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Simple regression‐based tests for spatial dependence

Author

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  • Benjamin Born
  • Jörg Breitung

Abstract

We propose two simple diagnostic tests for spatial error autocorrelation and spatial lag dependence. The idea is to reformulate the testing problem such that the test statistics are asymptotically equivalent to the familiar LM test statistics. Speci cally, our version of the test is based on a simple auxiliary regression and an ordinary regression t-statistic can be used to test for spatial autocorrelation and lag dependence. We also propose a variant of the test that is robust to heteroskedasticity. This approach gives practitioners an easy to implement and robust alternative to existing tests. Monte Carlo studies show that our variants of the spatial LM tests possess comparable size and power properties even in small samples.
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Suggested Citation

  • Benjamin Born & Jörg Breitung, 2011. "Simple regression‐based tests for spatial dependence," Econometrics Journal, Royal Economic Society, vol. 14(2), pages 330-342, July.
    • Handle: RePEc:ect:emjrnl:v:14:y:2011:i:2:p:330-342
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    Cited by:

    1. Pennerstorfer, Astrid & Pennerstorfer, Dieter, 2019. "How small are small markets? Local market size for child care services," Regional Science and Urban Economics, Elsevier, vol. 77(C), pages 340-355.
    2. 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.
    3. Berg, Tobias & Reisinger, Markus & Streitz, Daniel, 2021. "Spillover effects in empirical corporate finance," Journal of Financial Economics, Elsevier, vol. 142(3), pages 1109-1127.
    4. Riza Bayrak, Halim Tatli, 2018. "The Determinants of Youth Unemployment: A Panel Data Analysis of OECD Countries," European Journal of Comparative Economics, Cattaneo University (LIUC), vol. 15(2), pages 231-248, December.
    5. Richard Harris & John Moffat & Victoria Kravtsova, 2011. "In Search of ‘ W ’," Spatial Economic Analysis, Taylor & Francis Journals, vol. 6(3), pages 249-270, February.
    6. 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.
    7. 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).
    8. Astrid Pennerstorfer & Dieter Pennerstorfer, 2018. "How Small are Small Markets? Location Choice and Geographical Market Size for Child Care Services," Economics working papers 2018-14, Department of Economics, Johannes Kepler University Linz, Austria.
    9. 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.
    10. Arnab Bhattacharjee & Eduardo Castro & João Marques, 2012. "Spatial Interactions in Hedonic Pricing Models: The Urban Housing Market of Aveiro, Portugal," Spatial Economic Analysis, Taylor & Francis Journals, vol. 7(1), pages 133-167, March.
    11. Bhattacharjee, Arnab & Jensen-Butler, Chris, 2013. "Estimation of the spatial weights matrix under structural constraints," Regional Science and Urban Economics, Elsevier, vol. 43(4), pages 617-634.
    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. Badi H. Baltagi & Junjie Shu, 2024. "A Survey of Spatial Unit Roots," Mathematics, MDPI, vol. 12(7), pages 1-32, March.
    14. Deng, Mingyu & Wang, Mingxi, 2022. "Artificial regression test diagnostics for impact measures in spatial models," Economics Letters, Elsevier, vol. 217(C).
    15. 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.
    16. Bera Anil K. & Doğan Osman & Taşpınar Süleyman, 2019. "Testing Spatial Dependence in Spatial Models with Endogenous Weights Matrices," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-33, January.
    17. 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.
    18. 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.
    19. Julie Le Gallo & Fernando A. López & Coro Chasco, 2020. "Testing for spatial group-wise heteroskedasticity in spatial autocorrelation regression models: Lagrange multiplier scan tests," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 64(2), pages 287-312, April.
    20. 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.
    21. Tim Kutzker & Dominik Wied, 2024. "Testing the correct specification of a system of spatial dependence models for stock returns," Empirical Economics, Springer, vol. 66(5), pages 2083-2103, May.
    22. Zipeng Chen & Yongqiang Liu & Shuangshuang Tu, 2022. "Comprehensive Eco-Environmental Effects Caused by Land Use Transition from the Perspective of Production–Living–Ecological Spaces in a Typical Region: A Case Study of the Guangxi Zhuang Autonomous Region, China," Land, MDPI, vol. 11(12), pages 1-22, November.
    23. 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.
    24. Liu, Xiaodong & Prucha, Ingmar R., 2018. "A robust test for network generated dependence," Journal of Econometrics, Elsevier, vol. 207(1), pages 92-113.
    25. Yang, Zhenlin, 2015. "LM tests of spatial dependence based on bootstrap critical values," Journal of Econometrics, Elsevier, vol. 185(1), pages 33-59.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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