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.
Bibliographical note“Improving the J Test in the SARAR Model by Likelihood-based Estimation” (2012) has been included in an article collection marking the publication of the 10th volume of Spatial Economic Analysis.
Editor Bernard Fingleton chose the content for the collection, selecting articles which have made substantive contributions and which highlight the journal’s role as a source of innovation and excellence in spatial econometrics, economic geography and regional science.