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Heteroskedasticity and Non-normality Robust LM Tests for Spatial Dependence

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Abstract

The standard LM tests for spatial dependence in linear and panel regressions are derived under the normality and homoskedasticity assumptions of the regression disturbances. Hence, they may not be robust against non-normality or heteroskedasticity of the disturbances. Following Born and Breitung (2011), we introduce general methods to modify the standard LM tests so that they become robust against heteroskedasticity and non-normality. The idea behind the robustification is to decompose the concentrated score function into a sum of uncorrelated terms so that the outer product of gradient (OPG) can be used to estimate its variance. We also provide methods for improving the finite sample performance of the proposed tests. These methods are then applied to several popular spatial models. Monte Carlo results show that they work well in finite sample. Key Words: Centering; Heteroskedasticity; Non-Normality; LM Tests; Panel Model; Spatial Dependence JEL No. C21, C23, C5

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  • 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.
    • Handle: RePEc:max:cprwps:156
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    Cited by:

    1. Baltagi, Badi H. & Fingleton, Bernard & Pirotte, Alain, 2019. "A time-space dynamic panel data model with spatial moving average errors," Regional Science and Urban Economics, Elsevier, vol. 76(C), pages 13-31.
    2. Xu, Yuhong & Yang, Zhenlin, 2020. "Specification Tests for Temporal Heterogeneity in Spatial Panel Data Models with Fixed Effects," Regional Science and Urban Economics, Elsevier, vol. 81(C).
    3. Baltagi, Badi H. & Pirotte, Alain & Yang, Zhenlin, 2021. "Diagnostic tests for homoskedasticity in spatial cross-sectional or panel models," Journal of Econometrics, Elsevier, vol. 224(2), pages 245-270.
    4. Shew Fan Liu & Zhenlin Yang, 2015. "Asymptotic Distribution and Finite Sample Bias Correction of QML Estimators for Spatial Error Dependence Model," Econometrics, MDPI, vol. 3(2), pages 1-36, May.
    5. Giovanni Millo, 2024. "An Ad Hoc Procedure for Testing Serial Correlation in Spatial Fixed-Effects Panels," Mathematics, MDPI, vol. 12(10), pages 1-18, May.
    6. Sha Chen & Guan Li & Zhongguo Xu & Yuefei Zhuo & Cifang Wu & Yanmei Ye, 2019. "Combined Impact of Socioeconomic Forces and Policy Implications: Spatial-Temporal Dynamics of the Ecosystem Services Value in Yangtze River Delta, China," Sustainability, MDPI, vol. 11(9), pages 1-22, May.
    7. Badi H. Baltagi & Long Liu, 2015. "Testing for Spacial Lag and Spatial Error Dependence in a Fixed Effects Panel Data Model Using Double Length Artificial Regressions," Center for Policy Research Working Papers 183, Center for Policy Research, Maxwell School, Syracuse University.
    8. Jin, Fei & Lee, Lung-fei, 2018. "Outer-product-of-gradients tests for spatial autoregressive models," Regional Science and Urban Economics, Elsevier, vol. 72(C), pages 35-57.
    9. 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.
    10. Ji Uk Kim, 2020. "Technology diffusion, absorptive capacity, and income convergence for Asian developing countries: a dynamic spatial panel approach," Empirical Economics, Springer, vol. 59(2), pages 569-598, August.
    11. Shixiang Li & Jianru Shi & Qiaosheng Wu, 2020. "Environmental Kuznets Curve: Empirical Relationship between Energy Consumption and Economic Growth in Upper-Middle-Income Regions of China," IJERPH, MDPI, vol. 17(19), pages 1-27, September.
    12. Liu, Shew Fan & Yang, Zhenlin, 2015. "Improved inferences for spatial regression models," Regional Science and Urban Economics, Elsevier, vol. 55(C), pages 55-67.
    13. 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.
    14. 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.
    15. Badi H. Baltagi & Junjie Shu, 2024. "A Survey of Spatial Unit Roots," Mathematics, MDPI, vol. 12(7), pages 1-31, March.
    16. Deng, Mingyu & Wang, Mingxi, 2022. "Artificial regression test diagnostics for impact measures in spatial models," Economics Letters, Elsevier, vol. 217(C).
    17. Yang, Zhenlin & Yu, Jihai & Liu, Shew Fan, 2016. "Bias correction and refined inferences for fixed effects spatial panel data models," Regional Science and Urban Economics, Elsevier, vol. 61(C), pages 52-72.
    18. Debarsy, Nicolas & Yang, Zhenlin, 2018. "Editorial for the special issue entitled: New advances in spatial econometrics: Interactions matter," Regional Science and Urban Economics, Elsevier, vol. 72(C), pages 1-5.
    19. 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.

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    More about this item

    Keywords

    centering; heteroskedasticity; non-normality; lm tests; panel model; spatial dependence jel no. c21; c23; c5;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • 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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