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Testing for Heteroskedasticity and Spatial Correlation in a Random Effects Panel Data Model

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Abstract

A panel data regression model with heteroskedastic as well as spatially correlated disturbance is considered, and a joint LM test for homoskedasticity and no spatial correlation is derived. In addition, a conditional LM test for no spatial correlation given heteroskedasticity, as well as a conditional LM test for homoskedasticity given spatial correlation, are also deerived. These LM tests are compared with marginal LM tests that ignore heteroskedasticity in testing for spatial correlation, or spatial correlation in testing for homoskedasticity. Monte Carlo results show that these LM tests as well as their LR counterparts perform well even for small N and T. However, misleading inference can occur when using marginal rather than joint or conditional LM tests when spatial correlation or heteroskedasticity is present.

Suggested Citation

  • Badi H. Baltagi & Seuck Heun Song & Jae Hyeok Kwon, 2008. "Testing for Heteroskedasticity and Spatial Correlation in a Random Effects Panel Data Model," Center for Policy Research Working Papers 108, Center for Policy Research, Maxwell School, Syracuse University.
    • Handle: RePEc:max:cprwps:108
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    Cited by:

    1. Meghamrita Chakraborty, 2023. "Linking Migration, Diversity and Regional Development in India," Journal of Development Policy and Practice, , vol. 8(1), pages 55-72, January.
    2. Merkel, Axel, 2017. "Spatial competition and complementarity in European port regions," Journal of Transport Geography, Elsevier, vol. 61(C), pages 40-47.
    3. Baltagi, Badi H. & Feng, Qu & Kao, Chihwa, 2012. "A Lagrange Multiplier test for cross-sectional dependence in a fixed effects panel data model," Journal of Econometrics, Elsevier, vol. 170(1), pages 164-177.
    4. Zdeňka Malá & Gabriela Trnková, 2013. "Analysis of Unequal Distribution of Gross Value Added in Plant Production Business [Analýza nerovnoměrnosti rozdělení hrubé přidané hodnoty podniků polní výroby]," Acta Universitatis Bohemiae Meridionalis, University of South Bohemia in Ceske Budejovice, Faculty of Economics, vol. 16(2), pages 169-183.
    5. Jieun Lee, 2022. "Testing Endogeneity of Spatial Weights Matrices in Spatial Dynamic Panel Data Models," Papers 2209.05563, arXiv.org.
    6. Liu, Xiaodong & Prucha, Ingmar R., 2025. "On testing for spatial or social network dependence in panel data allowing for network variability," Journal of Econometrics, Elsevier, vol. 247(C).
    7. Kouassi, Eugene & Mougoué, Mbodja & Sango, Joel & Bosson Brou, J.M. & Amba, Claude M.O. & Salisu, Afeez Adebare, 2014. "Testing for heteroskedasticity and spatial correlation in a two way random effects model," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 153-171.
    8. Markus Eberhardt & Francis Teal, 2011. "Econometrics For Grumblers: A New Look At The Literature On Cross‐Country Growth Empirics," Journal of Economic Surveys, Wiley Blackwell, vol. 25(1), pages 109-155, February.
    9. Trnkova, Gabriela & Mala, Zdenka & Vasilenko, Alexandr, . "Analysis of the Effects of Subsidies on the Economic Behavior of Agricultural Businesses Focusing on Animal Production," AGRIS on-line Papers in Economics and Informatics, Czech University of Life Sciences Prague, Faculty of Economics and Management, vol. 4(4 Special), pages 1-12.
    10. Anil K. Bera & Osman Doğan & Süleyman Taşpınar & Monalisa Sen, 2020. "Specification tests for spatial panel data models," Journal of Spatial Econometrics, Springer, vol. 1(1), pages 1-39, December.
    11. Maly, Michal & Mala, Zdenka & Sobrova, L. & Halova, P., . "Partial equilibrium model of Czech beef trade," AGRIS on-line Papers in Economics and Informatics, Czech University of Life Sciences Prague, Faculty of Economics and Management, vol. 3(2), pages 1-12.
    12. LeSage, James & Banerjee, Sudipto & Fischer, Manfred M. & Congdon, Peter, 2009. "Spatial statistics: Methods, models & computation," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2781-2785, June.
    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. Baltagi, Badi H. & Jung, Byoung Cheol & Song, Seuck Heun, 2010. "Testing for heteroskedasticity and serial correlation in a random effects panel data model," Journal of Econometrics, Elsevier, vol. 154(2), pages 122-124, February.
    15. Sunge, Regret & Ngepah, Nicholas, 2022. "Agricultural trade liberalisation, agricultural total factor productivity growth and food security in Africa," Agrekon, Agricultural Economics Association of South Africa (AEASA), vol. 61(3), May.
    16. Bedoya-Maya, Felipe & Beckers, Joris & van Hassel, Edwin, 2023. "Spillover effects from inland waterway transport development: Spatial assessment of the Rhine-Alpine Corridor," Journal of Transport Geography, Elsevier, vol. 113(C).
    17. Yuxi Liu & Rizhao Gong & Wenzhong Ye & Changsheng Jin & Jianxin Tang, 2022. "Urban Spatial Structure and Water Ecological Footprint: Empirical Analysis of the Urban Agglomerations in China," Sustainability, MDPI, vol. 14(21), pages 1-14, October.
    18. Du, Zaichao, 2014. "Testing for serial independence of panel errors," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 248-261.
    19. 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.
    20. Baltagi, Badi H. & Liu, Long, 2025. "Testing for spatial lag dependence and homoskedasticity in a random effects panel data model," Economics Letters, Elsevier, vol. 254(C).
    21. Kuersteiner, Guido M. & Prucha, Ingmar R., 2013. "Limit theory for panel data models with cross sectional dependence and sequential exogeneity," Journal of Econometrics, Elsevier, vol. 174(2), pages 107-126.

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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