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Testing for spatial autocorrelation: the regressors that make the power disappear

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  • Martellosio, Federico

Abstract

We show that for any sample size, any size of the test, and any weights matrix outside a small class of exceptions, there exists a positive measure set of regression spaces such that the power of the Cliff-Ord test vanishes as the autocorrelation increases in a spatial error model. This result extends to the tests that define the Gaussian power envelope of all invariant tests for residual spatial autocorrelation. In most cases, the regression spaces such that the problem occurs depend on the size of the test, but there also exist regression spaces such that the power vanishes regardless of the size. A characterization of such particularly hostile regression spaces is provided.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 10542.

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Date of creation: Sep 2008
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Handle: RePEc:pra:mprapa:10542

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Keywords: Cliff-Ord test; point optimal tests; power; spatial error model; spatial lag model; spatial unit root;

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  1. A. F. Militino & M. D. Ugarte & L. GarcĂ­a-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.
  2. De Long, J Bradford & Summers, Lawrence H, 1991. "Equipment Investment and Economic Growth," The Quarterly Journal of Economics, MIT Press, vol. 106(2), pages 445-502, May.
  3. Baltagi, Badi H., 2006. "Random Effects And Spatial Autocorrelation With Equal Weights," Econometric Theory, Cambridge University Press, vol. 22(05), pages 973-984, October.
  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. Olivier Parent & James P. Lesage, 2007. "Using the Variance Structure of the Conditional Autoregressive Spatial Specification to Model Knowledge Spillovers," University of Cincinnati, Economics Working Papers Series 2007-03, University of Cincinnati, Department of Economics.
  6. Anselin, Luc, 2002. "Under the hood : Issues in the specification and interpretation of spatial regression models," Agricultural Economics, Blackwell, vol. 27(3), pages 247-267, November.
  7. Martellosio, Federico, 2010. "Power Properties Of Invariant Tests For Spatial Autocorrelation In Linear Regression," Econometric Theory, Cambridge University Press, vol. 26(01), pages 152-186, February.
  8. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-65, July.
  9. 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.
  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. Martellosio, Federico, 2008. "Power Properties of Invariant Tests for Spatial Autocorrelation in Linear Regression," MPRA Paper 7255, University Library of Munich, Germany.
  12. Oksanen, E.H., 1993. "Efficiency as Correlation," Econometric Theory, Cambridge University Press, vol. 9(01), pages 146-146, January.
  13. 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.
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Cited by:
  1. Badi H. Baltagi & Chihwa Kao & Long Liu, 2013. "The Estimation and Testing of a Linear Regression with Near Unit Root in the Spatial Autoregressive Error Term," Spatial Economic Analysis, Taylor & Francis Journals, vol. 8(3), pages 241-270, September.
  2. Mynbaev, Kairat, 2011. "Distributions escaping to infinity and the limiting power of the Cliff-Ord test for autocorrelation," MPRA Paper 44402, University Library of Munich, Germany, revised 18 Sep 2012.

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