Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/68524
Authors: 
Liu, Shuangzhe
Polasek, Wolfgang
Sellner, Richard
Year of Publication: 
2011
Series/Report no.: 
Reihe Ökonomie, Institut für Höhere Studien 262
Abstract: 
Estimators of spatial autoregressive (SAR) models depend in a highly non-linear way on the spatial correlation parameter and least squares (LS) estimators cannot be computed in closed form. We first compare two simple LS estimators by distance and covariance properties and then we study the local sensitivity behavior of these estimators using matrix derivatives. These results allow us to calculate the Taylor approximation of the least squares estimator in the spatial autoregression (SAR) model up to the second order. Using Kantorovich inequalities, we compare the covariance structure of the two estimators and we derive efficiency comparisons by upper bounds. Finally, we demonstrate our approach by an example for GDP and employment in 239 European NUTS2 regions. We find a good approximation behavior of the SAR estimator, evaluated around the non-spatial LS estimators. These results can be used as a basis for diagnostic tools to explore the sensitivity of spatial estimators.
Subjects: 
spatial autoregressive models
least squares estimators
sensitivity analysis
Taylor approximations
Kantorovich inequality
JEL: 
C11
C15
C52
E17
R12
Document Type: 
Working Paper

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