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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.

Suggested Citation

  • Badi H. Baltagi, 2006. "Random effects and Spatial Autocorrelations with Equal Weights," Center for Policy Research Working Papers 89, Center for Policy Research, Maxwell School, Syracuse University.
  • Handle: RePEc:max:cprwps:89
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    1. 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.
    2. 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.
    3. Magnus, J.R., 1982. "Multivariate error components analysis of linear and nonlinear regression models by maximum likelihood," Other publications TiSEM 9ffb33fe-f5af-470f-b405-f, Tilburg University, School of Economics and Management.
    4. 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.
    5. 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.
    6. 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.
    7. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-965, July.
    8. 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.
    9. 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.
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    Cited by:

    1. Harald Badinger & Peter Egger, 2015. "Fixed Effects and Random Effects Estimation of Higher-order Spatial Autoregressive Models with Spatial Autoregressive and Heteroscedastic Disturbances," Spatial Economic Analysis, Taylor & Francis Journals, vol. 10(1), pages 11-35, March.
    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. Baltagi, Badi H. & Liu, Long, 2009. "Spatial lag test with equal weights," Economics Letters, Elsevier, vol. 104(2), pages 81-82, August.
    4. 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].
    5. Martellosio, Federico, 2008. "Testing for spatial autocorrelation: the regressors that make the power disappear," MPRA Paper 10542, University Library of Munich, Germany.
    6. Martellosio, Federico, 2008. "Power Properties of Invariant Tests for Spatial Autocorrelation in Linear Regression," MPRA Paper 7255, University Library of Munich, Germany.

    More about this item

    Keywords

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

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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