Sensitivity Analysis of SAR Estimators

Shuangzhe Liu, Wolfgang Polasek and Richard Sellner
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Shuangzhe Liu: University of Canberra, Canberra, Australia

No 262, Economics Series from Institute for Advanced Studies

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.

Keywords: Spatial autoregressive models; least squares estimators; sensitivity analysis; Taylor Approximations; Kantorovich inequality (search for similar items in EconPapers)
JEL-codes: C11 C15 C52 E17 R12 (search for similar items in EconPapers)
Pages: 19 pages
Date: 2011-01
New Economics Papers: this item is included in nep-ecm, nep-geo and nep-ure
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Citations: View citations in EconPapers (4)

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https://irihs.ihs.ac.at/id/eprint/2036 First version, 2011 (application/pdf)

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