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Improved Lagrange Multiplier Tests in Spatial Autoregressions

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  • Peter M Robinson
  • Francesca Rossi

Abstract

For testing lack of correlation against spatial autoregressive alternatives, Lagrange multiplier tests enjoy their usual computational advantages, but the (x squared) 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 ones, generally significantly outperform x squared-based tests.

Suggested Citation

  • Peter M Robinson & Francesca Rossi, 2013. "Improved Lagrange Multiplier Tests in Spatial Autoregressions," STICERD - Econometrics Paper Series 566, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  • Handle: RePEc:cep:stiecm:566
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    References listed on IDEAS

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    1. 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.
    2. Taniguchi, Masanobu, 1991. "Third-order asymptomic properties of a class of test statistics under a local alternative," Journal of Multivariate Analysis, Elsevier, vol. 37(2), pages 223-238, May.
    3. 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.
    4. 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.
    5. Robinson, Peter M. & Rossi, Francesca, 2012. "Improved tests for spatial correlation," MPRA Paper 41835, University Library of Munich, Germany.
    6. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-965, July.
    7. 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.
    8. Ogasawara, Haruhiko, 2006. "Asymptotic expansion of the sample correlation coefficient under nonnormality," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 891-910, February.
    9. 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.
    10. repec:cep:stiecm:/2013/565 is not listed on IDEAS
    11. Ghazal, G. A., 1996. "Recurrence formula for expectations of products of quadratic forms," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 101-109, April.
    12. Koenker, Roger, 1981. "A note on studentizing a test for heteroscedasticity," Journal of Econometrics, Elsevier, vol. 17(1), pages 107-112, September.
    13. 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.
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    Cited by:

    1. repec:spr:empeco:v:55:y:2018:i:1:d:10.1007_s00181-018-1453-4 is not listed on IDEAS
    2. repec:bpj:jecome:v:8:y:2019:i:1:p:33:n:7 is not listed on IDEAS
    3. Robinson, Peter M. & Rossi, Francesca, 2015. "Refined Tests For Spatial Correlation," Econometric Theory, Cambridge University Press, vol. 31(06), pages 1249-1280, December.
    4. 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.
    5. 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.
    6. repec:eee:econom:v:207:y:2018:i:1:p:92-113 is not listed on IDEAS
    7. Liu, Shew Fan & Yang, Zhenlin, 2015. "Improved inferences for spatial regression models," Regional Science and Urban Economics, Elsevier, vol. 55(C), pages 55-67.
    8. repec:eee:regeco:v:65:y:2017:i:c:p:65-88 is not listed on IDEAS
    9. repec:eee:regeco:v:69:y:2018:i:c:p:130-142 is not listed on IDEAS

    More about this item

    Keywords

    Spatial autocorrelation; Lagrange multiplier test; Edgeworth expansion; bootstrap; finite-sample corrections.;

    JEL classification:

    • C29 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Other

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