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Improving the J Test in the SARAR Model by Likelihood-based Estimation


  • Peter Burridge


It has been demonstrated recently that in small-to-medium samples the empirical significance levels of the asymptotic J-type tests for the SARAR model introduced by Kelejian (2008) can be controlled in many cases by the use of a bootstrap to construct a reference distribution. A feature of the popular GMM estimator in this context that deserves to receive more attention is that in small samples it will often deliver spatial parameter estimates that lie outside the invertibility region of the model. Using such illegitimate estimates to construct bootstrap samples is then problematic; the present paper finds that this practical obstacle may be removed by the use of quasi-maximum likelihood estimates that guarantee invertibility. The effects of different spatial weight patterns and sample size on the empirical significance levels and power of the tests are illustrated, and the paper demonstrates that estimation using QMLE, allied to a simple bootstrap, yields tests with reliable significance levels and reasonable power, in a majority of cases. RÉSUMÉ dans des échantillons petits à moyens, il est possible, dans de nombreux cas, de contrôler les niveaux à signification empirique des tests asymptotiques introduits par Kelejian (2008) à l'aide d'un ‘bootstrap’. Dans ce contexte, une caractéristique de l'estimateur GMM, très répandu, est qu'il fournit, dans de petits échantillons, des estimations de paramètres spatiaux situés hors de la région d'inversibilité du modèle. L'emploi de telles estimations illégitimes pour la réalisation d’échantillons ‘bootstrap’ devient alors problématique; la présente communication indique que l'on peut supprimer cet obstacle pratique en utilisant le QMLE garantissant l'inversibilité. Les effets des tendances du poids spatial et la taille des échantillons sur les niveaux d'importance et la puissance sont illustrés, et la communication démontre que le QMLE, allié à un simple ‘bootstrap’, permet de réaliser des tests offrant, dans la plupart des vas, des niveaux d'importance fiables et une puissance raisonnable. EXTRACTO En muestras entre pequeñas y medianas, los niveles de significancia empírica de las pruebas asintóticas de tipo J para el modelo SARAR introducidas por Kelejian (2008) pueden controlarse en muchos casos mediante el uso de un bootstrap. Una característica del popular estimador GMM dentro de este contexto es que en las muestras pequeñas, a menudo producirá estimaciones de parámetros espaciales que están fuera de la región de reversibilidad del modelo. No obstante, el empleo de este tipo de estimaciones ilegítimas para construir muestras bootstrap es problemático; el estudio actual muestra que este obstáculo práctico puede eliminarse mediante el uso del QMLE que garantiza la reversibilidad. Se ilustran los efectos de las pautas de peso espacial y del tamaño de la muestra sobre el poder y los niveles de significancia, y el estudio demuestra que el QMLE, aliado a un bootstrap simple, dota a las pruebas de niveles de significancia fiables y de un poder razonable, en la mayoría de los casos.

Suggested Citation

  • Peter Burridge, 2012. "Improving the J Test in the SARAR Model by Likelihood-based Estimation," Spatial Economic Analysis, Taylor & Francis Journals, vol. 7(1), pages 75-107, March.
  • Handle: RePEc:taf:specan:v:7:y:2012:i:1:p:75-107
    DOI: 10.1080/17421772.2011.647055

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    References listed on IDEAS

    1. Bernard Fingleton (ed.), 2007. "New Directions in Economic Geography," Books, Edward Elgar Publishing, number 3818.
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    Cited by:

    1. Delgado, Miguel A. & Robinson, Peter M., 2013. "Non-nested testing of spatial correlation," LSE Research Online Documents on Economics 58169, London School of Economics and Political Science, LSE Library.
    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. Delgado, Miguel A. & Robinson, Peter, 2015. "Non-nested testing of spatial correlation," LSE Research Online Documents on Economics 61433, London School of Economics and Political Science, LSE Library.
    4. Nicolas DEBARSY & Cem ERTUR, 2016. "Interaction matrix selection in spatial econometrics with an application to growth theory," LEO Working Papers / DR LEO 2172, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
    5. 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.
    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. Masayoshi Hayashi & Wataru Yamamoto, 2017. "Information sharing, neighborhood demarcation, and yardstick competition: an empirical analysis of intergovernmental expenditure interaction in Japan," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 24(1), pages 134-163, February.
    10. Delgado, Miguel A. & Robinson, Peter M., 2015. "Non-nested testing of spatial correlation," Journal of Econometrics, Elsevier, vol. 187(1), pages 385-401.
    11. Yang, Zhenlin, 2015. "LM tests of spatial dependence based on bootstrap critical values," Journal of Econometrics, Elsevier, vol. 185(1), pages 33-59.
    12. 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.
    13. Solmaria Halleck Vega & J. Paul Elhorst, 2015. "The Slx Model," Journal of Regional Science, Wiley Blackwell, vol. 55(3), pages 339-363, June.
    14. Miguel A. Delgado & Peter M Robinson, 2013. "Non-Nested Testing of Spatial Correlation," STICERD - Econometrics Paper Series 568, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    15. 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.
    16. 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.
    17. Jesus Mur & Antonio Paez, 2011. "Local weighting or the necessity of flexibility," ERSA conference papers ersa11p942, European Regional Science Association.
    18. repec:eee:regeco:v:69:y:2018:i:c:p:48-68 is not listed on IDEAS
    19. repec:cep:stiecm:/2013/568 is not listed on IDEAS

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