Publication Type

Journal Article

Publication Date

3-2015

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

Discipline

Econometrics

Research Areas

Econometrics

Publication

Journal of Econometrics

Volume

185

Issue

1

First Page

33

Last Page

59

ISSN

0304-4076

Identifier

10.1016/j.jeconom.2014.10.005

Publisher

Elsevier

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Additional URL

http://dx.doi.org/10.1016/j.jeconom.2014.10.005

Included in

Econometrics Commons

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