'isotropie, dans le cadre de l'analyse de la convergence régionale en Italie dans les années 2000–2008. EXTRACTO La estacionariedad en el espacio denota homogeneidad e isotropía. La comprobación de la isotropía es una práctica común en muchos campos de aplicación, pero en la econometría espacial se ha descartado sin una comprobación formal. En este estudio introducimos un procedimiento para comprobar la isotropía en modelos econométricos espaciales basados en datos regionales que derivan del concepto de las aproximaciones unilaterales. El poder de la prueba se evalúa mediante un experimento de Monte Carlo. Finalmente, realizamos un análisis de datos empíricos para comprobar la isotropía al analizar la convergencia regional en Italia en los años 2000 al 2008. 摘要 : 太空中的定态表示了均匀性和各向同性。 检验各向同性是许多应用领域的常见做法, 但在空间计量经济学领域, 人们一直认为并没有正式的检验方法。 本文中, 我们引入了一个适用于各向同性的空间经济计量模型的检验程序, 模型基于从单方面近似概念推导出的区域数据。采用蒙特卡罗实验方法来对检定力进行评估。最后, 我们要在分析2000–2008年间意大利区域趋同的时候进行实证数据分析, 以检验各向同性。 Keywords: anisotropyasymmetrylikelihood ratio testspatial lag modelsspatial econometricsunilateral approximation Acknowledgments Paper presented at the Special Session in honor of Harry Kelejian at the V World Conference of the Spatial Econometrics Association held in Toulouse 6–8 July 2011. We wish to thank the participants to the sessions for the comments received. We also acknowledge the comments of two anonymous referees and of Ingmar R. Prucha that considerably improved the presentation of the work. Notes 1. For a particular form of anisotropy, generated by a set of covariates, see Deng (Citation2008). 2. Indeed Paelinck & Klaassen (Citation1979) identify five fundamental characteristics of spatial econometrics, that are: (i) the role of interdependence in spatial models, (ii) the asymmetry of spatial relations, (iii) the importance of explanatory factors located in other spaces, (iv) the differentiation between ex-post and ex-ante interaction and (v) the explicit modelling of space. 3. Negative spatial correlation is also sometimes observed in the residuals of spatial lag models (e.g. Bloningen et al., Citation2004; Mizobuchi & Kakamu, Citation2007). Recent attempts to provide a theoretical explanation for the presence of negative spatial correlation can be found in Frank & Botolf (Citation2007) who explain it as a manifestation of Myrdal's (Citation1957) backwash effect.