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A Robust LM Test for Spatial Error Components

Author

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  • Zhenlin Yang

    (School of Economics, Singapore Management University)

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 Anselin’s 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," Working Papers 04-2009, Singapore Management University, School of Economics.
    • Handle: RePEc:siu:wpaper:04-2009
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Zhenlin Yang, 2018. "Bootstrap LM tests for higher-order spatial effects in spatial linear regression models," Empirical Economics, Springer, vol. 55(1), pages 35-68, August.
    2. Yang, Zhenlin, 2015. "A general method for third-order bias and variance corrections on a nonlinear estimator," Journal of Econometrics, Elsevier, vol. 186(1), pages 178-200.
    3. 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, vol. 3(4), pages 1-36, November.
    4. Jieun Lee, 2022. "Testing Endogeneity of Spatial Weights Matrices in Spatial Dynamic Panel Data Models," Papers 2209.05563, arXiv.org.
    5. 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.
    6. Huettel, Silke & Odening, Martin & Kataria, Karin & Balmann, Alfons, 2013. "Price Formation on Land Market Auctions in East Germany – An Empirical Analysis," German Journal of Agricultural Economics, Humboldt-Universitaet zu Berlin, Department for Agricultural Economics, vol. 62(02), pages 1-17, May.
    7. Liu, Shew Fan & Yang, Zhenlin, 2015. "Modified QML estimation of spatial autoregressive models with unknown heteroskedasticity and nonnormality," Regional Science and Urban Economics, Elsevier, vol. 52(C), pages 50-70.
    8. 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).
    9. Badi H. Baltagi & Peter Egger & Michael Pfaffermayr, 2013. "A Generalized Spatial Panel Data Model with Random Effects," Econometric Reviews, Taylor & Francis Journals, vol. 32(5-6), pages 650-685, August.
    10. 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.
    11. 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.
    12. Zhenlin Yang, 2013. "LM Tests of Spatial Dependence Based on Bootstrap Critical Values," Working Papers 03-2013, Singapore Management University, School of Economics.
    13. Giuseppe Arbia, 2011. "A Lustrum of SEA: Recent Research Trends Following the Creation of the Spatial Econometrics Association (2007--2011)," Spatial Economic Analysis, Taylor & Francis Journals, vol. 6(4), pages 377-395, July.
    14. Alain Pirotte & Jesús Mur, 2017. "Neglected dynamics and spatial dependence on panel data: consequences for convergence of the usual static model estimators," Spatial Economic Analysis, Taylor & Francis Journals, vol. 12(2-3), pages 202-229, July.
    15. Yang, Zhenlin, 2015. "LM tests of spatial dependence based on bootstrap critical values," Journal of Econometrics, Elsevier, vol. 185(1), pages 33-59.
    16. 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.
    17. Li, Liyao & Yang, Zhenlin, 2020. "Estimation of fixed effects spatial dynamic panel data models with small T and unknown heteroskedasticity," Regional Science and Urban Economics, Elsevier, vol. 81(C).
    18. Liu, Shew Fan & Yang, Zhenlin, 2015. "Improved inferences for spatial regression models," Regional Science and Urban Economics, Elsevier, vol. 55(C), pages 55-67.
    19. Taşpınar, Süleyman & Doğan, Osman & Bera, Anil K., 2017. "GMM gradient tests for spatial dynamic panel data models," Regional Science and Urban Economics, Elsevier, vol. 65(C), pages 65-88.
    20. Bera, Anil K. & Doğan, Osman & Taşpınar, Süleyman, 2018. "Simple tests for endogeneity of spatial weights matrices," Regional Science and Urban Economics, Elsevier, vol. 69(C), pages 130-142.
    21. David M. Drukker & Peter Egger & Ingmar R. Prucha, 2013. "On Two-Step Estimation of a Spatial Autoregressive Model with Autoregressive Disturbances and Endogenous Regressors," Econometric Reviews, Taylor & Francis Journals, vol. 32(5-6), pages 686-733, August.

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    More about this item

    Keywords

    Distributional misspecification; Robustness; Spatial layouts; Spatial error components; LM tests;
    All these keywords.

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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