Skip to main content
    • Aa
    • Aa


  • Federico Martellosio (a1)

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). 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.

Corresponding author
*Address correspondence to Federico Martellosio, School of Economics, University of Reading, URS Building, Whiteknights PO Box 219, Reading RG6 6AW, UK; e-mail:
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

B.H Baltagi . (2006) Random effects and spatial autocorrelation with equal weights. Econometric Theory 22, 973–984.

R Bartels . (1992) On the power function of the Durbin-Watson test. Journal of Econometrics 51, 101–112.

K.P. Bell & N.E. Bockstael (2000) Applying the generalized-moments estimation approach to spatial problems involving microlevel data. Review of Economics and Statistics 82, 72–82.

J.E. Besag & C. Kooperberg (1995) On conditional and intrinsic autoregression. Biometrika 82, 733–746.

A Case . (1991) Spatial patterns in household demand. Econometrica 59, 953–966.

D.R. Cox & D.V. Hinkley (1974) Theoretical Statistics. Chapman & Hall.

C.B. Cordy & D.A. Griffith (1993) Efficiency of least squares estimators in the presence of spatial autocorrelation. Communications in Statistics: Simulation and Computation 22, 1161–1179.

D.E. Dielman & R.C. Pfaffenberger (1989) Efficiency of ordinary least squares for linear models with autocorrelation. Journal of the American Statistical Association 84, 248.

J Durbin . (1970) An alternative to the bounds test for testing for serial correlation in least-squares regression. Econometrica 38, 422–29.

B Fingleton . (1999) Spurious spatial regression: Some Monte Carlo results with a spatial unit root and spatial cointegration. Journal of Regional Science 39, 1–19.

R.J.G.M. Florax & T. de Graaff (2004) The performance of diagnostic tests for spatial dependence in linear regression models: A meta-analysis of simulation studies. In L. Anselin , R.J.G.M. Florax , & S.J. Rey (eds.), Advances in Spatial Econometrics: Methodology, Tools and Applications, pp. 29–65. Springer.

R Goldstein . (2000) The term structure of interest rates as a random field. Review of Financial Studies 13, 365–384.

J.P Imhof . (1961) Computing the distribution of quadratic forms in normal variables. Biometrika 48, 419–26.

A.T James . (1954) Normal multivariate analysis and the orthogonal group. Annals of Mathematical Statistics 25, 40–75.

K.R Kadiyala . (1970) Testing for the independence of regression disturbances. Econometrica 38, 97–117.

T Kariya . (1980) Locally robust tests for serial correlation in least squares regression. Annals of Statistics 8, 1065–1070.

T Kariya . (1988) The class of models for which the Durbin-Watson test is locally optimal. International Economic Review 29, 167–175.

H.H. Kelejian & I.R. Prucha (2001) On the asymptotic distribution of the Moran I test statistic with applications. Journal of Econometrics 104, 219–257.

H.H. Kelejian & I.R. Prucha (2002) 2SLS and OLS in a spatial autoregressive model with equal spatial weights. Regional Science and Urban Economics 32, 691–707.

D Kennedy . (1994) The term structure of interest rates as a Gaussian random field. Mathematical Finance 4, 247–258.

M.L King . (1980) Robust tests for spherical symmetry and their application to least squares regression. Annals of Statistics 8, 1265–1271.

M.L King . (1988) Towards a theory of point optimal testing. Econometric Reviews 6, 169–255.

C. Kleiber & W. Krämer (2005) Finite-sample power of the Durbin-Watson test against fractionally integrated disturbances. Econometrics Journal 8, 406–417.

W Krämer . (1985) The power of the Durbin-Watson test for regressions without an intercept. Journal of Econometrics 28, 363–370.

W Krämer . (2005) Finite sample power of Cliff–Ord-type tests for spatial disturbance correlation in linear regression. Journal of Statistical Planning and Inference 128, 489–496.

W. Krämer & C. Donninger (1987) Spatial autocorrelation among errors and relative efficiency of OLS in the linear regression model. Journal of the American Statistical Association 82, 577–579.

A.F. Militino , M.D. Ugarte , & L. García-Reinaldos (2004) Alternative models for describing spatial dependence among dwelling selling prices. Journal of Real Estate Finance and Economics 29, 193–209.

P.A.P Moran . (1950) Notes on continuos stochastic phenomena. Biometrika 37, 17–23.

J.K Ord . (1975) Estimation methods for models of spatial interaction. Journal of the American Statistical Association 70, 120–6.

R.K. Pace & J.P. LeSage (2002) Semiparametric maximum likelihood estimates of spatial dependence. Geographical Analysis 34, 76–90.

V Paulauskas . (2007) On unit roots for spatial autoregressive models. Journal of Multivariate Analysis 98, 209–226.

S. Rahman & M.L. King (1997) Marginal-likelihood score-based tests of regression disturbances in the presence of nuisance parameters. Journal of Econometrics 82, 81–106.

J.A Tillman . (1975) The power of the Durbin-Watson test. Econometrica 43, 959–974.

P Whittle . (1954) On stationary processes in the plane. Biometrika 41, 434–449.

H Zeisel . (1989) On the power of the Durbin-Watson test under high autocorrelation. Communications in Statistics: Theory and Methods 18, 3907–3916.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
Please enter your name
Please enter a valid email address
Who would you like to send this to? *