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OLS-based estimation of the disturbance variance under spatial autocorrelation

Author

Listed:
  • Prof. Dr. Walter Krämer

    (Faculty of Statistics, Dortmund University of Technology)

  • Dr. Christoph Hanck

    (Department of Quantitative Economics, Universiteit Maastricht)

Abstract

We investigate the OLS-based estimator s2 of the disturbance variance in the standard linear regression model with cross section data when the disturbances are homoskedastic, but spatially correlated. For the most popular model of spatially autoregressive disturbances, we show that s2 can be severely biased in finite samples, but is asymptotically unbiased and consistent for most types of spatial weighting matrices as sample size increases.

Suggested Citation

  • Prof. Dr. Walter Krämer & Dr. Christoph Hanck, "undated". "OLS-based estimation of the disturbance variance under spatial autocorrelation," Working Papers 7, Business and Social Statistics Department, Technische Universität Dortmund, revised Oct 2006.
    • Handle: RePEc:dor:wpaper:7
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    References listed on IDEAS

    as
    1. Kelejian, Harry H & Prucha, Ingmar R, 1999. "A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 509-533, May.
    2. Kiviet, Jan F & Kramer, Walter, 1992. "Bias of SDE 2 in the Linear Regression Model with Correlated Errors," The Review of Economics and Statistics, MIT Press, vol. 74(2), pages 362-365, May.
    3. Luc Anselin & Raymond J. G. M. Florax, 1995. "Small Sample Properties of Tests for Spatial Dependence in Regression Models: Some Further Results," Advances in Spatial Science, in: Luc Anselin & Raymond J. G. M. Florax (ed.), New Directions in Spatial Econometrics, chapter 2, pages 21-74, Springer.
    4. Kelejian, Harry H. & Prucha, Ingmar R., 2002. "2SLS and OLS in a spatial autoregressive model with equal spatial weights," Regional Science and Urban Economics, Elsevier, vol. 32(6), pages 691-707, November.
    5. Case, Anne, 1992. "Neighborhood influence and technological change," Regional Science and Urban Economics, Elsevier, vol. 22(3), pages 491-508, September.
    6. Kramer, Walter & Berghoff, Sonja, 1991. "Consistency of sDE 2 in the Linear Regression Model with Correlated Errors," Empirical Economics, Springer, vol. 16(3), pages 375-377.
    7. 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.
    8. Sathe, S T & Vinod, H D, 1974. "Bounds on the Variance of Regression Coefficients Due to Heteroscedastic or Autoregressive Errors," Econometrica, Econometric Society, vol. 42(2), pages 333-340, March.
    9. Harry H. Kelejian & Ingmar R. Prucha & Yevgeny Yuzefovich, 2006. "Estimation Problems In Models With Spatial Weighting Matrices Which Have Blocks Of Equal Elements," Journal of Regional Science, Wiley Blackwell, vol. 46(3), pages 507-515, August.
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    Keywords

    regression; spatial error correlation; bias; variance;
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