Martellosio, Federico (2008): Testing for spatial autocorrelation: the regressors that make the power disappear.

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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 CliffOrd 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.
Item Type:  MPRA Paper 

Original Title:  Testing for spatial autocorrelation: the regressors that make the power disappear 
Language:  English 
Keywords:  CliffOrd test; point optimal tests; power; spatial error model; spatial lag model; spatial unit root 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C12  Hypothesis Testing: General C  Mathematical and Quantitative Methods > C2  Single Equation Models; Single Variables > C21  CrossSectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions 
Item ID:  10542 
Depositing User:  Federico Martellosio 
Date Deposited:  18. Sep 2008 10:02 
Last Modified:  12. Feb 2013 09:26 
References:  Anselin, L. (1988). Spatial Econometrics: Methods and Models. Boston: Kluwer Academic Publishers. Anselin, L. (2002). Under the hood: issues in the specification and interpretation of spatial regression models. Agricultural Economics 27, 247267. Arnold, S. F. (1979). Linear models with exchangeably distributed errors. Journal of the American Statistical Association 74, 194199. Baltagi, B. H. (2006). Random effects and spatial autocorrelation with equal weights. Econometric Theory 22, 973984. Bell, P. K. and N. E. Bockstael (2000). Applying the generalizedmoments estimation approach to spatial problems involving microlevel data. The Review of Economics and Statistics 82, 7282. Besley, T. and A. Case (1995). Incumbent behavior: voteseeking, taxsetting, and yardstick competition. The American Economic Review 85, 2545. Biggs, N. L. (1993). Algebraic Graph Theory (2nd ed.). Cambridge: Cambridge University Press. Case, A. (1991). Spatial patterns in household demand. Econometrica 59, 953966. Cliff, A. D. and J. K. Ord (1981). Spatial Processes: Models and Applications. London: Pion. Cordy, C. B. and D. A. Griffith (1993). Efficiency of least squares estimators in the presence of spatial autocorrelation. Communications in Statistics: Simulation and Computation 22, 11611179. De Long, J. B. and L. H. Summers (1991). Equipment investment and economic growth. The Quarterly Journal of Economics 106, 445502. Fingleton, B. (1999). Spurious spatial regression: Some Monte Carlo results with a spatial unit root and spatial cointegration. Journal of Regional Science 39, 119. Horn, R. and C.R. Johnson (1985). Matrix Analysis. Cambridge: Cambridge University Press. James, A. T. (1954). Normal multivariate analysis and the orthogonal group. Annals of Mathematical Statistics 25, 4075. Kariya, T. (1980b). Note on a condition for equality of sample variances in a linear model. Journal of the American Statistical Association 75, 701703. Kelejian, H. H. and I. R. Prucha (2001). On the asymptotic distribution of the Moran I test statistic with applications. Journal of Econometrics 104, 219257. Kelejian, H. H. and I. R. Prucha (2002). 2SLS and OLS in a spatial autoregressive model with equal spatial weights. Regional Science and Urban Economics 32, 691707. Kelejian, H. H., I. R. Prucha and Y. Yuzefovich, (2006). Estimation problems in models with spatial weighting matrices which have blocks of equal elements, Journal of Regional Science 46, 507515. Kelejian, H. H. and I. R. Prucha (2007). Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances. Journal of Econometrics, forthcoming. King, M. L. (1980). Robust tests for spherical symmetry and their application to least squares regression. Annals of Statistics 8, 12651271. King, M. L. (1981). A small sample property of the CliffOrd test for spatial autocorrelation. Journal of the Royal Statistical Society B 43, 2634. King, M. L. (1988). Towards a theory of point optimal testing. Econometric Reviews 6, 169255. Krämer, W. (2005). Finite sample power of CliffOrdtype tests for spatial disturbance correlation in linear regression. Journal of Statistical Planning and Inference 128, 489496. Lee, L. F. and J. Yu (2008). Near unit root in the spatial autoregressive model. Manuscript, The Ohio State University. Lehmann, E. L. and J. Romano (2005). Testing Statistical Hypotheses (3rd ed.). New York: Springer. Martellosio, F. (2008). Power properties of invariant tests for spatial autocorrelation in linear regression. Econometric Theory, forthcoming. Militino, A. F., M. D. Ugarte and L. GarcíaReinaldos (2004). Alternative models for describing spatial dependence among dwelling selling prices. Journal of Real Estate Finance and Economics 29, 193209. Parent, O. and J. P. LeSage (2008). Using the variance structure of the conditional autoregressive spatial specification to model knowledge spillovers. Journal of Applied Econometrics 23, 235256. Smith, T. E. (2008). Estimation bias in spatial models with strongly connected weight matrices. Manuscript, University of Pennsylvania. Tillman, J. A. (1975). The power of the DurbinWatson test. Econometrica 43, 95974. Watson, G. S. (1955). Serial correlation in regression analysis I. Biometrika 42, 327341. Whittle, P. (1954). On stationary processes in the plane. Biometrika 41, 434449. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/10542 