Sensitivity Analysis of SAR Estimators: A numerical approximation

Liu, Shuangzhe and Polasek, Wolfgang and Sellner, Richard (January 2011) Sensitivity Analysis of SAR Estimators: A numerical approximation. IHS Economics Series 262


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Abstract or Table of Contents

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.;

Item Type: IHS Series
Keywords: 'Spatial autoregressive models' 'Least squares estimators' 'Sensitivity analysis' 'Taylor Approximations' 'Kantorovich inequality'
Classification Codes (e.g. JEL): C11, C15, C52, E17, R12
Status: Published
Date Deposited: 26 Sep 2014 10:39
Last Modified: 21 Jul 2017 17:40

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