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A Robust LM Test for Spatial Error Components

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  • Zhenlin Yang

    (SMU)

Abstract

This paper presents a modified LM test of spatial error components, which is shown to be robust against distributional misspecifications and spatial layouts. The proposed test differs from the LM test of Anselin (2001) by a term in the denominators of the test statistics. This term disappears when either the errors are normal, or the variance of the diagonal elements of the product of spatial weights matrix and its transpose is zero or approaching to zero as sample size goes large. When neither is true, as is often the case in practice, the effect of this term can be significant even when sample size is large. As a result, there can be severe size distortions of the Anselins LM test, a phenomenon revealed by the Monte Carlo results of Anselin and Moreno (2003) and further confirmed by the Monte Carlo results presented in this paper. Our Monte Carlo results also show that the proposed test performs well in general.

Suggested Citation

  • Zhenlin Yang, 2009. "A Robust LM Test for Spatial Error Components," Development Economics Working Papers 22488, East Asian Bureau of Economic Research.
  • Handle: RePEc:eab:develo:22488
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    References listed on IDEAS

    as
    1. Bera, Anil K. & Sosa-Escudero, Walter & Yoon, Mann, 2001. "Tests for the error component model in the presence of local misspecification," Journal of Econometrics, Elsevier, pages 1-23.
    2. Kelejian, Harry H & Prucha, Ingmar R, 1999. "A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 509-533, May.
    3. Anil Bera & Walter Sosa Escudero & Mann Yoon, 2000. "Test for the Error Component Model in the Presence of Local Misspecification," Department of Economics, Working Papers 022, Departamento de Economía, Facultad de Ciencias Económicas, Universidad Nacional de La Plata.
    4. Bera, Anil K. & Sosa-Escudero, Walter & Yoon, Mann, 2001. "Tests for the error component model in the presence of local misspecification," Journal of Econometrics, Elsevier, pages 1-23.
    5. 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.
    6. H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, pages 219-257.
    7. Lee, Lung-fei, 2007. "Identification and estimation of econometric models with group interactions, contextual factors and fixed effects," Journal of Econometrics, Elsevier, pages 333-374.
    8. H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, pages 219-257.
    9. Koenker, Roger, 1981. "A note on studentizing a test for heteroscedasticity," Journal of Econometrics, Elsevier, pages 107-112.
    10. Bera, Anil K. & Yoon, Mann J., 1993. "Specification Testing with Locally Misspecified Alternatives," Econometric Theory, Cambridge University Press, vol. 9(04), pages 649-658, August.
    11. 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.
    12. Lee, Lung-Fei, 2002. "Consistency And Efficiency Of Least Squares Estimation For Mixed Regressive, Spatial Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 18(02), pages 252-277, April.
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    Citations

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    Cited by:

    1. Fang, Ying & Park, Sung Y. & Zhang, Jinfeng, 2014. "A simple spatial dependence test robust to local and distributional misspecifications," Economics Letters, Elsevier, vol. 124(2), pages 203-206.
    2. Badi H. Baltagi & Zhenlin Yang, 2013. "Heteroskedasticity and Non-normality Robust LM Tests for Spatial Dependence," Center for Policy Research Working Papers 156, Center for Policy Research, Maxwell School, Syracuse University.
    3. Baltagi, Badi H. & Yang, Zhenlin, 2013. "Heteroskedasticity and non-normality robust LM tests for spatial dependence," Regional Science and Urban Economics, Elsevier, vol. 43(5), pages 725-739.
    4. Yang, Zhenlin, 2015. "LM tests of spatial dependence based on bootstrap critical values," Journal of Econometrics, Elsevier, pages 33-59.
    5. He, Ming & Lin, Kuan-Pin, 2015. "Testing spatial effects and random effects in a nested panel data model," Economics Letters, Elsevier, vol. 135(C), pages 85-91.
    6. Liu, Shew Fan & Yang, Zhenlin, 2015. "Modified QML estimation of spatial autoregressive models with unknown heteroskedasticity and nonnormality," Regional Science and Urban Economics, Elsevier, pages 50-70.
    7. Badi H. Baltagi & Zhenlin Yang, 2013. "Standardized LM tests for spatial error dependence in linear or panel regressions," Econometrics Journal, Royal Economic Society, vol. 16(1), pages 103-134, February.
    8. Yang, Zhenlin, 2015. "A general method for third-order bias and variance corrections on a nonlinear estimator," Journal of Econometrics, Elsevier, pages 178-200.
    9. Huettel, Silke & Odening, Martin & Kataria, Karin & Balmann, Alfons, 2013. "Price Formation on Land Market Auctions in East Germany – An Empirical Analysis," Journal of International Agricultural Trade and Development, Journal of International Agricultural Trade and Development, vol. 62(2).
    10. Badi H. Baltagi & Peter Egger & Michael Pfafermayr, 2009. "A Generalized Spatial Panel Data Model with Random Effects," Center for Policy Research Working Papers 113, Center for Policy Research, Maxwell School, Syracuse University.
    11. Liu, Shew Fan & Yang, Zhenlin, 2015. "Improved inferences for spatial regression models," Regional Science and Urban Economics, Elsevier, vol. 55(C), pages 55-67.
    12. Badi H. Baltagi & Peter Egger & Michael Pfaffermayr, 2013. "A Generalized Spatial Panel Data Model with Random Effects," Econometric Reviews, Taylor & Francis Journals, pages 650-685.
    13. repec:eee:regeco:v:65:y:2017:i:c:p:65-88 is not listed on IDEAS
    14. Zhenlin Yang, 2013. "LM Tests of Spatial Dependence Based on Bootstrap Critical Values," Working Papers 03-2013, Singapore Management University, School of Economics.
    15. Ming He & Kuan-Pin Lin, 2015. "Testing in a Random Effects Panel Data Model with Spatially Correlated Error Components and Spatially Lagged Dependent Variables," Econometrics, MDPI, Open Access Journal, vol. 3(4), pages 1-36, November.

    More about this item

    Keywords

    Distributional misspecification; Robustness; Spatial layouts; Spatial error components; LM tests;

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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