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Random Effects And Spatial Autocorrelation With Equal Weights

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  • Baltagi, Badi H.

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, Prucha, and Yuzefovich (2005, Journal of Regional Science, forthcoming), 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 generalized least squares (GLS) on this model as a simple ordinary least squares (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, Kelejian, and Prucha (2005, Journal of Econometrics, forthcoming) alternative to modeling panel data with spatially correlated error components.I thank Paolo Paruolo and an anonymous referee for helpful comments and suggestions.

Suggested Citation

  • Baltagi, Badi H., 2006. "Random Effects And Spatial Autocorrelation With Equal Weights," Econometric Theory, Cambridge University Press, vol. 22(5), pages 973-984, October.
    • Handle: RePEc:cup:etheor:v:22:y:2006:i:05:p:973-984_06
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    Cited by:

    1. Grant Hillier & Federico Martellosio, 2013. "Properties of the maximum likelihood estimator in spatial autoregressive models," CeMMAP working papers 44/13, Institute for Fiscal Studies.
    2. Grant Hillier & Federico Martellosio, 2013. "Properties of the maximum likelihood estimator in spatial autoregressive models," CeMMAP working papers CWP44/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Martellosio, Federico, 2008. "Power Properties of Invariant Tests for Spatial Autocorrelation in Linear Regression," MPRA Paper 7255, University Library of Munich, Germany.
    4. Baltagi, Badi H. & Liu, Long, 2024. "Testing for spatial correlation under a complete bipartite network," Economics Letters, Elsevier, vol. 241(C).
    5. 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.
    6. Baltagi, Badi H. & Liu, Long, 2010. "Spurious spatial regression with equal weights," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1640-1642, November.
    7. Baltagi, Badi H. & Liu, Long, 2009. "Spatial lag test with equal weights," Economics Letters, Elsevier, vol. 104(2), pages 81-82, August.
    8. 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].
    9. Martellosio, Federico, 2008. "Testing for spatial autocorrelation: the regressors that make the power disappear," MPRA Paper 10542, University Library of Munich, Germany.
    10. Yang, Kai & Lee, Lung-fei, 2021. "Estimation of dynamic panel spatial vector autoregression: Stability and spatial multivariate cointegration," Journal of Econometrics, Elsevier, vol. 221(2), pages 337-367.

    More about this item

    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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