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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.

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Article provided by Taylor & Francis Journals in its journal Spatial Economic Analysis.

Volume (Year): 7 (2012)
Issue (Month): 1 (March)
Pages: 75-107

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Handle: RePEc:taf:specan:v:7:y:2012:i:1:p:75-107
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