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Bootstrap Inference in Spatial Econometrics: the J-test

Author

Listed:
  • Peter Burridge
  • Bernard Fingleton

Abstract

Abstract Kelejian (2008) introduces a J-type test for the situation in which a null linear regression model, Model0, is to be tested against one or more rival non-nested alternatives, Model1, …, Model g , where typically the competing models possess endogenous spatial lags and spatially autoregressive error processes. Concentrating on the case g=1, in this paper we examine the finite sample properties of a spatial J statistic that is asymptotically under the null, and an alternative version that is conjectured to be approximately , both introduced by Kelejian. We demonstrate numerically that the tests are excessively liberal in some leading cases and conservative in others using the relevant chi-square asymptotic approximations, and explore how far this may be corrected using a simple bootstrap resampling method. Inférence ‘bootstrap’ dans l'économétrie spatiale: le test ‘J’ Résumé Kelejian (2008) présente un test de type J pour la situation dans laquelle on doit tester un modèle a régression linéaire nulle, Model0, par rapport à une ou plusieurs alternatives concurrentes non imbriquées, Model1, …, Model g , dans laquelle les modèles concurrents possèdent généralement des retards spatiaux endogènes et des procédés d'erreur spatialement autorégressifs. En nous concentrant sur le cas g=1, nous examinons, dans la présente communication, les propriétés d'échantillon finies d'une statistique spatiale J qui se trouve asymptotiquement sous le zéro, et une version alternative supposée être égale à environ , introduites toutes les deux par Kelejian. Nous démontrons de façon numérique que les tests sont excessivement libéraux, dans certains des principaux cas, et plutôt prudents dans d'autres, en faisant usage des approximations asymptotiques au chi carré, et nous explorons la mesure dans laquelle nous pouvons le corriger en appliquant un simple processus empirique ré-échantillonné. La inferencia bootstrap en la econometría espacial: el test J Résumén Kelejian (2008) introduce un test de tipo J para la situación en que un modelo de regresión lineal nulo, Model0, se pone a prueba contra una o más alternativas rivales no anidadas, Model1, …, Model g , donde típicamente los modelos competidores poseen lapsos espaciales endógenos y procesos de error espacialmente autorregresivos. Concentrándose en el caso, g=1, este trabajo examina las propiedades de muestra finita de una estadística espacial J que es asimptóticamente bajo el nulo, y una versión alternativa que se conjetura que es aproximadamente , ambas introducidas por Kelejian. Demostramos numéricamente que los tests son excesivamente liberales en ciertos casos destacados y conservadores en otros, utilizando las aproximaciones chi cuadradas oportunas, y exploramos hasta qué punto esto podría corregirse empleando un método simple bootstrap de remuestreo.

Suggested Citation

  • Peter Burridge & Bernard Fingleton, 2010. "Bootstrap Inference in Spatial Econometrics: the J-test," Spatial Economic Analysis, Taylor & Francis Journals, vol. 5(1), pages 93-119.
  • Handle: RePEc:taf:specan:v:5:y:2010:i:1:p:93-119
    DOI: 10.1080/17421770903511346
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    Citations

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    Cited by:

    1. Luisa Corrado & Bernard Fingleton, 2012. "Where Is The Economics In Spatial Econometrics?," Journal of Regional Science, Wiley Blackwell, vol. 52(2), pages 210-239, May.
    2. Jesus Mur & Marcos Herrera & Manuel Ruiz, 2011. "Selecting the W Matrix. Parametric vs Nonparametric Approaches," ERSA conference papers ersa11p1055, European Regional Science Association.
    3. Raffaele Paci & Emanuela Marrocu & Stefano Usai, 2014. "The Complementary Effects of Proximity Dimensions on Knowledge Spillovers," Spatial Economic Analysis, Taylor & Francis Journals, vol. 9(1), pages 9-30, March.
    4. Paelinck, Jean & Mur, Jesús & Trivez, F. Javier, 2015. "Modelos para datos espaciales con estructura transversal o de panel. Una revisión/Models for Spatial Data with Panel or Cross-Sectional Structure. A Review," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 33, pages 7-30, Enero.
    5. Harry H. Kelejian & Gianfranco Piras, 2013. "A J-Test for Panel Models with Fixed Effects, Spatial and Time," Working Papers Working Paper 2013-03, Regional Research Institute, West Virginia University.
    6. Zhenlin Yang, 2013. "LM Tests of Spatial Dependence Based on Bootstrap Critical Values," Working Papers 03-2013, Singapore Management University, School of Economics.
    7. Herrera Gómez, Marcos & Mur Lacambra, Jesús & Ruiz Marín, Manuel, 2011. "¿Cuál matriz de pesos espaciales?. Un enfoque sobre selección de modelos
      [Which spatial weighting matrix? An approach for model selection]
      ," MPRA Paper 37585, University Library of Munich, Germany.
    8. Marcos Herrera & Jesus Mur & Manuel Ruiz-Marin, 2017. "A Comparison Study on Criteria to Select the Most Adequate Weighting Matrix," Working Papers 18, Instituto de Estudios Laborales y del Desarrollo Económico (IELDE) - Universidad Nacional de Salta - Facultad de Ciencias Económicas, Jurídicas y Sociales.
    9. Han, Xiaoyi & Lee, Lung-fei, 2013. "Model selection using J-test for the spatial autoregressive model vs. the matrix exponential spatial model," Regional Science and Urban Economics, Elsevier, vol. 43(2), pages 250-271.
    10. Marcos Herrera & Manuel Ruiz & Jesús Mur, 2013. "Detecting Dependence Between Spatial Processes," Spatial Economic Analysis, Taylor & Francis Journals, vol. 8(4), pages 469-497, February.
    11. repec:eee:regeco:v:65:y:2017:i:c:p:65-88 is not listed on IDEAS
    12. Harry H. Kelejian & Gianfranco Piras, 2016. "A J test for dynamic panel model with fixed effects, and nonparametric spatial and time dependence," Empirical Economics, Springer, vol. 51(4), pages 1581-1605, December.
    13. Jin, Fei & Lee, Lung-fei, 2015. "On the bootstrap for Moran’s I test for spatial dependence," Journal of Econometrics, Elsevier, vol. 184(2), pages 295-314.
    14. Herrera Gómez, Marcos & Mur Lacambra, Jesús & Ruiz Marín, Manuel, 2012. "Selecting the Most Adequate Spatial Weighting Matrix:A Study on Criteria," MPRA Paper 73700, University Library of Munich, Germany.
    15. Bernard FINGLETON & Silvia PALOMBI, 2013. "The Wage Curve Reconsidered: Is It Truly An 'Empirical Law Of Economics'?," Region et Developpement, Region et Developpement, LEAD, Universite du Sud - Toulon Var, vol. 38, pages 49-92.
    16. Delgado, Miguel A. & Robinson, Peter M., 2015. "Non-nested testing of spatial correlation," Journal of Econometrics, Elsevier, vol. 187(1), pages 385-401.
    17. Yang, Zhenlin, 2015. "LM tests of spatial dependence based on bootstrap critical values," Journal of Econometrics, Elsevier, vol. 185(1), pages 33-59.
    18. Jin, Fei & Lee, Lung-fei, 2013. "Cox-type tests for competing spatial autoregressive models with spatial autoregressive disturbances," Regional Science and Urban Economics, Elsevier, vol. 43(4), pages 590-616.
    19. Solmaria Halleck Vega & J. Paul Elhorst, 2015. "The Slx Model," Journal of Regional Science, Wiley Blackwell, vol. 55(3), pages 339-363, June.
    20. Jesus Mur & Antonio Paez, 2011. "Local weighting or the necessity of flexibility," ERSA conference papers ersa11p942, European Regional Science Association.

    More about this item

    Keywords

    Spatial econometrics; bootstrap; J-test; C; C21;

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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