LM tests of spatial dependence based on bootstrap critical values

Zhenlin Yang

Journal of Econometrics, 2015, vol. 185, issue 1, 33-59

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.

Keywords: Asymptotic refinements; Bootstrap; Edgeworth expansion; LM tests; Spatial dependence; Size; Power; Local misspecification; Heteroskedasticity; Wild bootstrap (search for similar items in EconPapers)
JEL-codes: C12 C15 C18 C21 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (20)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:185:y:2015:i:1:p:33-59

DOI: 10.1016/j.jeconom.2014.10.005

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