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Power Properties of Invariant Tests for Spatial Autocorrelation in Linear Regression

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Martellosio, Federico

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Abstract

This paper derives some exact power properties of tests for spatial autocorrelation in the context of a linear regression model. In particular, we characterize the circumstances in which the power vanishes as the autocorrelation increases, thus extending the work of Krämer (2005, Journal of Statistical Planning and Inference 128, 489-496). More generally, the analysis in the paper sheds new light on how the power of tests for spatial autocorrelation is affected by the matrix of regressors and by the spatial structure. We mainly focus on the problem of residual spatial autocorrelation, in which case it is appropriate to restrict attention to the class of invariant tests, but we also consider the case when the autocorrelation is due to the presence of a spatially lagged dependent variable among the regressors. A numerical study aimed at assessing the practical relevance of the theoretical results is included.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 7255.

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Date of creation: Apr 2006
Date of revision: Aug 2008
Handle: RePEc:pra:mprapa:7255

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Related research
Keywords: Cliff-Ord test invariant tests linear regression model point optimal tests power similar tests spatial autocorrelation.

Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Kramer, W., 1985. "The power of the Durbin-Watson test for regressions without an intercept," Journal of Econometrics, Elsevier, vol. 28(3), pages 363-370, June. [Downloadable!] (restricted)
  2. Goldstein, Robert S, 2000. "The Term Structure of Interest Rates as a Random Field," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 13(2), pages 365-84.
  3. Kathleen P. Bell & Nancy E. Bockstael, 2000. "Applying the Generalized-Moments Estimation Approach to Spatial Problems Involving Microlevel Data," The Review of Economics and Statistics, MIT Press, vol. 82(1), pages 72-82, February. [Downloadable!] (restricted)
  4. Bartels, Robert, 1992. "On the power function of the Durbin-Watson test," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 101-112. [Downloadable!] (restricted)
  5. Kadiyala, Koteswara Rao, 1970. "Testing for the Independence of Regression Disturbances," Econometrica, Econometric Society, vol. 38(1), pages 97-117, January. [Downloadable!] (restricted)
  6. Badi H. Baltagi, 2006. "Random effects and Spatial Autocorrelations with Equal Weights," Center for Policy Research Working Papers 89, Center for Policy Research, Maxwell School, Syracuse University. [Downloadable!]
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  7. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-65, July. [Downloadable!] (restricted)
  8. Tillman, John A, 1975. "The Power of the Durbin-Watson Test," Econometrica, Econometric Society, vol. 43(5-6), pages 959-74, Sept.-Nov. [Downloadable!] (restricted)
  9. Christian Kleiber & Walter Krämer, 2005. "Finite-sample power of the Durbin--Watson test against fractionally integrated disturbances," Econometrics Journal, Royal Economic Society, vol. 8(3), pages 406-417, December. [Downloadable!] (restricted)
  10. Rahman, Shahidur & King, Maxwell L., 1997. "Marginal-likelihood score-based tests of regression disturbances in the presence of nuisance parameters," Journal of Econometrics, Elsevier, vol. 82(1), pages 81-106. [Downloadable!] (restricted)
  11. Kariya, Takeaki, 1988. "The Class of Models for which the Durbin-Watson Test is Locally Optimal," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(1), pages 167-75, February. [Downloadable!] (restricted)
  12. Durbin, J, 1970. "An Alternative to the Bounds Test for Testing for Serial Correlation in Least-Squares Regression," Econometrica, Econometric Society, vol. 38(3), pages 422-29, May. [Downloadable!] (restricted)
  13. 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. [Downloadable!] (restricted)
  14. A. F. Militino & M. D. Ugarte & L. García-Reinaldos, 2004. "Alternative Models for Describing Spatial Dependence among Dwelling Selling Prices," The Journal of Real Estate Finance and Economics, Springer, vol. 29(2), pages 193-209, 09. [Downloadable!]
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Martellosio, Federico, 2008. "Testing for spatial autocorrelation: the regressors that make the power disappear," MPRA Paper 10542, University Library of Munich, Germany. [Downloadable!]
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