LM tests of spatial dependence based on bootstrap critical values |
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Institution: | 1. UMR 729 MISTEA, INRA-SupAgro, 2 place Pierre Viala, 34060 Montpellier, France;2. LMAP, UMR CNRS 5142, Université de Pau et des Pays de l’Adour, Avenue de l’Université, 64000 Pau, France;1. Laboratoire de Mathématiques Appliquées de Compiègne-L.M.A.C., Université de Technologie de Compiègne, B.P. 529, 60205 Compiègne Cedex, France;2. L.S.T.A., Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris Cedex 05, France;1. Department of Administrative and Accounting Science, University of the Andes-Táchira-Venezuela, Venezuela;2. Department of Statistics, University of the Andes-Táchira-Venezuela, Venezuela |
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Abstract: | To test the existence of spatial dependence in an econometric model, a convenient test is the Lagrange Multiplier (LM) test. However, evidence shows that, in finite samples, the LM test referring to asymptotic critical values may suffer from the problems of size distortion and low power, which become worse with a denser spatial weight matrix. In this paper, residual-based bootstrap methods are introduced for asymptotically refined approximations to the finite sample critical values of the LM statistics. Conditions for their validity are clearly laid out and formal justifications are given in general, and in detail under several popular spatial LM tests using Edgeworth expansions. Monte Carlo results show that when the conditions are not fully met, bootstrap may lead to unstable critical values that change significantly with the alternative, whereas when all conditions are met, bootstrap critical values are very stable, approximate much better the finite sample critical values than those based on asymptotics, and lead to significantly improved size and power. The methods are further demonstrated using more general spatial LM tests, in connection with local misspecification and unknown heteroskedasticity. |
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Keywords: | Asymptotic refinements Bootstrap Edgeworth expansion LM tests Spatial dependence Size Power Local misspecification Heteroskedasticity Wild bootstrap |
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