Random effects and Spatial Autocorrelations with Equal Weights
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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- Baltagi, Badi H. & Song, Seuck Heun & Koh, Won, 2003.
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- repec:ner:tilbur:urn:nbn:nl:ui:12-153211 is not listed on IDEAS
- 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.
- 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.
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