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Sensitivity Analysis of SAR Estimators

Author

Listed:
  • Liu, Shuangzhe

    (University of Canberra, Canberra, Australia)

  • Polasek, Wolfgang

    (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria)

  • Sellner, Richard

    (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria)

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.

Suggested Citation

  • Liu, Shuangzhe & Polasek, Wolfgang & Sellner, Richard, 2011. "Sensitivity Analysis of SAR Estimators," Economics Series 262, Institute for Advanced Studies.
    • Handle: RePEc:ihs:ihsesp:262
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    File URL: https://irihs.ihs.ac.at/id/eprint/2036
    File Function: First version, 2011
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    Citations

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    Cited by:

    1. Xiaowen Dai & Libin Jin & Lei Shi & Cuiping Yang & Shuangzhe Liu, 2016. "Local influence analysis in general spatial models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(3), pages 313-331, July.
    2. Liu, Shuangzhe & Ma, Tiefeng & Polasek, Wolfgang, 2014. "Spatial system estimators for panel models: A sensitivity and simulation study," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 101(C), pages 78-102.

    More about this item

    Keywords

    Spatial autoregressive models; least squares estimators; sensitivity analysis; Taylor Approximations; Kantorovich inequality;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

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