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Random effects and Spatial Autocorrelations with Equal Weights

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Abstract

This note considers a panel data regression model with spatial autoregressive disturbances and random effects where the weight matrix is normalized and has equal elements. This is motivated by Kelejian et al. (2005), who argue that such a weighting matrix, having blocks of equal elements, might be considered when units are equally distant within certain neighborhoods but unrelated between neighborhoods. We derive a simple weighted least squares transformation that obtains GLS on this model as a simple OLS. For the special case of a spatial panel model with no random effects, we obtain two sufficient conditions where GLS on this model is equivalent to OLS. Finally, we show that these results, for the equal weight matrix, hold whether we use the spatial autoregressive specification, the spatial moving average specification, the spatial error components specification or the Kapoor et al. (2005) alternative to modeling panel data with spatially correlated error components.

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Bibliographic Info

Paper provided by Center for Policy Research, Maxwell School, Syracuse University in its series Center for Policy Research Working Papers with number 89.

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Length: 15 pages
Date of creation: Dec 2006
Date of revision:
Handle: RePEc:max:cprwps:89

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Keywords: Panel data; spatial error correlation; equal weights; error components;

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References

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  1. Holtz-Eakin, Douglas, 1994. "Public-Sector Capital and the Productivity Puzzle," The Review of Economics and Statistics, MIT Press, vol. 76(1), pages 12-21, February.
  2. Magnus, J.R., 1982. "Multivariate error components analysis of linear and nonlinear regression models by maximum likelihood," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153211, Tilburg University.
  3. Baltagi, Badi H. & Song, Seuck Heun & Koh, Won, 2003. "Testing panel data regression models with spatial error correlation," Journal of Econometrics, Elsevier, vol. 117(1), pages 123-150, November.
  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. Lee, Lung-Fei, 2002. "Consistency And Efficiency Of Least Squares Estimation For Mixed Regressive, Spatial Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 18(02), pages 252-277, April.
  6. Boozer, Michael A., 1997. "Econometric Analysis of Panel Data Badi H. Baltagi Wiley, 1995," Econometric Theory, Cambridge University Press, vol. 13(05), pages 747-754, October.
  7. Kapoor, Mudit & Kelejian, Harry H. & Prucha, Ingmar R., 2007. "Panel data models with spatially correlated error components," Journal of Econometrics, Elsevier, vol. 140(1), pages 97-130, September.
  8. Magnus, Jan R., 1982. "Multivariate error components analysis of linear and nonlinear regression models by maximum likelihood," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 239-285, August.
  9. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-65, July.
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Cited by:
  1. Harald Badinger & Peter Egger, 2014. "Fixed Effects and Random Effects Estimation of Higher-Order Spatial Autoregressive Models with Spatial Autoregressive and Heteroskedastic Disturbances," Department of Economics Working Papers wuwp173, Vienna University of Economics, Department of Economics.
  2. Baltagi, Badi H. & Liu, Long, 2010. "Spurious spatial regression with equal weights," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1640-1642, November.
  3. Schanne, Norbert, 2012. "The formation of experts' expectations on labour markets : do they run with the pack?," IAB Discussion Paper 201225, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany].
  4. Martellosio, Federico, 2008. "Power Properties of Invariant Tests for Spatial Autocorrelation in Linear Regression," MPRA Paper 7255, University Library of Munich, Germany.
  5. Martellosio, Federico, 2008. "Testing for spatial autocorrelation: the regressors that make the power disappear," MPRA Paper 10542, University Library of Munich, Germany.
  6. Baltagi, Badi H. & Liu, Long, 2009. "Spatial lag test with equal weights," Economics Letters, Elsevier, vol. 104(2), pages 81-82, August.

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