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Testing for Unit Roots and Cointegration in Spatial Cross-Section Data


  • Michael Beenstock
  • Dan Feldman
  • Daniel Felsenstein


Spatial impulses are derived for SAR models containing a spatial unit root. Analytical solutions are obtained for lateral space where the number of spatial units tends to infinity. Numerical solutions are obtained for finite regular lattices where edge-effects are shown to influence spatial impulses, and for irregular lattices. Monte Carlo simulation methods are used to compute critical values for spatial unit root tests in SAR models estimated from spatial cross-section data for regular and irregular lattices. We also compute critical SAC values for spatial cointegration tests for cross-section data that happen to be spatially nonstationary. We show that parameter estimates in spatially cointegrated models are ‘superconsistent’. RÉSUMÉ On dérive des impulsions spatiales de modèles SAR contenant une racine unité spatiale. On obtient des solutions analytiques pour l'espace latéral lorsque le nombre d'unités spatiales tend vers l'infini. On obtient des solutions numériques pour des réseaux réguliers finis, où l'on relève l'influence d’« edge effects » sur les impulsions spatiales, et pour des réseaux irréguliers. Des méthodes de simulation Monte Carlo sont utilisées pour calculer des valeurs critiques pour des tests de racine unité spatiale dans des modèles SAR estimés sur la base de données transversales spatiales pour réseaux réguliers et irréguliers. Nous calculons également des valeurs critiques de SAC pour essais de co-intégration spatiale, concernant des données transversales qui s'avèrent être spatialement non stationnaires. Nous démontrons que les estimations de paramètres dans des modèles spatialement co-intégrés sont « ultra cohérentes ». EXTRACTO Se derivan impulsos espaciales para modelos SAR que contienen una raíz unitaria espacial. Se obtienen soluciones analíticas para espacio lateral donde el número de unidades espaciales tiende al infinito. Se obtienen soluciones numéricas para retículos finitos regulares que demuestran que los efectos de borde influyen sobre los impulsos espaciales, así como para retículos irregulares. Se utilizan métodos de simulación de Monte Carlo para computar valores críticos destinados a las pruebas espaciales de raíces unitarias en modelos SAR, estimados a partir de datos espaciales de corte transversal para retículos regulares e irregulares. También computamos valores SAC críticos destinados a pruebas de cointegración espacial para datos de corte transversal que no son espacialmente estacionarios. Mostramos que las estimaciones de parámetros en modelos espacialmente cointegrados son ‘superconsistentes’.

Suggested Citation

  • Michael Beenstock & Dan Feldman & Daniel Felsenstein, 2012. "Testing for Unit Roots and Cointegration in Spatial Cross-Section Data," Spatial Economic Analysis, Taylor & Francis Journals, vol. 7(2), pages 203-222, June.
  • Handle: RePEc:taf:specan:v:7:y:2012:i:2:p:203-222
    DOI: 10.1080/17421772.2012.669491

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    Cited by:

    1. Badi H. BALTAGI & Bernard FINGLETON & Alain PIROTTE, 2014. "Multilevel And Spillover Effects Estimated For Spatial Panel Data, With Application To English House Prices," Region et Developpement, Region et Developpement, LEAD, Universite du Sud - Toulon Var, vol. 40, pages 25-36.
    2. Baltagi, Badi H. & Fingleton, Bernard & Pirotte, Alain, 2014. "Spatial lag models with nested random effects: An instrumental variable procedure with an application to English house prices," Journal of Urban Economics, Elsevier, vol. 80(C), pages 76-86.
    3. Beenstock, Michael & Felsenstein, Daniel, 2015. "Estimating spatial spillover in housing construction with nonstationary panel data," Journal of Housing Economics, Elsevier, vol. 28(C), pages 42-58.

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