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Heteroskedasticity and non-normality robust LM tests for spatial dependence

  • Baltagi, Badi H.
  • Yang, Zhenlin

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.

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Article provided by Elsevier in its journal Regional Science and Urban Economics.

Volume (Year): 43 (2013)
Issue (Month): 5 ()
Pages: 725-739

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Handle: RePEc:eee:regeco:v:43:y:2013:i:5:p:725-739
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  1. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
  2. Kelejian, Harry H. & Prucha, Ingmar R., 2010. "Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances," Journal of Econometrics, Elsevier, vol. 157(1), pages 53-67, July.
  3. Nicolas DEBARSY (CERPE De Namur) & Cem ERTUR, 2009. "Testing for Spatial Autocorrelation in a Fixed Effects Panel Data Model," Working Papers 1546, Orleans Economic Laboratorys, University of Orleans.
  4. Nicolas Debarsy & Cem Ertur, 2009. "Testing for Spatial Autocorrelation in a Fixed Effects Panel Data Model," Post-Print halshs-00414133, HAL.
  5. Zhenlin Yang, 2009. "A Robust LM Test for Spatial Error Components," Development Economics Working Papers 22488, East Asian Bureau of Economic Research.
  6. Benjamin Born & Jörg Breitung, 2009. "Simple Regression Based Tests for Spatial Dependence," Bonn Econ Discussion Papers bgse23_2009, University of Bonn, Germany.
  7. Lin, Xu & Lee, Lung-fei, 2010. "GMM estimation of spatial autoregressive models with unknown heteroskedasticity," Journal of Econometrics, Elsevier, vol. 157(1), pages 34-52, July.
  8. Badi H. Baltagi & Zhenlin Yang, 2010. "Standardized LM Tests for Spatial Error Dependence in Linear or Panel Regressions," Working Papers 11-2010, Singapore Management University, School of Economics.
  9. DAVIDSON, Russel & MACKINNON, James G., . "Heteroskedastcity-robust tests in regressions directions," CORE Discussion Papers RP -678, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September.
  11. Lee, Lung-fei & Yu, Jihai, 2010. "Estimation of spatial autoregressive panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 154(2), pages 165-185, February.
  12. Glaeser, Edward L & Sacerdote, Bruce & Scheinkman, Jose A, 1996. "Crime and Social Interactions," The Quarterly Journal of Economics, MIT Press, vol. 111(2), pages 507-48, May.
  13. Badi H. Baltagi & Seuck Heun Song & Won Koh, 2002. "Testing Panel Data Regression Models with Spatial Error Correlation," 10th International Conference on Panel Data, Berlin, July 5-6, 2002 B6-4, International Conferences on Panel Data.
  14. 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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