LM Tests of Spatial Dependence Based on Bootstrap Critical Values
AbstractTo test the existence of spatial dependence in an econometric model, a convenient test is the Lagrange Multiplier (LM) test. However, evidence shows that, infinite 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.
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Bibliographic InfoPaper provided by Singapore Management University, School of Economics in its series Working Papers with number 03-2013.
Date of creation: May 2013
Date of revision:
Publication status: Published in SMU Economics and Statistics Working Paper Series
Find related papers by JEL classification:
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
- C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-09-06 (All new papers)
- NEP-ECM-2013-09-06 (Econometrics)
- NEP-GEO-2013-09-06 (Economic Geography)
- NEP-SEA-2013-09-06 (South East Asia)
- NEP-URE-2013-09-06 (Urban & Real Estate Economics)
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