Publication Type

Working Paper

Version

publishedVersion

Publication Date

5-2013

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 details 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

LM Tests, Bootstrapped critical values, Power, Size, Spatial dependence, Heteroscedasticity

Discipline

Econometrics

Research Areas

Econometrics

First Page

1

Last Page

49

Publisher

SMU Economics and Statistics Working Paper Series, No. 03-2013

City or Country

Singapore

Copyright Owner and License

Authors

Comments

Published in Journal of Econometrics https://doi.org/10.1016/j.jeconom.2014.10.005

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