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Spatial Nonstationarity and Spurious Regression: the Case with a Row-normalized Spatial Weights Matrix

  • Lung-Fei Lee
  • Jihai Yu

Abstract This paper investigates the spurious regression in the spatial setting where the regressant and regressors may be generated from possible nonstationary spatial autoregressive processes. Under the near unit root specification with a row-normalized spatial weights matrix, it is shown that the possible spurious regression phenomena in the spatial setting are relatively weaker than those in the nonstationary time series scenario. The regression estimates might or might not converge to 0. The divergence might occur only when the regressant has a near unit root much closer to unity than that of the regressor. For the t and F statistics, there could be over-rejection of the null of uncorrelatedness under certain situations, but they do not diverge. However, the coefficient of determination R 2 converges to 0, which provides strong evidence of the spurious regression even when t and F statistics are large. Simulation results about different statistics are in line with the theoretical results we derive in this paper. Non-stationnarité spatiale et fausse régression: l'argument pour la matrice de pondération spatiale à normalisation ‘row-normalized’ RÉSUMÉ La présente communication se penche sur la fausse régression dans les cadres spatiaux, où des variables dépendantes et des variables explicatives peuvent être produites par d’éventuels procédés autorégressifs spatiaux non stationnaires. Dans le cadre de la spécification de la racine quasi-unitaire, avec une matrice de pondération spatiale normalisée ‘row-normalized’, il est démontré que les phénomènes de fausse régression dans les cadres spatiaux sont relativement plus faibles que ceux du scénario à série chronologique non stationnaire. Pour les statistiques t et F, on pourra assister à une sur-réjection du néant de la non corrélation dans certaines circonstances, mais aucune divergence. Toutefois, le coefficient de détermination R2 converge vers 0, en apportant ainsi une preuve substantielle de la fausse, même en présence de statistiques t et F élevées. Les résultats des simulations sur différentes statistiques sont en accord avec les résultats théoriques que nous dérivons dans la présente communication. No estacionariedad espacial y regresión falsa: el caso con la matriz de pesos espaciales standardizada por filas RÉSUMÉ Este trabajo investiga la regresión falsa en el ámbito espacial donde la variable dependiente y las variables independientes pueden generarse a partir de posibles procesos autorregresivos espaciales no estacionarios. Bajo la especificación de raíz unitaria con una matriz de pesos espaciales estandarizada por filas, se muestra que los posibles fenómenos de regresión falsa son relativamente más débiles que los del caso de la serie de tiempo no estacionario. En las estadísticas t y F, podría producirse un sobrerrechazo de la hipótesis nula de incorrelación bajo ciertas situaciones, pero no son divergentes. No obstante, el coeficiente de determinación R2 converge a 0, lo que ofrece una evidencia fuerte de la regresión falsa incluso cuando las estadísticas t y F son amplias. Los resultados de simulación sobre diferentes estadísticas se mantienen en línea con los resultados teóricos que obtenemos en este trabajo.

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File URL: http://www.taylorandfrancisonline.com/doi/abs/10.1080/17421770903114703
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Article provided by Taylor & Francis Journals in its journal Spatial Economic Analysis.

Volume (Year): 4 (2009)
Issue (Month): 3 ()
Pages: 301-327

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Handle: RePEc:taf:specan:v:4:y:2009:i:3:p:301-327
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