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On the I -super-2( q ) Test Statistic for Spatial Dependence: Finite Sample Standardization and Properties


  • David M. Drukker
  • Ingmar R. Prucha


One of the most widely used tests for spatial dependence is Moran's (1950) I test. The power of the test will depend on the extent to which the spatial-weights matrix employed in computing the Moran I test statistic properly specifies existing interaction links between spatial units. Empirical researchers are often unsure about the use of a particular spatial-weights matrix. In light of this Prucha (2011) introduced the I-super- 2 ( q ) test statistic. This test statistic combines quadratic forms based on several, say q, spatial-weights matrices, while at the same time allows for a proper controlling of the size of the test. In this paper, we first introduce a finite-sample standardized version of the I-super- 2 ( q ) test. We then perform a Monte Carlo study to explore the finite-sample performance of the I-super- 2 ( q ) tests. For comparison, the Monte Carlo study also reports on the finite-sample performance of Moran I tests as well as on Moran I tests performed in sequence.

Suggested Citation

  • David M. Drukker & Ingmar R. Prucha, 2013. "On the I -super-2( q ) Test Statistic for Spatial Dependence: Finite Sample Standardization and Properties," Spatial Economic Analysis, Taylor & Francis Journals, vol. 8(3), pages 271-292, September.
  • Handle: RePEc:taf:specan:v:8:y:2013:i:3:p:271-292
    DOI: 10.1080/17421772.2013.804630

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    References listed on IDEAS

    1. Federico Martellosio, 2012. "Testing for Spatial Autocorrelation: The Regressors that Make the Power Disappear," Econometric Reviews, Taylor & Francis Journals, vol. 31(2), pages 215-240.
    2. 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.
    3. Kelejian, Harry H. & Prucha, Ingmar R., 2007. "HAC estimation in a spatial framework," Journal of Econometrics, Elsevier, vol. 140(1), pages 131-154, September.
    4. 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.
    5. Martellosio, Federico, 2008. "Testing for spatial autocorrelation: the regressors that make the power disappear," MPRA Paper 10542, University Library of Munich, Germany.
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