From a theoretical point of view, a spatial econometric model can contain both a spatially lagged dependent variable (spatial lag) and a spatially autocorrelated error term (spatial error). However, such models are rarely used in practice. This is because (assuming a lattice model approach is used for both the spatial lag and spatial error) the model is difficult to estimate1 unless the weight matrices are different for the spatial lag and the spatial error.
Dubin, R. (2004), "SPATIAL LAGS AND SPATIAL ERRORS REVISITED: SOME MONTE CARLO EVIDENCE", Lesage, J. and Kelley Pace, R. (Ed.) Spatial and Spatiotemporal Econometrics (Advances in Econometrics, Vol. 18), Emerald Group Publishing Limited, Bingley, pp. 75-98. https://doi.org/10.1016/S0731-9053(04)18002-XDownload as .RIS
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