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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- Koenker, Roger, 1981. "A note on studentizing a test for heteroscedasticity," Journal of Econometrics, Elsevier, vol. 17(1), pages 107-112, September.
- Peter Burridge & Bernard Fingleton, 2010. "Bootstrap Inference in Spatial Econometrics: the J-test," Spatial Economic Analysis, Taylor and Francis Journals, vol. 5(1), pages 93-119.
- H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September.
- Anselin, Luc & Moreno, Rosina, 2003.
"Properties of tests for spatial error components,"
Regional Science and Urban Economics,
Elsevier, vol. 33(5), pages 595-618, September.
- Davidson, Russell & MacKinnon, James G., 1999.
"The Size Distortion Of Bootstrap Tests,"
Cambridge University Press, vol. 15(03), pages 361-376, June.
- Russell Davidson & Emmanuel Flachaire, 2000.
"The Wild Bootstrap, Tamed at Last,"
Econometric Society World Congress 2000 Contributed Papers
1413, Econometric Society.
- Emmanuel Flachaire, 2001. "The Wild Bootstrap, Tamed at Last," STICERD - Distributional Analysis Research Programme Papers 58, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Russell Davidson & Emmanuel Flachaire, 2001. "The Wild Bootstrap, Tamed at Last," Working Papers 1000, Queen's University, Department of Economics.
- Davidson, R. & Flachaire, E., 1999. "The Wild Bootstrap, Tamed at Last," G.R.E.Q.A.M. 99a32, Universite Aix-Marseille III.
- Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-65, July.
- Anselin, Luc & Bera, Anil K. & Florax, Raymond & Yoon, Mann J., 1996. "Simple diagnostic tests for spatial dependence," Regional Science and Urban Economics, Elsevier, vol. 26(1), pages 77-104, February.
- Horowitz, Joel L., 1994. "Bootstrap-based critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395-411, April.
- Badi H. Baltagi & Zhenlin Yang, 2013.
"Standardized LM tests for spatial error dependence in linear or panel regressions,"
Royal Economic Society, vol. 16(1), pages 103-134, 02.
- Badi H. Baltagi & Zhenlin Yang, 2010. "Standardized LM Tests for Spatial Error Dependence in Linear or Panel Regressions," Working Papers 11-2010, Singapore Management University, School of Economics.
- Badi H. Baltagi & Zhenlin Yang, 2012. "Standardized LM Tests for Spatial Error Dependence in Linear or Panel Regressions," Center for Policy Research Working Papers 142, Center for Policy Research, Maxwell School, Syracuse University.
- Kuan-Pin Lin & Zhi-He Long & Bianling Ou, 2011. "The Size and Power of Bootstrap Tests for Spatial Dependence in a Linear Regression Model," Computational Economics, Society for Computational Economics, vol. 38(2), pages 153-171, August.
- Russell Davidson & James G. MacKinnon, 2004.
"The Power of Bootstrap and Asymptotic Tests,"
1035, Queen's University, Department of Economics.
- Peter Burridge, 2012. "Improving the J Test in the SARAR Model by Likelihood-based Estimation," Spatial Economic Analysis, Taylor and Francis Journals, vol. 7(1), pages 75-107, March.
- Benjamin Born & Jörg Breitung, 2011.
"Simple regression‐based tests for spatial dependence,"
Royal Economic Society, vol. 14(2), pages 330-342, 07.
- Benjamin Born & Jörg Breitung, 2009. "Simple Regression Based Tests for Spatial Dependence," Bonn Econ Discussion Papers bgse23_2009, University of Bonn, Germany.
- Zhenlin Yang, 2009.
"A Robust LM Test for Spatial Error Components,"
04-2009, Singapore Management University, School of Economics.
- Lin, Xu & Lee, Lung-fei, 2010. "GMM estimation of spatial autoregressive models with unknown heteroskedasticity," Journal of Econometrics, Elsevier, vol. 157(1), pages 34-52, July.
- Lung-Fei Lee, 2004. "Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models," Econometrica, Econometric Society, vol. 72(6), pages 1899-1925, November.
- Robinson, P.M., 2008. "Correlation testing in time series, spatial and cross-sectional data," Journal of Econometrics, Elsevier, vol. 147(1), pages 5-16, November.
- James G. MacKinnon, 2002. "Bootstrap inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 35(4), pages 615-645, November.
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