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Improved Lagrange multiplier tests in spatial autoregressions

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  • Robinson, Peter M.
  • Rossi, Francesca

Abstract

For testing lack of correlation against spatial autoregressive alternatives, Lagrange multiplier tests enjoy their usual computational advantages, but the (χ2) first-order asymptotic approximation to critical values can be poor in small samples. We develop refined tests for lack of spatial error correlation in regressions, based on Edgeworth expansion. In Monte Carlo simulations, these tests, and bootstrap tests, generally significantly outperform χ2-based tests.

Suggested Citation

  • Robinson, Peter M. & Rossi, Francesca, 2014. "Improved Lagrange multiplier tests in spatial autoregressions," LSE Research Online Documents on Economics 56049, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:56049
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    File URL: http://eprints.lse.ac.uk/56049/
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    1. Phillips, Peter C B, 1977. "Approximations to Some Finite Sample Distributions Associated with a First-Order Stochastic Difference Equation," Econometrica, Econometric Society, vol. 45(2), pages 463-485, March.
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    6. Ogasawara, Haruhiko, 2006. "Asymptotic expansion of the sample correlation coefficient under nonnormality," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 891-910, February.
    7. Robinson, Peter M. & Rossi, Francesca, 2012. "Improved tests for spatial correlation," MPRA Paper 41835, University Library of Munich, Germany.
    8. 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.
    9. Kelejian, Harry H. & Robinson, Dennis P., 1992. "Spatial autocorrelation : A new computationally simple test with an application to per capita county police expenditures," Regional Science and Urban Economics, Elsevier, vol. 22(3), pages 317-331, September.
    10. Robinson, Peter, 2008. "Correlation testing in time series, spatial and cross-sectional data," LSE Research Online Documents on Economics 25470, London School of Economics and Political Science, LSE Library.
    11. Robinson, P.M., 2008. "Correlation testing in time series, spatial and cross-sectional data," Journal of Econometrics, Elsevier, vol. 147(1), pages 5-16, November.
    12. Ghazal, G. A., 1996. "Recurrence formula for expectations of products of quadratic forms," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 101-109, April.
    13. Koenker, Roger, 1981. "A note on studentizing a test for heteroscedasticity," Journal of Econometrics, Elsevier, vol. 17(1), pages 107-112, September.
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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. Francesca Rossi & Peter M. Robinson, 2020. "Higher-Order Least Squares Inference for Spatial Autoregressions," Working Papers 04/2020, University of Verona, Department of Economics.
    3. Robinson, Peter M. & Rossi, Francesca, 2015. "Refinements in maximum likelihood inference on spatial autocorrelation in panel data," Journal of Econometrics, Elsevier, vol. 189(2), pages 447-456.
    4. 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.
    5. Rossi, Francesca & Robinson, Peter M., 2023. "Higher-order least squares inference for spatial autoregressions," Journal of Econometrics, Elsevier, vol. 232(1), pages 244-269.
    6. Robinson, Peter M. & Rossi, Francesca, 2015. "Refined Tests For Spatial Correlation," Econometric Theory, Cambridge University Press, vol. 31(6), pages 1249-1280, December.
    7. 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.
    8. 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.
    9. Maria Kyriacou & Peter C. B. Phillips & Francesca Rossi, 2017. "Indirect inference in spatial autoregression," Econometrics Journal, Royal Economic Society, vol. 20(2), pages 168-189, June.
    10. 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.
    11. 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.
    12. Maria Kyriacou & Peter C. B. Phillips & Francesca Rossi, 2017. "Indirect inference in spatial autoregression," Econometrics Journal, Royal Economic Society, vol. 20(2), pages 168-189, June.
    13. Liu, Xiaodong & Prucha, Ingmar R., 2018. "A robust test for network generated dependence," Journal of Econometrics, Elsevier, vol. 207(1), pages 92-113.
    14. Zhenlin Yang, 2021. "Joint tests for dynamic and spatial effects in short panels with fixed effects and heteroskedasticity," Empirical Economics, Springer, vol. 60(1), pages 51-92, January.
    15. Pinto, Allan & Griffin, Terry W., 2022. "Detecting bubbles via single time-series variable: applying spatial specification tests to farmland values," 2022 Annual Meeting, July 31-August 2, Anaheim, California 322534, Agricultural and Applied Economics Association.
    16. Liu, Shew Fan & Yang, Zhenlin, 2015. "Improved inferences for spatial regression models," Regional Science and Urban Economics, Elsevier, vol. 55(C), pages 55-67.

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    More about this item

    Keywords

    bootstrap; Edgeworth expansion; finite-sample corrections; Lagrange multiplier test; spatial autocorrelation;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General

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